A collaborative jet airfoil optimization design method based on combined parameterization
By employing CST parameterization and joint design space optimization methods, the parameter coupling problem in collaborative jet airfoil design was solved, achieving efficient airfoil optimization and improving aerodynamic performance and computational efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-03-09
- Publication Date
- 2026-06-05
Smart Images
Figure CN122154072A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of aerodynamic optimization design and flow control of aircraft, and specifically relates to a cooperative jet airfoil optimization design method based on combined parameterization. Background Technology
[0002] Co-flow Jet (CFJ) technology is a novel active flow control technique. It incorporates inlet and outlet ports on the airfoil surface, utilizing the momentum exchange between the jet and the mainstream flow to effectively suppress flow separation and transition phenomena under low Reynolds number conditions, thereby increasing lift, reducing drag, and delaying stall angle of attack. However, the aerodynamic performance of CFJ airfoils is influenced by their geometry and flow control parameters. The key to achieving high-performance design lies in establishing an accurate geometric representation model and an efficient global optimization architecture.
[0003] Currently, existing cooperative jet airfoil design methods mainly suffer from the following technical bottlenecks: During the optimization process of cooperative jet airfoils, there is often a severe parameter coupling problem between the basic airfoil geometry and the sinking channel. Existing CFJ parameterization methods typically treat the sinking channel as an independent geometric segment for parameter fitting. This local modeling approach often only focuses on the parameter design of the jet channel itself, failing to achieve global cooperative optimization of the channel geometry and the overall profile of the basic airfoil. This results in a lack of effective physical coordination between the jet inlet position, depth variables, and the original airfoil profile parameters during the optimization process. Geometric topology problems such as curve discontinuities and physical distortions easily occur during variable perturbation optimization, limiting the optimization algorithm's in-depth search of the design space. Existing technologies design airfoil shape parameters and cooperative jet flow control parameters separately, failing to achieve cooperative optimization of the two types of parameters, resulting in an inability to balance geometric rationality and aerodynamic control performance. Furthermore, due to the lack of a comprehensive balance between the global geometric weights of the airfoil and the flow control parameters, it is difficult to uncover the optimal aerodynamic potential of the cooperative jet airfoil. Furthermore, collaborative jet airfoil design involves multiple variables such as airfoil shape, channel geometry, and jet momentum coefficient, which typically constitute a design space of more than 20 dimensions. Existing optimization methods are computationally expensive when dealing with such nonlinear aerodynamic response surfaces, and due to the lack of an efficient adaptive point update mechanism, the algorithm is difficult to converge efficiently to the global optimum under limited computing resources.
[0004] Therefore, how to establish a collaborative jet airfoil optimization design method that can achieve geometric decoupling, has high-fidelity characterization capabilities, and can efficiently find the best solution is a key problem that urgently needs to be solved in the field of flow control. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention provides a collaborative jet airfoil optimization design method based on combined parameterization, which can effectively solve the above problems.
[0006] The technical solution adopted in this invention is as follows:
[0007] This invention provides a collaborative jet airfoil optimization design method based on combined parameterization, comprising the following steps:
[0008] Step S1: Select the original base airfoil, perform CST parameterization on the original base airfoil, and obtain CST parameterization variables that characterize the airfoil shape parameters of the original base airfoil.
[0009] Step S2, construct the original cooperative jet airfoil:
[0010] Determine the design variables of the co-jet airfoil shape and determine the design value of each of the co-jet airfoil shape design variables; transform the original base airfoil based on the design values of the co-jet airfoil shape design variables to obtain the original co-jet airfoil corresponding to the original base airfoil;
[0011] Step S3: Determine the design conditions, combined design variables, design space, optimization objectives, and constraints;
[0012] The combined design variables include the synergistic jet airfoil shape design variables, synergistic jet flow control parameters, and the CST parameterization variables;
[0013] Step S4: Select a sampling method and extract several initial sample points within the design space; use a high-precision numerical simulation CFD module to solve the aerodynamic performance of the initial sample points to obtain the response value of each initial sample point, which includes the optimization objective function value and constraint value.
[0014] Step S5: Construct a surrogate model based on the input-output mapping relationship of each initial sample point and response value; use the point addition criterion to iterate the surrogate model, continuously updating the surrogate model until the generated sample point sequence converges to a local or global optimal solution; wherein, during the iterative optimization process, the cooperative jet airfoil shape design variables, cooperative jet flow control parameters and CST parameterized variables are simultaneously adapted to achieve cooperative optimization of various parameters, balancing the cooperative jet flow control parameters while ensuring the optimization objective;
[0015] Step S6: Output the optimal values of the combined design variables.
