CN114626313B - High-speed aerodynamic thermal CFD solving method capable of resolving time-varying thermal response - Google Patents
High-speed aerodynamic thermal CFD solving method capable of resolving time-varying thermal response Download PDFInfo
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Abstract
The invention provides a high-speed aerodynamic thermal CFD solving method capable of resolving time-varying thermal response, which comprises the following steps: according to the basic theory of heat transfer, the surface heating problem of the heat-proof structure is assumed to be a semi-infinite flat plate unsteady state heat conduction problem, so that an integral relation between time-varying temperature and heat flow near the heating surface is constructed, the integral relation is substituted into a surface temperature-heat flow linear correlation obtained based on CFD calculation of given surface temperature and given heat flow, and a surface heat flow result capable of analyzing time-varying heat response is obtained through integration. According to the invention, large-scale unsteady state calculation of air flow and structural heat conduction coupling is not needed, only CFD calculation is needed, and a pneumatic heating result under a resolvable time-varying thermal response condition can be obtained.
Description
Technical Field
The invention relates to the technical field of numerical simulation, in particular to a high-speed aerodynamic thermal CFD solving method capable of resolving time-varying thermal response.
Background
CFD is widely used in the field of aircraft design and evaluation, where thermal boundary conditions need to be determined in order to ensure the fitness of the Navier-Stokes equation in high-speed compressible flow aerodynamic thermal CFD numerical simulation. It is common today to use either a given temperature alone (boundary condition of the first type) or a heat flow (boundary condition of the second type), or a given radiation balance (boundary condition of the generalized third type). The aerodynamic heating results under thermal response conditions when resolving materials are difficult to obtain by a single CFD calculation based on the above boundary conditions, and need to be obtained by unsteady coupling calculation of high-speed flow and structural heat conduction. However, the coupling calculation costs are greatly increased compared to the uncoupled pneumatic heating calculation, which is detrimental to thermal protection assessment and aircraft engineering applications. Therefore, according to the physical characteristics and mathematical connotation of the thermal response of the material, an analysis scheme of the thermal response of the time-varying material for the CFD thermal boundary is established, and a high-speed aerodynamic thermal Computational Fluid Dynamics (CFD) solving method capable of avoiding large-scale coupling calculation is realized.
Disclosure of Invention
The invention aims to provide a high-speed aerodynamic thermal CFD solving method capable of resolving time-varying thermal response, so as to avoid the problem that the cost is greatly increased due to large-scale coupling calculation for acquiring aerodynamic heating results through unstable coupling calculation of high-speed flow and structural heat conduction.
The invention provides a high-speed aerodynamic thermal CFD solving method capable of resolving time-varying thermal response, which comprises the following steps:
step A, setting a given temperature T according to the free incoming flow condition w (x, 0) and a given heat flow q w,g (x) And the surface temperature T is obtained by two CFD calculations w,g (x) And an initial heat flow q w (x,0)；
Step B, constructing a surface temperature-heat flow linear correlation type at the moment t based on the two CFD calculation results of the step A;
step C, given temperature T w (x, 0) and initial heat flow q w (x, 0) is known, or based on the linear relationship of the surface temperature and the heat flow at time t, t after i cycle steps i Time surface temperature T w (x,t i ) And heat flow q w (x,t i ) Known then heat flow q w (x,t i ) Subtracting the surface radiant heat flow q r Obtaining a net heat flow q introduced into the heat-resistant structure c ；
Step D, neglecting the influences of transverse heat conduction in the heat-proof structure and convection heat conduction in the cabin, and assuming the surface heating problem of the heat-proof structure as a semi-infinite flat plate unsteady heat conduction problem, thereby utilizing the net heat flow q c Establishing a time-varying temperature-heat flow integral relation; then at time step Deltat i ＝t i+1 -t i Performing finite difference dispersion on the internal time-to-time temperature-heat flow integral relation, and solving t i+1 Surface temperature at time; to this end, the present time step Δt i Ending the integral calculation in the inner part;
step E, let i=i+1, if i < n, return to step B to perform integration calculation at the next time until solving to t n Surface temperature T at time w (x,t n ) And heat flow q w (x,t n )。
Further, the temperature T is set in the step A w (x, 0) is the temperature at the initial moment of thermal response, given the heat flow q w,g (x) Is an adiabatic condition; then respectively to the set temperature T w (x, 0) and a given heat flow q w,g (x) CFD calculations were performed:
according to a given temperature T w (x, 0) performing CFD calculation to obtain initial heat flow q w (x,0)；
According to a given heat flow q w,g (x) Performing CFD calculation to obtain surface temperature T w,g (x)。
Further, the linear correlation of the surface temperature and the heat flow at the time t in the step B is as follows:
wherein the surface temperature T at time T w (x, t) and heat flow q w (x, T) is an unknown variable but the two are related to each other and the surface temperature T w The time t corresponding to (x, t) is unknown.
