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At least 577 records · Page 32

Unstructured-grid large-eddy simulation of flow over an airfoil

Historically, large-eddy simulations (LES) have been restricted to simple geometries where spectral or finite difference methods have dominated due to their efficient use of structured grids. Structured grids, however, not only difficulty representing complex domains and adapting to complicated flow features, but also are rather inefficient for simulating flows at high Reynolds numbers. The lack of efficiency stems from the need to resolve the viscous sublayer, which requires very fine resolution in all three directions near the wall. Structured grids make use of a stretching to reduce the normal grid spacing but must carry the fine resolution in the streamwise and spanwise directions throughout the domain. The unnecessarily fine grid for much of the domain leads to disturbingly high grid estimates. Chapman (1979), and later Moin & Jimenez (1993), pointed out that, in order to advance the technology to airfoils at flight Reynolds numbers, structured grids must be abandoned in lieu of what are known as nested or unstructured grids. The finite element method can efficiently solve the Navier-Stokes equations on unstructured grids. Although the CPU cost per time step per element is somewhat higher than structured grid methods, this effect is more than offset by the reduction in the number of elements. The use of unstructured grids, coupled with the advances in dynamic subgrid-scale modeling such as those made by Germano et al. (1991) and Ghosal et al. (1994), make LES of an airfoil tractable. We have chosen the NACA 4412 airfoil at maximum lift as the first simulation since this flow has not been successfully simulated with the Reynolds-averaged Navier-Stokes equations.

Jansen, Kenneth↗

Alternating Direct Current (ADC) - A New Form of Efficient Energy Transmission for Renewable Sources

The prevailing means of electricity transmission through Direct Current (DC) and Alternating Current (AC) have limitations with the ongoing transition to renewable energy sources. In this paper, we discuss a new form of energy transmission, known as alternating direct current (ADC) that would provide significant savings in energy consumption and simultaneously allow efficient utilization of generated energy from renewable sources. This has become possible due to substantial advances in electronics and optoelectronics technologies since the days of Nicholas Tesla and Thomas Edison. Recent efforts of implementing the proposed ADC technology in relevant environments have demonstrated significant energy savings and opened a new paradigm that has the potential to provide an efficient and cost-effective pathway for transition to renewable energy sources even with the existing grid infrastructure. The DC power utilization initiated by Thomas Edison can be stored in battery arrangement but suffers from line loss and hence is not efficient for long-distance transmission. However, AC power developed by Nicholas Tesla cannot be stored efficiently but can be transmitted over long distances due to significantly lower line losses. Currently, AC power is the global foundational energy transmission methodology used because of events that took place over 135 years ago involving Edison, Tesla, and Westinghouse, and since AC power can transmit long distances from power plants to end users efficiently and economically. Approximately 50 years ago, the introduction of semiconductors in commercialized electronic devices and products changed the way people consume electricity. Also, over the years, the expanding adaptation of nonlinear loads has adversely affected the grid stability and hence the utility infrastructures worldwide.

AC↗

Simulations of Cryogenic Line Chilldown with Advanced Sub-Grid Wall Boiling Models

A meso-scale model developed at MIT [2][11] for boiling processes in water was adapted for cryogens and demonstrated for chilldown of propellant transfer lines in both liquid nitrogen and hydrogen. The sub-grid boiling model accurately captures the contributions to heat transfer from the generation of bubble nuclei, growth, and interaction of the bubbles in the microlayer as well as quenching of the boiling surface following bubble departure. It was adapted for cryogenic fluids using thermodynamic scaling concepts taking into account non-dimensional pressures and temperatures that are scaled by the corresponding critical values for the fluid. The boiling model was demonstrated for line chilldown in liquid nitrogen (Darr et al. [6]). The predicted wall temperature at which quenching occurs was close to the test data while the slope of the temperature curve after quenching is initiated, showing a steeper variation than the test data. Simulations were also performed for liquid hydrogen by simulating experiments of Hartwig et al. [7]. Chilldown times in liquid hydrogen are much more rapid due to higher heat transfer in the film boiling regime and accounting for the higher turbulence levels were found to be important. Furthermore, at the much lower fluid temperatures in liquid hydrogen flows, accounting for the variable thermal properties of the solid material is critical and has a dramatic impact on the quench times. The need for additional studies to better understand the evolution of the quench front in liquid hydrogen was noted.

