A rocket aerodynamic shape optimization method considering carrying capacity

Abstract

The present invention proposes a method for optimizing the aerodynamic shape of a rocket that takes carrying capacity into consideration. Step 1: Determine an optimization problem with carrying capacity as the optimization objective, including the optimization objective and constraints. Step 2: Determine design variables to describe the aerodynamic shape of the launch vehicle, confirm the launch vehicle's optimized design space, and construct a sample set. Step 3: Calculate the aerodynamic characteristic parameters of the sample points using computational fluid dynamics simulation. Step 4: Calculate the aerodynamic drag coefficient of the sample points based on the simulation results, and calculate the actual payload mass under aerodynamic drag considerations using the velocity loss formula. Step 5: Construct surrogate models using different methods based on the sample set, and select the optimal surrogate model. Step 6: Use a global optimization algorithm to search for the optimal solution that satisfies the optimization problem, i.e., to obtain the maximum payload carrying mass. This method provides a systematic and efficient optimization approach for the aerodynamic shape design of launch vehicles.

Description

Technical Field

[0001] The invention designs a method for optimizing the aerodynamic shape of a rocket taking the carrying capacity into consideration, and belongs to the field of launch vehicle shape design. Background Art

[0002] Carrying capacity refers to the maximum mass a rocket can deliver a payload into a designated orbit or target space location. It is the most important metric for measuring launch vehicle performance and determines the diversity and complexity of its missions. Overestimating carrying capacity can lead to mission failure due to overloading, while underestimating it can result in redundant carrying capacity and increased project costs. A rocket's carrying capacity does not simply rely on increases in engine thrust and fuel load; aerodynamic design plays a crucial role. During flight, a rocket encounters a complex aerodynamic environment, particularly when passing through the atmosphere, where the impact of aerodynamic shape on flight performance becomes particularly pronounced. An optimized aerodynamic shape can effectively reduce air resistance, improve flight efficiency, and enhance the rocket's carrying capacity. Traditional methods require repeated iterations of the "design-simulation-refinement" process, which is costly, inefficient, and not necessarily optimal. Therefore, a rocket's carrying capacity and aerodynamic shape are closely related, and their optimization needs to complement each other. This paper designs a method for optimizing a rocket's aerodynamic shape that takes carrying capacity into consideration. Summary of the Invention

[0003] Aiming at the problems of high iteration cost of optimizing the aerodynamic shape of a launch vehicle and difficulty in obtaining the global optimal solution when improving the carrying capacity, the present invention proposes a method for optimizing the aerodynamic shape of a launch vehicle taking the carrying capacity into consideration.

[0004] In order to solve the above technical problems, the present invention is implemented through the following technical solutions:

[0005] A method for optimizing aerodynamic shape of a rocket taking into account carrying capacity comprises the following steps:

[0006] Step 1: Determine the optimization problem with carrying capacity as the optimization objective, including the optimization objective and constraints;

[0007] Step 2: Determine the design variables to fully describe the aerodynamic shape of the launch vehicle and confirm the design space to construct a sample set;

[0008] Step 3: Calculate the aerodynamic characteristic parameters of the sample points using computational fluid dynamics simulation;

[0009] Step 4: Calculate the aerodynamic drag coefficient of the sample point based on the simulation results, and calculate the actual payload mass considering the aerodynamic drag using the speed loss formula;

[0010] Step 5: Use different methods to build proxy models based on the sample set and select the best proxy model;

[0011] Step 6: Use the global optimization algorithm to find the best solution that satisfies the optimization problem, that is, to obtain the maximum payload carrying mass.

[0012] The optimization problem with carrying capacity as the optimization objective determined in step 1 includes optimization objectives and constraints.

[0013] The optimization goal is to maximize the payload mass of the launch vehicle under special working conditions; the constraints are that the mass of each stage of the launch vehicle's engine is constant, the maximum surface heat flux does not exceed the maximum heat flux of the initial shape, and the main body volume of the launch vehicle is not less than the initial shape.

[0014] In step 2, the design variables include: continuous variables (main body leading edge radius, launch vehicle aspect ratio, booster leading edge radius, and booster wing geometry); and discrete variables (launch vehicle flight angle of attack). The launch vehicle optimization design space is composed of the range of continuous variables and discrete variables. Appropriate sampling is performed across all dimensions of the design variables to ensure sampling efficiency and accuracy.

[0015] In step 3, computational fluid dynamics simulation is used to calculate the aerodynamic drag at the sample point.

