Camber Line Research Articles

Optimizing Bionic Blades for Multi-blade Centrifugal Fans: Asymmetric Thickness Inspired by Carangiform Fish

Multi-blade centrifugal fans find wide application across various fields, with their internal airflow exhibiting complex turbulent behavior in three dimensions. Historically, blade optimization relied on constant thickness airfoils, limiting the effectiveness of optimization efforts. However, marine organisms have developed airfoil structures with highly efficient drag reduction, offering a novel approach to optimizing multi-blade centrifugal fans. This study proposes an airfoil optimization design method utilizing variable-thickness airfoils to maintain consistent pressure surface leading-edge parameters. By integrating the Non-dominated Sorting Genetic Algorithm II with biomimetic optimization design, performance improvements are achieved. The study constructs an asymmetric bionic blade using a Bezier curve to fit the mean camber line of the blade. Experimental testing validates the optimized fan's performance, demonstrating the effectiveness of the proposed design approach in reducing the unsteady interaction between the impeller and the volute tongue. This reduction significantly diminishes sound pressure fluctuations on the blade surface. Notably, at the maximum volume flow rate, the optimized fan featuring the asymmetric bionic blade exhibits a remarkable enhancement, with a 10.5% increase in volume flow rate and a notable 1.7 dB reduction in noise compared to the original fan configuration.

Design optimization of a snowboard performing an ollie

The ollie, a fundamental manoeuver in snowboarding, serves as a basis for various tricks requiring high altitude and extended airtime. The maximum ollie height depends on the snowboard’s geometry and structural characteristics. In this study, the influence of these properties is investigated with a flexible multibody dynamics simulation, where the snowboard is modeled by geometrically non-linear finite elements, snow contact is considered by a penetration depth and velocity proportional normal force and ollie motion is achieved by imposing measured loads to the bindings. To maximize the height, a genetic optimization procedure is presented, which yields substantial improvements. Optimizing the camber line and the bending stiffness distribution yields enhanced performance. Less damping as well as lighter boards lead to higher jumps, no noteworthy correlation between axial stiffness and damping distribution and jump height was found, and the strain energy stored in the board during takeoff is a useful indicator for estimating ollie heights. Nevertheless, further investigations should take a more advanced and realistic rider interaction into account.

Inverse aerodynamic design for distributed propulsion wing with expected circulation distribution

Distributed Propulsion Wing (DPW) technology offers significant advantages in terms of flight energy savings, but the strong aerodynamic coupling between the propulsive internal flow and aerodynamic external flow brings significant design challenges. As the primary DPW profile design is of great significance, this paper proposes a hybrid method to solve the inverse problem mainly based on the formula relationship between the required aerodynamic loads and the profile shape, which is more direct and instructive compared with traditional parametric iterative methods. The aerodynamic characteristics are described by the circulation distribution in the Fourier series form, then the mean camber line of the profile is solved through the re-derived airfoil theory considering disk’s influence. Further CFD correction methods are also proposed. To validate the effectiveness and feasibility of the proposed hybrid inverse method, several DPW profile design tests are then conducted. Finally, the relationship between 2D and realistic 3D unit shape is also researched. The results show that the proposed inverse design method has great accuracy and convergence speed in the design tests, and shows good robustness against changes of the design parameters. The 2D profile shape and the actual 3D shape of DPW unit can establish an aerodynamic-propulsion equivalent relationship based on the same internal mass fluxes.

Conformally Decambered Natural Laminar Flow Blades for Vertical-Axis Wind Turbines

