Total Pressure Loss Coefficient Research Articles

Flow disturbance by intrusive instrumentation located on the surface of a compressor blade

In this paper, we present an experimental and numerical investigation into the flow disturbance by intrusive instrumentation in the form of spanwise pressure tubes mounted on the pressure and suction side of a compressor blade in a linear cascade wind tunnel at a moderate subsonic Mach number of 0.5 and a Reynolds number of 790,000. The pressure tubes were modelled as simplified bumps extending over the entire span with a width of 24% of the chord length and a height of 67% of the maximum blade thickness. The leading edge of the bumps is located at 30% of the streamwise surface length. We found that the total pressure losses generated by these pressure tubes are considerably larger when they are placed on the suction side of the blade. The suction-sided bump increases the total pressure loss coefficient by a factor of four, while the pressure-sided bump approximately doubles it. CFD simulations reveal that the suction-sided bump causes the flow to form a large, open recirculation zone, while for the pressure-sided bump, the flow reattaches near the trailing edge. In conclusion, we provide insights into the effects of pressure tubes on the losses generated by compressor blades. The mounted tubes significantly impact the flow and should be carefully considered during instrumentation design.

Aerodynamic investigation of an S-shaped intake employing sweeping jet actuators based on proper orthogonal decomposition

The central curvature change of the S-shaped intake exacerbates the three-dimensional flow separation, resulting in total pressure and swirl distortions at the outlet. In this paper, an efficient active flow control technique, the sweeping jet actuator, was applied to control flow separation. The instantaneous characteristics of the flow field inside and outside the actuator were revealed by using validated numerical simulation methods. In addition, the effect of the sweeping jet on the aerodynamic performance of the S-shaped intake was investigated. Proper orthogonal decomposition (POD), an analysis method used to extract the main feature components of data, was applied to decompose the flow field structure at the S-shaped intake outlet in this study. The results highlight the external flow field characteristics of the actuator, with a jet sweeping range of up to ±40° and a sweeping frequency of 1 500 Hz, corresponding to a Strouhal number of 0.018. When the jet momentum coefficient is only 0.116%, the total pressure loss coefficient and pressure distortion index are reduced by 5.6% and 24.76%, respectively. This study demonstrates the critical role of momentum injection and discretization in inhibiting flow separation in the channel. The POD-based analysis indicates that a sweeping jet with high momentum can significantly enhance the energy in the flow passage and reduce the vorticity intensity of the first three modes. The stable mode structures exist near the outlet, exhibiting excitation frequency and frequency-doubling properties. The findings of this research provide essential input conditions for subsequent distortion studies.

Effect of Local Concave Non-axisymmetric Endwall Profiling on Endwall Secondary Flows of a Highly-Loaded Turbine Cascade

Non-axisymmetric endwall profiling (NAEP) has been widely utilized in reducing secondary flow loss of turbines. However, most of NAEP are designed for the endwall of the entire blade passage, which presents challenges to the design of cooling structures of turbine endwall. This study aims to explore the local concave non-axisymmetric endwall profiling (LCNP) method with the same effect as whole passage NAEP, and reveal the influence mechanism of LCNP on endwall secondary flow structures of a highly-loaded turbine cascade. Under the condition that the maximum depth of LCNP is unchanged, the axial length effect and pitchwise location effect of LCNP are studied, the influence mechanism of LCNP on the secondary flow loss is analyzed, and the genetic algorithm is utilized to optimize LCNP at the optimal position. Results show that as the axial length of the LCNP increases and the pitchwise location gets closer to the suction surface, the intensity and range of the passage vortex are decreased, and the total pressure loss coefficient (loss coefficient) of the turbine cascade is decreased. When LCNP is 100% axial chord in length and at the position of 2/9 pitch, the loss coefficient is reduced by 5.49%. LCNP was optimized at the optimal position, and the optimal LCNP reduced the loss coefficient of the turbine cascade by 6.73%. After the local concave endwall profiling, the loading in the middle of the endwall of the turbine cascade is reduced, and the intensity of the passage vortex is effectively inhibited, which is the mechanism that the loss coefficient of the turbine cascade is reduced. However, after the local concave endwall profiling, the loading in the trailing of the endwall of the turbine cascade is increased, the transverse migration of the new boundary layer in the endwall is accelerated, and the loss coefficient of the near endwall is increased.

