CN108255781B - Hypersonic speed target surface dynamic temperature modeling method - Google Patents

Hypersonic speed target surface dynamic temperature modeling method Download PDF

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CN108255781B
CN108255781B CN201810007755.2A CN201810007755A CN108255781B CN 108255781 B CN108255781 B CN 108255781B CN 201810007755 A CN201810007755 A CN 201810007755A CN 108255781 B CN108255781 B CN 108255781B
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段然
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Abstract

The invention discloses a hypersonic speed target surface dynamic temperature modeling method, which establishes a turbulent flow N-S equation and further comprises the following steps: (1) modeling according to process data of pneumatic heating of the hypersonic target; (2) simulating data of transient heat conduction of surface materials and structures of the hypersonic speed target and modeling; (3) coupling calculation is carried out on the process data of pneumatic heating of the hypersonic target and the data of transient heat conduction of the simulated target material structure; (4) and determining the dynamic surface temperature of the hypersonic speed target, and completing dynamic temperature modeling according to the value of the dynamic surface temperature. The method effectively simulates the dynamic change process of the surface temperature of the hypersonic target, forms a coupling technology of pneumatic heating and structural heat transfer, and improves the calculation precision and efficiency of the hypersonic target temperature field simulation.

Description

Hypersonic speed target surface dynamic temperature modeling method
Technical Field
The invention relates to the field of spaceflight, in particular to a hypersonic velocity target surface dynamic temperature modeling method.
Background
The hypersonic speed target in the close space of the gliding class does not generally have an active power device, and obtains very high flying speed through the process of launching and reentry in high altitude. The flying speed of the near space target can reach 15-25 Ma, so that on one hand, a strong pneumatic heating effect can be generated; on the other hand, in order to protect the structural integrity and system safety of the hypersonic target, the hypersonic target is usually covered with an insulating material to reduce the heat conduction from the surface to the interior, so that the hypersonic target will experience a longer ballistic time to reach thermal equilibrium. From the angle of target characteristic research, the surface temperature of a hypersonic speed target in an adjacent space presents a time-related change process along the trajectory of the hypersonic speed target, the two main methods are the conventional pneumatic heating calculation methods, one method is to simulate the surface temperature distribution in a thermal equilibrium state, and the method cannot accurately predict the temperature and the infrared radiation characteristics of the glide adjacent space target in the actual combat process; the other method is that the flow field and the structural heat transfer are respectively calculated and manually coupled at regular intervals by assuming an isothermal wall surface, and the method has the defects in precision and efficiency.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a hypersonic velocity target surface dynamic temperature modeling method which can effectively simulate the hypersonic velocity target surface temperature dynamic change process, form a coupling technology of pneumatic heating and structural heat transfer and improve the calculation precision and efficiency of hypersonic velocity target temperature field simulation.
The invention provides a hypersonic speed target surface dynamic temperature modeling method, which establishes a turbulent flow N-S equation and is characterized by comprising the following steps:
(1) modeling according to process data of pneumatic heating of the hypersonic target;
(2) simulating data of transient heat conduction of surface materials and structures of the hypersonic speed target and modeling;
(3) coupling calculation is carried out on the process data of pneumatic heating of the hypersonic target and the data of transient heat conduction of the simulated target material structure;
(4) and determining the dynamic surface temperature of the hypersonic speed target, and completing dynamic temperature modeling according to the value of the dynamic surface temperature.
Preferably, the turbulent flow N-S equation is established during dynamic temperature modeling, wherein:
solving a turbulent flow N-S equation by adopting a Reynolds average method;
the turbulence model adopts a k omega-SST model;
time integral is solved by adopting an implicit format;
the spatial dispersion is solved by adopting a second-order windward format.
Preferably, when modeling is performed according to the process data of pneumatic heating of the hypersonic target in the step (1), the boundary layer of the windward shock wave on the surface of the hypersonic target is divided by adopting hexahedral meshes, and the dimensionless distance value (y + value) from the centroid of the first layer of meshes to the wall surface is not more than 1.
Preferably, the step (1) generates a thermodynamic non-equilibrium process comprising the bypass flow of the hypersonic target, a chemical reaction non-equilibrium process of air ionization and a surface catalysis reaction process when the hypersonic target is pneumatically heated;
when a thermodynamic non-equilibrium process of the hypersonic speed target streaming is generated, a thermodynamic non-equilibrium process of the hypersonic speed target streaming is established by adopting a dual-temperature model;
when the chemical reaction unbalanced process of air ionization is generated, calculating parameters by adopting an independent reverse reaction rate in an Arrhenius equation;
when a surface catalytic reaction process is generated, a complete catalytic wall is used to establish the surface catalytic reaction process of the hypersonic target.
