CN115048775B - Thermochemical non-equilibrium flowing component limiting method - Google Patents

Thermochemical non-equilibrium flowing component limiting method Download PDF

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CN115048775B
CN115048775B CN202210584299.4A CN202210584299A CN115048775B CN 115048775 B CN115048775 B CN 115048775B CN 202210584299 A CN202210584299 A CN 202210584299A CN 115048775 B CN115048775 B CN 115048775B
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丁明松
李鹏
陈坚强
刘庆宗
高铁锁
董维中
江涛
郭勇颜
梅杰
何磊
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The invention discloses a thermochemical unbalanced flow component limiting method, which starts from time correlation among multiple mechanisms of an unbalanced flow multi-reaction system, introduces a comprehensive limiting function, and physically ensures that quality and element conservation are not destroyed in the estimation process. The method does not need to determine the source and the destination of the components and the elements, avoids a complex tracing process, has relatively simple and efficient realization process and has strong universality. And a micro-component tolerance mechanism is introduced, and the calculation effectiveness, stability and efficiency are considered in combination with the correction range limitation and normalization treatment.

Description

Thermochemical non-equilibrium flowing component limiting method
Technical Field
The invention belongs to the field of numerical simulation calculation, and particularly relates to a mixed gas component constraint limiting method for an iterative process of a thermochemical unbalanced flow simulation process.
Background
In hypersonic unbalanced flow numerical simulation, iterative calculation of mass fractions of various gas components of a mixed gas is generally involved. In the numerical iteration process, due to the difference between the flow characteristic time and the chemical reaction characteristic time, numerical iteration error and the like, the mass fraction of the mixed gas component may have a negative value, which is not in accordance with physical reality, and the next step of chemical unbalanced source item calculation is disabled, so that the iterative calculation is interrupted.
To avoid this problem, it is common practice to forcibly set a certain gas component to zero or a certain small amount when it comes out to be negative (hereinafter referred to as "conventional non-negative treatment"). This is possible under most conditions because as the steady or quasi-steady iteration proceeds, the component variation per step decreases gradually, so that the negative component appearance gradually diminishes and eventually disappears. However, the processing method is equivalent to artificially introducing mass flux in the iterative process, destroying the element conservation and mass conservation of fluid microelements, and under certain conditions, non-physical solutions can be obtained, even the numerical iterative process diverges and the numerical simulation fails. There is therefore a need to construct more reliable thermochemical non-equilibrium flowing component processing methods.
This phenomenon will be described below with a specific example. For example, when the temperature of a certain region of a thermochemical unbalanced flow field drops greatly, it is assumed that only the recombination reaction of oxygen atoms occurs in the flow field:
O+O—>O 2
this reaction produces O for a certain period of time Deltat 2 And the mass fraction of consumed O is-Deltac. If the mass fraction of the oxygen atom component is negative due to the difference between the flow calculation time and the chemical reaction characteristic time or numerical iteration error and the like, namely:
c O n+1 ＝c O n -Δc＜0
here, theThe mass fraction of oxygen atoms (O) for the n+1th and n-th iterations, respectively.
To ensure efficient computation of chemically unbalanced source terms, the usual process is:
c O n+1 ＝ε
where ε is 0 or an artificially set component minimum. At the same time, due to oxygen (O 2 ) No negative values of the component mass fraction occur, so the iteration of oxygen is unchanged:
therefore, for this iteration, it is equivalent to the artificial introduction of a certain amount of oxygen elements as a whole:
it can be seen that the conservation of oxygen element mass is destroyed at this time. As the numerical simulation proceeds, if such errors accumulate, non-physical solutions may be obtained, and even the numerical iterative process diverges, thereby failing the numerical simulation.
For the "single, irreversible" reaction, since the "source and direction of oxygen element" is easily determined, the correction process is easily performed, and only the iterative process needs to be changed to:
the conservation of oxygen element can be ensured.
