Simulation Of Transonic Flow Research Articles

Wall-Modeled Large-Eddy Simulation of Transonic Buffet over NASA-CRM Using FFVHC-ACE

This study investigates the capability of wall-modeled large-eddy simulation (WMLES) in predicting the transonic buffet phenomenon over three-dimensional aircraft configurations at high Reynolds numbers. The WMLES is conducted using the Cartesian-grid-based flow solver FrontFlow/Violet Hierarchical Cartesian for Aeronautics Based on Compressible-Flow Equations (FFVHC-ACE). To extend the capability of FFVHC-ACE to transonic flow simulations with shock waves, a hybrid kinetic energy and entropy preserving/upwind scheme is implemented in FFVHC-ACE. To validate the employed simulation framework, the flow around the NASA Common Research Model in the near-cruise condition is simulated. In this case, the surface pressure distributions and force coefficients are reasonably predicted and show the trend of grid convergence. Furthermore, the WMLES at the buffet conditions reproduces the wavy structures of the shock wave (i.e., buffet cells) propagating outboard. The obtained propagation speed of the buffet cells and surface pressure spectra show reasonable agreement with the wind tunnel experiments.

Hybrid Lattice Boltzmann Approach for Simulation of High-Speed Flows

A lattice Boltzmann approach utilizing hybrid lattices for accurate simulation of high-speed transonic (TS) flows is presented in this study. Single-layer lattice models, such as D3Q19, are computationally efficient with low numerical dissipation, but are limited to simulate weakly compressible flows within subsonic Mach regime. Multilayer lattice models, such as D3Q33, are capable of simulating thermal and high-speed compressible flows in TS Mach regime, but suffer from a higher numerical dissipation and higher computational cost. To take full advantages of these two types of lattices, a simulation domain is divided into two regions, high-subsonic (HS) flow regions to be solved by single-layer lattices and TS flow regions to be solved by multilayer lattices. The interface connecting the HS and TS flow regions are represented by double-sided surfels to realize smooth flow transition and ensure satisfaction of fundamental conservation laws. The hybrid lattice Boltzmann approach is stable and robust, and it allows multiple HS/TS flow regions with arbitrary shapes. Extensive validation studies demonstrate that the proposed approach is capable of obtaining accurate aerodynamic prediction of flows with a wide range of Mach numbers, and preserving the low numerical dissipation advantage of single-layer lattices in aeroacoustic computations.

Drag force of compressible flows past random arrays of spheres

We perform particle-resolved simulations of subsonic and transonic flows past random arrays of spherical particles. The particle Reynolds number is held at Re≈300 to ensure the flow remains in the continuum regime. At low volume fractions, the drag force increases sharply near a critical Mach number due to the formation of shock waves and reaches a maximum value when the bulk flow is supersonic. Neighbor-induced aerodynamic interactions reduce the critical Mach number at higher volume fractions. An effective Mach number is introduced to capture the increase in compressibility effects on drag. A new drag correlation is proposed valid for subsonic and weakly supersonic flow from dilute to moderately dense suspensions.

Bayesian uncertainty quantification analysis of the SST model for transonic flow around airfoils simulation

Transonic flow simulation is a common but complex task in engineering, and poses a great challenge to computational fluid dynamics using the Reynolds-averaged Navier–Stokes approach. One of the important factors influencing the complexity of this task is the uncertainty introduced by turbulence models. In this paper, to improve the performance of the shear stress transport model, a Bayesian uncertainty quantification analysis of turbulence model parameters is carried out on transonic flow around the RAE2822 airfoil and the ONERA M6 wing. First, the Sobol indices are obtained for sensitivity analysis, the results of which show that the pressure coefficients are mainly sensitive to four parameters a1, κ, β⁎, and β1. A posterior uncertainty analysis is then performed based on the pressure coefficients of two-dimensional sections. The maximum a posteriori estimates from the two examples indicate opposite trends for the predicted shock wave positions. In the predictions for RAE2822, the shock wave position is advanced, while in those for ONERA M6, it is delayed. The estimates from RAE2822 enable a better prediction capability at a small angle of attack, while those from ONERA M6 enables an ability to simulate flow with separation at a large angle of attack, mainly because of the increase in a1. In practical engineering applications, the choice between the two sets of calibrated parameters to achieve the best simulation results may be facilitated by reference to experimental data.