Shock waves characteristics and losses estimation of non-equilibrium condensation flow in nozzle and steam turbine cascade

The investigation of transonic non-equilibrium condensation is paramount due to its profound influence on the shock patterns and the distribution of losses. This study numerically investigates the shock wave morphology, evolution, and quantitative loss calculation under the influence of non-equilibrium condensation within the Moses-Stein nozzle and Dykas cascade. The results indicate that the vapor near the nozzle wall undergoes phase transition first and forms “X-shaped” condensation shock, which impervious to back pressure variations. Conversely, the “λ-shaped” aerodynamic shock moves towards the throat with increasing back pressure, triggering boundary layer separation. The entropy generation of “λ-shocks” accounts for over 98% and represents the primary source of shock losses. Strong pressure side shock induces shock wave-boundary layer interactions with the blade suction wall, resulting in reflected shocks. However, the latent heat released by non-equilibrium condensation mitigates this effect, increasing the total pressure loss coefficient by 0.188. The decrease in Mach number under high back pressure causes a notable increase in the trailing edge shock angle, with the wave foot shifting upstream. Notably, the proportion of shock losses attributed to the suction side of trailing edge exceeds 80%, significantly surpassing other regions, which progressively increases with rising back pressure. Therefore, it is crucial for cascade optimization. The findings can provide references for the optimization design of low-pressure steam turbine blade profiles. The results can serve as a guide for optimizing the blade profiles of low-pressure steam turbine.

The Law of the Total Pressure Loss in Supersonic Streamwise Corner Flow

Abstract The total pressure loss is a critical issue in the design of internal flow channels for hypersonic vehicles. In the flow through the streamwise corner region, the adjacent walls induce secondary flows that exacerbate the viscous effects, thereby intensifying the total pressure loss. This study investigates the impact of the corner’s dihedral angle and the compressibility of the flow on the total pressure loss in the streamwise corner region. The results indicated that as the dihedral angle increases, the distribution of the total pressure contour in the corner region became significantly distorted. The proportion of the boundary layer area within the corner region concurrently increased as the dihedral angle deviates from 90 degrees. Furthermore, we deduce that the total pressure loss is the largest in the supersonic flat plate boundary layer. This paper normalized the total pressure loss coefficient for different dihedral angles in the corner region and established an empirical relationship for the distribution of normalized total pressure loss coefficients along the flow path. It is discovered that under supersonic inflow conditions, the distribution law of the total pressure loss in the corner region exhibits higher predictive accuracy.

Flow field reconstruction of compressor blade cascade based on deep learning methods

In the design process of compressors, calculating the S1 flow surface involves solving the Navier-Stokes equations, which results in slow convergence and makes determining cascade characteristics time-consuming. However, deep learning offers significant advantages in flow field reconstruction by not only automatically extracting complex flow features and reducing prediction time but also providing high accuracy in reconstruction. This paper implements the rapid reconstruction of the compressor S1 flow surface cascade flow field using two deep learning models: U-Net and 1D-CNN. Using a double-circular arc airfoil as an example, we selected four key design parameters that define the geometry and position of the airfoil, ultimately designing 5,292 sets of cascade geometries. By performing batch meshing and CFD simulations, we built a cascade flow field dataset. The U-Net neural network uses design parameters as input and outputs the aerodynamic distribution of the cascade flow field. After training, it can directly predict the flow field based on the design parameters. Since the U-Net model cannot directly obtain the aerodynamic parameter distribution and flow field aerodynamic coefficients on the airfoil surface, a 1D-CNN model is used as a complementary approach. The 1D-CNN model takes the design parameters as input and outputs the aerodynamic parameter distribution on the airfoil surface and the flow field aerodynamic coefficients. The prediction results show that the U-Net model achieves an average relative error of less than 1% in cascade flow field reconstruction, while the 1D-CNN model achieves an average relative error of less than 1% in predicting the pressure recovery coefficient and less than 2% in predicting the total pressure loss coefficient. This study presents a method for the rapid reconstruction of compressor blade cascade flow fields, which helps improve design efficiency and shorten the design cycle.

