JP4329503B2 - Heat exchanger simulation method, simulation program, and simulator thereof - Google Patents

Description

  The present invention relates to a heat exchanger simulator. The heat exchanger is divided into test volumes (control volumes, hereinafter referred to as CVs) to clarify the connection relationship between the CVs, and heat is applied to each CV. The present invention relates to a heat exchanger simulator that simulates the exchange amount and calculates the total heat exchange amount by integrating the results.

  Conventionally, there has been a calorimeter test method as a method for evaluating the performance of a refrigerant circuit including a heat exchanger, but there are disadvantages such as the need for special test equipment and the time and labor of the test. There is a need for an effective alternative to this, and computer simulation is an appropriate method.

One of the refrigerant circuit simulation methods using such a computer is disclosed in Patent Document 1. An object of the invention described in Patent Document 1 is to provide a simulation method capable of easily performing accurate refrigerant pipe connection setting. As a means for realizing this, an operator can operate a compressor and an evaporator or a condenser from a keyboard. A connection relationship with a heat exchanger such as a heat exchanger is input, and the input pipe connection data is expressed as a matrix in a simulation. With this method, refrigerant piping settings can be constructed with a minimum of input operations, and a refrigerant circuit model having multiple compressors and heat exchangers in parallel can be created in a short time. Mistakes can be reduced.
JP-A-9-257319

  The invention described in Patent Document 1 is intended to easily set the connection relationship between a compressor and a heat exchanger such as an evaporator or a condenser. We went as a whole exchanger. However, in recent years, different types of fin-tube heat exchangers have been used in various refrigerant circuits, and the entire heat exchanger has been covered as before by applying new types of fins and improved tubes and using mixed refrigerants. In order to cope with the case where the fins and tubes are partially changed, a simulation method capable of obtaining the heat exchange amount in each part of the heat exchanger in detail is required. .

  As a specific method, a method of dividing a heat exchanger into arbitrary local areas called a control volume (hereinafter referred to as CV) has been proposed. In this method, first, a simplified heat exchanger as shown in FIG. 6 is converted into a CV including three parts of a working fluid, refrigerant and air, and a fin-tube as shown in FIG. This is a method of dividing, constructing a governing equation for each of the divided CVs, and solving the governing equation to obtain a heat exchange amount in the CV, thereby obtaining a heat exchange amount of the entire heat exchanger. Hereinafter, a method for obtaining the heat exchange amount by dividing into CVs will be described in detail.

  Within a single CV as shown in FIG. 7, there are three parts: refrigerant, air, and fin-tube. As governing equations between these parts, it is necessary to construct three equations: a mass conservation equation, an energy conservation equation, and a momentum conservation equation. However, when considering the performance in a steady state within a single CV as shown in FIG. 7, since the refrigerant flow rate is kept constant in the flow path, there are only two equations of energy conservation equation and momentum conservation equation. If it solves, it will become possible to obtain | require the heat exchange amount in CV. The governing equations for the refrigerant side and the air side of CV can be expressed as follows.

ここで、Q_1rはエンタルピーの差による冷媒側の熱交換量、Q_2rは温度の差による冷媒側の熱交換量、G_rは冷媒流量、h_r,inとh_r,outはそれぞれＣＶの流入側と流出側における冷媒の固有エンタルピー、T_r,inとT_r,outはそれぞれＣＶの流入側と流出側における冷媒の温度、α_rは冷媒の局所熱伝達係数、T_wallはチューブ壁の温度をそれぞれ表している。
冷媒に関する運動量保存方程式：

ここで、Δp_totalは冷媒の総圧力降下、Δp_accは冷媒の加速圧力降下であり、式（５）は二相領域での加速圧力降下を表している。また、G_rは冷媒流量、χ_rは冷媒の乾度、ξはボイド率、ρ_vとρ_lはそれぞれ蒸気と液体の密度である。 (The governing equation on the refrigerant side)
Energy conservation equations for refrigerants:

Here, Q _1r is the amount of heat exchange on the refrigerant side due to the difference in enthalpy, Q _2r is the amount of heat exchange on the refrigerant side due to the difference in temperature, G _r is the flow rate of refrigerant, and h _{r, in} and h _{r, out} are CVs respectively. specific enthalpy of the refrigerant at the inlet side and the outlet _side, T _{r, in} a T _{r, out} temperature of the refrigerant at the inlet side and the outlet side of the CV, respectively, alpha _r is the local heat transfer coefficient of the refrigerant, T _wall is the tube wall Each temperature is shown.
The momentum conservation equation for refrigerants:

Here, Δp _total is the total pressure drop of the refrigerant, Δp _acc is the acceleration pressure drop of the refrigerant, and Equation (5) represents the acceleration pressure drop in the two-phase region. Further, the G _r refrigerant flow rate, the chi _r refrigerant Inuido, xi] is the void fraction, the [rho _v and [rho _l is the density of each vapor and liquid.

ここで、Q_1aはエンタルピーの差による空気側の熱交換量、Q_2aは温度の差による空気側の熱交換量、G_aは空気流量、h_a,inとh_a,outはそれぞれＣＶの流入側と流出側における空気の固有エンタルピー、T_a,inとT_a,outはそれぞれＣＶの流入側と流出側における乾球温度、η_oはフィンの効率、α_aは空気の局所熱伝達係数をそれぞれ表している。 (Air side governing equation)
The pressure drop on the air side is usually so small that it is ignored and only the energy conservation equation is considered.

