An aero-engine low-pressure turbine blade leading edge modeling numerical optimization design method and structure based on response surface modeling

Abstract

The present application relates to the technical field of aero-engine aerodynamic optimization and computer-aided design, and discloses a numerical optimization design method and structure for aero-engine low-pressure turbine blade leading edge modeling based on response surface modeling. The method realizes precise matching of Klebanoff stripe and large-scale vortex generation timing by adjusting flow or rotor speed to change wake injection angle, and promotes stripe impact and accelerates large-scale vortex breakup. Meanwhile, by constructing a blade leading edge modeling parameterization model and establishing a response surface proxy model for the combination of modeling design variable parameters and boundary layer velocity mean square deviation, the optimal design variable parameter combination is determined in the constraint domain with the maximum velocity mean square deviation in the boundary layer as the target. The present application effectively reduces the boundary layer momentum thickness and total pressure loss under the premise of ensuring constant blade load, improves the design efficiency and engineering applicability under low Reynolds number conditions, and does not need to introduce additional flow control structures, thus being simple in structure and easy to implement.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine aerodynamic optimization and computer-aided design technology, and relates to unsteady flow control, parameter optimization and structural design of high-load low-pressure turbines for aero-engines. In particular, it relates to a flow control technology that enhances Klebanoff stripe intensity and precisely controls phase by co-optimizing the local geometry of the blade leading edge and the upstream wake injection morphology, so as to promote efficient interaction between Klebanoff stripes and Kelvin-Helmholtz large-scale vortices and suppress laminar separation bubbles on the suction surface. Specifically, it is a numerical optimization design method and structure for the leading edge shape of aero-engine low-pressure turbine blades based on response surface modeling. Background Technology

[0002] To improve thrust-to-weight ratio, modern aero-engines typically employ high-load, low-Reynolds-number designs for their low-pressure turbines. Under low Reynolds-number conditions, the boundary layer momentum on the suction surface of high-load low-pressure turbine blades is insufficient, making it difficult to overcome the adverse pressure gradient at the rear. This easily leads to the formation of laminar separation bubbles, resulting in a significant increase in airfoil losses and consequently reducing turbine efficiency. In such designs, the unsteady wake generated by the upstream blade row is a core factor in regulating the boundary layer transition of the downstream blades and suppressing laminar separation bubbles on the suction surface. As a key parameter influencing the wake-boundary layer interference process, the optimized design of the low-pressure turbine blade leading-edge geometry, geared towards flow control objectives, is of great significance for improving the overall aerodynamic efficiency of the low-pressure turbine.

[0003] Traditional control methods based on wake-induced boundary layer transition to suppress separation are relatively mature. However, existing techniques mostly focus on experimental observation, single-parameter variation analysis, or local geometric modification relying on empirical rules, and have not yet solved the time mismatch problem of the interaction between wake-induced Klebanoff fringes and the Kelvin-Helmholtz (KH) large-scale eddies in the separation region. Because the fringe propagation velocity lags significantly behind the wake body, it often misses the optimal opportunity to interact with the large-scale eddies when it reaches the separation region, or causes the large-scale eddies to maintain a two-dimensional coherent structure for a long time without effective three-dimensional perturbation. This results in the boundary layer shape factor H12 remaining at a high level greater than 3.5, significantly increasing momentum thickness and total pressure loss.

[0004] Klebanoff fringes can enhance the effect of wake-induced boundary layer transition. Specifically, when the upstream wake sweeps across the leading edge of the downstream blade, it induces significantly enhanced Klebanoff fringes (alternating structures of flow-elongated low-velocity and high-velocity fluids) within the boundary layer through a "shear-masking" mechanism. These wake-amplified Klebanoff fringes propagate downstream at approximately 0.5–0.88 times the free-flow velocity, while the wake body propagates at a velocity close to the free-flow velocity. When the Klebanoff fringes reach the laminar separation bubble region behind the blade's suction surface, they interact with large-scale spanwise vortices (KH vortices) generated within the boundary layer due to KH instabilities. This interaction distorts the two-dimensional coherence of the KH vortices through the spanwise inhomogeneity of the fringes, causing the KH vortices to break up and rapidly transition into turbulence, thereby suppressing the momentum loss caused by the long-term presence of large-scale vortices. However, this process is characterized by strong nonlinearity and high-dimensional parameter coupling, involving complex mapping relationships between wake injection state, local geometry, boundary layer integral parameters and flow field statistics. Traditional methods that rely on single-condition trial calculations or empirical shaping are difficult to balance computational efficiency, prediction accuracy and optimization convergence.

[0005] In summary, existing research on the leading edge design of low-pressure turbine blades for aero-engines still has shortcomings in terms of unsteady flow field data characterization, key spatiotemporal feature extraction, aerodynamic response prediction, and numerical optimization design for separation suppression objectives. Therefore, how to construct an optimization design method for low-pressure turbine blade leading edge design that can accurately characterize the large-scale vortex coupling law between wake-induced fringes and separation zone and support efficient numerical optimization is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] (a) Purpose of the invention

[0007] To address the aforementioned deficiencies and shortcomings in existing technologies, particularly the technical problems of Klebanoff fringes arriving later than large-scale vortex formation and the significant increase in momentum thickness due to the prolonged existence of large-scale vortices, this invention aims to provide a numerical optimization design method and structure for the leading edge shape of low-pressure turbine blades for aero-engines based on response surface modeling. By synergistically optimizing the mapping relationship between the local geometry of the blade leading edge, the upstream wake injection morphology, and the unsteady response of the boundary layer, this invention achieves enhanced Klebanoff fringe intensity and precise phase control, promotes efficient interaction between the fringes and Kelvin-Helmholtz (KH) large-scale vortices, accelerates the rupture of large-scale vortices, thereby suppressing laminar separation bubbles on the suction surface, reducing boundary layer momentum thickness, and improving the prediction accuracy, efficiency, and engineering applicability of the leading edge shape optimization design.

