This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2014-078785 filed on Apr. 7, 2014, the entire contents of which are incorporated herein by reference.
The embodiments discussed herein are related to a thermal fluid analysis method, an information processing device, and a recording medium that stores a thermal fluid analysis program.
When designing a server apparatus or a data center, a thermal fluid simulation has been used to grasp a heat distribution or an air (fluid) flow in a normal state without using an apparatus that is to be designed. In the thermal fluid simulation, a plurality of time steps which are time-serially continuous are set, and a time series simulation, in which an analysis process of proceeding calculation for each time step is repeated, is performed.
Japanese Laid-open Patent Publication No. 2012-216173 is an example of the related art.
According to an aspect of the embodiments, a thermal fluid analysis method, includes: calculating, by a computer, a first component of a new first sample different from a plurality of second samples; setting a second component obtained by unitizing the first component to a first base; adding the first base to a plurality of second bases of the plurality of second samples when the first component is greater than a threshold value; and correcting a low-dimensional model that expresses a plurality samples with superposition of a plurality of bases by using the first base and the plurality of second bases.
The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention, as claimed.
For example, in a thermal fluid simulation, a pre-simulation of a flow velocity field and a temperature field is performed. In the pre-simulation, snapshot data (sample) at an arbitrary time step is collected with respect to each of the flow velocity field and the temperature field. Main component analysis is performed with respect to the samples that are collected to acquire an orthogonal base that most efficiently expresses all of the samples, and an undesirable orthogonal base is reduced. For example, in the pre-simulation, time evolution of the flow velocity field and the temperature field is performed by using a incompressive Navier-Stokes equation of the following Equation (1), and a heat equation of the following Equation (2). Navier-Stokes equation may be used.
u represents a velocity vector of a fluid, p represents a pressure, p represents a density, f represents an external force vector that acts per unit mass, v represents a coefficient of kinematic viscosity, T represents a temperature, x represents a coefficient of heat conduction, and S represents an amount of heat received from the outside. Nabla V represents a space differential operator.
For example, in the thermal fluid simulation, an analysis model of the flow velocity field is expressed with superposition of the orthogonal bases which are obtained, and the simulation of the flow velocity field is executed. For example, in the thermal fluid simulation, an analysis model of the temperature field is expressed with superposition of the orthogonal bases which are obtained, and the simulation of the temperature field is executed.
An application range of the analysis model of the thermal fluid simulation is limited to a range of a set of samples. Accordingly, when a new sample increases, time may be taken to recreate a new analysis model. For example, when the sample increases, the pre-simulation is performed in the thermal fluid simulation in a state of including the increased sample. A new analysis model in which the increased sample is also set to the application range is created by using superposition of orthogonal bases which are obtained.
The following examples may be applied to an information processing device that executes the thermal fluid analysis or may be broadly applied to overall devices which execute the thermal fluid analysis.
In the thermal fluid analysis, the post-simulation (post-process) is performed with respect to the flow velocity field. In the post-process, an analysis model (low-dimensional model) of the flow velocity field is expressed with superposition of the orthogonal bases which are obtained in the pre-process. For example, the low-dimensional model of the flow velocity field is expressed with superposition of the mean umean of samples and m orthogonal bases b0 to bm−1 which are generated due to a difference between analysis conditions. Each of r0(t) to rm−1(t) represents the magnitude of a component of each sample at an arbitrary point of time t. Accordingly, in the thermal fluid analysis, a flow velocity field at an arbitrary point of time t is simulated. For example, in the thermal fluid analysis, all samples of the flow velocity field at an arbitrary point of time t are expressed. For example, as an analysis result, a flow velocity field at an arbitrary point of time that is an analysis target is expressed. Arrows represent air flows.
In the thermal fluid analysis, as is the case with the flow velocity field, a low-dimensional model of the temperature field is expressed with superposition of orthogonal bases which are obtained in a pre-process corresponding to the temperature field. As a method of creating the low-dimensional model, a method that is disclosed in Japanese Laid-open Patent Publication No. 2012-216173 and the like may be used.
