KR101975919B1 - Velocity pressure enthalpy coupled analyzing method and computing system implementing the same - Google Patents

Abstract

According to the present invention, a velocity pressure enthalpy coupled analyzing method comprises: a step (101) of inputting a predetermined speed, pressure and temperature; a step (102) of calculating a pressure-velocity-enthalpy coupled loop; a step (103) of calculating a density field; a step (104) of calculating speed and pressure field; a step (105) of correcting a first flux by the pressure; a step (106) of dividing the first flux into a field value by the Kurganov-Tadmor technique; a step (107) of recalculating the density field; a step (108) of calculating the pressure and temperature fields; a step (109) of correcting a second flux by the pressure; a step (110) of dividing the second flux into a field value by the Kurganov-Tadmor technique; and a step (111) of determining iter < innerIter. The present invention can greatly improve accuracy of speed correction.

Description

Velocity PRESSURE ENTHALPY COUPLED ANALYZING METHOD AND COMPUTING SYSTEM IMPLEMENTING THE SAME}

The present invention relates to a velocity pressure enthalpy linked analysis method and a computing system using the same, and more particularly, to a velocity pressure enthalpy linked analysis method in a compressible flow with a shock wave and a computing system for performing the same.

The compressible flow is premised on the compressible effect (significant density change caused by the flow) in the gas flow. The change of density becomes important when the gas moves at a speed close to the speed of sound, and the flow becomes compressible. Considering this point, the criteria for classification are Mach numbers (Ma = V / a).

Ma <0.3: Incompressible, the density effect is ignored.

0.3 <Ma <0.8: As a subsonic flow, the density effect is important but no shock wave occurs.

-0.8 <Ma <1.2: Transonic flow, shock wave first appears and subdivided into subsonic and supersonic flow zones. Power flight in the transonic region is difficult due to the mixed nature of the flow field.

-1.2 <Ma <3.0: Supersonic flow, shock wave present but no subsonic region.

 -Ma <3.0: Ultrasonic flow, shock wave and other flow changes are particularly strong.

On the other hand, the shock wave is a powerful pressure wave that is delivered in the gas, such as air faster than the speed of sound, the pressure wave in the gas is usually delivered at a constant speed, such as the sound of the compressed portion and the expanded portion, but the pressure change is If it suddenly occurs, the expanded portion is gradually changed, and the compressed portion is rapidly changed and the waveform is distorted. As the wave passes, it is felt that the pressure, density, speed, etc. increase abruptly. This is a shock wave. Normally, if the number of Ma is small, the change in fluid density is small everywhere in the flow field, the energy equation becomes independent, and the state equation is a simple statement that the density is almost constant, so incompressible flow only needs to analyze the momentum and continuity. Shall be.

However, density change is important in compressible flow, and pressure and temperature change are also important by the state equation. Therefore, it should be expanded to four equations from two basic equations.

Continuity equation

2. Momentum equation

3. Energy equation

4. equation of state

Analysis in such compressible flows plays an important role in the analysis of elemental behavior in various hydrodynamic fields such as thermal fluids, shipbuilding, railroads, and internal aerodynamics such as aircraft.

Referring to FIG. 1, a conventional pressure-velocity coupled analysis technique is described. The pressure-based coupled solver transforms the equation of the continuous equation transformed into the equation for the pressure value and pressure of the term 항 p of the momentum equation. This method uses the speed value of the term Φ to be calculated at the current iteration time. This has the advantage of being able to perform the calculation more robustly in the compressible flow region than the conventional segregated solver, but has the disadvantage of increasing the memory capacity and the computation time required per one iteration. On the other hand, in the case of a flow in which a change in density is suddenly caused by thermal energy (enthalpy), there is an inconvenience of analyzing the energy equation and then analyzing the continuous equation again.

Referring to FIG. 2, a conventional pressure-enthalpy linkage analysis method using an energy equation for analyzing enthalpy in a portion of analyzing a pressure equation in a conventional SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm will be described. -Enthalpy-linked analysis technique is advantageous in terms of analysis robustness in terms of analytical robustness in terms of analysis robustness in the case of flows with large pressure changes due to temperature, rather than velocity-pressure coupling. The energy change is easy to apply to large flow.

In the case of a flow analysis such as a shock wave or a nozzle problem that has a large speed change and a large energy change, there is a limit to applying a conventional speed-pressure coupling algorithm or a pressure-enthalpy coupling algorithm.