Where Q _1a is the heat exchange amount on the air side due to the difference in enthalpy, Q _2a is the heat exchange amount on the air side due to the difference in temperature, G _a is the air flow rate, h _{a, in} and h _{a, out} are the CV Intrinsic enthalpy of air on the inflow side and outflow side, Ta, _in and _{Ta, out} are the dry bulb temperatures on the inflow side and outflow side of CV, respectively, η _o is the efficiency of the fin, and α _a is the local heat transfer coefficient of air Respectively.

(Fin-tube governing equation)
For fin-tubes, only the energy conservation equation is considered. Under steady state conditions, there is no energy storage in the fins and tubes, and the incoming energy is equal to the outgoing energy. In other words, the energy Q _w stored in the fins and tubes is
Q _w = Q _1r + Q _1a = 0 (9)
Equations (1), (4), (6), and (9) above are all governing equations for a single CV.

  The governing equation regarding CV constructed in this way is solved based on a specific algorithm. Conventionally, a local alternating iterative algorithm has been generally used as an algorithm for solving the governing equation of the heat exchanger. FIG. 8 is a flowchart for solving a governing equation using a typical local alternating iteration algorithm, which will be described in the order of flow.

  After setting the initial value in (S801), the CV number (initially i = 1) is designated in (S802), and the governing equation is solved for the designated CV. In (S803), the energy conservation equation is solved based on the given initial value, and in (S804), the momentum conservation equation is solved based on the given initial value. Next, in (S805), it is determined whether the solution of the energy conservation equation solved in (S803) has converged, and in (S806), it is determined whether the solution of the momentum conservation equation solved in (S804) has converged. However, if the solutions have not converged in each case, the procedure (S809) or procedure (S810) returns to (S803), and the calculation is repeated until the solutions of the energy conservation equation and the momentum conservation equation converge. Once the solutions of the energy conservation equation and momentum conservation equation of one CV are obtained in this way, the calculation is performed in the same manner for each CV until it is confirmed that it is the last CV in the procedure (S807). Find the solution of the momentum conservation equation. Finally, in the procedure (S808), the overall convergence determination condition is determined, and the iterative process is continued by the procedure (S812) until the overall convergence is satisfied. When the convergence is completed, the process ends in (S813).

  Further, as a method for obtaining the solution of the energy conservation equation in (S803), the three-stage iterative method shown in FIG. 9 is generally used, and the iteration for solving the energy conservation equation regarding the refrigerant shown in the above equation (1). The procedure (S914), the iterative procedure (S915) for solving the energy conservation equation for the fin-tube shown in equation (9), and the iteration procedure for solving the energy conservation equation for air shown in equation (6) ( 3 iterations with S916) will solve the energy conservation equation in one CV.

  As problems of the above-mentioned conventional technology, the following can be cited. First, the conventional local alternating iteration algorithm shown in FIG. 8 is composed of a three-stage nested iteration procedure (S809, S810, S812) and a loop procedure (S811). In addition, since the three-stage iterative method is used to solve the energy conservation equation, the number of iterations is very large as a whole. For this reason, this method has a problem that it is difficult to obtain a convergent solution of the governing equation and it is difficult to guarantee the stability of the software.

  Second, due to the extremely large number of iterations of the local alternating iteration algorithm, it takes a very long time to obtain the simulation results by solving the governing equations for all CVs. there were.

  Thirdly, when a simulation of a heat exchanger composed of complicated refrigerant flow paths is performed, the connection relationship between the tubes constituting each divided refrigerant flow path is simply expressed, and each refrigerant flow path There is a problem that it is difficult to store the simulation results of the state parameters in and to efficiently apply them to the simulation.

  The present invention has been made in view of the above problems, and has a memory structure in which the connection relationship between divided tubes is clarified and information of each CV can be easily stored, and the governing equations of all CVs are solved. It is an object of the present invention to provide a heat exchanger simulator that uses an algorithm that easily converges the solution and does not require simulation time.

  The invention according to claim 1 divides a heat exchanger composed of fins and tubes into a test volume (control volume, hereinafter referred to as CV) which is an arbitrary local area including three parts of refrigerant, air, and fin-tube. In the heat exchanger simulation method characterized in that the heat exchange characteristics of the entire heat exchanger are obtained based on the simulation results of the heat exchange characteristics in the CV, and all CVs are arranged in a predetermined order along the refrigerant flow path. Iterative procedure 1 that solves only the energy conservation equation and repeats the calculation until each solution converges, and solves only the momentum conservation equation for all CVs in a predetermined order determined along the refrigerant flow path after the iteration procedure 1. Iterative procedure 2 that repeats the calculation until each solution converges, and the solution of the energy conservation equation for each CV obtained in iteration procedure 1 Each CV is repeated according to the iterative procedure 3 that repeats the iterative procedure 1 and the iterative procedure 2 until the heat exchange characteristics of each CV obtained from the solution of the momentum conservation equation for each CV obtained in the recovery procedure 2 converge for all the CVs. And a heat exchanger simulation method characterized by obtaining heat exchange characteristics of the entire heat exchanger.

  In the invention of claim 2, in addition to claim 1, in the iterative procedure 1, a temperature field is obtained by applying a pressure field and solving the energy conservation equation. In the iterative procedure 2, the temperature obtained in the iterative procedure 1 is obtained. The corrected pressure field is obtained by solving the momentum conservation equation given the field. In the iterative procedure 3, the temperature field and the pressure field obtained in each of the iterative procedure 1 and the iterative procedure 2 are updated alternately. In this heat exchanger simulation method, the calculation of the energy conservation equation and the momentum conservation equation is obtained for all CVs by repeating the calculation.