A two-element natural laminar flow airfoil—commonly used on medium-altitude, long-endurance, unmanned air vehicles—was conformally decambered for application on a two-bladed, H-rotor, vertical-axis wind turbine. Blade kinematics were used to determine the virtual camber line, which was then used to conformally map the original profile onto the chord line. Both decambered and original blade profiles were evaluated experimentally using large chord-radius ratios (0.6 and 0.75) that exploited dynamic stall to produce the driving torque. Decambered blades showed substantially greater power and torque coefficients than the original blades, up to 60 and 27%, respectively, which represents the first experimental validation of conformal decambering. Relatively large peak power coefficients of 0.28 were attained, despite maximum chord-based Reynolds numbers being less than 2×105. Depending upon the chord-radius ratio, either light or deep dynamic stall occurred in the second upstream quadrant, and the flap flow remained attached virtually throughout. In contrast, on the original profiles, massive separation was observed on the blades, and the flap flow remained separated due to assumed outer surface flow separation. Future research should consider surface pressure and flowfield measurements, significantly higher Reynolds numbers, and variable intracycle flap deflection mechanisms to optimize performance and minimize unsteady loads.

Effect of asymmetric leading edge on transition of suction side

Abstract Asymmetric leading edge offers several advantages over conventional leading edge. However, there are few related published research on compressor blades. This study proposes a blade parameterization method that superimposing the thickness distribution on the camber line at the middle and curve fitting at the leading and trailing edges. This parameterization method is applied to a stator in the final stage of an axial compressor, and numerical simulation is used to calculate the aerodynamic performance at various attack angles under the designed inlet Mach number. There is an optimal deflection angle regardless of which side of the leading edge deflects, and deflection toward the pressure side is conducive to the suppression of separation bubble near the leading edge at positive attack angle. When the maximum curvature of the pressure side is decreased, the operating range changed slightly, but the positive attack angle range grew from 5.166° to 5.466°.

Axial Compressor Transonic Rotor Shock Interaction With Upstream Stator Row

Abstract Modern multistage axial compressors are designed for high aerodynamic loading and wide range with front stages rotor inlet relative Mach number above one over a large portion of span. Rotor shock waves propagate and reflect in the upstream stator where they provoke extra aerodynamic losses and aeromechanic risks. This paper discusses stator–rotor shock interactions using both steady and unsteady numerical simulations. The computations focus on three different stage designs with the same capacity and total pressure ratio, but different axial gaps and load distribution in stator and rotor. Speedlines from steady and unsteady computations compare the designs, and the detailed flow fields are analyzed at design and close to stall conditions. The steady and unsteady calculations predict similar stage performance, but different stator–rotor loss split. The analyses reveal how the rotor shocks orientation with respect to the upstream stator camber line controls the intensity of shocks interaction with the stator row and its propagation upstream. Finally, the paper indicates the ways to reduce the shock-driven rotor–stator interaction and suggests simple criteria to determine when to switch from steady to unsteady calculations for a reliable transonic stage performance prediction.

Aerodynamic design of a double slotted morphed flap airfoil– a numerical study

Introduction:The objective of this study is to develop and simulate a double slotted morphed flap with the intention of reducing drag and enhancing lift, thereby leading to a smaller flap size and reduced weight.Methods:A flap was meticulously designed to accommodate conditions at Mach 0.2 and Reynolds numbers of 4.7×106. To conduct the simulation, ANSYS FLUENT flow solver and POINTWISE grid generator were utilized. The morphing technique employed involved adjusting both flap mean camber and flap slots, ensuring minimal flow interferences. By discretizing the flap mean camber line, various flap geometries were achieved.Results and Discussions:The findings reveal a significant enhancement in the airfoil’s aerodynamic efficiency attributed to the implementation of the new flap design. The study shows that utilizing double-slotted morphing in the NACA 4412 airfoil at a 30° flap deflection angle increased the lift coefficient by 82% compared to the un-morphed state. A comparison of lift coefficients between this research and the NACA 4412 split flap at a 60° deflection angle indicates that the double-slotted morphing in the NACA 4412 airfoil at a smaller deflection angle of 30° results in a 14% higher maximum lift coefficient.

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.