Aerodynamics simulations of three-dimensional inviscid flow using curvilinear discontinuous Galerkin method on unstructured meshes

Over the last decades, the discontinuous Galerkin (DG) method has demonstrated its excellence in accurate, higher-order numerical simulations for a wide range of applications in aerodynamics simulations. However, the development of practical, computationally accurate flow solvers for industrial applications is still in the focus of active research, and applicable boundary conditions and fluxes are also very important parts. Based on curvilinear DG method, we have developed a flow solver that can be used for solving the three-dimensional subsonic, transonic and hypersonic inviscid flows on unstructured meshes. The development covers the geometrical transformation from the real curved element to the rectilinear reference element with the hierarchical basis functions and their gradient operation in reference coordinates up to full third order. The implementation of solid wall boundary conditions is derived by the contravariant velocities, and an enhanced algorithms of Harten-Lax-van Leer with contact (HLLC) flux based on curved element is suggested. These new techniques do not require a complex geometric boundary information and are easy to implement. The simulation of subsonic, transonic and hypersonic flows shows that the linear treatment can limit the accuracy at high order and demonstrates how the boundary treatment involving curved element overcomes this restriction. In addition, such a flow solver is stable on a reasonably coarse meshes and finer ones, and has good robustness for three-dimensional flows with various geometries and velocities. For engineering practice, a reasonable accuracy can be obtained at reasonably coarse unstructured meshes.

The Finite Element Numerical Study of Transonic Flow of Moist Air with Nonequilibrium Condensation

The finite element numerical simulation of the transonic flow with condensation is studied in this paper. The transformed weak form is numerically discretized by using the classical Galerkin finite element spatial discretization scheme and the backward Euler difference time discretization scheme. Because the coupled Euler equations are convection equations, the results obtained by the classical Galerkin method often have nonphysical numerical oscillations, so the stabilization method is introduced. Another important feature of compressible Euler equation is the existence of shock wave. Because the thickness of shock wave is small and difficult to capture, the shock wave can be better captured by adding artificial viscosity term. Here, the streamline upwind/Petrov–Galerkin (SUPG) finite element method with good stability and the isotropic diffusion method with shock capture ability are used to solve the problem of transonic flow with condensation. In the simulation of steady problems, in order to improve the calculation accuracy of the existing area of the shock wave, the adaptive mesh refinement technology is added, which refines the mesh in the region of the shock wave to improve the resolution of the shock wave. Numerical experiments verify the feasibility and stabilization of the numerical method. Finally, the simulation of transonic flow around NACA-0012 and parallel-jet nozzle A1 has obtained the better numerical results.

CFD Simulation of Transonic Flow Through the Tip-Section Turbine Blade Cascade Intended for the Long Turbine Blade

The paper deals with numerical simulations of transonic flow through the turbine blade cascade consisting of flat profiles. The cascade is one of variants of the tip section of ultra-long blades, which were designed for the last stage of the steam turbine. CFD simulations were realized by means of the ANSYS CFX commercial software using the γ-Reθ bypass transition model completed by the two-equation SST turbulence model. Some simulations were made only by the SST turbulence model for comparison. Numerical results were compared with experimental data. Calculations performed for two nominal regimes and two computational domains. In addition to the standard computational domain, the calculation was performed for a domain with an extended output part for the suppression of reflected shock waves. The interaction of the inner branch of the exit shock wave with the boundary layer on the blade suction side leads in the both flow regimes to the flow separation followed by the transition to turbulence. The flow structure in the blade cascade obtained for the extended domain corresponds well to experimental results.