[0008] (II) Technical Solution

[0009] To achieve the objective of this invention and solve its technical problems, the present invention adopts the following technical solution:

[0010] The first objective of this invention is to provide a numerical optimization design method for the leading edge shape of low-pressure turbine blades for aero-engines based on response surface modeling. This method enhances the intensity of wake-induced Klebanoff fringes, improves the temporal matching relationship between Klebanoff fringes and the large-scale KH vortex on the suction surface, suppresses laminar separation bubbles on the suction surface of low-pressure turbine blades, and reduces the total pressure loss of the blade profile through numerical optimization design of the blade leading edge geometry under high load and low Reynolds number conditions. The method includes at least the following steps:

[0011] SS1. Flow field data acquisition: For the target low-pressure turbine blade, obtain the time-space distribution data of the integral parameters of the blade suction surface boundary layer under the set operating conditions through numerical simulation or experimental measurement;

[0012] SS2. Spatiotemporal Feature Identification: Based on the distribution data, the wake head range, wake tail range, laminar separation range, wake-induced transition interval, and Klebanoff fringe passage interval within the boundary layer of the suction surface of the target low-pressure turbine blade under the upstream wake sweeping action are identified, and the spatial relationship between the Klebanoff fringe and the spanwise vortex and the timing of the Klebanoff fringe reaching the wake-induced transition interval are determined.

[0013] SS3. Wake Injection State Matching: Based on the airflow angle, the relative linear velocity of the upstream blade and the axial velocity of the airflow, the wake injection angle of the upstream wake relative to the leading edge of the target low-pressure turbine blade is calculated, and the wake injection angle is adjusted by changing the upstream turbine speed and / or the incoming flow rate so that the arrival time of Klebanoff fringes and the formation time of KH large-scale vortex meet the preset matching conditions.

[0014] SS4. Parametric Modeling and Evaluation of Leading Edge Shape: Based on the preset matching conditions, a parametric model of the leading edge shape of the target low-pressure turbine blade is constructed. Its geometric shape is characterized by multiple continuous design variables. Multiple sets of design variable parameter combinations are randomly generated in the design variable space using a sampling method, and numerical calculations or experimental evaluations are performed one by one. The velocity root mean square error in the boundary layer at a preset axial position (e.g., 50%) of the suction surface is extracted as a flow response evaluation quantity.

[0015] SS5. Construction of Response Surface Surrogate Model: Based on the combination of design variable parameters and their corresponding flow response evaluation quantities, a response surface surrogate model is constructed between the design variables and the mean square error of the velocity within the boundary layer. The accuracy of the response surface surrogate model is verified by residual analysis to ensure that the prediction error is within the allowable range.

[0016] SS6. Optimization Solution: With the goal of maximizing the mean square error of velocity within the boundary layer, the validated response surface surrogate model is optimized within the parameter constraint domain to obtain the optimal combination of design variable parameters that meets the flow control requirements of the target low-pressure turbine blade leading edge.

[0017] SS7. Optimization Result Verification (Preferred Step): Based on the optimal design variable parameter combination obtained in step SS6, reconstruct the leading edge shape of the target low-pressure turbine blade, and conduct verification experiments or numerical calculations under the same working boundary conditions as steps SS4 and SS5 to obtain the corresponding verification results; compare the deviation between the verification results and the prediction results of the response surface surrogate model. If the relative error between the two is lower than the preset allowable error threshold (e.g., 5%), then the optimal design variable parameter combination is confirmed to be effective and the corresponding leading edge shape structure of the target low-pressure turbine blade is output. Otherwise, new design variable parameter combination samples need to be added and the response surface surrogate model needs to be reconstructed. Steps SS6 and SS7 are executed again until the optimal design variable parameter combination that meets the preset allowable error threshold requirement is obtained and the corresponding leading edge shape structure scheme is output.

[0018] The second objective of this invention is to provide a leading edge styling structure for a low-pressure turbine blade of an aero-engine obtained based on the above method.

[0019] (III) Technical Effects

[0020] Compared with the prior art, the numerical optimization design method and structure for the leading edge shape of low-pressure turbine blades of aero-engines based on response surface modeling of the present invention has the following beneficial and significant technical effects:

[0021] (1) This invention constructs a parameterized model of the blade leading edge shape and establishes a response surface proxy model between design variables and boundary layer response quantities, transforming the traditional design method that relies on experience-based shaping and single-parameter trial into a quantifiable, predictable, and verifiable numerical optimization process; and while ensuring that the blade load and steady blade loss remain unchanged, by adjusting the flow rate and rotational speed and combining it with the leading edge shape structure, the precise matching of the formation timing of Klebanoff stripes and Kelvin-Helmholtz large-scale vortices is achieved, so that the Klebanoff stripes impact wake and the Kelvin-Helmholtz large-scale vortex generated by the separation action can achieve rapid rupture of the large-scale vortex, reduce the boundary layer momentum thickness and the total pressure loss of the blade, and at the same time improve the computational efficiency, parameter optimization ability and result repeatability of the leading edge shape design.

[0022] (2) This invention deeply couples the geometric parameterization modeling of the leading edge shape with the response surface surrogate model technique. Using the mean square error of boundary layer velocity fluctuations as the evaluation metric for flow response, a high-precision explicit surrogate mapping relationship between design variables and aerodynamic flow response is constructed. The effectiveness of the model is rigorously verified through residual statistical hypothesis testing. This method replaces the computationally expensive direct CFD evaluation with a surrogate model to drive optimization iteration, significantly reducing the overall computational resource consumption while ensuring the reliability of optimization. It provides an efficient and engineering-feasible computational framework for leading-edge aerodynamic optimization design in complex unsteady turbulent fields.

