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At least 217 records · Page 12

Comparative Study of Advanced Turbulence Models for Turbomachinery

A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).

Hadid, Ali H.↗

CFD flowfield simulation of Delta Launch Vehicles in a power-on configuration

This paper summarizes recent work at McDonnell Douglas Aerospace (MDA) to develop and validate computational fluid dynamic (CFD) simulations of under expanded rocket plume external flowfields for multibody expendable launch vehicles (ELVs). Multi engine reacting gas flowfield predictions of ELV base pressures are needed to define vehicle base drag and base heating rates for sizing external nozzle and base region insulation thicknesses. Previous ELV design programs used expensive multibody power-on wind tunnel tests that employed chamber/nozzle injected high pressure cold or hot-air. Base heating and pressure measurements were belatedly made during the first flights of past ELV's to correct estimates from semi-empirical engineering models or scale model tests. Presently, CFD methods for use in ELV design are being jointly developed at the Space Transportation Division (MDA-STD) and New Aircraft Missiles Division (MDA-NAMD). An explicit three dimensional, zonal, finite-volume, full Navier-Stokes (FNS) solver with finite rate hydrocarbon/air and aluminum combustion kinetics was developed to accurately compute ELV power-on flowfields. Mississippi State University's GENIE++ general purpose interactive grid generation code was chosen to create zonal, finite volume viscous grids. Axisymmetric, time dependent, turbulent CFD simulations of a Delta DSV-2A vehicle with a MB-3 liquid main engine burning RJ-1/LOX were first completed. Hydrocarbon chemical kinetics and a k-epsilon turbulence model were employed and predictions were validated with flight measurements of base pressure and temperature. Zonal internal/external grids were created for a Delta DSV-2C vehicle with a MB-3 and three Castor-1 solid motors burning and a Delta-2 with an RS-27 main engine (LOX/RP-1) and 9 GEM's attached/6 burning. Cold air, time dependent FNS calculations were performed for DSV-2C during 1992. Single phase simulations that employ finite rate hydrocarbon and aluminum (solid fuel) combustion chemistry are currently in progress. Reliable and efficient Eulerian algorithms are needed to model two phase (solid-gas) momentum and energy transfer mechanisms for solid motor fuel combustion products.

Pavish, D. L.↗

Unsteady vortex-dominated flows around maneuvering wings over a wide range of Mach numbers

The problem of unsteady flow around maneuvering wings is solved using the unsteady Euler equations. The unsteady conservative Euler equations are derived for the flow relative motion with respect to a moving (translating and rotating) frame of reference. The resulting equations can handle the most general case for unsteady three-dimensional flow around maneuvering wings or wing-body configurations undergoing six degrees of freedom motion; three translations and three rotations. The equations are solved using two computational schemes; an explicit multistage finite-volume scheme and an implicit approximately factored finite-volume scheme. The computational applications cover two cases. The first case is for a locally conical supersonic flow of rolling oscillation of a sharp-edged delta wing at zero angle of attack. The second case is for a pitching oscillation around a mean angle of attack of a NACA 0012 airfoil in transonic flow.

Kandil, Osama A.↗

Progress in multi-dimensional upwind differencing

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

Vanleer, Bram↗

DAO's Next Generation Physical-Space/Finite-Volume Data Assimilation System: Formulation and Initial Evaluation

