Turbulent Transonic Flow Research Articles

Data-driven aerodynamic shape design with distributionally robust optimization approaches

We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. DRO aims to minimize the worst-case expected performance in a set of distributions that is informed by observed data with uncertainties. Building on the findings of the work Gotoh, et al. (2018), we study the connections between a class of DRO and robust design optimization, which is classically based on the mean–variance (standard deviation) optimization formulation pioneered by Taguchi. Our results provide a new perspective to the understanding and formulation of robust design optimization problems. It enables data-driven and statistically principled approaches to quantify the trade-offs between robustness and performance, in contrast to the classical robust design formulation that captures uncertainty only qualitatively. Our preliminary computational experiments on aerodynamic shape optimization in transonic turbulent flow show promising design results.

Adaptative finite element simulation of unsteady turbulent compressible flows on unstructured meshes

The simulation of high-speed turbulent compressible flows using Large Eddy Simulation (LES) combined with the Characteristic-Based Split scheme (CBS) and a mesh adaptation strategy is presented in this work. A compressible dynamic Smagorinsky model is employed for the compressible LES model and the CBS scheme is employed in a Finite Element Method (FEM) context for space and time discretization using unstructured meshes. An accurate mesh adaptation scheme is frequently applied along the simulation including mesh refinement, mesh coarsening, edge or face swapping and a vertex smoothing technique in order to control the interpolation error and the mesh size. A feature-based error estimation is employed considering multi-scale and multi-metric intersection in order to capture turbulence effects. Two and three-dimensional applications are evaluated in order to investigate the capabilities of the present approach for evaluating external turbulent and compressible aerodynamics problems. The turbulent transonic flow around a circular cylinder in 2D and 3D domains and the turbulent supersonic flow past a blunt cylinder-flare model are investigated. Aerodynamic coefficients, frequency analysis and pressure distributions are compared against experimental data and other numerical simulations.

Instabilities of Transonic Turbulent Flow over a Flat-Sided Wedge

The transonic turbulent two-dimensional airflow over a symmetric flat-sided double wedge is studied numerically. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with ANSYS-18.2 CFX finite-volume solver of second order accuracy on a fine mesh. The solutions demonstrate an extreme sensitivity of the flow field and lift coefficient to variation of the angle of attack α or free-stream Mach number M∞. Non-unique flow regimes and hysteresis in certain bands of α and M∞ are identified. Interaction of shock waves and local supersonic regions is discussed. The study confirms a concept of shock wave instability due to a coalescence/rupture of supersonic regions. In addition to the instability of shock wave locations, the numerical simulation shows a buffet onset, i.e., self-exciting oscillations due to instability of a boundary layer separation at the rear of wedge. Curious flow regimes with positive lift at negative angles α and, vice versa, with negative lift at positive angles α, are pointed out. A piecewise continuous dependence of the lift coefficient on two free-stream parameters, α and M∞, is discussed.

Comparative study of inner–outer Krylov solvers for linear systems in structured and high-order unstructured CFD problems

Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner–outer GMRES strategy combined with most relevant preconditioning and deflation techniques. The choice of this specific class of Krylov solvers for challenging problems is based on its outstanding convergence properties. Typically in our implementation the efficiency of the preconditioner is enhanced with a domain decomposition method with overlapping. However, maintaining the performance of the preconditioner may be challenging since scalability and efficiency of a preconditioning technique are properties often antagonistic to each other. In this paper we demonstrate how flexible inner–outer Krylov methods are able to overcome this critical issue. A numerical study is performed considering either a Finite Volume (FV), or a high-order Discontinuous Galerkin (DG) discretization which affect the arithmetic intensity and memory-bandwidth of the algebraic operations. We consider test cases of transonic turbulent flows with RANS modeling over the two-dimensional supercritical OAT15A airfoil and the three-dimensional ONERA M6 wing. Benefits in terms of robustness and convergence compared to standard GMRES solvers are obtained. Strong scalability analysis shows satisfactory results. Based on these representative problems a discussion of the recommended numerical practices is proposed.