Study on the influence of labyrinth seal structure on the performance of shrouded stator cascades with inter-stage cavities

Numerical simulations of a shrouded stator cascade with an inter-stage cavity were conducted using validated numerical methods to investigate the impact of different labyrinth seal structures and positions on the aerodynamic performance of the stator cascade. The study discussed the development trends of secondary flow motion and corner separation within the cascade under different labyrinth seal structures, evaluated the stator performance using total pressure loss coefficient and entropy-based loss coefficient, and revealed the interaction between cavity leakage flow and mainstream flow. The results indicate that individually changing the labyrinth seal structure or position has a negligible impact on stator performance, but simultaneously altering both the structure and position of the labyrinth seal can effectively reduce stator losses. The structure case 1-position case 2 labyrinth seal structure can reduce total pressure loss by 6.25%, while structure case 4-position case 4 reduces entropy increase loss coefficient by 7.67%. Additionally, it was found that changing the labyrinth seal structure and position can increase the circumferential velocity and momentum of cavity leakage flow at the cavity outlet, enhance the resistance of cavity leakage flow to circumferential secondary flow within the stator passage, and reduce stator losses. Altering the structure and position of the labyrinth seal effectively reduces the cavity leakage vortex at the leading edge of the cascade during the mixing process of cavity leakage flow with the mainstream, causing the passage vortex to move rearward axially.

Analysis of film cooling and flow resistance characteristics of turbine blades with thermal barrier coatings

This paper employs numerical simulation to investigate the influence of thermal barrier coatings' (TBCs) thickness and surface roughness on the cooling and flow resistance characteristics of turbine blades. The results indicate that the application of TBCs significantly enhances the surface cooling efficiency of the blades. Turbine blades coated with a 0.4 mm thickness of TBC compared to blades without thermal barrier coatings, the average cooling efficiency of the blade surface increases by 12.3 %, and the maximum temperature drop at the leading edge(LE) is 317.8 K. However, the small increment in TBCs thickness leads to an increase in aerodynamic losses in the vane passage. The static pressure coefficient continuously decreases in the suction side(SS) within the interval 0.3 < x/C < 1.0. The average flow coefficient of the film holes exhibits distinct variations in different regions of the blade. As surface roughness increases, the cooling efficiency on the SS and pressure side(PS) of the blade decreases, while the heat transfer enhancement at the LE and cooling efficiency improve. Compared to a smooth coated surface, when the surface roughness height increases to 20 μm, the blade surface cooling efficiency decreases by 1.12 %, and the average temperature rise is 10.3 K. Simultaneously, the energy loss coefficient and total pressure loss coefficient in the vane passage rise with the increase in surface roughness, while the variation in the average flow coefficient of the film cooling holes remains relatively small.

Toward high-lift low-solidity design for incidence tolerant gas turbine blade profile

Gas turbines operating under wide operational conditions require minimizing losses across a wide range of incidences. This study employed a blade profile efficient within a 50° incidence range to assess the effect of solidity on performance across wide incidences. The aim was to evaluate the feasibility of adopting high-lift, low-solidity designs for incidence-tolerant blade profiles. The results showed that solidity has both positive and negative effects on loss across a wide range of incidence angles. Increasing the pitch-to-axis chord ratio (the inverse of solidity) from 0.8 to 1.1 not only reduces the blade count by 37.5 % but also enhances performance at negative incidences, reducing the total pressure loss coefficient by up to 17.5 %. However, at positive incidences, the losses increased significantly as the solidity decreased. To expand the operational range of the low-solidity blade profile at positive incidences, strategic integration of leading-edge refinement and maximum deflection adjustment was applied to precisely control losses. This enabled the low-solidity blade profile to maintain lower loss levels compared to conventional high-solidity profiles up to an incidence of 7°, at which point the losses become comparable. The findings indicate that employing high-lift designs with optimized leading-edge and maximum deflection for incidence-tolerant blade profiles is feasible.

EFFECTS OF CONTINUOUS AND FRACTURED RIBS PLACED AT THE ENDWALL SURFACE UPSTREAM OF THE TURBINE-VANE LEADING-EDGE

Total pressure loss, chaotic and heavy flow downstream of the turbine passage exit area are a few effects of the desired increase in inlet temperature input at the upstream part of the turbine vane passage. Huge amount of energy from the cross-flows near the middle of the vane actual chord are transported downstream by this chaotic flow which often results in aerodynamic loss and differential heat penalties. To compare the different arrangement, comparisons of the two geometries, the impact of adding various rib configurations upstream are studied for heat augmentation efficacies. The leading-edge rib(s) effects at the mid-stream of the vane passage are quantitatively examined in this work using computational fluid dynamics (CFD) technique. With the employment of Reynolds Averaged Navier-Stoke energy equations, the geometries are modelled choosing the appropriate boundary conditions. Polyhedral mesh is used with fifteen prism layer mesh at the endwall and vane surfaces to capture the flow physics close to the endwall area. Although the two configurations employed showed relative reduction in the total pressure loss coefficient, however, the fractured ribs produced superior outcomes of Nusselt number reduction of over 10% along the passage exit region. The data demonstrate a considerable difference in the overall pressure loss between the two configurations.