[0023] (3) This invention integrates unsteady flow field measurement or numerical simulation, spatiotemporal feature identification, response surface proxy modeling, parameter optimization and result verification into the same optimization design process, which can improve the prediction efficiency, optimization accuracy and engineering feasibility of leading edge shape parameter design; at the same time, this invention does not require the introduction of new flow control structure, and has the characteristics of simple structure, convenient design and processing and easy implementation. Attached Figure Description

[0024] The accompanying drawings, which form part of this specification, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. Hereinafter, embodiments of the invention will be described in detail with reference to the accompanying drawings, wherein:

[0025] Figure 1 This is a schematic diagram illustrating the implementation process of the numerical optimization design method for the leading edge shape of low-pressure turbine blades for aero-engines provided in this embodiment of the invention.

[0026] Figure 2 This is a schematic diagram of the wake injection angle and flow control mechanism.

[0027] Figure 3 This is a geometric schematic diagram of the leading edge shape structure of the blade. In the diagram, A, B, and C are the tip of the leading edge, the dividing point between the leading edge compression section and the smooth transition section, and the connection point between the end of the leading edge shape structure and the original blade shape, respectively.

[0028] Figure 4 This is a spatiotemporal evolution diagram of the interaction between the wake, stripes, and separation bubble. In the diagram: the horizontal axis s / S0 represents the dimensionless position along the flow direction of the suction surface of the target low-pressure turbine blade, where s is the current flow direction arc length coordinate of the suction surface, and S0 is the reference total arc length of the suction surface; the vertical axis t / T represents the dimensionless time phase, where t is the current time, and T is the characteristic time corresponding to the upstream wake passing through one cycle.

[0029] Figure labeling: 1-Wake injection angle, 2-Klebanoff stripes, 3-Kelvin-Helmholtz large-scale vortex, 4-Protoblade shape, 5-Leading edge shape structure, 6-Curvature comb of the shape, 7-Propagation path of Klebanoff stripes formed at the tail of the wake, 8-Propagation path of the large-scale vortex triggered at the center of the wake, 9-Separation bubble region, 10-Quiet zone formed after induced transition. Detailed Implementation

[0030] This invention aims to provide a numerical optimization design method and structure for the leading edge shape of low-pressure turbine blades in aero-engines based on response surface modeling. To make the technical solutions and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. The described embodiments are some, but not all, embodiments of this invention, and are exemplary, intended to explain this invention, and should not be construed as limiting this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0031] like Figure 1 As shown in the embodiment of the present invention, the numerical optimization design method for the leading edge shape of aero-engine low-pressure turbine blades based on response surface modeling is used to enhance the intensity of wake-induced Klebanoff fringes, improve the temporal matching relationship between Klebanoff fringes and large-scale vortices of the suction surface KH, suppress laminar separation bubbles on the suction surface of low-pressure turbine blades, and reduce the total pressure loss of the airfoil by numerically optimizing the leading edge geometry of the blade under high load and low Reynolds number conditions. The method mainly includes the following steps in its implementation:

[0032] SS1. Flow Field Data Acquisition:

[0033] For target low-pressure turbine blades, time-space distribution data of integral parameters of the blade suction surface boundary layer under specified operating conditions are obtained through numerical simulation or experimental measurement. Specifically, the transient flow field evolution process within multiple wake passage periods can be monitored, and parameters such as suction surface boundary layer displacement thickness, momentum thickness, shape factor, wall friction coefficient, and surface hydrostatic coefficient can be continuously collected and temporally correlated. This generates a time-space distribution dataset reflecting the unsteady evolution characteristics of the boundary layer, providing fundamental data support for subsequent wake identification, separation determination, and fringe propagation analysis.

[0034] In this embodiment, any rotor speed or inlet flow rate is selected for numerical simulation or experimental measurement. The transient flow field within the passing period of multiple wakes under the set operating conditions is analyzed, and the time-space distribution data of the integral parameters of the blade suction surface boundary layer are extracted accordingly. These parameters include at least the boundary layer displacement thickness, momentum thickness, shape factor, wall friction coefficient, surface static pressure coefficient, and flow direction coordinate distribution information corresponding to the time phase. When experimental measurement is used, any one of a high-frequency response pressure sensor, a hot-wire anemometer, or a time-resolved particle image velocimetry (PIV) is used to measure the transient flow field within the passing period of multiple wakes. The unsteady flow of the boundary layer of the target low-pressure turbine blade suction surface is also collected to obtain the time-space data of the integral parameters of the blade suction surface boundary layer.

[0035] When using numerical simulation, the three-dimensional unsteady Reynolds-averaged Navier-Stokes equations are preferred for solving the flow field. The γ-Reθ transition model is chosen as the turbulent closed-loop model to accurately capture the laminar-turbulent transition process within the boundary layer and the formation and evolution of Klebanoff fringes. The computational domain employs a multi-channel periodic grid containing at least one upstream blade channel and a downstream target blade channel. Dynamic-static interference effects are handled using a dynamic-static interface sliding grid technique, and the dimensionless wall distance y of the first grid layer near the wall is specified. + The value must be less than 1, and the mesh should be refined in the near-wall region of the blade suction surface. The time step should be set to ensure that each upstream blade passes through no less than 200 physical time steps within the cycle to fully distinguish the temporal evolution characteristics of the unsteady sweep of the wake. The convergence criterion is based on the residual of each conserved quantity decreasing by no less than four orders of magnitude, supplemented by the periodic convergence of the boundary layer parameter time series at the suction surface monitoring point as a supplementary criterion to ensure the full development and periodic stability of the unsteady flow field.

