A high-efficiency and high-precision calculation method for a multi-variable transient fluid-structure coupling temperature field

Abstract

The application discloses a kind of high-efficiency high-precision calculation method for flight envelope fluid-solid temperature field, belong to heat transfer field.Method is:1) for the transition stage in flight envelope, fluid-solid coupling temperature field is obtained by using conjugate heat transfer calculation of transition stage;2) after the completion of conjugate heat transfer calculation of transition stage in flight envelope, fluid-solid decoupling is extracted;3) for the steady-state stage in flight envelope, the efficient calculation of finite element reduction is carried out to solid temperature field, and the full-time-domain solid temperature field of stable stage is obtained;4) the solid temperature of last time is extracted, and the fluid-solid temperature field is re-coupled, and the parameter is used as the initial field of fluid-solid coupling temperature field calculation of next transition stage;5) for the second transition stage, conjugate heat transfer calculation of fluid-solid coupling temperature field is carried out again, and 1) is repeated;By analogy, the fluid-solid transient temperature field calculation of whole flight envelope is completed.The application can quickly obtain the temperature field of transient process, reduce the consumption of calculation resources while ensuring the calculation precision, and greatly improve the calculation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of heat transfer and relates to an efficient and high-precision calculation method for transient temperature fields in fluid-solid systems. Background Technology

[0002] Currently, common numerical solution methods for fluid-structure interaction temperature fields, such as the finite element method, finite volume method, and finite difference method, suffer from several drawbacks. First, the large number of degrees of freedom in the discrete scheme leads to long computation times and large storage requirements. Second, transient monitoring of fluid-structure interaction temperature fields during multivariable transient processes, such as those involving the entire flight envelope, consumes excessive computational resources. The flight envelope includes transition and steady-state phases. If coupled solutions are used for all stages of the fluid-structure interaction temperature field within the entire flight envelope, the computation time and storage requirements will be too long. Traditional numerical solution methods are difficult to meet the requirements of real-time control and rapid prediction in practical engineering.

[0003] Kazemi-Kamyab[V.KAZEMI-KAMYAB,VAN ZUIJLEN AH,BIJL H.Analysis and application of high order implicit Runge-Kutta schemes for unsteady conjugateheat transfer:A strongly-coupled approach[J].Journal of [Computational Physics, 2014, 272:471-486] et al. developed a transient tightly coupled heat transfer algorithm that combines all physical processes within a fluid and solid. The algorithm was illustrated and verified using an example of unsteady conjugate natural convection heat transfer in a rectangular closed body. The results showed that the algorithm could achieve a high degree of agreement between the calculated and experimental results. However, this transient tightly coupled fluid-solid temperature field algorithm requires a large amount of computational resources and is difficult to use to solve practical complex engineering problems. On the other hand, a typical algorithm in fluid-solid transient temperature field calculation decouples the fluid-solid temperature field: it is approximately assumed that the boundary conditions for the solid temperature field calculation are constant during the calculation time, transforming the transient problem of the flow field into a steady-state problem. Then, the thermal boundary obtained from the flow field calculation is used for the solid temperature field calculation. This algorithm improves computational efficiency to some extent, but it does not consider the influence of the solid temperature field on the flow field, nor the influence of transient changes in the flow field during the transition phase on the fluid-solid temperature field. This algorithm leads to a loss of accuracy in the fluid-solid temperature field calculation. Currently, it is difficult to balance computational efficiency and accuracy in the calculation of temperature fields under long-term and multi-condition conditions such as flight envelopes, and there is a lack of a set of efficient and high-precision calculation methods. Summary of the Invention

[0004] To address the aforementioned problems in existing technologies, this invention provides an efficient and high-precision method for calculating the fluid-structure interaction temperature field of variable transient processes such as flight envelopes. Variable transient heat transfer processes refer to the alternating changes in the flow field between steady-state and transitional phases during solid transient heat transfer; the calculation of the fluid-structure interaction temperature field of the flight envelope is a typical variable transient heat transfer problem. Figure 3 In the flight envelope shown, t1 * t2 * t3 * Let t1, t2, and t3 be symmetrical operating points, where (t2-t1) >> t1, (t3) >> t2. * -t3)>>(t3-t2).