For example, when a new sample increases due to a new analysis condition, in the thermal fluid analysis, the new sample is not expressed by an existing low-dimensional model, and thus a new low-dimensional model is recreated. For example, in the thermal fluid analysis, a pre-process and a post-process are performed by adding a new sample to existing samples, and the low-dimensional model is corrected in order for the new sample to be set to an application range. Time may be taken to recreate a new low-dimensional model.
For example, an information processing device, which corrects the low-dimensional model by only data processing with respect to a new sample, may be provided.
For example, when changing a layout of a server apparatus in a data center or changing a setting of an air conditioner, the information processing device 1 performs the thermal fluid simulation before actual operation, and executes a power-saving operation of the data center. For example, the information processing device 1 executes the thermal fluid analysis by setting a region in which the server apparatus or the air conditioner is provided as an analysis target. The analysis target may be a region in which the server apparatus or the air conditioner is provided, or a space which is desired to grasp a heat distribution and air flows.
The storage unit 10 stores a sample 11, a low-dimensional model 12, and intermediate information 13. For example, the storage unit 10 may be a semiconductor memory element such as a random access memory (RAM) and a flash memory, or a storage device such as a hard disk and an optical disc.
The sample 11 may be a sample that is used when the low-dimensional model 12 is created. A plurality of the samples 11 may exist. The sample 11 may be snapshot data of each of the flow velocity field and the temperature field which are used when the existing low-dimensional model 12 is created. The sample 11 may be a snapshot of the flow velocity field and the temperature field which correspond to various analysis conditions at each point of time, and may include analysis conditions, a flow velocity, or a temperature. The analysis conditions may be conditions when performing the thermal fluid analysis, and may include, for example, a shape model that is used in the thermal fluid analysis, physical properties, heat generation conditions, convergence conditions, resistance conditions, or fluid feeding conditions. As an example, the analysis conditions may include blowing strength or a setting temperature of an air blower.
The low-dimensional model 12 may be a low-dimensional model that is created by using the samples 11 which are stored in advance. The intermediate information 13 may be various pieces of intermediate information which are desirable for correction of the low-dimensional model 12. For example, the mean value of the samples 11 or a covariance matrix may be included in the intermediate information 13. The mean value of the samples 11 may include the mean value of flow velocities (velocity vectors of a fluid) of the samples 11 or the mean value of temperatures (temperature vectors of the fluid) of the samples 11. The mean value of the flow velocities of the samples 11 is used when correcting the low-dimensional model of the flow velocity field. The mean value of the temperatures of the samples 11 is used when correcting the low-dimensional model of the temperature field.
The reception unit 20 includes a sensor information receiving unit 21, an analysis result receiving unit 22, and a model receiving unit 23. The model receiving unit 23 receives information regarding a shape model in which an analysis target is three-dimensionally modeled or analysis conditions of a new sample, for example, from an external device of the information processing device 1. For example, the external device may be a removable disk or a hard disk drive (HDD). The external device may be coupled to the information processing device 1 through a network or may not be coupled to the information processing device 1. The shape model-related information may include, for example, a shape model that is used in the thermal fluid analysis, a plurality of pieces of mesh information including the shape model, or characteristics of the air blower.
The sensor information receiving unit 21 receives sensor information with respect to a new sample from each sensor. The sensor information may be discrete numerical data in an analysis target space, or a measured value such as a spatial distribution with respect to a temperature and air flows is reproduced. For example, the sensor information may be information in which a new sample is not expressed as a type of an analysis result. The sensor information may include information corresponding to analysis conditions during measurement of each sensor. For example, the sensor information may include a position in an analysis target of each sensor, a temperature or a flow velocity value which is detected by the each sensor, and analysis conditions during measurement.
The analysis result receiving unit 22 receives information, in which a new sample is expressed with a type of an analysis result, from an external device of the information processing device 1. For example, the external device may be a removable disk, or a HDD. The external device may be coupled to the information processing device 1 through a network, or may not be coupled to the information processing device 1. The analysis result may include a position, a temperature, a flow velocity distribution, or analysis conditions. The position represents a position of a mesh in a shape model in which an analysis target is modeled. For example, the temperature and the flow velocity distribution represent a temperature and a flow velocity value distribution which correspond to a position at an arbitrary point of time. For example, the analysis conditions represent analysis conditions which correspond to a position at that point of time.