The Physical-space/Finite-volume Data Assimilation System (fvDAS) is the next generation global atmospheric data assimilation system in development at the Data Assimilation Office at NASA's Goddard Space Flight Center. It is based on a new finite-volume general circulation model jointly developed by NASA and NCAR, and on the Physical-Space Statistical Analysis System (PSAS) developed at the DAO. In this talk we will describe the general system formulation, the adaptive quality control and general aspects of the error covariance modeling. The NASA-NCAR GCM is a completely new model which replaces the CEOs GCM used in the previous GEOS-1/2/3 Data Assimilation systems. A particular configuration of adaptive Statistical Quality Control and the Physical-space Statistical Analysis System (PSAS) are currently implemented in DAO's operational Data Assimilation System. However, the unique finite-volume formulation of the NASA-NCAR GCM, combined with the generality of the observation-space formulation of PSAS, provides for a very simple and accurate model-analysis interface. The system assimilates a variety of conventional and satellite observations. In particular, TOVS Level 1B radiances are assimilated using a 1-D variational scheme, both in clear sky and cloudy conditions. Computationally, the fvDAS runs approximately 10 times faster than the operational GEOS-Terra system. We will show that the next-generation fvDAS has much improved observation-minus-6hr forecast (O-F) statistics, as well as 5-day forecast skills. Top of the atmosphere radiation fields are in closer agreement with CERES measurements, with realistic precipitation and moisture fields. We will also show that the finite-volume formulation of the fvDAS produce assimilated fields which are more suitable for driving constituent transport models.

daSilva, A.↗

Computational methods for vortex dominated compressible flows

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

Murman, Earll M.↗

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↗

Efficient computation of volume in flow predictions

An efficient method for calculating cell volumes for time-dependent three-dimensional flow predictions by finite volume calculations is presented. Eight arbitrary corner points are considered and the shape face is divided into two planar triangles. The volume is then dependent on the orientation of the partitioning. In the case of a hexahedron, it is noted that any open surface with a boundary that is a closed curve possesses a surface vector independent of the surface shape. Expressions are defined for the surface vector, which is independent of the partitioning surface diagonal used to quantify the volume. Using a decomposition of the cell volume involving two corners, with each the vertex of three diagonals and six corners which are vertices of one diagonal, gives portions which are tetrahedra. The resultant mesh is can be used for time-dependent finite volume calculations one requires less computer time than previous methods.

Vinokur, M.↗

A 3-D upwind Euler solver for unstructured meshes

A three-dimensional finite-volume upwind Euler solver is developed for unstructured meshes. The finite-volume scheme solves for solution variables at vertices of the mesh and satisfies the integral conservation law on nonoverlapping polyhedral control volumes surrounding vertices of the mesh. The schene achieves improved solution accuracy by assuming a piecewise linear variation of the solution in each control volume. This improved spatial accuracy hinges heavily upon the calculation of the solution gradient in each control volume given pointwise values of the solution at vertices of the mesh. Several algorithms are discussed for obtaining these gradients. Details concerning implementation procedures and data structures are discussed. Sample calculations for inviscid Euler flow about isolated aircraft wings at subsonic and transonic speeds are compared with established Euler solvers as well as experiment.

Barth, Timothy J.↗

Free-Stream-Capturing Metrics

Report summarizes techniques for preservation of free-stream flows in finite-volume and finite-difference flow computations involving transformations between moving and stationary coordinates. Techniques necessary for accurate computations of complicated flows; such as, computing flow about helicopter rotor by use of grid conforming to and moving with rotor blades.

Obayashi, Shigeru↗

A comparison of two formulations for high-order accurate essentially non-oscillatory schemes

The finite-volume and finite-difference implementations of high-order accurate essentially nonoscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

Casper, J.↗

A comparison of two formulations for high-order accurate essentially non-oscillatory schemes

The finite-volume and finite-difference implementations of high-order accurate essentially non-oscillatory shock-capturing schemes are discussed and compared. Results obtained with fourth-order accurate algorithms based on both formulations are examined for accuracy, sensitivity to grid irregularities, resolution of waves that are oblique to the mesh, and computational efficiency. Some algorithm modifications that may be required for a given application are suggested. Conclusions that pertain to the relative merits of both formulations are drawn, and some circumstances for which each might be useful are noted.

Casper, Jay↗

2-D/Axisymmetric Formulation of Multi-dimensional Upwind Scheme

A multi-dimensional upwind discretization of the two-dimensional/axisymmetric Navier-Stokes equations is detailed for unstructured meshes. The algorithm is an extension of the fluctuation splitting scheme of Sidilkover. Boundary conditions are implemented weakly so that all nodes are updated using the base scheme, and eigen-value limiting is incorporated to suppress expansion shocks. Test cases for Mach numbers ranging from 0.1-17 are considered, with results compared against an unstructured upwind finite volume scheme. The fluctuation splitting inviscid distribution requires fewer operations than the finite volume routine, and is seen to produce less artificial dissipation, leading to generally improved solution accuracy.