Numerical Heat Transfer, Part B, 45: 410-.444, 2014, M. Darwish and F. Moukalled, "A FULLY COUPLED NAVIER-STOKES SOLVER FOR FLUID FLOW AT ALL SPEEDS"

The present invention overcomes the limitations of the two algorithms described above, and can be applied to compressible flows in which various kinds of shock waves exist by applying a flux splitting technique for discontinuous flow analysis such as shock waves, and correcting accuracy. To provide a speed-pressure-enthalpy linkage algorithm and a computational fluid dynamics analysis computing system using the same, which can greatly improve the accuracy and accuracy of analysis.

Speed pressure enthalpy linkage analysis method according to the present invention, the step of inputting a predetermined speed, pressure, temperature (101); Computing 102 a pressure-velocity-enthalpy coupled loop; Calculating 103 a density field; Calculating 104 a velocity and pressure field; A first flux correction step 105 by pressure; Dividing (106) the first flux into field values by the Kurganov-Tadmor technique; Recalculating a density field (107); Computing 108 pressure and temperature fields; A second flux correction step 109 by pressure; Dividing the second flux into field values by the Kurganov-Tadmor technique (110); And determining 111 iter <innerIter.

In the velocity pressure enthalpy linkage analysis method according to the present invention, if the result of the step 111 of determining iter <innerIter is affirmative, the process may return to the step 103.

In the velocity pressure enthalpy linkage analysis method according to the present invention, if the result of the step 111 of determining iter <innerIter is No, executing the turbulence equation, updating the density field, and determining whether to converge. It may further include.

In the velocity pressure enthalpy linkage analysis method according to the present invention, if the result of the step of determining whether the convergence is positive (Yes) is terminated, and if the result of the step of determining the convergence and negative (No), the new speed, The value of new pressure, new temperature can be used to return to step 103 above.

Computing system for performing a speed pressure enthalpy linked analysis according to the present invention, the module 201 for inputting a predetermined speed, pressure, temperature; A module 202 for computing a pressure-velocity-enthalpy coupled loop; A module 203 for calculating a density field; A module 204 for calculating velocity and pressure fields; A first flux correction module 205 by pressure; A module 206 for dividing the first flux into field values by the Kurganov-Tadmor technique; A module 207 for recalculating a density field; A module 208 for calculating pressure and temperature fields; A second flux correction module 209 by pressure; A module 210 for dividing the second flux into field values by a Kurganov-Tadmor technique; And a module 211 for determining iter <innerIter.

In the computing system for performing the velocity pressure enthalpy linkage analysis according to the present invention, when the determination result of the module 211 for determining the iter <innerIter is affirmative, the module 203 may be executed again. have.

In the computing system for performing velocity pressure enthalpy linkage analysis according to the present invention, if the determination result of the module 211 for determining the iter <innerIter is No, the turbulence equation is executed, the density field is updated, and converged. It may further include a module for determining whether or not.

In the computing system for performing the velocity pressure enthalpy linkage analysis according to the present invention, when the determination result of the convergence is yes, the computing system is terminated, and when the determination result of the convergence is negative, The values of new speed, new pressure, and new temperature can be used to return to running the module 203 again.

First, according to the velocity-pressure-enthalpy linkage analysis method and a computing system (apparatus) implementing the same, a physical module such as a turbulence model or combustion can be applied in addition to external flow conditions.

Second, according to the velocity-pressure-enthalpy linkage analysis method and a computing system (apparatus) executing the same, the first flux correction by pressure after the density field calculation and the second flux correction after calculating the density field again This can greatly improve the accuracy of the speed correction.

Third, according to the velocity-pressure-enthalpy linkage analysis method and the computing system implementing the same, the instability of the pressure-based solver in the high-speed flow analysis in which the shock wave or the compressive effect is prominent can be solved, and the density-based The segregated solver of CEM requires low CFL number (Courant Friedrichs Lewy number) compared to high accuracy, and solves problems that are difficult to solve with existing OpenFOAM platform solver. It can solve by employing.

Fourth, in the case of a flow in which a change in density is rapidly generated by thermal energy (enthalpy), the continuous equation and the energy equation can be analyzed simultaneously through the linking matrix without reinterpreting the continuous equation after the energy equation analysis.

Effects of the present invention are not limited to the effects mentioned above, and other effects not mentioned will be clearly understood by those skilled in the art from the following description.