[0016] In step 4, the aerodynamic drag coefficient of each sample point is calculated using the aerodynamic drag obtained in step 3, and the surface reference area of ​​the aerodynamic shape is obtained through the modeling software. The corresponding dynamic pressure of the incoming atmosphere is obtained by querying the atmospheric parameter table according to the working conditions. After obtaining the aerodynamic drag coefficient, the aerodynamic drag loss coefficient of the launch vehicle is obtained by looking up the table according to the altitude and Mach number. When the thrust remains unchanged, the speed loss caused by the aerodynamic drag is considered in the design link. According to the calculation formula of the speed loss and the payload of the launch vehicle, the actual payload of the launch vehicle is calculated when the mass of other components remains unchanged and the speed loss of the remaining links is constant, forming a training set consisting of design variables and payloads. The calculation formulas for the aerodynamic drag coefficient, speed loss, and the relationship between the two and the rocket payload are as follows:

[0017] ;

[0018] Where R represents aerodynamic resistance, which is decomposed into resistance X, lift Y and side force Z, C y α is the lift coefficient versus angle of attack α The derivative of S ref is the reference area of ​​the rocket, q is the dynamic pressure, α is the angle of attack, β is the sideslip angle, ΔV D Indicates the speed loss caused by aerodynamic drag during the flight segment, K Dis the aerodynamic drag loss coefficient, which can be calculated based on the aerodynamic drag coefficient C D The corresponding height and Mach number are obtained from the table. D V ideal is the ideal speed increment, ΔV real is the actual speed increment, ΔV need The speed increment required to complete the task, ΔV g is the velocity loss due to gravity, ΔV T is the nozzle pressure velocity loss, ΔV α is the angular velocity loss, m 0 represents the total mass excluding the payload, m payload represents the payload mass, t represents the engine shutdown time, I SPV Indicates vacuum specific impulse.

[0019] The surrogate model that can be used in step 5 is one of the following models: Kring model, response surface model (RSM), radial basis function model (RBF), etc. Three error analysis indicators are selected to compare the prediction accuracy of the surrogate model: determination coefficient R 2 , root mean square error RMSE, maximum error ME, and select the best surrogate model.

[0020] The global optimization algorithm used is the genetic algorithm, which searches for the global optimal point through iterative genetics.

[0021] The advantages of the present invention compared with the prior art are:

[0022] The present invention proposes an aerodynamic shape optimization method that considers carrying capacity, comprising the following steps: determining an optimization problem with carrying capacity as the optimization objective, including the optimization objective and constraints; determining design variables to fully describe the aerodynamic shape of the launch vehicle; determining a design space and sampling sample points using an appropriate method; calculating the aerodynamic characteristic parameters of the sample points using computational fluid dynamics simulation; calculating the aerodynamic drag coefficient of the sample points based on the simulation results, and calculating the actual payload mass under aerodynamic drag consideration using a velocity loss formula; constructing proxy models using different methods based on the sample set and selecting the optimal proxy model; and optimizing using a global optimization algorithm to find the optimal solution that satisfies the optimization problem, i.e., to obtain the maximum payload carrying mass. This method directly incorporates aerodynamic shape design into the calculation of the rocket payload, simplifying the complex iterative process and improving design efficiency.

[0023] Any technical solution of the present invention may not necessarily achieve all of the above beneficial effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Flowchart for obtaining a training set for an invention.

[0025] Figure 2 Schematic diagram of the aerodynamic parameters of the launch vehicle. DETAILED DESCRIPTION

[0026] The present invention is further described below with reference to the accompanying drawings and embodiments.

[0027] In the current embodiment, an optimization problem with carrying capacity as the optimization goal is determined, including optimization goals and constraints; design variables are determined to fully describe the aerodynamic shape of the launch vehicle; the design space is determined, and sample points are obtained by sampling using appropriate methods; a sample set is constructed, and the carrying capacity parameters of the sample points are calculated using simulation calculation methods and theoretical formulas; proxy models are constructed using different methods based on the sample set, and the best proxy model is selected; a global optimization algorithm is used to search for the best solution that satisfies the optimization problem, that is, to obtain the maximum payload carrying mass. The flow chart is as follows: Figure 1 As shown, specifically including:

[0028] Determine the optimization problem with carrying capacity as the optimization goal, including: optimization goal and constraints. The optimization goal is to maximize the payload mass of the launch vehicle under special operating conditions; the constraints are that the mass of each stage of the launch vehicle engine is constant, the maximum heat flux on the surface does not exceed the maximum heat flux of the initial shape, and the volume of the launch vehicle body is not less than the initial shape. The specific function is as follows:

[0029] ；

[0030] in,m i is the mass of the engines at each stage of the launch vehicle, Q max is the peak heat flux on the launch vehicle surface, Volume is the volume of the launch vehicle, subscript initial Represents the initial shape.

