KR102287504B1 - Improved velocity pressure enthalpy coupled analyzing method and computing system implementing the same using energy equation - Google Patents

Abstract

The improved velocity pressure enthalpy linkage analysis method using the energy equation according to the present invention includes a predetermined velocity, pressure, and temperature input step 1101, a step 1102 of calculating a pressure-velocity-enthalpy coupled loop, calculating the density field (1103), calculating the velocity, pressure, and enthalpy fields (1104), calculating the flux by the pressure, velocity and temperature (1105), pressure, velocity and temperature Bounding the field (1106), dividing the flux into new field values by the Kurganov-Tadmor technique (1107), and iter<innerIter or Max Resi. <determining innerConv (1108).

Description

Improved Velocity Pressure Enthalpy Linkage Analysis Method Using Energy Equation and Computing System for Performing the Same

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

The above compressible flow is premised on the compressibility effect (significant density change caused by the flow) in the gas flow. When the gas moves at a speed close to the speed of sound, the change in density becomes important, and the flow becomes compressible. Considering this point, the standard for classification is the Mach number (Ma=V/a) and is as follows.

- Ma < 0.3 : Incompressible, density effect is neglected.

- 0.3 < Ma < 0.8 : subsonic flow, the density effect is important but no shock wave is generated.

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

- 1.2 < Ma < 3.0 : Supersonic flow, with shock waves but no subsonic range.

- Ma < 3.0: As hypersonic flow, shock waves and other flow changes are particularly strong.

On the other hand, the shock wave is a powerful pressure wave that is transmitted faster than the speed of sound in a gas such as air. In general, the pressure wave in the gas is transmitted at a constant speed such as sound in both the compressed part and the expanded part, but the pressure change When it occurs rapidly, the expansion part gradually changes and the compression part changes rapidly, so that the waveform is distorted. This is a shock wave. In general, if the number of Ma is small, the change in fluid density is small everywhere in the flow field, the energy equation is independent, and the equation of state is a simple statement that the density is almost constant, so incompressible flow requires only momentum and continuity analysis. do it with

However, density change is important in compressible flow, and changes in pressure and temperature are also important according to the equation of state. Therefore, it is necessary to expand the analysis from the existing two basic equations to four equations.

1. Continuity equation

2. Momentum equation

3. Energy equation

4. Equation of state

Analysis of such compressive flow plays an important role in element behavior analysis in various hydrodynamic fields such as thermal fluid, shipbuilding, railway and external aerodynamic analysis such as internal flow and aircraft.

Of these, when the conventional pressure-velocity linkage analysis technique is described with reference to FIG. 1, the pressure-based coupled solver of the continuity equation transformed into the pressure value and pressure of the ∇p term of the momentum equation This is a method of using the values calculated at the current iteration time for the velocity value of the Φ term. This has the advantage of being able to perform calculations more robustly in the compressible flow domain compared to the conventional segregated solver, but there are disadvantages in that the memory capacity and the calculation time required per iterative calculation increase. On the other hand, in the case of a flow in which a change in density is abruptly caused by thermal energy (enthalpy), there is an inconvenience in that the continuity equation must be analyzed again after analyzing the energy equation.

Referring to FIG. 2, the conventional pressure-enthalpy linkage analysis technique using an energy expression to analyze enthalpy in the part of analyzing the pressure expression in the existing SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is described. -In the case of flow with a large pressure change due to temperature, the application of a numerical analysis algorithm using the linkage of pressure and enthalpy rather than the linkage of speed and pressure is advantageous in terms of analysis robustness in terms of analysis robustness, and contrasts with the speed-pressure linkage analysis algorithm. Therefore, it is easy to apply to a flow with a large change in energy.

In the case of flow analysis in which the change in velocity is large and the change in energy is also large, such as the shock wave or nozzle problem, there is a limit to applying the conventional velocity-pressure linkage algorithm or pressure-enthalpy linkage 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 applies a flux splitting technique for discontinuous flow analysis such as shock waves, so that it can be applied to compressible flows in which various types of shock waves exist, and accuracy of correction The purpose of this study is to provide a velocity-pressure-enthalpy linkage algorithm and a computational fluid dynamics analysis computing system that can greatly increase the improvement and analysis accuracy.

