SD7003 Airfoil Research Articles

Effects of turbulence boundary conditions on Spalart-Allmaras RANS simulations for active flow control applications

We assess the suitability of Reynolds-Averaged Navier–Stokes (RANS) simulation using the Spalart-Allmaras (SA) turbulence model as a closure in analysing the performance of fluidic Active Flow Control (AFC) applications. In particular, we focus on the optimal set of actuation parameters found by Tousi et al. (Appl Math Model, 2021) and Tousi et al. (Aerospace Sci Technol 127:107679, 2022) for a SD7003 airfoil at a Reynolds number Re=6×104 and post-stall angle of attack α=14∘ fitted with a Synthetic Jet Actuator (SJA). The Large Eddy Simulation (LES) presented in that work is taken as the reference to identify the best choice of boundary conditions for the turbulence field ν~ at both domain inlet and jet orifice in two-dimensional SA-RANS computations. Although SA-RANS is far less accurate than LES, our findings show that it can still predict macroscopic aggregates such as lift and drag coefficients quite satisfactorily and at a much lower computational cost, provided that turbulence levels of the actuator jet are set to a realistic value. An adequate value of ν~ is instrumental in capturing the correct flow behaviour of the reattached boundary layers for close-to-optimal actuated cases. This validates the use of RANS-SA as a reliable and cost-effective simulation method for the preliminary optimisation of SJA parameters in AFC applications, provided that thorough sensitivity analysis on turbulence-related boundary conditions is performed. Given the strong sensitivity of flow detachment on the laminar or turbulent nature of boundary layers, our results suggest that such analyses are particularly indispensable for vastly separated flow scenarios in general, notably for bluff bodies at moderate transcritical Reynolds numbers.

Lift enhancement via leading edge vortex delay in flapping flight utilizing kinematic modifications

Flapping-winged micro aerial vehicles (MAVs) are an innovative approach to indoor flight, useful for reconnaissance. However, challenges remain in improving the maneuverability of these drones in low-speed flight, specifically using wing kinematics for different flight profiles. This work focuses on the plunge motion of the SD7003 airfoil in forward flight. Unsteady simulations are carried out at a Reynolds number of 10,000 in Ansys Fluent upon validation against experimental, theoretical, and numerical results from literature. Modification of the kinematics is performed by skewing the sinusoidal curve that dictates the effective angle of attack of the airfoil, leading to what is termed “peak-shifted” (PS) kinematics. The skewness of the curve is varied systematically to delay the peak of plunge velocity during the downstroke. Due to this, the leading edge vortex formation and shedding were also found to be delayed, with stronger vortex cores causing a surge in lift force. Results indicate that with the PS kinematics, mean lift increased by 4.5% and mean drag reduced by 7.9%, at the cost of an increase in power requirement of 42.9% compared to the baseline kinematics. Since lift augmentation and drag reduction are obtained with no change in plunge amplitude or frequency, this opens up opportunities in tail-less MAV design to use PS kinematics in short intervals for maneuvers or flight controls, including roll, pitch, and yaw.

Large eddy simulation of low-Reynolds-number flow past the SD7003 airfoil with an improved high-precision IPDG method

Large eddy simulation of low-Reynolds-number flow past the SD7003 airfoil with an improved high-precision IPDG method

Gridder-HO: Rapid and efficient parallel software for high-order curvilinear mesh generation

The advancement in high-order computational methods is reshaping the landscape of mesh generation in Computational Fluid Dynamics (CFD), steering the focus towards curvilinear mesh techniques to meet the escalating accuracy demands. Gridder-HO, the software designed to generate high-order curvilinear mesh efficiently and rapidly, has been developed. Gridder-HO supports the elevation of meshes to P2 (quadratic-order) or P3 (cubic-order). It features a layered architecture and utilizes the concurrent hash table and the Alternating Digital Tree (ADT) data structure, supporting thread-level parallelism to convert straight-edge mesh into high-order curvilinear mesh seamlessly. Gridder-HO utilizes the projection method based on a thread pool to precisely preserve geometry, and employs a novel localized RBF method with ADT for volume node interpolation to untangle the mesh, which aims to achieve a satisfactory balance between efficiency and accuracy. Validated through CFD simulations using the GPU-accelerated Python Flux Reconstruction (PyFR) solver, the practicality of Gridder-HO is demonstrated across various Reynolds numbers in typical cases such as sphere, cylinder, and SD7003 airfoil. These results confirm the high-order curvilinear meshes generated by Gridder-HO meet the high-order requirements of emerging computational methods. Moreover, Gridder-HO exemplifies its effectiveness in generating large-scale, high-order curvilinear meshes for the DLR-F6 transport aircraft configuration standard test cases. It elevates a mesh with 5 million elements to P2 in 3 min 39 sec at 68% parallel efficiency on 16 threads, and another with 14 million elements to P3 in 52 min 39 sec at 60% efficiency, illustrating its efficiency and potential in satisfying the demands of complex geometries in engineering applications.

