Patent Application
20110257898
The present application claims priority under 35 U.S.C. §119 to Japanese Patent Application No. 2010-097139, filed Apr. 20, 2010, which is incorporated herein by reference.
The present invention relates to a thermal diffusivity measuring system, a concentration of caloric component measuring system, and a flow rate measuring system in relation to a gas inspection technology.
Conventionally, it has been necessary to use costly gas chromatography equipment, or the like, to analyze the compliments of a mixed gas when calculating the amount of heat production of a mixed gas. Additionally, there have been proposals for a method for calculating the amount of heat production from a mixed gas by calculating the ratio of methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide gas (CO2) components included in the mixed gas through measuring the thermal conductivity of the mixed gas and the speed of sound in the mixed gas (See, for example, Japanese Examined Patent Application Publication 2004-514138 (“JP '138”). However, the method disclosed in JP '138 requires a costly speed-of-sound sensor to measure the speed of sound, in addition to a sensor for measuring the thermal conductivity. Because of this, measuring the amount of heat production by a mixed gas has not been easy.
Conventionally, not only has the measurement of the amount of heat production of a mixed gas been difficult, but also the measurement of properties of a mixed gas, such as the thermal diffusivity and the concentration of caloric component, and the like, has been difficult as well. Given this, the object of the present invention is to provide a thermal diffusivity measuring system, a concentration of caloric component measuring system, and a flow rate measuring system wherein the characteristics of a gas can be measured easily.
A form of the present invention provides a thermal diffusivity calculating equation generating system that includes (a) a heater element for heating each of a plurality of mixed gases; (b) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for each of the plurality of mixed gases when the heater element has produced heat at a plurality of heat producing temperatures; and (c) a thermal diffusivity calculating equation generating portion for generating a thermal diffusivity calculating equation, based on known values for the thermal diffusivities for each of a plurality of mixed gases and on values for radiation coefficients and thermal conductivities measured at a plurality of heat producing temperatures, using the radiation coefficients or the thermal conductivities for the plurality of heat producing temperatures as independent variables and using the thermal diffusivity as the dependent variable.
Another form of the present invention provides a method for generating a thermal diffusivity calculating equation having the steps of preparing a plurality of mixed gases including gas components of a plurality of types; measuring a radiation coefficient or a value for thermal conductivity for each of the plurality of mixed gases when the heater element has produced heat at a plurality of heat producing temperatures; and generating a thermal diffusivity calculating equation, based on known values for the thermal diffusivities for each of a plurality of mixed gases and on values for radiation coefficients and thermal conductivities measured at a plurality of heat producing temperatures, using the radiation coefficients or the thermal conductivities for the plurality of heat producing temperatures as independent variables and using the thermal diffusivity as the dependent variable.
Another form of the present invention provides a thermal diffusivity measuring system, including (a) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; (b) a thermal diffusivity calculating equation storing device for storing a thermal diffusivity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; and (c) a thermal diffusivity calculating portion for calculating a value for the thermal diffusivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the thermal diffusivity calculating equation.
Another form of the present invention provides a method for measuring a thermal diffusivity, having the steps of measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; preparing a thermal diffusivity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; and calculating a value for the thermal diffusivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the thermal diffusivity calculating equation.
Another form of the present invention provides a flow rate measuring system having (a) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; (b) a thermal diffusivity calculating equation storing device for storing a thermal diffusivity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; (c) a thermal diffusivity calculating portion for calculating a value for the thermal diffusivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the thermal diffusivity calculating equation; (d) a flow rate sensor, for detecting a flow rate of a mixed gas being measured, calibrated using a calibration gas; and (e) a correcting portion for correcting detection error in the flow rate due to a difference between the value for the thermal diffusivity of the calibration gas and the value for the thermal diffusivity of the mixed gas being measured.
Another form of the present invention provides a method for measuring a flow rate, including the steps of measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; preparing a thermal diffusivity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; calculating a value for the thermal diffusivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the thermal diffusivity calculating equation; detecting a flow rate of a mixed gas being measured, by a flow rate sensor that is calibrated using a calibration gas; and correcting the detection error in the flow rate due to a difference between the value for the thermal diffusivity of the calibration gas and the value for the thermal diffusivity of the mixed gas being measured.
Another form of the present invention provides a thermal diffusivity calculating equation generating system, having (a) containers for the injection of each of a plurality of mixed gases; (b) a temperature measuring element disposed in the container; (c) a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; (d) a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of each of a plurality of mixed gases, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; and (e) a thermal diffusivity calculating equation generating portion for generating a thermal diffusivity calculating equation, based on known values for the thermal diffusivities for a plurality of mixed gases, on a value of an electric signal from a temperature measuring element, and on values for electric signals from a heater element at a plurality of heat producing temperatures, using the electric signal from the temperature measuring element and the electric signals from the heater element at the plurality of heat producing temperatures as independent variables and using the thermal diffusivity as the dependent variable.
Another form of the present invention provides a method for generating a thermal diffusivity calculating equation, including the steps of preparing a plurality of mixed gases; acquiring a value for an electric signal from a temperature measuring element that is dependent on the temperature of each of a plurality of mixed gases; causing the heater elements that are in contact with each of the plurality of mixed gases to produce heat at a plurality of heat producing temperatures; acquiring a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; and generating a thermal diffusivity calculating equation, based on known values for the thermal diffusivities for a plurality of mixed gases, on a value of an electric signal from a temperature measuring element, and on values for electric signals from a heater element at a plurality of heat producing temperatures, using the electric signal from the temperature measuring element and the electric signals from the heater element at the plurality of heat producing temperatures as independent variables and using the thermal diffusivity as the dependent variable.
Another form of the present invention provides a thermal diffusivity measuring system, having (a) a container for the injection of a mixed gas being measured for which the thermal diffusivity is unknown; (b) a temperature measuring element disposed in the container; (c) a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; (d) a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; (e) a thermal diffusivity calculating equation storing device for storing a thermal diffusivity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; and (f) a thermal diffusivity calculating portion for calculating the value for the thermal diffusivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation.
Another form of the present invention provides a method for measuring a thermal diffusivity, having the steps of preparing a plurality of a mixed gas being measured for which the thermal diffusivity is unknown; acquiring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured; causing the heater element that is in contact with a mixed gas being measured to produce heat at a plurality of heat producing temperatures; acquiring a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; preparing a thermal diffusivity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; and calculating the value for the thermal diffusivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation.
Another form of the present invention provides a flow rate measuring system, having (a) a container for the injection of a mixed gas being measured for which the thermal diffusivity is unknown; (b) a temperature measuring element disposed in the container; (c) a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; (d) a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; (e) a thermal diffusivity calculating equation storing device for storing a thermal diffusivity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; (f) a thermal diffusivity calculating portion for calculating the value for the thermal diffusivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation; (g) a flow rate sensor, for detecting a flow rate of a mixed gas being measured, calibrated using a calibration gas; and (h) a correcting portion for correcting detection error in the flow rate due to a difference between the value for the thermal diffusivity of the calibration gas and the value for the thermal diffusivity of the mixed gas being measured.
Another form of the present invention provides a method for measuring a flow rate, including the steps of (a) the preparation of a plurality of a mixed gas being measured for which the thermal diffusivity is unknown; (b) the acquisition of a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured; (c) the heater element that is in contact with a mixed gas being measured being caused to produce heat at a plurality of heat producing temperatures; (d) the acquisition of a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; (e) the preparation of a thermal diffusivity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the thermal diffusivity as the dependent variable; (f) the calculation of the value for the thermal diffusivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation; (g) the detection of a flow rate of a mixed gas being measured, by a flow rate sensor that is calibrated using a calibration gas; and (h) the correction of detection error in the flow rate due to a difference between the value for the thermal diffusivity of the calibration gas and the value for the thermal diffusivity of the mixed gas being measured.
Another form of the present invention provides a concentration of caloric component calculating equation generating system, having (a) a heater element for heating each of a plurality of mixed gases; (b) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for each of the plurality of mixed gases when the heater element has produced heat at a plurality of heat producing temperatures; and (c) a concentration of caloric component calculating equation generating portion for generating a concentration of caloric component calculating equation, based on known values for the caloric component densities for each of a plurality of mixed gases and on values for radiation coefficients and thermal conductivities measured at a plurality of heat producing temperatures, using the radiation coefficients or the thermal conductivities for the plurality of heat producing temperatures as independent variables and using the concentration of caloric component as the dependent variable.
Another form of the present invention provides a method for generating a concentration of caloric component calculating equation, having the steps of preparing a plurality of mixed gases including gas components of a plurality of types; measuring a radiation coefficient or a value for thermal conductivity for each of the plurality of mixed gases when the heater element has produced heat at a plurality of heat producing temperatures; and generating a concentration of caloric component calculating equation, based on known values for the caloric component densities for each of a plurality of mixed gases and on values for radiation coefficients and thermal conductivities measured at a plurality of heat producing temperatures, using the radiation coefficients or the thermal conductivities for the plurality of heat producing temperatures as independent variables and using the concentration of caloric component as the dependent variable.
Another form of the present invention provides a concentration of caloric component measuring system, including a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; a concentration of caloric component calculating equation storing device for storing a concentration of caloric component calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the caloric component as the dependent variable; and a concentration of caloric component calculating portion for calculating a value for the concentration of caloric component of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the concentration of caloric component calculating equation.
Another form of the present invention provides a method for measuring a concentration of caloric component, having the steps of measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; preparing a concentration of caloric component calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the concentration of caloric component as the dependent variable; and calculating a value for the concentration of caloric component of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the concentration of caloric component calculating equation.
Another form of the present invention provides a flow rate measuring system, including (a) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; (b) a concentration of caloric component calculating equation storing device for storing a concentration of caloric component calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the caloric component as the dependent variable; (c) a concentration of caloric component calculating portion for calculating a value for the concentration of caloric component of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the concentration of caloric component calculating equation; (d) a flow rate sensor, for detecting a flow rate of the mixed gas being measured; and (e) a calorific flow rate calculating portion for calculating the flow rate of a caloric component in the mixed gas being measured, based on a detection value for the flow rate of the mixed gas being measured and a calculated value for the concentration of caloric component of the mixed gas being measured.
Another form of the present invention provides a method for measuring a flow rate, including the steps of (a) the measurement of a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; (b) the preparation of a concentration of caloric component calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the concentration of caloric component as the dependent variable; (c) the calculation of a value for the concentration of caloric component of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the concentration of caloric component calculating equation; (d) the detection of the flow rate of the mixed gas being measured; and (e) the calculation of the flow rate of a caloric component in the mixed gas being measured, based on a detection value for the flow rate of the mixed gas being measured and a calculated value for the concentration of caloric component of the mixed gas being measured.
Another form of the present invention provides a concentration of caloric component calculating equation generating system, having (a) containers for the injection of each of a plurality of mixed gases; (b) a temperature measuring element disposed in the container; (c) a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; (d) a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of each of a plurality of mixed gases, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; and (e) a concentration of caloric component calculating equation generating portion for generating a concentration of caloric component calculating equation, based on known values for the caloric component densities for a plurality of mixed gases, on a value of an electric signal from a temperature measuring element, and on values for electric signals from a heater element at a plurality of heat producing temperatures, using the electric signal from the temperature measuring element and the electric signals from the heater element at the plurality of heat producing temperatures as independent variables and using the concentration of caloric component as the dependent variable.