Large-eddy lattice-Boltzmann modeling of transonic flows

A D3Q19 hybrid recursive regularized pressure based lattice-Boltzmann method (HRR-P LBM) is assessed for the simulation of complex transonic flows. Mass and momentum conservation equations are resolved through a classical LBM solver coupled with a finite volume resolution of entropy equation for a complete compressible solver preserving stability, accuracy, and computational costs. An efficient treatment for wall and open boundaries is coupled with a grid refinement technique and extended to the HRR-P LBM in the scope of compressible aerodynamics. A Vreman subgrid turbulence model and an improved coupling of immersed boundary method with turbulence wall model on Cartesian grid accounts for unresolved scales by large-eddy simulation. The validity of the present method for transonic applications is investigated through various test cases with increasing complexity starting from an inviscid flow over a 10% bump and ending with a turbulent flow over a ONERA M6 three-dimensional wing.

High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)

Mesh-free methods have significant potential for simulations of flows in complex geometries, with the difficulties of domain discretisation greatly reduced. However, many mesh-free methods are limited to low order accuracy. In order to compete with conventional mesh-based methods, high order accuracy is essential. The Local Anisotropic Basis Function Method (LABFM) is a mesh-free method introduced in King et al. (2020) [20], which enables the construction of highly accurate difference operators on disordered node discretisations. Here, we introduce a number of developments to LABFM, in the areas of basis function construction, stencil optimisation, stabilisation, variable resolution, and high order boundary conditions. With these developments, direct numerical simulations of the Navier Stokes equations are possible at extremely high order (up to 10th order in characteristic node spacing internally). We numerically solve the isothermal compressible Navier Stokes equations for a range of geometries: periodic and channel flows, flows past a cylinder, and porous media. Excellent agreement is seen with analytical solutions, published numerical results (using a spectral element method), and experiments. The potential of the method for direct numerical simulations in complex geometries is demonstrated with simulations of subsonic and transonic flows through an inhomogeneous porous media at pore Reynolds numbers up to Rep=968.

Predicting high-speed feedback mechanisms in rectangular cavities using lattice-Boltzmann very-large eddy simulations

Aeroacoustic feedback mechanisms in rectangular cavities are strongly dependent on length-to-depth ratio and free stream velocity. The capability to predict the effects of these parameters using a scale-resolving transonic lattice-Boltzmann flow simulations is assessed, for the first time, by considering the M219 benchmark configuration for two different length-to-depth ratios (10:1 and 5:1) and two free-stream Mach numbers (0.85 and 1.35). Numerical results are compared and validated using unsteady wall pressure measured in wind tunnel tests. Tonal and broadband components of the pressure fluctuations are properly captured. For the shallow cavity configuration, an increase in Mach number is found to enhance the development of Rossiter modes inside the cavity. A more detailed analysis of these Rossiter modes is carried out for the shallow cavity at supersonic speed, for which physical insight is gained through the usage of spectral proper-orthogonal decomposition and wavelet/Fourier analyses.

Output-based adaptive aerodynamic simulations using convolutional neural networks

This paper presents a new method to perform output error estimation and mesh adaptation in computational fluid dynamics (CFD) using machine-learning techniques. The error of interest is the functional output error induced by the numerical discretization, including the finite computational mesh and approximation order. Given the data of adaptive flow simulations guided by adjoint-based error estimates, a surrogate model is trained to predict the output error and drive the mesh adaptation with only the low-fidelity solution as input. The goal is to generalize the error estimation and mesh adaptation knowledge from the simulation data at hand. The proposed method uses an encoder-decoder type convolutional neural network (CNN), supervised by both the adaptive error indicator field and the total output error, to capture both the local and global features related to the numerical error. To handle geometries and irregular meshes in adaptive simulations, topology mapping and local projection are introduced into traditional CNN models. The feasibility of the proposed machine-learning approach for error prediction and mesh adaptation is demonstrated in inviscid transonic flow simulations over airfoils. Both the output error and the localized adaptive indicators are well predicted by the trained CNN model, which is then used to drive the mesh adaptation as an alternative to standard adjoint-based methods. The good performance and relatively simple deployment encourage more study and development of the proposed method.