But for true high temperature gas thermochemical unbalanced flow processes, in generalIs multi-element and multi-component (N) 2 、O 2 、NO、NO + 、O、N、O + 、CO 2 、CO、H、H 2 O … …), and multiple reactions, and multiple mechanisms such as convection and diffusion of each gas component in high-speed flow are considered, so that the sources and the directions of the components and elements are uncertain. Once the component mass is negative in the iterative process, after "conventional non-negative treatment", which gas component is corrected, how it is corrected and the magnitude of the correction are closely related to the chemical imbalance system in the whole flow process, and it is difficult to effectively treat.
There is therefore a need to establish a more reliable, relatively simple method of component correction or confinement treatment.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a thermochemical unbalanced flow component limiting method which solves the problems of calculation effectiveness, stability and efficiency.
The aim of the invention is achieved by the following technical scheme:
a method of thermochemical non-equilibrium flowing, composition limiting, the method comprising the steps of:
step 1: taking a value; in the solving process of the flow control equation set, obtaining the initial value of each component mass fraction of the n-th step iteration mixed gasAnd the variation thereof>Wherein s=1, 2, … … Ns, ns is the mixed gas component fraction;
step 2: estimating; constructing a limiting function according to the physical time equivalent principle, and limiting component iteration to obtain a predicted value of component mass fraction of the next iteration step
Step 3: is provided withLimiting; according to conservation of elements, by predicted valuesCalculating the mass fraction upper limit value of each gas component
Step 4: classifying and calibrating; according to the mass fraction of each component of the mixed gasSelecting a component with the largest mass fraction, namely a maximum component, and recording the number of the maximum component as nmax; other gas components are referred to as "non-maximum components";
step 5: correcting; according to the upper limit of the mass fraction of the componentsCorrecting the non-maximum component, then calculating the mass fraction of the maximum component again by combining the normalized definition of the mass fraction to obtain the +.1 in the n+1 step>
According to a preferred embodiment, in step 2,
wherein f min Is a physical time comprehensive equivalent constraint factor, and the expression is that
f min ＝min(f 1 ,f 2 ,……,f Ns )
Wherein f 1 ,f 2 ,……,f Ns Is an equivalent time factor for each component.
According to a preferred embodiment, for the negative component, i.eEquivalent time factor f of the s-th component s Is that
ε 0 Epsilon is a small amount;
for components not negative, i.e.The equivalent time factor is:
f s ＝1.0。
according to a preferred embodiment epsilon 0 ＝0.05～0.1，ε＝1×10 -20 。
According to a preferred embodiment, in step 3,
wherein m is the number of substance elements included in the mixed gas, A s,j The mass ratio of the element in the j-th component,maximum achievable value of s component determined for j-th element, C j The mass fraction of the j-th element in the mixed gas.
According to a preferred embodiment, in step 5,
ε 1 is the lower limit of the mass fraction of the gas component.
According to a preferred embodiment epsilon 1 ＝0。
The foregoing inventive concepts and various further alternatives thereof may be freely combined to form multiple concepts, all of which are contemplated and claimed herein. Various combinations will be apparent to those skilled in the art from a review of the present disclosure, and are not intended to be exhaustive or all of the present disclosure.
The invention has the beneficial effects that: the method of the invention starts from the time correlation among multiple mechanisms of the unbalanced flow multi-reaction system, introduces the comprehensive restriction function, and physically ensures that the quality and the element conservation in the pre-estimation process are not destroyed. The method does not need to determine the source and the destination of the components and the elements, avoids a complex tracing process, has relatively simple and efficient realization process and has strong universality. And a micro-component tolerance mechanism is introduced, and the calculation effectiveness, stability and efficiency are considered in combination with the correction range limitation and normalization treatment.
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FIG. 1 is a schematic flow chart of the method of the present invention.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict.
It should be noted that, for the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described below, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments.
