This invention relates to devices and methods for measuring fluid flow. More specifically, the invention relates to fluid delivery systems that introduce a thermal tracer into the fluid and monitor the progress of the thermal tracer by optically detecting the change of index of refraction inherent in the thermal tracer.
Devices and methods for measuring the flow of a fluid in a conduit using the thermal “time of flight” method are known. Such flow sensors are useful in measuring fluid flow in analytical systems such as high performance liquid chromatography (HPLC) systems, in drug delivery systems, and other systems such as fluid mixing systems where accurate knowledge of the quantity of fluid being delivered to a delivery site is needed. Jerman et al in U.S. Pat. No. 5,533,412 teach an integrated thermal time of flight device on a substrate where elements to introduce a thermal tracer into the flowing stream using thermal elements are in contact with the conduit along which the stream flows. Others, including Sobek et al in application publication US 20050066747, teach devices where the elements to introduce the thermal marker and to detect the thermal marker are in contact with the fluid. Bornhop in U.S. Pat. No. 6,381,025 and Yin et al in U.S. Pat. No. 6,386,050 teach a non contact system where an optical probe is used to detect the passage of the thermal marker based on the motion of an interference pattern caused by changes in the index of refraction inherent in the thermal marker. Sage, in application Ser. No. 10/786,562 teaches a second non contact system that uses radiant energy to introduce a thermal marker into the flowing stream but uses an optical probe to detect the passage of the thermal marker based on diffraction of the probing optical beam caused by changes in the index of refraction inherent in the thermal marker.
Thermal time of flight methods that are not physically isolated from the fluid flow rely on the thermal conductivity of the probes to create both the thermal marker and to detect the passage of the thermal marker. Such systems are inherently relatively slow since the flow of thermal energy is not a rapid phenomenon. The measured time of flight in such systems is seldom less than a few tens of milliseconds.
The optical probes described by Bornhop, Yin et al, and Sage overcome this problem. The measured time of flight can be as short as 100 microseconds and the resolution of the time of flight can be as short as 1 microsecond. However, to achieve this level of performance, relatively sophisticated and expensive lasers should be used.
Further, in all of these non-contact flow measurement teachings, only the velocity of the flowing stream is measured. Measurement of a true volumetric flow rate additionally requires the cross sectional area of the conduit. This is especially important in a conduit of circular cross section where the volumetric flow depends on the diameter of the conduit to the fourth power. In a fluid delivery system that is to be used over a wide temperature range, the dimensions of the conduit will change due to thermal expansion. In a fluid delivery system where the conduit is disposable and replaced frequently, the dimensions of the new conduit will be unknown. Thus there is a need for improved flow sensors, especially a system that measures geometrical changes of the flow channel as well as the velocity of the flow stream.
An apparatus and method for accurately measuring volumetric flow of a liquid along a conduit is described. Bornhop in U.S. Pat. No. 6,381,025 and Yin, et al in U.S. Pat. No. 6,386,050 describe an interferometric method of measuring index of refraction changes in a liquid flowing along a conduit and the use of this method to measure the index of refraction of the liquid and the velocity of the liquid flowing along the conduit. These devices and methods have the distinct advantage that the flow of the fluid may be monitored without contact with either the fluid or the conduit within which the fluid is flowing. This invention expands the teachings of Bornhop and Yin et al in several important ways. First, it teaches that interference is not necessary in order to measure the refractive index or the liquid velocity as described. Thus, a light source with sufficient coherence to establish an interference patterns is not required. Although a laser may be used, virtually any light source with sufficient intensity to activate the detectors may be used.
Second, while Bornhop and Yin et al realize the value of their non-contact interferometric methods in maintaining a contamination free conduit and in eliminating the thermal effects of contact based thermal time of flight systems, they have not realized the further advantage of being able to use a removable and disposable conduit that mates with the heat source and interferometric flow sensor. Such a removable and disposable conduit has the advantage of providing a two-part system, such as a drug delivery system or an analyzer such as an HPLC that does not requiring cleaning between uses, thereby providing enhanced user convenience and overall lower cost.