[0036] SS2. Spatiotemporal Feature Recognition:

[0037] Based on the temporal-spatial distribution data of the integral parameters of the blade suction surface boundary layer, the wake head range, wake tail range, laminar separation range, wake-induced transition zone, and Klebanoff fringe passage zone within the boundary layer of the target low-pressure turbine blade suction surface under upstream wake sweeping are calibrated. The spatial relationship between the Klebanoff fringes and the spanwise vortex, as well as the timing of the Klebanoff fringes reaching the wake-induced transition zone, are also determined. In practice, the boundary layer shape factor, wall friction coefficient, velocity deficit distribution, and temporal phase evolution characteristics can be combined to jointly identify key regions during the wake sweeping process.

[0038] Specifically, it is necessary to determine the spatial relationship between Klebanoff fringes and spanwise vortices, and to focus on observing the timing of the Klebanoff fringes reaching the wake-induced transition region. The following key moments need to be determined: the moment when the large-scale vortex begins to form in the separation region, and the moment when the strongest region of the Klebanoff fringes reaches the wake-induced transition region. If the arrival time of the Klebanoff fringes is later than the formation time of the large-scale vortex, it indicates that the Klebanoff fringes arrive late. Conversely, it indicates that the Klebanoff fringes arrive early.

[0039] In this embodiment, based on the simulation or measurement data obtained in step SS1, the following key regions are first identified: the wake head region, i.e., the leading edge boundary of the high turbulence intensity region; the wake tail region, i.e., the trailing edge of the region where the boundary layer edge velocity recovers to the incoming flow level; the laminar separation region, i.e., the boundary layer recirculation region; the wake-induced transition region, i.e., the transition region where the laminar boundary layer transforms into turbulence; and the Klebanoff fringe passage region, i.e., the propagation path of the spanwise periodic low-velocity fringes. The propagation path of the wake core, the generation location and propagation trajectory of the Klebanoff fringes, and the spatiotemporal evolution range of the separation bubble are recorded to establish a spatiotemporal map of the interaction between the wake, fringes, and separation bubble. The established time-space map is shown below. Figure 4 As shown, the horizontal axis represents the flow direction of the blades, and the vertical axis represents time. In the figure, mark 7 shows the propagation path of the Klebanoff stripes formed at the tail of the wake, mark 8 shows the propagation path of the large-scale eddy triggered at the center of the wake, mark 9 shows the separation bubble region, and mark 10 shows the calm zone formed after induced transition.

[0040] The wake head and wake tail ranges are jointly calibrated based on the abrupt change range of the boundary layer integral parameters and the velocity deficit range; the laminar separation range is determined based on the range where the wall friction coefficient changes from positive to negative and then back to positive; the wake-induced transition range is determined based on the range where the boundary layer shape factor decreases rapidly, the pulsation intensity increases, and the velocity profile evolves from laminar to turbulent; and the Klebanoff stripes are determined by the range based on the continuous appearance of the high- and low-velocity alternating structure of the flow velocity stripes inside the boundary layer. Based on this, the spatiotemporal correspondence between separation, transition, wake, and stripes is established.

[0041] Furthermore, in step SS2, when determining the spatial relationship between Klebanoff fringes and spanwise vortices, it is necessary to determine the central propagation trajectory of Klebanoff fringes within the boundary layer behind the blade suction surface, the axial spacing and phase difference between the fringe peak perturbation position and the core region of the large-scale KH vortex; and to determine the timing of Klebanoff fringes reaching the wake-induced transition zone, including extracting the time when the large-scale KH vortex begins to form in the laminar separation zone of the suction surface based on the time phase sequence, and determining the time when the peak intensity region of Klebanoff fringes reaches the wake-induced transition zone. When the latter is later than the former, it is determined that the arrival of Klebanoff fringes is delayed; when the latter is earlier than the former, it is determined that the arrival of Klebanoff fringes is advanced. The above determination results are quantitatively recorded in the form of phase angles to provide criteria for subsequent wake injection state matching.

[0042] It should be noted that step SS2, by jointly identifying the abrupt change characteristics of boundary layer integral parameters, velocity deficit evolution characteristics, fringe propagation trajectory, and phase change of the separation bubble, incorporates wake sweeping, fringe generation, separation development, and induced transition into a unified spatiotemporal criterion system. This enables quantitative characterization of the arrival timing of Klebanoff fringes and their correspondence with the large-scale vortex space of KH, providing direct criteria for subsequent wake injection state adjustment and leading edge shape numerical optimization, thereby establishing a stable mapping relationship between flow mechanism identification and structural design variables.

[0043] SS3. Trail Injection State Matching:

[0044] The wake injection angle of the upstream wake relative to the leading edge of the target low-pressure turbine blade is calculated based on the airflow angle, the relative linear velocity of the upstream blade, and the axial velocity of the airflow. The wake injection angle is adjusted by changing the upstream turbine speed and / or the incoming flow rate so that the arrival time of Klebanoff fringes and the formation time of KH large-scale vortex meet the preset matching conditions.

[0045] Specifically, based on the judgment result of step SS2, the injection angle of the upstream wake relative to the leading edge of the blade is adjusted by regulating the flow rate or rotor speed, and step SS1 is repeated. The timing of the generation of Klebanoff stripes and Kelvin-Helmholtz large-scale vortices is related to the wake injection angle; the larger the injection angle, the later the Kelvin-Helmholtz large-scale vortex is generated. The wake injection angle is defined as the angle between the wake flow direction and the axial chord of the blade, such as... Figure 2 As shown in mark 1, its value can be determined by the following formula based on the kinematic parameters of the upstream blades and the incoming flow conditions:

[0046]

[0047] in, α Inject an angle into the wake;β The airflow angle is based on the axial direction. U b The relative linear velocity of the upstream blade; U x The axial velocity of the airflow is denoted as . The parameter on the right side of the equation can be adjusted by the flow rate or rotor speed. By adjusting the flow rate or rotor speed, a precise match can be achieved between the formation timing of Klebanoff fringes and the KH large-scale vortex, allowing the Klebanoff fringes to impact the wake and the KH large-scale vortex generated by the separation process, thereby achieving rapid rupture of the large-scale vortex and reducing the boundary layer momentum thickness.