In the hypersonic unbalanced flow simulation process, the mass fraction of the components is generally obtained by simultaneous iterative solution of control equations such as a mass continuity equation, a total mass continuity equation of mixed gas, a charge conservation equation and the like of each component in a flow control equation. Although the form and kind of the flow control equation can be different according to the simulation object and the simulation method, the mass fraction of each component is required to be obtained at the beginning of the nth iteration of solving the control equationAs the basis of iterative computation; after the n-th iteration is completed, the variation of the mass fraction of each component of the n-th iteration can be obtained by controlling the display of the equation set or implicit solving>At this time, based on the mathematical meaning of the iterative calculation, the initial value +.1 needed for the n+1 th iteration of the control equation is calculated>Can be expressed directly as (hereinafter referred to as direct iterative processing):
the iterative calculation processing is obtained by solving the control equations such as the mass continuity equation, the total mass continuity equation of mixed gas, the charge conservation equation and the like of each component in the flow control equation simultaneously, so that the iterative calculation processing meets the conservation laws such as the mass conservation, the element conservation, the charge conservation and the like of each component, which is one of the starting points of the invention.
Due to mass fraction of gas componentThe mass fraction of the gas component cannot be negative, so that the n-th iteration is started beforeAfter the n-th iteration is completed, the requirement of +.>However, due to the difference between the flow calculation time and the characteristic time of the chemical reaction or numerical iteration error, the direct iteration process cannot ensure that the mass fraction of the gas component is ++>The absence of negative values may result in a calculation failure requiring correction.
The main purpose of the invention is to provide a novel structureAnd->Relatively accurately and efficiently obtain +.>Ensure->And meanwhile, the quality of a flow control equation and the conservation law of elements are not destroyed.
Referring to FIG. 1, a method of thermochemical non-equilibrium flow component confinement is disclosed. The thermochemical non-equilibrium flowing component confinement method comprises the steps of:
step 1: and (5) taking a value. In the solving process of the flow control equation set, obtaining the initial value of each component mass fraction of the n-th step iteration mixed gasAnd the variation thereof>Where s=1, 2, … … Ns, ns is the mixed gas component fraction.
Step 2: estimating; constructing a limiting function according to the physical time equivalent principle, and limiting component iteration to obtain a predicted value of component mass fraction of the next iteration step
Wherein,
wherein f min Is a physical time comprehensive equivalent constraint factor, and the expression is that
f min ＝min(f 1 ,f 2 ,……,f Ns )
Wherein f 1 ,f 2 ,……,f Ns Is an equivalent time factor for each component.
For the negative component, i.eEquivalent time factor f of the s-th component s Is that
ε 0 Epsilon is a small amount; advice epsilon 0 ＝0.05～0.1，ε＝1×10 -20 。
For components not negative, i.e.The equivalent time factor is:
f s ＝1.0。
theoretical deduction of step 2:
based on the principle of time dispersion of numerical simulationIn direct iterationCan be expressed as a time first order discrete form
Wherein,for the instantaneous change rate of the mass fraction of the s-th component along with time in the n-th iteration, the instantaneous influence of complex physical mechanisms such as chemical reaction, convection, diffusion and the like on the mass fraction of the s-th component is comprehensively represented, and the instantaneous influence is objectively represented by the complex physical mechanisms, so that artificial modification is not allowed; Δt (delta t) n The equivalent time of the influence of complex physical mechanisms such as chemical reaction, convection and diffusion in the n-th iteration process is represented as a time infinitesimal; o ((Δt) n ) 2 ) Is of a higher order infinitely small, when deltat n Small enough that the effect of this term approaches zero and can be ignored.
For steady (or quasi-steady) flow, the flow state is time independent (or approximately independent), so long as Δt is ensured n Is small enough to adjust the delta t within a certain range n The numerical simulation results are not affected theoretically. For unsteady flow, when Deltat n And when the time accuracy of numerical simulation is improved.
