Hybrid Unstructured Grids Research Articles

Validation of Arbitrary Unstructured CFD Code for Aerodynamic Analyses

An unstructured grid CFD code capable of handling arbitrary polyhedra, named ‘‘LS-FLOW,’’ is developed for aerodynamic analyses of complex geometries. Through a series of numerical test cases, it is demonstrated that LS-FLOW can handle both structured and body-fitted/Cartesian hybrid unstructured grids successfully. Then, the code is validated by comparison with experimental data and theoretical solutions. In addition, it is shown that when a Baldwin-Lomax algebraic turbulence model is employed on the body-fitted/Cartesian grid, the portion of the body-fitted grid should be large enough to contain the whole boundary-layer. Finally, LS-FLOW is applied to a rocket configuration, and its future prospects are addressed.

The unconditionally positive-convergent implicit time integration scheme for two-equation turbulence models: Revisited

The unconditionally positive-convergent implicit scheme for two-equation turbulence models, originally developed by Mor-Yossef and Levy, is revisited. A compact, simple, and uniform reformulation of the method for the use of both structured and unstructured grid based flow solvers is presented. An analytical proof of the scheme revision is given showing that positivity of the turbulence model solutions and convergence of the turbulence model equations are guaranteed for any time step. Numerical experiments are conducted, simulating two test cases of three-dimensional complex flow fields using structured and hybrid unstructured grids. To demonstrate the overall scheme’s robustness, it is applied to non-linear k- ω and non-linear k- ϵ turbulence models. Results from the numerical simulations show that the scheme exhibits very good convergence characteristics, is robust, and it always preserves the positivity of the turbulence model dependent variables, even for an infinite time step.

Analysis of Magnetohydrodynamic Generator Power Generation

The three-dimensional current and fluid flow characteristics of diagonally connected magnetohydrodynamics generators are studied by means of numerical solutions. The formulation solves the Navier-Stokes equations in conjunction with the magnetic diffusion equation and a two-equation turbulence model on a hybrid unstructured grid. The current is obtained from Ampere's law, and a generalized Ohm's law is used to include the Hall effect. A flux-split upwind discretization is used for the convective terms along with a nonconservative correction that drives the divergence of the magnetic field to zero. Physical difficulties with boundary conditions are removed by extending the computational domain into the far field to encompass the plasma channel, the conducting and dielectric walls, and the surrounding air. The fluid flow and magnetic field solvers can be updated in loosely or closely coupled fashion depending on the magnetic Reynolds number. Results are shown for supersonic flow generators with both constant and diverging area channels. Properties are based on equilibrium table lookup for combustion gas products with potassium seedant.

Flame structures and combustion efficiency computed for a Mach 6 scramjet engine

Our hydrogen-fueled scramjet engines with a length of 2.1 m delivered net thrusts exceeding the engine drags and exhibited fuel specific impulses of about 10 km/s under Mach 4 to 8 flight conditions. A three-dimensional, reactive CFD code using unstructured hybrid grids was developed to accelerate the engine studies. Combustion in the scramjet engine under the Mach 6 condition was simulated by using this code. In this paper, the engine testing and the CFD code were outlined first. Timewise progress of hydroxyl radicals was investigated to understand autoignition and upstream-wise developments of combustion in the engine. Autoignition occurred from the cowl section at 0.1 ms after fuel mixing was completed. The reaction zones propagated upstream at speeds of about 500 m/s and reached the backward-facing steps in the combustor at 1 ms after the autoignition. Steady-state solutions showed small flames around individual fuel jets in the combustor and a large-scale diffusion flame downstream in the engine. Sonic combustion was autonomously realized in the combustor, resulting in delivery of a maximum thrust of 2250 N in the stoichiometric condition. Variations of combustion efficiency indicated that combustion performance was determined in a narrow region with a length of 0.15 m in the combustor and that the combustion downstream of the engine was rate-controlled by a large diffusion flame. The results found by the CFD computations enable us to not only improve engine performances but also to optimize computations for scramjet engines.