Another form of the present invention provides a method for generating a concentration of caloric component calculating equation, having the steps of (a) preparing a plurality of mixed gases; (b) acquiring a value for an electric signal from a temperature measuring element that is dependent on the temperature of each of a plurality of mixed gases; (c) causing the heater elements that are in contact with each of the plurality of mixed gases to produce heat at a plurality of heat producing temperatures; (d) acquiring a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; and (e) generating a concentration of caloric component calculating equation, based on known values for the caloric component densities for a plurality of mixed gases, on a value of an electric signal from a temperature measuring element, and on values for electric signals from a heater element at a plurality of heat producing temperatures, using the electric signal from the temperature measuring element and the electric signals from the heater element at the plurality of heat producing temperatures as independent variables and using the concentration of caloric component as the dependent variable.
Another form of the present invention provides a concentration of caloric component measuring system, including a container for the injection of a mixed gas being measured for which the concentration of caloric component is unknown; a temperature measuring element disposed in the container; a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; a concentration of caloric component calculating equation storing device for storing a concentration of caloric component calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the concentration of caloric component as the dependent variable; and a concentration of caloric component calculating portion for calculating the value for the concentration of caloric component of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the concentration of caloric component calculating equation.
Another form of the present invention provides a method for measuring a concentration of caloric component, including the steps of preparing a plurality of a mixed gas being measured for which the concentration of caloric component is unknown; acquiring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured; causing the heater element that is in contact with a mixed gas being measured being caused to produce heat at a plurality of heat producing temperatures; acquiring a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; preparing a concentration of caloric component calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the concentration of caloric component as the dependent variable; and calculating the value for the concentration of caloric component of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the concentration of caloric component calculating equation.
Another form of the present invention provides a flow rate measuring system, having a container for the injection of a mixed gas being measured for which the concentration of caloric component is unknown; a temperature measuring element disposed in the container; a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; a concentration of caloric component calculating equation storing device for storing a concentration of caloric component calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the concentration of caloric component as the dependent variable; a concentration of caloric component calculating portion for calculating the value for the concentration of caloric component of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the concentration of caloric component calculating equation; and a flow rate sensor, for detecting a flow rate of the mixed gas being measured; and a calorific flow rate calculating portion for calculating the flow rate of a caloric component in the mixed gas being measured, based on a detection value for the flow rate of the mixed gas being measured and a calculated value for the concentration of caloric component of the mixed gas being measured.
Another form of the present invention provides a method for measuring a flow rate, having the steps of preparing a plurality of a mixed gas being measured for which the concentration of caloric component is unknown; acquiring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed being measured; causing the heater element that is in contact with a mixed gas being measured being caused to produce heat at a plurality of heat producing temperatures; acquiring a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; preparing a concentration of caloric component calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the concentration of caloric component as the dependent variable; calculating the value for the concentration of caloric component of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the concentration of caloric component calculating equation; detecting the flow rate of the mixed gas being measured; and calculating the flow rate of a caloric component in the mixed gas being measured, based on a detection value for the flow rate of the mixed gas being measured and a calculated value for the concentration of caloric component of the mixed gas being measured.
Another form of the present invention provides a specific heat capacity calculating equation generating system, having:
(a) a heater element for heating each of a plurality of mixed gases;
(b) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for each of the plurality of mixed gases when the heater element has produced heat at a plurality of heat producing temperatures; and
(c) a specific heat capacity calculating equation generating portion for generating a specific heat capacity calculating equation, based on known values for specific heat capacities divided by thermal conductivities for each of a plurality of mixed gases and on values for radiation coefficients and thermal conductivities measured at a plurality of heat producing temperatures, using the radiation coefficients or the thermal conductivities for the plurality of heat producing temperatures as independent variables and using the specific heat capacity divided by the thermal conductivity as the dependent variable.
Another form of the present invention provides a method for generating a specific heat capacity calculating equation, having the steps of:
(a) the preparation of a plurality of mixed gases including gas components of a plurality types;
(b) the measurement of a radiation coefficient or a value for thermal conductivity for each of the plurality of mixed gases when the heater element has produced heat at a plurality of heat producing temperatures; and
(c) the generation of a specific heat capacity calculating equation, based on known values for specific heat capacities divided by thermal conductivities for each of a plurality of mixed gases and on values for radiation coefficients and thermal conductivities measured at a plurality of heat producing temperatures, using the radiation coefficients or the thermal conductivities for the plurality of heat producing temperatures as independent variables and using the specific heat capacity divided by the thermal conductivity as the dependent variable.
Another form of the present invention provides a specific heat capacity measuring system, including:
(a) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures;
(b) a specific heat capacity calculating equation storing device for storing a specific heat capacity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the specific heat capacity, divided by the thermal conductivity, as the dependent variable; and
(c) a specific heat capacity calculating portion for calculating a value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the specific heat capacity calculating equation.
Another form of the present invention provides a method for measuring a specific heat capacity, including the steps of:
(a) the measurement of a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures;
(b) the preparation of a specific heat capacity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the specific heat capacity, divided by the thermal conductivity, as the dependent variable; and
(c) the calculation of a value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the specific heat capacity calculating equation.
Another form of the present invention provides a flow rate measuring system, having (a) a measuring mechanism for measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; (b) a specific heat capacity calculating equation storing device for storing a specific heat capacity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the specific heat capacity, divided by the thermal conductivity, as the dependent variable; (c) a specific heat capacity calculating portion for calculating a value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the specific heat capacity calculating equation; (d) a flow rate sensor, for detecting a volumetric flow rate of the mixed gas being measured; and (e) a mass flow rate calculating portion for calculating a mass flow rate of the gas being measured, based on the calculated value for the specific heat capacity divided by the thermal conductivity and the detected value for the volumetric flow rate of the mixed gas being measured.
Another form of the present invention provides a method for measuring a flow rate, having the steps of (a) measuring a radiation coefficient or a value for thermal conductivity for a mixed gas being measured when the heater element has produced heat at a plurality of heat producing temperatures; (b) preparing a specific heat capacity calculating equation that uses the radiation coefficients or the thermal conductivities for a plurality of heat producing temperatures as independent variables and uses the specific heat capacity, divided by the thermal conductivity, as the dependent variable; (c) calculating a value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured through substituting the values of the radiation coefficients or the thermal conductivities of the mixed gas being measured, for the plurality of heat producing temperatures, for the independent variables of the radiation coefficients or thermal conductivities, for the plurality of heat producing temperatures, in the specific heat capacity calculating equation; (d) detecting the volumetric flow rate of the mixed gas being measured; and (e) calculating a mass flow rate of the gas being measured, based on the calculated value for the specific heat capacity divided by the thermal conductivity and the detected value for the volumetric flow rate of the mixed gas being measured.
Another form of the present invention provides a specific heat capacity calculating equation generating system, including:
(a) containers for the injection of each of a plurality of mixed gases;
(b) a temperature measuring element disposed in the container;
(c) a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures;
(d) a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of each of a plurality of mixed gases, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; and
(e) a specific heat capacity calculating equation generating portion for generating a specific heat capacity calculating equation, based on known values for the specific heat capacities divided by thermal conductivities for a plurality of mixed gases, on a value of an electric signal from a temperature measuring element, and on values for electric signals from a heater element at a plurality of heat producing temperatures, using the electric signal from the temperature measuring element and the electric signals from the heater element at the plurality of heat producing temperatures as independent variables and using the specific heat capacity divided by the thermal conductivity as the dependent variable.
Another form of the present invention provides a method for generating a specific heat capacity calculating equation, utilizing (a) the preparation of a plurality of mixed gases; (b) the acquisition of a value for an electric signal from a temperature measuring element that is dependent on the temperature of each of a plurality of mixed gases; (c) the heater elements that are in contact with each of the plurality of mixed gases being caused to produce heat at a plurality of heat producing temperatures; (d) the acquisition of a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; and (e) the generation of a specific heat capacity calculating equation, based on known values for the specific heat capacities divided by thermal conductivities for a plurality of mixed gases, on a value of an electric signal from a temperature measuring element, and on values for electric signals from a heater element at a plurality of heat producing temperatures, using the electric signal from the temperature measuring element and the electric signals front the heater element at the plurality of heat producing temperatures as independent variables and using the specific heat capacity divided by the thermal conductivity as the dependent variable.
Another form of the present invention provides a specific heat capacity measuring system, including (a) a container for the injection of a mixed gas being measured for which the specific heat capacity divided by the thermal conductivity is unknown; (b) a temperature measuring element disposed in the container; (c) a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; (d) a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; (e) a specific heat capacity calculating equation storing device for storing a specific heat capacity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the specific heat capacity divided by the thermal conductivity as the dependent variable; and (f) a specific heat capacity calculating portion for calculating the value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation.
Another form of the present invention provides a method for measuring a specific heat capacity, having the steps of preparing a plurality of a mixed gas being measured for which the specific heat has to divided by the thermal conductivity is unknown; acquiring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured; causing the heater element that is in contact with a mixed gas being measured being caused to produce heat at a plurality of heat producing temperatures; acquiring a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; preparing a specific heat capacity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the specific heat capacity divided by the thermal conductivity as the dependent variable; and calculating the value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation.
Another form of the present invention provides a flow rate measuring system, having (a) a container for the injection of a mixed gas being measured for which the specific heat capacity divided by the thermal conductivity is unknown; (b) a temperature measuring element disposed in the container; (c) a heater element, disposed in the container, for producing heat at a plurality of heat producing temperatures; (d) a measuring portion for measuring a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured, and a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; (e) a specific heat capacity calculating equation storing device for storing a specific heat capacity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the specific heat capacity divided by the thermal conductivity as the dependent variable; (f) a specific heat capacity calculating portion for calculating the value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation; (g) a flow rate sensor, for detecting a volumetric flow rate of the mixed gas being measured; and (h) a mass flow rate calculating portion for calculating a mass flow rate of the mixed gas being measured, based on the calculated value for the specific heat capacity divided by the thermal conductivity and the detected value for the volumetric flow rate of the mixed gas being measured.
Another form of the present invention provides a method for measuring a flow rate, including (a) the preparation of a plurality of a mixed gas being measured for which the specific heat has to divided by the thermal conductivity is unknown; (b) the acquisition of a value for an electric signal from a temperature measuring element that is dependent on the temperature of a mixed gas being measured; (c) the heater element that is in contact with a mixed gas being measured being caused to produce heat at a plurality of heat producing temperatures; (d) the acquisition of a value for an electric signal from a heater element at each of a plurality of heat producing temperatures; (e) the preparation of a specific heat capacity calculating equation that uses an electric signal from a temperature measuring element and electric signals from a heater element at a plurality of heat producing temperatures as independent variables and uses the specific heat capacity divided by the thermal conductivity as the dependent variable; (f) the calculation of the value for the specific heat capacity divided by the thermal conductivity of the mixed gas being measured by substituting the value of an electric signal from the temperature measuring element and the value of an electric signal from the heater element into the independent variable that is the electric signal from the temperature measuring element and the independent variable that is the electric signal from the heater element, in the thermal diffusivity calculating equation; (g) the detection of the volumetric flow rate of the mixed gas being measured; and (h) the calculation of a mass flow rate of the gas being measured, based on the calculated value for the specific heat capacity divided by the thermal conductivity and the detected value for the volumetric flow rate of the mixed gas being measured.
