Spacecraft nonlinear thermal network solving method based on analysis and iteration fusion

Abstract

The invention discloses a spacecraft nonlinear thermal network solving method based on analysis and iteration fusion. According to the method, starting from the physical mechanism of actual radiative heat transfer, a thermal network equation representing the conduction-radiation problem is discretized into equations containing a first power and a fourth power, direct analysis and solution are carried out through a rooting formula, and then numerical iteration methods such as Jacobi and Gaussian-Seidel are fused, so that the temperature of each node is solved and obtained. The method is particularly suitable for the field of spacecraft heat transfer with radiation as a main heat transfer mode, can also be used for solving a heat network in a conventional heat transfer scene, and has important practical engineering application significance.

Description

Technical Field

[0001] The present application relates to the technical field of spacecraft heat transfer, and in particular to a method for solving a spacecraft nonlinear thermal network by integrating analysis and iteration. Background Art

[0002] The basic modes of heat transfer include conduction, convection and radiation.

[0003] After the thermal analysis model is established, the energy balance equation of the node thermal network of N nodes is as follows:

[0004]

[0005] Among them, the subscripts i and j represent nodes. i is the temperature of node i, C i is the heat capacity of node i, t is the time, q i The heat absorbed by node i, including the heat generated by the device itself, temperature control heating, and heat flow received from the outside; D ji and G ji They represent the linear thermal conductivity and fourth-power nonlinear radiation thermal conductivity from node j to i respectively.

[0006] The left side of the above equation is the rate of change of the internal energy of the node, and the right side is the heat absorbed by the node, the linear heat transfer rate flowing into the node, and the radiation heat transfer rate flowing into the node. By solving the above equations, the temperature of each node is obtained.

[0007] For most spacecraft, since they are in vacuum conditions, their heat transfer methods are mainly conduction and radiation. For some nodes where the conduction heat transfer is relatively small (such as in the insulation state) or there is no conduction heat transfer, the relevant node equations may not converge due to the simplification of the fourth power terms characterizing the radiation into constant terms or linear terms, which may lead to the failure of solving the spacecraft thermal network. Summary of the invention

[0008] The present application provides a method for solving a spacecraft nonlinear thermal network by integrating analysis and iteration, the purpose of which is to effectively reduce the number of iterations and improve the success rate and speed of solving a spacecraft nonlinear thermal network. The method is particularly suitable for the field of spacecraft heat transfer where radiation is the main heat transfer method.

[0009] In the first aspect, a method for solving a spacecraft nonlinear thermal network by analytic and iterative fusion is provided, including:

[0010] (1) Perform solution settings, including setting the initial temperature value of each node, convergence criteria, and relaxation factor;

[0011] (2) Update the thermal network equation AT according to the first iteration step of the current time as the time step increases i4 +BT i +E=0 coefficients A, B, E;

[0012] (3) At the current iteration step at the current time, the thermal network equations are analytically solved in the order of i = 1 to N, where N is the total number of nodes;

[0013] (4) Determine whether all nodes meet the convergence criterion; if all meet the convergence criterion, output the temperature results of all nodes at the current moment and go to step (7); otherwise, go to step (5);

[0014] (5) Relax the temperature results of all nodes;

[0015] (6) The iteration step increases, enters the next iteration step, and returns to step (3);

[0016] (7) If the current solution time is greater than or equal to the solution end time, the entire solution is completed; otherwise, return to step (2).

[0017] In combination with the first aspect, in certain implementations of the first aspect, in step (1), a solution end time and a time step are also set.

[0018] In conjunction with the first aspect, in certain implementations of the first aspect, in step (2),

[0019]

[0020] Subscripts i and j represent nodes, T i is the temperature of node i at the current moment, T i,t-Δt is the temperature of node i at the last moment, Δt is the time step, T j is the temperature of node j, C i is the heat capacity of node i, q i is the heat absorbed by node i, D ji represents the linear thermal conductivity from node j to i, G ji represents the fourth-power nonlinear radiation thermal conductivity from node j to i.