Flow instability of an axial flow pump-as-turbine using relative streamline coordinates

When axial flow pumps-as-turbines (PATs) operate under off-design conditions, unstable and unsteady flow structures appear in the internal flow field, resulting in suboptimal functioning. These operating conditions not only decrease the efficiency of the hydraulic machines but also affect their mechanical reliability. This study establishes relative streamline coordinates, based on the blade's mean camber line, to investigate flow instabilities in axial flow PATs from a new perspective. Numerical simulations on an axial flow PAT were performed and validated using experimental data. The results show that flow separation is more likely to occur due to the more curved profile at the blade's suction surface, leading to considerable fluctuations in velocity along the flow direction and enstrophy amplitude near both the hub and impeller shroud. Moreover, the poor matching of the relative inflow angle of the impeller with the blade inlet angle leads to impingement losses near their leading edge, generating unstable flows and significant pressure pulsations, which induces hydraulic instability within the impeller. In addition to rotor-stator interference effects, the curvature of the blade suction surface profile and the bend structure of inlet conduit are significant factors that influence the pressure pulsation distribution of the PAT. An analysis of the enstrophy transport equation indicates that the relative vortex generation and the Reynolds stress dissipation terms play a key role in both vortex generation and dissipation, whereas the viscous term has a lower influence. These findings can serve as a reference for the optimization and efficient design of axial flow PATs.

Numerical Simulation of the Transient Flow around the Combined Morphing Leading-Edge and Trailing-Edge Airfoil.

An integrated approach to active flow control is proposed by finding both the drooping leading edge and the morphing trailing edge for flow management. This strategy aims to manage flow separation control by utilizing the synergistic effects of both control mechanisms, which we call the combined morphing leading edge and trailing edge (CoMpLETE) technique. This design is inspired by a bionic porpoise nose and the flap movements of the cetacean species. The motion of this mechanism achieves a continuous, wave-like, variable airfoil camber. The dynamic motion of the airfoil's upper and lower surface coordinates in response to unsteady conditions is achieved by combining the thickness-to-chord (t/c) distribution with the time-dependent camber line equation. A parameterization model was constructed to mimic the motion around the morphing airfoil at various deflection amplitudes at the stall angle of attack and morphing actuation start times. The mean properties and qualitative trends of the flow phenomena are captured by the transition SST (shear stress transport) model. The effectiveness of the dynamically morphing airfoil as a flow control approach is evaluated by obtaining flow field data, such as velocity streamlines, vorticity contours, and aerodynamic forces. Different cases are investigated for the CoMpLETE morphing airfoil, which evaluates the airfoil's parameters, such as its morphing location, deflection amplitude, and morphing starting time. The morphing airfoil's performance is analyzed to provide further insights into the dynamic lift and drag force variations at pre-defined deflection frequencies of 0.5 Hz, 1 Hz, and 2 Hz. The findings demonstrate that adjusting the airfoil camber reduces streamwise adverse pressure gradients, thus preventing significant flow separation. Although the trailing-edge deflection and its location along the chord influence the generation and separation of the leading-edge vortex (LEV), these results show that the combined effect of the morphing leading edge and trailing edge has the potential to mitigate flow separation. The morphing airfoil successfully contributes to the flow reattachment and significantly increases the maximum lift coefficient (cl,max)). This work also broadens its focus to investigate the aerodynamic effects of a dynamically morphing leading and trailing edge, which seamlessly transitions along the side edges. The aerodynamic performance analysis is investigated across varying morphing frequencies, amplitudes, and actuation times.

Inviscid modeling of unsteady morphing airfoils using a discrete-vortex method

Abstract A low-order physics-based model to simulate the unsteady flow response to airfoils undergoing large-amplitude variations of the camber is presented in this paper. Potential-flow theory adapted for unsteady airfoils and numerical methods using discrete-vortex elements are combined to obtain rapid predictions of flow behavior and force evolution. To elude the inherent restriction of thin-airfoil theory to small flow disturbances, a time-varying chord line is proposed in this work over which to satisfy the appropriate boundary condition, enabling large deformations of the camber line to be modeled. Computational fluid dynamics simulations are performed to assess the accuracy of the low-order model for a wide range of dynamic trailing-edge flap deflections. By allowing the chord line to rotate with trailing-edge deflections, aerodynamic loads predictions are greatly enhanced as compared to the classical approach where the chord line is fixed. This is especially evident for large-amplitude deformations. Graphical abstract