The present invention provides a thermal diffusivity measuring system, a concentration of caloric component measuring system, and a flow rate measuring system wherein the characteristics of a mixed gas can be measured easily.
Examples of the present invention are described below. In the descriptions of the drawings below, identical or similar components are indicated by identical or similar codes. Note that the diagrams are schematic. Consequently, specific measurements should be evaluated in light of the descriptions below. Furthermore, even within these drawings there may, of course, be portions having differing dimensional relationships and proportions.
A microchip 8A that is used in a thermal diffusivity calculating equation generating system as set forth in an example is described in reference to
The heater element 61A is disposed in the center of the portion of the diaphragm of the dielectric layer 65A that covers the cavity 66A. The heater element 61A is, for example, a resistor, and produces heat through the supply of electric power thereto, to heat the ambient gas that contacts the heater element 61A. The first temperature measuring element 62A, the second temperature measuring element 63A, and the third temperature measuring element 64A are, for example, each resistors and each detect the gas temperature of the ambient gas prior to the production of heat by the heater element 61A. Note that the gas temperature may be measured using any single one of the first temperature measuring element 62A, the second temperature measuring element 63A, or the third temperature measuring element 64A. Conversely, an average value of the gas temperature detected by the first temperature measuring element 62A and the gas temperature detected by the second temperature measuring element 63A may be used as the gas temperature. While the description below is for an example wherein the average value of the gas temperatures detected by the first temperature measuring element 62A and the second temperature measuring element 63A is used as the gas temperature, there is no limitation thereto.
Silicon (Si), or the like, may be used as the material for the substrate 60A. Silicon dioxide (SiO2), or the like, may be used as the material for the dielectric layer 65A. The cavity 66A may be formed through anisotropic etching, or the like. Furthermore, platinum (Pt) or the like may be used as the material for the first temperature measuring element 62A, the second temperature measuring element 63A, and the third temperature measuring element 64A, and they may be formed through a lithographic method, or the like.
As illustrated in
A switch SW1 is connected between the resistive element 162 and the resistive element 163 and the − input terminal of the operational amplifier 170, and a switch SW2 is connected between the resistive element 163 and the resistive element 164 and the − input terminal of the operational amplifier 170. Furthermore, a switch SW3 is connected between the resistive element 164 and the resistive element 165 and the − input terminal of the operational amplifier 170, and a switch SW4 is connected between the resistive element 165 and ground terminal and the − input terminal of the operational amplifier 170.
When applying the voltage VL3 of 2.4 V to the − input terminal of the operational amplifier 170, only switch SW1 is turned ON, and switches SW2, SW3, and SW4 are turned OFF. When applying the voltage VL2 of 1.9 V to the − input terminal of the operational amplifier 170, only switch SW2 is turned ON, and switches SW1, SW3, and SW4 are turned OFF. When applying the voltage VL1 of 1.4 V to the − input terminal of the operational amplifier 170, only switch SW3 is turned ON, and switches SW1, SW2, and SW4 are turned OFF. When applying the voltage VL0 of 0V to the − input terminal of the operational amplifier 170, only switch SW4 is turned ON, and switches SW1, SW2, and SW3 are turned OFF. Consequently, 0V and any of three levels of voltages can be applied to the − input terminal of the operational amplifier 170 through turning the switches SW1, SW2, SW3, and SW4 ON and OFF, Because of this, the applied voltage that determines the heat producing temperature of the heater element 61A can be set to any of three levels through turning the switches SW1, SW2, SW3, and SW4 ON and OFF.
In the heater element 61A illustrated in
R
H
=R
STD×[1+α(TH−TSTD)+β(TH−TSTD)2] (1)
Here TSTD indicates a standard temperature of, for example, 20° C. RSTD indicates a resistance value that is measured in advance at the standard temperature of TSTD. α is the first-order temperature coefficient of resistance, and β is the second-order temperature coefficient of resistance. Moreover, the resistance value RH of the heater element 61A is given by Equation (2), below, from the driving power PH of the heater element 61A and the current IH flowing in the heater element 61A:
R
H
=P
H
/I
H
2 (2)
Conversely, the resistance value RH of the heater element 61A is given by Equation (3), below, from the voltage VH applied to the heater element 61A and the current IH flowing in the heater element 61A:
R
H
=V
H
/I
H (3)
Here the heat producing temperature TH of the heater element 61A reaches a thermal equilibrium and stabilizes between the heater element 61A and the ambient gas. Note that this “thermal equilibrium” refers to a state wherein there is a balance between the heat production by the heater element 61A and the heat dissipation from the heater element 61A into the ambient gas. As indicated in Equation (4), below, radiation coefficient MI of the ambient gas is obtained by dividing the driving power PH of the heater element 61A by the difference between the heat producing temperature TH of the heater element 61A and the temperature TI of the ambient gas in this equilibrium state. Note that the units for the radiation coefficient MI are, for example, W/° C.
M
I
=P
H/(TH−TI) (4)
Because the current IH flowing in the heater element 61A and the driving power PH or the voltage VH can be measured, the heat producing temperature TH of the heater element 61A can be calculated from Equation (1) through Equation (3), above. Moreover, the temperature TI of the ambient gas can be measured by the first temperature measuring element 62A and the second temperature measuring element 63A in
Microchip 8A is secured, in a chamber, or the like, that is filled with the ambient gas, through, for example, a thermally insulating member that is disposed on the bottom face of the microchip 8A. Securing the microchip 8A through a thermally insulating member within a chamber, or the like, makes the temperature of the microchip 8A less susceptible to temperature variations of the inner wall of the chamber, or the like. The thermally insulating member is made from glass, or the like, with a thermal conductivity of, for example, no more than 1.0 W/(m·K).
As illustrated in
Here the ambient gas is a mixed gas, where the mixed gas is assumed to comprise four gas components: gas A, gas B, gas C, and gas D. The sum of the volume fraction VA of the gas A, the volume fraction VB of the gas B, the volume fraction VC of the gas C, and the volume fraction VD of the gas D, as given by Equation (5), below, is 1:
V
A
+V
B
+V
C
+V
D=1 (5)
Furthermore, defining the inverse of the thermal diffusivity of the gas A as 1/KA, the inverse of the thermal diffusivity of the gas B as 1/KB, the inverse of the thermal diffusivity of the gas C as 1/KC, and the inverse of the thermal diffusivity of the gas D as 1/KD, the inverse of the thermal diffusivity of the mixed gas, 1/α, is given by the sum of the product of the inverses of the thermal diffusivities of the individual gas components. Consequently, the inverse 1/α of the thermal diffusivity of the mixed gas is given by Equation (6), below.
Note that the thermal diffusivity α (m2/s) is given by Equation (7), below, wherein k is the thermal conductivity (Js−1m−1K−1), ρ is the density (kgm−3), and Cp is the specific heat capacity (Jkg−1K−1).
1/α=1/KA×VA±1/KB×VB+1/KC×VC+1/KD×VD (6)
α=k/(ρCp) (7)
Next, when the radiation coefficient of gas A is defined as MA, the radiation coefficient of gas B is defined as MB, the radiation coefficient of gas C is defined as MC and the radiation coefficient of gas D is defined as MD, the radiation coefficient MI of the mixed gas is given by the sum of the products of the radiation coefficients of the individual gas components with the volume fractions of those gas components. Consequently, the radiation coefficient MI of the mixed gas is given by Equation (8), below.
M
I
=M
A
×V
A
+M
B
V
B
+M
C
×V
C
+M
D
×V
D (8)
Moreover, because the radiation coefficient of the gas is dependent on the heat producing temperature TH of the heater element 61A, the radiation coefficient Mt of the mixed gas is given by Equation (9) as a function of the heat producing temperature TH of the heater element 61A:
M
I(TH)=MA(TH)×VA+MB(TB)×VB+MC(TH)×VC+MD(TH)×VD (9)
Consequently, the radiation coefficient MI(TH1) of the mixed gas, when the heat producing temperature of the heater element 61A is TH1, is given by Equation (10), below. Moreover, the radiation coefficient MI(TH2) of the mixed gas, when the heat producing temperature of the heater element 61A is TH2, is given by Equation (11), below, and the radiation coefficient MI(TH3) of the mixed gas, when the heat producing temperature of the heater element 61A is TH3, is given by Equation (12), below. Note that the heat producing temperature TH1, the heat producing temperature TH2, and the heat producing temperature TH3, are each different temperatures.
M
I(TH1)=MA(TH1)×VA+MB(TH1)×VB+MC(TH1)×VC+MD(TH1)×VD (10)
M
I(TH2)=MA(TH2)×VA+MB(TH2)×VB+MC(TH2)×VC+MD(TH2)×VD (11)
M
I(TH3)=MA(TH3)×VA+MB(TH3)×VB+MC(TH3)×VC+MD(TH3)×VD (12)
If the radiation coefficients MA(TH), MB(TH), MC(TH), and MD(TH) have non-linearity with respect to the heat producing temperature TH of the heater element 61A, the aforementioned Equations (10) through (12) will have a linearly independent relationship. Moreover, even if the radiation coefficients MA(TH), MB(TH), MC(TH), and MD(TH) have linearity with respect to the heat producing temperature TH of the heater element 61A, the aforementioned Equations (10) through (12) will have a linearly independent relationship if the rates of change of the radiation coefficients MA(TH), MB(TH), MC(TH), and MD(TH) of the individual gases with respect to the heat producing temperature TH of the heater element 61A are different. Moreover, if Equations (10) through (12) have a linearly independent relationship, then Equation (5) and Equations (10) through (12) will have a linearly independent relationship.
The values for the radiation coefficients MA(TH1), MB(TH1), MC(TH1), MD(TH1), MA(TH2), MB(TH2), MC(TH2), MD(TH2), MA(TH3), MB(TH3), MC(TH3), and MD(TH3) for the individual gas components in Equations (10) through (12) can be obtained in advance through measurements, or the like. Consequently, as illustrated in Equations (13) through (16), below, the volume fraction VA of the gas A, the volume fraction VB of the gas B, the volume fraction VC of the gas C, and the volume fraction VD of the gas D, of the mixed gas can be obtained as functions of the radiation coefficients MI(TH1), MI(TH2), and MI(TH3), by solving the system of equations of Equation (5) and Equations (10) through (12). Note that in Equations (13) through (16), below, fn, where n is a non-negative integer, is a code indicating a function:
V
A
=f
1
[M
I(TH1),MI(TH2),MI(TH3)] (13)
V
B
=f
2
[M
I(TH1),MI(TH2),MI(TH3)] (14)
V
C
=f
3
[M
I(TH1),MI(TH2),MI(TH3)] (15)
V
D
=f
4
[M
I(TH1),MI(TH2),MI(TH3)] (16)
Moreover, the gas volume is proportional to the temperature of the gas itself by Boyle-Charles law. If, for example, the temperature of the mixed gas prior to the causing the heater element 61A to produce heat is defined as TI, the volume fraction VA of the gas A, the volume fraction VB of the gas B, the volume fraction VC of the gas C, and the volume fraction VD of the gas D can be obtained as functions of the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas, and of the temperature of the mixed gas, as indicated in Equations (17) through (20), below.