[0016] Furthermore, the original basic airfoil is parameterized using CST, specifically as follows:
[0017] Step S11, using class functions sum type function The product of these factors, superimposed with a function describing the trailing edge thickness, represents the geometry of the original basic airfoil, thus achieving CST parameterization of the original basic airfoil. Its mathematical expression is:
[0018] upper surface of the airfoil:
[0019]
[0020] Lower surface of the airfoil:
[0021]
[0022] in: It is the upper surface of the airfoil coordinate; It is an airfoil surface ; It is a function class; It is the upper surface shape function of the airfoil; The trailing edge of the upper surface of the airfoil coordinate; It is the lower surface of the airfoil coordinate; It is the lower surface profile function of the airfoil; It is the trailing edge of the lower surface of the airfoil coordinate;
[0023] Class function The definition is as follows:
[0024]
[0025] in: , The values are 0.5 and 1.0, which are fixed values and represent the first and second exponents, respectively.
[0026] The type function is defined as follows:
[0027]
[0028]
[0029]
[0030] in: For the first A Bernstein polynomial, =0,1,…, ; Subtract 1 from the total number of Bernstein polynomials; and , respectively the first on the upper surface of the airfoil The undetermined coefficients and the first undetermined coefficient on the lower surface of the airfoil. One undetermined coefficient;
[0031] for Undetermined coefficient of upper surface of airfoil when = 0 Undetermined coefficients of the lower surface of the airfoil With respect to the leading edge radius of the airfoil It has the following relationship:
[0032]
[0033] For airfoil surfaces When =1, its airfoil upper surface shape function and airfoil lower surface shape function It has the following relationship:
[0034]
[0035]
[0036] in: and These are the trailing edge tangent angles of the upper surface and the lower surface of the airfoil, respectively.
[0037] Step S12, establish equations ;
[0038]
[0039] in: It is the number of known airfoil coordinate points on the upper surface of the airfoil; It is the number of known airfoil coordinate points on the lower surface of the airfoil; The first of the upper surface of the airfoil Known airfoil coordinates coordinate; The first of the lower surface of the airfoil Known airfoil coordinates coordinate;
[0040] equation middle, for Undetermined coefficients and shape function of the upper surface of the airfoil when = 0 The product term; for =1,…, The sum of the products of the undetermined coefficients of the upper surface of the airfoil and the shape function; for Undetermined coefficients and shape function of the lower surface of the airfoil when = 0 The product term; for =1,…, The sum of the products of the undetermined coefficients of the lower surface of the airfoil and the shape function;
[0041] Step S13: Ensure the number of known airfoil coordinate points is greater than the number of undetermined coefficients, and solve the equation using the least squares method. The minimum value is obtained to get the values of each undetermined coefficient, which are the variable values of the CST parameterized variables; the number of CST parameterized variables is... .
[0042] Furthermore, the design variables for the coordinated jet airfoil include the position of the air inlet. Air inlet size Intake port position and intake port size At least one of them.
[0043] Furthermore, based on the design values of the cooperative jet airfoil shape design variables, the original base airfoil is transformed to obtain the original cooperative jet airfoil corresponding to the original base airfoil, including:
[0044] According to the location of the air outlet Design values and air intake position The design values are used to determine the air inlet and air inlet at the corresponding positions of the original basic airfoil, and to make the normals of the air inlet and air inlet tangent to the original basic airfoil.
[0045] Between the air inlet and air inlet of the original basic airfoil, a sinking section airfoil is constructed to transform the original basic airfoil and obtain the original cooperative jet airfoil corresponding to the original basic airfoil.
[0046] The method for constructing the lower airfoil is as follows: the original airfoil is obtained by translating the original airfoil point between the air inlet and the air inlet inward along the normal direction of the original airfoil by a certain distance.
[0047] Translation distance Determine using the following formula:
[0048]
[0049]
[0050] in: This represents the c-th airfoil point starting from the intake end; This indicates the number of airfoil points from the intake end to the exhaust end; This represents the movement coefficient of the c-th airfoil point; and These represent the sizes of the air inlet and outlet. Design values and intake port size Design values; This represents the translation distance of the c-th airfoil point;
[0051] Therefore, translation distance Based on the dimensions of the air inlet, air outlet, and the distance between the airfoil point and the air outlet determined by linear interpolation, an adaptive association between the airfoil curve of the sinking section and the original basic airfoil curve is achieved through linear mapping.
