Kazuhiro Nakahashi

Hybrid prismatic/tetrahedral grid generation for viscous flow applications

A method for the automatic generation of unstructured grids composed of tetrahedra and prisms is proposed. The prismatic semistructured grid is generated around viscous boundary surfaces and covers viscous regions, whereas the tetrahedral grid covers the rest of the computational domain. The Delaunay approach for tetrahedral grid generation is used. The proposed prismatic grid is structured in directions normal to the boundary faces, but the number of prisms generated from one boundary face is variable from face to face. Unlike conventional prismatic grid generators, this technique works well even in regions of cavities and gaps. The Delaunay background grid generated for surface nodes serves as an efficient data structure to check possible intersections of prisms. Particular attention is given to the boundary-constraining problem. A robust algorithm for the boundary recovery by edge swapping followed by a direct subdivision of tetrahedra is used. Grid examples for internal and external flow problems of complex shapes demonstrate the efficiency of the method

Intergrid-Boundary Definition Method for Overset Unstructured Grid Approach

The use of the overset concept for the unstructured grid method is relatively unexplored. However, the overset approach can extend the applicability of the unstructured grid method for real engineering problems without much need for code development. The multiple moving-body problem is one of those applications. Improvement in local resolution for Euler/Navier-Stokes computations on unstructured grids is another use of the overset concept. An efficient and robust algorithm to localize the intergrid boundaries for the overset unstructured grid method is proposed. Simplicity and automation in the intergrid-boundary definition are realized using the wall distance as a basic parameter. The neighbor-to-neighbor jump search algorithm is efficiently utilized in the method. The robustness and efficiency of the search is improved by the use of subsidiary grids that are generated as a byproduct of the Delaunay triangulation method. The basic procedure of the present method is described for a multielement airfoil problem. The effects of the overset method on the solution accuracy and the convergence are tested by ONERA M6-wing

Applications of unstructured hybrid grid method to high-Reynolds number viscous flows

An unstructured hybrid grid method is discussed for its capability to compute three-dimensional compressible viscous flows of complex geometry. A hybrid of prismatic and tetrahedral grids is used to accurately resolve the wall boundary layers for high-Reynolds number viscous flows. The Navier-Stokes equations for compressible flows are solved by a finite volume, cell-vertex scheme. The LU-SGS implicit time integration method is used to reduce the computational time for very fine grids in boundary layer regions. Two kinds of one-equation turbulence models are evaluated here for their accuracy. The method is applied to computations of transonic flows around the ONERA M5 airplane and ONERA M6 wing, and supersonic shock/boundary layer interacting flows inside a scramjet inlet to validate the accuracy and efficiency of the method

Drags in Scramjet Engine Testing: Experimental and Computational Fluid Dynamics Studies

No-fuel internal drag of a side-compression scramjet engine was evaluated by using two one-e fth-subscaled models, one forwall pressure measurement and theother forforce measurement under conditionsof a e ight Mach number of 4. The pressure and frictional drags in various parts of the models were estimated from these windtunnel tests. Comparison between the pressure measurement and the force measurement revealed that the drag derived by these wind-tunnel tests agreed within 5%. After examining the consistency between the pressure and the force experiments, these results were used to calibrate a newly developed computational e uid dynamics code. The frictional drag and the heating rate on the engine internal walls were evaluated with the unstructured-grid code to be compared with those obtained from the one-e fth-subscale model and the full-scale engine. The total drag coefe cient of the scramjet engine, including the installation drag, was found to be 0.281 and the internal drag coefe cient was found to be 0.093. Consequently, two-thirds of the total drag measured in engine testing in the Ramjet Engine Test Facility was produced by the external e ow over the engine module. Subtracting the external drag, the internal performance delivered by the H 2-fueled scramjet engine is discussed.