A Preconditioner-Based Data-Driven Polynomial Expansion Method: Application to Compressor Blade With Leading Edge Uncertainty

Abstract In engineering practice, the amount of measured data is often scarce and limited, posing a challenge in uncertainty quantification (UQ) and propagation. Data-driven polynomial chaos (DDPC) is an effective way to tackle this challenge. However, the DDPC method faces problems from the lack of robustness and convergence difficulty. In this paper, a preconditioner-based data-driven polynomial chaos (PDDPC) method is developed to deal with UQ problems with scarce measured data. Two numerical experiments are used to validate the computational robustness, convergence property, and application potential in case of scarce data. Then, the PDDPC is first applied to evaluate the uncertain impacts of real leading edge (LE) errors on the aerodynamic performance of a two-dimensional compressor blade. Results show that the overall performance of compressor blade is degraded and there is a large performance dispersion at off-design incidence conditions. The actual blade performance has a high probability of deviating from the nominal performance. Under the influence of uncertain LE geometry, the probability distributions of the total pressure loss coefficient and static pressure ratio have obvious skewness characteristics. Compared with the PDDPC method, the UQ results obtained by the fitted Gaussian and Beta probability distributions seriously underestimate the performance dispersion of compressor blade. The mechanism analysis illustrates that the large flow variation around the leading edge is the main reason for the overall performance degradation and the fluctuations of the entire flow field.

Influence of a novel leading-edge winglet on the aerodynamic characteristics of a highly loaded turbine

In order to decrease the flow loss of the region close to the endwall, a novel leading-edge modification strategy is proposed in this paper. Specifically, the winglet is installed at the leading edge of the first-stage blade of the highly loaded PW-E3 (Energy Efficient Engine designed by Pratt & Whitney Aircraft Group) turbine. The numerical methods used in this study are validated with the experimental data of the original blade profile of PW-E3. The SST (Shear Stress Transport model) γ-θ turbulence model is employed to calculate the flow field. The schemes of the forward bending winglet and reverse bending winglet are compared with the base case to prove the superiority of this modification strategy. The numerical results indicate a significant increase in stage efficiency by reducing the total pressure loss coefficient. Reverse bending winglets perform better than forward bending ones in terms of efficiency promotion. The effects of the normalized winglet height and bending angle are further explored. For reverse bending winglets, increasing the normalized winglet height and bending angle leads to improved flow control. Conversely, for forward bending winglets, reducing the normalized winglet height and bending angle is more favorable for loss reduction.

A simplified numerical method based on anisotropic porous media model for the precooler of the hypersonic precooled engine

The precooler is a key component of hypersonic precooled engine, and its actual structural have a high anisotropy in the axial, circumferential, and radial direction. Considering the non-uniform flow inside the precooler is crucial to study the flow and heat transfer characteristics of the precooler. The previous simplified method for the precooler has not fully considered the flow non-uniformity of the axial, radial and circumferential direction. In this paper, a simplified numerical method based on anisotropic porous media model for the precooler was proposed. The unique aspect of this method is the integration of anisotropic surface porosity of porous media model with the zero-dimensional heat transfer model. In addition, the influence of key structural parameters on the flow and heat transfer characteristics of precooler was studied. It is found that as the tube transverse pitch increases from 2 to 3.5, the total flow rate increases by 11%, and the heat exchange rate decreases by 25%. As the number of tube rows increases from 7 to 13, the heat exchange rate increases by 22%, but the total pressure loss coefficient increases from 0.046 to 0.082. In addition, the decrease of inner diameter of the precooler improves the heat exchange rate, but reduces the flow capacity of the precooler. These results indicate that the simplified numerical method is capable of simulating the behavior of precooler and provides some guidance on the design of precooler.