[0052] Furthermore, in step S3, the design conditions include the incoming Mach number. Reynolds number Angle of attack The coordinated jet flow control parameters are: a constant mass flow rate is given at the blowing and suction ports. For the control parameters of the coordinated jet flow;
[0053] The optimization objectives include maximizing the lift coefficient and minimizing the drag coefficient;
[0054] The constraints include: under the design conditions, the lift coefficient of the optimized airfoil is greater than that of the original optimized airfoil; the drag coefficient of the optimized airfoil is less than that of the original optimized airfoil; and the absolute value of the difference between the thickness of the base airfoil corresponding to the optimized airfoil and the original base airfoil is less than a certain proportion of the thickness of the original base airfoil.
[0055] Furthermore, step S4 includes:
[0056] Step S41: Within the design space, initial sample points are extracted using Latin hypercube sampling.
[0057] Step S42: Use the high-precision numerical simulation CFD module to solve the aerodynamic performance of the initial sample points and obtain the response value including the equivalent lift-to-drag ratio.
[0058] Furthermore, step S5 includes:
[0059] Step S51: Based on the input-output mapping relationship of the initial sample points, construct the Kriging surrogate model, optimize the model hyperparameters using the Hooke-Jeeves method, and establish a preliminary response surface prediction for the aerodynamic characteristics of the cooperative jet airfoil.
[0060] Step S52: The SBMO framework based on the surrogate model is adopted. In each iteration, the MSP minimization prediction and EI expectation improvement hybrid point addition criteria are used to generate new sample points in parallel, and the new sample points in each round are submitted to the high-precision numerical simulation CFD module for calculation.
[0061] Step S53: Feed the calculation results back to the sample set to retrain the Kriging surrogate model. By continuously correcting local biases, the prediction accuracy of the Kriging surrogate model in the high-dimensional extreme value region is improved.
[0062] Step S54: Repeat the iterative process from step S52 to step S53 until the total number of sample points reaches the preset value or the objective function convergence criterion is met.
[0063] Step S55: On the finally updated global response surface, extract the optimal design scheme that meets the preset target according to the optimization criterion, and output the cooperative jet airfoil parameters and geometric model that achieve the best balance between aerodynamic efficiency and jet control parameters.
[0064] The present invention provides a collaborative jet airfoil optimization design method based on combined parameterization, which has the following advantages:
[0065] This invention first employs the CST parameterization method to parametrically characterize the basic airfoil, obtaining the CST parameterized variables of the basic airfoil. When constructing the original cooperative jet airfoil, the position and size of the inlet and the position and size of the inlet are set as independent variables. Crucially, the airfoil in the lower section between the inlet and inlet is not independently fitted, but rather obtained from the original basic airfoil through linear interpolation based on the size and position of the inlet / inlet. This linear mapping achieves an adaptive association between the lower section airfoil and the basic airfoil, mathematically solving the coupling distortion problem between the lower section and the airfoil.
[0066] At the optimization level, this invention constructs a joint design space including the CST parameterized variables of the basic airfoil, the cooperative jet airfoil shape design variables, and the cooperative jet flow control parameters. An initial surrogate model is constructed using Latin hypercube sampling, and the hyperparameters of the Kriging model are optimized using the Hooke-Jeeves method. During the iterative phase, a surrogate model-based multi-objective optimization algorithm (SBMO) framework is employed, along with a hybrid approach of the minimum surrogate model prediction criterion (MSP) and the improvement expectation criterion (EI) to update the surrogate model in parallel until convergence, thereby balancing the jet control parameters while ensuring aerodynamic efficiency. Attached Figure Description
[0067] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0068] Figure 1 This is a flowchart of a collaborative jet airfoil optimization design method based on combined parameterization provided by the present invention;
[0069] Figure 2 This is a schematic diagram of the basic airfoil of this invention;
[0070] Figure 3 This is a schematic diagram of the design parameters for the synergistic jet airfoil of the present invention;
[0071] Figure 4 This is a structural diagram of the final approximate Pareto front and the three optimized airfoils Opt1, Opt2, and Opt3 selected from it in Embodiment 2 of the present invention;
[0072] Figure 5 This is a comparison diagram of the geometric shapes of the optimized airfoil Opt1 and the CFJ6415 airfoil in Embodiment 2 of the present invention;
[0073] Figure 6 This is a comparison diagram of the geometric shapes of the optimized airfoil Opt2 and the CFJ6415 airfoil in Embodiment 2 of the present invention;
[0074] Figure 7 This is a comparison diagram of the geometric shapes of the optimized airfoil Opt3 and the CFJ6415 airfoil in Embodiment 2 of the present invention.