[0021] In combination with the first aspect, in some implementations of the first aspect, for a steady-state condition,

[0022] In conjunction with the first aspect, in certain implementations of the first aspect, in step (3), there are specifically the following cases:

[0023] a. When A = 0, that is, there is no radiation heat coupling with other nodes, then

[0024] b. When B = 0, that is, there is no conduction thermal coupling with other nodes in the steady state, then

[0025] c. For other cases, use the root-finding formula to find the real number solution as follows:

[0026]

[0027] in

[0028] In combination with the first aspect, in certain implementations of the first aspect, in step (3), when performing T i When solving the problem, the coefficients A, B and E of the equation group are updated according to the obtained temperature.

[0029] In combination with the first aspect, in some implementations of the first aspect, for the Jacobi iteration method, T j Take the temperature after relaxation in the previous iteration.

[0030] In combination with the first aspect, in some implementations of the first aspect, for the Gauss-Seidel iterative method, if the temperature T j , T j Take the value already calculated in this iteration, otherwise take the temperature after relaxation in the previous iteration step.

[0031] In combination with the first aspect, in certain implementations of the first aspect, in step (4), the convergence criterion is that the absolute value of the temperature difference between the current iteration step and the previous iteration step does not exceed the convergence criterion.

[0032] In combination with the first aspect, in certain implementations of the first aspect, in step (5), the relaxation process satisfies: T i (n) =T i (n-1) +α(T i (n) -T i (n-1) ), where α is the relaxation factor, T i (n) is the temperature of node i at the current iteration step number n, T i (n-1) is the temperature of node i in the previous iteration step number n-1.

[0033] Compared with the prior art, the solution provided by this application includes at least the following beneficial technical effects:

[0034] Starting from the physical mechanism of actual radiation heat transfer, this method discretizes the thermal network equations that characterize the conduction-radiation problem into equations containing first-order and fourth-order equations, and directly solves them analytically through root-finding formulas, and then integrates numerical iteration methods such as Jacobi and Gauss-Seidel to solve the temperature of each node, making the node temperature solution success rate of the spacecraft thermal analysis model higher and the convergence speed faster. It is particularly suitable for the field of spacecraft heat transfer where radiation is the main heat transfer method, and can also be used for thermal network solutions in conventional heat transfer scenarios, which has important practical engineering application significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the implementation steps of the present invention. DETAILED DESCRIPTION

[0036] The present application is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] The present invention provides a method for solving a spacecraft nonlinear thermal network by analytic and iterative fusion, taking transient state as an example (steady state can be regarded as a special value situation), comprising the following steps.

[0038] (1) Perform solution settings, including setting the initial temperature value of each node, convergence criteria, and relaxation factor. For transient solutions, it is also necessary to set the solution end time and time step.

[0039] (2) Update the thermal network equation AT according to the first iteration step of the current time as the time step increases i 4 +BT i +E=0 coefficients A, B, E.

[0040] Subscripts i and j represent nodes, T i is the temperature of node i at the current moment (to be determined), T i,t-Δt is the temperature of node i at the last moment (known), Δt is the time step, T j is the temperature of node j (known), C i is the heat capacity of node i, q i is the heat absorbed by node i, D ji and G ji They represent the linear thermal conductivity and fourth-order nonlinear radiation thermal conductivity from node j to i. The temperature unit is K, the heat capacity unit is J / K, the time unit is s, and D ji The unit is W / K, G ji The unit is W / K 4 ,q i The unit is W. For steady-state conditions, Among the three parameters A, B, and E, parameter E changes with temperature; for transient solutions, due to qi It is very likely that E will change over time, and it is also very likely that A and B will not change over time. In most cases, the parameters A and B remain unchanged.

[0041] (3) At the current iteration step at the current time, the thermal network equations are analytically solved in the order of i=1 to N (N is the total number of nodes).

[0042] The specific cases are as follows:

[0043] a. When A = 0, that is, there is no radiation heat coupling with other nodes, then

[0044] b. When B = 0, that is, there is no conduction thermal coupling with other nodes in the steady state, then

[0045] c. For other cases, use the root-finding formula to find the real number solution as follows:

[0046]

[0047] in

[0048] In progress i When solving the problem, the coefficients A, B, and E of the equation system are updated according to the obtained temperature. For Jacobi iteration, T j The temperature after the relaxation process of the previous iteration step is taken (if it is the first iteration, the initial temperature is taken, the same below); for the Gauss-Seidel iteration method, if the temperature T has been solved in this iteration, j , T j Take the value already calculated in this iteration, otherwise take the temperature after relaxation in the previous iteration step.