  In addition to claim 1 or 2, the invention described in claim 3 is a procedure for solving the energy conservation equation of each CV in the iterative procedure 1 and solving the energy conservation equation on the air side and repeating the calculation until the solution converges Iterative procedure 4, iterative procedure 5 that solves the energy conservation equation on the refrigerant side and repeats the calculation until the solution converges, and iterative procedure 4 and iteration procedure 5 that solves the fin-tube energy conservation equation and converges until the solution converges It is the simulation method of the heat exchanger characterized by consisting of the repetition procedure 6 which repeats.

  A fourth aspect of the present invention is a simulation program for executing any one of the first to third aspects.

  The invention according to claim 5 divides a heat exchanger composed of fins and tubes into a test volume (control volume, hereinafter referred to as CV) which is an arbitrary local area including three parts of refrigerant, air, and fin-tube, In the heat exchanger simulator characterized in that the heat exchange characteristics of the entire heat exchanger are obtained based on the simulation results of the heat exchange characteristics in the CV, and for all CVs in a predetermined order determined along the refrigerant flow path. Iterative means 1 that solves only the energy conservation equation and repeats the calculation until each solution converges, and solves only the momentum conservation equation for all CVs in a predetermined order after the iteration means 1 along the refrigerant flow path. Iterative means 2 that repeats the calculation until the solution of the above converges, and the solution and iterative means of the energy conservation equation for each CV obtained by the iterative means 1 Each CV and heat exchange is performed by the iterating means 3 that repeats the iterating means 1 and the iterating means 2 until the heat exchange characteristics of each CV obtained from the solution of the momentum conservation equation for each CV obtained in step S converge for all the CVs. The heat exchanger simulator is characterized in that the heat exchange characteristics of the entire heat exchanger are obtained.

  According to the sixth aspect of the present invention, in addition to the fifth aspect, the iterative means 1 obtains a temperature field by applying a pressure field and solving the energy conservation equation, and the iterative means 2 obtains the temperature obtained by the iterative means 1. By giving a field and solving the momentum conservation equation, a corrected pressure field is obtained, and the iterative means 3 alternately updates the temperature field and the pressure field obtained by the respective iterative means in the iterative means 1 and the iterative means 2. In this heat exchanger simulator, the calculation of the energy conservation equation and the momentum conservation equation is obtained for all CVs by repeating the calculation.

  According to the seventh aspect of the invention, in addition to the fifth or sixth aspect, the means for solving the energy conservation equation of each CV in the iteration means 1 solves the energy conservation equation on the air side and repeats the calculation until the solution converges. The iterative means 4, the iterative means 5 that solves the energy conservation equation on the refrigerant side and repeats the calculation until the solution converges, and the iterative means 4 and the iterative means 5 that solve the fin-tube energy conservation equation and the solution converges. It is a simulator of a heat exchanger characterized by comprising repeating means 6 for repeating.

  According to the first aspect of the present invention, solutions of the energy conservation equation and the momentum conservation equation are obtained by two parallelly arranged iteration procedures 1 and 2, respectively, and the entire two iteration procedures 1 and 2 are nested. The iterative procedure 3 is used to obtain the energy conservation equation and the momentum conservation equation while correcting one after another, and the algorithm with this two-stage nest structure is higher than the conventional three-stage nest structure. Convergence and simulation time can be greatly reduced.

  According to the second aspect of the invention, in the iterative procedure 1, a temperature field is obtained by solving the energy conservation equation by giving a pressure field, and in the iteration procedure 2, a temperature field is given by solving the energy conservation equation. Since the corrected pressure field is obtained and the procedure 3 is repeated while updating the temperature field and the pressure field alternately in the iteration procedure 1 and the iteration procedure 2, the energy conservation equation within one CV in the conventional method is obtained. In addition, there is no problem that the temperature and pressure generated by trying to solve the momentum conservation equation at the same time falls into the hunting state, ensuring the convergence stability of the solution, and the overall simulation time is about 1/12 of that of the conventional method. It is possible to shorten to ~ 1/200.

  According to the third aspect of the present invention, the iterative procedure 4 for solving the energy conservation equation on the air side and repeating the calculation until the solution converges, and the iteration for solving the energy conservation equation on the refrigerant side and repeating the calculation until the solution converges are performed. Since the energy conservation equation of each CV is solved by the procedure 5 and the iteration procedure 6 in which the iteration procedure 4 and the iteration procedure 5 are repeated until the fin-tube energy conservation equation is solved and the solution is converged. Compared with the three-step iterative method, the calculation time of this part can be shortened to about 1/40 to 1/60.

  According to invention of Claim 4, since it was set as the simulation program for performing any one of Claim 1 thru | or 3, it is any one of Claim 1 thru | or 3 to a computer by this simulation program Simulation can be executed.

  The simulator according to the fifth aspect of the present invention obtains solutions of the energy conservation equation and the momentum conservation equation by the two iteration means 1 and 2 arranged in parallel, respectively, and the entire two iteration means 1 and 2 are nested. The iterative means 3 determines the energy conservation equation and the momentum conservation equation while correcting each other one after another, and the algorithm based on this two-stage nested structure is higher than the conventional three-stage nested structure. Convergence and simulation time can be greatly reduced.