[0075] Explanation of the attached diagram: 1 indicates the location of the air inlet. 2 indicates the air intake position. 3 represents the size of the air inlet. 4 represents the size of the air intake. . Detailed Implementation
[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0077] Example 1
[0078] like Figure 1 As shown, this invention provides a collaborative jet airfoil optimization design method based on combined parameterization, which includes at least the following steps in its implementation:
[0079] Step S1: Select the original base airfoil and perform CST (Class function / Shape function Transformation) parameterization on the original base airfoil to obtain CST parameterization variables that characterize the airfoil shape parameters of the original base airfoil;
[0080] In this step, the original basic airfoil is parameterized using CST, specifically as follows:
[0081] Step S11, using class functions sum type function The product of these factors, superimposed with a function describing the trailing edge thickness, represents the geometry of the original basic airfoil, thus achieving CST parameterization of the original basic airfoil. Its mathematical expression is:
[0082] upper surface of the airfoil:
[0083]
[0084] Lower surface of the airfoil:
[0085]
[0086] in: It is the upper surface of the airfoil coordinate; It is an airfoil surface ; It is a function class; It is the upper surface shape function of the airfoil; The trailing edge of the upper surface of the airfoil coordinate; It is the lower surface of the airfoil coordinate; It is the lower surface profile function of the airfoil; It is the trailing edge of the lower surface of the airfoil coordinate;
[0087] Class function The definition is as follows:
[0088]
[0089] in: , The values are 0.5 and 1.0, which are fixed values and represent the first and second exponents, respectively.
[0090] The type function is defined as follows:
[0091]
[0092]
[0093]
[0094] in: For the first A Bernstein polynomial, =0,1,…, ; Subtract 1 from the total number of Bernstein polynomials; and , respectively the first on the upper surface of the airfoil The undetermined coefficients and the first undetermined coefficient on the lower surface of the airfoil. There are undetermined coefficients; when the coefficients are... and Confirmed, the entire airfoil is now determined.
[0095] for Undetermined coefficient of upper surface of airfoil when = 0 Undetermined coefficients of the lower surface of the airfoil With respect to the leading edge radius of the airfoil It has the following relationship:
[0096]
[0097] Specifically, to ensure the continuity and differentiability of the airfoil geometry at the leading edge, there is... .
[0098] For airfoil surfaces When =1, its airfoil upper surface shape function and airfoil lower surface shape function It has the following relationship:
[0099]
[0100]
[0101] in: and These are the trailing edge tangent angles of the upper surface and the lower surface of the airfoil, respectively.
[0102] Step S12, establish equations ;
[0103]
[0104] in: It is the number of known airfoil coordinate points on the upper surface of the airfoil; It is the number of known airfoil coordinate points on the lower surface of the airfoil; The first of the upper surface of the airfoil Known airfoil coordinates coordinate; The first of the lower surface of the airfoil Known airfoil coordinates coordinate;
[0105] equation middle, for Undetermined coefficients and shape function of the upper surface of the airfoil when = 0 The product term; for =1,…, The sum of the products of the undetermined coefficients of the upper surface of the airfoil and the shape function; for Undetermined coefficients and shape function of the lower surface of the airfoil when = 0 The product term; for =1,…, The sum of the products of the undetermined coefficients of the lower surface of the airfoil and the shape function;
[0106] Step S13: Ensure the number of known airfoil coordinate points is greater than the number of undetermined coefficients, and solve the equation using the least squares method. The minimum value is obtained to get the values of each undetermined coefficient, which are the variable values of the CST parameterized variables; the number of CST parameterized variables is... .
[0107] Step S2, construct the original cooperative jet airfoil:
[0108] Determine the design variables of the co-jet airfoil shape and determine the design value of each of the co-jet airfoil shape design variables; transform the original base airfoil based on the design values of the co-jet airfoil shape design variables to obtain the original co-jet airfoil corresponding to the original base airfoil;
[0109] For example, the collaborative jet airfoil shape design variables include the location of the air inlet. Air inlet size Intake port position and intake port size At least one of them.
[0110] Based on the design values of the synergistic jet airfoil shape design variables, the original base airfoil is transformed to obtain the original synergistic jet airfoil corresponding to the original base airfoil, including:
[0111] According to the location of the air outlet Design values and air intake position The design values are used to determine the air inlet and air inlet at the corresponding positions of the original basic airfoil, and to make the normals of the air inlet and air inlet tangent to the original basic airfoil.