[0048] Preferably, the aforementioned preset matching condition is that the phase deviation between the peak value of the Klebanoff fringe main disturbance reaching the upstream boundary of the laminar separation bubble or the initial entrainment zone of the KH large-scale vortex and the characteristic moment of KH large-scale vortex formation is within a preset allowable range, and the Klebanoff fringe disturbance intensity corresponding to the phase deviation is sufficient to cause the two-dimensional coherent structure of the KH large-scale vortex to break; when the Klebanoff fringe arrives late, the wake injection angle is increased by increasing the upstream turbine speed and / or adjusting the inflow flow rate; when the Klebanoff fringe arrives ahead, the wake injection angle is reduced by adjusting in the opposite direction, so that the arrival time of the Klebanoff fringe and the formation time of the KH large-scale vortex satisfy the preset matching condition.

[0049] It should be noted that the key to step SS3 lies in constructing the wake injection angle as an intermediate control parameter connecting the incoming flow conditions, the upstream blade motion state, and the downstream unsteady flow response. By converting the Klebanoff fringe arrival phase deviation into adjustable variables of rotational speed and / or flow rate, an iterative matching path consisting of identification, judgment, and correction can be formed, thereby improving the temporal controllability and flow control effectiveness of the interaction between the fringe and the large-scale KH eddy.

[0050] SS4. Parametric Modeling and Evaluation of Leading Edge Shape:

[0051] Based on the confirmation that the Klebanoff stripes and the KH large-scale vortex timing matching conditions are satisfied, a parametric model of the leading edge shape of the target low-pressure turbine blade is constructed. Its geometric shape is characterized by multiple continuous design variables. Multiple sets of design variable parameter combinations are randomly generated in the design variable space using a sampling method, and numerical calculations or experimental evaluations are performed one by one. The velocity root mean square error in the boundary layer at the preset axial position of the suction surface (preferably at 50% axial position of the suction surface) is extracted as the flow response evaluation quantity.

[0052] Preferably, the leading edge shaping structure corresponding to the parametric model of the leading edge shape includes, along the flow direction, a leading edge compression section (AB section) and a smooth transition section (BC section), as follows: Figure 3As shown, the leading-edge compression section extends from the leading-edge tip of the blade outward and adopts a rapid lift profile design to compress the local boundary layer thickness and enhance the penetration of wake disturbances into the boundary layer. The smooth transition section is smoothly connected to the leading-edge compression section and maintains curvature continuity with the optimized blade profile at the end to avoid introducing additional flow separation around the surface. Furthermore, the design variables of the leading-edge profile parameterization model include at least the maximum thickness, starting position, total length, and the length ratio of the leading-edge compression section to the smooth transition section. The maximum thickness is controlled within 2% of the axial chord length of the target low-pressure turbine blade, the starting position is within 5% of the axial chord length from the leading edge, the total length is less than 5% of the axial chord length, and the length ratio is controlled within the range of 0.5 to 0.8.

[0053] Furthermore, sampling methods can employ stratified random sampling, Latin hypercube sampling, or low-difference sequence sampling with uniform coverage of the design variable space. Before sampling, each design variable is dimensionless to reduce the impact of differences in dimensions and value ranges on the stability of the response surface surrogate model construction, thereby improving the coverage of the design variable space and the accuracy of flow response fitting under finite sample conditions. For each set of design variable parameter combinations, a computational grid is independently constructed for the blade leading edge morphology structure, and three-dimensional unsteady CFD numerical calculations are performed. The root mean square error of velocity within the boundary layer at 50% axial chord length of the suction surface is extracted as a flow response evaluation metric to reflect the degree to which Klebanoff stripes enhance boundary layer disturbances.

[0054] It should be noted that step SS4 transforms the leading-edge local shape problem into a parametric modeling problem under continuous design variable control, and obtains the correspondence between multiple sets of design variable parameter combinations and flow response evaluation quantities through high-coverage sampling. Using the boundary layer velocity root mean square error as a unified evaluation index, it can directly characterize the degree of stripe amplification and the strength of local disturbance response, thus providing a stable and computable data foundation for surrogate model construction and subsequent optimization.

[0055] SS5. Response Surface Proxy Model Construction:

[0056] Based on the combination of design variable parameters and their corresponding flow response evaluation quantities obtained in step SS4, a response surface surrogate model is constructed between the design variables and the mean square error of the velocity within the boundary layer. The accuracy of the response surface surrogate model is verified by residual analysis to ensure that the prediction error is within the allowable range.

[0057] Specifically, the response surface surrogate model can be established using at least one of the following: quadratic polynomial response surface, Kriging surrogate model, and radial basis function surrogate model. The model coefficients are determined by least squares regression, and the accuracy of the surrogate model is evaluated using cross-validation, coefficient of determination test, root mean square error analysis, and / or residual independence analysis. All of the above accuracy evaluation indicators must simultaneously meet set threshold requirements (such as the coefficient of determination R0). 2 A surrogate model can be considered to have sufficient accuracy if its root mean square error (RMSE) is not less than 0.95 and is less than 5% of the response range. When the surrogate model shows a prediction deviation exceeding the limit in a local highly nonlinear region, the location and range of the region are actively identified by the residual plot and prediction error distribution. The design variable parameter combination samples are added to the region and iteratively updated to improve the surrogate model's ability to express the nonlinear mapping relationship between changes in leading edge shape parameters and flow response.