New Insights into Flow for a Low-Bypass-Ratio Transonic Fan with Optimized Rotor

In this paper, a three-dimensional aerodynamics optimization system is built and applied to optimize a rotor blade to balance the conflicts between stall margin, total pressure ratio, adiabatic efficiency, and mass flow rate for the high-loading and transonic-flow fan. A novel flow diagnostic method based on vorticity dynamics theory is utilized to analyze the reasons for the improvement in aerodynamic performance in the optimized transonic fan. In the established aerodynamic optimization method, use the blade profile camber line curvature and its leading edge metal angle as the optimization variables, which are optimized by modifying the coordinates of their control points and introducing a genetic algorithm. Finally, the vorticity dynamics parameters, such as the boundary vorticity flux (BVF), azimuthal vorticity and skin-friction lines are used to diagnose the key flow features in the optimized and baseline fan passage. The results indicate that, by controlling skillfully the blade camber line curvature in the optimization improves the aerodynamic performance of the fan stage, increasing the total pressure ratio by 1.90% while increasing the mass flow rate and adiabatic efficiency by 5.82% and 4.45%, respectively. The formulas from the vorticity dynamics diagnosis method indicate a close link between the aerodynamic performance and vorticity dynamic parameters for the axial fan/compressor passage flow, and that both azimuthal vorticity and boundary vorticity flux have significant influence on fan stage performance. Moreover, the boundary layer separation flow on the rotor blade surface is accompanied by a spike of entropy and static pressure, and their derivative/gradient also suffer drastic changes under the effect of shock waves. Detailed flow information can be obtained about the on-wall with high accuracy based on the vorticity dynamics diagnosis method, which provides researchers with a novel method for the turbomachinery aerodynamic design and analysis in the aero-engine engineering development field.

Numerical Investigation of Blade-to-Blade Surface Layout in the Ram-rotor

A numerical investigation has been conducted on the ram-rotor with various blade-to-blade profiles to achieve potential benefits in enhancing their performance. The blade-to-blade profile is changed by adjusting the strake camber line to enable the formation of expansive and contractive flow paths. Results indicate that the expansive flow path can significantly improve the total pressure ratio of the ram-rotor by altering the position of shock trains. Subsonic airflow after the shock train is decelerated and pressurized, which further contributes to the pressure rising capacity. The leakage flow is suppressed as the flow path is contractive in the blade-to-blade view. This, in turn, leads to a significant reduction of both tip leakage loss and the interference effect between the leakage and the shocks.

Velocity Increment on Incidence Angle near the Leading Edge of the Compressor Cascade

The geometry of a compressor leading edge has an important effect on the aerodynamic performance at an off-designed incidence angle. The current geometric design methods of the leading edge are usually developed based on the flow characteristics at the designed incidence angle. However, few research focuses on the quantitative rules of the leading edge flow characteristics at the off-designed incidence angle in a compressor cascade. This situation restricts the further optimization and development of the leading edge geometry design method. In this paper, starting from the research of a potential cascade theory, the singularity point, where the surface velocity approaches infinity in the leading edge region, is eliminated by applying the characteristic that the ratio of the velocity increasement on the incidence angle in the plate cascade and the isolated plate flow is finite. Secondly, the equivalent pitch lengths based on 1/cos(β) and VI caused by a diffuser deceleration in the cascade passage were employed to correct the effect of the stagger angle. Finally, by introducing the isolated flow around the thick airfoil and considering the influence of the camber line geometry, a model of the variation of the surface velocity near the leading edge under the off-designed incidence angle, named the velocity increment on incidence angle, is derived from any compressor cascade. Hence, the relation between the off-designed incidence angle and the designed incidence angle of the surface velocity in a cascade blade is established, and it depends only on the geometrical parameters. Through a verification using numerical calculations and experimental measurement, the explicit formula for the velocity increment on incidence angle proposed in this paper has high precision near the leading edge.