  In the simulator according to the sixth aspect of the invention, the iterative means 1 gives a pressure field and solves the energy conservation equation to obtain the temperature field, and the iteration means 2 gives the temperature field and solves the momentum conservation equation. Since the corrected pressure field is obtained and the iterative means 3 is repeated while updating the temperature field and the pressure field alternately in the iterative means 1 and the iterative means 2, the energy conservation equation within one CV in the conventional method is obtained. In addition, there is no problem that the temperature and pressure generated by trying to solve the momentum conservation equation at the same time falls into the hunting state, ensuring the convergence stability of the solution, and the overall simulation time is about 1/12 of that of the conventional method. It is possible to shorten to ~ 1/200.

  The simulator according to the seventh aspect of the invention is an iterative means 4 for solving an energy conservation equation on the air side and repeating the calculation until the solution converges, and an iteration for solving the energy conservation equation on the refrigerant side and repeating the computation until the solution converges. Since the energy conservation equation of each CV is solved by means 5 and the iterative means 6 which solves the fin-tube energy conservation equation and repeats the iterative means 4 and 5 until the solution converges, Compared with the three-step iterative method, the calculation time of this part can be shortened to about 1/40 to 1/60.

  The heat exchanger simulation method according to the present invention divides a heat exchanger composed of fins and tubes into a test volume (control volume, hereinafter referred to as CV) which is an arbitrary local area including three parts of refrigerant, air, and fin-tube. Then, in the heat exchanger simulation method characterized in that the heat exchange characteristics of the entire heat exchanger are obtained based on the simulation results of the heat exchange characteristics at each CV, in a predetermined order determined along the refrigerant flow path. Iterative procedure 1 that solves only the energy conservation equation for all CVs and repeats the calculation until each solution converges, and the momentum conservation equation for all CVs in a predetermined order determined along the refrigerant flow path after the iteration procedure 1 Iterative procedure 2 that repeats the calculation until each solution converges, and the error for each CV obtained in iteration procedure 1 Iterative procedure 1 and iteration 2 are repeated until the heat exchange characteristics of each CV obtained from the solution of the Lugie conservation equation and the solution of the momentum conservation equation for each CV obtained in iteration procedure 2 converge for all CVs. It is characterized in that the heat exchange characteristics of each CV and the entire heat exchanger are obtained by the procedure 3. Further, in the iterative procedure 1, a temperature field is obtained by solving the energy conservation equation by giving a pressure field. In the iterative procedure 2, the temperature field obtained in the iterative procedure 1 is given and the momentum conservation equation is solved to obtain a corrected pressure field. In the iterative procedure 3, the iterative procedure 1 and the iterative procedure 2 are respectively repeated. By repeating the calculation while alternately updating the temperature field and pressure field obtained in step 1, the solution of the energy conservation equation and the momentum conservation equation was obtained for all CVs. To.

  Embodiments of the present invention will be described with reference to the drawings. First, the whole structure of the simulator of the heat exchanger of this invention is demonstrated using FIG. As shown in FIG. 1, although it is necessary to provide a data input process, the heat exchanger simulator of the present invention is composed of three main elements: a preprocessor, a main processor, and a postprocessor. Hereinafter, each process will be described in detail.

[Data input process];
First, before operating the heat exchanger simulator, the user needs to input the following given information. The information includes (1) structural parameters of the fin-tube heat exchanger, (2) parameters of refrigerant and air inflow state of working fluid (pressure, enthalpy, refrigerant flow rate, windward air velocity, etc.) (3) There is a connection relationship between the tubes, etc., and a simulation of the heat exchanger is performed using this input information.

[preprocessor];
This preprocessor is intended to represent the connection relationship between tubes in an adjacent matrix, and requires five steps as the flow. In Step 1, each tube used in the heat exchanger is coded based on the input data. In Step 2, the arrangement of the refrigerant circuit is converted into a directional graph. In Step 3, the tube is directional. The graph is converted into an adjacency matrix. In step 4, the refrigerant flow path is searched and generated based on the adjacency matrix. In step 5, the matrix created in step 4 is modified to store refrigerant information. Hereinafter, each step will be described in detail.

Step 1) Code each tube used in the heat exchanger based on the input data.
The general rules used to code tube numbers are as follows: (1) The tube numbers in the first row are encoded as 1, 2, 3,... (2) The tube numbers in the remaining rows are coded sequentially from the lower tube up until the end of the last row. (3) Add two other virtual tubes. It represents the inlet part for the incoming refrigerant and the outlet part for the outgoing refrigerant, respectively. The inflow refrigerant introduction part is coded as tube No. 0, and the outflow refrigerant lead-out part is coded as tube No. obtained by adding 1 to the total number of tubes.
Specifically, when the contents of step 1 are applied to a heat exchanger composed of two rows and four stages of tubes as shown in FIG. From the rule (2), the tubes in the second row are coded as tube Nos. 5 to 8, and from the rule (3), the inflow refrigerant introduction part is coded with tube No. 0 and flows out. By coding the refrigerant outlet portion with tube No. 9, the tube No. as shown in FIG.

Step 2) The refrigerant circuit arrangement is converted into a directional graph.
The arrangement of the refrigerant circuit is converted into a directional graph. The vertex of the graph with directionality represents a tube, and the side of the graph with directionality represents the relationship between two tubes. In the heat exchanger composed of two rows and four stages of tubes shown in FIG. 6, the connection relationship between the tubes on the front side in the drawing is represented by a solid line, and the connection relationship between the tubes on the back side is represented by a broken line. 2 is converted into a graph having directionality as shown in FIG.