[0058] It should be noted that step SS5, by introducing a response surface surrogate model, transforms the high-cost, high-dimensional, and highly nonlinear unsteady flow calculation problem into an explicit approximate mapping problem between design variables and the target response. This approach not only significantly reduces the dependence on repeated CFD solutions in the optimization stage but also allows the influence of leading-edge shaping on the boundary layer disturbance response to be expressed in a unified model form, providing a stable data foundation and algorithmic support for subsequent rapid optimization, multi-scheme comparison, and sample iterative updates. Furthermore, the adaptive iterative supplementation mechanism of the surrogate model is a key technical means to ensure the accurate characterization of the nonlinear flow response. Changes in leading-edge shaping parameters in certain regions may trigger abrupt changes in the boundary layer topology (such as the disappearance of separated bubbles or transition position jumps), leading to highly localized nonlinear characteristics on the response surface, which the initial uniformly sampled samples cannot fully cover. By actively identifying highly nonlinear regions and directionally supplementing samples through residual analysis, the accuracy of the surrogate model is dynamically and adaptively improved, effectively avoiding the problem of spurious optimization extrema caused by insufficient local fitting and ensuring the physical rationality of the final optimization results.

[0059] SS6. Optimization Solution:

[0060] With the objective of maximizing the mean square error of the velocity within the boundary layer, the validated response surface surrogate model is optimized within the parameter constraint domain to obtain the optimal combination of design variable parameters that satisfies the leading-edge flow control requirements of the target low-pressure turbine blade. In this embodiment, the validated response surface model is optimized within the parameter constraint domain with the objective of maximizing the mean square error of the boundary layer velocity. Optimization strategies such as gradient descent or genetic algorithms are employed to determine the leading-edge shaping parameter combination that optimizes flow stability.

[0061] Specifically, the optimization process can employ gradient descent or a genetic algorithm for global optimization. The genetic algorithm uses real-number encoding, has a population size of no less than 100 individuals, a maximum number of generations of evolution of no less than 500, uses a roulette wheel selection strategy, a uniform crossover operator, and a Gaussian mutation operator, with a crossover probability of 0.8 and a mutation probability of 0.05. After optimization, a new computational grid is established for the obtained globally optimal design variable parameter combination, and a three-dimensional unsteady CFD numerical simulation is conducted. The simulated total pressure loss coefficient of the airfoil is quantitatively compared with the predicted value of the response surface model to verify the accuracy of the surrogate model prediction. At the same time, the reduction in the total pressure loss coefficient of the optimized leading-edge shape compared with the original baseline airfoil and the degree of effective suppression of the laminar separation bubble on the suction surface are quantitatively analyzed to evaluate the actual improvement effect of the leading-edge shape optimization.

[0062] In addition to maximizing the mean square error of the boundary layer velocity as the main optimization objective, the optimization solution can also use the laminar separation bubble length, total pressure loss coefficient, peak boundary layer shape factor, and Klebanoff fringe arrival phase deviation as joint optimization indices to construct a multi-objective optimization problem. The optimization process can also adopt a non-dominated sorting genetic algorithm (NSGA-II), a sequential quadratic programming algorithm, or a hybrid optimization strategy combining the two. First, search for Pareto solutions that satisfy the constraints in the global scope, and then select the objective compromise solution based on the flow control priority and engineering design constraints to take into account the comprehensive performance of fringe enhancement, phase matching, and aerodynamic loss reduction.

[0063] It should be noted that step SS6 unifies fringe enhancement, phase matching, separation suppression, and loss reduction into a numerical optimization problem under objective function and constraints, transforming the leading-edge morphology design from an empirical shaping approach to an optimization design process with clear evaluation indicators, parameter boundaries, and solution paths. Furthermore, by combining the primary optimization objective of maximizing the mean square error of the boundary layer velocity with engineering constraints such as the total pressure loss coefficient and the length of the laminar separation bubble, a multi-indicator collaborative optimization framework driven by physical mechanisms can be constructed. The global random search characteristics of the genetic algorithm and the efficient function evaluation capability of the response surface surrogate model complement each other, significantly reducing the computational cost of direct CFD optimization while ensuring global optimum.

[0064] SS7. Optimization Result Verification:

[0065] Based on the optimal design variable parameter combination obtained in step SS6, the leading edge shape of the target low-pressure turbine blade is reconstructed. Under the same working boundary conditions as steps SS4 and SS5, a verification experiment or numerical calculation is carried out to verify the result. The deviation between the verification result and the prediction result of the response surface surrogate model is compared. If the relative error between the two is lower than the preset allowable error threshold (e.g., 5%), the optimal design variable parameter combination is confirmed to be effective and the corresponding leading edge shape structure of the target low-pressure turbine blade is output. Otherwise, a new design variable parameter combination sample needs to be added and the response surface surrogate model needs to be reconstructed. Steps SS6 and SS7 are executed again until the optimal design variable parameter combination that meets the preset allowable error threshold requirement is obtained and the corresponding leading edge shape structure scheme is output.

[0066] This embodiment further provides a leading edge styling structure for enhanced Klebanoff stripes on low-pressure turbine blades of aero-engines obtained based on the above method, such as... Figure 3 As shown in the figure (4 is the original blade profile, 5 is the leading edge profile structure, and 6 is the curvature comb of the profile). Arranged on the leading edge profile structure of the blade, it is divided into two sections along the flow direction: a leading edge compression section (AB section) and a smooth transition section (BC section). The leading edge compression section extends from the leading edge endpoint to the outside of the blade and adopts a rapid lifting profile design to compress the local boundary layer thickness. The smooth transition section is smoothly connected to the leading edge compression section and maintains a smooth and continuous curvature with the original blade profile at its end.