1 is a flow chart illustrating a conventional pressure-velocity coupled analysis technique.
2 is a flowchart illustrating a conventional pressure-enthalpy linkage analysis technique.
3 is a flow chart illustrating a method for improving the compressible flow analysis algorithm.
4 is a flow chart showing a speed-pressure-enthalpy linkage analysis method according to the present invention.
5 is a diagram showing the structure of a computing system for performing the velocity-pressure-enthalpy linkage analysis method according to the present invention.
6 to 17 show exemplary analysis results according to the analysis method according to the present invention.

Hereinafter, with reference to the accompanying drawings will be described an exemplary embodiment of the present invention. Advantages and features of the present invention and methods for achieving them will be apparent with reference to the embodiments described below in detail with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but may be implemented in various different forms, only the embodiments to make the disclosure of the present invention complete, and to those skilled in the art to fully know the scope of the invention. It is provided for the purposes of illustration and the invention is defined only by the scope of the claims.

Although the first, second, etc. are used to describe various components, modules and / or sections, the components, modules and / or sections are of course not limited by these terms. These terms are only used to distinguish one component, module or section from other components, modules or sections. Therefore, the first component, the first module or the first section mentioned below may be a second component, a second module or a second section within the technical spirit of the present invention.

In this specification, the singular forms also include the plural unless specifically stated otherwise in the phrases.

As used herein, "comprises" and / or "comprising" refers to the presence or addition of one or more other components, modules and / or sections in addition to the components, modules and / or sections mentioned. Do not exclude

Unless otherwise defined, all terms used in the present specification (including technical and scientific terms) may be used in a sense that can be commonly understood by those skilled in the art. Also, the terms defined in the dictionary are not to be interpreted ideally or excessively unless they are specifically defined clearly.

Referring to FIG. 3, the method for improving the compressible flow analysis algorithm is described. Applying the flux splitting method to the pressure-based algorithm requires the application of the flux splitting method for the discontinuous flow analysis. Apply pressure based flux splitting central scheme, apply flux calculation on grid side, Kurganov-Tadmor flux splitting scheme and low Mach number correction. .

In the velocity pressure enthalpy linkage analysis method of the present invention as shown in FIG. 4, a step 101 of inputting a predetermined speed, pressure, and temperature, a step of calculating a pressure-speed-enthalpy linkage loop 102, and a density field Calculating (103), calculating the velocity and pressure fields (104), correcting the first flux by pressure (105), and dividing the first flux into new field values by the Kurganov-Tadmor technique. Step 106, recalculating the density field 107, calculating the pressure and temperature fields 108, correcting the second flux by pressure 109, and using the Kurganov-Tadmor technique Dividing into a new field value by 110, and determining 111 by iter <innerIter.

Here, pUpH is used to indicate that the pressure (p), the speed (U), the enthalpy (energy) is to be interpreted in conjunction with each other, as described in the description of the following sign, the pressure-speed-enthalpy linkage loop in the present invention It means.

In addition, when the determination result of the step 111 of determining iter <innerIter is affirmative (Yes), the process returns to the step 103 of calculating a density field and continues the loop. On the other hand, when the determination result of the step 111 of determining iter <innerIter is negative (No, No), the density field updating step 113 is performed via the turbulence equation 112. Then, after the step 115 of determining whether to converge or not, the loop is terminated and when the convergence is not performed, the density field is calculated using the new velocity, pressure, and temperature values 114. Perform step 103 again.

The term "iter <innerIter" is a step for determining whether an internal iteration calculation is necessary before reaching the determining 115 in the present invention, and means an expression of an internal iteration calculation value. In other words, when the CFL (Courant Friedrichs Lewy number) is large, convergence is made by increasing the number of internal repetitions. The process of determining whether to repeat the internal repetition according to the internal repetition value specified by the user it means.

According to the present invention, a flux correction by pressure before performing the density field update step 113 through the step 111 of determining iter <innerIter and the turbulence equation 112 by improving the compressible flow analysis algorithm as shown in FIG. Is divided into two times (105, 109), and for this purpose, the calculation of the density field is also performed by dividing twice.

That is, after first calculating the velocity and pressure fields (104) and then pressure compensating the first flux (105), the flux is split into new field values by the Kurganov-Tadmor technique as shown in FIG. Then, the density field is calculated (107), the pressure and temperature fields are calculated, and the second flux is corrected again by the pressure (109).

For the Kurganov-Tadmor technique, reference may be made to the following document.