[0031] The geometrical shape model of the carrier rocket in the embodiment is as follows: Figure 2 As shown, the design parameters are shown in Table 1 below:

[0032] Table 1 Design variables of launch vehicle optimization design problem

[0033]

[0034] During the launch vehicle optimization design process, an optimal Latin hypercube sampling method was used to select sample points from the design space to effectively improve performance and efficiency. This method evenly covers the entire design space, ensuring that the selected sample points fully represent the characteristics of the design space, thereby being used to construct a high-precision surrogate model.

[0035] Specifically, these sample points are first constructed into a three-dimensional geometric model using modeling software such as SolidWorks to ensure that the shape and size of the design can be accurately expressed. Then, the model is meshed using mesh generation software such as Pointwise to generate the high-quality computational mesh required for the calculation. Next, based on these meshes, computational fluid dynamics (CFD) software is used to perform numerical calculations of aerodynamic performance, and the theoretical formula between payload and aerodynamic relationship is used to calculate the payload mass corresponding to each aerodynamic shape. The calculation formulas for the aerodynamic drag coefficient, speed loss, and the relationship between the two and the rocket payload are as follows:

[0036] ;

[0037] Where R represents aerodynamic resistance, which is decomposed into resistance X, lift Y and side force Z, C y α is the lift coefficient versus angle of attack α The derivative of S ref is the reference area of ​​the rocket, q is the dynamic pressure, α is the angle of attack, β is the sideslip angle, ΔV D Indicates the speed loss caused by aerodynamic drag during the flight segment, K D is the aerodynamic drag loss coefficient, which can be calculated based on the aerodynamic drag coefficient C D The corresponding height and Mach number are obtained from the table. DV ideal is the ideal speed increment, ΔV real is the actual speed increment, ΔV need The speed increment required to complete the task, ΔV g is the gravitational velocity loss, ΔV T is the nozzle pressure velocity loss, ΔV α is the angular velocity loss, m 0 represents the total mass excluding the payload, m payload represents the payload mass, t represents the engine shutdown time, I SPV Indicates vacuum specific impulse.

[0038] After obtaining the aerodynamic drag parameters through computational fluid dynamics simulation, the aerodynamic drag coefficient is calculated using the drag calculation formula in the incoming flow direction. After obtaining the aerodynamic drag coefficient, the aerodynamic drag loss coefficient of the launch vehicle is obtained by looking up the table according to the set altitude and Mach number. When the thrust remains unchanged, the speed loss caused by aerodynamic drag is considered in the design process. ΔV D , according to the calculation formula of speed loss and launch vehicle payload, the total mass of other components m 0 The speed of other links remains unchanged. ΔV g 、 ΔV T 、 ΔV α The actual payload of the launch vehicle is calculated under constant conditions, and the final training set is composed of the 12 shape design variables in Table 1 as input and the actual payload considering the speed loss caused by aerodynamic drag as output.

[0039] The payload data obtained through the above process, along with the design parameters of the sample points, constitutes a training set for the RBF network proxy model. The RBF network surrogate model has a simple structure and high training efficiency, especially when using parameter update algorithms such as the least squares method. The local response characteristics of the RBF network enable excellent performance in classification and regression tasks, while also possessing good generalization capabilities. To evaluate the accuracy of the surrogate model, a randomly sampled test set was used for validation, and model fit metrics including the coefficient of determination (R²), root mean square error (RMSE), and mean error (ME) were calculated.

[0040] After constructing the radial basis network model, the agent model was combined with the island genetic algorithm (IGA) to optimize the aerodynamic shape of the launch vehicle. The IGA is a parallel evolutionary strategy that divides a population into multiple subpopulations, or "islands," where each island evolves independently within a local region, while periodically exchanging information and migrating between islands. This method accelerates convergence, avoids getting stuck in local optima, and thus improves global search capabilities. Standard genetic algorithm operations, such as selection, crossover, and mutation, are used within each island population, while migration between islands is achieved by periodically exchanging a certain proportion of individuals. The algorithm parameters were set as follows: the number of islands was 4, the population size per island was 10, the maximum number of evolutionary generations was 1500, and the stagnation threshold was 1e-10 to ensure prompt termination upon convergence. A mixed encoding scheme of real and integer numbers was used within each island to flexibly represent design variables. The migration period between islands was set to 50 generations, and the migration ratio was set to 10%. This multi-island parallel strategy allows for simultaneous optimization in multiple search spaces, avoiding the early convergence issues that can occur in traditional genetic algorithms. Ultimately, the optimal launch vehicle geometry parameters that meet the constraints are obtained through the multi-island genetic algorithm optimization process.

