CN110807249B - Rigid chemical reaction flow semi-hidden semi-explicit self-adaptive time step propulsion simulation method - Google Patents

Rigid chemical reaction flow semi-hidden semi-explicit self-adaptive time step propulsion simulation method Download PDF

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CN110807249B
CN110807249B CN201910998330.7A CN201910998330A CN110807249B CN 110807249 B CN110807249 B CN 110807249B CN 201910998330 A CN201910998330 A CN 201910998330A CN 110807249 B CN110807249 B CN 110807249B
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张斌
刘洪�
余彬
谢名云
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Shanghai Jiaotong University
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Abstract

A rigid chemical reaction flow semi-hidden semi-explicit self-adaptive time step propulsion simulation method is characterized in that an initial flow field is set according to initial physical state parameters of a supersonic rigid combustion flow problem, system rigidity is calculated through flow characteristic time and reaction characteristic time in a chemical reaction item calculation stage, the maximum time step causing evolution to be capable of stably propelling is selected according to the system rigidity, and time propulsion is continuously carried out through the time step so as to update flow field data information. The method greatly improves the calculation efficiency of the semi-hidden semi-explicit algorithm and realizes the maximization of the time step length.

Description

Rigid chemical reaction flow semi-hidden semi-explicit self-adaptive time step propulsion simulation method
Technical Field
The invention relates to a technology in the field of chemical reaction control, in particular to a rigid chemical reaction flow semi-implicit semi-explicit (IMEX) self-adaptive time step propulsion simulation method.
Background
With the continuous development of Computational Fluid Dynamics (CFD), researchers have coupled chemical reaction source terms and flow NS equations, and developed a series of calculation methods for chemical reaction flow problems. But the equations are extremely rigid due to chemical reactions and inconsistencies in flow time scales, and are therefore computationally inefficient. Therefore, a great research focus for the chemical reaction flow problem is the improvement of the calculation efficiency. Research has found that the time step of advancing can be increased by implicit processing of chemical reaction source items, and the existing three algorithms: the time step length is increased by a full-hidden method, a semi-hidden semi-obvious method and a decoupling method in an implicit processing mode. But they basically adopt fixed CFL (Courant-Friedrichs-Lewy) number or fixed time step for selecting the time step, and neglect the influence of combustion characteristics on the selection of the time step. This is clearly disadvantageous for the improvement of the computational efficiency.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a rigid chemical reaction flow semi-hidden semi-explicit self-adaptive time step advancing simulation method, which is characterized in that the hidden characteristic time step is deduced through deep analysis of the hidden processing solving process of a chemical reaction source item, the hidden characteristic time step is further expanded to obtain a self-adaptive time step advancing form, the combustion characteristic is integrated into a time step selecting mechanism, so that the time step is changed along with the physical transient characteristic to obtain the maximum time step for stable evolution advancing, and the calculation efficiency is improved.
The invention is realized by the following technical scheme:
the invention relates to a rigid chemical reaction flow semi-hidden semi-explicit self-adaptive time step propulsion simulation method, which comprises the steps of setting an initial flow field according to initial physical state parameters of a supersonic velocity rigid combustion flow problem, calculating system rigidity through flow characteristic time and reaction characteristic time in a calculation stage of a chemical reaction item, selecting the maximum time step which can lead to stable propulsion of evolution according to the system rigidity, and continuously carrying out time propulsion by using the time step so as to update flow field data information.
The supersonic velocity rigid combustion flow problem refers to that: the governing equation is an euler equation with chemical reaction source terms without considering viscosity effects:
Figure BDA0002240475000000011
wherein: u is conservation quantity, E and F are flux, and S is chemical reaction source item.
The semi-hidden and semi-obvious means: solving the coupling of flow and chemical reaction, explicit processing flow, and chemical reaction source itemImplicit processing is carried out to obtain:
Figure BDA0002240475000000012
wherein: residual error
Figure BDA0002240475000000013
Figure BDA0002240475000000014
The system is rigid
Figure BDA0002240475000000021
Wherein: maximum characteristic time tau max I.e. characteristic time of flow
Figure BDA0002240475000000022
Minimum characteristic time tau min I.e. minimum chemical reaction characteristic time
Figure BDA0002240475000000023
Wherein: tau. f For the flow characteristic time, Δ x is the grid spacing, u is the flow field velocity, and c is the acoustic velocity.
The maximum time step is obtained by the following method: maximum time step for enabling system evolution to stably advance
Figure BDA0002240475000000024
Wherein: omega is the system stiffness, tau f As the flow characteristic time, it can be regarded as a constant in the case where the rigidity does not change much, k is usually a constant not more than 1 and less than the CFL number; using adjusted chemical reaction characteristic time in solving system rigidity
Figure BDA0002240475000000025
To perform a calculation wherein
Figure BDA0002240475000000026
τ c Is the characteristic time of the chemical reaction, δ t 0 Is a constant of the same order of magnitude as the step of the propulsion time.
The stable propulsion refers to that: the simulation process does not exhibit non-object understanding, i.e., negative density, and does not exhibit divergence, i.e., an infinite maximum step of propulsion time.
The flow field data information comprises: keeping constant and basic physical quantities such as temperature, pressure and density, and updating the basic physical quantities by the following modes: and updating flow field data information by using the self-adaptive time step obtained by calculation through a semi-hidden semi-explicit method.
The invention relates to a system for realizing the method, which comprises the following steps: the device comprises a flow solving module, a time step selecting module, a chemical reaction module and a data updating module.
The semi-hidden semi-explicit method comprises explicit processing and implicit processing, wherein:
