Unstructured Solver Research Articles

Delusive Influence of Nondimensional Numbers in Canonical Hypersonic Nonequilibrium Flows

AbstractA finite volume–based unstructured inviscid flow solver has been developed for the study of nonequilibrium effects in high enthalpy flows. Four different inviscid flux computation schemes are tested for literature reported test cases like unsteady wave motion in a shock tube and high enthalpy flow over cylinder/sphere. During the present assessment, encouraging agreement has been noticed in capturing all the essential flow features in the reacting media. Here, the Rusanov scheme is noticed to be computationally cheaper among all the schemes with noticeable diffusion around strong gradients. Shock tube test case revealed the existence of various shock Mach numbers for a given driving pressure ratio in the presence of reactions. Similarly, freestream Mach number is found to have limitations in representing the shock standoff distance in case of high enthalpy flow over cylinder and sphere. In line with this, real gas effects are prominently observed for the case of the cylinder in comparison with the...

Coupled Overset Unstructured Discontinuous Galerkin Method for Launch Environment Acoustics Prediction

A novel approach for the accurate prediction of launch environment acoustic physics is presented. Launch vehicles experience extreme acoustic loads during liftoff, driven by the interaction of rocket plumes and plume-generated acoustic waves with ground structures. In this work, a well-established hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation unstructured mesh solver is used to efficiently model the complex turbulent plume physics, and a high-order accurate discontinuous Galerkin solver is used to accurately propagate acoustic waves across large distances throughout the launch environment. The two solvers operate on separate overlapping meshes, and an innovative overset coupling approach is used to transmit the plume-generated acoustics to the far field in a one-way manner in which the turbulent plume prediction is unaffected by the outer acoustic propagation physics. The framework upon which the solvers are developed is described along with details outlining the overset domain connectivity and interpolation methods. Results are presented that demonstrate the accuracy of the capability for aeroacoustic predictions, and the merits of the approach are evaluated using a notional space launch system launch environment in which rocket plumes are represented by transient acoustic sources.

Stability and Control Investigations of Generic 53 Degree Swept Wing with Control Surfaces

A contribution for the assessment of the static and dynamic aerodynamic behavior of a generic unmanned combat air vehicle configuration with control devices using computational fluid dynamics methods is given. For the study, various computational approaches have been used to predict stability and control parameters for aircraft undergoing nonlinear flight conditions. For the computational fluid dynamics simulations, three different computational fluid dynamics solvers are used: the unstructured grid-based solvers DLR TAU code and USM3D from NASA, as well as the structured grid-based National Aerospace Laboratory/NLR solver ENSOLV. The numerical methods are verified by experimental wind-tunnel data. The correlations with experimental data are made for static longitudinal/lateral sweeps and at varying frequencies of prescribed roll/pitch/yaw sinusoidal motions for the vehicle operating with and without control surface deflections. Furthermore, the investigations should support the understanding of the flow physics around the trailing-edge control devices of highly swept configurations with a vortex-dominated flowfield. Design requirements should be drawn by analyzing the interaction between the vortical flow and the control devices. The present work is part of the North Atlantic Treaty Organization’s Science and Technology Organization/ Applied Vehicle Technology Task Group AVT-201 on stability and control prediction methods.

An efficient implicit unstructured finite volume solver for generalised Newtonian fluids

ABSTRACTAn implicit finite volume solver is developed for the steady-state solution of generalised Newtonian fluids on unstructured meshes in 2D. The pseudo-compressibility technique is employed to couple the continuity and momentum equations by transforming the governing equations into a hyperbolic system. A second-order accurate spatial discretisation is provided by performing a least-squares gradient reconstruction within each control volume of unstructured meshes. A central flux function is used for the convective terms and a solution jump term is added to the averaged component for the viscous terms. Global implicit time-stepping using successive evolution–relaxation is utilised to accelerate the convergence to steady-state solutions. The performance of our flow solver is examined for power-law and Carreau–Yasuda non-Newtonian fluids in different geometries. The effects of model parameters and Reynolds number are studied on the convergence rate and flow features. Our results verify second-order accuracy of the discretisation and also fast and efficient convergence to the steady-state solution for a wide range of flow variables.

