Oh Hyun Rho

An improvement of AUSM schemes by introducing the pressure-based weight functions

Abstract This paper proposes a new scheme called AUSMPW (AUSM by pressure-based weight functions) improved from the previous AUSM schemes by introducing the pressure-based weight functions. AUSMPW scheme is essentially developed to improve such performances as the removal of numerical oscillations near a wall and overshoot phenomena behind shock waves, which are the main shortcomings of AUSM+ scheme. In order to investigate the computational characteristics of AUSMPW in detail, it has been applied to various hypersonic flow problems. The results, compared with those of AUSM type schemes, are summarized as follows; no carbuncle phenomena and high resolution at discontinuities such as shock waves, the removal of numerical oscillations, better computational convergence, and accuracy in boundary layer. It is concluded that AUSMPW can effectively be applied to complex hypersonic flow problems.

Navier-Stokes Computation of Flows in Arc Heaters

The existing computer code ARCFLO, which calculates the flow through the constricted-arc heater, is modified and expanded by the use of the modern computational fluid dynamics technique. The entire flowfield within an arc-heated wind tunnel, that is, from the upstream electrode chamber to the nozzle exit, is described by the Navier-Stokes equations, but the joule heating and radiative transfer phenomena are described as in the ARCFLO code. The modeling of turbulence in the constrictor region is different from that in ARCFLO. The code developed in the present work, tentatively designated as Arcflo2, requires only the mass flow rate and electrical current as inputs and describes the flow conditions from the upstream electrode region to the nozzle throat. The code reproduces the measured operating characteristics of several wind tunnels closer than the ARCFLO code

ACCURATE COMPUTATIONS OF HYPERSONIC FLOWS USING AUSMPW+ SCHEME AND SHOCK-ALIGNED GRID TECHNIQUE

There are two problems in computation of hypersonic flow. One is the inaccuracy of the physical modeling and the other is an error due to inaccurate numerical dissipation. Until now the distribution of species can not calculate accurately in the region of the strong interaction between vibration and chemical reaction. The computation in large expansion region such as nozzle is also inaccurate due to the inaccurate reaction rate coefficient. From the view of numerical difficulty, a stiff pressure discontinuity may cause large numerical oscillations and degenerate robustness and convergence. Numerical dissipation is especially sensitive in boundary layer since it can easily contaminate physical viscosity, leading to the inaccurate resolution of skin friction or heat transfer coefficients. In this paper we focus on the issue of numerical discretization. A newly improved scheme of AUSMPW, so called AUSMPW+, and ShockAligned Grid Technique (SAGT) are proposed for an accurate computation of hypersonic flows. Compared to AUSMPW, AUSMPW+ scheme is more efficient to implement while it maintains the same level of robustness and accuracy in capturing the stiff pressure discontinuity or boundary layer. SAGT combined with AUSMPW+ can capture the oblique shock as well as the normal shock with little numerical dissipation.

Aerodyamic Optimization for the Subsonic S-Shaped Diffuser Using Two-Equation Turbulence Models

A parallelized design optimization approach is presented for a subsonic S-shaped inlet using aerodynamic sensitivity analysis. Two-equation turbulence model is adopted to predict the strong counter vortices in the S-shaped duct more precisely. Sensitivity analysis is performed for the three-dimensional NavierStokes equations coupled with two-equation turbulence models using a discrete adjoint method. For code validation, the result of the flow solver is compared with experiment data and bench marking data of other computation researches. To study the influence of turbulence models and grid refinement in the duct flow analysis, the results using several turbulence models are compared with each other on various grid systems. The adjoint variable code is validated by comparison with the finite difference results. The capability and the efficiency of the present design tools are successfully demonstrated in three-dimensional subsonic inlet flow analysis and design optimization.

Numerical Analysis of Hypersonic Flow over a Double-Cone Geometry Using Eu's GH Equations

Eus GH(Genera1ized Hydrodynamic) equations are presented for analyzing a hypersonic flow over a double-cone geometry which shows various aerodynamic phenomena such as shock-shock interaction, shock-boundary layer interaction, etc. In order to analyze rarefied hypersonic flow, axisymrnetric generalized hydrodynamic equations are developed and validated by Rothe nozzle flow problem. Two kinds of solid surface boundary conditions nonslip and Langmuirs slip BC are examined, too. The hypersonic rarefied flow results acquired by GH equations are compared with experimental data and Navier-Stokes equations calculations with slip and nonslip boundary conditions. The calculations by GH equations show the more accurate flow predictions than those of NavierStokes equations, and GH equastion with some assumptions was able to be found that it is a useful tool to analyze rarefied hypersonic flows.