[0112] Between the air inlet and air inlet of the original basic airfoil, a sinking section airfoil is constructed to transform the original basic airfoil and obtain the original cooperative jet airfoil corresponding to the original basic airfoil.
[0113] The method for constructing the lower airfoil is as follows: the original airfoil is obtained by translating the original airfoil point between the air inlet and the air inlet inward along the normal direction of the original airfoil by a certain distance.
[0114] Translation distance Determine using the following formula:
[0115]
[0116]
[0117] in: This represents the c-th airfoil point starting from the intake end; This indicates the number of airfoil points from the intake end to the exhaust end; This represents the movement coefficient of the c-th airfoil point; and These represent the sizes of the air inlet and outlet. Design values and intake port size Design values; This represents the translation distance of the c-th airfoil point;
[0118] Therefore, translation distance Based on the dimensions of the air inlet, air outlet, and the distance between the airfoil point and the air outlet determined by linear interpolation, an adaptive association between the airfoil curve of the sinking section and the original basic airfoil curve is achieved through linear mapping.
[0119] Step S3: Determine the design conditions, combined design variables, design space, optimization objectives, and constraints;
[0120] As one specific implementation method, the design operating conditions include at least the incoming Mach number. Reynolds number Angle of attack ;
[0121] The combined design variables include: the cooperative jet airfoil shape design variables, the cooperative jet flow control parameters, and the CST parameterization variables; when the Bernstein polynomials of the upper and lower surfaces of the airfoil are both of order N, the number of CST parameterization variables is 2N+2; the cooperative jet flow control parameters are: given a constant mass flow rate at the inlet and outlet. The parameters are for coordinated jet flow control; therefore, the design variables of this invention simultaneously cover the airfoil shape parameters in step S1 and the coordinated jet airfoil shape design variables in step S2, breaking the limitation of separate design of the two types of parameters and lack of coordinated optimization in the prior art.
[0122] The optimization objectives and constraints are determined based on the optimization design objectives; the design space is constructed based on the range of values for the design variables.
[0123] For example, the optimization objectives include maximizing the lift coefficient and minimizing the drag coefficient; the constraints include: under the design conditions, the lift coefficient of the optimized airfoil is greater than that of the original optimized airfoil; the drag coefficient of the optimized airfoil is less than that of the original optimized airfoil; and the absolute value of the difference in thickness between the base airfoil corresponding to the optimized airfoil and the original base airfoil is less than a certain proportion of the thickness of the original base airfoil.
[0124] Step S4: Select a sampling method and extract several initial sample points within the design space; use a high-precision numerical simulation CFD module to solve the aerodynamic performance of the initial sample points to obtain the response value of each initial sample point, which includes the optimization objective function value and constraint value.
[0125] Step S41: Within the design space, initial sample points are extracted using Latin hypercube sampling.
[0126] Step S42: Use the high-precision numerical simulation CFD module to solve the aerodynamic performance of the initial sample points and obtain the response value including the equivalent lift-to-drag ratio.
[0127] Step S5: Construct a surrogate model based on the input-output mapping relationship of each initial sample point and response value; use the point addition criterion to iterate the surrogate model, continuously update the surrogate model, until the generated sample point sequence converges to a local or global optimal solution;
[0128] In the iterative optimization process, the collaborative jet airfoil shape design variables, collaborative jet flow control parameters and CST parameterization variables are adapted simultaneously to achieve collaborative optimization of various parameters. While ensuring the optimization objective, the collaborative jet flow control parameters are balanced. This is different from the shortcomings of existing technologies where the two types of parameters lack coordination and cannot take into account the overall aerodynamic performance.
[0129] Step S51: Based on the input-output mapping relationship of the initial sample points, construct the Kriging surrogate model, optimize the model hyperparameters using the Hooke-Jeeves method, and establish a preliminary response surface prediction for the aerodynamic characteristics of the cooperative jet airfoil.
[0130] Step S52: The SBMO framework based on the surrogate model is adopted. In each iteration, the MSP minimization prediction and EI expectation improvement hybrid point addition criteria are used to generate new sample points in parallel, and the new sample points in each round are submitted to the high-precision numerical simulation CFD module for calculation.
[0131] Step S53: Feed the calculation results back to the sample set to retrain the Kriging surrogate model. By continuously correcting local biases, the prediction accuracy of the Kriging surrogate model in the high-dimensional extreme value region is improved.
[0132] Step S54: Repeat the iterative process from step S52 to step S53 until the total number of sample points reaches the preset value or the objective function convergence criterion is met.