Instability of local supersonic regions over a flat-sided airfoil with a blunt trailing edge

The two-dimensional turbulent transonic flow over a symmetric flat-sided airfoil with a blunt trailing edge is studied numerically. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver on a fine computational mesh. The non-uniqueness of flow field in certain bands of the given free-stream Mach number and angle of attack is demonstrated. Intricate dependence of the lift coefficient on the free-stream parameters is discussed. Adverse free-stream parameters, which admit abrupt changes of the flow structure and lift, are identified.

An efficient edge based data structure for the compressible Reynolds‐averaged Navier–Stokes equations on hybrid unstructured meshes

AbstractAn efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds‐averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open‐source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR‐F6 wing‐body‐nacelle‐pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.

Oscillations of transonic flow past a symmetric profile with a blunt trailing edge

We study the two-dimensional turbulent transonic flow past a symmetric profile with a blunt base and flat sides. The numerical simulation is based on the unsteady Reynolds-averaged Navier-Stokes equations. The obtained solutions reveal both symmetric and asymmetric oscillating flows past the profile at zero angle of attack. An occurrence of the symmetric or asymmetric flow regime depends on the time history of boundary conditions. A jet injection into the wake does not eliminate the flow non-uniqueness, though attenuates flow oscillations.

Validation of a new fluid—structure interaction framework for non-linear instabilities of 3D aerodynamic configurations

A new framework developed at CIRA to deal with Fluid–Structure Interaction phenomena in a partitioned approach has been developed. A multi-block structured flow solver for unsteady Navier–Stokes equations, UZEN, was updated and tightly coupled with the open-source FEM code CalculiX in a modular approach.The solvers are interfaced through the open source library preCICE (Bungartz, 2016), that takes care of exchanging data, synchronization and controls the executing processes by means of specific adapters.The framework was designed with the capability to simulate large variety of configurations with complex motions, including rotorcrafts; it has growth potential to include multi-body dynamics and possibly other tools for multi-disciplinary analyses.The present work is focused on numerical validation, by demonstrating the solution of external aerodynamics problems in Euler and viscous flows. In details, instabilities in subsonic and supersonic Euler flows of 2D and 3D panels are verified, comparing the results in terms of static divergence and Limit Cycle Oscillation amplitude with literature works. Furthermore, the AGARD 445.6 wing flutter behavior is investigated in transonic turbulent flow.

On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization—Part II: Viscous Flows

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

Fluid-Structure interaction framework based on structured RANS solver

A Fluid Structure Interaction framework developed at CIRA to deal with multi-physics problems in a partitioned approach is presented. The CIRA multi-block structured flow solver for unsteady Navier-Stokes equations UZEN was updated and tightly coupled with an open-source solver for non-linear structural dynamics in a modular approach. The solvers are glued in space and time through an open source library, able to control the executing processes and to deliver exchanging data by specific adapters. The validity of the framework is tested on vortex-induced vibration effects of a cantilevered beam in low Reynolds flow and on as three-dimensional wing flutter in transonic turbulent flow.

Efficient uncertainty quantification of CFD problems by combination of proper orthogonal decomposition and compressed sensing

In the current paper, an efficient surrogate model based on combination of Proper Orthogonal Decomposition (POD) and compressed sensing is developed for affordable representation of high dimensional stochastic fields. In the developed method, instead of the full (or classical) Polynomial Chaos Expansion (PCE), the ℓ1-minimization approach is utilized to reduce the computational work-load of the low-fidelity calculations. To assess the model capability in the real engineering problems, two challenging high-dimensional CFD test cases namely; i) turbulent transonic flow around RAE2822 airfoil with 18 geometrical uncertainties and ii) turbulent transonic flow around NASA Rotor 37 with 3 operational and 21 geometrical uncertainties are considered. Results of Uncertainty Quantification (UQ) analysis in both test cases showed that the proposed multi-fidelity approach is able to reproduce the statistics of quantities of interest with much lower computational cost than the classical regression-based PCE method. It is shown that the combination of the POD with the compressed sensing in RAE2822 and Rotor 37 test cases gives respectively computational gains between 1.26–7.72 and 1.79–9.05 times greater than the combination of the POD with the full PCE.