On the other hand, an analysis method and computing system that can improve both the speed-pressure-enthalpy linkage algorithm and the problem of inefficiency and error generation due to the inevitably going through the pressure calculation and correction process in the computational fluid dynamics analysis computing system using the same would like to provide

The improved velocity pressure enthalpy linkage analysis method using the energy equation according to the present invention includes a predetermined velocity, pressure, and temperature input step 1101, a step 1102 of calculating a pressure-velocity-enthalpy coupled loop, calculating the density field (1103), calculating the velocity, pressure and enthalpy fields (1104), calculating the flux by means of the pressure, velocity and temperature (1105), the pressure, velocity and temperature fields 1106, dividing the flux into new field values by the Kurganov-Tadmor technique 1107, and iter<innerIter or Max Resi. <determining innerConv (1108).

In the velocity pressure enthalpy linkage analysis method using the energy equation according to the present invention, the iter<innerIter or Max Resi. < If the result of step 1108 of determining innerConv is affirmative (Yes), the process may return to step 1103 .

In the velocity pressure enthalpy linkage analysis method using the energy equation according to the present invention, the iter<innerIter or Max Resi. < If the result of step 1108 of determining innerConv is negative (No), the method may further include executing a turbulence equation, updating the density field, and determining whether convergence or not.

In the improved velocity pressure enthalpy linkage analysis method using the energy equation according to the present invention, if the result of the step of determining whether to converge is positive (Yes), it ends, and the result of the step of determining whether to converge and the negative (No) , it is possible to return to step 1103 using the new velocity, new pressure, and new temperature values.

The computing system for performing the improved velocity-pressure-enthalpy-linked analysis using the energy equation according to the present invention calculates a module 1201 for inputting a predetermined velocity, pressure, and temperature, and a pressure-velocity-enthalpy coupled loop. module 1202 for calculating the density field, module 1203 for calculating the density field, module 1204 for calculating the velocity, pressure, and enthalpy fields, and module 1205 for calculating the flux by pressure, velocity, and temperature. , module 1206 for bounding pressure, velocity and temperature fields, module 1207 for dividing flux into new field values by the Kurganov-Tadmor technique, and iter<innerIter or Max Resi. < Including a module 2108 for determining innerConv.

In the computing system performing the improved velocity pressure enthalpy linkage analysis using the energy equation according to the present invention, the iter<innerIter or Max Resi. < When the determination result of the module 1208 for determining innerConv is affirmative (Yes), it is possible to return to executing the module 1203 again.

In the computing system performing the improved velocity pressure enthalpy linkage analysis using the energy equation according to the present invention, the iter<innerIter or Max Resi. < When the determination result of the module 1208 for determining innerConv is negative, a module for executing the turbulence equation, updating the density field, and determining whether convergence may be additionally included.

In the computing system for performing the improved velocity pressure enthalpy linkage analysis using the energy equation according to the present invention, if the determination result of whether the convergence is positive (Yes), the computing system is terminated, and the determination result of whether the convergence is negative If it is (No), we can go back to running the module 1203 again using the values of the new speed, new pressure, and new temperature.

First, according to the velocity-pressure-enthalpy linkage analysis method and the computing system (device) executing the same according to the present invention, a physics 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 according to the present invention and the computing system (device) executing the same, after calculating the density field, the first flux correction is performed by the pressure, and then the density field is calculated again, and then the secondary flux correction is performed. can greatly improve the accuracy of speed correction.

Third, according to the velocity-pressure-enthalpy linkage analysis method and the computing system (device) executing the same according to the present invention, it is possible to solve the instability of the pressure-based analyzer in the high-speed flow analysis where the shock wave or compressibility effect is prominent, and the density-based In the case of a segregated solver of This can be solved by hiring.

Fourth, in the case of a flow in which a change in density occurs rapidly due to thermal energy (enthalpy), the continuity equation and the energy equation can be simultaneously analyzed through the linkage matrix without reinterpreting the continuity equation after analyzing the energy equation.