M. Kraposhin (ISP RAS), S. Strizhak (HP) and A. Bovtrikova (ISP RAS), "Adaptation of Kurganov-Tadmor's numerical scheme for applying in combination with the PISO method in numerical simulation of flows in a wide range of Mach numbers ", Procedia Computer Science, Vol. 66, 2015, pp 43-52

In addition, the density field calculation steps 103 and 107 may be based on a continuity equation, and the continuity equation is an equation describing that a certain physical quantity is transferred in a state of being preserved. Has a form.

[Equation (1)]

는 그 물리량의 유량(flux)을 나타내는 함수이다(또는 그 물리량이 생성되거나 감소되는 양까지 반영한 값을 나타낸다).Where ρ is a given physical quantity,

Is a function representing the flux of the physical quantity (or the value reflecting the amount of the physical quantity generated or reduced).

In addition, the step 104 of calculating the velocity and pressure fields uses a matrix in which a momentum equation and a continuous equation are linked or combined. The momentum equation is represented by Equation 2 below.

[Equation (2)]

In operation 108, the pressure and temperature fields are calculated using a matrix in which the continuous equation and the energy equation are linked, and the energy equation is represented by Equation (3) below.

[Equation (3)]

In this regard, the present invention has the unique feature of analyzing (combining) the continuous equations, momentum equations, and energy equations of Equations (1) to (3) above.

In particular, in the step 106 of dividing the first flux into new field values by the Kurganov-Tadmor technique, the speed after the correction of the step 105 of correcting the first flux by the pressure may not be accurate. Recalculating the flux by pressure after step 107 of recalculating the density field by equation, and more specifically, after step 108 of calculating the pressure and temperature field By performing flux dividing (110) after performing the step correcting step 109, an advantageous effect can be expected that the speed accuracy can be greatly increased by the first and second corrected pressures.

Computing device for performing the velocity pressure enthalpy linked analysis method according to the present invention with reference to FIG. 4 also belongs to the scope of the present invention, for example, each module including a number of modules constituting the computing device as shown in FIG. The function of corresponding to each step of to perform the velocity pressure enthalpy linked analysis method according to the present invention of FIG.

That is, a computing system for performing an exemplary speed pressure enthalpy linked analysis method of the present invention as shown in FIG. 5 includes a predetermined speed, pressure, temperature input module 201, pUpH linked loop operation module 202, and a density field. Calculation module 203, velocity and pressure field calculation module 204, first and second flux correction modules 205 and 209, and first and second flux by pressure to new field values by Kurganov-Tadmor technique Splitting modules 206 and 210, density field recalculation module 207, pressure and temperature field calculation module 208, iter <innerIter determination module 211, turbulence equation module 212, density field updating module 213 ), A convergence determination module 215 may be included, and although not shown in FIG. 5, a module 214 for allocating a new speed, a new pressure, and a new temperature may be included.

5 shows the first and second flux correction modules 205 and 209 due to pressure, and the first and second flux splitting modules 206 and 210 as new field values by the Kurganov-Tadmor technique as one module. However, as shown in FIG. 4, two reference numerals may be assigned to each of the two reference modules, respectively.

In this case, the module of the present invention may be a personal computer (PC) such as a desktop, a laptop, and the like. Alternatively, the module of the present invention may be a portable electronic device such as a smartphone, a personal digital assistant (PDA), a tablet PC, or the like. The module of the present invention may be other computer device, not illustrated, including a processor, an input / output device, and a communication device.

In addition, the computing device of the present invention may be configured as various computing systems, and such various "systems" may be personal computers (PCs) such as desktop tops, laptop tops, and the like, unless specifically limited otherwise. ), A portable device such as a smartphone, a personal digital assistant (PDA), a tablet PC, or the like, or a server or software controlling these, or other computing device including such a server or software.

Two or more modules of the present invention may be connected to each other as shown in FIG. 5, or may be functionally connected to each other such as convergence determination module 215 and density field calculation module 203 of FIG. 5. Can be. The network may be wired or wireless. The network may be composed of one or more of a wide area netrow (WAN), a metropolitan area network (MAN), a local area network (LAN), or a combination thereof. The network may include a mobile communication network such as Global System for Mobile Communication (GSM), Code Division Multiple Access (CDMA), Wideband CDMA (WCDMA), WiFi, Wireless Broadband (Wibro), or the like.