[0133] Step S55: On the finally updated global response surface, extract the optimal design scheme that meets the preset target according to the optimization criterion, and output the cooperative jet airfoil parameters and geometric model that achieve the best balance between aerodynamic efficiency and jet control parameters.
[0134] Step S6: Output the optimal values of the combined design variables.
[0135] Embodiment 1 of this invention illustrates a collaborative jet airfoil optimization design method based on combined parameterization provided by this invention. This method uses the CST method to parameterize the original basic airfoil, taking the position of the air inlet as an example. Air inlet size Intake port position Inlet size A primitive cooperative jet airfoil is constructed for the variables, and a joint design space is built that includes the CST parameterized variables of the primitive basic airfoil, the shape design variables of the cooperative jet airfoil, and the jet control parameters. An initial surrogate model is constructed using Latin hypercube sampling, and the hyperparameters of the Kriging model are optimized using the Hooke-Jeeves method. During the iterative phase, the surrogate model is updated in parallel using the SBMO framework and the MSP and EI hybrid point addition criteria until convergence, balancing the jet control parameters while ensuring aerodynamic efficiency, and outputting the optimal combination of design variables.
[0136] This method achieves geometric decoupling of the co-jet airfoil, possesses high-fidelity characterization capability, realizes adaptive association between the sinking section airfoil and the original basic airfoil, and can globally and collaboratively optimize the geometry of the sinking section channel and the overall profile of the original basic airfoil to uncover the optimal aerodynamic potential of the co-jet airfoil.
[0137] Example 2
[0138] Based on the above embodiment 1, this embodiment 2 presents the implementation process of a collaborative jet airfoil optimization design method based on combined parameterization provided by the present invention, combined with actual parameters.
[0139] like Figure 1 As shown, in this embodiment, a collaborative jet airfoil optimization design method based on combined parameterization includes at least the following steps during implementation:
[0140] Step 1, select the original base airfoil:
[0141] like Figure 2As shown, the existing NACA6415 airfoil is selected as the original base airfoil, and the original base airfoil is parameterized using the 8th order CST parameterization method, resulting in 18 CST parameterization variables.
[0142] Step S2, construct the original cooperative jet airfoil:
[0143] Using the design values of the air inlet size of 0.65%c, located at 7.5%c, and the air inlet size of 1.3%c, located at 88.5%c, as the design variables for the synergistic jet airfoil shape, the method of step S2 in embodiment 1 of this invention is adopted to construct the airfoil as shown below. Figure 3 The original cooperative jet airfoil shown is denoted as CFJ6415. Where c is the airfoil chord length.
[0144] Step S3: Determine the design conditions, combined design variables, design space, optimization objectives, and constraints;
[0145] Design conditions: Incoming Mach number 0.03, Reynolds number Angle of attack 5°;
[0146] Design variable: Air inlet size Inlet size 18 design variables for CST parameterization of the NACA6415 airfoil; jet mass flow rate It is 0.0508 kg / s;
[0147] Design Space: , The airfoil design variables fluctuate by 25%.
[0148] Optimization objective: Maximize the lift coefficient and minimize the drag coefficient;
[0149] Constraints: The lift coefficient is greater than the lift coefficient of the CFJ6415 airfoil under this design condition (1.29); the drag coefficient is less than the drag coefficient of the CFJ6415 airfoil under this condition (-0.0194).
[0150] The absolute value of the difference in thickness between the base airfoil corresponding to the synergistic jet optimized airfoil and the original base airfoil is less than 20% of the thickness of the original base airfoil. Here, the base airfoil corresponding to the synergistic jet optimized airfoil refers to the base airfoil obtained by restoring the lower section airfoil of the synergistic jet optimized airfoil.
[0151] Step S4: Using the Latin hypercube sampling method, 24 initial sample points are randomly selected in the multidimensional design space. The aerodynamic performance of the initial sample points is solved using the CFD module to obtain the response values containing the optimization objective function and constraints.
[0152] Step S5: Based on the input-output mapping relationship of 24 initial sample points, a Kriging surrogate model is constructed. A multi-objective optimization (SBMO) framework based on the surrogate model is adopted. In each iteration, 8 new sample points are generated through a hybrid parallel approach of MSP and EI, and these new sample points are submitted to a high-precision CFD module for calculation to iterate and update the surrogate model. Iteration continues until 600 sample points are reached, at which point the iteration stops, ultimately obtaining the model as shown below. Figure 4 The final approximate Pareto front and the three optimized airfoils Opt1, Opt2, and Opt3 selected from it are shown in the figure. The geometric comparison figures of Opt1, Opt2, and Opt3 with CFJ6415 are shown in the figure. Figure 5 , Figure 6 , Figure 7 As shown; see Table 1 for comparison:
[0153] Table 1 shows the three optimized airfoils selected on the final approximate Pareto front obtained through optimization.