Development of a New Algorithm for Modeling Viscous Transonic Flow on Unstructured Grids at High Reynolds Numbers

Abstract This study investigates a new algorithm for modeling viscous transonic flow at high Reynolds number cases suitable for unstructured grids. The challenge of modeling viscous transonic flow around airfoils becomes intense at high Reynolds number cases due to a variety of flow regimes encountered, such as boundary layer growth and the shockwave/turbulent boundary-layer interaction, accompanied by large separation bubble. Therefore, it is highly demanded to develop robust and efficient models that can capture the shock-induced problems of turbulent flows for aircraft design purposes. The new model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a collocated finite volume scheme with minimum aliasing errors was implemented to model the turbulent region in the combination of a semidiscrete, central difference scheme to capture discontinuities with adequately low numerical dissipation for the minimal effect on turbulent flows. To evaluate the effectiveness of the model, it was tested in three conventional cases. The computational results are close to measured data for predicting the shock locations. This implies that the model is able to predict the scale of the separation bubble and the main characteristics of turbulent transonic flow adequately.

Numerical simulation of separation flows induced by shockwave using an anisotropic turbulence model

This paper studies the performance of a nonlinear anisotropic turbulence model developed in the basis of a statistical partial average scheme. The first order velocity of turbulent fluctuations, retained by a novel average scheme, and turbulent length scale can be determined from the momentum equations and mechanical energy equation of the fluctuation flow, respectively. The two physical quantities are readily to construct the nonlinear anisotropic eddy viscosity tensor and to significantly improve computational results. Two typical shock-wave-boundary-layer-interaction (SWBLI) separation flows are deeply studied using CFD method. One is an incident oblique shock wave impinging on a flat plate with a turbulent boundary layer, and the other one is a transonic turbulent separation flow in a converging-diverging transonic diffuser. Comparisons between the computational results and experimental data are carried out for velocity profiles, density contours, pressure distribution, skin friction coefficient, Reynolds stress as well as streamline vectors distribution. Without using any empirical coefficients and wall functions, the numerical results are in good agreement with the available experimental data, which further confirms that the nonlinear anisotropic eddy viscosity tensor is of the decisive factor for the success of the computational results.

High-order strand grid methods for shock turbulence interaction

ABSTRACTIn this work, we examine the flux correction method for three-dimensional transonic turbulent flows on strand grids. Building upon previous work, we treat flux derivatives along strands with high-order summation-by-parts operators and penalty-based boundary conditions. A finite-volume like limiting strategy is implemented in the flux correction algorithm in order to sharply capture shocks. To achieve turbulence closure in the Reynolds-Averaged Navier–Stokes equations, a robust version of the Spalart–Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. Validation studies are considered which demonstrate the flux correction method achieves a high degree of accuracy for turbulent shock interaction flows.

Turbulent Flow Simulations of the Common Research Model Using Immersed Boundary Method

Transonic turbulent flows around the NASA Common Research Model are simulated to investigate the capability of the Cartesian-grid-based flow solver UTCart in three-dimensional high-Reynolds-number flow simulations. UTCart consists of an automatic Cartesian grid generator based on an octree structure and a compressible flow solver that uses an immersed boundary method with a turbulent wall function for the wall boundary condition. Using the UTCart grid generator, the medium grid (approximately 50 million cells) around the NASA Common Research Model is generated in 43 min. For the prediction of the drag coefficient at the cruise condition, the difference between the medium-grid result and the grid-converged value is 24 drag counts (8%). For the fine-grid (approximately 97 million cells) result, the difference reduces to 15 drag counts (5%). Although the drag coefficient is slightly overestimated, the componentwise aerodynamic coefficient shows a consistent trend of grid convergence. Furthermore, the qualitative flow features, including flow separation at high angles of attack, agree well with the experimental data and the computational results on conventional body-fitted grids.

