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

Abstract

A semi-implicit and semi-explicit adaptive time-step advancement simulation method for rigid chemical reaction flow. The initial flow field is set according to the initial physical state parameters of the supersonic rigid combustion flow problem. The system stiffness is calculated by time, and the maximum time step that can lead to stable advancement of the evolution is selected according to the system stiffness, and the time step is used to continuously advance time to update the flow field data information. This method greatly improves the computational efficiency of the semi-implicit and semi-explicit algorithm, and maximizes the time step.

Description

Half-hidden and half-explicit adaptive time-step advancing simulation method for rigid chemical reaction flow

technical field

The invention relates to a technology in the field of chemical reaction control, in particular to a semi-hidden and semi-explicit (IMEX) self-adaptive time step advancing simulation method for rigid chemical reaction flow.

Background technique

With the continuous development of Computational fluid dynamics (CFD), scholars have coupled the chemical reaction source term with the flow NS equation, and gradually developed a series of calculation methods for chemical reaction flow problems. However, due to the inconsistency of chemical reaction and flow time scales, the equations are extremely rigid, resulting in extremely low computational efficiency. Therefore, a major research focus on chemical reaction flow problems is the improvement of computational efficiency. The study found that the time step of the advance can be increased through the implicit processing of the chemical reaction source term. The three existing algorithms: the full implicit method, the semi-implicit and semi-explicit method, and the decoupling method all increase the time step by implicit processing. large time steps. However, they basically adopted fixed CFL (Courant-Friedrichs-Lewy) number or fixed time step for the selection of time step, ignoring the influence of combustion characteristics on the selection of time step. This is obviously not conducive to the improvement of computational efficiency.

Contents of the invention

Aiming at the above-mentioned deficiencies in the prior art, the present invention proposes a half-hidden and half-explicit adaptive time step advancement simulation method for rigid chemical reaction flow, and derives the implicit The characteristic time step is further expanded to obtain an adaptive time step advancement form, and the combustion characteristics are integrated into the time step selection mechanism, so that the time step changes with the physical transient characteristics, and the maximum time step for evolutionary stable advancement is obtained length to improve computational efficiency.

The present invention is achieved through the following technical solutions:

The invention relates to a half-hidden and half-explicit self-adaptive time step advancement simulation method for rigid chemical reaction flow, which sets the initial flow field according to the initial physical state parameters of the supersonic rigid combustion flow problem, and passes through the flow characteristic time in the calculation stage of the chemical reaction item The system rigidity is calculated based on the reaction characteristic time and the system rigidity. According to the system rigidity, the maximum time step that leads to the evolution can be stably advanced is selected, and the time step is used to continuously advance the time to update the flow field data information.

其中：U为守恒量，E、F为通量，S为化学反应源项。The supersonic rigid combustion flow problem refers to: the governing equation is the Euler equation with no consideration of the viscosity influence and a chemical reaction source term:

Among them: U is the conserved quantity, E and F are the fluxes, and S is the chemical reaction source term.

其中：残差

The semi-implicit and semi-explicit means: to solve the coupling of flow and chemical reaction, the flow is explicitly processed, and the chemical reaction source item is implicitly processed to obtain:

where: residual

其中：最大的特征时间τ_max即流动特征时间

最小的特征时间τ_min即最小化学反应特征时间

其中：τ_f为流动特征时间，Δx为网格间距，u为流场速度，c为声速。The rigidity of the system

Where: the largest characteristic time τ _max is the flow characteristic time

The minimum characteristic time τ _min is the minimum chemical reaction characteristic time

Where: τ _f is the characteristic time of the flow, Δx is the grid spacing, u is the velocity of the flow field, and c is the speed of sound.