Improvements in the reliability and quality of unstructured hybrid mesh generation

AbstractThis paper presents a reliable and automated approach to the generation of unstructured hybrid grids comprised of tetrahedra, prisms and pyramids for high Reynolds number viscous flow simulations. To enhance robustness, the hybrid mesh generation process starts with the formation of an isotropic tetrahedral grid. Prismatic layers are then added on no‐slip walls fully automatically by obeying user‐specified boundary conditions and three parameters: the number of the layers, an initial layer thickness normal to the walls, and a stretching factor. Topological modifications to the original isotropic tetrahedral elements are prohibited during the layer generation process. The tetrahedral elements near no‐slip walls are shifted inward and the resulting gap between the tetrahedra and the walls is filled up with prismatic elements. To enhance the quality of the prismatic layers around sharp corners, two normals are evaluated for the marching process in these regions. The addition of prismatic elements is locally stopped if negative‐volume elements are created or not enough space is left. An angle‐based smoothing method ensures that the quality of the tetrahedral elements is retained for a reasonable computational cost. The method is demonstrated for two scaled experimental supersonic airplane models designed at the National Aerospace Laboratory of Japan (NAL). Numerical results are compared with wind tunnel experimental data. Copyright © 2004 John Wiley & Sons, Ltd.

A time‐accurate pseudo‐compressibility approach based on an unstructured hybrid finite volume technique applied to unsteady turbulent premixed flame propagation

AbstractA preconditioning approach based on the artificial compressibility formulation is extended to solve the governing equations for unsteady turbulent reactive flows with heat release, at low Mach numbers, on an unstructured hybrid grid context. Premixed reactants are considered and a flamelet approach for combustion modelling is adopted using a continuous quenched mean reaction rate. An overlapped cell‐vertex finite volume method is adopted as a discretisation scheme. Artificial dissipation terms for hybrid grids are explicitly added to ensure a stable, discretised set of equations. A second‐order, explicit, hybrid Runge–Kutta scheme is applied for the time marching in pseudo‐time. A time derivative of the dependent variable is added to recover the time accuracy of the preconditioned set of equations. This derivative is discretised by an implicit, second‐order scheme. The resulting scheme is applied to the calculation of an infinite planar (one‐dimensional) turbulent premixed flame propagating freely in reactants whose turbulence is supposed to be frozen, homogeneous and isotropic. The accuracy of the results obtained with the proposed method proves to be excellent when compared to the data available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.

A numerical method for large-eddy simulation in complex geometries

We discuss the development of a numerical algorithm, and solver capable of performing large-eddy simulation in the very complex geometries often encountered in industrial applications. The algorithm is developed for unstructured hybrid grids, is non-dissipative, yet robust at high Reynolds numbers on highly skewed grids. Simulation results for a variety of flows are presented.

Large eddy simulation of multi-phase turbulent flows in realistic combustors

An overview is provided of the recent advances in performing LES in complex combustor geometries using a non-dissipative, massively parallel, unstructured grid solver (CDP). A new numerical algorithm that is discretely energy conserving on hybrid unstructured grids is developed. This allows simulations at high Reynolds numbers without the use of numerical dissipation. This LES methodology has been extended to include advanced turbulent combustion models and a Lagrangian particle tracking methodology for simulating turbulent multiphase flows. Results for single and multi-phase flow simulations in realistic Pratt & Whitney (P&W) combustor geometries are discussed.

