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DOE OSTI2016

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Modeling of Ice Accretion over Aircraft Wings Using a Compressible OpenFOAM Solver

A method to simulate ice accretion on an aircraft wing using a three-dimensional compressible Navier-Stokes solver, a Eulerian droplet flow field model, a mesh morphing model, and a thermodynamic model, is presented in this paper. The above models are combined together into one solver and implemented in OpenFOAM. Two-way coupling is achieved between airflow field calculation and ice simulation. The density-based solver rhoEnergyFoam is used to calculate the airflow field. The roughness wall function is proposed to simulate the roughness effect caused by ice accretion. For droplet flow field calculation, the Eulerian model is applied and the permeable wall boundary condition is used on the wing to simulate the droplet impingement. The icing thermodynamic model is built based on the Messinger model. The mesh morphing model adjusts the wing’s shape every time step based on the amount of accreted ice so that the airflow field is updated during the simulation. The effect of the ice accretion on the airflow is studied by comparing the aerodynamic performance—with and without ice. The ice accretion on the ONERA M6 wing model under a specific condition has been simulated to validate the solver’s performance and investigate the effect of the accreted ice on the aerodynamic performance.

Li, Sibo↗

NASA NTRS1995

Computational Investigation of a Semi-Span Flap

The current study computationally examines one of the principle three-dimensional features of the flow over a high-lift system, the flow associated with a flap edge. Structured, overset grids were used in conjunction with an incompressible Navier-Stokes solver to compute the flow over a two-element high-lift configuration. The computations were run in a fully turbulent mode using the one-equation Baldwin-Barth model. Specific interest was given to the details of the flow in the vicinity of the flap edge, so the geometry was simplified to isolate this region. The geometry consisted of an unswept wing, which spanned a wind tunnel test section, equipped with a single element flap. Two flap configurations were computed; a full-span and a half-span Fowler flap. The chord based Reynolds number was 3.7 million for all cases. The results for the full-span flap agreed with two-dimensional experimental results and verified the method. Grid topologies and related issues for the half-span flap geometry are discussed. Results of the half-span flap case are presented with emphasis on the flow features associated with the flap edge.

Mathias, Donovan, L.↗

NASA NTRS1987

Analysis of viscous transonic flow over airfoil sections

A full Navier-Stokes solver has been used to 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 be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.

Huff, Dennis L.↗

NASA NTRS1987

Analysis of viscous transonic flow over airfoil sections

Huff, Dennis L.↗

NASA NTRS1991

Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver

A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.

Kim, S.-W.↗

NASA NTRS1991

Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver

Kim, S.-W.↗

NASA NTRS2018

Aerodynamics and Aeroacoustic Sources of a Coaxial Rotor

Vehicles with coaxial, contra-rotating rotor systems (CACR) are being considered for a range of applications. Design parameters are identified that effect the fundamental aerodynamics and fluid dynamic features of a CACR in hover, vertical, and edgewise flight. Understanding the fluid dynamic features is a precursor to studying the aeroacoustics of a coaxial rotor. Rotor performance was computed initially using Navier-Stokes solver with prescribed blade section aerodynamic properties, the results validated against generic experimental test cases. Using a A 2D potential flow code and 2D OVERFLOW compressible-flow Navier-Stokes solver, the fluid dynamics of blade interactions was simplified and broken into a 2D blade crossing problem, with crossing locations and velocity fields from the rotor results to understand circulation, thickness, compressibility, shed vorticity, downwash, and viscosity effects. A calculation tool has been developed to identify time and location of blade overlap and BVI time location for CACR. Specific aerodynamic phenomena that occur for each noise source relevant to CACR are presented, along with computational tools to predict these occurrences.