其中：Ω为系统刚性，τ_f为流动特征时间，在刚性变化不大的情况下可视为常数，k通常为不大于1的常数，且小于CFL数；在求解系统刚性时，使用调整后的化学反应特征时间

来进行计算，其中

τ_c为化学反应特征时间，δt₀为与推进时间步长相同量级的常数。The maximum time step is obtained by the following method: the maximum time step that enables the system evolution to advance stably

Where: Ω is the system rigidity, τ _f is the flow characteristic time, which can be regarded as a constant when the rigidity changes little, and k is usually a constant not greater than 1 and smaller than the CFL number; when solving the system rigidity, use the adjusted The characteristic time of the chemical reaction

to calculate, where

τ _c is the characteristic time of the chemical reaction, and δt ₀ is a constant of the same magnitude as the advancing time step.

The stable propulsion refers to: no non-physical understanding occurs in the simulation process, that is, negative density and no divergence, that is, the maximum propulsion time step of infinity.

The flow field data information includes: conserved quantities and basic physical quantities such as temperature, pressure and density, and its update is realized in the following way: using the calculated adaptive time step to update the flow field data information through a half-hidden and half-explicit method .

The invention relates to a system for realizing the above method, comprising: a flow solution module, a time step selection module, a chemical reaction module and a data update module.

The semi-hidden and semi-explicit includes explicit processing and implicit processing, wherein:

The explicit processing refers to: the flux is calculated by the flow solution module through the AUSM+ (Advection Upstream Splitting Method) method; the chemical reaction source item is implicitly processed, and the corresponding preprocessing matrix and residual matrix are obtained through the diagonally simplified Jacobi matrix. Difference;

得到自适应时间步长

其中k为常数；数据更新模块通过推进时间步长对流场物理量如温度，压力等物理量进行更新。The implicit processing refers to: the chemical reaction module calculates the characteristic time τ _c of the explicit chemical reaction source item; calculates the flow characteristic time according to the flow velocity data, etc., thereby obtaining τ _f ; the time step selection module is based on the first two The characteristic time is calculated to obtain the system stiffness

get adaptive time step

Where k is a constant; the data update module updates the physical quantities of the flow field such as temperature and pressure by advancing the time step.

technical effect

Compared with the prior art, the present invention realizes that the advance time step can be determined according to the combustion characteristics of the flow field during the calculation process, so that the calculation always advances with the optimal time step when the rigidity changes, which improves the previously used fixed The unreasonable way of CFL number or fixed time step greatly improves the calculation efficiency of the system.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Figure 2 is a schematic diagram of system efficiency improvement;

The area enclosed by the 1/dt line graph and the horizontal axis in the figure is proportional to the calculation time;

Fig. 3 is a one-dimensional CJ detonation wave pressure diagram with a calculation domain of 2.5m:

Figure 4 is a schematic diagram of the one-dimensional CJ detonation wave efficiency improvement with a calculation domain of 2.5m:

Figure 5 is a two-dimensional oblique detonation temperature cloud map:

Figure 6 is a schematic diagram of two-dimensional oblique detonation efficiency improvement;

The circled part in the figure is the maximum rigidity, and the time step should be smaller than a certain constant at this time;

Figure 7 is a two-dimensional superdetonation temperature cloud map:

Figure 8 is a two-dimensional superdetonation central axis pressure distribution line diagram:

Figure 9 is a schematic diagram of two-dimensional superdetonation efficiency improvement.

Detailed ways

The implementation environment of this embodiment is that the integrated development environment (IDE, Integrated Development Environment) is Visual Studio Community 2017, and the compiler is the Intel(R)Visual Fortran Compiler in the Intel Parallel Studio XE2019 software, adopts Release mode to run, and the computer CPU is an Intel Core i7 6700K.