For components that appear negative in "direct iteration", i.e. when the mass fraction of the s-th componentWhen, i.eThis essentially indicates Δt n Is too large, resulting in +.>The rate of this instantaneous change of the rate of change,cannot approximate the characterization time period Δt n Average rate of change of the mass fraction of the inner s-th component over time; at the same time, it also shows that the higher order is infinitely small O ((delta t) n ) 2 ) Cannot be ignored. Therefore, a limiting factor f is introduced here s To reduce deltat n Obtaining the new equivalent time delta t of the s-th component s n,*
Δt s n,* ＝Δt n ·f s
From the following componentsAvailable->Thus 0.ltoreq.f s And is less than or equal to 1. In order to prevent numerical value out of limits due to too small a denominator in the limit case, a small numerical value ε=10 is introduced here -20 。
For components that do not appear negative for "direct iteration", i.e. when the s-th component mass fractionWhen, i.eNo additional treatment was performed: Δt (delta t) s n,* ＝Δt n It is written here in a similar form Δt s n,* ＝Δt n ·f s ，f s ＝1.0。
Because various physical mechanisms such as chemical reactions, thermodynamic excitation, convection and diffusion of unbalanced flow occur synchronously, that is to say, time correlation exists among various physical mechanisms, when the equivalent time infinitesimal of one component in the mixed gas is reduced, the equivalent time infinitesimal of other gas components also needs to be reduced synchronously. The combined equivalent time reduction must therefore take into account all negative component-to-time bin constraints at the same time and apply to all gas components:
Δt n,* ＝Δt n ·f min
f min ＝min(f s＝1 ,f s＝2 ,……,f s＝Ns )
here Δt n,* F is the integral equivalent time infinitesimal min And synthesizing equivalent constraint factors for physical time. Since 0.ltoreq.f s Less than or equal to 1, thus f min ≤f s 、0≤f min And is less than or equal to 1. At this time, the corrected component variation amountThe method can be written according to time first order discrete:
therefore, all the components iterate and can be uniformly corrected as follows:
from the time analysis of the steady and unsteady flow simulations, it can be seen that this will not affect the numerical simulation results (or improve the accuracy of the numerical simulation time), i.e. the original conservation law can be guaranteed.
At the same time, this correction ensures that all component mass fractions do not exhibit negative values:
when (when)When in use, by->Available->Thus there is
When (when)When (i.e.)>By->And f is 0.ltoreq.f min Less than or equal to 1, get->f min Namely there is
Although the correction method is adopted for iteration, all the component mass fractions do not have negative values, and the principle of time action and the principle of numerical dispersion of a physical mechanism are met, so that the conservation law (such as component mass conservation, element conservation, charge conservation and the like) related to a flow control equation is ensured not to be destroyed. But in the case of the micro-component,very small, possibly +_due to numerical errors>Relatively large, at this point f s Near zero, f min Is also compressed to approximately 0, an equivalent time step deltat n,* The numerical iteration converges slowly and the calculation efficiency is low. Therefore, the correction method should be further improved, a tolerance mechanism for the occurrence of negative values of the micro-components is established, and the calculation efficiency is improved.
When directly iterating the s-th componentWhen the micro component is introduced, a tolerance mechanism that the micro component takes negative value is introduced, and the factor f is limited s The writing is as follows:
here ε 0 As a micro-component thresholdWhen the composition is used, the composition is a micro-component; on the contrary, for non-minor components, epsilon is suggested 0 Taking 0.05 to 0.1.
After introducing tolerance mechanism that the micro component takes negative value, f of non-micro component s Is not affected; and f of minor component s The method is not too small due to the influence of numerical errors, so that the overall iteration efficiency is improved. At the same time, when the micro component takes on a negative valueWhen in use, by->0≤f min ≤f s Less than or equal to 1, get-> I.e. there is->Thus, the amplitude of the negative value of the micro component is limited:
it follows that the amplitude of the negative values of the micro-components is also limited to small amounts, with relatively little effect on the overall gas properties. That is, the overall gas properties do not fluctuate greatly due to the negative values of the micro-components, thereby ensuring the stability of the calculation.