Numerical modelling of transonic centripetal flow in radial turbine blade cascade

Numerical modelling of transonic centripetal turbulent flow in radial blade cascade is described in this paper. Method of the confusor buffer zone is applied to overcome some numerical obstacles related with specifical properties of the outlet confusor. Kinetic energy loss coeficient of the radial blade cascade is compared with its linear representation and with experimental data.

Hybrid central–WENO scheme for the large eddy simulation of turbulent flows with shocks

ABSTRACTTo provide an effective numerical method for the large eddy simulation (LES) of turbulent flows with shocks, a hybrid scheme is developed in a finite volume framework based on the fourth-order central scheme and the third-order weighted essentially non-oscillatory (WENO) scheme. A total of six easy-to-implement and promising switch functions (SFs) are examined in the hybrid central–WENO scheme for the LES of compressible turbulent flows. Both the dissipation and dispersion of the developed hybrid central–WENO scheme are theoretically confirmed using the Fourier technique. Then, the effectiveness and accuracy of this scheme and the SFs are numerically tested by three problems: decaying compressible isotropic turbulence, inviscid, and turbulent transonic flow over a bump. The numerical results show the developed hybrid scheme, coupled with the SF based on local velocity divergence and pressure gradient, has excellent capabilities of capturing shocks and resolving turbulence.

Convergence Acceleration of Fluid Dynamics Solvers Using a Reduced-Order Model

A new method based on reduced-order modeling is presented for the purpose of accelerating the convergence of an iterative solver via solution prediction in the framework of a computational fluid dynamics solver. Using a number of flow solutions as snapshots at preconvergent iterations of the explicit time-marching solver, the reduced-order-modeling-based acceleration technique is used to project to a more accurate solution. The method is first applied to accelerate the convergence of an incompressible Navier–Stokes solver, and the classical two-dimensional lid-driven cavity flow case is revisited for this purpose. Next, the proposed convergence acceleration technique is used in the framework of a density-based computational fluid dynamics solver, and subsonic as well as transonic (inviscid) flows over the NACA 0012 airfoil are studied. Additionally, the performance of the proposed convergence acceleration technique is investigated for turbulent transonic flow over the RAE 2822 airfoil.

A gas‐kinetic scheme for the simulation of turbulent flows on unstructured meshes

SummaryThis paper presents a numerical method for simulating turbulent flows via coupling the Boltzmann BGK equation with Spalart–Allmaras one equation turbulence model. Both the Boltzmann BGK equation and the turbulence model equation are carried out using the finite volume method on unstructured meshes, which is different from previous works on structured grid. The application of the gas‐kinetic scheme is extended to the simulation of turbulent flows with arbitrary geometries. The adaptive mesh refinement technique is also adopted to reduce the computational cost and improve the efficiency of meshes. To organize the unstructured mesh data structure efficiently, a non‐manifold hybrid mesh data structure is extended for polygonal cells. Numerical experiments are performed on incompressible flow over a smooth flat plate and compressible turbulent flows around a NACA 0012 airfoil using unstructured hybrid meshes. These numerical results are found to be in good agreement with experimental data and/or other numerical solutions, demonstrating the applicability of the proposed method to simulate both subsonic and transonic turbulent flows. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical simulation of the transonic turbulent flow around a wedge-shaped body with a backward-facing step

A fully three-dimensional near-wall complex turbulent flow around a wedge-shaped body with a backward-facing step is considered with the transonic flow regime (Mach number M = 0.913) at the Reynolds number Re = 7.2 × 106. The technology of the numerical simulation of problems of the class under study is represented in detail. A series of preliminary auxiliary calculations is carried out for choosing the optimal computational algorithm. The numerical results of the problem simulation based on the eddy-resolving hybrid RANS-LES approach IDDES are finally given for the full configuration. The validity of the results obtained is confirmed by comparing them to the corresponding experimental data.