Third, the methods of Bornhop and Yin et al do not accommodate variations in the cross-sectional area of the flow tube. In a system where the conduit is not disposable, the system may be calibrated to accommodate the cross sectional area such that the measured time of flight corresponds to a true volumetric flow rate. In a system with a disposable conduit, this process will not provide an accurate flow rate. When a new conduit is mated to the heat source and flow sensor the cross sectional area of the new conduit will be different than the cross sectional area of the previous one due to manufacturing tolerances. Further, in a fluid delivery system where the conduit is not disposable and is used over a wide temperature range, thermal expansion will cause the dimensions of the conduit to change. These differences, although typically small, are critically important because the volumetric flow rate varies with the fourth power of the conduit dimension. Hence any calibration that may have been done with an earlier conduit will not be appropriate for the new conduit. And a calibration performed at one temperature will not be appropriate for other temperatures. Nothing in the teachings of Yin et al and Bornhop teach measurement of the cross sectional area of the conduit when the conduit is in use to provide a true volumetric flow rate. It is noteworthy that a dimension of the conduit can be obtained directly from the interference pattern of Bornhop and Yin et al, or the refraction pattern of this invention. Bornhop and Yin et al teach that the liquid velocity may be measured by the motion of the interference pattern due to the transit of a thermal market. This invention notes that a dimension of the conduit may be obtained from measurements of the interference pattern. For example, the height of a rectangular conduit may be calculated from the spacing of the maxima of the pattern. In the case of a rectangular conduit, a second orthogonal sensor may be used to obtain the orthogonal dimension of the conduit, but in the case where even a square conduit is manufactured by injection molding, since a primary variance from conduit to conduit is variation in shrinkage as the conduit cools, a single measurement of a dimension of the conduit may provide sufficient compensation to achieve the desired level of accuracy of flow measurement. From a practical point of view, the measurement of the dimension of the conduit may be taken when the fluid in the conduit is air since the refractive index of air is low and the stability of the measurement is high. Such a practical matter is perhaps more important when the fluid that will eventually flow in the conduit is a liquid. Liquids in general have a relatively high variation of refractive index with temperature. Making the measurement of the conduit dimension when there is no liquid in the conduit, such as before an IV infusion set is primed for delivery of the therapeutic solution, avoids the issue of the temperature dependence of the refractive index of the liquid. One could also provide a temperature sensor and data related to the temperature dependence of the refractive index of the liquid to overcome this problem.
When the measurement of the conduit dimension is made with no liquid in the conduit, the location of the maxima and minima of the reflection pattern may also be noted as well as the separation of the maxima or minima. When the liquid to be delivered is added to the conduit such that the liquid flows through the interrogation region, the reflection pattern will be shifted to a new position. The magnitude of this shift is directly proportional to the refractive index of the liquid. Note that no thermal marker has been added to the liquid to make this measurement. In this way, the refractive index of the liquid may be determined. With knowledge of the temperature and the dependence of the various liquid that may flow in the conduit, the identity of the liquid may be determined.
Fourth, both Bornhop and Yin et al teach the determination of velocity as the ratio of the distance from the point of placing the thermal marker in the stream to the point of detection of the thermal marker and the measured elapsed time between placing the thermal marker in the stream and detecting the thermal marker. Yin et al fuel teach that the thermal marker may be time dependent, for example sinusoidal such that the phase difference between the thermally introduced sinusoid and the detected sinusoid can be used to determine the stream velocity. In each of these teachings, the time required to place the thermal marker in the stream introduces an uncertainty in the measurement of the time of flight and hence the stream velocity. In one embodiment of this invention, this uncertainty is overcome by noting that if the thermal marker is introduced quickly such that its length in the conduit is short compared to the spacing of the pattern, the elapsed time between the passing of the thermal marker through each of the beams provides a time of flight independent of the nature of introduction of the thermal marker. Further, since the thermal marker passes through all of the beams of the pattern, several independent measures of the time of flight may be made, which may be averaged to improve the precision of the measurement.
Fifth, both Yin et al and Bornhop are silent on the methods of calibration that may be needed to obtain accurate flow measurements over a useful range of flow rates. This invention teaches that the volumetric flow rate within a specific conduit is best described as a polynomial function of the measured “time of flight”, or the calculated velocity using the measured “time of flight”.
Conduit 11 may be glass or may be one of many common engineering plastics such as polyethylene or polypropylene. The main criteria for selecting the material for conduit 11 is that it is transparent to incident beam 12 and that it has smooth surfaces when formed. Conduit 11 also has raised surfaces in the area where incident beam 12 enters the conduit. As shown, these raised surfaces facilitate the exit of the reflected and refracted portions of incident beam 12.