Preferably, the pneumatic heating of the hypersonic speed target in the step (1) is a nonlinear process, a finite element method is adopted to solve a heat transfer equation corresponding to the hypersonic speed target, and a heat conduction process and a transient temperature field of the structure of the hypersonic speed target are calculated;
when the finite element method is adopted for solving, the set values comprise: thermal conductivity, specific heat capacity, emissivity of the material, temperature of the structure and thermal boundary conditions of the heat flow.
Preferably, in the heat transfer equation, the temperature value and the heat flow value and the heat exchange coefficient in the finite element method satisfy the following expression:
Figure GDA0002998792680000021
wherein epsilon is the emissivity of the outer surface material; σ is Stefan-Boltzmann constant; ksThermal conductivity of the heat-proof material; delta is the thickness of the surface heat-proof material; t is0Is the transient temperature value in the heat transfer equation; t is∞Is ambient temperature; t isbThe temperature of the inner layer of the heat-proof layer; h is the convective heat transfer coefficient.
Preferably, the step of performing the coupling calculation in step (3) includes:
1) declaring a real-time call of CFD-ACE + in CFD-Fastran;
2) the coupling mode of the heat transfer is stated in the CFD-Fastran, and the transient temperature value T in the heat transfer equation is defined in the statement0Coupling parameters of the bottom and the wall surface of the gas boundary layer;
3) generating a boundary file in the CFD-Fastran, wherein the boundary file comprises grid data of a gas boundary layer;
4) correlating the boundary file in the CFD-ACE + to enable the solid wall surface grids participating in calculation in the CFD-ACE + to correspond to the gas boundary layer grids participating in calculation in the CFD-Fastran one by one;
5) in the setting of the boundary condition of the CFD-ACE +, the interaction parameter on the boundary is stated by using a ubend function as the transient temperature value T in the heat transfer equation0And heat flux density to complete the coupling setup.
Preferably, when the double-temperature model is used for establishing the thermodynamic non-equilibrium process of the hypersonic velocity target streaming, the energy balance equation is as follows:
Figure GDA0002998792680000031
E＝Et+Ev；
wherein t is time; rho is density; x is the number ofjIs the length tensor; h is the total enthalpy; u. ofjIs the velocity tensor; lambda [ alpha ]tA translational heat transfer coefficient; lambda [ alpha ]rIs the rotational heat transfer coefficient; t is the temperature; lambda [ alpha ]vIs the vibration heat transfer coefficient; lambda [ alpha ]eIs the electron heat transfer coefficient; t isVIs the vibration temperature; h issIs the enthalpy per unit mass of component s; dsIs the diffusion coefficient of component s; chi shapesIs the molar mass fraction of the component s; μ is the viscosity coefficient; u. ofiIs the velocity tensor; x is the number ofiIs the length tensor; u. ofkIs the velocity tensor; x is the number ofkIs the length tensor; deltaijIs a kronecker function; qradIs radiant energy; e is the total energy; etIs kinetic-rotational energy; evIs the vibration-electron energy.
More preferably, when the parameters are calculated by using the independent inverse reaction rates in the arrhenius equation, the method includes:
chemical reaction step k, the expression of which is:
Figure GDA0002998792680000032
wherein M isiIs the chemical symbol of component i; v'ikAnd v ″)ikThe number of chemical equivalents of component i in the reactants and the product, respectively, in reaction step k;
in reaction step k, the rate of formation ω of component iikThe expression of (a) is:
Figure GDA0002998792680000033
wherein, WiIs the molecular weight of component i, KfkAnd KbkForward and reverse reaction rates, respectively;
Figure GDA0002998792680000034
is a forward reaction rate index;
Figure GDA0002998792680000035
is a reverse reaction rate index;
in the Arrhenius formula, the reaction rate K is calculatedfkThe expression of (a) is:
Figure GDA0002998792680000036
wherein A is a pre-index factor, T is temperature, n is a temperature index, E is activation energy, and R is a gas constant;
the constituent elements of component i include O2，N2，O，N，O+，N+，O2 +，N2 +，NO，NO+And E-。
Preferably, when the complete catalytic wall is adopted to establish the surface catalytic reaction process of the hypersonic target, the components on the wall surface inject the flow
Figure GDA0002998792680000041
The expression of (a) is:
Figure GDA0002998792680000042
wherein u is the normal velocity; d is the diffusivity; ρ is the gas density; sigmaspeciesIs the mass fraction of the components species.
