Aug 2026· Journal of turbomachinery· Vol 148· 0 citations
Abstract
Traditional compressor deviation angle models, primarily developed for NACA and double-circular-arc airfoils, cannot accurately predict the deviation characteristics of modern aerodynamically optimized blades and generally neglect Reynolds number (Re) and Mach number (Ma) effects, limiting their applicability to low-Re compressor designs. To improve prediction accuracy for high-loading compressors under varying Reynolds and Mach numbers, this study develops a physics-enhanced two-stage symbolic regression (PE-TSR) model based on a data-fusion framework. The first-stage symbolic regression model captures the primary effects of blade geometry and aerodynamic loading on deviation angle, while the second-stage model introduces physics-based correction terms associated with Mach-geometry coupling and viscous flow development. The proposed PE-TSR model achieves an average relative error of 2.17% on the test set, representing a 73.9% improvement over the classical Lieblein empirical model. On an independent experimental dataset outside the training set, the model yields a mean absolute error of 1.68° in deviation angle prediction. Sobol global sensitivity analysis indicates that inlet metal angle, loading distribution, and blade camber angle dominate the primary deviation trend, whereas Mach number, Reynolds number, and maximum reverse-flow velocity mainly act as corrective factors that compensate for systematic biases of the primary model under extreme operating conditions. Furthermore, analysis of the PE-TSR analytical formulation reveals that the influence of flow compressibility on the deviation angle is strongly dependent on the blade geometric loading state.
In the actual operation of fuel-cell systems, providing the most accurate centrifugal compressor aerodynamic performance prediction in real-time is crucial for system efficiency and control. One key factor influencing the prediction is choke, which causes blade vibrations, limits the system’s maximum power and leads to a sharp decline in efficiency. However, the embedded multi-dimensional look-up tables typically necessitates a substantial amount of bench tests and makes extrapolation difficult. To address this, the study innovatively introduces a hybrid modeling framework that uses a small-sample physics-based model as a prior constraint and a data-driven method to compensate for physics-based prediction errors. The residual learning serves as a bridge trained with Gaussian process regression (GPR) by minimizing the root mean square error (RMSE). The hybrid model is implemented and validated on a fuel cell centrifugal compressor. Results show that, the physics-based prediction effectively constrains the shape of the characteristic curves, while the data-driven method significantly improves accuracy, especially in the choke region, with a 5% enhancement. In real-time prediction, as training samples expand, the accuracy improves further with the validation data almost all falling within the 95% confidence interval. The maximum training time is 20.96 s, indicating suitability for real-time prediction. This study highlights the potential of hybrid model of fuel-cell centrifugal compressors in engineering applications.
Zizhuo Wang, Bingjie Li, Ben Zhao et al.· International Journal of Eng...· 0 citations
Modern ultra-large wind turbines can expose their outboard blade sections to Reynolds numbers above 1 × 107 and Mach numbers above 0.3. In conventional fixed-geometry tests, both parameters vary with inflow velocity. Their individual aerodynamic effects are, therefore, difficult to distinguish. This study presents a variable-chord sectional framework to examine the Reynolds- and Mach-number effects separately. Transitional unsteady Reynolds-averaged Navier–Stokes simulations are conducted for the FFA-W3-211 airfoil. The results reveal a regime-dependent competition between viscous scaling and compressibility. Increasing the isolated Reynolds number promotes earlier transition, strengthens boundary-layer momentum exchange, and accelerates flow reattachment. The lift-hysteresis intensity decreases by 67.2%. Increasing the isolated Mach number enhances lift in attached flow. During deep stall, however, local supersonic flow and shock–boundary-layer interaction promote earlier separation and delay pressure recovery. The downstroke aerodynamic efficiency decreases by 68.1% at the selected post-stall state. These findings indicate that extrapolating traditional uncorrected dynamic stall models to modern large-scale blades may substantially mispredict stall margins. The results suggest that incorporating distinct, decoupled time constants for viscous scaling and compressibility-induced structural persistence may improve predictions of unsteady sectional loads. Their quantitative implications for complete rotors remain to be established through three-dimensional rotating aeroelastic simulations.
Chengyong Zhu, Xiufeng Huang, Zeling Zhu et al.· The Physics of Fluids· 0 citations
Rapid prediction of vehicle lift coefficient is an important issue in aerodynamic design. Traditional CFD/DSMC methods have high computational costs. Although commonly used machine-learning surrogate models offer high prediction efficiency, they struggle to provide explicit mathematical expressions. To balance prediction accuracy and model interpretability, this paper introduces the symbolic regression method and establishes an explicit modeling process for the lift coefficient. Using Mach number, angle of attack, and related flow parameters as inputs, validation is conducted on two-dimensional blunt body DSMC data and three-dimensional missile aerodynamic data, with comparisons against linear regression, quadratic polynomial regression, Kriging, random forest, XGBoost, and multilayer perceptron. The results show that symbolic regression can obtain high-precision explicit expressions on the two-dimensional blunt body data and can also build analytical models with certain predictive capability on the three-dimensional missile data with limited samples. Compared with traditional explicit regression methods, symbolic regression does not require a pre-specified fixed functional form; compared with black-box models, its advantage lies in providing interpretable and editable algebraic expressions. The findings indicate that symbolic regression has application potential in rapid explicit modeling of the lift coefficient.