[0005] To achieve the above objectives, the specific technical solution adopted by the present invention is as follows:

[0006] An efficient and high-precision method for calculating the transient fluid-solid temperature field of a flight envelope, which calculates the fluid-solid coupled temperature field during the transition phase and the solid temperature field during the steady phase of the flight envelope, while ensuring the continuity of the fluid and solid temperature fields throughout the entire flight envelope, includes the following steps:

[0007] The first step involves using conjugate heat transfer calculations to obtain the fluid-structure interaction temperature field during the transition phase of the flight envelope, as detailed below:

[0008] 1.1) The fluid and solid geometry models share a topology, ensuring that the computational meshes of the fluid and solid share nodes at the fluid-solid interface;

[0009] 1.2) The governing equations for calculation include the solid heat conduction equation and the fluid flow and heat transfer equation, among which the fluid heat transfer equation includes convective heat transfer, fluid self-conduction and viscous heat dissipation.

[0010] 1.3) Considering the influence of fluid flow and solid wall interaction on the wall heat transfer boundary, the wall temperature, heat flux density, and convective heat transfer coefficient are used as intermediate iterative variables in the process, determined by the dynamic process of heat exchange between the fluid and the solid. That is, it is necessary to consider both the convective heat transfer between the fluid and the solid and the heat conduction of the solid itself. The temperature parameter is implicitly handled in the iterative equation during the solution. Based on the iterative exchange of boundary conditions at each fluid-solid interface, thermal equilibrium is eventually reached at each interface. The solution condition is that the heat flux density and temperature at the coupling surface are continuous.

[0011] The second step, after completing the conjugate heat transfer calculation during the transition phase in the flight envelope, involves fluid-structure decoupling and extracting relevant parameters for the next calculation, as follows:

[0012] 2.1) Extract the fluid temperature field T at the last moment t1 of the transition phase. f (x,y,z)|t＝t1 ;

[0013] 2.2) Calculate the heat transfer coefficient h(x,y,z) at the fluid-structure interaction surface at the last moment of the transition phase. t＝t1 The heat transfer coefficient is obtained from the fluid temperature field results obtained in 2.1) and the solution conditions in 1.3);

[0014] 2.3) Extracting the solid-state temperature T at the final moment of the transition phase. s (x, y, z)| t＝t1 ;

[0015] After completing the second step, we obtain h(x, y, z)| t＝t1 Used as parameters for the next calculation process; the resulting T s (x, y, z)| t＝t1 This serves as the initial value for the next step in the solid temperature field calculation process.

[0016] The third step involves performing efficient finite element method (FEM) calculations on the solid temperature field during the steady-state phase of the flight envelope, using third-type boundary conditions and a heat transfer coefficient of h(x, y, z). t＝t1 Let it be abbreviated as h below, and the initial temperature as T. s (x, y, z)| t＝t1 The details are as follows:

[0017] 31) Finite element discretization scheme for transient heat conduction problems:

[0018]

[0019] Where C, K, and F are the overall structural heat capacity matrix, heat conduction matrix, and temperature load vector matrix, respectively, and T is the temperature matrix.

[0020] When the influence of heat sources is not considered and the third type of boundary condition is used:

[0021]

[0022] in, The element matrices that make up matrices C, K, and F:

[0023]

[0024]

[0025]

[0026]

[0027] Where, k iLet i be the thermal conductivity of the material, i = 1, 2, 3, and the subscripts x, y, z indicate the direction; h is the heat transfer coefficient h(x, y, z)| t＝t1 This is obtained from the second step; ρ is the material density; c is the material specific heat; T a T obtained in 2.1) f (x, y, z)| t＝t1 Components at the fluid-structure interaction surface; N i N j Γ represents a structure-dependent function; Ω represents the entire computational domain of the solid; Γ represents the computational boundary region.