Flow Development Over An SD7003 Airfoil At Different Accelerations From Rest

This work examines the effect of acceleration on the formation of a laminar separation bubble (LSB). The experiments were performed in a water towing tank with an SD7003 airfoil model accelerated from rest to a constant chord Reynolds number. Quantitative flow field measurements were performed using two-component time-resolved Particle Image Velocimetry (PIV) over a range of accelerations. A detailed analysis of the spatio-temporal flow development is conducted focusing on the LSB formation and dynamics. The results provide insight into the mechanism of LSB formation. The associated transient flow development is shown to persist over several convective time units after steady state free-stream velocity is reached, with no significant effect of acceleration on the overall transient duration. However, the acceleration rate has a substantial effect on flow development during the acceleration phase.

Use of machine learning to optimize actuator configuration on an airfoil

Machine learning was used to optimize the geometric arrangement of a pair of unsteady actuators on flow separation over an efficient low Reynolds number airfoil in post-tall conditions. Large eddy simulation was used to validate the results. Two actuators: one with blowing and the other with suction openings were installed on the top surface of an airfoil at low Reynolds number of 60,000. An SD7003 airfoil at a post stall angle of attack of 13° was utilized. The boundary layer flow of the top surface was manipulated by the actuators to control flow separation. The influence of several actuator parameters: frequency, energy input, opening area, location and orientation angle were considered in an optimization of the dual actuator configuration. A genetic algorithm-based optimization was implemented to find the most effective configuration of this coupling. Since the optimization process is time-consuming, machine learning was used to train artificial neural networks to be coupled with genetic algorithm to reduce the computational cost. The artificial neural networks and their training was constantly upgraded during the optimization cycle. Results for the optimal case indicated an increase in lift coefficient and the objective function in comparison to uncontrolled case by factors of 1.88 and 3.33 respectively. We also found a reduction in drag coefficient. It was also found that using a pair of actuators was more efficient than using a single actuator.

Effects of a Nonlinear Boundary Condition on the Steady Aerodynamics of Porous Airfoils

This paper considers the lift coefficient of an airfoil with nonzero prescribed thickness and camber, along with a prescribed porosity distribution in a steady incompressible flow. In similar prior work, considering a Darcy-type porosity condition on the airfoil surface provides a Fredholm integral equation that can be solved exactly for Hölder-continuous porosity distributions. However, the generated lift predicted by the model diverges from the experimental data for porous airfoils with large values of the porosity parameter. This indicates a fundamental characteristic is missing in the mathematical model. Consequently, in this paper, the (linear) Darcy porosity condition is replaced by the (nonlinear) Forchheimer porosity condition. The Forchheimer porosity condition is decomposed into linear sections and furnishes a modified system of Fredholm integral equations, enabling an approximate solution by superposition for Hölder-continuous porosity distributions. The solution is then verified against the SD7003 airfoil results, and the comparison shows better agreement than considering the Darcy porosity condition. The methodology and results presented here may be combined with previous work on the aeroacoustics of porous airfoils with a Forchheimer boundary condition to address the conflicting aims of improving aerodynamic performance while reducing unwanted aeroacoustic emissions.

High-Order Implicit Large Eddy Simulation using Entropically Damped Artificial Compressibility

Performing industrial scale incompressible Large Eddy Simulation (LES) remains particularly challenging due to computational cost limitations. Recently, the Entropically Damped Artificial Compressibility (EDAC) method was introduced, which does not require coupled global solves or pseudo-time stepping. Parallel to this, high-order unstructured methods, such as the Flux Reconstruction (FR) approach, have been proposed for Implicit LES (ILES) of compressible turbulent flows. This work presents EDAC with FR as an ILES framework for incompressible flows. Results from a Taylor–Green vortex, turbulent channel flow, and transitional and turbulent flow over an SD7003 airfoil demonstrate the approach is accurate and stable for solutions polynomials of degree ps≤4, while some instabilities were observed beyond this. Higher-order solutions were found to be significantly more accurate than their lower-order counterparts compared to reference direct numerical simulation, and had lower divergence error even with less strict incompressibility factors. These results demonstrate that combining EDAC with FR provides a simple, accurate, efficient, and stable framework for performing ILES of incompressible flows. Additionally, this fully explicit framework does not require coupled solvers, pseudo-time stepping, or explicit subgrid scale models.