Aeroacoustic↗

NASA NTRS1992

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗

DOE OSTI2025

In situ multi-tier auto-ignition detection applied to dual-fuel combustion simulations

Here we use an anomaly detection methodology that is centered on analyzing fourth-order joint moments (co-kurtosis), particularly focusing on its application in auto-ignition of combustion problems with large numbers of species. Unsupervised anomaly detection is challenging to generalize across problem types and domains. A recent technique, centered on analyzing information in the fourth-order joint moment co-kurtosis, has shown promise, especially for high-dimensional scientific data. In this work we present developments to the co-kurtosis based anomaly detection method needed to make it effective and scalable for large-scale distributed scientific data, such as those generated by massively parallel simulations. An in situ co-kurtosis algorithm is employed as the anomaly detection method for identifying ignition kernels in simulations of turbulent combustion. Here, we extend an existing methodology which identifies regions of the domain where anomalies are present, and add another tier of anomaly detection where the individual samples contributing to the anomaly are identified. We apply this algorithm on-the-fly to a variety of turbulent reacting flow problems and compare it to the widely used (but significantly more expensive) chemical explosive mode analysis (CEMA). We demonstrate the ability of the method to detect and identify the onset of low and high temperature ignition which can be used for computational steering, as chemical and combustion anomalies occur intermittently at spatio-temporal locations unknown a priori. Finally, we apply our lightweight in situ algorithm to an exascale high-fidelity simulation with a total of 2.4 Trillion degrees of freedom, performed using an adaptive mesh refinement solver. Furthermore, through a scalability analysis, we show that the relative computational cost of this in-situ anomaly detection algorithm compared to an iteration of the reacting flow solver is negligible.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2017

Fully Coupled Aero-Thermochemical-Elastic Simulations of an Eroding Graphite Nozzle

A multiphysics simulation capability has been developed that incorporates mutual interactions between aerodynamics, structural response from aero/thermal loading, ablation/pyrolysis, heating, and surface-to-surface radiation to perform high-fidelity, fully coupled aerothermoelastic ablation simulations, which to date had been unattainable. The multiphysics framework couples CHAR (a 3-D implicit charring ablator solver), Loci/CHEM (a computational fluid dynamics solver for high-speed chemically reacting flows), and Abaqus (a nonlinear structural dynamics solver) to create a fully coupled aerothermoelastic charring ablative solver. The solvers are tightly coupled in a fully integrated fashion to resolve the effects of the ablation pyrolysis and charring process and chemistry products upon the flow field, the changes in surface geometry due to recession upon the flow field, and thermal-structural analysis of the body from the induced aerodynamic heating from the flow field. The multiphysics framework was successfully demonstrated on a solid rocket motor graphite nozzle erosion application. Comparisons were made with available experimental data that measured the throat erosion during the motor firing. The erosion data is well characterized, as the test rig was equipped with a windowed nozzle section for real-time X-ray radiography diagnostics of the instantaneous throat variations for deducing the instantaneous erosion rates. The nozzle initially undergoes a nozzle contraction due to thermal expansion before ablation effects are able to widen the throat. A series of parameters studies were conducted using the coupled simulation capability to determine the sensitivity of the nozzle erosion to different parameters. The parameter studies included the shape of the nozzle throat (flat versus rounded), the material properties, the effect of the choice of turbulence model, and the inclusion or exclusion of the mechanical thermal expansion. Overall, the predicted results match the experiment very well, and the predictions were able to bound the data within acceptable limits.

Blades, E. L.↗

NASA NTRS1997

Creating a Simple Single Computational Approach to Modeling Rarefied and Continuum Flow About Aerospace Vehicles

We proposed to create a single computational code incorporating methods that can model both rarefied and continuum flow to enable the efficient simulation of flow about space craft and high altitude hypersonic aerospace vehicles. The code was to use a single grid structure that permits a smooth transition between the continuum and rarefied portions of the flow. Developing an appropriate computational boundary between the two regions represented a major challenge. The primary approach chosen involves coupling a four-speed Lattice Boltzmann model for the continuum flow with the DSMC method in the rarefied regime. We also explored the possibility of using a standard finite difference Navier Stokes solver for the continuum flow. With the resulting code we will ultimately investigate three-dimensional plume impingement effects, a subject of critical importance to NASA and related to the work of Drs. Forrest Lumpkin, Steve Fitzgerald and Jay Le Beau at Johnson Space Center. Below is a brief background on the project and a summary of the results as of the end of the grant.