V
A
=f
1
[M
I(TH1),MI(TH2),MI(TH3),TI] (17)
V
B
=f
2
[M
I(TH1),MI(TH2),MI(TH3),TI] (18)
V
C
=f
3
[M
I(TH1),MI(TH2),MI(TH3),TI] (19)
V
D
=f
4
[M
I(TH1),MI(TH2),MI(TH3),TI] (20)
Here Equation (21), below, is obtained through substituting Equation (17) through (20) into Equation (6), above.
As is clear from Equation (21), above, the inverse 1/α of the thermal diffusivity of the mixed gas is obtained from an equation having, as variables, the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas, and the temperature TI of the mixed gas, when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3, Consequently, the inverse 1/α of the thermal diffusivity of the mixed gas is given by Equation (22), below, where g1 is a code indicating a function.
1/α=g1[MI(TH1),MI(TH2),MI(TH3),TI] (22)
Consequently, the inventors discovered that, for a mixed gas comprising a gas A, a gas D, a gas C, and a gas D, wherein the volume fraction VA of the gas A, the volume fraction VB of the gas B, the volume fraction VC of the gas C, and the volume fraction VD of the gas D, are unknown, it is possible to calculate easily the inverse 1/α of the thermal diffusivity of the mixed gas to be measured if Equation (22) is obtained in advance, Specifically, the inverse 1/α of the thermal diffusivity of the mixed gas being measured can be obtained uniquely by measuring the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3, and then substituting into Equation (22). Note that if the temperature TI of the mixed gas previous to the heater element 61A being caused to produce heat is stable, then Equation (22) need not include the variable for the temperature TI of the mixed gas.
Note that the gas components of the mixed gas are not limited to four different components. For example, if the mixed gas comprises n types of gas components, then first an equation having, as variables, the radiation coefficients MI(TH1), MI(TH2), MI(TH3), . . . MI(THn-1) of the mixed gas when the heat producing temperatures of the heater element 61A are at least n−1 different temperatures TH1, TH2, TH3, . . . THn-1, as given in Equation (23), below, is obtained. Then, the inverse 1/α of the thermal diffusivity of the mixed gas being measured is obtained uniquely by measuring the radiation coefficients MI(TH1), MI(TH2), MI(TH3), . . . , MI(THn-1) of the mixed gas wherein the volume fractions of each of the n types of gas components is unknown when the heat producing temperatures of the heater element 61A are n−1 different temperatures of TH1, TH2, TH3, . . . , THn-1, and then substituting into Equation (23).
1/α=g1[MI(TH1),MI(TH2),MI(TH3), . . . ,MI(THn-1),TI] (23)
Note that if the mixed gas includes an alkane (CjH2j+2) other than methane (CH4) and propane (C3H8), where j is a natural number, in addition to methane (CH4) and propane (C3H8), then the alkane (CjH2j+2) other than methane (CH4) and propane (C3H8) will be seen as a mixture of methane (CH4) and propane (C3H8), and there will be no effect on the calculation in Equation (23). For example, as indicated in Equations (24) through (27), below, the calculation may be performed using Equation (23) by viewing ethane (C2H6), butane (C4H10), pentane (C5H12), and hexane (C6H14) as a mixture of methane (CH4) and propane (C3H8), with each multiplied by the respective specific factors.
C2H6=0.5CH4+0.5C3H8 (24)
C4H10=−0.5CH4+1.5C3H8 (25)
C5H12=−1.0CH4+2.0C3H8 (26)
C6H14=−1.5CH4±2.5C3H8 (27)
Consequently, with z as a natural number, if a mixed gas comprising n types of gas components includes, as gas components, z types of alkanes (CjH2j+2) other than methane (CH4) and propane (C3H8), in addition to methane (CH4) and propane (C3H8), an equation may be calculated having, as variables, the radiation coefficients MI of the mixed gas at, at least, n−z−1 different heat producing temperatures.
Note that if the types of gas components in the mixed gas used in the calculation in Equation (23) are the same as the types of gas components of the mixed gas to be measured, wherein the inverse 1/α of the thermal diffusivity is unknown, then, of course, Equation (23) can be used in calculating the inverse 1/α of the thermal diffusivity of gas to be measured. Furthermore, Equation (23) can also be used when the mixed gas to be measured comprises a number of gas components that is less than n, where the gas components of the less than n different types are included in the mixed gas that was used for calculating Equation (3). If, for example, the mixed gas used in calculating Equation (23) included four types of gas components, namely methane (CH4), propane (C3H8), nitrogen (N2) and carbon dioxide (CO2), then even if the mixed gas to be measured includes only three different components, namely methane (CH4), propane (C3H8), and carbon dioxide (CO2), without containing the nitrogen (N2), still Equation (23) can be used in calculating the inverse 1/α of the thermal diffusivity of the mixed gas to be measured.
Furthermore, if the mixed gas used in calculating Equation (23) included methane (CH4) and propane (C3H8) as gas components, Equation (23) could still be used even when the mixed gas being measured includes an alkane (CjH2j+2) that was not included in the mixed gas that was used in calculating Equation (23). This is because, as described above, even if the alkane (CjH2j+2) other than methane (CH4) and propane (C3H8) is viewed as a mixture of methane (CH4) and propane (C3H8) there is no effect on calculating the inverse 1/α of the thermal diffusivity using Equation (23).
Here the thermal diffusivity calculating equation generating system 20A according to the example illustrated in
The measuring mechanism 10 comprises the microchip 8A that has been explained using
When a four types of sample mixed gases, each having a thermal diffusivity with a different inverse 1/α are used, then, as illustrated in
A second flow gas pressure regulating device 31B is connected through a flow path 91B to the second gas canister 50B. Additionally, a second flow rate controlling device 32B is connected through a flow path 92B to the second gas pressure regulating device 31B. The second flow rate controlling device 32B controls the rate of flow of the second sample mixed gas that is fed into the thermal diffusivity calculating equation generating system 20A through the flow paths 92B, 93, and 102.
A third flow gas pressure regulating device 31C is connected through a flow path 91C to the third gas canister 50C. Additionally, a third flow rate controlling device 32C is connected through a flow path 92C to the third gas pressure regulating device 31C. The third flow rate controlling device 32C controls the rate of flow of the third sample mixed gas that is fed into the thermal diffusivity calculating equation generating system 20A through the flow paths 92C, 93, and 102.
A fourth flow gas pressure regulating device 31D is connected through a flow path 91D to the fourth gas canister 50D. Additionally, a fourth flow rate controlling device 32D is connected through a flow path 92D to the fourth gas pressure regulating device 31D. The fourth flow rate controlling device 32D controls the rate of flow of the fourth sample mixed gas that is fed into the thermal diffusivity calculating equation generating system 20A through the flow paths 92D, 93, and 102.
The first through fourth at sample mixed gases are each, for example, natural gas. The first through fourth sample mixed gases each include four different gas components of for example, methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide (CO2).
After the first sample mixed gas is filled into the chamber 101, the first temperature measuring element 62A and the second temperature measuring element 63A, illustrated in
After the removal of the first sample mixed gas from the chamber 101 illustrated in
Note that if there are n types of gas components in each of the sample mixed gases, the heater element 61A, illustrated in
Moreover, the measuring mechanism 10 illustrated in
Additionally, the radiation coefficient calculating portion 301 illustrated in
Furthermore, the radiation coefficient calculating portion 301 illustrated in
The thermal diffusivity calculating equation generating system 20 illustrated in
The thermal diffusivity calculating equation generating portion 302 collects the respective known inverse 1/α values for the thermal diffusivities for the first through fourth sample mixed gases, for example, the plurality of measured values for the radiation coefficients MI for when the heat producing temperature of the heater element 61A was 100° C., the plurality of measured values for the radiation coefficients MI for when the heat producing temperature of the heater element 61A was 150° C., and the plurality of measured values for the radiation coefficients MI for when the heat producing temperature of the heater element 61A was 200° C. Based on the inverse 1/α values for the thermal diffusivities and the plurality of radiation coefficients MI that have been collected, the thermal diffusivity calculating equation generating portion 302 then, through multivariate analysis, calculates a thermal diffusivity calculating equation having, as independent variables, the radiation coefficient MI when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 200° C., and the gas temperature TI, and having, as the dependent variable, the inverse 1/α of the thermal diffusivity.
Note that “multivariate analysis” includes support vector analysis disclosed in A. J. Smola and B. Schoikopf (eds.), “A Tutorial on Support Vector Regression” (NeuroCOLT Technical Report NC-TR-98-030), multiple linear regression analysis, the Fuzzy Quantification Theory Type II, disclosed in Japanese Unexamined Patent Application Publication H5-141999, and the like. Additionally, the radiation coefficient calculating portion 301 and the thermal diffusivity calculating equation generating portion 302 are included in the CPU 300.
The thermal diffusivity calculating equation generating system 20A is further provided with a thermal diffusivity calculating equation storing device 402, connected to the CPU 300. The thermal diffusivity calculating equation storing device 402 stores the thermal diffusivity calculating equation generated by the thermal diffusivity calculating equation generating portion 302. An inputting device 312 and an outputting device 313 are also connected to the CPU 300. A keyboard, a pointing device such as a mouse, or the like, may be used as the inputting device 312. An image displaying device such as a liquid crystal display or a monitor, or a printer, or the like, may be used as the outputting device 313.
The flowchart in
(a) In Step S100, the valve for the first flow rate controlling device 32A is opened while leaving the second through fourth flow rate controlling devices 32B through 32D, illustrated in
in Step S101, the first temperature measuring element 62A and the second temperature measuring element 63A detect the temperature TI of the first sample mixed gas. Thereafter, the driving circuit 303 illustrated in
(b) In Step S102, the driving circuit 303 evaluates whether or not the switching of the heat producing temperatures of the heater element 61A, illustrated in
(c) In Step S102, whether or not the switching of the heat producing temperatures of the heater element 61A, illustrated in
(d) If the switching of the heat producing temperature of the heater element 61A has been completed, then processing advances from Step S102 to Step S103. In Step S103, an evaluation is performed as to whether or not the switching of the sample mixed gases has been completed. If the switching to the second through fourth sample mixed gases has not been completed, processing returns to Step S100. In Step S100, the valve for the first flow rate controlling device 32A is closed and the valve for the second flow rate controlling device 32B is opened while leaving the third and fourth flow rate controlling devices 32C through 32D, illustrated in
(e) The loop of Step S101 through Step S102 is repeated in the same manner as for the first sample mixed gas. The value for the temperature TI of the second sample mixed gas is measured first, Additionally, the radiation coefficient calculating portion 301 calculates the value for the radiation coefficient MI for the second sample mixed gas when the heat producing temperature of the heater element 61A is 100° C. the value for the radiation coefficient MI for the second sample mixed gas when the heat producing temperature of the heater element 61A is 150° C., and the value for the radiation coefficient MI for the second sample mixed gas when the heat producing temperature of the heater element 61A is 200° C. Moreover, the radiation coefficient calculating portion 301 stores, in the radiation coefficient storing device 401, the value for the temperature TI measured for the second sample mixed gas and the calculated values for the radiation coefficients MI.