Wood, William A.↗

Finite Element Method for Capturing Ultra-relativistic Shocks

While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.

Richardson, G. A.↗

Tropical Diabatic Heating and the Role of Convective Processes as Represented in Several Contemporary Climate Models

One of the most fundamental properties of the global heat balance is the net heat input into the tropical atmosphere that helps drive the planetary atmospheric circulation. Although broadly understood in terms of its gross structure and balance of source / sink terms, incorporation of the relevant processes in predictive models is still rather poor. The work reported here examines the tropical radiative and water cycle behavior as produced by four contemporary climate models. Among these are the NSIPP-2 (NASA Seasonal to Interannual Prediction Project) which uses the RAS convective parameterization; the FVCCM, a code using finite volume numerics and the CCM3.6 physics; FVCCM-MCRAS again having the finite volume numerics, but MCRAS convective parameterization and a different radiation treatment; and, finally, the NCEP GSM which uses the RAS. Using multi-decadal integrations with specified SSTs we examine the statistics of radiative / convective processes and associated energy transports, and then estimate model energy flux sensitivities to SST changes. In particular the behavior of the convective parameterizations is investigated. Additional model integrations are performed specifically to assess the importance representing convective inhibition in regulating convective cloud-top structure and moisture detrainment as well as controlling surface energy fluxes. To evaluate the results of these experiments, a number of satellite retrievals are used: TRMM retrievals of vertical reflectivity structure, rainfall rate, and inferred diabatic heating are analyzed to show both seasonal and interannual variations in vertical structure of latent heat release. Top-of-atmosphere radiative fluxes from ERBS and CERES are used to examine shortwave and longwave cloud forcing and to deduce required seasonal energy transports. Retrievals of cloud properties from ISCCP and water vapor variations from SSM/T-2 are also used to understand behavior of the humidity fields. These observations are supplemented with output form the DOE Reanalysis-2.

Robertson, Franklin R.↗

High-Order Stabilized Finite Elements on Dynamic Meshes

The development of dynamic mesh capability for turbulent flow simulations using the Streamlined Upwind Petrov-Galerkin (SUPG) discretization is described. The current work extends previous research to include high-order spatial accuracy, including the satisfaction of the discrete geometric conservation law (GCL) on curved elements. Two closely-related schemes are described and the ability of these schemes to satisfy the GCL, while also maintaining temporal accuracy and conservation is assessed. Studies indicate that although one scheme discretizes the time derivative in conservative form, both schemes exhibit temporal conservation errors that decrease according to the expected design order of accuracy. The source of the temporal conservation errors is examined, and it is demonstrated that many finite-volume and finite-element schemes can also be expected to have difficulty strictly satisfying conservation in time. The effects on conservation are examined and, while present in the simulations, are seen to be negligible for the problems considered.

Anderson, W. Kyle↗

Development of the Joint NASA/NCAR General Circulation Model

The Data Assimilation Office at NASA/Goddard Space Flight Center is collaborating with NCAR/CGD in an ambitious proposal for the development of a unified climate, numerical weather prediction, and chemistry transport model which is suitable for global data assimilation of the physical and chemical state of the Earth's atmosphere. A prototype model based on the NCAR CCM3 physics and the NASA finite-volume dynamical core has been built. A unique feature of the NASA finite-volume dynamical core is its advanced tracer transport algorithm on the floating Lagrangian control-volume coordinate. The model currently has a highly idealized ozone production/loss chemistry derived from the observed 2D (latitude-height) climatology of the recent decades. Nevertheless, the simulated horizontal wave structure of the total ozone is in good qualitative agreement with the observed (TOMS). Long term climate simulations and NWP experiments have been carried out. Current up to date status and futur! e plan will be discussed in the conference.

Lin, S.-J.↗

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Bart, Timothy J.↗