Numerical validation and physical explanation of the universal force theory of three-dimensional steady viscous and compressible flow

In a recent paper, Liu et al. [“Lift and drag in three-dimensional steady viscous and compressible flow”, Phys. Fluids 29, 116105 (2017)] obtained a universal theory for the aerodynamic force on a body in three-dimensional steady flow, effective from incompressible all the way to supersonic regimes. In this theory, the total aerodynamic force can be determined solely with the vorticity distribution on a single wake plane locating in the steady linear far field. Despite the vital importance of this result, its validity and performance in practice has not been investigated yet. In this paper, we performed Reynolds-averaged Navier–Stokes simulations of subsonic, transonic, and supersonic flows over a three-dimensional wing. The aerodynamic forces obtained from the universal force theory are compared with those from the standard wall-stress integrals. The agreement between these two formulas confirms for the first time the validity of the theory in three-dimensional steady viscous and compressible flow. The good performance of the universal formula is mainly due to the fact that the turbulent viscosity in the wake is much larger than the molecular viscosity therein, which can reduce significantly the distance of the steady linear far field from the body. To further confirm the correctness of the theory, comparisons are made for the flow structures on the wake plane obtained from the analytical results and numerical simulations. The underlying physics relevant to the universality of the theory is explained by identifying different sources of vorticity in the wake.

INVESTIGATION OF COMPRESSIBLE FLOW THROUGH A TURBINE BLADE CASCADE FOR VARIOUS TRANSONIC FLOW REGIMES

This paper deals with the numerical simulation of 2D transonic flow through the SE1050 turbine blade cascade at various flow conditions. The first one concerns the design operation with a zero incidence angle involved in the ERCOFTAC Database CFD-QNET and the second one with a +20° incidence angle corresponding to an off-design operation. Advanced mathematical models with two different models of the bypass transition to turbulence were applied for the simulation of different regimes of transonic flows as well as with attached and separated flows. Transition models proposed by Dick et al. [1] and by Menter and Smirnov [2] are based on transport equations for the intermittency coefficient. Numerical results were compared with experimental data based on the optical and pressure measurements.

Numerical simulations of transonic flows with non-unique solutions

Inviscid, compressible flows are described by a first-order system of hyperbolic partial differential equations in conservation form, and are solved numerically with simple schemes. These schemes show the ability to reproduce well-known solutions and benchmarks for the two-dimensional Euler equations. Finally, the schemes are used to explore the anomaly of non-unique solutions in the transonic regime. Furthermore, numerical solutions for the isentropic Euler equations with γ = 2, which are analogous to the shallow water equations, also exhibit non-uniqueness. In the appendix, results computed with OVERFLOW also exhibit non-unique solutions for the same geometries considered in the text.

Preconditioned gridless methods for solving three-dimensional Euler equations at low Mach numbers

In this paper, preconditioned gridless methods are developed for solving the three-dimensional (3D) Euler equations at low Mach numbers. The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations, which are discretized under the clouds of points distributed in the computational domain by using a gridless technique. The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning, which may fail to have convergence for flow simulations at low Mach numbers, therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper. An explicit four-stage Runge–Kutta scheme is first applied for time integration, and the lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence. Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform, and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing. The gridless clouds of both regular and irregular points are used in the simulations, which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries. Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature. The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally, for nearly incompressible flow simulations at low Mach numbers as well. The convergence of the implicit preconditioned gridless method, as expected, is much faster than its explicit counterpart.