Computational Fluid Dynamics↗

Simulations of Cryogenic Line Chilldown with Advanced Sub-Grid Wall Boiling Models

A meso-scale model developed at MIT [2][11] for boiling processes in water was adapted for cryogens and demonstrated for chilldown of propellant transfer lines in both liquid nitrogen and hydrogen. The sub-grid boiling model accurately captures the contributions to heat transfer from the generation of bubble nuclei, growth, and interaction of the bubbles in the microlayer as well as quenching of the boiling surface following bubble departure. It was adapted for cryogenic fluids using thermodynamic scaling concepts taking into account non-dimensional pressures and temperatures that are scaled by the corresponding critical values for the fluid. The boiling model was demonstrated for line chilldown in liquid nitrogen (Darr et al. [6]). The predicted wall temperature at which quenching occurs was close to the test data while the slope of the temperature curve after quenching is initiated, showing a steeper variation than the test data. Simulations were also performed for liquid hydrogen by simulating experiments of Hartwig et al. [7]. Chilldown times in liquid hydrogen are much more rapid due to higher heat transfer in the film boiling regime and accounting for the higher turbulence levels were found to be important. Furthermore, at the much lower fluid temperatures in liquid hydrogen flows, accounting for the variable thermal properties of the solid material is critical and has a dramatic impact on the quench times. The need for additional studies to better understand the evolution of the quench front in liquid hydrogen was noted.

Computational Fluid Dynamics↗

A numerical investigation of the finite element method in compressible primitive variable Navier-Stokes flow

The results of a comprehensive numerical investigation of the basic capabilities of the finite element method (FEM) for numerical solution of compressible flow problems governed by the two-dimensional and axis-symmetric Navier-Stokes equations in primitive variables are presented. The strong and weak points of the method as a tool for computational fluid dynamics are considered. The relation of the linear element finite element method to finite difference methods (FDM) is explored. The calculation of free shear layer and separated flows over aircraft boattail afterbodies with plume simulators indicate the strongest assets of the method are its capabilities for reliable and accurate calculation employing variable grids which readily approximate complex geometry and capably adapt to the presence of diverse regions of large solution gradients without the necessity of domain transformation.

Cook, C. H.↗

Prediction of the Thrust Performance and the Flowfield of Liquid Rocket Engines

In an effort to improve the current solutions in the design and analysis of liquid propulsive engines, a computational fluid dynamics (CFD) model capable of calculating the reacting flows from the combustion chamber, through the nozzle to the external plume, was developed. The Space Shuttle Main Engine (SSME) fired at sea level, was investigated as a sample case. The CFD model, FDNS, is a pressure based, non-staggered grid, viscous/inviscid, ideal gas/real gas, reactive code. An adaptive upwinding differencing scheme is employed for the spatial discretization. The upwind scheme is based on fourth order central differencing with fourth order damping for smooth regions, and second order central differencing with second order damping for shock capturing. It is equipped with a CHMQGM equilibrium chemistry algorithm and a PARASOL finite rate chemistry algorithm using the point implicit method. The computed flow results and performance compared well with those of other standard codes and engine hot fire test data. In addition, the transient nozzle flowfield calculation was also performed to demonstrate the ability of FDNS in capturing the flow separation during the startup process.

Wang, T.-S.↗

Adaptive explicit and implicit finite element methods for transient thermal analysis

The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.

Probert, E. J.↗

Software systems used for unstructured grid generation at NASA Langley

These viewgraphs provide an overview of grid generation system for 3D configurations (Euler Grids) and grid generators of viscous and inviscid flow, solution adaptive for steady and unsteady flow. The five systems presented are VGRID, FELISA, TETRA, NGP, and TGRID.

Michael J Bockelie↗

Recent Progress on the Parallel Implementation of Moving-Body Overset Grid Schemes

Viscous calculations about geometrically complex bodies in which there is relative motion between component parts is one of the most computationally demanding problems facing CFD researchers today. This presentation documents results from the first two years of a CHSSI-funded effort within the U.S. Army AFDD to develop scalable dynamic overset grid methods for unsteady viscous calculations with moving-body problems. The first pan of the presentation will focus on results from OVERFLOW-D1, a parallelized moving-body overset grid scheme that employs traditional Chimera methodology. The two processes that dominate the cost of such problems are the flow solution on each component and the intergrid connectivity solution. Parallel implementations of the OVERFLOW flow solver and DCF3D connectivity software are coupled with a proposed two-part static-dynamic load balancing scheme and tested on the IBM SP and Cray T3E multi-processors. The second part of the presentation will cover some recent results from OVERFLOW-D2, a new flow solver that employs Cartesian grids with various levels of refinement, facilitating solution adaption. A study of the parallel performance of the scheme on large distributed- memory multiprocessor computer architectures will be reported.