(f) Thereafter, the loop of Step S100 through Step S103 is repeated. Doing so stores, in the radiation coefficient storing device 401, the value TI for the temperature of the third sample mixed gas, the values of the respective radiation coefficients MI for the third sample mixed gas when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C., the value TI for the temperature of the fourth sample mixed gas, and the values of the respective radiation coefficients MI for the fourth sample mixed gas when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C.
(g) In Step S104, the known value for the inverse 1/α of the thermal diffusivity of the first sample mixed gas, the known value for the inverse in of the thermal diffusivity of the second sample mixed gas, the known value for the inverse 1/α of the thermal diffusivity of the third sample mixed gas, and the known value for the inverse 1/α of the thermal diffusivity of the fourth sample mixed gas are inputted from the inputting device 312 into the thermal diffusivity calculating equation generating portion 302. Additionally, the thermal diffusivity calculating equation generating portion 302 reads in, from the radiation coefficient storing device 401, the values for the temperatures TI of the first through fourth sample mixed gases and the values for the radiation coefficients MI for the first through fourth sample mixed gases when the heat producing temperatures of the heater element 61A were 100° C., 150° C., and 200° C.
(h) In Step S105, the thermal diffusivity calculating equation generating portion 302 performs multiple linear regression analysis based on the values for the inverses 1/α of the thermal diffusivities of the first through fourth sample mixed gases, the values for the temperatures TI of the first through fourth sample mixed gases, and the values for the radiation coefficients MI for the first through fourth sample mixed gases when the heat producing temperatures of the heater element 61A were 100° C., 150° C., and 200° C. Based on the multiple linear analysis, the thermal diffusivity calculating equation generating portion 302 calculates a thermal diffusivity calculating equation having, as independent variables, the radiation coefficient MI when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 200° C., and the gas temperature TI, and having, as the dependent variable, the inverse 1/α of the thermal diffusivity. Thereafter, in Step S106, the thermal diffusivity calculating equation generating portion 302 stores, into the thermal diffusivity calculating equation storing device 402, the thermal diffusivity calculating equation that has been generated, to complete the method for generating the thermal diffusivity calculating equation as set forth in the first form of embodiment.
As described above, the method for generating a thermal diffusivity calculating equation as set forth enables the generation of a thermal diffusivity calculating equation that calculates a unique value for the thermal diffusivity α of a mixed gas being measured.
As illustrated in
The thermal diffusivity calculating equation storing device 402 stores the thermal diffusivity calculating equation described in the first form of embodiment. As an example, a case will be explained here wherein natural gases, including methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide (CO2), were used as the sample mixed gases for generating the thermal diffusivity calculating equation. Additionally, the thermal diffusivity calculating equation uses, as independent variables, the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 200° C., and the temperature TI of the gas.
In this example, a natural gas that includes, in unknown volume fractions, methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide (CO2), and for which the inverse 1/α of the thermal diffusivity is unknown, is introduced into the chamber 101 as the mixed gas to be measured. The first temperature measuring element 62A and the second temperature measuring element 63A, illustrated in
The radiation coefficient calculating portion 301, illustrated in
The thermal diffusivity calculating portion 305 substitutes the values of the radiation coefficients MI and the temperature TI of the mixed gas being measured into the independent variables of the radiation coefficients MI for the gas and the temperature TI of the gas in the thermal diffusivity calculating equation, to calculate the value of the inverse 1/α of the thermal diffusivity of the mixed gas being measured. The thermal diffusivity calculating portion 305 may further calculate the value of the thermal diffusivity a from the value of the inverse 1/α of the thermal diffusivity. A thermal diffusivity storing device 403 is also connected to the CPU 300. The thermal diffusivity storing device 403 stores the value of the inverse 1/α of the thermal diffusivity of the mixed gas being measured, calculated by the thermal diffusivity calculating portion 305. The requirements for the other structural elements in the thermal diffusivity measuring system 21A as set forth here are identical to those in the thermal diffusivity calculating equation generating system 20A set forth above, so explanations thereof are omitted.
The flowchart in
(a) In Step S200, the mixed gas to be measured is introduced into the chamber 101 illustrated in
(b) In Step S202, the driving circuit 303, illustrated in
(c) In Step S202, whether or not the switching of the heat producing temperatures of the heater element 61A, illustrated in
Thereafter, the driving circuit 303 stops the provision of the driving power to the heater element 61A.
(d) if the switching of the heat producing temperature of the heater element 61A has been completed, then processing advances from Step S202 to Step S203. In Step S203, the thermal diffusivity calculating portion 305 reads in, from the thermal diffusivity calculating equation storing device 402, the thermal diffusivity calculating equation that uses, as independent variables, the value for the temperature TI of the gas and the values for the radiation coefficients MI when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C. In addition, the thermal diffusivity calculating portion 305 region, from the radiation coefficient storing device 401, the value for the temperature TI of the mixed gas being measured and the values for the radiation coefficients MI of the mixed gas being measured for when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C.
(e) In Step S204, the thermal diffusivity calculating portion 305 substitutes the value of the temperature TI of the mixed gas being measured into the independent variable of the temperature T in the thermal diffusivity calculating equation, and substitutes the value of the radiation coefficients MI of the mixed gas being measured into the independent variable of the radiation coefficients MI in the thermal diffusivity calculating equation, to calculate the value of the inverse 1/α of the thermal diffusivity of the mixed gas being measured. Thereafter, the thermal diffusivity calculating portion 305 stores, into the thermal diffusivity storing device 403, the value calculated for the thermal diffusivity α, to complete the method for measuring the thermal diffusivity as set forth herein.
The method for measuring the thermal diffusivity as set forth in the example described above enables the measurement of the thermal diffusivity α of a mixed gas that is a mixed gas to be measured, from measured values for the radiation coefficients MI of the mixed gas to be measured, without using costly gas chromatography equipment or speed-of-sound sensors.
First, as illustrated in
Following this, the equation for calculating the inverse 1/α of the thermal diffusivity was used to calculate calculated values for the inverses 1/α of the thermal diffusivities for the 19 sample mixed gases, and the true values for the inverses 1/α of the thermal diffusivities for the 19 sample mixed gases were compared. When this was done, the error in the calculated values, relative to the true values for the inverses 1/α of the thermal diffusivities, as illustrated in
Through Equation (1), above, the temperature TH of the heater element 61A, illustrated in
T
H=(½β)×[−α+[α2−4β(1−RH/RH
Consequently, the difference ΔTH between the heat producing temperature TH of the heater element 61A and the temperature TI of the ambient gas is given by Equation (29), below:
ΔT
H=(½β)×[−α+[α2−4β(RH/RH
The temperature of the first temperature measuring element 62A, when power is applied to the extent that it does not produce heat itself, will approximate the ambient temperature TI. The relationship between the temperature TI of the first temperature measuring element 62A and the resistance value RI of the first temperature measuring element 62A is given by Equation (30), below:
R
I
=R
I
STD×[1+α(TI−TI
Here TI
T
I=(½β)×[−α+[α2−4βI(1−RI/RI
Consequently, the radiation coefficient MI of the ambient gas is also given by Equation (32), below.
Because the current IH flowing in the heater element 61A and the driving power PH or the voltage VH can be measured, the resistance RH of the heater element 61A can be calculated from Equation (2) through Equation (3), above. Similarly, it is also possible to calculate the resistance value RI of the first temperature measuring element 62A.
As is illustrated in Equation (22), above, the inverse 1/α of the thermal diffusivity of the mixed gas that comprises the four types of gas components is obtained from an equation having, as variables, the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3. Additionally, the radiation coefficient MI of the mixed gas, as indicated in Equation (32), above, depends on the resistance value RH of the heater element 61A and on the resistance value RI of the first temperature measuring element 62A. Given this, the inventors discovered that the inverse 1/α of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the resistances RH1(TH1), RH2(TH2), and RH3(TH3) of the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the resistance value RI of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (33), below.
1/α=g2[RH1(TH1),RH2(TH2),RH3(TH3),RI] (33)
Given this, the inverse 1/α of the thermal diffusivity of a mixed gas can be calculated uniquely by measuring the resistances RH1(TH1), RH2(TH2), and RH3(TH3) of the heater element 61A when the heat producing temperatures of the heater element 61A, which is in contact with the mixed gas, are TH1, TH2, and TH3, and the resistance value RI of the first temperature measuring element 62A that is in contact with the mixed gas prior to the heat production by the heater element 61A, for example, and then substituting into Equation (33).
Furthermore, the inverse 1/α of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the currents IH1(TH1), IH2(TH2), and IH3(TH3) flowing in the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the current II flowing in the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (34), below.
1/α=g3[IH1(TH1),IH2(TH2),IH3(TH3),II] (34)
Conversely, the inverse 1/α of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the voltages VH1(TH1), VH2(TH2), and VH3(TH3) of the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the voltage VI of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (35), below,
1/α=g4[VH1(TH1),VH2(TH2),VH3(TH3),VI] (35)
Conversely, the inverse 1/α of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, the output voltages ADH1(TH1), ADH2(TH2), and ADH3(TH3) of analog-digital converting circuits (hereinafter termed “A/D converting circuits”) that are connected to the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the output voltage ADI of an A/D converting circuit that is connected to the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (36), below.
1/α=g5[ADH1(TH1),ADH2(TH2),ADH3(TH3),ADI] (36)
Consequently, the inverse 1/α of the thermal diffusivity of a mixed gas can also be obtained from an equation having, as variables, electric signals SH1(TH1), SH2(TH2), and SH3(TH3) from the heater element 61A when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3, and an electric signal SI from the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (37), below.
1/α=g6[SH1(TH1),SH2(TH2),SH3(TH3),SI] (37)
Here a thermal diffusivity calculating equation generating system 20B as illustrated in
After a first sample mixed gas is filled into the chamber 101, the first temperature measuring element 62A of the microchip 8A, illustrated in
After the removal of the first sample mixed gas from the chamber 101, the second through fourth sample mixed gases are filled sequentially into the chamber 101, After the second sample mixed gas is filled into the chamber 101, the first temperature measuring element 62A of the microchip 8A, illustrated in
After the third sample mixed gas is filled into the chamber 101, illustrated in
After the fourth sample mixed gas is filled into the chamber 101, illustrated in
Note that if there are n types of gas components in each of the sample mixed gases, the heater element 61A, illustrated in
As illustrated in
Note that the electric signal SI from the first temperature measuring element 62A may be the resistance value RI of the first temperature measuring element 62A, the current II flowing in the first temperature measuring element 62A, the voltage VI applied to the first temperature measuring element 62A, or the output signal ADI from the A/D converting circuit 304 that is connected to the first temperature measuring element 62A. Similarly, the electric signal SH from the heater element 61A may be the resistance value RH of the heater element 61A, the current IH flowing in the heater element 61A, the voltage VH applied to the heater element 61A, or the output signal ADH from the A/D converting circuit 304 that is connected to the heater element 61A.