Yang-Yang Chen, W. Qin, Qi-Rong Tu et al.· Aerospace· 0 citations
Accurate prediction of centrifugal-pump performance under viscous operating conditions remains challenging, particularly for low specific-speed pumps operating at low Reynolds numbers. This study develops a Reynolds-number-based correction-factor framework derived from a physically based energy-loss analysis. The method explicitly accounts for major internal loss mechanisms, including hydraulic losses, disk friction, leakage flow, recirculation, mixing and diffusion losses, slip-factor deviation, and blade blockage. The model was calibrated using water-test data from an FM-50 centrifugal pump at 1200 rpm and validated using an independent dataset at 900 rpm. The validation results showed accurate head prediction, with and . Efficiency prediction showed larger deviation, with percentage points, reflecting the sensitivity of efficiency to measurement uncertainty and combined loss mechanisms. After validation, the model was extended to viscous-flow conditions and used to derive compact analytical correction factors for head and efficiency as functions of Reynolds number. The proposed expressions showed strong cross-validation performance within the investigated range, with mean for the head correction factor and for the efficiency correction factor. Comparison with ANSI/HI, KSB, and Gülich methods shows that the proposed formulation follows the expected Reynolds-number-dependent trend while providing a more physically interpretable basis for viscous-performance correction. The proposed method offers a practical alternative to conventional correction charts for low specific-speed centrifugal pumps operating under viscous or low-Reynolds-number conditions.
A. Kara Omar, A. Khaldi, A. Ladouani et al.· Journal of Applied Fluid Mec...· 0 citations
This study investigates the effectiveness of surface microcavities as a passive flow-control technique for reducing drag on a NACA 0012 airfoil over a range of Reynolds numbers and angles of attack. Two-dimensional RANS and URANS simulations were performed using the SU2 solver and validated against benchmark data for the smooth airfoil. A preliminary analysis at Reynolds numbers of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] evaluated the sensitivity of cavity performance to flow conditions. A Taguchi design-of-experiments approach was then used to optimize cavity diameter, depth, and chordwise location at Reynolds numbers of [Formula: see text] and [Formula: see text]. Under specific optimized conditions, the two-dimensional simulations predict drag reductions of up to 39% and lift-to-drag ratio improvements exceeding 290%. However, the aerodynamic benefits were highly dependent on Reynolds number and angle of attack, with some configurations causing drag penalties at off-design conditions. Flowfield analysis showed that cavity-induced vortical structures can either suppress or intensify near-wall turbulence. This study provides the first systematic, multiparameter optimization of microcavities on an airfoil, addressing a gap in passive flow-control literature.
High-speed low-pressure turbines (HS-LPTs) operate under transonic and low-Reynolds-number conditions, making their boundary layers highly sensitive to transition and separation. Accurate numerical prediction of these effects requires a realistic representation of inflow turbulence, which strongly influences separation, transition onset, and wake development. Conventional turbulence generation methods for internal compressible flows often fail to reproduce experimental turbulence characteristics, leading to significant discrepancies in performance predictions. This study proposes a numerical wind-tunnel replication strategy based on the Dynamic Actuator Line Method (DALM), designed to model the effects of passive turbulence grids commonly used in turbomachinery experiments. The approach generates realistic turbulent inflow conditions without explicitly meshing the grid geometry, significantly reducing computational cost. The method is applied to the SPLEEN C1 transonic cascade, experimentally tested at the von Karman Institute, at Reout,is = 70k and Mout,is from 0.70 to 0.95. Simulations are performed using the YALES2 explicit compressible solver and a wall-resolved LES framework. The DALM successfully reproduces experimental inflow turbulence characteristics: TIx = 2.5% and Λint = 13.5 mm. Accounting for realistic turbulence substantially improves predictions of boundary-layer behavior and wake losses compared to clean inflow conditions. In particular, suction-side separation is delayed, transition occurs earlier, and flow reattachment is promoted at low Mach numbers. Velocity and turbulence statistics in the blade passage and wake show good agreement with PIV measurements, highlighting the importance of realistic inflow turbulence under compressible HS-LPT operating conditions.
P. Tene Hedje, L. Bricteux, Yacine Bechane et al.· Journal of turbomachinery· 0 citations