[0049] (4) Determine whether all nodes meet the convergence criterion, that is, whether the temperature of the current iteration step and the temperature of the previous iteration step do not exceed the convergence criterion. If the convergence criterion is met, output the temperature results of all nodes at the current moment and enter step (7); otherwise, enter step (5).

[0050] (5) Relax the temperature results of all nodes, that is, T i (n) =T i (n-1) +α(T i (n) -T i (n-1) ), where α is the relaxation factor, T i (n) is the temperature of node i at the current iteration step number n, T i (n-1)is the temperature of node i at the previous iteration step number n-1. That is, under the processing of relaxation factor α, according to the temperature T of node i at the current iteration step number n i (n) and the temperature T of node i at the previous iteration step number n-1 i (n-1) Perform relaxation calculation and assign the relaxed temperature value to T i (n) .

[0051] (6) The iteration step increases, enters the next iteration step, and returns to step (3).

[0052] (7) If the current solution time is greater than or equal to the solution end time, the entire solution is completed; otherwise, return to step (2).

[0053] Although the present invention is disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope defined by the claims of the present invention.

Claims

1. A method for solving a spacecraft nonlinear thermal network by analytic and iterative fusion, characterized in that: include: (1) Perform solution settings, including setting the initial temperature value of each node, convergence criteria, and relaxation factor; (2) Update the thermal network equation according to the first iteration step of the current time as the time step increases Coefficients A, B, E; (3) At the current iteration step at the current time, the thermal network equations are analytically solved in the order of i = 1 to N, where N is the total number of nodes; (4) Determine whether all nodes meet the convergence criterion; if all meet the convergence criterion, output the temperature results of all nodes at the current moment and go to step (7); otherwise, go to step (5); (5) Relax the temperature results of all nodes; (6) The iteration step increases, enters the next iteration step, and returns to step (3); (7) If the current solution time is greater than or equal to the solution end time, the entire solution is completed; otherwise, return to step (2).

2. The method according to claim 1, characterized in that In step (1), the solution end time and time step are also set.

3. The method according to claim 1, characterized in that In step (2), Subscripts i and j represent nodes, T i is the temperature of node i at the current moment, T i,t -Δt is the temperature of node i at the last moment, Δt is the time step, T j is the temperature of node j, C i is the heat capacity of node i, q i is the heat absorbed by node i, D ji represents the linear thermal conductivity from node j to i, G ji represents the fourth-power nonlinear radiation thermal conductivity from node j to i.

4. The method according to claim 3, characterized in that For steady-state conditions, 5. The method according to claim 3, characterized in that: In step (3), the specific cases are as follows: a. When A = 0, that is, there is no radiation heat coupling with other nodes, then b. When B = 0, that is, there is no conduction thermal coupling with other nodes in the steady state, then c. For other cases, use the root-finding formula to find the real number solution as follows: in 6. The method according to claim 1, characterized in that In step (3), when performing T i When solving the problem, the coefficients A, B and E of the equation group are updated according to the obtained temperature.

7. The method according to claim 6, characterized in that For the Jacobi iteration method, T j Take the temperature after relaxation in the previous iteration.

8. The method according to claim 6, characterized in that For the Gauss-Seidel iterative method, if the temperature T has been solved in this iteration j , T j Take the value already calculated in this iteration, otherwise take the temperature after relaxation in the previous iteration step.

9. The method according to claim 1, characterized in that: In step (4), the convergence criterion is that the absolute value of the temperature difference between the current iteration step and the previous iteration step does not exceed the convergence criterion.

10. The method according to claim 6, characterized in that In step (5), the relaxation process satisfies: Where α is the relaxation factor, is the temperature of node i at the current iteration step number n, T i (n-1) is the temperature of node i in the previous iteration step number n-1.

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