The thermal diffusivity calculating equation generating portion 302 that is included in the CPU 300 collection the respective known values for the inverses 1/α of the thermal diffusivities for, for example, each of the first through fourth sample mixed gases, the plurality of measured values for the electric signals SI from the first temperature measuring element 62A, and the plurality of measured values for the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A. Furthermore, the thermal diffusivity calculating equation generating portion 302 uses multivariate analysis based on the collected values for the inverses 1/α of the thermal diffusivities, the electric signals SI, and the electric signals SH, to generate a thermal diffusivity calculating equation having the electric signal SI from the first temperature measuring element 62A and the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A as the independent variables, and the inverse 1/α of the thermal diffusivity as the dependent variable. The other structural elements of the thermal diffusivity calculating equation generating system 20B illustrated in
As illustrated in
The thermal diffusivity calculating equation includes, for example, as independent variables, the electric signal SI from the first temperature measuring element 62A, the electric signal SH1 (TH1) from the heater element 61A at a heat producing temperature TH1 of 100° C., the electric signal SH2 (TH2) from the heater element 61A at a heat producing temperature TH2 of 150° C., and the electric signal SH3 (TH3) from the heater element 61A at a heat producing temperature TH3 of 200° C.
The first temperature measuring element 62A of the microchip 8A illustrated in
The measuring portion 321, illustrated in
The thermal diffusivity calculating portion 305 substitutes the respected respective measured values into the independent variables of the electric signal SI from the first temperature measuring element 62A and the electric Signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A in the thermal diffusivity calculating equation that is stored in the thermal diffusivity calculating equation storing device 402, to calculate the value of the inverse 1/α of the thermal diffusivity of the mixed gas. The other structural elements of the thermal diffusivity measuring system 21B illustrated in
Q=K
A
×V
A
+K
B
×V
B
+K
C
×V
C
+K
D
×V
D (38)
Here Equation (39), below, is obtained through substituting Equations (17) through (20), above, into Equation (38), above.
As is clear from Equation (39), above, the unit-volume calorific value Q of the mixed gas is obtained from an equation having, as variables, the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas, and the temperature TI of the mixed gas, when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3. Consequently, the calorific value Q of the mixed gas is given by Equation (40), below, where hI is a code indicating a function.
Q=h
I
[M
I(TH2),MI(TH2),MI(TH3),TI] (40)
Consequently, the inventors discovered that, for a mixed gas comprising a gas A, a gas B, a gas C, and a gas D, wherein the volume fraction VA of the gas A, the volume fraction VB of the gas B, the volume fraction VC of the gas C, and the volume fraction VD of the gas D, are unknown, it is possible to calculate easily the unit-volume calorific value of the mixed gas Lobe measured if Equation (40) is Obtained in advance. Specifically, the calorific value Q of the mixed gas being measured can be obtained uniquely by measuring the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3, and then substituting into Equation (40).
Additionally, the calorific value Q of the mixed gas is proportional to the concentration of caloric component C0 of the alkanes, and the like, in the mixed gas. Consequently, the concentration of caloric component C0 in the mixed gas is given by Equation (41), below, where h2 is a code indicating a function.
C
0
=h
2
[M
I(TH1),MI(TH2),MI(TH3),TI] (41)
Furthermore, if the mixed gas comprises n types of gas components, then the concentration of caloric component C0 in the mixed gas is given by Equation (42), below.
C
0
=h
2
[M
I(TH1),MI(TH2),MI(TH3), . . . ,MI(THn-1),TI] (42)
Note that, as with Equation (23), if the mixed gas includes an alkane (CjH2j+2) other than methane (CH4) and propane (C3H8), where j is a natural number, in addition to methane (CH4) and propane (C31H8), then the alkane (CjH2j+2) other than methane (CH4) and propane (C3H8) will be seen as a mixture of methane (CH4) and propane (C3H8), so there will be no effect on the calculation in Equation (42). Also, if the temperature TI of the mixed gas previous to the heater element 61A, illustrated in
The concentration of caloric component calculating equation generating system 22A according to the example illustrated in
The measuring mechanism 10 and heat dissipation factor storing device 401 are the same as in the above examples, so the explanations thereof are omitted. The density calculating equation generating portion 352 collects the respective known caloric component densities C0 of the first through fourth sample mixed gases, for example, the plurality of measured values for the radiation coefficients MI for the gas when the heat producing temperature of the heater element 61A was 100° C., the plurality of measured values for the radiation coefficients MI for the gas when the heat producing temperature of the heater element 61A was 150° C., and the plurality of measured values for the gas the radiation coefficients MI for when the heat producing temperature of the heater element 61A was 200° C. Based on the caloric component densities C0 and the plurality of radiation coefficients MI that have been collected, the density calculating equation generating portion 352 then, through multivariate analysis, calculates a concentration of caloric component calculating equation having, as independent variables, the radiation coefficient MI when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 200° C., and the gas temperature TI, and having, as the dependent variable, the concentration of caloric component C0.
The concentration of caloric component calculating equation generating system 22A is further provided with a density calculating equation storing device 452, connected to the CPU 300. The density calculating equation storing device 452 stores the concentration of caloric component calculating equation generated by the density calculating equation generating portion 352.
The flowchart in
(a) First, Step S100 through Step S103 are performed in the same way as above. Next, in Step S104, the known value for the concentration of caloric component C0 of the first sample mixed gas, the known value for the concentration of caloric component C0 of the second sample mixed gas, the known value for the concentration of caloric component C0 of the third sample mixed gas, and the known value for the concentration of caloric component C0 of the fourth sample mixed gas are inputted from the inputting device 312 into the density calculating equation generating portion 352. Additionally, the density calculating equation generating portion 352 reads in, from the radiation coefficient storing device 401, the values for the temperatures TI of the first through fourth sample mixed gases and the values for the radiation coefficients MI for the first through fourth sample mixed gases when the heat producing temperatures of the heater element 61A were 100° C., 150° C., and 200° C.
(b) In Step S105, the density calculating equation generating portion 352 performs multiple linear regression analysis based on the values for the caloric component densities C0 of the first through fourth sample mixed gases, the values for the temperatures TI of the first through fourth sample mixed gases, and the values for the radiation coefficients MI for the first through fourth sample mixed gases when the heat producing temperatures of the heater element 61A were 100° C., 150° C., and 200° C. Based on the multiple linear analysis, the density calculating equation generating portion 352 calculates a concentration of caloric component calculating equation having, as independent variables, the radiation coefficient MI when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 200° C., and the gas temperature TI, and having; as the dependent variable, the concentration of caloric component C0. Thereafter, in Step S106, the density calculating equation generating portion 352 stores, into the density calculating equation storing device 452, the concentration of caloric component calculating equation that has been generated, to complete the method for generating the concentration of caloric component calculating equation as above.
As described above, the method for generating a concentration of caloric component calculating equation as set forth enables the generation of a concentration of caloric component calculating equation that calculates a unique value for the concentration of caloric component C0 of a mixed gas being measured.
A concentration of caloric component measuring system 23A according to a further example illustrated in
The density calculating equation storing device 452 stores the concentration of caloric component calculating equation as described above. As an example, a case is explained here wherein natural gases, including methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide (CO2), were used as the sample mixed gases for generating the concentration of caloric component calculating equation. Additionally, the concentration of caloric component calculating equation uses, as independent variables, the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient of the gas when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 200° C., and the temperature TI of the gas.
In yet another example, a natural gas that includes, in unknown volume fractions, methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide (CO2), and for which the concentration of caloric component C0 is unknown, is introduced into the chamber 101 as the mixed gas to be measured. The measuring mechanism 10 and heat dissipation factor storing device 401 are the same as above, so the explanations thereof are omitted.
The density calculating portion 355 substitutes the values of the radiation coefficients MI and the temperature TI of the mixed gas being measured into the independent variables of the radiation coefficients MI for the gas and the temperature TI of the gas in the concentration of caloric component calculating equation, to calculate the value of the concentration of caloric component C0 of the mixed gas being measured. A density storing device 453 is also connected to the CPU 300. The density storing device 453 stores the value of concentration of caloric component C0 of the mixed gas being measured, calculated by the density calculating portion 355. The requirements for the other structural elements in the concentration of caloric component measuring system 23A as set forth therein are identical to those in the concentration of caloric component calculating equation generating system 22A set forth above, so explanations thereof are omitted.
The flowchart in
(a) First, Step S200 through Step S202 are performed in the same way as above. Next, in Step S203, the density calculating portion 355 reads in, from the density calculating equation storing device 452, the concentration of caloric component calculating equation that uses, as independent variables, the value for the temperature TI of the gas and the values for the radiation coefficients MI when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C. In addition, the density calculating portion 355 region, from the radiation coefficient storing device 401, the value for the temperature TI of the mixed gas being measured and the values for the radiation coefficients MI of the mixed gas being measured for when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C.
(c) In Step S204, the density calculating portion 355 substitutes the value of the temperature TI of the mixed gas being measured into the independent variable of the temperature TI in the concentration of caloric component calculating equation, and substitutes the value of the radiation coefficients MI of the mixed gas being measured into the independent variable of the radiation coefficients MI in the concentration of caloric component calculating equation, to calculate the value of the concentration of caloric component C0 of the mixed gas being measured. Thereafter, the density calculating portion 355 stores, into the density storing device 453, the value calculated for the concentration of caloric component C0, to complete the method for measuring the concentration of caloric component.
The method for measuring the concentration of caloric component as described above, enables the measurement of the concentration of caloric component C0 in a mixed gas that is a mixed gas to be measured, from measured values for the radiation coefficients MI of the mixed gas to be measured, without using costly gas chromatography equipment or speed-of-sound sensors.
First, as illustrated in
Following this, the equation for calculating the alkane density C0 was used to calculate calculated values for the alkane densities C0 for the 19 sample mixed gases, and the true values for the alkane densities C0 for the 19 sample mixed gases were compared. When this was done, the error in the calculated values, relative to the true values for the alkane densities C0, as illustrated in
As is illustrated in Equation (41), above, the concentration of caloric component C0 of the mixed gas that comprises the four types of gas components is obtained as an equation having, as variables, the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3. Additionally, the radiation coefficient MI of the mixed gas, as indicated in Equation (32), above, depends on the resistance value RH of the heater element 61A and on the resistance value RI of the first temperature measuring element 62A. Given this, the inventors discovered that the concentration of caloric component C0 of a mixed gas can also be obtained as an equation having, as variables, the resistances RH1(TH1), RH2(TH2), and RH3(TH3) of the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the resistance value RI of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (43), below.
