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NASA NTRS1999

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

White, J. A.↗

NASA NTRS1999

X-33 Aerodynamic and Aeroheating Computations for Wind Tunnel and Flight Conditions

This report provides an overview of hypersonic Computational Fluid Dynamics research conducted at the NASA Langley Research Center to support the Phase II development of the X-33 vehicle. The X-33, which is being developed by Lockheed-Martin in partnership with NASA, is an experimental Single-Stage-to-Orbit demonstrator that is intended to validate critical technologies for a full-scale Reusable Launch Vehicle. As part of the development of the X-33, CFD codes have been used to predict the aerodynamic and aeroheating characteristics of the vehicle. Laminar and turbulent predictions were generated for the X 33 vehicle using two finite- volume, Navier-Stokes solvers. Inviscid solutions were also generated with an Euler code. Computations were performed for Mach numbers of 4.0 to 10.0 at angles-of-attack from 10 deg to 48 deg with body flap deflections of 0, 10 and 20 deg. Comparisons between predictions and wind tunnel aerodynamic and aeroheating data are presented in this paper. Aeroheating and aerodynamic predictions for flight conditions are also presented.

Hollis, Brian R.↗

NASA NTRS2003

Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue

Models of gas bubble dynamics employed in probabilistic analyses of decompression sickness incidence in man must be theoretically consistent and simple, if they are to yield useful results without requiring excessive computations. They are generally formulated in terms of ordinary differential equations that describe diffusion-limited gas exchange between a gas bubble and the extravascular tissue surrounding it. In our previous model (Ann. Biomed. Eng. 30: 232-246, 2002), we showed that with appropriate representation of sink pressures to account for gas loss or gain due to heterogeneous blood perfusion in the unstirred diffusion region around the bubble, diffusion-limited bubble growth in a tissue of finite volume can be simulated without postulating a boundary layer across which gas flux is discontinuous. However, interactions between two or more bubbles caused by competition for available gas cannot be considered in this model, because the diffusion region has a fixed volume with zero gas flux at its outer boundary. The present work extends the previous model to accommodate interactions among multiple bubbles by allowing the diffusion region volume of each bubble to vary during bubble evolution. For given decompression and tissue volume, bubble growth is sustained only if the bubble number density is below a certain maximum.

Evaluation Studies↗

NASA NTRS1997

Hypersonic Flow Computations on Unstructured Meshes

A method for computing inviscid hypersonic flow over complex configurations using unstructured meshes is presented. The unstructured grid solver uses an edge{based finite{volume formulation. Fluxes are computed using a flux vector splitting scheme that is capable of representing constant enthalpy solutions. Second{order accuracy in smooth flow regions is obtained by linearly reconstructing the solution, and stability near discontinuities is maintained by locally forcing the scheme to reduce to first-order accuracy. The implementation of the algorithm to parallel computers is described. Computations using the proposed method are presented for a sphere-cone configuration at Mach numbers of 5.25 and 10.6, and a complex hypersonic re-entry vehicle at Mach numbers of 4.5 and 9.8. Results are compared to experimental data and computations made with established structured grid methods. The use of the solver as a screening tool for rapid aerodynamic assessment of proposed vehicles is described.

Bibb, K. L.↗

NASA NTRS2004

Testing the PV-Theta Mapping Technique in a 3-D CTM Model Simulation

Mapping lower stratospheric ozone into potential vorticity (PV)- potential temperature (Theta) coordinates is a common technique employed to analyze sparse data sets. Ozone transformed into a flow-following dynamical coordinate system is insensitive to meteorological variations. Therefore data from a wide range of times/locations can be compared, so long as the measurements were made in the same airmass (as defined by PV). Moreover, once a relationship between ozone and PV/Theta is established, a full 3D ozone field can be estimated from this relationship and the 3D analyzed PV field. However, ozone data mapped in this fashion can be hampered by noisy PV fields, or "mis-matches" in the resolution and/or exact location of the ozone and PV measurements. In this study, we investigate the PV-ozone relationship using output from a recent 50-year run of the Goddard 3D chemical transport model (CTM). Model constituents are transported using off-line dynamics from the finite volume general circulation model (FVGCM). By using the internally consistent model PV and ozone fields, we minimize noise due to mis-matching and resolution issues. We calculate correlations between model ozone and PV throughout the stratosphere, and test the sensitivity of the technique to initial data resolution. To do this we degrade the model data to that of various satellite instruments, then compare the mapped fields derived from the sub-sampled data to the full resolution model data. With these studies we can determine appropriate limits for the PV-theta mapping technique in latitude, altitude, and as a function of original data resolution.