According to the technical scheme, the dynamic change process of the surface temperature of the hypersonic target is effectively simulated, a coupling technology of pneumatic heating and structural heat transfer is formed, and the calculation precision and efficiency of the hypersonic target temperature field simulation are improved. The method also provides a calculation method for simulating the real-time surface temperature distribution condition of the hypersonic speed target in the whole flight envelope or flight trajectory, and has important application value for the research of the thermal protection technology and target characteristics of the hypersonic speed target.
The method adopts a dual-temperature model to establish the thermodynamic non-equilibrium process of the high supersonic speed target streaming, so that the method has higher precision and accords with the physical reality of the high supersonic speed flying target.
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FIG. 1 is a flow chart of a dynamic temperature modeling method according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings by way of examples of preferred embodiments. It should be noted, however, that the numerous details set forth in the description are merely for the purpose of providing the reader with a thorough understanding of one or more aspects of the present invention, which may be practiced without these specific details.
The flow chart of the method for modeling the dynamic temperature of the surface of the hypersonic target provided by the embodiment is shown in fig. 1, and a turbulent flow N-S equation is generally established, wherein:
solving a turbulent flow N-S equation by adopting a Reynolds average method;
the turbulence model adopts a k omega-SST model;
time integral is solved by adopting an implicit format;
the spatial dispersion is solved by adopting a second-order windward format. The embodiment specifically comprises the following steps:
(1) modeling according to process data of pneumatic heating of the hypersonic target; during modeling, hexahedral meshes are adopted in the boundary layer of the windward shock wave of the hypersonic target surface for division, and the dimensionless distance value (namely the y + value) from the centroid of the first layer of meshes to the wall surface is not more than 1. Because the pneumatic heating of the hypersonic speed target is a nonlinear process, a finite element method is adopted to solve a heat transfer equation corresponding to the hypersonic speed target, and the heat conduction process and the transient temperature field of the structure of the hypersonic speed target are calculated.
In the heat transfer equation, the temperature value and the heat flow value and the heat exchange coefficient in the finite element method satisfy the following expression:
Figure GDA0002998792680000051
wherein epsilon is the emissivity of the outer surface material; σ is Stefan-Boltzmann constant; ksThermal conductivity of the heat-proof material; delta is the thickness of the surface heat-proof material; t is0Is the heat transfer equationA temperature value of (1); t is∞Is ambient temperature; t isbThe temperature of the inner layer of the heat-proof layer; h is the convective heat transfer coefficient.
When the finite element method is adopted for solving, the set values comprise: thermal conductivity, specific heat capacity, emissivity of the material, temperature of the structure and thermal boundary conditions of the heat flow. In transient calculations, a time step is defined that fits the entire calculation time (typically 0.001 of the entire time).
It is also worth noting that when the hypersonic target is pneumatically heated, a thermodynamic nonequilibrium process including the circumfluence of the hypersonic target, a chemical reaction nonequilibrium process of air ionization and a surface catalysis reaction process can be generated;
when a thermodynamic non-equilibrium process of the hypersonic target streaming is generated, a two-temperature model is adopted to establish the thermodynamic non-equilibrium process of the hypersonic target streaming, namely, a single temperature T is used for describing the distribution of translational energy and rotational energy of molecules, and another single temperature Tv is used for describing the excitation and translational energy of vibration energy and electrons. The energy balance equation is:
Figure GDA0002998792680000052
E＝Et+Ev；
wherein t is time; rho is density; x is the number ofjIs the length tensor; h is the total enthalpy; u. ofjIs the velocity tensor; lambda [ alpha ]tA translational heat transfer coefficient; lambda [ alpha ]rIs the rotational heat transfer coefficient; t is the temperature; lambda [ alpha ]vIs the vibration heat transfer coefficient; lambda [ alpha ]eIs the electron heat transfer coefficient; t isVIs the vibration temperature; h issIs the enthalpy per unit mass of component s; dsIs the diffusion coefficient of component s; chi shapesIs the molar mass fraction of the component s; μ is the viscosity coefficient; u. ofiIs the velocity tensor; x is the number ofiIs the length tensor; u. ofkIs the velocity tensor; x is the number ofkIs the length tensor; deltaijIs a kronecker function; qradIs radiant energy; e is the total energy; etIs kinetic-rotational energy; evIs the vibration-electron energy.