Step 3: and setting a limit. According to conservation of elements, by predicted valuesCalculating the mass fraction upper limit value of each gas componentWherein,
wherein m is the number of substance elements included in the mixed gas, A s,j The mass ratio of the element in the j-th component,maximum achievable value of s component determined for j-th element, C j The mass fraction of the j-th element in the mixed gas.
Specifically, m is the number of substance elements included in the mixed gas. For example, consider only O in pure air 2 、N 2 、CO 2 、H 2 When the main gas components such as O are contained, the air contains 4 elements including the substance element number m=4, namely 4 elements including nitrogen element, oxygen element, hydrogen element and carbon element.
The upper limit value of the mass fraction of the s-th component gas is determined by the amount of the substance element constituting the s-th component gas in the mixed gas. In pure air CO 2 In the case of an example of this,its maximum mass fraction is determined by the content of carbon element and oxygen element in air, and its size is "CO calculated by carbon element content in air 2 Maximum value of mass fraction and CO calculated from oxygen element content in air 2 The smallest of the mass fraction maxima ".
Step 4: classifying and scaling. According to the mass fraction of each component of the mixed gasSelecting a component with the largest mass fraction, namely a maximum component, and recording the number of the maximum component as nmax; other gas components are referred to as "non-maximum fractions".
Step 5: correcting; according to the upper limit of the mass fraction of the componentsCorrecting the non-maximum component, then calculating the mass fraction of the maximum component again by combining the normalized definition of the mass fraction to obtain the +.1 in the n+1 step>
Wherein,
ε 1 for the lower limit of the mass fraction of the gas component, epsilon is recommended 1 ＝0。
Theoretical description of step 5:
because the step 2 is estimated to be obtained in order to achieve both the calculation efficiency and the stabilityAllowing the minor component mass fraction to take on negative values may result in someThe composition exceeds->Is not in line with physical reality. And also may cause failure of the chemical reaction source term calculation due to the presence of negative mass fraction components. Therefore, it is necessary to do->Further corrections are made. Here, the non-largest constituent is treated
By this treatment, the "non-maximum component" does not take on negative values nor exceedThe effectiveness of the calculation result conforming to the physical reality and the chemical reaction source item calculation is ensured to the greatest extent. Meanwhile, the influence caused by the negative value of the trace component is corrected, and the integral property of the mixed gas is not changed too much, so that the stability of calculation is ensured to the greatest extent.
From the definition of mass fractions, the sum of the mass fractions of all the gas components is 1 (referred to herein as normalization). The mass fraction of the "largest component" is therefore determined by
The processing is carried out in this way, on the one hand, the artificial modification of the mass fraction of the non-maximum component is avoided in order to meet the normalization requirement of the mass fraction; on the other hand, all the errors of the "non-maximum component" are accumulated to the maximum component, thereby ensuring that their relative errors are minimal:
where eta is the relative error and,is the error of the s component of the n+1 step. It can be seen that due to +.>Is the largest component and therefore the relative error η is the smallest.
Examples
Taking the thermo-chemical unbalanced flow of the jet pipe of the numerically-simulated JF10 shock tunnel as an example, the application effect of the invention is described. Using a typical cone nozzle of JF-10, the half cone angle is 7.1 degrees, the exit diameter is 500mm, the throat diameter is 11mm, and the expansion ratio is 2066. The total pressure of the residence chamber is 19.6MPa, the total temperature is 7920K, and the outlet back pressure is about 30Pa. The test gas is air, the mass of oxygen element is 0.233, the mass ratio of nitrogen element is 0.767, and the chemical reaction of air at high temperature is considered, so that the wall surface of the spraying tube is in a complete catalysis condition. The intermediate results at 3000 steps of the numerical iteration are compared (this state does not converge at this time).