The shaping unit 30 shapes sensor information with respect to a new sample into the same type as that of the analysis result. For example, the shaping unit 30 calculates a flow velocity value or a temperature at each mesh of the shape model based on the sensor information, which is received by the sensor information receiving unit 21, with respect to the new sample, and reproduces a spatial distribution of an analysis target. For example, the shaping unit 30 may reproduce the spatial distribution from discrete data in a space by using a least-square method, or may reproduce the spatial distribution from discrete data in the space by using a technology in the related art. For example, space interpolation such as smoothing spline or polynomial regression may be used.
The difference calculating unit 40 calculates a difference between a new sample and the existing low-dimensional model 12. For example, the difference calculating unit 40 acquires a new sample that is expressed by an analysis result received by the analysis result receiving unit 22, or a new sample that is shaped by the shaping unit 30. The difference calculating unit 40 calculates a difference between a flow velocity value of the new sample, and the mean value of flow velocities of the samples 11 which are included in the intermediate information 13 by using the following Equation (3) and Equation (4). usnapshot represents a flow velocity value of a snapshot that is a new sample. umean represents the mean value of flow velocities of the samples 11 for each mesh. m represents the number of orthogonal bases of the existing low-dimensional model 12. udiff represents a component of the snapshot which is a new sample.
The difference calculating unit 40 calculates the magnitude of the calculated difference as the component of the new sample by using the following Equation (5). E represents a component of a snapshot that is a new sample.
E=∥udiff∥ Equation (5)
The correction and non-correction determining unit 50 determines whether or not the magnitude of the component of the new sample is greater than a threshold value that is determined in advance. For example, the correction and non-correction determining unit 50 determines whether or not the new sample is in the application range of the existing low-dimensional model 12. In a case where the component of the new sample is greater than the threshold value, the correction and non-correction determining unit 50 determines that correction of the existing low-dimensional model 12 is desirable. For example, the correction and non-correction determining unit 50 may determine that the new sample may not be expressed with the existing low-dimensional model 12. In a case where the component of the new sample is equal to or less than the threshold value, the correction and non-correction determining unit 50 determines that correction of the existing low-dimensional model 12 may not be desirable. For example, the correction and non-correction determining unit 50 may determine that the new sample is in the application range of the existing low-dimensional model 12.
For example, new samples s1 to s6 may be received. The difference calculating unit 40 calculates a difference between a flow velocity value of each of the new samples, and the mean value of the flow velocities of the samples 11, and calculates the calculated difference as a component of the new sample. For example, in
The correction and non-correction determining unit 50 determines whether or not the component of the new sample is greater than a threshold value. For example, since the component of the sample s1 is greater than the threshold value, the correction and non-correction determining unit 50 may determine that correction of the low-dimensional model 12 is desirable. For example, the component of the new sample s1 may be determined as a component which is out of the application range of the low-dimensional model 12, and which may not be expressed with the low-dimensional model 12. Similarly, the component of each of the samples s2 to s4 may be determined as a component which is out of the application range of the low-dimensional model 12 and which may not be expressed with the low-dimensional model 12.
Since the component of the sample s5 is equal to or less than the threshold value, the correction and non-correction determining unit 50 determines that correction of the low-dimensional model 12 is not desirable. For example, the component of the new sample s5 is determined as a component which is in the application range of the low-dimensional model 12, and which may be expressed with the low-dimensional model 12. Similarly, the component of the sample s6 is determined as a component which is in the application range of the low-dimensional model 12 and which may be expressed with the low-dimensional model 12.
In
For example, in a case where the correction and non-correction determining unit 50 determines that a component of a new sample is greater than the threshold value, the low-dimensional model correcting unit 60 newly adds a vector, which is obtained by unitizing the component of the new sample by using the following Equation (6), as a new orthogonal base. udiff represents a component of a snapshot that is a new sample used in Equation (4) and Equation (5). bnew represents a new orthogonal base.
