Direct Numerical Simulation of 2D Transonic Flows around Airfoils, Tapan K. Sengupta, Ashish Bhole and N. A. Sreejith. Computers and Fluids, 88, pp 19-37 (2013) (original) (raw)

Two-dimensional turbulent viscous flow simulation past airfoils at fixed incidence

Computers & Fluids, 1997

The present work discusses the computation of the time-mean, turbulent, two-dimensional incompressible viscous flow past an airfoil at fixed incidence. A new physically consistent method is presented fo-r the reconstruction of velocity fluxes which arise from discrete equations for the mass and momentum balance. This closure method for fluxes makes possible the use of a cell-centred grid in which velocity and pressure unknowns share the same location, while circumventing the occurrence of spurious pressure modes. The influence of several turbulent models is investigated. The models involve either an algebraic eddy viscosity or determine the eddy viscosity from transport equations. The method is tested on the following airfoils in pre-stall or post-stall conditions: NACA4412, AS-240 B, GAW- airfoil, for which documented experimental data are available. 0 1997 Elsevier Science Ltd. All rights reserved. *Author for correspondence. 135 136 E. Guilmineau et al.

Flow past rotating cylinders at high Reynolds numbers using higher order upwind scheme

Computers & fluids, 1998

a b s t r a c t High-accuracy, time-accurate compressible Navier-Stokes solvers have been developed for transonic flows. These solvers use optimized upwind compact schemes (OUCS) and four-stage, fourth order explicit Runge-Kutta (RK4) time integration scheme, details of which can be obtained in Sengupta [Sengupta TK. High Accuracy Computing Methods, fluid flows and wave phenomena. UK: Cambridge Univ. Press; 2013]. Although these compact schemes have been developed originally for direct simulation of incompressible flows, it is shown here that the same can be used for compressible flows, with shock-boundary layer interactions clearly captured for flow past NACA 0012 and NLF airfoils. Numerical higher order diffusion terms which are used for incompressible flows, have been replaced here by the pressure-based artificial diffusions proposed by Jameson et al. [Jameson A, Schmidt W, Turkel E. Numerical solution of the Euler equations by finite volume methods using Ruge-Kutta time stepping schemes. AIAA Paper 1981-1259. AIAA 14th fluid and plasma dynamics conference. Palo Alto, CA;. Such second and fourth order diffusion terms are used adaptively at selective points, located by the pressure switch. Developed computational methods used here are validated for cases with and without shocks, for which experimental results are available. Apart from surface pressure coefficient, contours of physical quantities are presented to explain the time-accurate results. Presented methods are robust and the results can be gainfully used to study shock formation, drag divergence and buffet onset of flow over airfoils.

Numerical Solution of the Navier-Stokes Equations for Arbitrary Two-Dimensional Airfoils

1975

A finite difference method for solving the Navier-Stokes equations for an incompressible fluid has been developed. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Essentially it constitutes an extension to time dependent problems of the artificial compressibility method introduced in [l] for steady flow problems.

NUMERICAL SIMULATION OF THE TRANSONIC LAMINAR FLOW IN AIRFOILS WITH HIGH AMPLITUDE PLUNGING MOTIONS

CIT06-0594, 2006

This work is a direct numerical simulation of the transonic laminar flow in airfoils with high amplitude plunging motions. The problem is solved for a non-inertial system of reference that is moving with the airfoil, and for this reason, the associated pseudo-force is included as a source in the momentum equation and the work done is also included as a source in the energy equation. This methodology allows the solution of high amplitude plunging motions, since the problem is solved from a non-inertial frame of reference that is moving with the airfoil and, for this reason, no grid deformation is needed to account for the motion. The compressible Navier-Stokes equations are solved using the skew-symmetric form of Ducros’ shock-capturing algorithm, with fourth order accuracy in space and third-order accuracy in time. Five cases are studied: the static airfoil and the plunging motions with amplitudes of 2.5%, 13%, 22% of the airfoil chord. For all the cases, the Reynolds number is 10,000, the Mach number of the free flow is 0.8 and the plunging frequency has same value of the vortex emission frequency of the static case. The numerical results show a very complex and unsteady interaction between the boundary layer, the detached vortex wake and the transonic shock-wave system for the four cases studied. There are also some characteristic shock phenomena at the last two cases.

Case C1.2: Flow over the NACA0012 airfoil

2015

We submit 5 sets of results: 1 for the inviscid subsonic case, 2 for the viscous case (with sharp and with rounded trailing edge), 2 for the transonic case (with and without shock capturing, see below for the detailed description of the shock capturing scheme). For this test case, we generated a fine O-grid of 577 × 513 vertices using the hyperbolic grid generation capabilities of the commercial software Pointwise [1]. The farfield is located at 1000 chords, as requested. The trailing edge is sharp, unless stated otherwise. For the subsonic configurations, the vertex distribution on the airfoil is the same on pressure and suction side, as shown in fig. 1. Instead, for the transonic configuration, vertices are clustered on the suction side, in particular close to the shock region, fig. 2. Initial guesses are obtained via grid sequencing, where appropriate. The coarser grids are obtained by deleting every other grid line from the finer grid (regular coarsening).