On the development of an agglomeration multigrid solver for turbulent flows

The paper describes the implementation details and validation results for an agglomeration multigrid procedure developed in the context of hybrid, unstructured grid solutions of aerodynamic flows. The governing equations are discretized using an unstructured grid finite volume method, which is capable of handling hybrid unstructured grids. A centered scheme as well as a second order version of Liou’s AUSM+ upwind scheme are used for the spatial discretization. The time march uses an explicit 5-stage Runge-Kutta time-stepping scheme. Convergence acceleration to steady state is achieved through the implementation of an agglomeration multigrid procedure, which retains all the flexibility previously available in the unstructured grid code. The calculation capability created is validated considering 2-D laminar and turbulent viscous flows over a flat plate. Studies of the various parameters affecting the multigrid acceleration performance are undertaken with the objective of determining optimal numerical parameter combinations.

A NODE-CENTERED PRESSURE-BASED METHOD FOR ALL SPEED FLOWS ON UNSTRUCTURED GRIDS

This article proposes a node-centered pressure-based method for predicti ng flows at all speeds on unstructured grids. The compressible version of the SIMPLE algorithm is extended to unstructured grids. For memory and computing time efficiency of arbitrary cell topologies, a node-centered scheme with edge-based data structure is applied to the segregated unstructur ed-grid algorithm. Convection terms are discretized using the second-order scheme with a deferred-correction approach. Diffusion-term discretization is based on the structured-grid analogy, which can be easily adapted to hybrid unstructured grid solvers. By using the proposed approach, three test cases in the continuum regime are computed. The demonstration of this method is extended to a slip flow problem that has low Reynolds number and compressibility effect. Predictions are compared to other results, which show that the proposed method can improve efficiency in memory usage and computing time without losing any accuracy even in mixed-element grids.

A Three-Dimensional Parallel Discontinuous Galerkin Solver for Acoustic Propagation Studies

The paper presents recent developments of a computational code for the numerical investigation of acoustic propagation. The code solves the three-dimensional linear Euler equations using a Discontinuous Galerkin (DG) method for the spatial discretization and an explicit high-order low-storage Runge-Kutta method for advancing the solution in time. Thanks to DG discretization, high-order accurate numerical solutions on arbitrary unstructured hybrid grids have been easily computed. The code has been parallelized using MPI and preliminary results on a small 10-processor Linux cluster seem very promising.

전 속도영역 유동을 위한 비정렬격자 압력기반해법

This article proposes a pressure based method for predicting flows at all speeds. The compressible SIMPLE algorithm is extended to unstructured grid framework. Convection terms are discretized using second-order scheme with deferred correction approach. Diffusion term discretization is based on structured grid analogy that can be easily adopted to hybrid unstructured grid solver. This method also uses node centered scheme with edge based data structure for memory and computing time efficiency of arbitrary grid types. Both incompressible and compressible benchmark problems are solved using the above methodology. The demonstration of this method is extended to slip flow problem that has low Reynolds number but compressibility effect. It is shown that the proposed method can improve efficiency in memory usage and computing time without losing any accuracy.br/

Edge-Based Multigrid and Preconditioning for Hybrid Grids

A multigrid method has been developed for the Euler and Navier-Stokes equations on unstructured hybrid grids in two and three dimensions. The coarse grids are automatically generated from the finest grid through element collapsing. This has been used in preference to a previous edge-collapsing technique to preserve as much structure as possible within semistructured grids. The performance of the multigrid is significantly improved through the use of Jacobi preconditioning within a Runge-Kutta iterative smoother. Results are presented for a variety of two-dimensional and three-dimensional problems, both inviscid and viscous, with the Spalart-Allmaras turbulence model

Improvement of Drag Prediction for Transonic Transport Aircraft Configuration Using Hybrid Unstructured Navier-Stokes Solver.