Wissink, Andrew↗

Cyclotron Resonant Scattering Feature Simulations I. Thermally Averaged Cyclotron Scattering Cross Sections, Mean Free Photon-Path Tables, and Electron Momentum Sampling

Electron cyclotron resonant scattering features (CRSFs) are observed as absorption-like lines in the spectra of X-ray pulsars. A significant fraction of the computing time for Monte Carlo simulations of these quantum mechanical features is spent on the calculation of the mean free path for each individual photon before scattering, since it involves a complex numerical integration over the scattering cross section and the (thermal) velocity distribution of the scattering electrons. We aim to numerically calculate interpolation tables which can be used in CRSF simulations to sample the mean free path of the scattering photon and the momentum of the scattering electron. The tables also contain all the information required for sampling the scattering electron's final spin. The tables were calculated using an adaptive Simpson integration scheme. The energy and angle grids were refined until a prescribed accuracy is reached. The tables are used by our simulation code to produce artificial CRSF spectra. The electron momenta sampled during these simulations were analyzed and justified using theoretically determined boundaries. We present a complete set of tables suited for mean free path calculations of Monte Carlo simulations of the cyclotron scattering process for conditions expected in typical X-ray pulsar accretion columns (0.01 B/B(sub crit) is less than or equal to 0.12, where B(sub crit) = 4.413 x 1013 G, and 3 keV kBT 15 keV). The sampling of the tables is chosen such that the results have an estimated relative error of at most 1/15 for all points in the grid. The tables are available online (see link in footnote, page 1).

Schwarm, F.-W.↗

Unstructured grid large eddy simulation of wall bounded turbulent flows

Historically, large eddy simulations (LES) have been restricted to simple geometries where spectral or finite difference methods have dominated due to their efficient use of structured grids. Structured grids, however, not only have difficulty representing complex domains and adapting to complicated flow features, but also are rather inefficient for simulating flows at high Reynolds numbers. The lack of efficiency stems from the need to resolve the viscous sub layer which requires very fine resolution in all three directions near the wall. Structured grids make use of a stretching to reduce the normal grid spacing but must carry the fine resolution in the streamwise and spanwise directions throughout the domain. The unnecessarily fine grid for much of the domain leads to disturbingly high grid estimates. Chapman (1979), and later Moin & Jimenez (1993), pointed out that, in order to advance the technology to airfoils at flight Reynolds numbers, structured grids must be abandoned in lieu of what are known as nested or unstructured grids. We illustrate the ability of an unstructured mesh to refine only the near wall region. Note the large number of points near the wall (where the fine vortical features need better resolution) and the coarseness in all directions away from the wall (where the scales are much larger). The important difference between this approach and the usual structured grid stretching is that the number of elements used to discretize the spanwise and streamwise features of the flow is reduced in each successive layer coming off the wall. This is due to the fact that the elements not only grow in the normal direction, but in the other directions as well. This greatly reduces the total number of points or elements required for a given Reynolds number flow.

Jansen, Kenneth↗

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗

Verification of Anisotropic Mesh Adaptation for Complex Aerospace Applications

The stabilized finite element solver, FUN3D-SFE, along with the grid mechanics package refine are verified for aerospace applications of laminar and turbulent flow simulations. The current verification exercise represents an extension of previous research using FUN3D-SFEwith adjoint-based mesh adaptation to generate highly anisotropic adapted meshes for inviscid problems. Adaptations are performed using a solution-based approach that controls the Lpnorm of Mach number interpolation error and an adjoint-based approach that controls the error in some output functional. Adaptive results are shown for laminar subsonic flow over a delta wing, laminar subsonic flow over ONERA M6 wing, inviscid supersonic flow over a sonic boom test case, and a turbulent flow over a high lift configuration (JAXA Standard Model). Mesh convergence results are also compared with results from FUN3D-FV (Finite Volume) whenever available. For all test cases considered, FUN3D-SFE gives significantly better accurate results than FUN3D-FV on coarse meshes.

Aravind Balan↗

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗

Multigrid solution of the Euler equations on unstructured and adaptive meshes

A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structured multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.

Mavriplis, Dimitri↗

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Coirier, William J.↗