The low-dimensional model correcting unit 60 corrects the low-dimensional model 12 by using the newly added orthogonal base bnew and the plurality of orthogonal bases which already exist. When the new orthogonal base is newly added, a component of the new sample which is not expressed with the low-dimensional model 12 before correction becomes equal to or less than the threshold value. The low-dimensional model correcting unit 60 adds the new sample to the storage unit 10, and updates the corrected low-dimensional model 12.
The low-dimensional model correcting unit 60 updates various pieces of intermediate information which are desirable for correction of the new low-dimensional model. For example, the low-dimensional model correcting unit 60 calculates the mean value of the flow velocities of the samples 11 by using the following Equation (7). unew represents a flow velocity value of a new sample.
The low-dimensional model correcting unit 60 sets the mean value of the flow velocities of the calculated samples 11 as the intermediate information 13.
For example, a new sample that is not expressed with the low-dimensional model before correction may be added. In a lower drawing of
The reception unit 20 waits for reception of input information and receives the input information (operation S11). For example, the sensor information receiving unit 21 receives sensor information of a new sample as the input information. For example, the sensor information may include a position of the new sample, a temperature, a flow velocity distribution, or data of arbitrary combination of the position of the sample, the temperature, and the flow velocity distribution. The analysis result receiving unit 22 receives information, in which the new sample is expressed with an analysis result type, as the input information. For example, the analysis result may include the position of the new sample, the temperature, the flow velocity distribution, or data of arbitrary combination of the position of the new sample, the temperature, and the flow velocity distribution. The model receiving unit 23 receives a shape model and analysis conditions of the new sample as the input information. The sensor information reception unit 21 may receive the sensor information, or may not receive the sensor information as the input information.
The sensor information reception unit 21 determines whether or not the sensor information is received (operation S12). In a case where it is determined that the sensor information is not received (No in operation S12), the sensor information reception unit 21 determines that an analysis result is received, and the process transitions to operation S14.
In a case where it is determined that the sensor information is received (Yes in operation S12), the shaping unit 30 shapes the sensor information in the same type as that of the analysis result (operation S13). For example, the shaping unit 30 calculates a flow velocity value and a temperature at each mesh of a shape model based on the sensor information received by the sensor information receiving unit 21, and reproduces a spatial distribution of an analysis target. The process transitions to operation S14.
In operation S14, based on the analysis result from the sensor information reception unit 21 or information after shaping from the shaping unit 30 as a new sample, the difference calculating unit 40 calculates the magnitude E of a component of a new sample (operation S14). For example, in a case of the flow velocity field, the difference calculating unit 40 calculates a difference between a flow velocity value of the new sample and the mean value of flow velocities of the samples 11 which are included in the intermediate information 13. The difference calculating unit 40 calculates the calculated difference as a component of the new sample. In a case of the temperature field, the difference calculating unit 40 calculates a difference between a temperature value of the new sample and the mean value of temperatures of the samples 11 which are included in the intermediate information 13. The difference calculating unit 40 calculates the calculated difference as a component of the new sample.
The correction and non-correction determining unit 50 determines whether or not the magnitude E of a component of the new sample is greater than the threshold value (operation S15). The threshold value may be set in advance. In a case where it is determined that the magnitude E of the component of the new sample is equal to or less than the threshold value (No in operation S15), the low-dimensional model correcting unit 60 does not perform any process, and the process transitions to operation S17.
In a case where it is determined that the magnitude E of the component of the new sample is greater than the threshold value (Yes in operation S15), the low-dimensional model correcting unit 60 corrects the low-dimensional model 12 (operation S16). For example, the low-dimensional model correcting unit 60 newly adds a vector obtained by unitizing the component of the new sample as a new orthogonal base. The low-dimensional model correcting unit 60 corrects the low-dimensional model 12 by using the newly added orthogonal base and a plurality of orthogonal bases which already exist. The process transitions to operation S17.
In operation S17, the low-dimensional model correcting unit 60 outputs a low-dimensional model that is used in the thermal fluid analysis (operation S17). Then, in the thermal fluid analysis process, the thermal fluid analysis is executed by using the low-dimensional model that is output.
