Transonic Flow Calculations Research Articles

Data-driven reduced-order modeling for nonlinear aerodynamics using an autoencoder neural network

The design of commercial air transportation vehicles heavily relies on understanding and modeling fluid flows, which pose computational challenges due to their complexity and high degrees of freedom. To overcome these challenges, we propose a novel approach based on machine learning (ML) to construct reduced-order models (ROMs) using an autoencoder neural network coupled with a discrete empirical interpolation method (DEIM). This methodology combines the interpolation of nonlinear functions identified based on selected interpolation points using DEIM with an ML-based clustering algorithm that provides accurate predictions by spanning a low-dimensional subspace at a significantly lower computational cost. In this study, we demonstrate the effectiveness of our approach by the calculation of transonic flows over the National Advisory Committee of Aeronautics 0012 airfoil and the National Aeronautics and Space Administration Common Research Model wing. All the results confirm that the ROM captures high-dimensional parameter variations efficiently and accurately in transonic regimes, in which the nonlinearities are induced by shock waves, demonstrating the feasibility of the ROM for nonlinear aerodynamics problems with varying flow conditions.

Comparison of Euler and Modified Tsp Solutions for Unsteady Transonic Flow Calculations

Many prediction methods have been developed for the transonic flow calculations, most of them solve the Euler equations. The solution of Euler equations is usually complex and takes long computer time. However, in many practical applications, viz, flutter calculation faster transonic flow calculation is preferred. One such approach is based on modified transonic small perturbation (TSP) theory approach. Here in this paper modified TSP theory incorpo- rating entropy and vorticity effects has been studied by comparing the results with those of Euler equations. The paper presents the description of both the Euler solver and the TSP solver incorporating entropy vorticity effects. The calculated results have been compared with the available experimental results or with available Euler results from literatures. The comparison shows good agreement with the experimental data as well as available data from open literature. The modified TSP code provides acceptable accuracy for most transonic flow calculations. Thus in most cases long computation involved in Euler code can be avoided.

Results of calculation of transonic gas flow in a flat channel separated by perforated walls

Results of calculation of transonic gas flow in a flat channel separated by perforated walls

Liquid phase evaporation on the normal shock wave in moist air transonic flows in nozzles

This paper presents a numerical analysis of the atmospheric air transonic flow through de Laval nozzles. By nature, atmospheric air always contains a certain amount of water vapor. The calculations were made using a Laval nozzle with a high expansion rate and a convergent-divergent (CD) “half-nozzle”, referred to as a transonic diffuser, with a much slower expansion rate. The calculations were performed using an in-house CFD code. The computational model made it possible to simulate the formation of the liquid phase due to spontaneous condensation of water vapor contained in moist air. The transonic flow calculations also take account of the presence of a normal shock wave in the nozzle supersonic part to analyze the effect of the liquid phase evaporation.

Numerical calculations of 2D transonic flow in GAMM channel and over the profile

The aim of this work is to make a 2D numerical model of the solution of the transonic inviscid and viscous compressible flow around the profile. In a case of viscous flow several turbulent models are used. For the verification of the calculation Baldwin-Lomax model is compared with Wilcox k-omega model and SST turbulent model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in the turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution. Comparisons are done with the experimental data for the 8% DCA profile.

Algebraic Calculation Method of One-Dimensional Steady Compressible Gas Flow

This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.

An approach for the numerical prediction of the compressible supercavitating flows over ultrahigh-speed underwater object

Purpose Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating flows is usually difficult, thus high-speed model reflecting the compressibility of both the liquid and the vapor phases should be introduced to model such flow. The purpose of this paper is to achieve a model within an in-house developed solver to simulate the ultrahigh-speed subsonic supercavitating flows. Design/methodology/approach An improved TAIT equation adjusted by local temperature is adopted as the equation of state (EOS) for the liquid phase, and the Peng-Robinson EOS is used for the vapor phase. An all-speed variable coupling algorithm is used to unify the computations and regulate the convergence at arbitrary Mach number. The ultrahigh-speed (Ma=0.7) supercavitating flows around circular disk are investigated in contrast with the case of low subsonic (Ma=0.007) flow. Findings The characteristic physical variables are reasonably predicted, and the cavity profiles are compared to be close to the experimental empirical formula. An important conclusion in the compressible cavitating flow theory is verified by the numerical result that, at any specific cavitation number the cavity’s size and the drag coefficient both increase along with the rise of Mach number. On the contrary, it is found as well that the cavity’s slenderness ratio decreases when Mach number goes up. It indicates that the compressibility has different influences on the length and the radius of the supercavity. Originality/value A high-speed model reflecting the compressibility of both the liquid and the vapor phases was suggested to model the ultrahigh-speed supercavitating flows around underwater projectiles.