Control of squealer-tip leakage flow with perforated-rib coolant injection in an axial turbine cascade

A novel perforated-rib configuration is proposed for controlling the tip leakage flow at the rotor tip of an axial turbine. Three perforated-rib layouts are considered, wherein a perforated rib is installed at (A) the Suction-Side squealer (SS-rib), (B) the Pressure-Side squealer (PS-rib), and (C) the additional squealer along the blade Camber Line (CL-rib). A numerical method is used to show how the novel rib layouts affect the aerodynamic performance of the tip leakage flow. Results show that the coolant jets issuing from the perforated-rib injection holes penetrate deeper into the tip clearance than those in the baseline squealer-tip case, and how the perforated-rib coolant injection affects the tip leakage flow depends strongly on the rib layout. The PS-rib and CL-rib layouts appear promising for controlling the tip leakage flow, playing a significant role in reducing the total pressure loss and improving the turbine blade’s isentropic efficiency. In particular, under an injection mass flow ratio of 1% and a tip clearance of 1% blade span, the PS-rib layout reduces the leakage mass flow rate by 27% and increases the isentropic efficiency by 1.25% compared with those in the baseline squealer-tip case. Meanwhile, the advantages of the PS-rib layout in tip leakage control are confirmed under small and large tip clearances.

Aerodynamic performance-preserving construction method for a near-net-shape blade cross section

Aeroengine blades are typical thin-walled structural parts, which are prone to deformations when forming near-net-shape blade blanks. The qualified blade body is produced by a precision blanking process, but with a small deformation. Moreover, the leading edge and trailing edge (LE/TE) connected to the blade body have excess material to be removed. Using the design blade model, it is difficult to machine the LE/TE to a contour that smoothly transitions to the deformed body. However, a LE/TE with smooth joints to the blade body can be machined by constructing a temporary guiding model that guides the finishing process based on blank measurement data. Unfortunately, this model has a discrepancy between its LE/TE shape and design's in order to smoothly join with the deformed blade body, which causes its aerodynamic performance to deviate from the design value. To address the above issues, we have developed an innovative method for constructing aerodynamic performance-preserving cross sections for temporary guiding models. First, geometric features that have a significant impact on the aerodynamic performance are selected as constraints. Second, we define the constraint equations for the geometric features of the thickness curve and the camber line. Finally, an affine transformation is used to construct the camber lines, and a progressive iterative least square fitting algorithm is refined to construct the thickness curves. The total pressure loss coefficient of the constructed cross sections is simulated using computational fluid dynamics tools. The results show that the proposed method can effectively reduce the effect of blank forming deformations on the aerodynamic performance of machined blades.

Numerical investigations on the unsteady leakage flow and heat transfer characteristics of the turbine blade squealer tip

The unsteady leakage flow and heat transfer characteristics of the turbine blade squealer tip was numerically investigated using three-dimensional Unsteady Reynolds-Averaged Naiver-Stokes (URANS) and standard k-ω turbulence model. The numerical simulated heat transfer coefficients of the turbine blade tip were well agreement with the experimental data. The accuracy of the numerical method was validated. The steady and unsteady leakage flow and heat transfer coefficient of the turbine blade squealer tip with and without film cooling was conducted. The unsteady leakage flow and heat transfer characteristics of the turbine blade squealer tip with film cooling design at three different blow ratios was numerically investigated. The obtained results show that the corner vortex and scraping vortex near the pressure side shows periodic fluctuation along the separation line of the leakage flow under the function of the pressure difference between the suction and pressure side of the blade tip, as well as the upstream vane unsteady wake flow. This unsteady flow behavior results in the fluctuation of the high heat transfer coefficients at the blade tip. The film cooling design along the camber line can effectively reduce the thermal load of the turbine blade squealer tip by comparison to without film cooling case. The time-averaged heat transfer coefficients of the turbine blade squealer tip reduce 9.0%, 12.4% and 13.2% at blowing ratio of .0.5, 1.0 and 1.5 comparison to without film cooling design in respective. The present work can provide the reference of the film cooling design for the turbine blade squealer tip.