Angle-of-attack and Mach number effects on the aeroacoustics of an SD7003 airfoil at Reynolds number 60,000

The aeroacoustics of an SD7003 airfoil at Reynolds number 60,000 is investigated using Large Eddy Simulation. Five simulations are performed to study the effects of angle-of-attack and Mach number at fixed Reynolds number. For the three cases with angle-of-attack equal to 0° (M = 0.1, 0.3 and 0.6), a pure tonal noise associated with a 2D organisation of the flow is obtained. This flow topology is due to the establishment of a well known aeroacoustic feedback loop between the separation point on the suction side of the airfoil and the trailing edge. The occurrence of this loop is corroborated by the presence of a standing wave pattern with characteristic mode number in accordance with Panda’s model. The main effect of the Mach number is to promote flow separation and hence increase separation length and mode number. In addition, the first harmonic and the sub-harmonic of the tone, observed in the far field acoustic spectrum, are found to be generated in the wake, presumably due to non-linear vortex interactions. For the two other angles-of-attack 4° and 8° at M = 0.1, the feedback loop does not establish and a Laminar Separation Bubble (LSB) is observed. When increasing the angle-of-attack, the LSB shrinks with earlier reattachment. For those two cases, far-field spectra are characterized by a low frequency associated with the breathing motion of the LSB and the reattachment point fluctuating in space. The frequency of this fluctuation depends on the curvature of the bubble. Far-field spectra are also characterized by a broadband trailing edge noise whose frequency range decreases with the angle-of-attack. Again, this evolution is found to depend on the curvature of the bubble which may promote a centrifugal instability in the separated shear layer.

Pitch–Plunge Equivalence in Dynamic Stall of Ramp Motion Airfoils

Large-eddy simulations (LES) are employed to investigate the pitch–plunge equivalence of an SD7003 airfoil undergoing constant ramp motions at Reynolds number . The equivalence is constructed based on the geometric effective angle of attack according to the quasi-steady thin-airfoil theory. Two rates of descent (or pitch up) are analyzed for different Mach numbers in order to investigate the effects of compressibility on the evolution of the dynamic stall vortex (DSV). During the onset of the DSV and its transport along the airfoil surface, remarkable similarities are found between pitch and plunge in terms of flow topology, aerodynamic loads, and signatures of wall pressure and friction coefficients. However, these flow similarities cease at high-load conditions as the DSV becomes more susceptible to the peculiarities of the airfoil motion, manifested here by different trailing-edge vortices. Employing a correction for the rotation-induced apparent camber effect present in the pitching case, which results from the quasi-steady thin-airfoil theory, improves the agreement between pitch and plunge. However, it is not sufficient to assimilate their disparate trailing-edge systems. Results also demonstrate that the limit angle at which pitch–plunge equivalence remains valid decreases for higher Mach numbers.

Model-form uncertainty quantification of Reynolds-averaged Navier–Stokes modeling of flows over a SD7003 airfoil

Reynolds-averaged Navier–Stokes (RANS) models are known to be inaccurate in complex flows, for instance, laminar-turbulent transition, and RANS uncertainty quantification (UQ) is essential to estimate the uncertainty in their predictions. In this study, a recent physics-based UQ framework that introduces eigenvalue, eigenvector, and turbulence kinetic energy perturbations to the modeled Reynolds stress tensor has been used to estimate the uncertainty in the flow field. We introduce a regression-based marker function that focuses on the turbulence kinetic energy perturbation for the simulation of laminar-turbulent transitional flows over an Selig–Donovan 7003 airfoil. We observed a monotonic behavior of the magnitude of the predicted uncertainty bounds varying with the turbulence kinetic energy perturbation. Importantly, the predicted uncertainty bounds show a synergy behavior that dramatically increases the size of uncertainty bounds and can successfully encompass the reference data when the eigenvalue perturbations are augmented with the marker function.

Quantification of Reynolds-averaged-Navier–Stokes model-form uncertainty in transitional boundary layer and airfoil flows

It is well known that the Boussinesq turbulent-viscosity hypothesis can introduce uncertainty in predictions for complex flow features such as separation, reattachment, and laminar-turbulent transition. This study adopts a recent physics-based uncertainty quantification (UQ) approach to address such model-form uncertainty in Reynolds-averaged Naiver–Stokes (RANS) simulations. Thus far, almost all UQ studies have focused on quantifying the model-form uncertainty in turbulent flow scenarios. The focus of the study is to advance our understanding of the performance of the UQ approach on two different transitional flow scenarios: a flat plate and a SD7003 airfoil, to close this gap. For the T3A (flat-plate) flow, most of the model-form uncertainty is concentrated in the laminar-turbulent transition region. For the SD7003 airfoil flow, the eigenvalue perturbations reveal a decrease as well as an increase in the length of the separation bubble. As a consequence, the uncertainty bounds successfully encompass the reattachment point. Likewise, the region of reverse flow that appears in the separation bubble is either suppressed or bolstered by the eigenvalue perturbations. This is the first successful RANS UQ study for transitional flows.