C
0
=h
3
[R
H1(TH1),RH2(TH2),RH3(TH3),RI] (43)
Given this, the concentration of caloric component C0 of a mixed gas can be calculated uniquely by measuring the resistances RH1(TH1), RH2(TH2), and RH3(TH3) of the heater element 61A when the heat producing temperatures of the heater element 61A, which is in contact with the mixed gas, are TH1, TH2, and TH3, and the resistance value RI of the first temperature measuring element 62A that is in contact with the mixed gas prior to the heat production by the heater element 61A, for example, and then substituting into Equation (43).
Furthermore, the concentration of caloric component C0 of a mixed gas can also be obtained as an equation having, as variables, the currents IH1(TH1), IH2(TH2), and IH3(TH3) flowing in the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the current II flowing in the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (44), below.
C
0
=h
4
[I
H1(TH1),IH2(TH2),IH3(TH3),II] (44)
Conversely, the concentration of caloric component C0 of a mixed gas can also be obtained from an equation having, as variables, the voltages VH1(TH1), VH2(TH2), and VH3(TH3) of the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the voltage VI of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (45), below.
C
0
=h
5
[V
H1(TH1),VH2(TH2),VH3(TH3),VI] (45)
Conversely, the concentration of caloric component C0 of a mixed gas can also be obtained as an equation having, as variables, the output voltages ADH1(TH1), ADH2(TH2), and ADH3(TH3) of analog-digital converting circuits that are connected to the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the output voltage ADI of an A/D converting circuit that is connected to the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (46), below.
C
0
=h
6
[AD
H1(TH1),ADH2(TH2),ADH3(TH3),ADI] (46)
Consequently, the concentration of caloric component C0 of a mixed gas can also be obtained from an equation having, as variables, electric signals SH1(TH1), SH2(TH2), and SH3(TH3) from the heater element 61A when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3, and an electric signal SI from the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (47), below.
C
0
=h
7
[S
H1(TH1),SH2(TH2),SH3(TH3),SI] (47)
Here a concentration of caloric component calculating equation generating system 22B as illustrated in
As with the above examples, the measuring portion 321 measures the value of the electric signal SI from the first temperature measuring element 62A, and, from the heater element 61A, the values of the electric signal SH1 (TH1) at the heat producing temperature TH1, the electric signal SH2 (TH2) at the heat producing temperature TH2, and the electric signal SH3 (TH3) at the heat producing temperature TH3, and stores the measured values in the electric signal storing device 421.
The concentration of caloric component calculating equation generating portion 352 that is included in the CPU 300 collection the respective known values for the caloric component densities C0 of for example, each of the first through fourth sample mixed gases, the plurality of measured values for the electric signals SI from the first temperature measuring element 62A, and the plurality of measured values for the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A. Furthermore, the concentration of caloric component calculating equation generating portion 352 uses multivariate analysis based on the collected values for the caloric component densities C0, the electric signals SI, and the electric signals SH, to generate a concentration of caloric component calculating equation having the electric signal SI from the first temperature measuring element 62A and the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A as the independent variables, and the concentration of caloric component C0 as the dependent variable. The other structural elements of the concentration of caloric component calculating equation generating system 22B illustrated in
As illustrated in
The concentration of caloric component calculating equation includes, for example, as independent variables, the electric signal SI from the first temperature measuring element 62A, the electric signal SH1 (TH1) from the heater element 61A at a heat producing temperature TH1 of 100° C., the electric signal SH2 (TH2) from the heater element 61A at a heat producing temperature TH2 of 150° C., and the electric signal SH3 (TH3) from the heater element 61A at a heat producing temperature TH3 of 200° C.
The first temperature measuring element 62A of the microchip 8A illustrated in
The measuring portion 321 measures the value of the electric signal SI from the first temperature measuring element 62A, which is in contact with the mixed gas being measured, and, from the heater element 61A, which is in contact with the mixed gas being measured, the values of the electric signal SH1 (TH1) at the heat producing temperature TH1, the electric signal SH2 (TH2) at the heat producing temperature TH2, and the electric signal SH3 (TH3) at the heat producing temperature TH3, and stores the measured values in the electric signal storing device 421.
The density calculating portion 355 substitutes the respected respective measured values into the independent variables of the electric signal SI from the first temperature measuring element 62A and the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A in the concentration of caloric component calculating equation that is stored in the density calculating equation storing device 452, to calculate the value of the concentration of caloric component C0 of the mixed gas being measured. The other structural elements of the concentration of caloric component measuring system 23B illustrated in
As is clear from Equation (7), above, the inverse 1/α of the thermal diffusivity is proportional to the system the heat capacity Cp divided by the thermal conductivity k. Consequently, Equation (22), above, can be modified with so that the specific heat capacity Cp divided by the thermal conductivity k can be obtained, as shown in Equation (48), below, from an equation having, as variables, the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas, and the temperature TI of the mixed gas, when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3.
Cp/k=g
7
[M
I(TH1),MI(TH2),MI(TH3),TI] (48)
Consequently, the inventors discovered that, for a mixed gas comprising a gas A, a gas B, a gas C, and a gas D, wherein the volume fraction VA of the gas A, the volume fraction VB of the gas B, the volume fraction VC of the gas C, and the volume fraction VD of the gas D, are unknown, it is possible to calculate easily the specific heat capacity Cp divided by the thermal conductivity k in the mixed gas to be measured if Equation (48) is obtained in advance. Specifically, the specific heat capacity Cp divided by the thermal conductivity k in the mixed gas being measured can be obtained uniquely by measuring the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3, and then substituting into Equation (48).
Note that if the mixed gas comprises n types of gas components, then the specific heat capacity Cp divided by the thermal conductivity k in the mixed gas is given by Equation (49), below
Cp/k=g
7
[M
I(TH1),MI(TH2),MI(TH3),TI] (49)
Note that, as with Equation (23), if the mixed gas includes an alkane (CjH2j+2) other than methane (CH4) and propane (C3H8), where j is a natural number, in addition to methane (CH4) and propane (C3H8), then the alkane (CjH2j+2) other than methane (CH4) and propane (C3H8) will be seen as a mixture of methane (CH4) and propane (C3H8), so there will be no effect on the calculation in Equation (49). Also, if the temperature TI of the mixed gas previous to the heater element 61A, illustrated in
The specific heat capacity calculating equation generating system 24A according to
The measuring mechanism 10 and heat dissipation factor storing device 401 are the same as above, so the explanations thereof are omitted. The specific heat capacity calculating equation generating portion 362 collects the respective known specific heat capacities Cp divided by the thermal conductivities k in the first through fourth sample mixed gases, for example, the plurality of measured values for the radiation coefficients MI for the gas when the heat producing temperature of the heater element 61A was 100° C., the plurality of measured values for the radiation coefficients MI for the gas when the heat producing temperature of the heater element 61A was 150° C., and the plurality of measured values for the gas the radiation coefficients MI for when the heat producing temperature of the heater element 61A was 200° C. Based on the specific heat capacities Cp divided by the thermal conductivities k and the plurality of radiation coefficients MI that have been collected, the specific heat capacity calculating equation generating portion 362 then, through multivariate analysis, calculates a specific heat capacity calculating equation having, as independent variables, the radiation coefficient MI when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 200° C., and the gas temperature TI, and having, as the dependent variable, the specific heat capacity Cp divided by the thermal conductivity k.
The specific heat capacity calculating equation generating system 24A is further provided with a specific heat capacity calculating equation storing device 462, connected to the CPU 300. The specific heat capacity calculating equation storing device 462 stores the specific heat capacity calculating equation generated by the specific heat capacity calculating equation generating portion 362.
The flowchart in
(a) First, Step S100 through Step S103 are performed in the same way as above. Next, in Step S104, the known value for the specific heat capacity Cp divided by the thermal conductivity k in the first sample mixed gas, the known value for the specific heat capacity Cp divided by the thermal conductivity k in the second sample mixed gas, the known value for the specific heat capacity Cp divided by the thermal conductivity k in the third sample mixed gas, and the known value for the specific heat capacity Cp divided by the thermal conductivity k in the fourth sample mixed gas are inputted from the inputting device 312 into the specific heat capacity calculating equation generating portion 362. Additionally, the specific heat capacity calculating equation generating portion 362 reads in, from the radiation coefficient storing device 401, the values for the temperatures TI of the first through fourth sample mixed gases and the values for the radiation coefficients MI for the first through fourth sample mixed gases when the heat producing temperatures of the heater element 61A were 100° C., 150° C., and 200° C.
(b) In Step S105, the specific heat capacity calculating equation generating portion 362 performs multiple linear regression analysis based on the values for the specific heat capacities Cp divided by the thermal conductivities k in the first through fourth sample mixed gases, the values for the temperatures TI of the first through fourth sample mixed gases, and the values for the radiation coefficients MI for the first through fourth sample mixed gases when the heat producing temperatures of the heater element 61A were 100° C., 150° C., and 200° C. Based on the multiple linear analysis, the specific heat capacity calculating equation generating portion 362 calculates a specific heat capacity calculating equation having, as independent variables, the radiation coefficient MI when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI when the heat producing temperature of the heater element 61A is 200° C., and the gas temperature TI, and having, as the dependent variable, the specific heat capacity Cp divided by the thermal conductivity k. Thereafter, in Step S106, the specific heat capacity calculating equation generating portion 362 stores, into the specific heat capacity calculating equation storing device 462, the specific heat capacity calculating equation that has been generated, to complete the method for generating the specific heat capacity calculating equation.
As described above, the method for generating a specific heat capacity calculating equation enables the generation of a specific heat capacity calculating equation that calculates a unique value for the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas being measured.
A specific heat capacity measuring system 25A according to an example illustrated in
The specific heat capacity calculating equation storing device 462 stores the specific heat capacity calculating equation. As an example, a case is explained here wherein natural gases, including methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide (CO2), were used as the sample mixed gases for generating the specific heat capacity calculating equation. Additionally, the specific heat capacity calculating equation uses, as independent variables, the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 100° C., the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 150° C., the radiation coefficient MI of the gas when the heat producing temperature of the heater element 61A is 200° C., and the temperature TI of the gas.
In a yet further example, a natural gas that includes, in unknown volume fractions, methane (CH4), propane (C3H8), nitrogen (N2), and carbon dioxide (CO2), and for which the value of the specific heat capacity Cp divided by the thermal conductivity k is unknown, is introduced into the chamber 101 as the mixed gas to be measured. The measuring mechanism 10 and heat dissipation factor storing device 401 are the same as in the first form of embodiment, so the explanations thereof are omitted.
The specific heat capacity calculating portion 365 substitutes the values of the radiation coefficients MI and the temperature TI of the mixed gas being measured into the independent variables of the radiation coefficients MI for the gas and the temperature TI of the gas in the specific heat capacity calculating equation, to calculate the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured. A specific heat capacity storing device 463 is also connected to the CPU 300. The specific heat capacity storing device 463 stores the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured, calculated by the specific heat pass the calculating portion 365. The requirements for the other structural elements in the specific heat capacity measuring system 25A are identical to those in the specific heat capacity calculating equation generating system 24A set forth above, so explanations thereof are omitted.