Research on Centrifugal Blower Design and Optimization Method Based on Mean Camber Line Optimization and CFD

In recent years, with the development of domestic industry and the progress of production technology, the centrifugal blower, as a piece of nuclear equipment in the industry, needs to be upgraded and optimized to improve its performance. Thus, based on the mean camber line optimization and CFD, this paper carries out the design and aerodynamic optimization for a centrifugal blower, and a corresponding 3D aerodynamic optimization platform is built. Then the effects the mean camber lines have on the aerodynamic performance of the centrifugal blower are further analyzed. The results show that the stall margin and efficiency of the centrifugal blower are improved, going up to nearly 8.5% and 1.5%, respectively, after the optimization, while the total pressure ratio basically remains unchanged. The optimized mean camber lines can control the Mach number and restrain the separating flow more effectively, which contributes to improving the carrying capacity of the blower and verifies the advancement of the optimized platform. This provides a novel method for the design and optimization of centrifugal blowers.

The acoustic impedance of three-dimensional turbines

Thermoacoustic stability assessment of gas turbine combustors requires an acoustic impedance boundary condition for the downstream turbomachinery. Actuator disk type analytical methods offer rapid predictions of acoustic impedance in an iterative design process; previous studies show that this class of models works well for cascades consistent with a two-dimensional assumption. Real turbines, however, are three-dimensional with multiple stages, coolant flows, and leakage flows. The first part of this paper validates a cambered semi-actuator disk model for the acoustic impedance of a realistic multi-stage turbine using non-linear time-marching computations: the two methods agree to within 9% for incident pressure waves and 14% for incident entropy waves. Simulations of the multi-stage turbine with different inlet conditions confirm that, to a close approximation, inlet corrected flow and hence Mach numbers and acoustic impedance are constant during off-design operation. The second part of the paper then applies both analytical and computational approaches to families of parametrically generated turbine stages to quantify three-dimensional design effects. The results show that the influence of hub-to-tip ratio on acoustic impedance is weak, and the two-dimensional analytical model is accurate even for high aspect ratio stages. Front-loaded camber lines increase axial Mach number within blade passages, raising acoustic impedance by up to 51% compared to a datum quadratic camber line. Varying the stator–rotor axial gap changes the relative phase of reflections from vanes and blades, causing the total impedance to either increase or decrease, at different frequencies, by up to 11%. The cambered semi-actuator disk method consistently captures the correct trends, showing that the physical basis of the model is sufficient to produce a broadly applicable design tool for rapid assessment of turbine impedance boundary conditions.

Single-step deep reinforcement learning for two- and three-dimensional optimal shape design

This research gauges the capabilities of deep reinforcement learning (DRL) techniques for direct optimal shape design in computational fluid dynamics (CFD) systems. It uses policy based optimization, a single-step DRL algorithm intended for situations where the optimal policy to be learnt by a neural network does not depend on state. The numerical reward fed to the neural network is computed with an in-house stabilized finite elements environment combining variational multi-scale modeling of the governing equations, immerse volume method, and multi-component anisotropic mesh adaptation. Several cases are tackled in two and three dimensions, for which shapes with fixed camber line, angle of attack, and cross-sectional area are generated by varying a chord length and a symmetric thickness distribution (and possibly extruding in the off-body direction). At a zero incidence, the proposed DRL-CFD framework successfully reduces the drag of the equivalent cylinder (i.e., the cylinder of same cross-sectional area) by 48% at a Reynolds numbers in the range of a few hundreds. At an incidence of 30°, it increases the lift to drag ratio of the equivalent ellipse by 13% in two dimensions and 5% in three dimensions at a chord Reynolds numbers in the range of a few thousands. Although the low number of degrees of freedom inevitably constrains the range of attainable shapes, the optimal is systematically found to perform just as well as a conventional airfoil, despite DRL starting from the ground up and having no a priori knowledge of aerodynamic concepts. Such results showcase the potential of the method for black-box shape optimization of practically meaningful CFD systems. Since the resolution process is agnostic to details of the underlying fluid dynamics, they also pave the way for a general evolution of reference shape optimization strategies for fluid mechanics and any other domain where a relevant reward function can be defined.