An immersed boundary method for unstructured meshes in depth averaged shallow water models

SummaryThe representation of geometries as buildings, flood barriers or dikes in free surface flow models implies tedious and time‐consuming operations in order to define accurately the shape of these objects when using a body fitted numerical mesh. The immersed boundary method is an alternative way to define solid bodies inside the computational domain without the need of fitting the mesh boundaries to the shape of the object. In the direct forcing immersed boundary method, a solid body is represented by a grid of Lagrangian markers, which define its shape and which are independent from the fluid Eulerian mesh. This paper presents a new implementation of the immersed boundary method in an unstructured finite volume solver for the 2D shallow water equations. Moving least‐squares is used to transmit information between the grid of Lagrangian markers and the fluid Eulerian mesh. The performance of the proposed implementation is analysed in three test cases involving different flow conditions: the flow around a spur dike, a dam break flow with an isolated obstacle and the flow around an array of obstacles. A very good agreement between the classic body fitted approach and the immersed boundary method was found. The differences between the results obtained with both methods are less relevant than the errors because of the intrinsic shallow water assumptions. Copyright © 2015 John Wiley & Sons, Ltd.

Advanced validation of CFD-FDTD combined method using highly applicable solver for reentry blackout prediction

An analysis model of plasma flow and electromagnetic waves around a reentry vehicle for radio frequency blackout prediction during aerodynamic heating was developed in this study. The model was validated based on experimental results from the radio attenuation measurement program. The plasma flow properties, such as electron number density, in the shock layer and wake region were obtained using a newly developed unstructured grid solver that incorporated real gas effect models and could treat thermochemically non-equilibrium flow. To predict the electromagnetic waves in plasma, a frequency-dependent finite-difference time-domain method was used. Moreover, the complicated behaviour of electromagnetic waves in the plasma layer during atmospheric reentry was clarified at several altitudes. The prediction performance of the combined model was evaluated with profiles and peak values of the electron number density in the plasma layer. In addition, to validate the models, the signal losses measured during communication with the reentry vehicle were directly compared with the predicted results. Based on the study, it was suggested that the present analysis model accurately predicts the radio frequency blackout and plasma attenuation of electromagnetic waves in plasma in communication.

Applicability of URANS and DES Simulations of Flow Past Rectangular Cylinders and Bridge Sections

This paper discusses the results of computational fluid dynamics simulations carried out for rectangular cylinders with various side ratios of interest for many civil engineering structures. A bridge deck of common cross-section geometry was also considered. Unsteady Reynolds-averaged Navier–Stokes (URANS) equations were solved in conjunction with either an eddy viscosity or a linearized explicit algebraic Reynolds stress model. The analysis showed that for the case studies considered, the 2D URANS approach was able to give reasonable results if coupled with an advanced turbulence model and a suitable computational mesh. The simulations even reproduced, at least qualitatively, complex phenomena observed in the wind tunnel, such as Reynolds number effects for a sharp-edged geometry. The study focused both on stationary and harmonically oscillating bodies. For the latter, self-excited forces and flutter derivatives were calculated and compared to experimental data. In the particular case of a benchmark rectangular 5:1 cylinder, 3D detached eddy simulations were also carried out, highlighting the improvement in the accuracy of the results with respect to both 2D and 3D URANS calculations. All of the computations were performed with the Tau code, a non-commercial unstructured solver developed by the German Aerospace Center.

An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yields second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.

Enhancement of a Correlation-Based Transition Turbulence Model for Simulating Crossflow Instability

A new laminar–turbulence transition model for capturing three-dimensional boundary layers involving crossflow-induced transition has been developed by extending the existing transition model. In the present transition model, to resolve transition due to crossflow instability, the C1-criterion was evaluated locally using the Falkner–Skan–Cooke velocity profiles. Thus, only local flow quantities are used in determining the onset of three-dimensional transition. As a result, the extended transition model is compatible and works well with modern computational fluid dyanmics flow solvers, particularly for those based on unstructured meshes, under massive parallel environment. The new transition model was implemented in a three-dimensional incompressible unstructured mesh flow solver. Validations of the new transition model were made for an infinite swept-wing configuration and an inclined prolate spheroid by comparing the results with those of the baseline model and experiment. It was found that the new transition model works well by capturing the crossflow-induced transition inside three-dimensional boundary layers more accurately than the baseline model.