When the chemical reaction unbalanced process of air ionization is generated, calculating parameters by adopting an independent reverse reaction rate in an Arrhenius equation; the method specifically comprises the following steps:
chemical reaction step k, the expression of which is:
Figure GDA0002998792680000053
wherein M isiIs the chemical symbol of component i; v'ikAnd v ″)ikThe number of chemical equivalents of component i in the reactants and the product, respectively, in reaction step k;
in reaction step k, the rate of formation ω of component iikThe expression of (a) is:
Figure GDA0002998792680000061
wherein, WiIs the molecular weight of component i, KfkAnd KbkForward and reverse reaction rates, respectively;
Figure GDA0002998792680000062
is a forward reaction rate index;
Figure GDA0002998792680000063
is a reverse reaction rate index;
in the Arrhenius formula, the reaction rate K is calculatedfkThe expression of (a) is:
Figure GDA0002998792680000064
wherein A is a pre-index factor, T is temperature, n is a temperature index, E is activation energy, and R is a gas constant;
the constituent elements of component i include O2，N2，O，N，O+，N+，O2 +，N2 +，NO，NO+And E-(i.e., electrons).
When a surface catalytic reaction process is generated, a complete catalytic wall is used to establish the surface catalytic reaction process of the hypersonic target. The component on the wall surface of which is guided
Figure GDA0002998792680000065
The expression of (a) is:
Figure GDA0002998792680000066
wherein u is the normal velocity; d is the diffusivity; ρ is the gas density; sigmaspeciesIs the mass fraction of the components species.
(2) Simulating data of transient heat conduction of surface materials and structures of the hypersonic speed target and modeling;
(3) coupling calculation is carried out on the process data of pneumatic heating of the hypersonic target and the data of transient heat conduction of a simulated target material structure, and the method comprises the following steps:
1) declaring a real-time call of CFD-ACE + in CFD-Fastran;
2) the coupling mode of the heat transfer is stated in the CFD-Fastran, and the transient temperature value T in the heat transfer equation is defined in the statement0Coupling parameters of the bottom and the wall surface of the gas boundary layer;
3) generating a boundary file in the CFD-Fastran, wherein the boundary file comprises grid data of a gas boundary layer;
4) correlating the boundary file in the CFD-ACE + to enable the solid wall surface grids participating in calculation in the CFD-ACE + to correspond to the gas boundary layer grids participating in calculation in the CFD-Fastran one by one;
5) in the setting of the boundary condition of the CFD-ACE +, the interaction parameter on the boundary is stated by using a ubend function as the transient temperature value T in the heat transfer equation0And heat flux density to complete the coupling setup.
(4) And determining the dynamic surface temperature of the hypersonic speed target, and completing dynamic temperature modeling according to the value of the dynamic surface temperature.
The hypersonic target comprises a reentry target flying at a speed of more than 10 Mach or a hypersonic target near a space vehicle.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be construed as the protection scope of the present invention.

Claims (8)

1. A hypersonic speed target surface dynamic temperature modeling method is used for establishing a turbulent flow N-S equation and is characterized by comprising the following steps:
(1) modeling according to process data of pneumatic heating of the hypersonic target;
(2) simulating data of transient heat conduction of surface materials and structures of the hypersonic speed target and modeling;
(3) coupling calculation is carried out on the process data of pneumatic heating of the hypersonic target and the data of transient heat conduction of the simulated target material structure;
(4) determining the dynamic surface temperature of the hypersonic speed target, and completing dynamic temperature modeling according to the value of the dynamic surface temperature;
when the hypersonic target is pneumatically heated, a thermodynamic non-equilibrium process comprising hypersonic target streaming, a chemical reaction non-equilibrium process of air ionization and a surface catalytic reaction process are generated in the step (1);
when a thermodynamic non-equilibrium process of the hypersonic speed target streaming is generated, a thermodynamic non-equilibrium process of the hypersonic speed target streaming is established by adopting a dual-temperature model;
when the chemical reaction unbalanced process of air ionization is generated, calculating parameters by adopting an independent reverse reaction rate in an Arrhenius equation;
when a surface catalytic reaction process is generated, adopting a complete catalytic wall to establish the surface catalytic reaction process of the hypersonic target;
when the double-temperature model is adopted to establish the thermodynamic non-equilibrium process of the hypersonic speed target streaming, the energy balance equation is as follows:
Figure FDA0002967679090000011
E＝Et+Ev；
wherein t is time; rho is density; x is the number ofjIs the length tensor; h is the total enthalpy; u. ofjIs the velocity tensor; lambda [ alpha ]tA translational heat transfer coefficient; lambda [ alpha ]rIs the rotational heat transfer coefficient; t is the temperature; lambda [ alpha ]vIs the vibration heat transfer coefficient; lambda [ alpha ]eIs the electron heat transfer coefficient; t isVIs the vibration temperature; h issIs the enthalpy per unit mass of component s; dsIs the diffusion coefficient of component s; chi shapesIs the molar mass fraction of the component s; μ is the viscosity coefficient; u. ofiIs the velocity tensor; x is the number ofiIs the length tensor; u. ofkIs the velocity tensor; x is the number ofkIs the length tensor; deltaijIs a kronecker function; qradIs radiant energy; e is the total energy; etIs kinetic-rotational energy; evIs the vibration-electron energy.