[0067] The leading-edge compression section employs a rapid-lift profile design, which rapidly compresses the boundary layer thickness through localized protrusions, reducing shear shielding effects and significantly enhancing the penetration efficiency and energy transfer of wake disturbances into the boundary layer, thus promoting the rapid generation of high-intensity Klebanoff fringes. The smooth transition section uses a gentle transition method to avoid flow separation and ensure that the wake airflow smoothly enters the boundary layer. The maximum thickness of this structure is controlled within 2% of the axial chord length. This size range ensures effective amplification of wake disturbances while avoiding excessive protrusions that could lead to localized flow separation or additional profile losses. The starting position of the structure is within 5% of the axial chord length from the leading edge; the total length of the structure is less than 5% of the axial chord length; and the ratio of the compression section length to the smooth transition section length is controlled within the range of 0.5 to 0.8.

[0068] The objectives of this invention have been fully and effectively achieved through the above embodiments. Those skilled in the art will understand that this invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments described above. Although the invention has been described with reference to what is currently considered the most practical and preferred embodiments, it should be understood that the invention is not limited to the disclosed embodiments, and any modifications that do not depart from the functional and structural principles of the invention will be included within the scope of the claims.

Claims

1. A numerical optimization design method for the leading edge shape of low-pressure turbine blades in aero-engines based on response surface modeling, characterized in that, At least the following steps are included: SS1. For the target low-pressure turbine blade, obtain the time-space distribution data of the integral parameters of the blade suction surface boundary layer under the set operating conditions through numerical simulation or experimental measurement; SS2. Based on the distribution data, calibrate the wake head range, wake tail range, laminar separation range, wake-induced transition interval, and Klebanoff fringe passage interval within the boundary layer of the suction surface of the target low-pressure turbine blade under the upstream wake sweeping action, and determine the spatial relationship between Klebanoff fringe and spanwise vortex, as well as the timing of Klebanoff fringe reaching the wake-induced transition interval. SS3. Calculate the wake injection angle of the upstream wake relative to the leading edge of the target low-pressure turbine blade based on the airflow angle, the relative linear velocity of the upstream blade and the axial velocity of the airflow, and adjust the wake injection angle by changing the upstream turbine speed and / or the incoming flow rate so that the arrival time of Klebanoff fringes and the formation time of KH large-scale vortex meet the preset matching conditions. SS4. Based on the preset matching conditions, construct a parametric model of the leading edge shape of the target low-pressure turbine blade, use a sampling method to randomly generate multiple sets of design variable parameter combinations in the design variable space and perform numerical calculations or experimental evaluations one by one, and extract the velocity root mean square error in the boundary layer at the preset axial position of the suction surface as the flow response evaluation quantity. SS5. Based on the combination of design variable parameters and their corresponding flow response evaluation quantities, construct a response surface surrogate model between the design variables and the mean square error of velocity within the boundary layer, and verify the accuracy of the response surface surrogate model through residual analysis; SS6. With the goal of maximizing the mean square error of velocity within the boundary layer, the validated response surface surrogate model is optimized within the parameter constraint domain to obtain the optimal combination of design variable parameters that meets the flow control requirements of the target low-pressure turbine blade leading edge.

2. The method according to claim 1, characterized in that, In step SS1, the numerical simulation or experimental measurement is performed on the transient flow field within the passing period of multiple wakes under the set operating conditions, and the time-space distribution data of the integral parameters of the blade suction surface boundary layer are extracted accordingly. These parameters include at least the boundary layer displacement thickness, momentum thickness, shape factor, wall friction coefficient, surface static pressure coefficient, and flow direction coordinate distribution information corresponding to the time phase. When experimental measurement is used, at least one of the following is selected: a high-frequency response pressure sensor, a hot-wire anemometer, or a time-resolved particle image velocimeter to collect data on the unsteady flow of the boundary layer of the target low-pressure turbine blade suction surface.

3. The method according to claim 2, characterized in that, In step SS1, when using numerical simulation, the flow field is solved using the three-dimensional unsteady Reynolds-averaged Navier-Stokes equations. The turbulent closed model is the γ-Reθ transition model. The computational domain uses a multi-channel periodic grid containing at least one upstream blade channel and a downstream target blade channel. The dynamic-static interference effect is handled using the dynamic-static interface sliding grid technique. The dimensionless wall distance y of the first layer of grids near the wall is... + The value must be less than 1, and the mesh should be refined in the near-wall region of the blade suction surface. The time step should be set to ensure that each upstream blade passes through no less than 200 physical time steps within the cycle to fully distinguish the temporal evolution characteristics of the unsteady sweep of the wake. The convergence criterion is based on the residual of each conserved quantity decreasing by no less than four orders of magnitude.

4. The method according to claim 1, characterized in that, In step SS2, the range of the wake head and the wake tail are jointly calibrated based on the abrupt change range of the boundary layer integral parameters and the velocity deficit range; the laminar separation range is determined based on the range where the wall friction coefficient changes from positive to negative and then back to positive; the wake-induced transition range is determined based on the range where the boundary layer shape factor decreases rapidly, the pulsation intensity increases, and the velocity profile evolves from laminar to turbulent; and the Klebanoff stripes are determined by the range based on the continuous appearance of the high- and low-velocity alternating structure of the flow velocity stripes inside the boundary layer, and the spatiotemporal correspondence between separation, transition, wake, and stripes is established accordingly.

5. The method according to claim 1 or 4, characterized in that, In step SS2, when determining the spatial relationship between Klebanoff fringes and spanwise vortices, it is necessary to determine the central propagation trajectory of Klebanoff fringes in the boundary layer behind the blade suction surface, the axial spacing and phase difference between the fringe peak perturbation position and the core region of the KH large-scale vortex; determine the timing of Klebanoff fringes reaching the wake-induced transition zone, including extracting the time when the KH large-scale vortex begins to form in the laminar separation zone of the suction surface based on the time phase sequence, and determining the time when the Klebanoff fringes intensity peak region reaches the wake-induced transition zone. When the latter is later than the former, it is determined that the Klebanoff fringes arrive late; when the latter is earlier than the former, it is determined that the Klebanoff fringes arrive ahead.