[0028] 3.2) Solve equation system (1) to obtain the total nodal temperatures of the solid:

[0029] T(t) = {T1(t),T2(t),…,T} D (t)} T (4)

[0030] Where D is the number of nodes in the computational grid space.

[0031] In the local time domain during the stable phase, T(t) is calculated to generate the instantaneous image matrix A:

[0032] A = {T(t1),T(t2),…,T(t)} M (5)

[0033] Where M is the number of nodes in the local time domain of the stable phase, which can usually be taken as 1 / 40 to 1 / 20 of the length of the entire time domain of the stable phase.

[0034] 3.3) Define the correlation matrix R, find its eigenvalues ​​and eigenvectors, and construct the POD basis:

[0035]

[0036] Where λ is the eigenvalue of the matrix. Let λ be the eigenvector corresponding to λ, and l be the number of eigenvalues.

[0037] The model is reduced in order by taking the first r basis. The selection rule for r is: when the first r POD modes after truncation account for more than 99.9% of the energy captured by the full order modes, the minimum value of r is taken, as shown in Equation (7).

[0038]

[0039] 3.4) As relevant studies show, the temperature at any time on a node in a discrete structural model can be represented by a linear combination of a set of POD bases. That is, in transient heat conduction problems, the temperature field at any time on any node can be represented as a linear combination of POD bases:

[0040] T=Φα (8)

[0041] Combining equation (1), we get:

[0042]

[0043] The unknown quantity in equation (9) is the correlation coefficient α. After obtaining α, it can be substituted into equation (8) to realize the calculation of the solid temperature field in the whole time domain during the steady stage.

[0044] After the third step of the calculation is completed, the solid temperature field in the whole time domain during the steady-state phase is obtained.

[0045] Step 4: Extract the solid temperature T at the final time t2 from the stable phase full-time domain solid temperature field obtained in Step 3. s (x,y,z)| t＝t2 Recouple the fluid-structure temperature field: Using the T obtained in 2.1) f (x,y,z)| t＝t1 With T s (x,y,z)| t＝t2 This serves as the initial field for calculating the fluid-structure interaction temperature field in the next transition stage.

[0046] Step 5: Perform fluid-structure interaction temperature field conjugate heat transfer calculations again for the second transition stage, repeating the calculation in step 1.

[0047] By analogy, the transient temperature field calculation of the fluid-structure interaction across the entire flight envelope is completed.

[0048] The beneficial effects of this invention are: it can efficiently and accurately calculate and predict the temperature field of the entire flight envelope, quickly obtain the temperature field of variable transient processes, reduce the consumption of computing resources while ensuring the accuracy of calculation, and greatly improve the calculation efficiency. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the efficient and high-precision calculation method for the variable transient fluid-structure interaction temperature field involved in this invention.

[0050] Figure 2 This is a schematic diagram illustrating the application of this efficient and high-precision calculation method for the variable transient fluid-structure interaction temperature field in flight envelope calculation.

[0051] Figure 3 This is a schematic diagram of the full flight envelope.

[0052] Figure 4 This is a flight envelope diagram used for calculation in an embodiment of the present invention.

[0053] Figure 5 This is the geometric model used for calculation in the embodiments of the present invention.

[0054] Figure 6 This is a verification diagram of some of the calculation results of this invention.

[0055] Figure 7 This is a comparison chart of the computational efficiency of the present invention. Detailed Implementation

[0056] The specific embodiments of the present invention are described in detail below with reference to the technical solutions and accompanying drawings.

[0057] The first step is to address, for example Figure 4 The transition phase ① in the semi-flight envelope shown employs a conjugate heat transfer algorithm. Figure 5 The temperature field of the aero-engine support plate structure was calculated, where A and B are temperature time history measurement points used for quantitative analysis of the structure's time-domain temperature field. After the first step, the fluid-structure interaction temperature field of the transition stage ① was obtained.