Fifth, according to the improved velocity-pressure-enthalpy linkage analysis method using the energy equation according to the present invention and the computing system (device) executing the same, the inefficiency of repeatedly interpreting the pressure-related equation and the analysis value due to speed correction and It is possible to solve the problem of the occurrence of differences in

Sixth, according to the improved velocity-pressure-enthalpy linkage analysis method using the energy equation according to the present invention and the computing system (device) executing the same, the momentum, continuity, and energy conservation equations are simultaneously updated based on the pressure equation, so the accuracy of the analysis This can be improved.

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 flowchart illustrating a conventional pressure-velocity linkage analysis technique.
2 is a flow chart illustrating a conventional pressure-enthalpy-linked analysis technique.
3 is a flowchart illustrating a method for improving a compressible flow analysis algorithm.
Figure 4a is a flow chart showing a velocity-pressure-enthalpy linkage analysis method according to the present invention.
4B is a flowchart illustrating an improved velocity-pressure-enthalpy linkage analysis method using the energy equation according to the present invention.
5A is a diagram showing the structure of a computing system for performing the velocity-pressure-enthalpy linkage analysis method according to the present invention;
5B is a diagram showing the structure of a computing system for performing the improved velocity-pressure-enthalpy linkage analysis method using the energy equation according to the present invention.
6 to 17 show exemplary analysis results according to the analysis method according to the present invention.

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

Although first, second, etc. are used to describe various components, modules, and/or sections, it should be understood that the components, modules, and/or sections are not limited by these terms. These terms are merely used to distinguish one component, module, or sections from another component, module, or sections. Accordingly, it goes without saying that the first component, the first module, or the first section mentioned below may be the second component, the second module, or the second section within the spirit of the present invention.

As used herein, the singular also includes the plural, unless the phrase specifically states otherwise.

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 stated components, modules and/or sections. do not exclude

Unless otherwise defined, all terms (including technical and scientific terms) used herein will have the meanings commonly understood by those of ordinary skill in the art. Also, terms defined in the dictionary are not to be interpreted ideally or excessively unless specifically defined explicitly.

Referring to FIG. 3, the method for improving the compressible flow analysis algorithm is described. Applying the flux splitting technique to the pressure-based algorithm requires the application of the flux splitting technique for discontinuous flow analysis. , apply a pressure based flux splitting central scheme and apply it to the flux calculation at the grid plane, and employ a Kurganov-Tadmor flux splitting scheme and a Low Mach number correction. .

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

Here, pUpH is to indicate that the pressure (p), velocity (U), and enthalpy (energy) are interpreted in conjunction with each other, as described in the description of the following symbols, and the pressure-velocity-enthalpy linkage loop in the present invention it means

In addition, if the determination result in step 111 of determining iter<innerIter is affirmative (eg, Yes), the process returns to step 103 of calculating the density field and continues the loop. On the other hand, if the determination result of the step 111 of determining iter<innerIter is negative (No, No), the density field update step 113 is performed through the turbulence equation 112 . Then, after performing the step 115 of determining whether convergence is performed, the loop is terminated if convergence is performed, and the density field is calculated using the new speed, pressure, and temperature values 114 if not converged. Step 103 is performed again.

The term "iter<innerIter" is a step for determining whether an inner iterative calculation is necessary before reaching the step 115 of determining whether convergence is performed in the present invention. In other words, when the CFL (Courant Friedrichs Lewy number) is large, convergence is achieved by increasing the number of internal iterations. it means.

According to the present invention, flux correction by pressure before performing the density field update step 113 through the step of determining iter<innerIter 111 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 density field operation is also performed by dividing it into two times.

That is, after first calculating (104) the velocity and pressure fields, the first flux is pressure corrected (105), and then the flux is divided into new field values by the Kurganov-Tadmor technique as in FIG. 4A (splitting) (106) Then, the density field is calculated again (107), the pressure and temperature fields are calculated, and the second flux correction is performed again by the pressure (109).

For the Kurganov-Tadmor technique, the following literature may be referred to.

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, pp43-52

In addition, the density field calculation steps 103 and 107 may be based on a continuity equation, which is an equation describing that a certain physical quantity is transferred to a state in which it is conserved, as in the following equation (1) have a form

[Formula (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 a value reflecting the amount that the physical quantity is 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 continuity equation are linked or combined, and the momentum equation is as shown in Equation (2) below.