このようにして生成された隣接マトリクスにおいて、ある列に含まれる要素の数の和は、その列に対応するNo.のチューブに合流するチューブの数を表す。また、ある行に含まれる要素の数の和は、その行に対応するNo.のチューブから分岐するチューブの数を表す。さらに、隣接マトリクスの行方向は流出方向の接続を、列方向は流入方向の接続をそれぞれ表し、図２の持つ方向性を表現している。
図２に示す方向性を持ったグラフに基づいて生成したものが、図３（ａ）に示す隣接マトリクスであり、図６に示す２列４段のチューブからなる熱交換器の接続関係を１０行１０列のマトリクスで表現している。この図３（ａ）に示す隣接マトリクスの外側に記されている０〜９の数字は、図６のチューブNo.に対応している。 Step 3) Convert a directional graph into an adjacency matrix.
The adjacency matrix is introduced in order to express the relationship between the tubes based on the graph having the above-mentioned directionality. Each element of the matrix is given as follows.

In the adjacent matrix generated in this way, the sum of the number of elements included in a certain column represents the number of tubes that join the No. tube corresponding to that column. Further, the sum of the numbers of elements included in a certain row represents the number of tubes branched from the No. tube corresponding to that row. Further, the row direction of the adjacent matrix represents the connection in the outflow direction, and the column direction represents the connection in the inflow direction, and expresses the directionality of FIG.
The adjacent matrix shown in FIG. 3A is generated based on the directional graph shown in FIG. 2, and the connection relationship of the heat exchanger composed of the two rows and four stages of tubes shown in FIG. It is expressed in a matrix with 10 rows and 10 columns. The numbers 0 to 9 written outside the adjacent matrix shown in FIG. 3A correspond to the tube numbers in FIG.

Step 4) Search and generate a refrigerant flow path based on the adjacent matrix.
In the numerical calculation, the arrangement of the refrigerant circuit is very important. Therefore, by defining the refrigerant flow path as a simple flow path based on the adjacent matrix, the calculation can be performed more easily. Specifically, a refrigerant flow path is defined by tracing a tube that starts from a certain junction or branch point and continues in the direction of the refrigerant flow until it meets another junction or branch point. When the refrigerant circuit branches from one branch point to several branches, search for the branch with the smallest tube number until another junction or branch point is met, and then search for the remaining branches in the same way To return to the previous branch point. In this way, all the refrigerant flow paths are searched and generated. When the refrigerant flow path is searched and generated based on the adjacent matrix shown in FIG. 3A, 0-8-4, 3-2, 7-6, 5-1 in the heat exchanger shown in FIGS. Nine four refrigerant flow paths can be found.

Step 5) The matrix created in Step 3 is modified to store the refrigerant information.
As can be seen from the directional graph shown in FIG. 2, the tube has a branch point, and the refrigerant before branching flows in each branch branched from the branch point. The ratio at which the refrigerant branches and flows at such a branch point is an important problem in calculation, and it is necessary to input this in advance as data. By replacing this input data with the “1” element portion of the adjacent matrix shown in FIG. 3A created in step 3 above, the refrigerant flow rate of each tube can be easily known. For example, in the graph having directionality shown in FIG. 2, the input data with the refrigerant flow rate before branching being 10 and the refrigerant flow rate being 5 when bifurcating is set to 5 in the adjacent matrix shown in FIG. Replacing it with the 1 "element part makes it possible to provide a simple memory structure as shown in FIG. 3B, thereby simplifying the data structure when data is read in subsequent calculations. Can do.

[Main processor];
In this main processor, all the governing equations of the divided CV are solved to obtain the heat exchange amount for each CV, but by using an algorithm different from the conventional method, the convergence of the solution is improved and the simulation time is shortened. Let Hereinafter, the flowchart of the algorithm according to the present invention for solving the governing equation of CV will be described with reference to FIGS.

  FIG. 4 is a flowchart showing the procedure of the overall alternating iteration algorithm used in the present invention. The iteration procedure is nested in two stages (one is S413 and S415, the other is S416) and two loops (S412 and S412). S414). In the conventional local alternating iterative algorithm shown in FIG. 8, an energy conservation equation and a momentum conservation equation are simultaneously solved in one CV by an iterative procedure nested in three stages, so that one equation is solved. Then, the parameter of the other equation falls into a state where it fluctuates greatly, the temperature and pressure hunting, and even if they converge and settle within a single CV, Since the calculation is performed again for each CV, there is a problem that it is very difficult to obtain a converged solution of the simulation of the entire heat exchanger. On the other hand, the overall alternating iterative algorithm of the present invention shown in FIG. 4 solves the problems of the conventional system by separating the energy conservation equation and the momentum conservation equation and solving them independently.

  In general, since the pressure field of the refrigerant is not known at the beginning of the overall calculation, it is assumed that the pressures in each CV are all equal. Given the assumed pressure field, the energy conservation equation is solved for all CVs by the iterative procedure of (S413). The temperature field is estimated in the process of solving the energy conservation equation with all the CVs. Given the estimated temperature field, the momentum conservation equations for all CVs are solved by the iterative procedure of (S415). A corrected pressure field can be obtained in the process of solving this momentum conservation equation, and it is returned to the beginning by the iterative procedure of (S416) and given all of the corrected pressure field again by the iterative procedure of (S413). The energy conservation equation of CV is solved, and further, the momentum conservation equation of all CVs is solved by the iterative procedure of (S415). In this way, the temperature field and the pressure field are alternately updated, and the accuracy of the temperature field and the pressure field is improved accordingly, so that the state where the temperature and pressure are hunting as in the conventional method is not caused. And faster computation and faster convergence. In the following, description will be given in order.