Assessment of Tip Shape Effect on Rotor Aerodynamic Performance in Hover

In the present study, an unstructured mixed mesh flow solver was used to conduct a numerical prediction of the aerodynamic performance of the S-76 rotor in hover. For the present mixed mesh methodology, the near-body flow domain was modeled by using body-fitted prismatic/tetrahedral cells while Cartesian mesh cells were filled in the off-body region. A high-order accurate weighted essentially non-oscillatory (WENO) scheme was employed to better resolve the flow characteristics in the off-body flow region. An overset mesh technique was adopted to transfer the flow variables between the two different mesh regions, and computations were carried out for three different blade configurations including swept-taper, rectangular, and swept-taper-anhedral tip shapes. The results of the simulation were compared against experimental data, and the computations were also made to investigate the effect of the blade tip Mach number. The detailed flow characteristics were also examined, including the tip-vortex trajectory, vortex core size, and first-passing tip vortex position that depended on the tip shape.

A note on material losses in unstructured transmission line modeling

ABSTRACTThe incorporation of material losses within an unstructured transmission line Modeling electromagnetic field solver is presented. A theoretical and numerical development is complemented by a number of quantified canonical examples. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:2218–2222, 2015

Japan Aerospace Exploration Agency Studies for the Second High-Lift Prediction Workshop

This paper summarizes Japan Aerospace Exploration Agency studies using a structured grid solver UPACS and an unstructured grid solver TAS-code for the second AIAA CFD High-Lift Prediction Workshop test cases and follow-on problems. Computations are performed for the grid convergence study using the configuration without any slat tracks and flap track fairings on a series of multi-block structured grids and a series of unstructured grids provided by the High Lift Prediction Workshop committee. In this paper, the following are mainly discussed: 1) grid convergence verification study of the turbulence models using a two-dimensional bump case, 2) grid convergence studies for Spalart–Allmaras and shear stress transport turbulence models using UPACS, 3) change of grid convergence and predicted flow fields with and without a nonlinear quadratic constitutive relation model for Spalart–Allmaras and shear stress transport turbulence models using UPACS including evaluation at higher angles of attack, and 4) comparison studies using different solvers UPACS and TAS on different grid systems with and without the quadratic constitutive relation model for the Spalart–Allmaras model.

An unstructured shock-fitting solver for hypersonic plasma flows in chemical non-equilibrium

A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron–atom and atom–atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.

Large-Eddy Simulations of Wall Bounded Turbulent Flows Using Unstructured Linear Reconstruction Techniques

Large-eddy simulations (LES) of wall bounded, low Mach number turbulent flows are conducted using an unstructured finite-volume solver of the compressible flow equations. The numerical method employs linear reconstructions of the primitive variables based on the least-squares approach of Barth. The standard Smagorinsky model is adopted as the subgrid term. The artificial viscosity inherent to the spatial discretization is maintained as low as possible reducing the dissipative contribution embedded in the approximate Riemann solver to the minimum necessary. Comparisons are also discussed with the results obtained using the implicit LES (ILES) procedure. Two canonical test-cases are described: a fully developed pipe flow at a bulk Reynolds number Reb = 44 × 103 based on the pipe diameter, and a confined rotor–stator flow at the rotational Reynolds number ReΩ = 4 × 105 based on the outer radius. In both cases, the mean flow and the turbulent statistics agree well with existing direct numerical simulations (DNS) or experimental data.

Numerical study of effects of accommodation coefficients on slip phenomena

An unstructured mesh Navier-Stokes solver employing a Maxwell slip boundary condition was developed. The present flow solver was applied to the simulation of flows around an axisymmetric hollow cylinder in a Mach 10.4 freestream, known as Calspan-UB Research Center (CUBRC) Run 14 case, and the velocity slip and the temperature jump on the cylinder surface were investigated. The effect of tangential momentum and thermal accommodation coefficients used in the Maxwell condition was also investigated by adjusting their values. The results show that the reverse flow region is developed on the body surface due to the interaction between the shock and the boundary layer. Also, the shock impingement makes pressure high. The flow properties on the surface agree well with the experimental data, and the velocity slip and the temperature jump vary consistently with the local Knudsen number change. The accommodation coefficients affect the slip phenomena and the size of the flow region. The slip phenomena become larger when both tangential momentum and thermal accommodation coefficients are decreased. However, the range of the reverse flow region decreases when the momentum accommodation coefficient is decreased. The characteristics of the momentum and thermal accommodation coefficients also are overlapped when they are altered together.