Frith, Stacey M.↗

NASA NTRS1997

Multi-Body Analysis of a Tiltrotor Configuration

The paper describes the aeroelastic analysis of a tiltrotor configuration. The 1/5 scale wind tunnel semispan model of the V-22 tiltrotor aircraft is considered. The analysis is performed by means of a multi-body code, based on an original formulation. The differential equilibrium problem is stated in terms of first order differential equations. The equilibrium equations of every rigid body are written, together with the definitions of the momenta. The bodies are connected by kinematic constraints, applied in form of Lagrangian multipliers. Deformable components are mainly modelled by means of beam elements, based on an original finite volume formulation. Multi-disciplinar problems can be solved by adding user-defined differential equations. In the presented analysis the equations related to the control of the swash-plate of the model are considered. Advantages of a multi-body aeroelastic code over existing comprehensive rotorcraft codes include the exact modelling of the kinematics of the hub, the detailed modelling of the flexibility of critical hub components, and the possibility to simulate steady flight conditions as well as wind-up and maneuvers. The simulations described in the paper include: 1) the analysis of the aeroelastic stability, with particular regard to the proprotor/pylon instability that is peculiar to tiltrotors, 2) the determination of the dynamic behavior of the system and of the loads due to typical maneuvers, with particular regard to the conversion from helicopter to airplane mode, and 3) the stress evaluation in critical components, such as the pitch links and the conversion downstop spring.

Ghiringhelli, G. L.↗

NASA NTRS1998

On Some Numerical Dissipation Schemes

Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.

Swanson, R. C.↗

NASA NTRS2004

Computation of Tone Noises Generated in Viscous Flows

Three benchmark problems from the current and previous CAA workshops involving tone noise generated in viscous flows are investigated using the CE/SE finite volume method. The CE/SE method is first briefly reviewed. Then, the benchmark problems, namely, flow past a single cylinder (CAA Workshop II problem), flow past twin cylinders (from the current CAA Workshop IV, Category 5, Problem 1) and flow past a deep cavity with overhang (CAA Workshop III problem) are investigated. Generally good results are obtained in comparison with the experimental data.

Loh, Ching Y.↗

NASA NTRS2004

A Fast Upwind Solver for the Euler Equations on Three-Dimensional Unstructured Meshes

An upwind scheme is presented for solving the three-dimensional Euler equations on unstructured tetrahedral meshes. Spatial discretization is accomplished by a cell-centered finite-volume formulation using flux-difference splitting. Higher-order differences are formed by a novel cell reconstruction process which results in computational times per cell comparable to those of structured codes. The approach yields highly resolved solutions in regions of smooth flow while avoiding oscillations across shocks without explicit limiting. Solutions are advanced in time by a 3-stage Runge-Kutta time-stepping scheme with convergence accelerated to steady state by local time stepping and implicit residual smoothing. Solutions are presented for a range of configurations in the transonic speed regime to demonstrate code accuracy, speed, and robustness. The results include an assessment of grid sensitivity and convergence acceleration by mesh sequencing.