Direct numerical simulation of subsonic, transonic and supersonic flow over an isolated sphere up to a Reynolds number of 1000

In the present study, compressible low-Reynolds-number flow past a stationary isolated sphere was investigated by direct numerical simulations of the Navier–Stokes equations using a body-fitted grid with high-order schemes. The Reynolds number based on free-stream quantities and the diameter of the sphere was set to be between 250 and 1000, and the free-stream Mach number was set to be between 0.3 and 2.0. As a result, it was clarified that the wake of the sphere is significantly stabilized as the Mach number increases, particularly at the Mach number greater than or equal to 0.95, but turbulent kinetic energy at the higher Mach numbers conditions is higher than that at the lower Mach numbers conditions of similar flow regimes. A rapid extension of the length of the recirculation region was observed under the transitional condition between the steady and unsteady flows. The drag coefficient increases as the Mach number increases mainly in the transonic regime and its increment is almost due to the increment in the pressure component. In addition, the increment in the drag coefficient is approximately a function of the Mach number and independent of the Reynolds number in the continuum regime. Moreover, the effect of the Mach and Reynolds numbers on the flow properties such as the drag coefficient and flow regime can approximately be characterized by the position of the separation point.

Study on the Numerical Model of Transonic Wind Tunnel Test Section

The authors consider numerical simulations of transonic flows through various turbine cascades in a confined channel which approximates boundaries of real wind tunnel. The boundaries of the wind tunnel are impermeable or there can be permeable tailboards to diminish shock wave reflections. The mathematical model is based on Favre-averaged Navier-Stokes equations closed by a turbulence model and model of transition to turbulence. The mathematical model is solved by an implicit finite volume method with multi-block grids. Several types of turbine blade cascades with subsonic or supersonic inlet are presented. The results are compared with optical measurements and simulations of periodic cascades. The validity of experimental reference flow parameters in relation to computed flow patterns is discussed.

Simulation of transonic low-Reynolds jets using quasi-gas dynamics equations

In this paper application of the OpenFOAM solver QGDFoam for numerical simulation of transonic viscous flows is considered. The developed solver, which implements regularized or quasi- gas dynamics (QGD) algorithms, is validated using the transonic low-Re jet flow case (Ma=0.9, Re=3600). The conducted numerical simulations allow the assessing applicability of the solver for modelling hydrodynamic instabilities and their interaction with transonic flow. Results of the numerical simulations are compared with experimental observations and Navier-Stokes-based code simulation. Results of the present study formulate a guideline for choosing (values of) QGD-algorithm tuning parameters.

Parallel Large-Eddy Simulation of Subsonic and Transonic Flows with Transition in Compressor Cascade

Laminar–turbulent transition plays a critical role in the aerodynamic performance of compressors and is sensitive to flow conditions and external disturbances. In the present work, a parallel large-eddy-simulation solver is developed and applied to investigate the effects of free-stream turbulence on the mode and location of transition on the blade suction surface of a compressor cascade under subsonic and transonic conditions. Both the parallel accuracy and efficiency of the solver are demonstrated. The transition location is observed to shift upstream as the free-stream turbulence level increases at both the subsonic and transonic conditions. Moreover, increasing the free-stream turbulence level from 0 to 4% causes the transition mode to change from Kelvin–Helmholtz instability-induced transition to bypass transition in the case of subsonic flow, whereas transition occurs in a Kelvin–Helmholtz instability-induced mode even at a high free-stream turbulence level of up to 7% in the case of transonic flow. The work demonstrates the ability of the parallel large-eddy-simulation method to capture the transitional-flow structures in compressor cascades and its potential application to the analysis and design of advanced compressor.

Determination of the laminar-turbulent transition location in numerical simulations of subsonic and transonic flows past a flat plate

The study is aimed at determining the position of the laminar-turbulent transition in subsonic and transonic two-dimensional boundary layers with the use of a novel software package LOTRAN 2.0 developed by the authors. The package is based on the eN-method and employs numerical data of numerical simulations of the laminar flow performed by standard gas-dynamic software systems based on the Reynolds-averaged Navier-Stokes equations. As an example, the flow past a flat plate is considered. The good agreement of the computed and experimental data on the laminar-turbulent transition location is demonstrated. New data on the laminar-turbulent transition in the boundary layer on a flat plate for transonic flow regimes are obtained.