Research on substitutability of single-dome versus triple-dome center staged combustor

To investigate the substitutability of the simulation results using the single-dome combustor as the computational domain to the triple-dome combustor, three-dimensional numerical simulations were conducted on both models and the differences in various performances between the two combustors were compared and analyzed. The findings reveal that the simulation results obtained using the single-dome combustor as the computational domain can effectively substitute for those of the triple-dome combustor in terms of critical performance metrics, including velocity distribution in the central cross-section, morphology and size of back-flow regions, total pressure loss coefficient, combustion efficiency, outlet temperature distribution and pollutant emissions. Under takeoff conditions, the flame tube outlet of the single-dome combustor exhibits higher OTDF and RTDF values compared to the triple-dome combustor, with similar radial temperature distribution shapes. Additionally, the NOx emissions of the flame tube outlet are slightly lower in the single-dome combustor compared to the triple-dome combustor, while the Soot emissions are slightly higher. However, both the NOx and Soot emissions are within the same order of magnitude for both combustors. Under idle conditions, both the single-dome and triple-dome combustors show almost zero CO emissions at the flame tube outlet section.

An investigation on film cooling and aerodynamic performance of squealer blade tip with inclined cavity bottom

The gas turbine blade tip poses as one of the most challenging areas for blade cooling, primarily due to its intricate three-dimensional flow characteristics, which make it one of the primary contributors to aerodynamic loss within the turbine stage. In this paper, the adiabatic film cooling effectiveness (η) distributions at five squealer tip structures (Original, PS7.5, PS15, SS7.5, SS15) with varying inclined angles of cavity bottom surface were obtained using pressure sensitive paint technique (PSP) under five coolant blowing ratios (BR = 0.4, 0.8, 1.2, 1.6, 2.0). Combined with the numerical simulations verified by the experimental data, the tip flow field details were described to reveal the cooling characteristics of the tip region. The results indicate that, at low BRs, the film hole downstream exhibits apparent cooling traces, which are most pronounced at the SS15 tip. With the increase of BR, the cooling traces gradually fade, and the area-averaged film cooling effectiveness (ηΑ-avg) rises. At low BRs (BR = 0.4, 0.8), the ηΑ-avg of the SS15 tip is 12.8 %, and 8.4 % higher than that of the Original tip, respectively. At BR = 1.6, the ηΑ-avg of the PS15 tip is the highest, 3.9 % higher than that of the Original tip. The ηΑ-avg of SS7.5 is the lowest at all BRs. In addition, the pitch-averaged η (ηavg) of PS7.5 at some BRs is higher in the front part of the tip, compared to the Original tip. At BR = 1.2, the area-averaged total pressure loss coefficient (Cpt¯)of the PS7.5 and PS15 is 1.46 % and 1.58 % higher than that of the Original tip, respectively. However, the Cpt¯ of the SS7.5 and SS15 is 1.77 % and 10.28 % lower than that of the Original tip, respectively.

Numerical studies on shock wave and boundary layer interaction in the high-load turbine rotor cascades

Design of transonic high-load turbine is the essential approach to improve thrust-to-weight ratio of gas turbine engines. The shock wave and boundary layer interaction (SWBLI) in high-load turbine is one of the important unsteady sources and the main source of loss in turbine stages. In order to study mechanism of SWBLI in high-load turbine, rotor blades with loading coefficients range from 1.6 to 2 were designed and Delayed Detached Eddy Simulations (DDES) were carried out. The influences of loading coefficient, exit isentropic Mach number and incidence angle on characteristics of shock wave, SWBLI as well as flow details in the blade passages were compared. Results indicated the shock wave was generated and enhanced as exit isentropic Mach numbers increased leading to the increase of 2.8% in the total pressure loss coefficient. There was not significant difference in the total pressure loss coefficient as loading coefficient increased, however the shock wave was stronger and the separation bubble was longer at the loading coefficient of 1.6. Meanwhile, the influence of strong separation near the leading edge of suction surface induced by variation of incidence angles on the characteristics of the shock wave and the loss was also obvious.

Experimental study on multi-angle pulsed jet actuators for controlling corner separation flow in a compressor cascade

Three-dimensional corner separation caused by the aerodynamic design of high-load compressor cascades is the main factor that limits their performance enhancement. Because of the unsteady characteristics of large-scale flow separation, injecting unsteady jets into the flow field has become a new flow control method. In this study, the essential flow characteristics of a compressor cascade were obtained through numerical simulations. Subsequently, the effect of pulsed jet angle on the aerodynamic performance of the cascade was experimentally investigated under different operating conditions using pulsed jet actuators. The results showed that at the design incidence angle of 0° and near-stall incidence angle of +4°, the starting point of the corner separation is located at 21 % and 9 % of the axial blade chord, respectively. The pulsation frequency downstream of the cascade trailing edge is 1454.5 Hz. Under the design conditions, the 20° pulsed jet exhibits the best control effect, reducing the total pressure loss coefficient by 13.4 % compared with that of the original cascade. Moreover, pulsed jets demonstrate strong applicability under variable operating conditions. At near-stall incidence angles, when the jet angle is 30°, the loss-reduction ability of the pulsed jet is maximized, decreasing the loss by 25.2 %. Pulsed jets reduce the cascade loss primarily by suppressing the secondary flow at the endwall and discretizing the vortex structures in the channel.