[0154] Comparison of optimization objectives and constraint values for the baseline airfoil
[0155] Optimization objective 1 (Cl) Optimize objective 2 (Cd) thickness CFJ6415 1.29 -0.0194 0.150 Opt1 1.93 -0.0385 0.165 Opt2 1.88 -0.0473 0.172 Opt3 1.63 -0.0514 0.150
[0156] As shown in Table 1, compared with the CFJ6415 airfoil before optimization, the lift coefficients of the optimized Opt1, Opt2, and Opt3 are significantly improved, and the drag coefficients are significantly reduced. Therefore, the synergistic jet airfoil obtained by the synergistic jet airfoil optimization design method based on combined parameterization of the present invention has better aerodynamic efficiency.
[0157] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A collaborative jet airfoil optimization design method based on combined parameterization, characterized in that, Includes the following steps: Step S1: Select the original base airfoil, perform CST parameterization on the original base airfoil, and obtain CST parameterization variables that characterize the airfoil shape parameters of the original base airfoil; Step S2, construct the original cooperative jet airfoil: Determine the design variables of the co-jet airfoil shape and determine the design value of each of the co-jet airfoil shape design variables; transform the original base airfoil based on the design values of the co-jet airfoil shape design variables to obtain the original co-jet airfoil corresponding to the original base airfoil; Step S3: Determine the design conditions, combined design variables, design space, optimization objectives, and constraints. The combined design variables include the synergistic jet airfoil shape design variables, synergistic jet flow control parameters, and the CST parameterization variables; Step S4: Select a sampling method and extract several initial sample points within the design space; use a high-precision numerical simulation CFD module to solve the aerodynamic performance of the initial sample points to obtain the response value of each initial sample point, which includes the optimization objective function value and constraint value. Step S5: Construct a surrogate model based on the input-output mapping relationship of each initial sample point and response value; use the point addition criterion to iterate the surrogate model, continuously updating the surrogate model until the generated sample point sequence converges to a local or global optimal solution; wherein, during the iterative optimization process, the cooperative jet airfoil shape design variables, cooperative jet flow control parameters and CST parameterized variables are simultaneously adapted to achieve cooperative optimization of various parameters, balancing the cooperative jet flow control parameters while ensuring the optimization objective; Step S6: Output the optimal values of the combined design variables.
2. The collaborative jet airfoil optimization design method based on combined parameterization according to claim 1, characterized in that, The original basic airfoil is parameterized using CST, specifically as follows: Step S11, using class functions sum type function The product of these factors, superimposed with a function describing the trailing edge thickness, represents the geometry of the original basic airfoil, thus achieving CST parameterization of the original basic airfoil. Its mathematical expression is: upper surface of the airfoil: ； Lower surface of the airfoil: ； in: It is the upper surface of the airfoil coordinate; It is an airfoil surface ; It is a function class; It is the upper surface shape function of the airfoil; The trailing edge of the upper surface of the airfoil coordinate; It is the lower surface of the airfoil coordinate; It is the lower surface shape function of the airfoil; It is the trailing edge of the lower surface of the airfoil coordinate; Class function The definition is as follows: ； in: , The values are 0.5 and 1.0, which are fixed values and represent the first and second exponents, respectively. The type function is defined as follows: ； ； ； in: For the first A Bernstein polynomial, =0,1,…, ; Subtract 1 from the total number of Bernstein polynomials; and , respectively the first on the upper surface of the airfoil The undetermined coefficients and the first undetermined coefficient on the lower surface of the airfoil. One undetermined coefficient; for Undetermined coefficient of upper surface of airfoil when = 0 Undetermined coefficients of the lower surface of the airfoil With respect to the leading edge radius of the airfoil It has the following relationship: ； For airfoil surfaces When =1, its airfoil upper surface shape function and airfoil lower surface shape function It has the following relationship: ； ； in: and These are the trailing edge tangent angles of the upper surface and the lower surface of the airfoil, respectively. Step S12, establish equations ; ； in: It is the number of known airfoil coordinate points on the upper surface of the airfoil; It is the number of known airfoil coordinate points on the lower surface of the airfoil; The first of the upper surface of the airfoil Known airfoil coordinates coordinate; The first of the lower surface of the airfoil Known airfoil coordinates coordinate; equation middle, for Undetermined coefficients and shape function of the upper surface of the airfoil when = 0 The product term; for =1,…, The sum of the products of the undetermined coefficients of the upper surface of the airfoil and the shape function; for Undetermined coefficients and shape function of the lower surface of the airfoil when = 0 The product term; for =1,…, The sum of the products of the undetermined coefficients of the lower surface of the airfoil and the shape function; Step S13: Ensure the number of known airfoil coordinate points is greater than the number of undetermined coefficients, and solve the equation using the least squares method. The minimum value is obtained to get the values of each undetermined coefficient, which are the variable values of the CST parameterized variables; the number of CST parameterized variables is... .