Further, in step C, the heat flow q is radiated from the surface r Expressed as:
wherein, E represents the surface emissivity; sigma represents a Stefan-Boltzmann constant in W/(m) 2 ·K 4 )；T w Represents the surface temperature in K, T ∞ The ambient temperature is indicated in K.
Further, the net heat flow q is utilized in step D c The established time-varying temperature-heat flow integral relationship is as follows:
where α represents the thermal diffusivity, κ represents the adiabatic index, and s represents the intermediate variable.
Further, in step D, at time step Δt i ＝t i+1 -t i Performing finite difference dispersion on the internal time-to-time temperature-heat flow integral relation, and solving t i+1 The formula of the surface temperature at the moment is as follows:
wherein T is w (x,t i+1 ) The surface temperature at time t+1 is shown.
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows:
according to the invention, large-scale unsteady state calculation of air flow and structural heat conduction coupling is not needed, only CFD calculation is needed, and a pneumatic heating result under a resolvable time-varying thermal response condition can be obtained.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following description will briefly describe the drawings in the embodiments, it being understood that the following drawings only illustrate some embodiments of the present invention and should not be considered as limiting the scope, and that other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for solving a CFD of high-speed aerodynamic heat with resolvable time-varying thermal response in an embodiment of the invention.
FIG. 2 is a schematic diagram showing the linear relationship between the surface temperature and the heat flow according to the embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Examples
In order to avoid the problem that the cost is greatly increased due to large-scale coupling calculation for acquiring the pneumatic heating result through unsteady coupling calculation of high-speed flow and structural heat conduction, the invention is characterized in that: according to the basic theory of heat transfer, the surface heating problem of the heat-proof structure is assumed to be a semi-infinite flat plate unsteady state heat conduction problem, so that an integral relation between time-varying temperature and heat flow near the heating surface is constructed, the integral relation is substituted into a surface temperature-heat flow linear correlation obtained based on CFD calculation of given surface temperature and given heat flow, and a surface heat flow result capable of analyzing time-varying heat response is obtained through integration. Thus solving for t with a steady solution by high-speed compressible flow aerodynamic thermal CFD n Surface temperature T at time w (x,t n ) And heat flow q w (x,t n ) For example, as shown in fig. 1, the present embodiment provides a method for solving a CFD of high-speed aerodynamic heat with resolvable time-varying thermal response, which includes the following steps:
step A, as shown in FIG. 1, in steps 01-04, a given temperature T is set according to the free incoming flow conditions w (x, 0) and a given heat flow q w,g (x) And the surface temperature T is obtained by two CFD calculations w,g (x) And an initial heat flow q w (x,0)；
Wherein the given temperature T w (x, 0) is the temperature at the initial moment of thermal response, given the heat flow q w,g (x) Is an adiabatic condition; then respectively to the set temperature T w (x, 0) and a given heat flow q w,g (x) CFD calculations were performed:
according to a given temperature T w (x, 0) performing CFD calculation to obtain initial heat flow q w (x,0)；
According to a given heat flow q w , g (x) Performing CFD calculation to obtain surface temperature T w , g (x)。
Step B, as shown in the step 05-06 of FIG. 1, based on the two CFD calculation results of the step A, constructing a linear correlation formula of the surface temperature and the heat flow at the time t:
wherein the surface temperature T at time T w (x, t) and heat flow q w (x, T) is an unknown variable but the two are related to each other to satisfy the linear relationship shown in FIG. 2, and the surface temperature T w The time t corresponding to (x, t) is unknown.
Step C, as shown in FIG. 1, at 07 th to 09 th steps, given a temperature T w (x, 0) and initial heat flow q w (x, 0) is known, or based on the linear relationship of the surface temperature and the heat flow at time t, t after i cycle steps i Time surface temperature T w (x,t i ) And heat flow q w (x,t i ) Known then heat flow q w (x,t i ) Subtracting the surface radiant heat flow q r Obtaining a net heat flow q introduced into the heat-resistant structure c 。
The surface radiant heat dissipation heat flow is expressed as:
wherein, E represents the surface emissivity; sigma represents a Stefan-Boltzmann constant in W/(m) 2 ·K 4 )；T w The surface temperature is expressed in K; t (T) ∞ The ambient temperature is indicated in K.
The following energy balance relationship is satisfied on the surface:
q c (x，t i )＝q w (x，t i )-q r (x，t i )
wherein q c (x,t i ) I.e. t after i cycle steps i Net heat flow at time; q r (x,t i ) I.e. t after i cycle steps i The surface at the moment radiates the heat dissipation heat flow.
Step D, as shown in step 10 of FIG. 1, ignoring the effects of lateral heat conduction in the heat-shielding structure and convection heat conduction in the cabin, and assuming the surface heating problem of the heat-shielding structure as a semi-infinite flat plate unsteady heat conduction problem, thereby utilizing the net heat flow q c Establishing a time-varying temperature-heat flow integral relation:
where α represents the thermal diffusivity, κ represents the adiabatic index, and s represents the intermediate variable.