  In FIG. 4, first, an initial value is set in (S401). Here, since the pressure field of the refrigerant is not known at the beginning of the overall calculation, it is assumed that the pressures in each CV are all equal. Next, the first CV is designated in (S402), and the energy conservation equation is solved in (S403). The algorithm for solving the energy conservation equation in (S403) is a two-stage iterative algorithm shown in FIG. 5, and details will be described later. Until the last CV is confirmed in (S404), the energy conservation equations are solved for all the CVs in a predetermined order determined along the refrigerant flow path by the loop means shown in (S412), and the last CV is obtained. After solving the energy conservation equation, the overall convergence is determined in (S405), and until the convergence is confirmed, the iterative procedure of (S413) is repeated (this is the iteration procedure 1), the energy conservation equation is solved repeatedly, When the whole has converged, the process proceeds from (S405) to (S406). Here, the temperature field is estimated by the iterative procedure 1 of (S413). The convergence determination condition in (S405) determines whether or not the energy conservation equation can be solved for all CVs (for example, whether or not the solution satisfies a certain determination condition).

  Next, in (S406), the first CV is specified, and the momentum conservation equation is solved in (S407). Until the final CV is confirmed in (S408), the momentum conservation equation is solved for all the CVs in a predetermined order determined along the refrigerant flow path by the loop means shown in (S414), and the final CV is determined. After solving the momentum conservation equation, the overall convergence is determined in (S409), and until the convergence is confirmed, the iterative procedure of (S415) is repeated (this is iteration procedure 2), and the momentum conservation equation is solved repeatedly. When the whole converges, the process proceeds from (S409) to (S410). Here, the pressure field corrected by the iterative procedure 2 of (S415) can be obtained. The convergence determination condition in (S409) determines whether or not the momentum conservation equation has been solved for all CVs (for example, whether or not the solution satisfies a certain determination condition).

  In (S410), it is determined whether the solution of the energy conservation equation obtained by the iteration procedure 1 of (S413) and the solution of the momentum conservation equation obtained by the iteration procedure 2 of (S415) are converged as a whole. . If not converged as a whole, calculation is performed again from the beginning by the iterative procedure of (S416) (this is assumed to be iterative procedure 3), but the temperature field is updated by the iterative procedure of (S413), (S415) Since the iterative procedure 3 of (S416) is performed while the temperature field and the pressure field are alternately updated, such as updating the pressure field by the iterative procedure of (2), the calculation based on the field with improved accuracy easily converges. If the whole has converged in (S410), the process ends in (S411). The convergence determination condition in (S410) is that the heat exchange characteristics for each CV obtained by the solution of the energy conservation equation obtained by the iteration procedure 1 and the solution of the momentum conservation equation obtained by the iteration procedure 2 are in an equilibrium state. (The heat exchange characteristic of each CV does not change out of the range of a certain determination condition even if the calculation is repeated further). Here, the heat exchange characteristic means a characteristic relating to heat exchange of the heat exchanger or CV such as heat exchange amount, refrigerant or air flow rate, inflow / outflow enthalpy, inflow / outflow temperature.

The two-step iterative algorithm used in solving the energy conservation equation in (S403) will be described with reference to FIG. The simulation process in this two-stage iterative algorithm starts for one CV based on a set of known inflow parameters on both the air side and the refrigerant side to estimate the unknown outflow. The energy conservation equations (1), (6), and (9) can be solved by estimating the refrigerant outflow specific enthalpy hr _{, out} , the outflow air temperature _{Ta, out} , and the tube wall temperature _Twall . In FIG. 5, in an iterative procedure consisting of (S503) to (S506) and (S514) (hereinafter referred to as iterative procedure 4), the energy conservation equation (6) on the air side is adjusted while adjusting the outflow air temperature _{Ta, out.} ). In an iterative procedure consisting of (S507) to (S510) and (S515) (this is assumed to be iterative procedure 5), the refrigerant energy conservation equation (1) is _expressed while adjusting the refrigerant outflow specific enthalpy hr _{, out.} solve. In (S511), the fin-tube energy conservation equation (9) is solved, and the tube wall temperature T _wall is adjusted until the Q _{w of the} equation (9) reaches the convergence judgment condition (| Q _w | <ε). while Repeat steps iteration (S516) (this is an iterative procedure 6), when Q _w has reached the stopping criterion, as has been released energy conservation equations are all in CV, at (S513) Then, the process returns to (S404) in FIG. Here, ε in each determination condition of (S506), (S510), and (S512) is a numerical value for determining the accuracy of the solution and may be an arbitrary value in each step.

[Post-processor];
All CV simulation results obtained in the main processor are structured in memory in the post processor and output for further operations such as display of simulation results and application to another simulation. This is because, similar to the method of structuring the memory by the preprocessor, each value of the CV simulation result is replaced with the element portion of “1” in the adjacent matrix shown in FIG. A simple memory structure for storage is provided. Specifically, for example, values obtained by the main processor such as flow rate, inflow / outflow temperature, inflow / outflow enthalpy as state parameters relating to air or refrigerant are shown in FIG. 3B as a matrix for each parameter. By making the memory structure, it becomes possible to easily use these data.

  As described above, the simulator of the heat exchanger according to the present invention expresses the connection relationship between the tubes in the preprocessor in the adjacent matrix and modifies the adjacent flow rate of the refrigerant flow rate into the memory structure, and the main processor stores the energy conservation equation of each CV. And the momentum conservation equation are solved independently by the new globally iterative algorithm shown in FIG. 4, and the solution of the governing equation of each CV is made into a memory structure so that data can be easily used in further operations in the post processor. And has the following effects.