Frink, Neal T.↗

NASA NTRS2004

Stratospheric Impact of Varying Sea Surface Temperatures

The Finite-Volume General Circulation Model (FVGCM) has been run in 50 year simulations with the: 1) 1949-1999 Hadley Centre sea surface temperatures (SST), and 2) a fixed annual cycle of SSTs. In this presentation we first show that the 1949-1999 FVGCM simulation produces a very credible stratosphere in comparison to an NCEP/NCAR reanalysis climatology. In particular, the northern hemisphere has numerous major and minor stratospheric warming, while the southern hemisphere has only a few over the 50-year simulation. During the northern hemisphere winter, temperatures are both warmer in the lower stratosphere and the polar vortex is weaker than is found in the mid-winter southern hemisphere. Mean temperature differences in the lower stratosphere are shown to be small (less than 2 K), and planetary wave forcing is found to be very consistent with the climatology. We then will show the differences between our varying SST simulation and the fixed SST simulation in both the dynamics and in two parameterized trace gases (ozone and methane). In general, differences are found to be small, with subtle changes in planetary wave forcing that lead to reduced temperatures in the SH and increased temperatures in the NH.

Newman, Paul A.↗

NASA NTRS2004

Sensitivity of the FVGCM to Changes in Ozone

We have carried out an experiment with the finite volume general circulation model (FVGCM). This experiment consisted of two different imposed changes in the climatological ozone fields assumed in the radiation code. for conditions with no significant ozone hole. This distribution was obtained from a 50-year simulation of the full stratospheric ozone chemistry, with a time-dependent chlorine loading, done with our off-line chemical transport model (CTM). Three years (1978-1980) of this simulation were averaged to form a monthly, zonal-mean ozone distribution that was used in the 20-year integration of the FVGCM for "unperturbed" conditions. The second 20-year GCM integration included a fully-developed ozone hole. This ozone distribution was from three years, 1998-2000, from the same CTM simulation. The goal of this work is to determine the coupled response of the chemistry and dynamics of the stratosphere. These experiments are the first step in understanding the coupled response. An important initial question concerns the significance of the signals: if 20-year integrations turn out to be too short, the runs will be extended.

Stolarski↗

NASA NTRS2004

Computation of Tone Noises Generated in Viscous Flows

Loh, Ching Y.↗

NASA NTRS2004

Computational Analysis of Gravitational Effects in Low-Density Gas Jets

This study deals with the computational analysis of buoyancy-induced instability in the nearfield of an isothermal helium jet injected into quiescent ambient air environment. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. The jet Richardson numbers of 1.5 and 0.018 were considered to encompass both buoyant and inertial jet flow regimes. Buoyancy effects were isolated by initiating computations in Earth gravity and subsequently, reducing gravity to simulate the microgravity conditions. Computed results concur with experimental observations that the periodic flow oscillations observed in Earth gravity subside in microgravity.

Satti, Rajani P.↗

NASA NTRS2004

Numerical Simulations of Buoyancy Effects in low Density Gas Jets

This paper deals with the computational analysis of buoyancy effects in the near field of an isothermal helium jet injected into quiescent ambient air environment. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. An orthogonal system with non-uniform grids was used to capture the instability phenomena. Computations were performed for Earth gravity and during transition from Earth to different gravitational levels. The flow physics was described by simultaneous visualizations of velocity and concentration fields at Earth and microgravity conditions. Computed results were validated by comparing with experimental data substantiating that buoyancy induced global flow oscillations present in Earth gravity are absent in microgravity. The dependence of oscillation frequency and amplitude on gravitational forcing was presented to further quantify the buoyancy effects.

Satti, R. P.↗

NASA NTRS2005

Effects of Aerosol on Atmospheric Dynamics and Hydrologic Processes during Boreal Spring and Summer