Third-order Paired Explicit Runge-Kutta schemes for stiff systems of equations

The ability to advance locally-stiff systems of equations in time depends on accurate and efficient temporal schemes. Recently, a new family of Paired Explicit Runge-Kutta (P-ERK) methods has been proposed. This approach allows different Runge-Kutta schemes with different numbers of active stages to be assigned based on local stiffness criteria. Whereas the original P-ERK formulation was only second-order accurate, in this paper we propose a new third-order family. We present the general formulation for these schemes, and then optimize them for the high-order discontinuous Galerkin method recovered via the flux reconstruction approach. We then verify that these schemes obtain their designed third-order accuracy for non-linear systems of equations. Performance results show that they achieve speedup factors up to four relative to a classical third-order Runge-Kutta methods for laminar and turbulent flow over an SD7003 airfoil, and turbulent flow over a tandem sphere configuration. Based on these results, this new family of third-order P-ERK schemes provides an appealing approach for accurate and efficient solution of locally-stiff systems of equations.

Data-driven reduced order modeling for parametrized time-dependent flow problems

This paper proposes a nonintrusive reduced basis (RB) method based on dynamic mode decomposition (DMD) for parameterized time-dependent flows. In the offline stage, the reduced basis functions are extracted by a two-step proper orthogonal decomposition algorithm. Then, a novel hybrid DMD regression model that combines windowed DMD and optimized DMD is introduced for the temporal evolution of the RB coefficients. To improve the stability of this method for complex nonlinear problems, we introduce a threshold value to modify the DMD eigenvalues and eigenvectors. Moreover, the interpolation of the coefficients in parameter space is conducted by a feedforward neural network or random forest algorithm. The prediction of the RB solution at a new time/parameter value can be recovered at a low computational cost in the online stage, which is completely decoupled from the high-fidelity dimension. We demonstrate the performance of the proposed model with two cases: (i) laminar flow past a two-dimensional cylinder and (ii) turbulent flow around a three-dimensional SD7003 airfoil. The results show reasonable efficiency and robustness of this novel reduced-order model.

Large Eddy Simulation of optimal Synthetic Jet Actuation on a SD7003 airfoil in post-stall conditions

Aerodynamic performances may be optimised by the appropriate tuning of Active Flow Control (AFC) parameters. For the first time, we couple Genetic Algorithms (GA) with an unsteady Reynolds-Averaged Navier-Stokes (RANS) solver using the Spalart-Allmaras (SA) turbulence model to maximise lift and aerodynamic efficiency of an airfoil in stall conditions [1], and then validate the resulting set of optimal Synthetic Jet Actuator (SJA) parameters against well-resolved three-dimensional Large Eddy Simulation (LES). The airfoil considered is the SD7003, at the Reynolds number Re=6×104 and the post-stall angle of attack α=14∘. We find that, although SA-RANS is not quite as accurate as LES, it can still predict macroscopic aggregates such as lift and drag coefficients, provided the free-stream turbulence is prescribed to reasonable values. The sensitivity to free-stream turbulence is found to be particularly critical for SJA cases. Baseline LES simulation agrees well with literature results, while RANS-SA would seem to remain a valid model to a certain degree. For optimally actuated cases, our LES simulation predicts far better performances than obtained by suboptimal SJA LES computations as reported by other authors [2] for the same airfoil, Re and α, which illustrates the applicability and effectiveness of the SJA optimisation technique applied, despite using the less accurate yet computationally faster SA-RANS. The flow topology and wake dynamics of baseline and SJA cases are thoroughly compared to elucidate the mechanism whereby aerodynamic performances are enhanced.