3. The collaborative jet airfoil optimization design method based on combined parameterization according to claim 1, characterized in that, The design variables for the synergistic jet airfoil include the location of the air inlet. Air inlet size Intake port position and intake port size At least one of them.
4. The collaborative jet airfoil optimization design method based on combined parameterization according to claim 1, characterized in that, Based on the design values of the synergistic jet airfoil shape design variables, the original base airfoil is transformed to obtain the original synergistic jet airfoil corresponding to the original base airfoil, including: According to the location of the air outlet Design values and air intake position The design values are used to determine the air inlet and air inlet at the corresponding positions of the original basic airfoil, and to make the normals of the air inlet and air inlet tangent to the original basic airfoil. Between the air inlet and air inlet of the original basic airfoil, a sinking section airfoil is constructed to transform the original basic airfoil and obtain the original cooperative jet airfoil corresponding to the original basic airfoil. The method for constructing the sinking section airfoil is as follows: the original airfoil is obtained by translating the original airfoil point between the air inlet and the air inlet inward along the normal direction of the original airfoil by a certain distance. Translation distance Determine using the following formula: ； ； in: This represents the c-th airfoil point starting from the intake end; This indicates the number of airfoil points from the intake end to the exhaust end; This represents the movement coefficient of the c-th airfoil point; and These represent the sizes of the air inlet and outlet. Design values and intake port size Design values; This represents the translation distance of the c-th airfoil point; Therefore, translation distance Based on the dimensions of the air inlet, air outlet, and the distance between the airfoil point and the air outlet determined by linear interpolation, an adaptive association between the airfoil curve of the sinking section and the original basic airfoil curve is achieved through linear mapping.
5. The collaborative jet airfoil optimization design method based on combined parameterization according to claim 1, characterized in that, In step S3, the design conditions include the incoming Mach number. Reynolds number Angle of attack The coordinated jet flow control parameters are: a constant mass flow rate is given at the blowing and suction ports. For the control parameters of the coordinated jet flow; The optimization objectives include maximizing the lift coefficient and minimizing the drag coefficient; The constraints include: under the design conditions, the lift coefficient of the optimized airfoil is greater than that of the original optimized airfoil; the drag coefficient of the optimized airfoil is less than that of the original optimized airfoil; and the absolute value of the difference between the thickness of the base airfoil corresponding to the optimized airfoil and the original base airfoil is less than a certain proportion of the thickness of the original base airfoil.
6. The collaborative jet airfoil optimization design method based on combined parameterization according to claim 1, characterized in that, Step S4 includes: Step S41: Within the design space, initial sample points are extracted using Latin hypercube sampling. Step S42: Use the high-precision numerical simulation CFD module to solve the aerodynamic performance of the initial sample points and obtain the response value including the equivalent lift-to-drag ratio.
7. The collaborative jet airfoil optimization design method based on combined parameterization according to claim 1, characterized in that, Step S5 includes: Step S51: Based on the input-output mapping relationship of the initial sample points, construct the Kriging surrogate model, optimize the model hyperparameters using the Hooke-Jeeves method, and establish a preliminary response surface prediction for the aerodynamic characteristics of the cooperative jet airfoil. Step S52: The SBMO framework based on the surrogate model is adopted. In each iteration, the MSP minimization prediction and EI expectation improvement hybrid point addition criteria are used to generate new sample points in parallel, and the new sample points in each round are submitted to the high-precision numerical simulation CFD module for calculation. Step S53: Feed the calculation results back to the sample set to retrain the Kriging surrogate model. By continuously correcting local biases, the prediction accuracy of the Kriging surrogate model in the high-dimensional extreme value region is improved. Step S54: Repeat the iterative process from step S52 to step S53 until the total number of sample points reaches the preset value or the objective function convergence criterion is met. Step S55: On the finally updated global response surface, extract the optimal design scheme that meets the preset target according to the optimization criterion, and output the cooperative jet airfoil parameters and geometric model that achieve the best balance between aerodynamic efficiency and jet control parameters.