Transonic Airfoil Flow Simulation. Part II: Inviscid-Viscous Coupling Scheme (original) (raw)
Related papers
Viscous-inviscid analysis of transonic and low Reynolds number airfoils
AIAA Journal, 1987
A method of accurately calculating transonic and low Reynolds number airfoil flows, implemented in the viscous-inviscid design/analysis code ISES, is presented. The Euler equations are discretized on a conservative streamline grid and are strongly coupled to a two-equation integral boundary-layer formulation, using the displacement thickness concept. A transition prediction formulation of the e 9 type is derived and incorporated into the viscous formulation. The entire discrete equation set, including the viscous and transition formulations, is solved as a fully coupled nonlinear system by a global Newton method. This is a rapid and reliable method for dealing with strong viscous-inviscid interactions, which invariably occur in transonic and low Reynolds number airfoil flows. The results presented demonstrate the ability of the ISES code to predict transitioning separation bubbles and their associated losses. The rapid airfoil performance degradation with decreasing Reynolds number is thus accurately predicted. Also presented is a transonic airfoil calculation involving shock-induced separation, showing the robustness of the global Newton solution procedure. Good agreement with experiment is obtained, further demonstrating the performance of the present integral boundary-layer formulation.
Analysis of viscous transonic flow over airfoil sections
25th AIAA Aerospace Sciences Meeting, 1987
A full Navier-Stokes solver has been used t o model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to held at the AIAA 25th Aerospace Sciences Meeting. "Jones" airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary 1 ayer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.
Transonic Airfoil Flow Simulation. Part I: Mesh Generation and Inviscid Method
INCAS BULLETIN, 2010
A calculation method for the subsonic and transonic viscous flow over airfoil using the displacement surface concept is described. Part I presents a mesh generation method for computational grid and a finite volume method for the time-dependent Euler equations. The inviscid solution is used for the inviscid-viscous coupling procedure presented in the Part II.
1987
A method is described for calculating unsteady transonic flow with viscous interaction by coupling a steady integral boundary-layer code with an unsteady, transonic, inviscid small-disturbance computer code in a quasi-steady fashion. Explicit coupling of the equations together with viscous -inviscid iterations at each time step yield converged solutions with computer times about double those required to obtain inviscid solutions. The accuracy and range of applicability of the method are investigated by applying it to four AGARD standard airfoils. The first-harmonic components of both the unsteady pressure distributions and the lift and moment coefficients have been calculated. Comparisons with inviscid calcualtions and experimental data are presented. The results demonstrate that accurate solutions for transonic flows with viscous effects can be obtained for flows involving moderate-strength shock waves.
Simulations of viscous transonic flows over lifting airfoils and wings
Computers & Fluids, 2007
In this paper, the hierarchical formulation for steady viscous transonic flow simulations of Refs. [Hafez M, Wahba E. Numerical Simulations of Transonic Aerodynamic Flows. AIAA paper 03-3564, 2003] and [Hafez M, Wahba E. Viscous/Inviscid Interaction Procedures for Compressible Aerodynamic Flow Simulations (in press)] is reviewed and a simplified version for the calculation of the vortical velocity components is presented. The results are compared to available solutions of standard Navier-Stokes equations for laminar flows.
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.
Calculation of the transonic dip of airfoils using viscous-inviscid aerodynamic interaction method
Aerospace Science and Technology, 2005
A numerical procedure for the calculation of the transonic dip of airfoils in the time domain is presented. A viscous-inviscid aerodynamic interaction method is taken to calculate the unsteady aerodynamic loads. In the present case the integral boundary layer equations are coupled with the Transonic Small Disturbance (TSD) Potential Equation. The coupling between structural motion and aerodynamic loads is carried out using State Space equation. It is solved by State Transition Matrix technique. Results are presented for NACA 64A010 and NLR 7301 airfoils with structural data from Isogai and DLR, respectively. Comparisons show good agreement with other numerical results. Certain deviations of experimental data taken from literature need more insight in the detailed test conditions.
A Review on Transonic Flow over an Airfoil
The paper focus on exclusive review in the field of Transonic flow over an airfoil. Various research and analysis has been done for the improvement and development of Airfoil in transonic regimes by means of Computational Fluid Dynamics (CFD), Direct Numerical Simulation (DNS) in form of analytical model and various experimental approach has been carried out by researchers in the field of transonic aerodynamics in order to overcome the trouble shoot occurs in form of instability and irreversibility during transonic and subsonic flight. During transonic flow Airfoil of Air vehicles exhibits shock wave in form of instability and If these shock waves are not been analyzed this may leads to tragic failure Since airfoils are subjected to both static and dynamic loads, due to which it pose great challenge to analyze the aerodynamic characteristics of an Airfoil.
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.
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.