Study of Convergence Time for Rarefied Gas Simulations Using an Unstructured DSMC Solver

This article studies the required convergence time for direct-simulation Monte Carlo (DSMC) simulations of rarefied gas flows. An arbitrary-geometry DSMC solver (RGS2D) with an efficient particle-tracking algorithm is introduced and employed for macro-/micro-scale flow applications. Convergence time study is performed by tracing different heat and flow parameters such as intermolecular collision rate, number of particles, drag coefficient, inlet/outlet mass flow rate, and distributions over the wall, i.e., pressure coefficient, skin friction coefficient, heat transfer coefficient, and wall collision rate. The results indicate that the required simulation time depends on the capturing parameter.

Design of implicit high-order filters on unstructured grids for the identification of large-scale features in large-eddy simulation and application to a swirl burner

The analysis of large-scale structures from highly refined unsteady simulations becomes challenging as the mesh resolution increases, and some new tools must be developed in order to perform their identification and extraction. A solution is to use filters to remove the smallest flow motions. High-order filters, characterized by their good selectivity properties, were implemented in an unstructured finite-volume solver for large-eddy simulation, and their ability to extract structures of a given scale was tested on canonical flows. Then, these filters were applied on an aeronautical swirl burner with a complex geometry. The results show that novel high-order filters are able to extract the precessing vortex core from this realistic turbulent flow. High-order filtering enables to study in detail this large-scale structure and to gain insight into the dynamic of swirl flows.

OpenACC acceleration of an unstructured CFD solver based on a reconstructed discontinuous Galerkin method for compressible flows

SummaryAn OpenACC directive‐based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier–Stokes equations on 3D hybrid unstructured grids with a third‐order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementation of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight‐core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC‐based parallel scheme is an effective and extensible approach to port unstructured high‐order CFD solvers to GPU computing. Copyright © 2015 John Wiley & Sons, Ltd.

High order moment method for polydisperse evaporating sprays with mesh movement: Application to internal combustion engines

Relying on two recent contributions by Massot et al. [SIAM J. Appl. Math. 70 (2010), 3203–3234] and Kah et al. [J. Comput. Phys. 231(2012)], where a Eulerian Multi-Size Moment (EMSM) model for the simulation of polydisperse evaporating sprays has been introduced, we investigate the potential of such an approach for the robust and accurate simulation of the injection of a liquid disperse phase into a gas for automotive engine applications. The original model used a high order moment method in droplet size to resolve polydispersity, with built-in realizability preserving numerical algorithm of high order in space and time, but only dealt with one-way coupling and was restricted to fixed meshes. Extending the approach to internal combustion engine and fuel injection requires solving two major steps forward, while preserving the properties of robustness, accuracy and realizability: 1 – the extension of the method and numerical strategy to two-way coupling with stable integration of potential stiff source terms, 2 – the introduction of a moving geometry and meshes. We therefore present a detailed account on how we have solved these two issues, provide a series of verification of the proposed algorithm, showing its potential in simplified configurations. The method is then implemented in the IFP-C3D unstructured solver for reactive compressible flows in engines and validated through comparisons with a structured fixed mesh solver. It finally proves its potential on a free spray jet injection where it is compared to a Lagrangian approach and its reliability and robustness are assessed, thus making it a good candidate for realistic injection applications.

GS15 超音速混合に対するキャビティ自励振動促進の効果

The present study reports of passive technique to enhance the cavity-induced pressure oscillations by modifying the cavity leading edge configuration. 3 (three) leading edge geometries namely circular-contoured, slanted and circular contour on 30° slant edge were used in the study. The density-based algorithm in ANSYS Fluent 13.0 was used to solve the time dependent Navier-Stokes equations. The SST k-ω model was used for modeling the turbulence within an unstructured mesh solver. Validation of the computational code used was accomplished and the results showed a good agreement between the numerical simulation and experimental data. The study comprised the analysis of pressure oscillations in and after the cavity. The modification of cavity leading edge shown influencing to the pressure fluctuations.