the explicit processing refers to: the flow solving module calculates flux by an AUSM + (adaptive Upstream partitioning Method); implicit processing is carried out on the chemical reaction source item, and a corresponding preprocessing matrix and a residual error are obtained through a diagonally simplified Jacobi matrix;
the implicit processing refers to: the chemical reaction module calculates the characteristic time tau of the explicit chemical reaction source item c (ii) a Calculating flow characteristic time from flow velocity data, etc., to obtain τ f (ii) a The time step length selection module calculates and obtains the system rigidity according to the first two characteristic times
Figure BDA0002240475000000027
Obtaining an adaptive time step
Figure BDA0002240475000000028
Wherein k is a constant; the data updating module updates the flow field physical quantity such as temperature, pressure and the like by advancing the time step.
Technical effects
Compared with the prior art, the method and the device have the advantages that the propulsion time step can be determined according to the combustion characteristics of the flow field in the calculation process, so that the calculation is always propelled with the optimal time step when the rigidity changes, the unreasonable mode of fixing the CFL number or the fixed time step used before is improved, and the calculation efficiency of the system is greatly improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of system efficiency enhancement;
the area enclosed by the 1/dt line graph and the horizontal axis in the graph is proportional to the calculation time;
FIG. 3 is a one-dimensional CJ detonation wave pressure line plot with a calculated domain of 2.5 m:
FIG. 4 is a diagram of principle of one-dimensional CJ detonation wave efficiency increase with a calculation domain of 2.5 m:
FIG. 5 is a two-dimensional oblique detonation temperature cloud:
FIG. 6 is a schematic diagram of two-dimensional oblique detonation efficiency enhancement;
the circled part in the figure is the position with the maximum rigidity, and the time step length is smaller than a certain constant;
FIG. 7 is a two-dimensional super detonation temperature cloud:
FIG. 8 is a two-dimensional super detonation axial line pressure distribution diagram:
fig. 9 is a two-dimensional superdetonation efficiency improvement schematic diagram.
Detailed Description
The implementation Environment of this embodiment is an Integrated Development Environment (IDE), which is Visual Studio Community 2017, the Compiler is an Intel (R) Visual Fortran Compiler in the Intel Parallel Studio XE 2019 software, the Release mode is adopted for operation, and the computer CPU is Intel core i7 6700K.
Example 1
The process of the embodiment comprises the following steps: in an equal cross-section area with the length of 2.5m, the left end is closed, and the right end is opened. The calculation region is filled with H 2 /O 2 A mixed gas of Ar (the mass ratio of substances is 2. The computational grid takes N =1250. Chemical reaction model a 9-component 19 reaction J model was selected. At the initial moment of calculation, the area of the front 5 grids on the left side of the calculation area is filled with high-temperature and high-pressure gas, and the pressure and the temperature of the high-temperature and high-pressure gas are 2000K and 2MPa respectively. The remainder of the calculated zone was cryogenic (298K) low pressure (6.67 kPa) gas. Method ITC (implicit time) used in this exampleStep size control) was compared to both fixed CFL number and fixed time step size algorithms.
The J model of the 9-component 19 reaction specifically refers to:
Figure BDA0002240475000000031
Figure BDA0002240475000000041
the calculated final time in this example is 14ms.
In this embodiment, the pressure diagram is shown in fig. 3, and the efficiency improvement principle diagram is shown in fig. 4.
The comparative table of the calculation efficiency in this example is shown in table 1.
TABLE 1 method ITC compares with fixed CFL number and fixed time step calculation efficiency
Figure BDA0002240475000000042
This embodiment shows that under the prerequisite of guaranteeing that the precision is approximately unchangeable, use ITC can make efficiency obtain very big promotion.
Example 2
Example 2 is an oblique detonation example, in which a rectangular calculation field, H, is set 2 :O 2 :N 2 A combustible mixed gas of = 2. The chemical reaction model used is still the J model.
This example is a steady problem with a calculation termination time of 6 x 10 -5 s。
In this embodiment, the temperature cloud is shown in fig. 5, and the calculation efficiency improvement schematic is shown in fig. 6.
The comparative table of the calculation efficiency in this example is shown in table 2.
TABLE 2 comparison of the method ITC with fixed CFL number and fixed time step calculation efficiency
Figure BDA0002240475000000051
Example 3
The calculation model for the embodiment is a sphere with a radius of 7.5mm, and the incoming flow is H satisfying the stoichiometric ratio 2 /O 2 The molar ratio of hydrogen, oxygen and nitrogen in the mixed gas/Air is 2. The far-field boundary adopts an incoming flow boundary condition, the wall boundary adopts an adiabatic non-catalytic wall condition, and the symmetric boundary adopts a symmetric boundary condition. The incoming stream has a Mach number of 8.5, a pressure of 42662Pa and a temperature of 250K. 100 grids are distributed along the normal direction of the spherical surface, and 125 grids are distributed along the tangential direction. The chemical reaction model used is still the J model. This example is a steady problem with a calculation termination time of 3 × 10 -5 s。
In the embodiment, a temperature cloud graph is shown in fig. 7, a central axis pressure line graph is shown in fig. 8, and a calculation efficiency improvement principle graph is shown in fig. 9.
The comparative table of the calculation efficiency in this example is shown in Table 3.
TABLE 3 comparison of the method ITC with fixed CFL number and fixed time step calculation efficiency
Figure BDA0002240475000000052
The conclusion shows that the calculation efficiency can be well improved by using the ITC on the premise of ensuring that the precision is approximately unchanged.
Which of the above components is original to the invention, has never been disclosed and its operation is different from any prior document: the ITC method is adopted for selecting the propulsion time step length, and the calculation efficiency is greatly improved.
Compared with the prior art, the performance index of the method is improved as follows: the time step length is selected according to the system rigidity, and the calculation efficiency is effectively improved compared with the existing CFL and fixed time step length methods.
The foregoing embodiments may be modified in many different ways by those skilled in the art without departing from the spirit and scope of the invention, which is defined by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (4)