Goldstein, David B.↗

NASA NTRS1993

Two-dimensional CFD modeling of wave rotor flow dynamics

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

Welch, Gerard E.↗

NASA NTRS1994

Two-dimensional CFD modeling of wave rotor flow dynamics

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Welch, Gerard E.↗

DOE OSTI2020

Direct numerical simulations of turbulent reacting flows with shock waves and stiff chemistry using many-core/GPU acceleration

Compressible reacting flows may display sharp spatial variation related to shocks, contact discontinuities or reactive zones embedded within relatively smooth regions. The presence of such phenomena emphasizes the relevance of shock-capturing schemes such as the weighted essentially non-oscillatory (WENO) scheme as an essential ingredient of the numerical solver. However, these schemes are complex and have more computational cost than the simple high-order compact or non-compact schemes. In this paper, we present the implementation of a seventh-order, minimally-dissipative mapped WENO (WENO7M) scheme in a newly developed direct numerical simulation (DNS) code called KAUST Adaptive Reactive Flows Solver (KARFS). In order to make efficient use of the computer resources and reduce the solution time, without compromising the resolution requirement, the WENO routines are accelerated via graphics processing unit (GPU) computation. The performance characteristics and scalability of the code are studied using different grid sizes and block decomposition. Furthermore, the performance portability of KARFS is demonstrated on a variety of architectures including NVIDIA Tesla P100 GPUs and NVIDIA Kepler K20X GPUs. In addition, the capability and potential of the newly implemented WENO7M scheme in KARFS to perform DNS of compressible flows is also demonstrated with model problems involving shocks, isotropic turbulence, detonations and flame propagation into a stratified mixture with complex chemical kinetics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Hybrid Optimization Software Suite

The hybrid optimization software suite (HOSS) is a general purpose fully 2D/3D parallel combined finite discrete element (FDEM) code that can be used to simulate problems involving fracture and fragmentation processes, large deformation and large rotations, discrete particle systems, solid-fluid interaction in hydro fracture problems, etc. HOSS uses a hybrid approach that combines finite-element and discrete-element methods with a novel computational fluid dynamics solver. The finite-element method is often used to analyze a material or object and how it responds to stress. The discrete-element method analyzes stresses and displacements in a volume containing a large number of particles, such as grains of sand. Fluid dynamics analyzes the fluid flow inside, around, or through solid domains. With these processes combined, HOSS represents a paradigm shift when it comes to generating accurate simulations of material deformations and failure. HOSS can perform the following: Resolves problems that consist of millions of deforming fracturing, and interacting solid particles; Requires no coupling—it naturally integrates with all regimes of fluid flow; Resolves all regimes of fluid flow, such as Stokes, low/high Reynolds, subsonic/transonic/supersonic/hypersonic, compressible/incompressible, viscid/inviscid, Newtonian/Non-Newtonian and turbulent/laminar flow; Combines all flow regimes in the same solver; Numerically stable for all flow regimes; Naturally combines different flow regimes in the same problem; Possesses material library for fluid behavior; Naturally matches fluid solver to solid solver; Includes non-inertial Eulerian formulation for fluids; Uses highly efficient parallel computing based on the Virtual Parallel Machine, thus enabling easy porting between different parallel architectures, including possible future architectures; Designed specifically for multi-physics problems in research and industry in virtual experimentation format, thereby complementing both theoretical-computational and experimental tools; Can be extended to address millions of deforming solid particles immersed in fluid flowing at all regimes; Can be extended to address biological applications, such as modeling bone fracture or red blood cells in blood plasma

Knight, Earl E.↗

DOE OSTI2015

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

Here, an 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.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

A semi-direct procedure using a local relaxation factor and its application to an internal flow problem

Generally, fast direct solvers are not directly applicable to a nonseparable elliptic partial differential equation. This limitation, however, is circumvented by a semi-direct procedure, i.e., an iterative procedure using fast direct solvers. An efficient semi-direct procedure which is easy to implement and applicable to a variety of boundary conditions is presented. The current procedure also possesses other highly desirable properties, i.e.: (1) the convergence rate does not decrease with an increase of grid cell aspect ratio, and (2) the convergence rate is estimated using the coefficients of the partial differential equation being solved.

Chang, S. C.↗