[Formula (2)]

In addition, in the step 108 of calculating the pressure and temperature fields, a matrix in which the continuity equation and the energy equation are linked is used, and the energy equation is as shown in Equation (3) below.

[Equation (3)]

In this respect, the present invention has a unique feature of analyzing the continuity equations, momentum equations, and energy equations by combining (connecting) the 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. After the step 107 of re-calculating the density field according to the equation, the step 109 of re-calibrating the flux by pressure is performed. More specifically, after the step 108 of calculating the pressure and temperature fields, 2 By performing the differential correction step 109 and then dividing the flux again 110 , an advantageous effect can be expected that the speed accuracy can be greatly increased by the first and second corrected pressure.

The computing device for performing the velocity pressure enthalpy linkage analysis method according to the present invention with reference to FIG. 4A is also within the scope of the present invention, illustratively each module including several modules constituting the computing device as shown in FIG. 5A is a function corresponding to each step of performing the velocity pressure enthalpy linkage analysis method according to the present invention of Figure 4a.

That is, the computing system for performing the exemplary velocity-pressure-enthalpy-linked analysis method of the present invention as in FIG. 5A includes a predetermined velocity, pressure, and temperature input module 201, a 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 by pressure, first and second fluxes into new field values by Kurganov-Tadmor technique Partitioning module 206 and 210 , density field recomputation module 207 , pressure and temperature field calculation module 208 , iter<innerIter determination module 211 , turbulence equation module 212 , density field update module 213 ), the convergence determination module 215 may be included, and although not shown in FIG. 5A , a module 214 for allocating a new speed, a new pressure, and a new temperature may be included.

Figure 5a shows the first and second flux correction modules 205 and 209 by pressure, and the first and second flux division modules 206 and 210 into a new field value by the Kurganov-Tadmor technique as one module. However, as can be done from the fact that two reference numerals are assigned to each, in performing the analysis method of FIG. 4A, they may each consist of two separate modules.

In this case, the module of the present invention may be a personal computer (PC) such as a desktop (desk top), a laptop (lap top), and the like. Alternatively, the module of the present invention may be a portable electronic device such as a smart phone, a personal digital assistant (PDA), or a tablet PC. Modules of the present invention may be other computer devices not illustrated, including processors, input/output devices, and communication devices.

In addition, the computing device of the present invention may be configured as various computing systems, and these various "systems" are personal computers (PCs) such as desktops and laptops, unless otherwise limited. ), a portable device such as a smartphone, a personal digital assistant (PDA), a tablet PC, or the like, or a server or software controlling them, or other computing device comprising such a server or software.

Two or more modules of the present invention may be connected to each other by a network as shown in FIG. 5A, or as a function of the convergence determination module 215 and density field calculation module 203 of FIG. can The network may be wired or wireless. The network may be configured of one or more of a wide area network (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), and the like.

On the other hand, although the velocity-pressure-enthalpy linkage analysis method of FIG. 4a is advantageous for analyzing a discontinuous flow such as a shock wave or a flow with a large change in density due to energy, as described above, the velocity-pressure in step 104 , and re-calculating the pressure-enthalpy in step 108, there is a problem of inefficiency in repeatedly interpreting the expression related to the pressure.

In addition, the velocity-pressure-enthalpy linkage analysis method of FIG. 4A requires a separate correction process for velocity, and in this process, a request for improvement of accuracy occurs in which a difference from the velocity calculated by the analytical formula occurs.

In order to improve this point, the improved velocity-pressure-enthalpy linkage analysis method using the energy equation as in FIG. 4b develops the velocity-pressure-enthalpy into one matrix as shown in the figure below to develop the flow field at a time. By calculating information, it is simpler than the existing algorithm and it is possible to obtain a value that satisfies the conservation equation in each cell without the need for a separate correction process. It becomes possible to solve the problem of occurrence of a difference from the calculated value.