Navier-Stokes computations of two- and three-dimensional cascade flowfields

Simplifying grid generations for cascade computations is one of the most important items in studying the use of computational fluid dynamics as an engineering tool for the design and analysis of cascades. In this paper, new practical techniques that simplify the grid generations for twoand three-dimensional viscous cascade flow computations are described. The accuracy of the computations has been examined by comparing it with experimental data of several turbine cascades. Particular attention has been given in investigating the ability of the Baldwin-Lomax turbulence model to predict the boundary-layer transition location. Results showed enough capability of the method to be considered an effective engineering tool for accurate and efficient prediction of cascade performance. However, an improvement of the transition/turbulence model is required for better prediction in transonic and off-design conditions.

Simulation of Vortex Breakdown Using Adaptive Grid Refinement with Vortex-Center Identification

A topological-feature adaptation method is proposed to compute vortical flows around a delta wing at high incidence. Vortex-center identification based on the locally applied critical-point method is utilized as an indicator of the grid refinement using Rivaras bisection algorithm. The three-dimensional Navier-Stokes equations are solved using the hybrid unstructured grid. The computed results show that the refinement at the vortex core is effective to improve the numerical accuracy of the flow around a delta wing. The present feature-adaptive refinement is especially effective to improve the prediction of the vortex breakdown positions at high incidence

Numerical simulation of vortical flows using vorticity confinement coupled with unstructured grid

This paper discusses the use of the vorticity confinement method coupled with the unstructured grid approach to simulate vortical flows. The method is evaluated by several vortical flow computations of the leading-edge separation vortices on delta wings and the wing tip vortices of NACA0012 wing. It is shown that the vorticity confinement can keep the vorticity away from the numerical diffusion effectively. Although further study to reduce the dependency of the confinement coefficient on the grid density is required, the present results indicate the possibility of accurate vortical flow computations by the vorticity confinement method coupled with unstructured and adaptive refinement grids.

Euler/Navier-Stokes Optimization of Supersonic Wing Design Based on Evolutionary Algorithm

This paper presents aerodynamic shape optimization of a supersonic wing for supersonic civil transportation (SST) using an Evolutionary Algorithm (EA) coupled with an Euler/Navier-Stokes code. To overcome enormous computational time necessary for the design, aerodynamic evaluations are parallelized on Numerical Wind Tunnel (NWT) at National Aerospace Laboratory, a parallel vector machine with 166 processing elements. Parallelization of function evaluations in EA is straightforward and its performance is extremely good since most of computational time is used by flow computations. The design result indicates that the present EA successfully minimizes both the induced drag and the volume wave drag in the given design space.

Numerical analysis of a three-dimensional cascade flow by solving Navier-Stokes Equations.

Three-dimensional viscous flowfields in two different types of cascades, such as a turbine nozzle and fan blade, were numerically simulated by solving the Navier-Stokes Equations. For turbine nozzle flows, computed flow patterns on a vane in stationary and rotating frames were compared with those on a differently stacked vane. In a fundamental case, the computed results showed good agreement with experimental data. Three-dimensional flow separations as well as secondary flows caused by passage vortices could be predicted and effectively visualized using surface oil flow and streakline techniques, which were useful methods of three-dimensional flow representation.

Inverse Design of Supersonic Airfoils Using Integral Equations

Introduction T HE next-generation supersonic transport (SST) is under consideration today because the Concorde has been in service for 20 years and is not fully successful economically. There are many ongoing researches in this x8e eld in the United States, Europe, and Japan. To guarantee its economic success, the next-generationSST is required to have higher lift-to-drag ratio than that of the Concorde. To achieve this goal, developmentof a new design technique for supersonicwings is of great interest. For the transonicwing design,Takanashi1 proposedan inversemethod that uses the “residualcorrection” concept and has shown successful design results. In this Note, this inverse method is extended to the supersonic wing design. In the supersonic x8f ow, the governing equation can be linearized. Therefore,the integrationbecomessimpler than thatof the transonic case, but the integration region must be selected carefully because the region contributing to the point on the wing surface is limited to the Mach forecone. Sample results of two-dimensional airfoil designs conx8e rm the validity of the present method.