Example 1

The process of this embodiment includes: a calculation area with a length of 2.5m and a constant cross-section area, the left end is closed and the right end is open. The calculation area is filled with the mixed gas of H ₂ /O ₂ /Ar (substance ratio is 2:1:7). The calculation grid takes N=1250. The chemical reaction model selects the J model of 9 components and 19 reactions. At the initial moment of calculation, the area of the first five grids on the left side of the calculation area is filled with high-temperature and high-pressure gas, and its pressure and temperature are 2000K and 2MPa, respectively. The rest of the calculation area is low temperature (298K) low pressure (6.67kPa) gas. The method ITC (Implicit Time Step Control) used in this example is compared with two algorithms of fixed CFL number and fixed time step.

The J model of described 9 components 19 reactions specifically refers to:

In this embodiment, the final calculation time is 14ms.

In this embodiment, the pressure line diagram is shown in Figure 3, and the efficiency improvement principle diagram is shown in Figure 4.

The calculation efficiency comparison table in this embodiment is shown in Table 1.

Table 1 Comparison of calculation efficiency between this method ITC and fixed CFL number and fixed time step

This embodiment shows that under the premise that the precision is kept approximately constant, the efficiency can be greatly improved by using the ITC.

Example 2

Example 2 is an oblique detonation calculation example, a rectangular calculation domain is set, the combustible gas mixture of H ₂ :O ₂ :N ₂ =2:1:3.76 shoots at the wall at an angle of attack of -25°, and the calculation domain is 5.25cm× 2cm, the Mach number of incoming flow is 7.5, the pressure and temperature are 40KPa and 293K respectively, and the grid number is 200×80. The chemical reaction model used is still the J model.

This embodiment is a stationary problem, and the calculation termination time is 6×10 ^-5 s.

In this embodiment, the temperature cloud diagram is shown in Figure 5, and the calculation efficiency improvement principle diagram is shown in Figure 6.

The calculation efficiency comparison table in this embodiment is shown in Table 2.

Table 2 Comparison of calculation efficiency between ITC and fixed CFL number and fixed time step in this method

Example 3

The calculation model for this embodiment is a sphere with a radius of 7.5 mm, the incoming flow is a mixed gas of H ₂ /O ₂ /Air satisfying the stoichiometric ratio, and the molar ratio of hydrogen, oxygen and nitrogen is 2:1:3.76. The far-field boundary adopts the incoming flow boundary condition, the wall boundary adopts the adiabatic non-catalytic wall condition, and the symmetrical boundary adopts the symmetrical boundary condition. The incoming Mach number is 8.5, the pressure is 42662Pa, and the temperature is 250K. Distribute 100 meshes along the normal of the sphere and 125 tangentially. The chemical reaction model used is still the J model. This embodiment is a steady problem, and the calculation termination time is 3×10 ^-5 s.

In this embodiment, the temperature cloud diagram is shown in Figure 7, the central axis pressure line diagram is shown in Figure 8, and the calculation efficiency improvement principle diagram is shown in Figure 9.

The calculation efficiency comparison table in this embodiment is shown in Table 3.

Table 3 Comparison of calculation efficiency between ITC and fixed CFL number and fixed time step in this method

In summary, it shows that under the premise of ensuring that the accuracy is approximately unchanged, the use of ITC can greatly improve the computational efficiency.

Which one of the above components is the original creation of the present invention, has never been disclosed, and its working method is different from any existing literature records: the selection of the advancing time step adopts the ITC method, which greatly improves the calculation efficiency.

Compared with the existing technology, the performance index of this method is improved in that: the time step is selected according to the rigidity of the system, and the calculation efficiency is effectively improved compared with the existing CFL and fixed time step methods.

The above specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The scope of protection of the present invention is subject to the claims and is not limited by the above specific implementation. Each implementation within the scope is bound by the invention.

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:

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:

wherein: residual error

The maximum time step is obtained by the following method: maximum time step for enabling stable propulsion of system evolution

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

To perform a calculation wherein

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

Wherein: maximum characteristic time tau _mαx I.e. characteristic time of flow

Minimum characteristic time tau _min I.e. minimum chemical reaction characteristic time

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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