[Figure: Determinant to explain the interpretation method of Fig. 4b]

The improved velocity-pressure-enthalpy linkage determinant using the above energy equation corresponds to the determinant of the right side in the figure above, and the left side is the determinant using the same analysis method as in FIG. 4A. That is, since the speed-pressure link matrix shown in red and the pressure-enthalpy matrix shown in blue are calculated on the left side, overlapping pressure parts occur. In the improved speed-pressure-enthalpy coupling matrix of FIG. By grouping them into a single determinant, the inefficiency of such duplicate calculations disappears.

In the analysis method of FIG. 4B, the momentum, continuity, and energy conservation equations are simultaneously updated based on the pressure equation.

Specifically, referring to FIG. 4B, in the improved velocity-pressure enthalpy-linked analysis method using the energy equation, a predetermined speed, pressure, and temperature input step 1101, pUpH-linked loop calculation step 1102, density field calculation step 1103) , velocity, pressure, enthalpy field calculation step 1104, flux calculation step 1105 by pressure, velocity and temperature field, pressure, velocity and temperature field bounding step 1106, flux to new field value by Kurganov-Tadmor technique In step 1107, iter<innerIter or Max Resi. <determining innerConv (1108), wherein iiter<innerIter or Max Resi. < If the determination result of step 1108 of determining innerConv is affirmative (eg, Yes), the process returns to step 1103 of calculating the density field and continues the loop. whereas the iter<innerIter or Max Resi. < If the determination result of the step 1108 of determining the innerConv is negative (No, No), the density field update step 1110 is performed through the turbulence equation 1109 . Then, after performing the step 1111 of determining whether convergence is performed, the loop is terminated when convergence is performed, and the density field is calculated using a new speed, pressure, and temperature value 1112 when not converging. Step 1103 is performed again.

Correspondingly, the computing system for performing the improved velocity-pressure-enthalpy-linked analysis method of the present invention as shown in FIG. 5b is a predetermined velocity, pressure, temperature input module 1201, pUpH-linked loop operation module 1202, density field calculation module 1203, velocity, pressure, enthalpy field calculation module 1204, flux by pressure, velocity, and temperature calculation module 1205, pressure, velocity and temperature field bounding module 1206, flux Module 1207 for partitioning into new field values by Kurganov-Tadmor technique, iter<innerIter or Max Resi. < The innerConv determination module 1208, the turbulence equation module 1209, the density field update module 1210, and the convergence determination module 1211 may include a new speed, a new pressure, a new temperature, although not shown in FIG. 5B It may also include a module 1212 for allocating

Comparing the analysis method of FIGS. 4A/ 5A and 4B/ 5B with the computing system, in the analysis method of FIG. 4B and the computing system of FIG. 5B, "the first and second flux correction steps by pressure and the module ( 105, 109, 205, 209)” and “Speed and Pressure Field Calculation Step and its Modules 104, 204” and “Pressure and Temperature Field Calculation Step and its Modules” It can be seen that the duplication of pressure calculation in "(108, 208)" is also eliminated.

In the improved velocity-pressure-enthalpy-linked analysis method of FIG. 4b, as in the figure above, for velocity, pressure, and enthalpy field operation in velocity, pressure, and enthalpy field operation 1104, momentum equation (Momentum Equation), continuity equation, and energy Since all equations use linked or concatenated matrices, the matrix in which the momentum equation and continuous equations are linked in the velocity and pressure field computation step 104 of FIG. 4A, and the continuity equation in the pressure and temperature field computation step 108 It is different from using each matrix in which the energy equation is linked.

That is, in the improved velocity-pressure-enthalpy-linked analysis method of FIG. 4B, it is possible to achieve efficiency and simplicity of calculating flow field information at once by developing velocity-pressure-enthalpy into one matrix.

In addition, through this, it is possible to improve the inefficiency of the redundant calculation of analyzing the speed and pressure and re-calculating the pressure-enthalpy.

In addition, since a separate correction process is not employed, it is possible to prevent a difference in the speed value from the analysis equation due to the correction. That is, it is possible to obtain a value that satisfies the conservation equation in each item without additional correction.

In addition, since a separate correction process is not employed, the analysis algorithm can be simplified such that the flux division can be performed only once in the analysis method of FIG. 4B unlike the analysis method of FIG. 4A .