  The adjacency matrix created in the preprocessor provides a simple and intuitive expression means for representing the connection relationship between tubes in an arbitrary arrangement of refrigerant circuits. In addition, it is possible to provide a simple memory structure for storing refrigerant information such as flow rate, inflow / outflow temperature, inflow / outflow enthalpy in the post processor. Therefore, information on tube connection, refrigerant flow information in the tube, calculation result information for each CV, and the like can be easily expressed.

  The overall alternating iteration algorithm used in the main processor is a two-step iterative method for solving the energy conservation equation because the three-stage nested structure in the conventional local alternating iteration algorithm is made into two steps, and the two-step iterative method as a whole. It realizes a heat exchanger simulator that not only reduces the number of iterations but also increases the ease of convergence and provides highly reliable simulation results. Further, by reducing the number of iterations as a whole, it is possible to greatly reduce the calculation time required for the simulation.

Here, in the conventional local alternating iterative algorithm and the overall alternating iterative algorithm of the present invention, the calculation time required for each simulation will be briefly compared. First, in the conventional local alternating iteration algorithm shown in FIG. 8, the simulation time used to solve the energy conservation equation of one CV in (S803) is τ _{e, 1,} and the momentum conservation of one CV is performed in (S804). The simulation time used to solve the equation is τ _{m, 1} , the number of iterations of the iteration procedure according to (S809) is N1, the iteration number of the iteration procedure according to (S810) is N2, and the number of loops according to (S811) (CV Is equal to N), and the number of iterations of the iteration procedure according to (S812) is N3. In the three-stage iteration method shown in FIG. 9 used to solve the energy conservation equation of one CV in (S803), the iteration number of the iteration procedure according to (S914) is set to N4, and the iteration procedure according to (S915) is repeated. The number of times is N5, and the number of iterations of the iteration procedure according to (S916) is N6. If the unit time consumption required to solve one equation regardless of either the energy conservation equation or the momentum conservation equation is τ ₀ , the _total simulation time consumption τ _total, when using the local alternating iteration algorithm _{, 1} can be represented by the following formula.

On the other hand, in the overall alternating iterative algorithm according to the present invention shown in FIG. 4, the simulation time used for solving the energy conservation equation of one CV in (S403) is τ _{e, 2,} and one in (S407). The simulation time used to solve the momentum conservation equation of CV is τ _{m, 2} , the iteration number of iteration procedure 1 according to (S413) is N7, the iteration number of iteration procedure 2 according to (S415) is N8, and (S416 ) Is N9, and the number of loops (equal to the number of CVs) according to (S412) or (S414) is N. Further, in the two-step iteration method shown in FIG. 5 used to solve the energy conservation equation of one CV in (S403), the number of iterations of iteration procedure 4 in (S514) is N10, and iteration procedure 5 in (S515). Let N11 be the number of iterations, and N12 be the number of iterations of iteration procedure 6 in (S516). Assuming that τ ₀ is the unit time consumption required to solve one equation regardless of either the energy conservation equation or the momentum conservation equation, the total simulation time consumption when using the overall alternating iteration algorithm of the present invention τ _{total, 2} can be expressed by the following equation.

この場合には、従来の局所交互反復アルゴリズムに比べて本発明の全体交互反復アルゴリズムの計算時間は、１／５０の時間で済むことを意味している。実際には、反復回数はそれぞれ異なり、一概に同一の値を用いて計算できるものではないが、前記反復回数N1〜N12の値を５〜２０に設定することで、全体としての計算時間を約１／１２〜１／２００に短縮することができる。 From the above equations (10) and (11), the simulation time consumption τ _{total, 1} required for the conventional local alternating iteration algorithm and the simulation time consumption τ _{total, 2} required for the overall alternating iteration algorithm of the present invention are obtained, respectively. be able to. Here, in order to compare these two time consumptions, when the values of the number of iterations N1 to N12 are all 10 and the two expressions are compared, the following is obtained.

In this case, it means that the calculation time of the overall alternating iterative algorithm of the present invention is only 1/50 as compared with the conventional local alternating iterative algorithm. Actually, the number of iterations is different and cannot be calculated using the same value. However, by setting the number of iterations N1 to N12 to 5 to 20, the total computation time is reduced. It can be shortened to 1/12 to 1/200.

  As described above, the actual calculation time is reduced to about 1/40 to 1/60 of the conventional calculation time by changing the three-stage iterative method for solving the energy conservation equation to the two-step iterative method. The total computation time can be reduced to about 1/12 to 1/200 by changing the three-stage nested structure in the conventional local alternating iteration algorithm into two stages in the overall alternating iteration algorithm. can do.

  In the above embodiment, the adjacent matrix is used to express the connection relationship of the tubes, and the same tube is processed with the same No., but the present invention is not limited to this. For example, if it is desired to perform the calculation separately even for the same tube on the front side and the back side of the heat exchanger as shown in FIG. Then, this can be easily handled by expressing it as an adjacency matrix. Using this method, no matter how the CV is divided, the connection relationship can be expressed using the adjacency matrix.

It is a schematic diagram which shows the whole structure of the simulator of the heat exchanger by this invention. 3 is a graph having directionality created in the preprocessor of the simulator of the heat exchanger of the present invention. (A) shows the adjacent matrix created in the preprocessor of the simulator of the heat exchanger of this invention, (b) represents the memory structure created by modifying the adjacent matrix. It is the flowchart figure which showed the whole alternating iteration algorithm used in the main processor of the simulator of the heat exchanger of this invention. FIG. 5 is a flowchart showing a two-stage iterative method used when solving the energy conservation equation in FIG. 4. It is a schematic diagram showing the heat exchanger which consists of a general 2 row | line | column of 4 steps | paragraphs. It is a schematic diagram for demonstrating the concept of CV used by this invention. It is the flowchart figure which showed the local alternating iteration algorithm for solving the governing equation of CV in a conventional system. FIG. 9 is a flowchart showing a three-step iterative method used when solving the energy conservation equation in FIG. 8.