6 to 17 show exemplary analysis results according to the analysis method according to the present invention. Figure 6 shows a comparison of the analysis results of the 1D Sod problem, Figure 7 shows a comparison of the analysis results of the 1D Lax problem, Figure 8 shows a comparison of the analysis results of the 1D Shu & Osher problem, Figure 9 to FIG. 15 shows a comparison of the analysis results of the 2D Euler 10% bump, and FIGS. 16 to 17 show the JPL nozzle test results, through which the superiority of the analysis method and the computing system of the present invention can be seen.

Although embodiments of the present invention have been described in detail with reference to the accompanying drawings, those skilled in the art will understand that the present invention can be implemented in other specific forms without changing the technical spirit or essential features. Therefore, it should be understood that the embodiments described above are exemplary in all respects and not restrictive.

In addition, it is obvious that the embodiments selectively combining the components and the steps of the system or method of the present invention described above also belong to the scope of the present invention.

p: pressure
U: speed
H: Enthalpy (Energy)
pU: pressure-velocity loop
pH: pressure-enthalpy (energy) linkage loop
pUpH: pressure-velocity-enthalpy (energy) linkage loop
101, 201: predetermined speed, pressure, temperature input step (module)
102, 202: pUpH linked loop operation step (module)
103, 203: Density field calculation step (module)
104, 204: Velocity and pressure field calculation steps (module)
105 (205), 109 (209): first and second flux correction step (module) by pressure
106 (206), 110 (210): dividing the first and second flux into new field values by the Kurganov-Tadmor technique (module)
107 (207): Density field recalculation step (module)
108 (208): Pressure and Temperature Field Computation Step (Module)
111 (211): iter <innerIter judgment step (module)
112 (212): Turbulent Equation Step (Module)
113 (213): Density Field Update Step (Module)
114 (214): Assigning New Velocity, New Pressure, New Temperature (Module) (214)
115 (215): Determination of convergence step (module)

Claims (8)

Inputting a predetermined speed, pressure, temperature (101),
Calculating 102 a pressure-velocity-enthalpy coupled loop,
Calculating 103 a density field;
Calculating 104 a velocity and pressure field,
First flux correction step 105 by pressure,
Dividing the first flux into field values by the Kurganov-Tadmor technique (106),
Recalculating a density field (107),
Calculating 108 the pressure and temperature fields,
Second flux correction step 109 by pressure,
Dividing the second flux into field values by a Kurganov-Tadmor technique (110), and
Velocity pressure enthalpy linkage analysis method comprising the step (111) of determining iter <innerIter. The method of claim 1
If the result of the step (111) of determining the iter <innerIter is yes (Yes), the speed pressure enthalpy linked analysis method, characterized in that to return to the step (103). The method of claim 1,
If the result of the step 111 of determining iter <innerIter is No, the method further includes executing a turbulent equation, updating the density field, and determining whether to converge. Linkage analysis method. The method of claim 3,
If the result of the step of determining whether the convergence is affirmative (Yes) is terminated,
If the result of the step of determining whether the convergence is negative (No), the speed pressure enthalpy linked analysis method, characterized in that to return to the step (103) using the value of the new speed, new pressure, new temperature. A module 201 for inputting a predetermined speed, pressure and temperature,
A module 202 for calculating a pressure-velocity-enthalpy coupled loop,
A module 203 for calculating a density field,
A module 204 for calculating velocity and pressure fields,
First flux correction module 205 by pressure,
A module 206 for dividing the first flux into field values by a Kurganov-Tadmor technique,
A module 207 for recomputing a density field,
A module 208 for calculating pressure and temperature fields,
Second flux correction module 209 by pressure,
A module 210 for dividing the second flux into field values by a Kurganov-Tadmor technique, and
Computing system for performing velocity pressure enthalpy linkage analysis comprising a module 211 for determining iter <innerIter. The method of claim 5
And if the determination result of the module (211) for determining the iter < innerIter is affirmative (Yes), return to executing the module (203) again. The method of claim 5,
Velocity pressure enthalpy further comprises a module for executing a turbulence equation, updating the density field, and determining whether convergence is determined if the determination result of the module 211 for determining the iter <innerIter is No. Computing system that performs linkage analysis. The method of claim 7, wherein
If the determination result of the convergence is affirmative (Yes), the computing system is terminated,
When the determination result of the convergence is negative, the speed pressure enthalpy linkage analysis is performed by returning to executing the module 203 again using the values of the new speed, the new pressure, and the new temperature. Computing system.

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