Multi-objective design optimization of a transonic axial fan stage using sparse active subspaces

In this paper, a multi-objective optimization strategy for efficient design of turbomachinery blades using sparse active subspaces is implemented for a turbofan stage design. The proposed strategy utilized sparse polynomial chaos expansion on a limited dataset to generate a function from which the differential and the covariance matrix can be obtained. Active subspace was used to compute the active variables via singular value decomposition and a hybrid polynomial correlated function expansion was used to construct a surrogate model on the active subspace. Coupled with freeform method and multi-objective genetic algorithm, an automated optimization loop was run at a single operating condition. An improvement in stage efficiency and total pressure ratio of 2.97% and 1.15% was achieved for the optimum design compared with the baseline. Additionally, total pressure loss coefficient decreased by 5.88%, exit flow angle by 34.65% and shock strength by 5.32%. The coupled effect of change in stagger angle, forward sweep, forward lean, and chord length reduced the recirculation at the hub, and blockage at the shroud due the tip leakage flow by decreasing the blade loading. The threshold value hyperparameter was found to be the most influential and must be accurately determined.

Aerothermal Optimization of Film Cooling Hole Locations on the Squealer Tip of an HP Turbine Blade

Abstract This article presents a time-efficient method to optimize the positions of film cooling holes on a gas turbine blade's squealer tip for cooling and aerodynamic performance. A computational approach is employed for the optimization, including validations against experiments. Five discrete film cooling holes are considered, and two different blowing ratios of 0.4 and 1.0 are studied. The positions of cooling holes on the tip along the tangential direction are varied as the input parameters of optimization. The multi-objective optimization uses an algorithm with an artificial neural network for fast fitness function predictions. The best cooling configuration found by the optimization achieves a 13.43% reduction in total heat flux and a 0.4% increase in aerodynamic loss when the blowing rate is 1.0. Including the casing relative motion in the computations results in a total pressure loss coefficient increase of about 8% for both blowing ratios. For M = 1.0, imposing the casing's motion results in a 10.2% reduction in total heat transfer to the tip compared to the stationary casing. For the lower blowing rate of 0.4, the total heat flux reduction to the tip is 12.0% because of the imposed casing motion. Hence, the cooling effectiveness can be improved by employing the particular position optimization method presented in this study. The results suggest that experimental and computational heat transfer studies on cooled turbine blade tips, especially in cascade arrangements, need to consider the relative motion of the blade tip.

Extraction of geometric features and analysis of flow mechanism of high loaded compressor airfoils at low Reynolds number

When the aircraft cruising at high altitude, the aerodynamic performance of the compressor sharply decreases due to the enhanced boundary layer separation loss. Therefore, it is of great significance to design the high-performance airfoils suitable for low Reynolds numbers (Re) to improve the aerodynamic performance of compressor. In this paper, numerical simulations were carried out on a high-loaded subsonic compressor cascade V103 at low Re. Meanwhile, a multi-objective optimization of blade profile was performed to get optimal solutions, and data mining techniques were applied to extract valuable design knowledge from the optimal database. The results show that the Pareto-optimal airfoils achieve a maximum reduction of 27.32% in total pressure loss coefficient under design condition and 36.71% under near stall condition. Compared with the original airfoil, the curvature distribution law of the camber line with larger values at both ends and smaller values in the middle is advantageous for the performance of the compressor cascade under design condition. This distribution pattern causes a forward shift for the loading distribution of airfoils, accompanied by an earlier transition onset. Additionally, it reduces adverse pressure gradient at the rear part of suction surface, which suppresses the development and growth of laminar separation bubble and delays the separation of turbulent boundary layer. Under near stall condition, maintaining larger leading edge angle and uniform flow diffusion is beneficial for improving the performance of compressor cascade. This is because the larger leading edge angle reduces incidence angle, while the uniform flow diffusion inhibits a great flow separation.