The temperature field changes very drastically at 3000 steps, and the temperature drops rapidly from 7500K above the residence chamber to below 1000K at the nozzle outlet in the flow direction, which can lead to drastic changes in chemical reactions, especially oxygen atom drastic complex reactions.
When 3000 steps are calculated without using the method, oxygen quality fraction cloud is obtained. The oxygen mass fraction in the local area is up to about 0.65, and is far beyond the oxygen element (0.233) ratio in the air, which shows that the mass conservation and the element conservation are seriously destroyed, and the calculated intermediate result deviates from the physical reality.
When the invention is used in the 3000 th step, oxygen quality fraction cloud is obtained. The temperature in the residence chamber is higher and reaches more than 7500K, oxygen is dissociated to a greater extent, and the mass fraction of the oxygen is lower; the temperature of the air flow is rapidly reduced to 3000-4000K through the throat of the spray pipe, oxygen atoms undergo relatively severe compound reaction, and the mass fraction of oxygen is rapidly increased; in the expansion section of the spray pipe, the temperature of the air flow is further reduced, but the chemical reaction is frozen due to the quicker air flow, and the mass fraction of oxygen in the main flow area is not greatly changed; near the wall surface of the expansion section of the spray pipe, oxygen atoms near the wall surface are compounded to a large extent due to the wall surface catalytic effect, and the oxygen mass fraction is relatively high; the mass fraction of oxygen in the jet pipe flow field is not more than the ratio of oxygen element (0.233) in the air, which accords with the expectations of element conservation. The changes conform to the change characteristics of the flow field of the high enthalpy shock tunnel, so that the credibility of flow field simulation is improved after the method is used.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.

Claims (5)

1. A method of thermochemical non-equilibrium flowing composition confinement, the method comprising the steps of:
step 1: taking a value; in the solving process of the flow control equation set, obtaining the initial value of each component mass fraction of the n-th step iteration mixed gasAnd the variation thereof>Wherein->，/>The gas mixture is the component fraction of the mixed gas;
step 2: estimating; constructing a limiting function according to the physical time equivalent principle, and limiting component iteration to obtain a predicted value of component mass fraction of the next iteration step；
In the step 2 of the process, the process is carried out,
wherein,is a physical time comprehensive equivalent constraint factor, and the expression is that
Wherein the method comprises the steps ofEquivalent time factors for each component;
for the negative component, i.eEquivalent time factor of the s-th component +.>Is that
Is small;
for components not negative, i.e.The equivalent time factor is:
；
step 3: setting a limit; according to conservation of elements, by predicted valuesCalculating the upper limit value +.about.mass fraction of each gas component>；
Step 4: classifying and calibrating; according to the mass fraction of each component of the mixed gasSelecting the component with the largest mass fraction, called the "largest component", and recording the number of the component as +.>The method comprises the steps of carrying out a first treatment on the surface of the Other gas components are referred to as "non-maximum components";
step 5: correcting; according to the upper limit of the mass fraction of the componentsCorrecting the non-maximum component, then calculating the mass fraction of the maximum component again by combining the normalized definition of the mass fraction to obtain the +.1 in the n+1 step>。
2. A method for limiting a thermochemical non-equilibrium flowing composition according to claim 1,，。
3. a method for limiting a thermochemical non-equilibrium flowing composition according to claim 1, wherein, in step 3,
wherein m is the number of substance elements included in the mixed gas,the mass ratio of the element in the j-th component,maximum value achievable by the s-component determined for the j-th element, < >>The mass fraction of the j-th element in the mixed gas.
4. A method for limiting a thermochemical non-equilibrium flowing composition according to claim 3, wherein, in step 5,
is the lower limit of the mass fraction of the gas component.
5. The thermochemical non-equilibrium flowing of claim 4The component limiting method is characterized in that,。
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