[0058] The second step, the transition phase ① After the conjugate heat transfer calculation is completed, the fluid-structure interaction is decoupled, and the relevant parameters for the next calculation are extracted:

[0059] 2.1) Extract the fluid temperature field T at the last moment t1 of the transition phase ①, i.e., at the 60th second in the example. f (x, y, z)| t＝t1 ;

[0060] 2.2) Calculate the heat transfer coefficient h(x, y, z) at the fluid-structure interaction surface at the last moment t1 of the transition phase ①, i.e., at the 60th second. t＝t1 ;

[0061] 2.3) Extracting the solid-state temperature T at the final moment t1 of the transition phase ① s (x, y, z)| t＝t1 ;

[0062] After completing the second step, we obtain h(x, y, z)| t＝t1 Used as parameters for calculating the steady-state phase ②; to obtain T s (x, y, z)| t＝t1 This serves as the initial value for the calculation process of the solid temperature field during the stable phase ②.

[0063] The third step involves performing efficient finite element method (FEM) calculations on the solid temperature field during the stable phase ② of the flight envelope. The calculations employ third-type boundary conditions, with a heat transfer coefficient of h(x, y, z). t＝t1 The initial temperature is T s (x, y, z)| t＝t1The full-order temperature field for duration Φt is calculated with time step Δt, forming the transient temperature matrix A. In this embodiment, Δt = 2s and Φt = 50s. A is processed by combining equations (6) and (7) to obtain the reduced-order basis Φ1. After substituting the correlation coefficient α1 into equation (9), the correlation coefficient α1 is substituted into equation (8) to obtain the solid temperature field of steady-state stage ② (t1-t2). In this embodiment, t1 = 60s and t2 = 2000s.

[0064] After the calculation in the third step is completed, the solid temperature field in the entire time domain of the stable stage ② (t1-t2) is obtained.

[0065] Step 4: Extract the solid temperature T at the last moment t2, i.e., the solid temperature at the 2000th second, from the steady-state full-time domain solid temperature field obtained in Step 3. s (x, y, z)| t＝t2 Recouple the fluid-structure temperature field: T s (x, y, z)| t＝t2 T obtained in 2.1) f (x, y, z)| t＝t1 As the initial field for calculating the fluid-structure interaction temperature field in the next transition stage ③ (t2-t3), t3 = 2010s in this example.

[0066] Step 5: For transition phase ③, perform conjugate heat transfer calculations on the fluid-structure interaction temperature field again, repeat step 1, and obtain the heat transfer coefficient h3(x, y, z) of the fluid-structure interaction surface at time t3 (2010s) and the overall solid temperature T. s (x, y, z)| t＝t3 Proceed to the next stable phase ④ solid temperature field reduction calculation, and so on, to complete the flight envelope 0-t3. * That is, the calculation of the transient temperature field of the fluid and solid during the period from 0 to 4000s in the example.