Computations of high-lift airfoil flows using two-equation turbulence models

Two-dimensional incompressible and compressible Navier-Stokes codes are developed for the computation of the viscous turbulent flow over high-lift airfoils. The compressible code involves a conventional upwind differencing scheme for the convective terms and LU-SGS scheme for femporal integration, The incompressible code with pseudo-compressibility and dual-time stepping method also adopts the same schemes as the compressible code. Three two-equation turbulence models are evaluated by computing the flow over single and multi-element airfoils. The compressible and incompressible codes are validated by predicting the flow around the RAE 2822 transonic airfoil and the NACA 4412 airfoil, respectively. Both the results show a good agreement with experimental surface pressure coefficients and velocity profiles in the boundary layers. Also, the NASA GA(W)-1 single airfoil, the NLR 7301 airfoil with a flap, and the GAW-1 high-lift airfoil with a leading-edge slat and a trailing-edge flap are computed using both the incompressible and compressible code with twoequation turbulence models. The grid systems around twoand three-element airfoils are efftciently generated using Chimera grid scheme, one of the overlapping grid generation methods. The compressible code shows more robust and stable convergence than the incompressible code for the flows of high-incidence angles where flow separation can occur. The k --o SST model has superiority to the other models, especially in the prediction of adverse pressure gradient region on the suction surfaces of high-lift airfoils. Introduction With the recent improvement of computer capability, the computational design method using computational fluid dynamics(CFD) becomes a new trend in multielement airfoil design. The accurate calculations of the flow around a multi-element airfoil are required to precede the practical design process. Thus, the interest of the present work is focused on the development of an accurate and efficient flow solver for multi-element airfoils. In general, the multi-element airfoil flow can be assumed incompressible because the free stream Mach number is about 0.1 to 0.4 and chord Reynolds numbers are usually 1 to 40 million. ’ Thus, an incompressible Navier-Stokes code is developed for efficient computation of multi-element airfoil flow. But, compressible effect can be significant in some cases of the multi-element airfoil with ’ a highly loaded leadingedge slat. For this reason, a compressible NavierStokes code is also developed and its results are compared with incompressible results to study the effect of compressibility. It is not easy to accurately predict the flow around multi-element airfoils due to confluent boundary layers and massive flow separation at wide range of angle-of-attack varying from -2 to 25 degree. So far, many turbulence models such as algebraic models, one-equation models, and two-equation models have been developed for accurate computations of various turbulent flows. In the present study, twoequation turbulence models are evaluated in the computation for high-lift airfoil flow. The several k-c models involving different wall functions for the accu* Graduate Research Assistant, Dep’t of Aerospace Engineering, Student Member AIAA + Assistant Professor, Dep’t of Aerospace Engineering, Member AI.&4 * Professor, Dep’t of Aerospace Engineering, Senior Member ALL4 Copyright Q 1999 by Chang Sung KiE. Published by the American Institute of Aeronautics and Astronautics Inc. with permission 1 American Institute of Aeronautics and Astronautics (c)l999 American Institute of Aeronautics & Astronautics rate calculation of the inner boundary layer has been developed and showed good results. Unlike the k E model, the k o model shows a good property in the sublayer without wall functions. Thus, the k--w model has superiority to other models for its simplicity, especially in parallel programming. On the other hand, the k -E model has the advantage of the freestream independence in the outer boundary layer while the k -w model is highly sensitive to freestream values. Menter’s base line model (BSL) was developed to achieve these two desired features in the sublayer and the outer boundary layer. This BSL model is similar to the original k -w model, but has no freestream dependency. The k--w shear stress transport (SST) model has the modified eddy viscosity to account for the transport of turbulent shear stress. The k w SST model was found to have the property of the original k o model in the near wall region, and the advantage of the free-stream independence of k E model in the outer of boundary layer. In the present study, the compressible and incompressible codes with different turbulence models are examined via numerous computations. Both the codes are parallel-processed using MPI(Message Passing Interface) programming method. The compressible code is validated by computing the flow around the RAE2822 transonic airfoil and shows good property to predict surface pressure coefficients and velocity profiles in the boundary layers. The incompressible code is validated by computing the flow over the NACA 4412 airfoil. The NASA GA(W)-1 single airfoil is computed using both the incompressible and compressible code with two-equation turbulence models. Also, the NLR730 1 airfoil with a flap, and the GAW1 high-lift airfoil with a leading-edge slat and a trailingedge flap are computed using both the incompressible and compressible code with two-equation turbulence models. Numerical Background Governing Equations The governing equations are two-dimensional unsteady compressible Navier-Stokes equations, and are written in conservation law form as g++& 0

Efficient calculations of a gas-kinetic BGK scheme for inviscid and viscous steady flows

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Accuracy of AUSM+ scheme in hypersonic blunt body flow calculations

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Investigation of Turbulent Flow Effect in Segmented Arc Heater

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The Modification of Airfoil Shape for Optimal Aerodynamic Performance on Flapping-Airfoil in Low-Reynolds number flow

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