Then at time step Deltat i ＝t i+1 -t i Performing finite difference dispersion on the internal time-to-time temperature-heat flow integral relation, and solving t i+1 Surface temperature at time:
wherein T is w (x,t i+1 ) Surface at time t+1A temperature;
to this end, the present time step Δt i The integral calculation in the inner is ended.
Step E, as shown in steps 10-11 of fig. 1, let i=i+1, if i < n, return to step B to perform the next time integration calculation until solving to t n Surface temperature T at time w (x,t n ) And heat flow q w (x,t n ) The solution ends.
According to the method, large-scale unsteady state calculation of air flow and structural heat conduction coupling is not needed, only CFD calculation is needed, pneumatic heating results under the resolvable time-varying thermal response condition can be obtained, the cost is greatly reduced, rapid assessment of the pneumatic thermal environment is facilitated, and design and engineering application of the aircraft thermal protection system are supported.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A high-speed aerodynamic thermal CFD solving method capable of resolving time-varying thermal response is characterized by comprising the following steps:
step A, setting a given temperature T according to the free incoming flow condition w (x, 0) and a given heat flow q w,g (x) And the surface temperature T is obtained by two CFD calculations w,g (x) And an initial heat flow q w (x,0)；
Step B, constructing a surface temperature-heat flow linear correlation type at the moment t based on the two CFD calculation results of the step A;
step C, given temperature T w (x, 0) and initial heat flow q w (x, 0) is known, or based on the linear relationship of the surface temperature and the heat flow at time t, t after i cycle steps i Time surface temperature T w (x,t i ) And heat flow q w (x,t i ) Known then heat flow q w (x,t i ) Subtracting outSurface radiation heat dissipation heat flow q r Obtaining a net heat flow q introduced into the heat-resistant structure c ；
Step D, neglecting the influences of transverse heat conduction in the heat-proof structure and convection heat conduction in the cabin, and assuming the surface heating problem of the heat-proof structure as a semi-infinite flat plate unsteady heat conduction problem, thereby utilizing the net heat flow q c Establishing a time-varying temperature-heat flow integral relation; then at time step Deltat i ＝t i+1 -t i Performing finite difference dispersion on the internal time-to-time temperature-heat flow integral relation, and solving t i+1 Surface temperature at time; to this end, the present time step Δt i Ending the integral calculation in the inner part;
step E, let i=i+1, if i < n, return to step B to perform integration calculation at the next time until solving to t n Surface temperature T at time w (x,t n ) And heat flow q w (x,t n )；
Using the net heat flow q in step D c The established time-varying temperature-heat flow integral relationship is as follows:
wherein α represents a thermal diffusivity, κ represents an adiabatic index, s represents an intermediate variable;
in step D at time step Δt i ＝t i+1 -t i Performing finite difference dispersion on the internal time-to-time temperature-heat flow integral relation, and solving t i+1 The formula of the surface temperature at the moment is as follows:
wherein T is w (x,t i+1 ) The surface temperature at time t+1 is shown.
2. The method of resolving a time-varying thermal response in a high-speed aerodynamic thermal CFD solution according to claim 1, wherein the temperature T is given in step a w (x, 0) is the temperature at the initial moment of thermal response, given the heat flow q w,g (x) Is an adiabatic condition; then respectively to the set temperature T w (x, 0) and a given heat flow q w,g (x) CFD calculations were performed:
according to a given temperature T w (x, 0) performing CFD calculation to obtain initial heat flow q w (x,0)；
According to a given heat flow q w,g (x) Performing CFD calculation to obtain surface temperature T w,g (x)。
3. The method of claim 2, wherein the linear correlation of the surface temperature and the heat flow at time t in the step B is as follows:
wherein the surface temperature T at time T w (x, t) and heat flow q w (x, T) is an unknown variable but the two are related to each other and the surface temperature T w The time t corresponding to (x, t) is unknown.
4. The method of claim 3, wherein in step C, the surface radiant heat flow q is r Expressed as:
wherein, E represents the surface emissivity; sigma represents a Stefan-Boltzmann constant in W/(m) 2 ·K 4 )；T w The surface temperature is expressed in K; t (T) ∞ The ambient temperature is indicated in K.
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| CN105095603A (en) * | 2015-09-09 | 2015-11-25 | 哈尔滨工业大学 | Multi-field coupling transient numerical method for hypersonic flow-heat transfer and structural response |
| CN109408926A (en) * | 2018-10-12 | 2019-03-01 | 大连理工大学 | The method for solving labyrinth multidimensional Transient Non-linear Heat Conduction indirect problem |
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| CN101916314B (en) * | 2010-08-16 | 2012-12-05 | 北京理工大学 | High-speed aircraft lifting surface aerodynamic heating structure multidisciplinary optimization design platform |
| GB2591972B8 (en) * | 2014-12-11 | 2022-03-16 | Fulton Group N A Inc | Ribbed tubeless heat exchanger for fluid heating systems including a rib component and methods of manufacture thereof |
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| CN109408926A (en) * | 2018-10-12 | 2019-03-01 | 大连理工大学 | The method for solving labyrinth multidimensional Transient Non-linear Heat Conduction indirect problem |
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