Calculation of transonic flows around profiles with blunt and angled leading edges

Transonic flow is a mixed flow of subsonic and supersonic regions. Because of this mixture, the solution of transonic flow problems is obtained only when solving the differential equations of motion with special treatments for the transition from subsonic region to supersonic region and vice versa. We built codes solving the full potential equation and Euler equations by applying the finite difference method and finite volume method, and also associated with software Fluent to consider the viscous effects. The analysis of results calculated for cases of transonic flow over profiles with blunt and angled leading edges shows more clearly the physical nature of the gas - solid interaction at leading edges in the mixed flow and the optimal application of each profile in transonic flows.

Computation of transonic internal flow around a biconvex airfoil with cavity

At transonic flow conditions, unsteady self-excited shock waves are frequently observed in several modern internal aeronautical applications such as in turbine cascades, compressor blades, butterfly valves, fans, nozzles, diffusers and so on. The appearance of shock oscillation often causes serious problems such as aero-acoustic noise, non-synchronous vibration (NSV), intense drag rise, high cycle fatigue failure (HCF) and buffeting. In recent years, the effect of various passive means on the airfoil are investigated both experimentally and numerically to find the effectiveness as a shock control device. In the present study, the transonic internal flow around an airfoil using a cavity as a passive means of shock control was investigated numerically. Computational results are validated with available experimental data. Results showed that the airfoil with cavity significantly reduced the flow field unsteadiness such as the amplitude of pressure oscillation and root mean square of pressure oscillation.

Study of separation phenomenon in transonic flows produced by interaction between shock wave and boundary layer

For compressible flows, the transonic state depends on the geometry, Mach number and the incidence. This effect can produce shock wave. Some studies showed that the interaction between shock wave and boundary layer concerns separation phenomenon. Studies in this report demonstrate conditions of separation in transonic flow and that it is not any interaction between shock wave and boundary layer which can cause boundary layer separation. The studies also show that maximum Mach number in the local supersonic region is not a unique factor influencing the separation, and the separation in transonic flows can occur at the incidence of 0\(^{\circ}\). For the calculation of viscous transonic flows, we use Fluent software with serious treatment of application operation based on the physical nature of phenomenon and the technique of numerical treatment. For the calculation of invicid transonic flows, we built a code solving the full potential equation with verification for accuracy. Results calculated from Fluent have been seriously compared with results of present program and published results in order to assure the accuracy of application operation in the domain of investigation. separation in transonic flows; shock wave and boundary layer

High-order discontinuous Galerkin computation of axisymmetric transonic flows in safety relief valves

This paper presents a discontinuous Galerkin (DG) discretization of the compressible RANS and k– ω turbulence model equations for two-dimensional axisymmetric flows. The developed code has been applied to investigate the transonic flow in safety relief valves. This new DG implementation has evolved from the DG method presented in [1]. An “exact” Riemann solver is used to compute the interface numerical inviscid flux while the viscous flux discterization relies on the BRMPS scheme [2,3]. Control of oscillations of high-order solutions around shocks is obtained by means of a shock-capturing technique developed and assessed within the EU ADIGMA project [4]. The code has been applied to compute the flow in a spring loaded safety valve at several back pressures and different disk lifts. The predicted device flow capacity and the pressure inside its bonnet have been checked against experimental data. The CFD simulations allow to clarify the complex flow patterns occurring and to explain the measured trends.

High effective WENO scheme for transonic inviscid flow computation on a helicopter rotor in hover

A high-order upwind scheme with high efficiency has been developed to compute the inviscid flow of a helicopter rotor in hover. For rotary-wing wake capturing, an improved fifth-order weighted essentially non-oscillatory (WENO) scheme is adopted to interpolate higher order left and right states across a cell interface with Roe Riemann solver updating inviscid flux. To improve the efficiency and convergence to steady state, three-level V-cycle multigrid relaxation scheme is used. The performance of the schemes is investigated in a transonic inviscid flow around hovering rotor. The results reveal that WENO has the great capabilities to capture shock with high resolution and has a lower numerical dissipation than MUSCL for capturing wake vorticity. Moreover, multigrid scheme can accelerate convergence to a great extent.