Explanation of symbols

(S401) to (S416): code representing each procedure in the overall alternating iterative algorithm, (S501) to (S516) ... code representing each procedure in the two-step iteration method, (S801) to (S813) ... local alternating A code representing each procedure in the iterative algorithm, (S901) to (S916)... A code representing each procedure in the three-stage iterative method.

Claims (5)

The heat exchanger consisting of fins and tubes is divided into an arbitrary local examination volume (control volume, hereinafter referred to as CV) containing three parts: refrigerant, air, and fin-tube, and energy conservation equations and momentum at each CV. In a heat exchanger simulation method characterized by calculating a solution of a conservation equation by a computer and obtaining a heat exchange characteristic at each CV and a heat exchange characteristic of the entire heat exchanger,
Input procedure for inputting initial conditions such as structural parameters of the heat exchanger, parameters of the inflow state of refrigerant and air, connection relation between tubes, and storing them in the memory of the computer,
Based on the initial conditions stored in the memory and the conditions of the given pressure field, solve only the energy conservation equations for all CVs in a predetermined order determined along the refrigerant flow path and calculate until each solution converges The iterative procedure 1 is performed in the arithmetic processing unit of the computer, the temperature field converged for each CV is obtained and stored in the memory , and
Based on the initial conditions stored in the memory and the temperature field obtained by the iterative procedure 1, only the momentum conservation equations are solved for all CVs in a predetermined order determined along the refrigerant flow path, and each solution converges. An iterative procedure 2 in which a calculation process is repeated in the computer processing unit until a pressure field converged for each CV is obtained and stored in a memory ;
The temperature field and the pressure field obtained by the calculation by the iteration procedure 1 and the calculation by the iteration procedure 2 are alternately updated and stored in the memory, and the solutions of the energy conservation equation and the momentum conservation equation converge for all CVs. Up to the heat of each CV and the entire heat exchanger by the iterative procedure 3 in which the processing of the iterative procedure 1 and the iterative procedure 2 is repeated in the computer processing unit based on the temperature field or pressure field updated by the mutual procedure. A method for simulating a heat exchanger, characterized by obtaining an exchange characteristic. Each arithmetic processing solving the energy conservation equation for CV in the arithmetic processing unit of the computer in the iterative procedure 1, and repeat step 4 to repeat the calculation until the solution solves the energy conservation equation for the air side converge, energy of the refrigerant side An iterative procedure 5 that solves the conservation equation and repeats the calculation until the solution converges, and an iterative procedure 6 that solves the fin-tube energy conservation equation and repeats the iterative procedure 4 and the iteration procedure 5 until the solution converges , respectively. The simulation method for a heat exchanger according to claim 1, wherein the simulation is performed by an arithmetic processing unit of a computer . Simulation program for executing any one of claims 1 or claim 2. The heat exchanger consisting of fins and tubes is divided into an arbitrary local examination volume (control volume, hereinafter referred to as CV) containing three parts: refrigerant, air, and fin-tube, and energy conservation equations and momentum at each CV. In a heat exchanger simulator characterized in that the solution of the conservation equation is calculated by a computer and the heat exchange characteristics at each CV and the heat exchange characteristics of the entire heat exchanger are obtained.
Input means for inputting initial conditions such as structural parameters of the heat exchanger, parameters of the inflow state of the refrigerant and air, connection relation between the tubes, etc., and storing them in the memory of the computer,
Based on the initial conditions stored in the memory and the conditions of the given pressure field, solve only the energy conservation equations for all CVs in a predetermined order determined along the refrigerant flow path and calculate until each solution converges Repetitive means 1 for performing the process of repeating the above in the arithmetic processing unit of the computer, obtaining the temperature field converged for each CV, and storing it in the memory ;
Based on the initial conditions stored in the memory and the temperature field obtained by the repetitive means 1, only the momentum conservation equations are solved for all the CVs in a predetermined order determined along the refrigerant flow path, and the respective solutions converge. Repetitive means 2 that repeats the calculation until it is performed in the arithmetic processing unit of the computer, obtains the pressure field converged for each CV, and stores it in the memory ;
The temperature field and pressure field obtained by the calculation by the repetition means 1 and the calculation by the repetition means 2 are alternately updated and stored in the memory, and the solutions of the energy conservation equation and the momentum conservation equation converge for all CVs. Up to the heat of each CV and the entire heat exchanger by the repetitive means 3 that performs the process of repeating the repetitive means 1 and the repetitive means 2 in the computer processing unit based on the temperature field or pressure field updated by the mutual procedure. A heat exchanger simulator characterized by obtaining an exchange characteristic. Each arithmetic processing solving the energy conservation equation for CV in the arithmetic processing unit of the computer in the repetitive unit 1, and repetition means 4 repeats the calculation until the solution solves the energy conservation equation for the air side converge, energy of the refrigerant side Iterative means 5 for solving the conservation equation and repeating the calculation until the solution converges, and iteration means 6 for solving the fin-tube energy conservation equation and repeating the iteration means 4 and the iteration means 5 until the solution converges , respectively. 5. The heat exchanger simulator according to claim 4 , wherein the simulator is executed by an arithmetic processing unit of a computer .

Images