The flowchart in
(a) First, Step S200 through Step S202 are performed in the same way as above. Next, in Step S203, the specific heat capacity calculating portion 365 reads in, from the specific heat capacity calculating equation storing device 462, the specific heat capacity calculating equation that uses, as independent variables, the value for the temperature TI of the gas and the values for the radiation coefficients MI when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C. In addition, the specific heat capacity calculating portion 365 region, from the radiation coefficient storing device 401, the value for the temperature TI of the mixed gas being measured and the values for the radiation coefficients MI of the mixed gas being measured for when the heat producing temperatures of the heater element 61A are 100° C., 150° C., and 200° C.
In Step S204, the specific heat capacity calculating portion 365 substitutes the value of the temperature TI of the mixed gas being measured into the independent variable of the temperature TI in the specific heat capacity calculating equation, and substitutes the value of the radiation coefficients MI of the mixed gas being measured into the independent variable of the radiation coefficients MI in the specific heat capacity calculating equation, to calculate the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured. Thereafter, the specific heat capacity calculating portion 365 stores, into the specific heat capacity storing device 463, the value calculated for the specific heat capacity Cp divided by the thermal conductivity k, to complete the method for measuring the specific heat capacity. The method for measuring the specific heat capacity described above, enables the measurement of the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas that is a mixed gas to be measured, from measured values for the radiation coefficients MI of the mixed gas to be measured, without using costly gas chromatography equipment or speed-of-sound sensors.
First, as illustrated in
Following this, the equation for calculating the specific heat capacity Cp divided by the thermal conductivity k was used to calculate calculated values for the specific heat capacities Cp divided by the thermal conductivities k in the 19 sample mixed gases, and the true values for the specific heat capacities Cp divided by the thermal conductivities k in the 19 sample mixed gases were compared. When this was done, the error in the calculated values, relative to the true values for the specific heat capacities Cp divided by the thermal conductivities k, as illustrated in
As is illustrated in Equation (48), above, the specific heat capacity Cp divided by the thermal conductivity k in the mixed gas that has the four types of gas components is obtained as an equation having, as variables, the radiation coefficients MI(TH1), MI(TH2), and MI(TH3) of the mixed gas when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3. Additionally, the radiation coefficient MI of the mixed gas, as indicated in Equation (32), above, depends on the resistance value RH of the heater element 61A and on the resistance value RI of the first temperature measuring element 62A. Given this, the inventors discovered that the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained as an equation having, as variables, the resistances RH1(TH1), RH2(T2), and RH3(TH3) of the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the resistance value RI of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (50), below.
Cp/k=g
8
[R
H1(TH1),RH2(TH2),RH3(TH3),RI] (50)
Given this, the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can be calculated uniquely by measuring the resistances RH1(TH1), RH2(TH2), and RH3(TH3) of the heater element 61A when the heat producing temperatures of the heater element 61A, which is in contact with the mixed gas, are TH1, TH2, and TH3, and the resistance value RI of the first temperature measuring element 62A that is in contact with the mixed gas prior to the heat production by the heater element 61A, for example, and then substituting into Equation (50).
Furthermore, the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained as an equation having, as variables, the currents IH1(TH1), IH2(TH2), and IH3(TH3) flowing in the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the current II flowing in the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (51), below.
Cp/k=g
9
[I
H1(TH1),IH2(TH2),IH3(TH3),II] (51)
Conversely, the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained from an equation having, as variables, the voltages VH1(TH1), VH2(TH2), and VH3(TH3) of the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the voltage VI of the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (52), below.
Cp/k=g
10
[V
H1(TH1),VH2(TH2),VH3(TH3),VI] (52)
Conversely, the specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained as an equation having, as variables, the output voltages ADH1(TH1), ADH2(TH2), and ADH3(TH3) of analog-digital converting circuits that are connected to the heater element 61A when the temperatures of the heater element 61A are TH1, TH2, and TH3, and the output voltage ADI of an A/D converting circuit that is connected to the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (53), below.
Cp/k=g
11
[AD
H1(TH1),ADH2(TH2),ADH3(TH3),ADI] (53)
Consequently, specific heat capacity Cp divided by the thermal conductivity k in a mixed gas can also be obtained from an equation having, as variables, electric signals SH1(TH1), SH2(TH2), and SH3(TH3) from the heater element 61A when the heat producing temperatures of the heater element 61A are TH1, TH2, and TH3, and an electric signal SI from the first temperature measuring element 62A that is in contact with the mixed gas, as shown in Equation (54), below.
Cp/k=g
12
[S
H1(TH1),SH2(TH2),SH3(TH3),SI] (54)
Here a specific heat capacity calculating equation generating system 24B as illustrated in
As above, the measuring portion 321 measures the value of the electric signal SI from the first temperature measuring element 62A, and, from the heater element 61A, the values of the electric signal SH1 (TH1) at the heat producing temperature TH1, the electric signal SH2 (TH2) at the heat producing temperature TH2, and the electric signal SH3 (TH3) at the heat producing temperature TH3, and stores the measured values in the electric signal storing device 421.
The specific heat capacity calculating equation generating portion 362 that is included in the CPU 300 collection the respective known values for the specific heat capacities Cp divided by the thermal conductivities k in, for example, each of the first through fourth sample mixed gases, the plurality of measured values for the electric signals SI from the first temperature measuring element 62A, and the plurality of measured values for the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A. Furthermore, the specific heat capacity calculating equation generating portion 362 uses multivariate analysis based on the collected values for the specific heat capacities Cp divided by the thermal conductivities k, the electric signals SI, and the electric signals SH, to generate a specific heat capacity calculating equation having the electric signal SI from the first temperature measuring element 62A and the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A as the independent variables, and the specific heat capacity Cp divided by the thermal conductivity k in as the dependent variable. The other structural elements of the specific heat capacity calculating equation generating system 24B illustrated in
As illustrated in
The specific heat capacity calculating equation includes, for example, as independent variables, the electric signal SI from the first temperature measuring element 62A, the electric signal SH1 (TH1) from the heater element 61A at a heat producing temperature TH1 of 100° C., the electric signal SH2 (TH2) from the heater element 61A at a heat producing temperature TH2 of 150° C., and the electric signal SH3 (TH3) from the heater element 61A at a heat producing temperature TH3 of 200° C.
The first temperature measuring element 62A of the microchip 8A illustrated in
The measuring portion 321 measures the value of the electric signal SI from the first temperature measuring element 62A, which is in contact with the mixed gas being measured, and, from the heater element 61A, which is in contact with the mixed gas being measured, the values of the electric signal SH1 (TH1) at the heat producing temperature TH1, the electric signal SH2 (TH2) at the heat producing temperature TH2, and the electric signal SH3 (TH3) at the heat producing temperature TH3, and stores the measured values in the electric signal storing device 421.
The specific heat capacity calculating portion 365 substitutes the respected respective measured values into the independent variables of the electric signal SI from the first temperature measuring element 62A and the electric signals SH1 (TH1), SH2 (TH2), and SH3 (TH3) from the heater element 61A in the specific heat capacity calculating equation that is stored in the specific heat capacity calculating equation storing device 462, to calculate the value of the specific heat capacity Cp divided by the thermal conductivity k of the mixed gas being measured. The other structural elements of the specific heat capacity measuring system 25B illustrated in
The flow rate measuring system as set forth in
The flow meter 41A, as illustrated in
A filling opening 13 and a discharge opening 14 are provided in the flow path holding unit 15, and a flow path 11 passes through the interior of the flow path holding unit 15 from the filling opening 13 to the discharge opening 14. A flow path 103, illustrated in
The microchip 8B, as illustrated in
The portion of the dielectric layer 65B that covers the cavity 66B forms a thermally insulating diaphragm. The peripheral temperature sensor 64B measures the temperature of the mixed gas being measured that has flowed into the flow path 11, illustrated in
Here, when the mixed gas being measured is stationary within the flow path 11 that is illustrated in
In contrast, when the mixed gas being measured flows from upstream to downstream within the flow path 11 that is illustrated in
An orifice 12 for narrowing the inner diameter of the flow path 11 is provided in a portion of the flow path 11. The cross-sectional area of the flow path 11 in the orifice 12 is set appropriately to cause the speed of flow of the mixed gas that is being measured in the flow path 11 to be within the measurement range of the microchip 8B. Additionally, the microchip SB is connected electrically to the CPU 330 of the controlling unit 30.
The flow rate calculating portion 331 of the CPU 330 receives, from the microchip 8B, the value of the electrical resistance of the downstream temperature measuring resistive element 63B, illustrated in
Here the flow rate Q of the gas, detected using the flow rate sensor that includes the microchip SB and the flow rate calculating portion 331, tends to have error that increases with the inverse 1/α of the thermal diffusivity of the gas. As an example, the flow rate sensor was first calibrated using, as the calibration gas, a public utility gas 13A wherein the calorific value was adjusted to 45 MJ/m3. Following this, the first through sixth mixed gases, having the components presented in
Consequently, if there is a difference between the inverse 1/α0 of the thermal diffusivity of the calibration gas and the inverse 1/α1 of the thermal diffusivity of the mixed gas being measured, then there may be error in the detected value for the flow rate Q of the mixed gas being measured. In this regard, the CPU 330, illustrated in
Furthermore, the correcting portion 332, illustrated in
Q
C
=Q×(1/α)/(1/α0)=Q×α0/α (55)
The flow rate measuring system as set forth and illustrated in
A flow rate measuring system as illustrated in
The CPU 330 of the flow meter 41C, as illustrated in
Here the detected value for the volumetric flow rate Q of the mixed gas being measured, calculated by the flow rate calculating portion 331, as shown by Equation (56), below, is proportional to the product of the thermal diffusivity a and the flow speed d. Here A is a constant.
Q=A×(1/α)×d=A×ρCp/k×d (56)
The mass flow rate calculating portion 334, illustrated in
Q/(ACp/k)=ρ×d (57)
Moreover, the mass flow rate calculating portion 334, as shown in Equation (58), below, calculate the mass flow rate m of the mixed gas being measured by multiplying the product of the density ρ and the flow speed d, thus obtained, by the cross-sectional area u of the orifice 12. Note that the units for the mass flow rate Qm are, for example, kg/s or kg/h.
Qm×ρ×d×u (58)
The other structural elements of the flow meter 41C are identical to those of the flow meter 41A that is illustrated in
A flow rate measuring system as illustrated in
The flow rate measuring system as set forth and illustrated in
The CPU 330 of the flow meter 41B, as illustrated in
Moreover, the calorific flow rate calculating portion 333, illustrated in
Q
C
=Qm×C
O (59)
When non-caloric components are included in a mixed gas being measured, such as natural gas, sometimes it is desirable to measure the flow rate of the caloric components, excluding the non-caloric components. In this regard, the flow rate measuring system enables the accurate measurement of the flow rate of the caloric components of the mixed gas being measured. The other structural elements of the flow meter 41B are identical to those of the flow meter 41A that is illustrated in
The flow rate measuring system as set forth in a 18th form of embodiment, as illustrated in
While there are descriptions of example as set forth above, the descriptions and drawings that form a portion of the disclosure are not to be understood to limit the present invention. A variety of alternate examples and operating technologies should be obvious to those skilled in the art. For example,
| Number | Date | Country | Kind |
|---|---|---|---|
| 2010-097139 | Apr 2010 | JP | national |