In general, an unstructured grid technique has a good flexibility for a complex geometry, and already its usefulness has been demonstrated for full aircraft computations. In the case of three-dimensional, high Reynolds number viscous flow calculations, however, the very fine and stretched grids are required to resolve accurately thin boundary layers developed along the body surface, and so we often have some difficulties in high quality grid generation. A hybrid unstructured grid technique is incorporated into CASPER, a CFD-based design system developed at TRDI-JDA. In this paper, transonic and high Reynolds number flows around an ONERA Model M5 configuration are computed using the CASPER. To validate the present code, with respect to pressure distributions, longitudinal forces and moment coefficients, and transition lines, the present computed results are quantitatively compared with the other computed results and wind-tunnel testing data. Furthermore, some approaches are discussed for reliable drag prediction using CFD method.

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 Rivara's 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

A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids

A new second-order time-accurate fractional-step method for solving unsteady incompressible Navier–Stokes equations on hybrid unstructured grids is presented. The nonstaggered grid method, originally developed by Rhie and Chow (1983, AIAA J.21, 1525) for steady flow and further extended by Zang et al. (1994, J. Comput. Phys.114, 18) to unsteady flow on structured grids, is employed in the present study to enforce mass conservation on hybrid unstructured grids. The pressure and Cartesian velocity components are defined at the center of each cell, while the face-normal velocities are defined at the mid-points of the corresponding cell faces. A second-order fully implicit time-advancement scheme is used for time integration and the resulting nonlinear equations are linearized without losing the overall time accuracy. Both the momentum and Poisson equations are integrated with the finite volume method and the flow variables at the cell face are obtained using an interpolation scheme independent of cell shape. The present numerical method is applied to four different benchmark problems and proves to be accurate and efficient.

Modeling of Three-Dimensional Viscous Compressible Turbomachinery Flows Using Unstructured Hybrid Grids

An advanced numerical model for the simulation of steady and unsteady viscous compressible e ows for turbomachinery applications is described. The compressible Favre-averaged Navier ‐Stokes equations are used together with a one-equation turbulence model. The e ow domain is discretized using unstructured hybrid grids that can contain a mixture of hexahedral, pentahedral, tetrahedral, and triangular prismatic cells. The e ow equations are discretized using a node-centered e nite volume scheme that relies on representing the mesh using an edge-based data structure. A dual time stepping technique is applied to a point implicit formulation so that time accuracy can be maintained with large Courant ‐Friedrichs‐Lewy numbers. Nonree ecting boundary conditions are applied at the ine ow and oute ow boundaries to prevent any spurious ree ections of the outgoing waves. The model was validated against measured data for two cases. Radial proe les of pressure and temperature rise were determined from the steady e ow analysis of a rig fan blade, and these were found to be in very good agreement with the measured quantities. A rotor/stator interaction was studied next. Detailed comparisons were carried out against measured steady and unsteady e ow data and good agreement was obtained in all cases.

Modeling of three-dimensional viscous compressible turbomachinery flows using unstructured hybrid grids

Modeling of three-dimensional viscous compressible turbomachinery flows using unstructured hybrid grids

Numerical Analysis of Scramjet Internal Flow by Hybrid Unstructured Grid Method.

Computations of internal viscous flowfields of scramjet models were conducted at inflow Mach numbers of 3.4 and 5.45. A hybrid unstructured grid method was used to compute the scramjet models with and without a short strut. The numerical method to solve the Navier-Stokes equations on the hybrid unstructured grid was developed using a finite volume cell vertex scheme and the lower-upper symmetric Gauss-Seidel (LU-SGS) implicit time integration algorithm. The computational results revealed that a thick subsonic region did not exist in the combustor near the top wall at Mach number 5.45. It was a desirable feature to avoid unstarting the engine. With the use of a strut, the relatively low velocity regions increased and the downward flow toward the cowl behind the step became strong. An overconcentration of fuel toward the top wall during weak combustion was observed in the experiment. The reason for this was that the airflow near the injector was turned to the top wall due to the small influence of combustion in the experiment.

G906 Hybrid 非構造格子法を用いた 65°/74°デルタ翼周り流れの数値シミュレーション

G906 Hybrid 非構造格子法を用いた 65°/74°デルタ翼周り流れの数値シミュレーション