Global and regional climate impacts of present-day aerosol loading during boreal spring are investigated using the NASA finite volume General Circulation Model (fvGCM). Three-dimensional distributions of loadings of five species of tropospheric aerosols, i.e., sulfate, black carbon, organic carbon, soil dust, and sea salt are prescribed from outputs of the Goddard Ozone Chemistry Aerosol Radiation and Transport model (GOCART). The aerosol loadings are used to calculate the extinction coefficient, single scattering albedo, and asymmetric factor at eleven spectral wavelengths in the radiative transfer code. We find that aerosol-radiative forcing during boreal spring excites a wavetrain-like pattern in tropospheric temperature and geopotential height that emanates from Northern Africa, through Eurasia, to northeastern Pacific. Associated with the teleconnection is strong surface cooling over regions with large aerosol loading, i.e., China, India, and Africa. Low-to-mid tropospheric heating due to shortwave absorption is found in regions with large loading of dust (Northern Africa, and central East Asia), and black carbon (South and East Asia). In addition pronounced surface cooling is found over the Caspian Sea and warming over Eurasian and northeastern Asia, where aerosol loadings are relatively low. These warming and cooling are components of teleconnection pattern produced primarily by atmospheric heating from absorbing aerosols, i.e., dust from North Africa and.black carbon from South and East Asia. Effects of aerosols on atmospheric hydrologic cycle in the Asian monsoon region are also investigated. Results show that absorbing aerosols, i.e., black carbon and dust, induce large-scale upper-level heating anomaly over the Tibetan Plateau in April and May, ushering in an early onset of the Indian summer monsoon. Absorbing aerosols also enhance lower-level heating and anomalous ascent over northern India, intensifying the Indian monsoon. Overall, the aerosol-induced large-scale surface temperature cooling leads to a reduction of monsoon rainfall over the East Asia continent, and adjacent oceanic regions.

Lau, William K. M.↗

NASA NTRS2005

Coupled fvGCM-GCE Modeling System, 3D Cloud-Resolving Model and Cloud Library

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional singlecolumn models in simulating various types of clouds and cloud systems from Merent geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloudscale model (termed a super-parameterization or multiscale modeling framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameteridon NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. A seed fund is available at NASA Goddard to build a MMF based on the 2D Goddard cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM). A prototype MMF in being developed and production nms will be conducted at the beginning of 2005. In this talk, I will present: (1) A brief review on GCE model and its applications on precipitation processes, (2) The Goddard MMF and the major difference between two existing MMFs (CSU MMF and Goddard MMF), (3) A cloud library generated by Goddard MMF, and 3D GCE model, and (4) A brief discussion on the GCE model on developing a global cloud simulator.

Tao, Wei-Kuo↗

NASA NTRS2004

Coupled fvGCM-GCE Modeling System, TRMM Latent Heating and Cloud Library

Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that cloud-resolving models (CRMs) agree with observations better than traditional single-column models in simulating various types of clouds and cloud systems from different geographic locations. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a super-parameterization or multi-scale modeling framework, MMF) to use these satellite data to imiprove the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign cloud related datasets can provide initial conditions as well as validation for both the MMF and CRMs. A seed fund is available at NASA Goddard to build a MMF based on the 2D GCE model and the Goddard finite volume general circulation model (fvGCM). A prototype MMF will be developed by the end of 2004 and production runs will be conducted at the beginning of 2005. The purpose of this proposal is to augment the current Goddard MMF and other cloud modeling activities. I this talk, I will present: (1) A summary of the second Cloud Modeling Workshop took place at NASA Goddard, (2) A summary of the third TRMM Latent Heating Workshop took place at Nara Japan, (3) A brief discussion on the Goddard research plan of using Weather Research Forecast (WRF) model, and (4) A brief discussion on the GCE model on developing a global cloud simulator.

Tao, Wei-Kuo↗

NASA NTRS2004

Age and Pathway Diagnostics for a Stratospheric General Circulation Model

Using a variety of age diagnostic experiments we examine the stratospheric age spectrum of the Goddard Finite Volume Generd Circulation Model. Pulse tracer release age-of-air computations are compared to forward and backward trajectory computations. These comparisons show good agreement, and the age-of-air also compares well with observed long lived tracers. Pathway diagnostics show how air arrives in the lowermost stratosphere and the age structure of that region. Using tracers with different lifetimes we can estimate the age spectrum - this technique should be useful in diagnosing transport from various trace gas observations.

Schoeberl, Mark R.↗