[0041] This optimization process not only ensures efficient exploration of the design space, but also significantly improves the rocket's launch performance by combining the radial basis network agent model and the multi-island genetic algorithm, and effectively reduces the computational cost of the design and analysis process.

[0042] This example uses an optimization method based on aerodynamic shape enhancement for launch vehicle payloads. By using a surrogate model, an accurate prediction model between aerodynamic shape and payload mass is constructed, replacing complex numerical calculations. This effectively improves the global optimality of the shape design and reduces the high cost of traditional iterative design.

[0043] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

Claims

1. A method for optimizing aerodynamic shape of a rocket considering carrying capacity, characterized in that: The following steps are involved: Step 1: Determine the optimization problem with carrying capacity as the optimization objective, including the optimization objective and constraints; Step 2: Determine the design variables to describe the aerodynamic shape of the launch vehicle and confirm the sample set of the launch vehicle's optimal design space; Step 3: Calculate the aerodynamic characteristic parameters of the sample points using computational fluid dynamics simulation; Step 4: Calculate the aerodynamic drag coefficient of the sample point based on the simulation results, and calculate the actual payload mass considering the aerodynamic drag using the speed loss formula; Step 5: Use different methods to build proxy models based on the sample set and select the best proxy model; Step 6: Use a global optimization algorithm to find the best solution that satisfies the optimization problem, that is, to obtain the maximum payload carrying mass; In step 1, the optimization objective is to maximize the payload mass of the launch vehicle under operating conditions; the constraints are that the mass of each stage of the launch vehicle's engines is constant, the maximum surface heat flux does not exceed the maximum heat flux of the initial shape, and the volume of the launch vehicle's main body is not less than the initial shape; In step 2, the design variables include continuous variables and discrete variables. The continuous variables include the main body leading edge radius, the launch vehicle aspect ratio, the booster leading edge radius, and the booster wing geometry parameters; the discrete variables include the launch vehicle flight angle of attack; the launch vehicle optimization design space is composed of the value range of the continuous variables and the discrete variables; sampling is performed on each dimension of the design variables, and shapes are generated in batches based on the sampled data. The obtained shapes are parameterized to generate sample points, and a sample set of the proxy model is constructed from these sample points; The method for optimizing the aerodynamic shape of a rocket considering the carrying capacity adopts the optimal Latin hypercube sampling method to select sample points from the design space; In step 3, computational fluid dynamics simulation is used to calculate the aerodynamic resistance of the sample point; In step 4, the aerodynamic drag coefficient of each sample point is calculated using the aerodynamic drag obtained in step 3, and the actual payload mass that the launch vehicle can carry considering the aerodynamic drag consumption is calculated using the speed loss formula. The calculation formula is as follows: ； Where R represents aerodynamic resistance, which is decomposed into resistance X, lift Y and side force Z, C y α is the lift coefficient versus angle of attack α The derivative of S ref is the reference area of ​​the rocket, q is the dynamic pressure, α is the angle of attack, β is the sideslip angle, ΔV D Indicates the speed loss caused by aerodynamic drag during the flight segment, K D is the aerodynamic drag loss coefficient, which can be calculated based on the aerodynamic drag coefficient C D The corresponding height and Mach number are obtained from the table. Δ V ideal is the ideal speed increment, ΔV real is the actual speed increment, ΔV need The speed increment required to complete the task, ΔV g is the velocity loss due to gravity, ΔV T is the nozzle pressure velocity loss, ΔV α is the angular velocity loss, m 0 represents the total mass excluding the payload, m payload represents the payload mass, I SPV Indicates vacuum specific impulse; In step 5, different surrogate model construction methods are used to construct continuous surrogate models in the design space, and three error analysis indicators are selected to compare the prediction accuracy of the surrogate models: determination coefficient R 2 , root mean square error RMSE, maximum error ME, and the best proxy model is selected based on the three indicators.

2. The method for optimizing aerodynamic shape of a rocket considering carrying capacity according to claim 1, characterized in that: The global optimization algorithm used is the Island Genetic Algorithm (IGA) algorithm, which selects the global optimal point through iterative genetic screening.

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