As described above, even when a new sample is added under new analysis conditions, in the thermal fluid analysis process, data processing with respect to the new sample is performed, and thus the low-dimensional model is corrected. According to this, a time taken to recreate the low-dimensional model that is used in the thermal fluid analysis may be shortened.
For example, with respect to a new sample different from the plurality of samples, the information processing device 1 calculates a component of the new sample. In a case where the calculated component of the new sample is greater than the threshold value, the information processing device 1 sets a component obtained by unitizing the component of the new sample as a base, and adds the base to the plurality of bases which already exist. The information processing device 1 corrects the low-dimensional model 12 by using the added base and the plurality of bases which already exist. As described above, even when a new sample is added, the information processing device 1 performs data processing with respect to only the new sample and corrects the low-dimensional model 12, and thus a time taken to recreate the low-dimensional model 12 that is used in the thermal fluid analysis may be shortened.
The information processing device 1 calculates a difference between the new sample and the mean of the plurality of samples which already exist as a component of the new sample. As described above, the information processing device 1 calculates the component of the new sample by using the mean of the plurality of samples which already exist, and thus a base, which is capable of expressing the new sample, may be easily calculated.
With regard to the flow velocity field, the information processing device 1 calculates a difference between a flow velocity value of a new sample and the mean value of the flow velocity values of the plurality of samples which already exist as a component of the flow velocity field of the new sample. As described above, the information processing device 1 calculates the component of the flow velocity field of the new sample by using the mean value of the flow velocity values of the plurality of samples which already exist, and thus a base, which is capable of expressing the flow velocity field of the new sample, may be easily calculated.
With regard to the temperature field, the information processing device 1 calculates a difference between a temperature value of the new sample and the mean value of temperature values of the plurality of samples which already exist as a component of the temperature field of the new sample. As described above, the information processing device 1 calculates the component of the temperature field of the new sample by using the mean value of the temperature values of the plurality of samples which already exist, and thus a base, which is capable of expressing the temperature field of the new sample may be easily calculated.
The model receiving unit 23 may receive information relating to a shape model obtained by three-dimensionally modelling an analysis target, and analysis conditions of a new sample. The storage unit 10 may store the information relating to the shape model and the analysis conditions of the new sample in advance.
Each component of the information processing device 1 may not have a configuration that is physically illustrated. For example, the entirety of or parts of the information processing device 1 may be functionally or physically divided or integrated in an arbitrary unit in accordance with various loads, a use situation, and the like. For example, the sensor information receiving unit 21, the analysis result receiving unit 22, and the model receiving unit 23 may be integrated as one unit. The correction and non-correction determining unit 50 and the low-dimensional model correcting unit 60 may be integrated as one unit. The difference calculating unit 40 may be divided into a calculation unit that calculates a difference, and a calculation unit that calculates the magnitude from the difference. The storage unit 10 may be coupled as an external device to the information processing device 1 through a network.
The above-described various processes may be executed by executing a program prepared in advance with a computer such as a personal computer and a workstation.
As illustrated in
The drive device 213 may be a device for a removable disk 211. The HDD 205 stores a thermal fluid analysis program 205a and thermal fluid analysis related information 205b.
The CPU 203 reads out the thermal fluid analysis program 205a, develops the thermal fluid analysis program 205a in the memory 201, and executes the thermal fluid analysis program 205a as a process. The process may correspond to each functional unit of the information processing device 1. For example, the thermal fluid analysis related information 205b may correspond to the sample 11, the low-dimensional model 12, and the intermediate information 13. For example, the removable disk 211 may store various kinds of information such as the thermal fluid analysis program 205a.
The thermal fluid analysis program 205a may be stored in the HDD 205 from the beginning, or may not be stored. For example, a program may be stored in a “portable physical medium” such as a flexible disk (FD), a CD-ROM, a DVD disk, a magneto-optical disc, and an IC card which are inserted into the computer 200. The computer 200 may read out the thermal fluid analysis program 205a from the portable physical media for execution.
All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although the embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.
Number | Date | Country | Kind |
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2014-078785 | Apr 2014 | JP | national |