Introduction of causality in integral methods

New solutions to the uniqueness and causality problems of transonic and supersonic flow calculations using the integral equation method are proposed. A variable unperturbed flow is used, which controls the source development and yields the right solution. Calculations are compared with the experiment. By introducing additional elliptic singularities in the elliptic integral equation, non-isotropic, hyperbolic elementary sources and vortexes can be constructed, which engender all the characteristics of transonic and supersonic flows.

Simulation of transonic flows using quad-core OpenMP Euler, flux modified transonic small disturbance, and Fluent codes

This article investigates what performance can be achieved when executing an aerodynamic code on a quad-core based personal computer with an OpenMP compiler in a Windows environment. Euler equations are solved in two dimensions for simplicity, to predict flow field around an aerofoil on an O-type boundary fitted structured grid. The grid is generated by solving a system of Poisson's equations utilising an efficient method of false transients, coupled with an approximate factorisation technique and variable time steps cycling process. Comparison between the OpenMP Euler, flux modified transonic small disturbance and Fluent results for transonic flow fields, with shock waves, around a NACA0012 aerofoil is presented. References Bailey, D., Barszcz, E., Barton, J., Browning, D., Carter, R., Dagum, L., Fatoohi, R., Fineberg, S., Frederickson, P., Lasinski, T., Schreiber, R., Simon, H., Venkatakrishnan, V., and Weeratunga, S., The NAS Parallel Benchmarks, Contractor Report 203186, NASA, USA, 1994. Engquist, B., and Osher, S., Stable and Entropy Satisfying Approximations for Transonic Flow Calculations, Mathematics of Computation, 34, 149, January 1980, pp. 45--75. Gear, J., Ly, E., and Phillips, N. J. T., A Time Marching, Type-Dependent, Finite Difference Algorithm for the Modified Transonic Small Disturbance Equation, Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences (ICAS98), ICAS and AIAA, Melbourne, Australia, 1998, Paper A98-31513. Hirsch, C., Numerical Computation of Internal and External Flows: Computational Methods for Inviscid and Viscous Flows, Volume 2, John Wiley and Sons, Great Britain, 1992. Jin, H., Frumkin, M., and Yan, J., The OpenMP Implementation of NAS Parallel Benchmarks and its Performance, Technical Report NAS-99-011, NASA, Moffett Field, USA, 1999. Liu, Y., and Vinokur, M., Nonequilibrium Flow Computations 1: An Analysis of Numerical Formulations of Conservation Laws, Contractor Report 177489, NASA, California, USA, 1988. Lock, R. C., Test Cases for Numerical Methods in Two-Dimensional Transonic Flows, Report Number 575, AGARD, 1970. Ly, E., Improved Approximate Factorisation Algorithm for the Steady Subsonic and Transonic Flow over an Aircraft Wing, Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences (ICAS98), ICAS and AIAA, Melbourne, Australia, 1998, Paper Number A98-31699. Ly, E., and Nakamichi, J., Time-Linearised Transonic Computations Including Entropy, Vorticity and Shock Wave Motion Effects, The Aeronautical Journal, November 2003, pp. 687--695. Ly, E., and Norrison, D., Automatic Elliptic Grid Generation by an Approximate Factorisation Algorithm, ANZIAM Journal, 48 (CTAC2006), pp. C188--C202, July 2007. Murman, E., Analysis of Embedded Shock Waves Calculated by Relaxation Methods, AIAA Journal, 12, 5, May 1974, pp. 626--633. Pulliam, T., Kutler, P., and Rossow, V., Harvard Lomax: His Quiet Legacy to Computational Fluid Dynamics, 14th AIAA Computational Fluid Dynamics Conference, Norfolk, VA, June 1999. Steger, J.L., and Warming, R. F., Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite Difference Methods, Technical Memorandum TM-78605, NASA, California, USA, 1979. Van Leer, B., Flux-Vector Splitting for the Euler Equations, Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, Aachen, West Germany, 1982.