1. A rigid chemical reaction flow semi-hidden semi-explicit self-adaptive time step propulsion simulation method is characterized in that an initial flow field is set according to initial physical state parameters of a supersonic rigid combustion flow problem, system rigidity is calculated through flow characteristic time and reaction characteristic time in a calculation stage of a chemical reaction item, the maximum time step which causes evolution to be capable of being stably propelled is selected according to the system rigidity, and time propulsion is continuously carried out through the time step so as to update flow field data information;
the supersonic velocity rigid combustion flow problem refers to that: the governing equation is an euler equation with chemical reaction source terms without considering viscosity effects:
Figure FDA0003829177060000011
wherein: u is conservation quantity, E and F are fluxes, and S is a chemical reaction source term;
the semi-hidden and semi-obvious means: solving the coupling of the flow and the chemical reaction, carrying out explicit processing on the flow, and carrying out implicit processing on a chemical reaction source item to obtain:
Figure FDA0003829177060000012
wherein: residual error
Figure FDA0003829177060000013
Figure FDA0003829177060000014
The maximum time step is obtained by the following method: maximum time step for enabling stable propulsion of system evolution
Figure FDA0003829177060000015
Figure FDA0003829177060000016
Wherein: omega is the system stiffness, tau f K is a constant not greater than 1 and less than CFL for flow characteristic time, and the adjusted chemical reaction characteristic time is used when solving for system stiffness
Figure FDA0003829177060000017
To perform a calculation wherein
Figure FDA0003829177060000018
τ c Is the characteristic time of the chemical reaction, δ t 0 Is a constant of the same order of magnitude as the step of the propulsion time.
2. The method of claim 1, wherein said system is rigid
Figure FDA0003829177060000019
Wherein: maximum characteristic time tau mαx I.e. characteristic time of flow
Figure FDA00038291770600000110
Minimum characteristic time tau min I.e. minimum chemical reaction characteristic time
Figure FDA00038291770600000111
Figure FDA00038291770600000112
Wherein: tau. f For the flow characteristic time, Δ x is the grid spacing, u is the flow field velocity, and c is the acoustic velocity.
3. The method of claim 1, wherein said steady advancement is: the simulation process does not exhibit non-physical understanding, i.e., negative density, and does not exhibit divergence, i.e., infinite maximum step of propulsion time.
4. The method of claim 1, wherein said flow field data information comprises: conservation of quantity and temperature, pressure and density, its renewal is achieved by: and updating flow field data information by using the self-adaptive time step obtained by calculation through a semi-hidden semi-explicit method.
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