A Galilean Invariant Variable–Based RANS Closure Model for Bypass and Laminar Separation Bubble–Induced Transition

A one-equation Reynolds-averaged Navier-Stokes (RANS) closure model has been established for bypass transition and laminar separation bubble (LSB)–induced transition. A new local indicator is proposed to describe the influence of turbulence intensities and pressure gradients, which makes the model Galilean invariant. Based on this new indicator, a novel and efficient transition criterion is formulated. For LSB-induced transition, an empirical correlation is developed to modify the intermittency factor and control the size of separation bubbles. Several flow cases, including flat plates with various pressure gradients, flat plates with LSBs, semicircular leading-edge flat plates, National Advisory Committee for Aeronautics (NACA) 0018 airfoil, and SD7003 airfoil, are employed for the model verification. The predictions show good agreement with the experimental data and large-eddy simulation data for different inlet conditions, which indicates the increment of free-stream turbulence intensity leads to the reduction of the size of laminar separation bubbles.

Laminar wake suppression of airfoil by rotating rod at low Reynolds number

The aerodynamic performance of an SD7003 airfoil with active control of the rotating rod through momentum injection into the boundary layer of the suction side is numerically explored at a low Reynolds number of 5000. Striking aerodynamic improvement is observed for a proper parameter combination of rod location and rotational speed. Pressure drop and recovery at the upstream and downstream sides of the rotating rod, respectively, is found to be the primary mechanism for the lift enhancement and drag reduction.

A comparison of plunging- and pitching-induced deep dynamic stall on an SD7003 airfoil using URANS and LES simulations

Dynamic stall is a fluid dynamics phenomenon experienced by airfoils undergoing a rapid variation in their operating conditions, such as in the presence of pitching or plunging motions, when the effective angle of attack exceeds the static stall angle. The flow field near the airfoil is characterized by the presence of a strong clockwise vortex originating near the leading edge, which is convected downstream along the suction side, generating a low-pressure region and a continuous rise in lift. A controlled form of dynamic stall is involved in the flight mechanism of some natural flapping-wing flyers, and this is currently a matter of interest for the design of biomimetic micro aerial vehicles. Dynamic stall is also responsible for limitations in helicopters' forward-flight velocity, it can lead to flutter in fixed-wing aircraft and vibration-induced damage in wind turbine blades. In this work, 2D URANS and LES numerical simulations have been carried out for incompressible dynamic stall flow cases over an SD7003 airfoil at a Reynolds number of 6⋅104 and at a reduced frequency of 0.25, with the aim of assessing the validity and the role of low fidelity simulations in dynamic stall prediction, at operating conditions relevant for micro air vehicles. Simulations have been conducted both in the case of periodic pitching and plunging, in order to investigate similarities and differences in the resulting flow fields and aerodynamic coefficients. The effect of the reduced frequency on the agreement between 2D URANS and LES has also been evaluated for an airfoil under periodic plunging.

Adjoint-based error estimation for grid adaptation for large eddy simulation

Goal-oriented grid adaptation for chaotic systems remains a challenging problem due to the tremendous computational and storage costs as well as the instability of the adjoint system for long time backward time integration. We propose two approximation methods to derive a single-solve adjoint system for statistically steady chaotic problems. The first approximation leads to an adjoint system based on the time-averaged Jacobian and the sensitivity of the functional; while, the second approximation is based on converting the LES flow solution to a Reynolds-averaged Navier–Stokes (RANS)-type steady flow solution, on which the steady adjoint approach could be applied. The approaches are further applied to derive an adjoint-based error estimator for LES. The error estimator was validated using the SD7003 airfoil case. Tests were carried out for two different Reynolds numbers on coarse, fine and adapted grids. Numerical results were validated through a comparison against reference LES and experimental data and it was shown that the adjoint-based adapted grids lead to fast convergence of the prediction of the functional as well as the capture of pertinent flow structures compared to feature-based and manually adapted grids.

Gradient-free aerodynamic shape optimization using Large Eddy Simulation

In this paper we demonstrate the ability to perform gradient-free aerodynamic shape optimization using Large Eddy Simulation (LES) with the Mesh Adaptive Direct Search (MADS) optimization algorithm. We first outline the challenges associated with performing gradient-based optimization using LES, specifically chaotic divergence of the adjoint. We then introduce a Dynamic Polynomial Approximation (DPA) procedure, which allows the high-order solution polynomial representation used by the flow solver to be increased, or decreased, depending on the poll size being used by MADS. This allows rapid convergence towards the optimal design space using lower-fidelity simulations, followed by automatic transition to higher-fidelity simulations when close to the optimal design point. We demonstrate the utility of MADS for optimization of simple chaotic problems, specifically the Lorenz system. We then demonstrate the utility of DPA for aerodynamic optimization of a low Reynolds SD7003 airfoil, highlighting the benefits of the binary DPA approach. Finally, we perform aerodynamic optimization of a turbulent SD7003 airfoil with a final design that increases the mean lift to drag ratio by 32% relative to experimental data, demonstrating that shape optimization using LES and MADS is feasible for aerodynamic design.