Effects of Surface Roughness on Turbulent Transonic Flow Over Circular Arc Bumps in a Channel

Turbulent transonic flow over circular arc bumps in a channel is computed to determine the effects of surface roughness on shock/boundary layer interaction. Initially the performance of several turbulence models for the computation of transonic flow over bumps is evaluated against the results of two different experiments. The k-ω model on the whole showed reasonable performance considering the optimal compromise between accuracy and CPU time requirement, which is subsequently employed for the surface roughness study for the confined channel flow over a bump. Computations are done for various equivalent sand grain surface roughness heights of the bump surface. The influence of the increase in surface roughness height transcends over onto the shock boundary layer zone and the observations are discussed. Upstream movement of the shock and increase in the skin friction coefficient with increasing surface roughness are observed.

Calculated Viscous and Scale Effects on Transonic Aeroelasticity

A viscous-inviscid interactive coupling method is used for the computation of unsteady transonic flows. A lagextrainment integral boundary layer method is used with a transonic small disturbance potential code to compute the transonic aeroelastic response for two wing flutter models. By varying the modeled length scale, viscous effects may be studied as the Reynolds number per reference chordlength varies. Appropriate variation of modeled frequencies and generalized masses then allows comparison of responses for varying scales or Reynolds number. Two wing planforms are studied: one a four percent thick swept wing and the other a typical business jet wing. Calculations for both wings show limit cycle oscillations at transonic speeds in the vicinity of minimum flutter speed indices.

Unstructured-Mesh Discretizations and Solvers for Computational Aerodynamics

An overview of current unstructured-mesh discretization and solution techniques is given. Cell-centered vs vertex-centered discretizations are discussed, as well as issues of grid alignment with flow features, higher-order reconstruction, and viscous-term formulation. With regard to solution techniques, implicit and multigrid methods are discussed, as well as efficient implementation on massively parallel computer hardware. Sample calculations are used to illustrate the importance of grid resolution and issues in solution accuracy. The examples are taken mostly from transonic flow calculations and are used to argue that unstructured-mesh technology has reached a level of maturity on a par with block-structured or overset-mesh methods in this area, although important outstanding issues remain for other application areas, such as high-speed flows.

A fast and accurate algorithm for computing radial transonic flows

An efficient algorithm is described for calculating stationary one-dimensional transonic outflow solutions of the compressible Euler equations with gravity and heat source terms. The stationary equations are solved directly by exploiting their dynamical system form. Transonic expansions are the stable manifolds of saddle-point-type critical points, and can be obtained efficiently and accurately by adaptive integration outward from the critical points. The particular transonic solution and critical point that match the inflow boundary conditions are obtained by a two-by-two Newton iteration which allows the critical point to vary within the manifold of possible critical points. The proposed Newton Critical Point (NCP) method typically converges in a small number of Newton steps, and the adaptively calculated solution trajectories are highly accurate. A sample application area for this method is the calculation of transonic hydrodynamic escape flows from extrasolar planets and the early Earth. The method is also illustrated for an example flow problem that models accretion onto a black hole with a shock.

Numerical Simulation of 3D Transonic Flow in a Compressor Rotor

This paper presents a new computational fluid dynamics (CFD) code developed at Universiti Tenaga Nasional for the numerical computation of transonic laminar flow in a compressor rotor. The 3D computational code solves the unsteady Navier-Stokes equations (NSE) on unstructured hexahedral mesh by using second-order accurate central differencing scheme on both convective and diffusive terms. Artificial damping terms are added to control the stability of the numerical scheme, and the explicit multistage Runge-Kutta time-integration technique is performed to solve the unsteady NSE. This paper discusses the simulation of compressible flow field in an axial-flow compressor rotor using the newly developed CFD code. The predicted flow is then compared with the results obtained from the commercial code, CFX-5, as well as experimental data; good agreement is found.

Investigation of the efficiency of using numerical schemes of a high order of accuracy for solving Navier-Stokes and Reynolds equations on unstructured adapted grids

The finite element discontinuous Galerkin method is implemented for solving the Navier-Stokes and Reynolds equations on unstructured adapted grids. A detailed description of the method is given. In problems concerning laminar flow around a cylinder and turbulent flow about a flat plate, solutions with a high order of accuracy are presented. Examples of the calculation of a viscous transonic flow around an isolated airfoil and the subsonic flow around a three-element configuration are considered. These important application problems are solved using the adapted grid technique.