As shown in
A first important parameter of conduit 11 that may be calculated from the patterns is the width W of conduit 11. If conduit 11 is circular in cross section, this measure would constitute the diameter of the conduit. If conduit 11 is rectangular in cross section, then W may represent either the width or the height of the cross section. A second similar optical system orthogonal to the one shown would determine the other dimension of a rectangular conduit. Since this measurement is made without touching conduit 11, this system may measure multiple conduits by simply placing the unknown conduit into the light beam as shown in
Referring again to
n1 Sin θ1=n2 Sin θ2
where n1 is the index of refraction of the conduit and
By simple geometry
z=2w Tan θ2
By further use of trigonometric identities, it can be shown that the width W of conduit 11 is related to the separation X of the various beams 14 as measured by detector array 16 in terms of the know parameters of conduit refractive index n1, fluid refractive index n2 and the angle of incidence θ1 of light beam 12 in the following manner:
w=xn2 [1−(n1 Sin θ1/n2)2]1/2/2n1 Sin θ1 Cos θ1
In a round capillary where W is the diameter of the capillary, the volumetric flow rate would be equal to the product of the conduit cross sectional area A (A=Πw2) and the fluid velocity. In a square capillary, the volumetric flow rate would be the product of the cross sectional area A (A=w2) and the stream velocity. In a rectangular conduit, the volumetric flow rate would be the product of the cross sectional area A (A=w*h) and the stream velocity where h is the dimension of the rectangular conduit orthogonal to w, where h may be assumed to have the same relationship to the nominal value as the measured w has to its nominal value or h may be measured using a second optical system similar to the one shown in
As noted above, the volumetric flow rate is the product of the cross sectional area of the conduit at the probing region times the velocity of the stream at the probing region. Using
As thermal marker 17 enters the probing region defined by transmitted beams 14 and reflected beams 15 and travels downstream, it will intersect beams b, c, d, e, and f in turn. It will not intersect beam a since this beam has not entered the conduit. Thus for each of the traverses of the beams array detector 16 will monitor the change of position of the beam on the array detector. While array detector 16 is shown monitoring transmitted beams 14, a similar array detector could monitor reflected beams 15 (not shown).
A typical output for detector array 16 is shown in
Because of the parabolic nature of laminar flow, thermal marker 17 will occupy the center of conduit 11. The separation of beams Z of beams b, d, and f may be calculated from the separation X of beams b, d, and f by detector array 16 in
Z=X/Cos θ1
The velocity of the fluid stream may now be calculated as Z/tof.
An alternative method for measuring the velocity of the fluid stream is described using
In a similar manner, a phase delay may be measured using detector array 17 and reflected beams c and e. However, since reflected beam a does not enter the fluid stream, the position of reflected beam a at detector array 17 does not change. The intensity of reflected beam a at detector array 17 does change as the temperature of the fluid changes according to the well known Fresnel reflection law and will also give a signal similar to signal 82 in
In general, the probing region generally depicted in
Referring again to
In operation, especially in a single conduit where the cross sectional area is fixed, the volumetric flow rate is the product of the stream velocity and the cross sectional area. As flow rate is changed, the stream velocity changes in direct proportion to the change in the flow rate. Since stream velocity is the ratio of the time required for a marker to travel a given distance, it is expected that as flow rate changes, the time of flight for the marker to travel the same distance would again be in direct proportion to the change in flow rate. Surprisingly, attempts to demonstrate this linearity are only relatively successful over a relatively short range of flow rates. As the range of flow rates is increased such that the highest flow rate is over a factor of 10 greater than the lowest flow rate, a polynomial relationship between the flow rate and the time of flight is required in order to have a high level of accuracy in predicting a flow rate from a measured time of flight. This need for a polynomial relationship is demonstrated with the following example. A flow sensor of the invention was assembled and tested over a flow rate range of 0.026 microliters per second to 1.076 microliters per second. A pressure cuff was applied to a one liter infusion bag of normal saline so that the driving pressure could be varied. Flow was initiated with a stopcock and the amount of fluid accumulated in a vessel on an electronic scale over a fixed period of time was recorded. During the time period that the fluid was being accumulated, time of flight measurements were made. For each flow episode, 25 time of flight measurements were made, and the mean and standard deviation of these 25 time of flight measurements was calculated. The mean was used to create a calibration curve, the standard deviation was used to determine the precision with which each of the measurements reflected the actual flow rate. These data are tabulated in Table 1 below.
The calibration curve generated from this data is shown in
Alternatively, the index of refraction of the fluid flowing in the conduit may be determined using reflected beams a, c, and e. Since reflected beam a does not pass through the fluid, its position on detector array 17 in
It is important to recognize that both the fluid flow rate and the fluid refractive index may be determined using the same optical probing system. Such a sensor has utility in systems where both the quantity of fluid moving in the system and the chemical makeup of the fluid are important. Examples of such systems are an HPLC analysis system where two fluids are mixed to provide a density gradient in the conduit and a fuel cell where the amount of fluid flowing to the fuel cell depends on the power required from the flow cell and the efficiency of the fuel cell depends upon the ratio of two or more components of the fuel such as a methanol fuel cell where the ratio of methanol to water is important.