[0067] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A highly efficient and accurate method for calculating the fluid-structure temperature field of a flight envelope, characterized in that, Includes the following steps: The first step is to use conjugate heat transfer calculations to obtain the fluid-structure interaction temperature field during the transition phase of the flight envelope. The second step is to decouple the fluid and solid structures after the conjugate heat transfer calculation in the transition phase of the flight envelope is completed, and extract the relevant parameters for the next step of the calculation. The second step is as follows: 2.1) Extract the last moment of the transition phase fluid temperature field ; 2.2) Calculate the heat transfer coefficient of the fluid-structure interaction surface at the last moment of the transition phase. The heat transfer coefficient is obtained from the fluid temperature field results in 2.1) and the boundary conditions in 1.3); 2.3) Extracting the solid-state temperature at the final moment of the transition phase. ; After completing the second step, you will get... Used as parameters for the next calculation process; to obtain As initial values ​​for the next step of solid temperature field calculation; The third step is to perform efficient finite element calculations with reduced order for the solid temperature field during the steady-state phase of the flight envelope, and obtain the solid temperature field in the entire time domain during the steady-state phase. The third step involves performing efficient finite element method (FEM) calculations on the solid temperature field during the steady-state phase of the flight envelope, using third-type boundary conditions and a heat transfer coefficient of [value missing]. The following is abbreviated as The initial temperature is The details are as follows: 3.1) Finite element discretization scheme for transient heat conduction problems: （1） Where C, K, and F are the overall structural heat capacity matrix, heat conduction matrix, and temperature load vector matrix, respectively, and T is the temperature matrix; When the influence of heat sources is not considered and the third type of boundary condition is used: （2） in, The element matrices that make up matrices C, K, and F: （3） in, The thermal conductivity of the material is given by i = 1, 2, 3, where the subscripts x, y, z indicate the direction. heat transfer coefficient This is obtained from the second step; The density of the material; c Specific heat of the material; for Components at the fluid-structure interaction surface; For structurally related functions Represents the entire computational domain of a solid; Indicates the region of the calculated boundary surface; 3.2) Solve the system of equations (1) to obtain the total nodal temperatures of the solid: Where D is the number of nodes in the computational grid space; Calculation in the local time domain during the stable phase Generate the instantaneous image matrix A: （5） Where M is the number of time length nodes in the local time domain of the stable phase, which can be taken as 1 / 40 to 1 / 20 of the length of the entire time domain of the stable phase; 3.3) Define the correlation matrix R, find its eigenvalues ​​and eigenvectors, and construct the POD basis: （6） in, These are the eigenvalues ​​of the matrix. for The corresponding feature vector, The number of eigenvalues; We take the first r bases for model order reduction analysis, where r is selected according to the following rules: （7） 3.4) As relevant research shows, the temperature at any time on a node in a discrete structural model can be represented by a linear combination of a set of POD bases. That is, in transient heat conduction problems, the temperature field at any time on any node can be represented as a linear combination of POD bases: （8） Combining equation (1), we get: （9） The unknown quantity in equation (9) is the correlation coefficient. Seeking Substituting equation (8) into the equation allows for the calculation of the solid temperature field across the entire time domain during the steady-state phase. After the third step of the calculation is completed, the solid temperature field in the whole time domain during the steady-state phase is obtained; Step 4: Extract the solid temperature at the last moment from the stable stage full-time domain solid temperature field obtained in Step 3; recouple the fluid-solid temperature field: use the relevant parameters obtained in Step 2 as the initial field for calculating the fluid-solid coupled temperature field in the next transition stage; Step 5: Perform fluid-structure interaction temperature field conjugate heat transfer calculations again for the second transition stage, repeating the calculation in step 1; By analogy, the transient temperature field calculation of the fluid-structure interaction across the entire flight envelope is completed.

2. The efficient and high-precision calculation method for the fluid-structure temperature field of a flight envelope according to claim 1, characterized in that, The first step is as follows: 1.1) The fluid and solid geometry models share a topology, ensuring that the computational meshes for the fluid and solid share nodes at the fluid-solid interface; 1.2) The governing equations for calculation include the solid heat conduction equation and the fluid heat transfer equation, wherein the fluid heat transfer equation includes convective heat transfer, fluid self-conduction, and viscous heat dissipation. 1.3) Considering the influence of fluid flow and solid wall interaction on the wall heat transfer boundary, the wall temperature, heat flux density and convective heat transfer coefficient are taken as unknown process parameters. The temperature parameter is implicitly handled in the iterative equation during the solution. Based on the iterative exchange of boundary conditions at each fluid-solid interface, thermal equilibrium is eventually reached at each interface. The boundary condition is that the heat flux density and temperature at the coupling surface are continuous.

3. The efficient and high-precision calculation method for the fluid-structure temperature field of a flight envelope according to claim 1, characterized in that, The fourth step is to extract the final moment from the stable phase full-time domain solid temperature field obtained in the third step. solid temperature Recouple the fluid-structure temperature field: The temperature field obtained in step 2.1) This serves as the initial field for calculating the fluid-structure interaction temperature field in the next transition stage.

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