6. The method according to claim 1, characterized in that, In step SS3, the wake injection angle is based on Perform calculations, where α The wake injection angle is defined as the angle between the wake's inflow direction projection vector and the blade's axial chord line. β The absolute angle of the airflow is measured using the axial chord line of the blade as the reference. U b Let be the relative linear velocity of the upstream blade. U x This refers to the axial velocity component of the airflow. The preset matching condition is that the phase deviation between the peak value of the Klebanoff fringe main disturbance reaching the upstream boundary of the laminar separation bubble or the initial entrainment zone of the KH large-scale vortex and the characteristic moment of KH large-scale vortex formation is within a preset allowable range, and the Klebanoff fringe disturbance intensity corresponding to the phase deviation is sufficient to cause the two-dimensional coherent structure of the KH large-scale vortex to break. When the Klebanoff fringe arrives late, the wake injection angle is increased by increasing the upstream turbine speed and / or adjusting the inflow rate. When the Klebanoff fringe arrives ahead, the wake injection angle is reduced by adjusting in the opposite direction, so that the arrival time of the Klebanoff fringe and the formation time of the KH large-scale vortex satisfy the preset matching condition.

7. The method according to claim 1, characterized in that, In step SS4, the leading edge styling structure corresponding to the parametric model of the leading edge styling includes a leading edge compression section and a smooth transition section along the flow direction. The leading edge compression section extends from the tip of the blade leading edge to the outside of the blade and adopts a rapid lift profile design to compress the local boundary layer thickness and enhance the penetration of the wake disturbance into the boundary layer. The smooth transition section is smoothly connected to the leading edge compression section and maintains curvature continuity with the optimized blade profile at the end. Furthermore, the design variables of the parametric model of the leading edge styling include at least the maximum thickness, the starting position, the total length, and the length ratio of the leading edge compression section to the smooth transition section. The maximum thickness is controlled within 2% of the axial chord length of the target low-pressure turbine blade, the starting position is within 5% of the axial chord length from the leading edge, the total length is less than 5% of the axial chord length, and the length ratio is controlled within the range of 0.5 to 0.

8.

8. The method according to claim 1, characterized in that, In step SS4, the sampling method adopts stratified random sampling, Latin hypercube sampling, or low-difference sequence sampling with uniform spatial coverage of design variables, and dimensionless processing is performed on each design variable before sampling. For each set of design variable parameter combinations, a computational grid is independently constructed for the blade leading edge shape structure and three-dimensional unsteady CFD numerical calculation is carried out. The root mean square error of the velocity change over time in the boundary layer at the 50% axial chord length position of the suction surface is extracted as the flow response evaluation quantity to reflect the degree of enhancement of boundary layer disturbance by Klebanoff stripes.

9. The method according to claim 1, characterized in that, In step SS5, the response surface surrogate model is established using at least one of quadratic polynomial response surface, Kriging surrogate model, and radial basis function surrogate model. The model coefficients are determined by least squares regression, and the accuracy of the surrogate model is evaluated by cross-validation, coefficient of determination test, root mean square error analysis and / or residual independence analysis. When the surrogate model shows an excessive prediction deviation in a local highly nonlinear region, the design variable parameter combination sample is added to the region and iteratively updated.

10. The method according to claim 1, characterized in that, In step SS6, the optimization process employs gradient descent or a genetic algorithm for global optimization. The genetic algorithm uses real-number encoding, with a population size of no less than 100 individuals and a maximum evolutionary generation of no less than 500 generations. The selection operator uses a roulette wheel strategy, the crossover operator uses uniform crossover, and the mutation operator uses Gaussian mutation. The crossover probability is set to 0.8, and the mutation probability is set to 0.

05. After optimization, a new computational grid is established for the obtained globally optimal design variable parameter combination, and a three-dimensional unsteady CFD numerical simulation is conducted. The total pressure loss coefficient of the blade obtained from the simulation is quantitatively compared with the predicted value of the response surface model to verify the accuracy of the surrogate model prediction. At the same time, the reduction in the total pressure loss coefficient of the optimized leading-edge shape compared with the original baseline blade shape and the degree of effective suppression of the laminar separation bubble on the suction surface are quantitatively analyzed to evaluate the actual improvement effect of the leading-edge shape optimization.

11. The method according to claim 1, characterized in that, In step SS6, in addition to maximizing the mean square error of the boundary layer velocity as the main optimization objective, the laminar separation bubble length, total pressure loss coefficient, peak boundary layer shape factor, and Klebanoff fringe arrival phase deviation are also used as joint optimization indices to construct a multi-objective optimization problem. The optimization process adopts a non-dominated sorting genetic algorithm, a sequential quadratic programming algorithm, or a hybrid optimization strategy combining the two. First, a Pareto solution set that satisfies the constraints is searched globally. Then, a compromise solution is selected based on the flow control priority and engineering design constraints.

12. The method according to claim 1, characterized in that, It also includes step SS7 for verifying the optimization results, which includes: reconstructing the leading edge shape of the target low-pressure turbine blade based on the optimal design variable parameter combination obtained in step SS6, and conducting verification experiments or numerical calculations under the same working boundary conditions as steps SS4 and SS5 to obtain the corresponding verification results; comparing the deviation between the verification results and the prediction results of the response surface surrogate model, and if the relative error between the two is lower than the preset allowable error threshold, then the optimal design variable parameter combination is confirmed to be effective.

13. A leading edge shaping structure for a low-pressure turbine blade of an aero-engine obtained by the method according to any one of claims 1 to 12.

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