Validation of Numerical Schemes and Turbulence Models Combinations for Transient Flow around Airfoil

In the present study, combinations of turbulence models and numerical schemes are evaluated in terms of accuracy and computational cost for the prediction of transient flow at fixed points around the non-symmetrical ONERA-A airfoil for pre- and stall conditions using a finite volume method. The computed results were validated by experimental data. The purpose is to investigate whether TVD discretization schemes, developed initially for compressible flows, can help computation of incompressible flows when accuracy and low computational cost are important considerations, as in the case of aeroelastic calculations. The TVD discretization schemes are applied to the convection terms of the momentum equations and they are compared to central difference, upwind, hybrid and QUICK discretization schemes for several turbulence models. From the parametric studies, it comes out that TVD schemes can be a promising tool for aeroelastic calculations. Keywords: CFD; TVD discretization schemes; transition; turbulence models; airfoil separation/stall

NUMERICAL SIMULATION OF THE LAMINAR TRANSONIC BUFFET IN AIRFOILS

CIT04-0609, 2004

The objective of this work is the numerical simulation of the shock wave-boundary layer interaction that appears in the transonic regime for the laminar flow in a NACA 0012 airfoil. The compressible Navier-Stokes equations are numerically solved using a finite volume discretization in combination with the skew-symmetric form of Ducros’ fourth-order numerical scheme. Results are obtained for angles of attack ranging from 0 to 9 degrees and for a Reynolds number of 10,000. For low angles of attack, the visualization shows the acoustics waves generated by a mild separation of the boundary layers along the upper and lower surface and the subsequent von Kármán’s vortex street. As the angle of attack increases, the acoustic waves turn into shock waves and a strong separation of the boundary layer is induced, generating a more complex vortex wake. The results also show a strong variation in the resultant unsteady aerodynamic coefficients. For low angles of attack, the unsteady normal force coefficient is characterized by a characteristic amplitude and frequency. As the angle of attack increases to a limit of 7 degrees, a strong shock wave-boundary layer interaction appears producing an increment of the amplitude of the normal force coefficient in conjunction with a reduction of the characteristic frequency. For 9 degrees of angle of attack, the unsteady normal force coefficient shows a departure, characterized by more than one characteristic frequency.

A Zonal Method For Unsteady, Viscous, Compressible Airfoil Flows

Journal of Fluids and Structures, 1994

The analysis and prediction of fluid-structure interaction for viscous, separated flows presents a great challenge to the aeroelastician. In this paper a zonal method for the computation of unsteady, viscous, separated flows over airfoils is presented. The flowfield is divided into a viscous inner zone, where higher grid resolution may be used, and an inviscid outer zone. Zonal grid solutions are presented for subsonic and transonic flows over a NACA-0012 airfoil subject to ramp and oscillatory motions. Transonic shock/boundary layer interaction and dynamic stall effects are encountered during the unsteady motion. The computed solutions are in good agreement with available experimental data.

Accelerated flow past a symmetric aerofoil: experiments and computations

Journal of Fluid Mechanics, 2007

Accelerated flow past a NACA 0015 aerofoil is investigated experimentally and computationally for Reynolds number Re = 7968 at an angle of attack α = 30 • . Experiments are conducted in a specially designed piston-driven water tunnel capable of producing free-stream velocity with different ramp-type accelerations, and the DPIV technique is used to measure the resulting flow field past the aerofoil. Computations are also performed for other published data on flow past an NACA 0015 aerofoil in the range 5200 6 Re 6 35 000, at different angles of attack. One of the motivations is to see if the salient features of the flow captured experimentally can be reproduced numerically. These computations to solve the incompressible Navier-Stokes equation are performed using high-accuracy compact schemes. Load and moment coefficient variations with time are obtained by solving the Poisson equation for the total pressure in the flow field. Results have also been analysed using the proper orthogonal decomposition technique to understand better the evolving vorticity field and its dependence on Reynolds number and angle of attack. An energy-based stability analysis is performed to understand unsteady flow separation.

IJERT-Numeric Investigation of Compressible Flow Over NREL Phase VI Airfoil

International Journal of Engineering Research and Technology (IJERT), 2013

https://www.ijert.org/numeric-investigation-of-compressible-flow-over-nrel-phase-vi-airfoil https://www.ijert.org/research/numeric-investigation-of-compressible-flow-over-nrel-phase-vi-airfoil-IJERTV2IS2178.pdf Abstarct This work deals with the numeric analysis of compressible flow around National Renewable Energy Laboratory (NREL) phase VI wind turbine blade airfoil S809. Although wind turbine airfoils are low Reynolds number airfoil, a reasonable investigation might be helpful for compressible flow under extreme condition. We considered a subsonic flow (mach no. 0.8) and determined the impact of this flow under seven different angle of attacks. The results show that shock takes place just after the mid span at the top surface and just before the mid span at the bottom surface. Slowly this transforms their position as angle of attack increases. A K-ω SST turbulent model is considered and the commercial CFD code ANSYS FLUENT is used to find the pressure coefficient (Cp) as well as the lift (C L) and drag coefficient (C D). A graphical comparison of shock propagation has been shown with different angle of attack. Flow separation is also calculated along the airfoil.