2. The dynamic temperature modeling method of claim 1, wherein a turbulent N-S equation is established during dynamic temperature modeling, wherein:
solving a turbulent flow N-S equation by adopting a Reynolds average method;
the turbulence model adopts a k omega-SST model;
time integral is solved by adopting an implicit format;
the spatial dispersion is solved by adopting a second-order windward format.
3. The dynamic temperature modeling method according to claim 2, wherein in the step (1), when modeling is performed according to the process data of the pneumatic heating of the hypersonic target, hexahedral meshes are adopted to divide the boundary layer of the windward shock wave of the hypersonic target surface, and the dimensionless distance value from the centroid of the first layer of meshes to the wall surface is not more than 1.
4. The dynamic temperature modeling method of claim 1, wherein step (1) the hypersonic velocity target is pneumatically heated to a nonlinear process, and the heat conduction process and the transient temperature field of the structure of the hypersonic velocity target are calculated by solving the corresponding heat transfer equation by a finite element method;
when the finite element method is adopted for solving, the set values comprise: thermal conductivity, specific heat capacity, emissivity of the material, temperature of the structure and thermal boundary conditions of the heat flow.
5. The dynamic temperature modeling method of claim 4, wherein the temperature and heat flow values in the heat transfer equation and the heat transfer coefficient in the finite element method satisfy the following expression:
Figure FDA0002967679090000021
wherein epsilon is the emissivity of the outer surface material; σ is Stefan-Boltzmann constant; ksThermal conductivity of the heat-proof material; delta is the thickness of the surface heat-proof material; t is0Is the transient temperature value in the heat transfer equation; t is∞Is ambient temperature; t isbThe temperature of the inner layer of the heat-proof layer; h is the convective heat transfer coefficient.
6. The dynamic temperature modeling method of claim 5, wherein the step of performing the coupling calculation of step (3) comprises:
1) declaring a real-time call of CFD-ACE + in CFD-Fastran;
2) the coupling mode of the heat transfer is stated in the CFD-Fastran, and the transient temperature value T in the heat transfer equation is defined in the statement0Coupling parameters of the bottom and the wall surface of the gas boundary layer;
3) generating a boundary file in the CFD-Fastran, wherein the boundary file comprises grid data of a gas boundary layer;
4) correlating the boundary file in the CFD-ACE + to enable the solid wall surface grids participating in calculation in the CFD-ACE + to correspond to the gas boundary layer grids participating in calculation in the CFD-Fastran one by one;
5) in the setting of the boundary condition of the CFD-ACE +, the interaction parameter on the boundary is stated by using a ubend function as the transient temperature value T in the heat transfer equation0And heat flux density to complete the coupling setup.
7. The dynamic temperature modeling method of claim 1, wherein said calculating parameters using independent inverse reaction rates in the arrhenius equation comprises:
chemical reaction step k, the expression of which is:
Figure FDA0002967679090000031
wherein M isiIs the chemical symbol of component i; v'ikAnd v ″)ikThe number of chemical equivalents of component i in the reactants and the product, respectively, in reaction step k;
in reaction step k, the rate of formation ω of component iikThe expression of (a) is:
Figure FDA0002967679090000032
wherein, WiIs the molecular weight of component i, KfkAnd KbkForward and reverse reaction rates, respectively;
Figure FDA0002967679090000033
is a forward reaction rate index;
Figure FDA0002967679090000034
is a reverse reaction rate index;
in the Arrhenius formula, the reaction rate K is calculatedfkThe expression of (a) is:
Figure FDA0002967679090000035
wherein A is a pre-index factor, T is temperature, n is a temperature index, E is activation energy, and R is a gas constant;
the constituent elements of component i include O2，N2，O，N，O+，N+，O2 +，N2 +，NO，NO+And E-。
8. The dynamic temperature modeling method of claim 1, wherein the components on the wall surface induce flow during the catalytic reaction process using the fully catalytic wall to create the hypersonic target
Figure FDA0002967679090000036
The expression of (a) is:
Figure FDA0002967679090000037
wherein u is the normal velocity; d is the diffusivity; ρ is the gas density; sigmaspeciesIs the mass fraction of the components species.
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