In the present invention, the step 1106 of the pressure, velocity and temperature field bounding step 1106 of FIG. 4b is a step of limiting the numerical upper and lower limits to the input values, or setting a numerical upper bound and a numerical lower bound. means

In addition, in the present invention, Max Resi of Figure 4b. To determine < innerConv is to stop the inner iteration when the residual becomes lower than the value entered by the user and proceed to the next outer iteration step. That is, it means to judge the convergence of the internal iteration.

In addition, in the improved method of FIG. 4B , the momentum equation, the continuity equation, and the energy equation are all linked or combined for the velocity, pressure, and enthalpy field operations in the velocity, pressure, and enthalpy field operation 1104. Therefore, momentum, continuity, and energy conservation equations can be updated at the same time.

Therefore, in the improved method of Figure 4b, it is not necessary to employ the density field recomputation step 107 as in Figure 4a.

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

Although the 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 may be embodied in other specific forms without changing the technical spirit or essential features thereof. Therefore, it should be understood that the embodiments described above are illustrative in all respects and not restrictive.

In addition, it is natural that embodiments in which the components and steps of the system or method of the present invention described above are selectively combined also fall within the scope of the present invention.

p: pressure
U: speed
H: Enthalpy (energy)
pU: pressure-velocity coupled loop
pH: Pressure-Enthalpy (Energy) Linked Loop
pUpH: pressure-velocity-enthalpy (energy) coupled loop
101, 201: predetermined speed, pressure, temperature input step (module)
102, 202: pUpH linkage loop operation step (module)
103, 203: Density field calculation step (module)
104, 204: speed and pressure field calculation steps (module)
105 (205), 109 (209): first and second flux correction steps by pressure (module)
106 (206), 110 (210): dividing the first and second flux into new field values by Kurganov-Tadmor technique (module)
107 (207): Density field recomputation step (module)
108 (208): Pressure and Temperature Field Calculation Step (Module)
111 (211): iter<innerIter judgment step (module)
112 (212): Turbulence Equation Step (Module)
113 (213): Density field update step (module)
114 (214): assigning a new speed, a new pressure, a new temperature (module) (214)
115 (215): convergence determination step (module)
1101: predetermined speed, pressure, temperature input step (module)
1102, 1202: pUpH associative loop operation step (module)
1103, 1203: Density field calculation step (module)
1104, 1204: velocity, pressure, enthalpy field calculation steps (modules)
1105, 1205: Flux calculation steps by pressure, speed and temperature (module)
1106, 1206: Pressure, Velocity, and Temperature Field Bounding Steps (Module)
1107, 1207: Partitioning the flux into new field values by the Kurganov-Tadmor technique (module)
1108, 1208: iter<innerIter or Max Resi. < innerConv judgment stage (module)
1109, 1209: Turbulence Equation Steps (Module)
1110, 1210: Density field update step (module)
1111, 1211: convergence determination step (module)
1112, 1212: allocating new speed, new pressure, new temperature (module)

Claims (8)

An improved velocity pressure enthalpy linkage analysis method in a computing system, the method comprising:
a predetermined speed, pressure, and temperature input step;
calculating a pressure-velocity-enthalpy coupled loop;
calculating a density field by the continuity equation;
calculating the velocity, pressure and enthalpy fields;
calculating flux by pressure, velocity and temperature;
bounding the pressure, velocity and temperature fields;
dividing the flux into new field values by the Kurganov-Tadmor technique; and
recomputing the density field by the continuity equation according to the division of the flux;
recalculating the velocity, pressure and enthalpy fields;
recalculating the flux by the recalculated pressure, velocity and temperature;
dividing the recalculated flux into new field values by the Kurganov-Tadmor technique; and
iter<innerIter or Max Resi. < Improved velocity pressure enthalpy linkage analysis method including the step of determining innerConv.
delete According to claim 1,
The iter<innerIter or Max Resi. < If the result of the step of determining the innerConv is negative (No), the improved velocity pressure enthalpy linkage analysis method, characterized in that it further comprises the steps of executing the turbulence equation, updating the density field, and determining whether convergence or not . delete delete delete delete delete

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