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At least 469 records · Page 26

Energy considerations in computational aeroacoustics

A finite-volume multistage time-stepping Euler code is used to investigate the use of CFD algorithms for the direct calculation of acoustics. The 2D compressible inviscid flow about an accelerating or decelerating circular cylinder is used as a model problem. The time evolution of the energy transfer from the cylinder to the fluid, as the cylinder is moved from rest to some nonnegligible velocity, is clearly seen. By examining the temporal and spatial characteristics of the numerical solution, a distinction can be made between the propagating acoustic energy, the convecting energy associated with the entropy change in the fluid, and the energy contained in the local aerodynamic field. Systematic variation of the cylinder acceleration shows that the radiated acoustic energy depends strongly upon the rate of acceleration or deceleration. The computational grid has a large effect on the ratio of acoustic energy to nonphysical entropy associated energy, while the role of the explicit artificial viscosity seems to be of second order. The entropy term was nearly negligible in all cases the cylinder was started slowly.

Brentner, Kenneth S.↗

Linkages between terrestrial ecosystems and the atmosphere

The primary research issue in understanding the role of terrestrial ecosystems in global change is analyzing the coupling between processes with vastly differing rates of change, from photosynthesis to community change. Representing this coupling in models is the central challenge to modeling the terrestrial biosphere as part of the earth system. Terrestrial ecosystems participate in climate and in the biogeochemical cycles on several temporal scales. Some of the carbon fixed by photosynthesis is incorporated into plant tissue and is delayed from returning to the atmosphere until it is oxidized by decomposition or fire. This slower (i.e., days to months) carbon loop through the terrestrial component of the carbon cycle, which is matched by cycles of nutrients required by plants and decomposers, affects the increasing trend in atmospheric CO2 concentration and imposes a seasonal cycle on that trend. Moreover, this cycle includes key controls over biogenic trace gas production. The structure of terrestrial ecosystems, which responds on even longer time scales (annual to century), is the integrated response to the biogeochemical and environmental constraints that develop over the intermediate time scale. The loop is closed back to the climate system since it is the structure of ecosystems, including species composition, that sets the terrestrial boundary condition in the climate system through modification of surface roughness, albedo, and, to a great extent, latent heat exchange. These separate temporal scales contain explicit feedback loops which may modify ecosystem dynamics and linkages between ecosystems and the atmosphere. The long-term change in climate, resulting from increased atmospheric concentrations of greenhouse gases (e.g., CO2, CH4, and nitrous oxide (N2O)) will further modify the global environment and potentially induce further ecosystem change. Modeling these interactions requires coupling successional models to biogeochemical models to physiological models that describe the exchange of water, energy, and biogenic trace gases between the vegetation and the atmosphere at fine time scales. There does not appear to be any obvious way to allow direct reciprocal coupling of atmospheric general circulation models (GCM's), which inherently run with fine time steps, to ecosystem or successional models, which have coarse temporal resolution, without the interposition of physiological canopy models. This is equally true for biogeochemical models of the exchange of carbon dioxide and trace gases. This coupling across time scales is nontrivial and sets the focus for the modeling strategy.

Bretherton, Francis↗

Scanning Backscatter Lidar Observations for Characterizing 4-D Cloud and Aerosol Fields to Improve Radiative Transfer Parameterizations

Clouds have a powerful influence on atmospheric radiative transfer and hence are crucial to understanding and interpreting the exchange of radiation between the Earth's surface, the atmosphere, and space. Because clouds are highly variable in space, time and physical makeup, it is important to be able to observe them in three dimensions (3-D) with sufficient resolution that the data can be used to generate and validate parameterizations of cloud fields at the resolution scale of global climate models (GCMs). Simulation of photon transport in three dimensionally inhomogeneous cloud fields show that spatial inhomogeneities tend to decrease cloud reflection and absorption and increase direct and diffuse transmission, Therefore it is an important task to characterize cloud spatial structures in three dimensions on the scale of GCM grid elements. In order to validate cloud parameterizations that represent the ensemble, or mean and variance of cloud properties within a GCM grid element, measurements of the parameters must be obtained on a much finer scale so that the statistics on those measurements are truly representative. High spatial sampling resolution is required, on the order of 1 km or less. Since the radiation fields respond almost instantaneously to changes in the cloud field, and clouds changes occur on scales of seconds and less when viewed on scales of approximately 100m, the temporal resolution of cloud properties should be measured and characterized on second time scales. GCM time steps are typically on the order of an hour, but in order to obtain sufficient statistical representations of cloud properties in the parameterizations that are used as model inputs, averaged values of cloud properties should be calculated on time scales on the order of 10-100 s. The Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE) provides exceptional temporal (100 ms) and spatial (30 m) resolution measurements of aerosol and cloud backscatter in three dimensions. HARLIE was used in a ground-based configuration in several recent field campaigns. Principal data products include aerosol backscatter profiles, boundary layer heights, entrainment zone thickness, cloud fraction as a function of altitude and horizontal wind vector profiles based on correlating the motions of clouds and aerosol structures across portions of the scan. Comparisons will be made between various cloud detecting instruments to develop a baseline performance metric.

Schwemmer, Geary K.↗

Stability of mixed time integration schemes for transient thermal analysis

A current research topic in coupled-field problems is the development of effective transient algorithms that permit different time integration methods with different time steps to be used simultaneously in various regions of the problems. The implicit-explicit approach seems to be very successful in structural, fluid, and fluid-structure problems. This paper summarizes this research direction. A family of mixed time integration schemes, with the capabilities mentioned above, is also introduced for transient thermal analysis. A stability analysis and the computer implementation of this technique are also presented. In particular, it is shown that the mixed time implicit-explicit methods provide a natural framework for the further development of efficient, clean, modularized computer codes.

Liu, W. K.↗

Computation of incompressible viscous flows through artificial heart devices with moving boundaries

The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.

Kiris, Cetin↗

3D Structured Grid Adaptation

Grid adaptation for structured meshes is the art of using information from an existing, but poorly resolved, solution to automatically redistribute the grid points in such a way as to improve the resolution in regions of high error, and thus the quality of the solution. This involves: (1) generate a grid vis some standard algorithm, (2) calculate a solution on this grid, (3) adapt the grid to this solution, (4) recalculate the solution on this adapted grid, and (5) repeat steps 3 and 4 to satisfaction. Steps 3 and 4 can be repeated until some 'optimal' grid is converged to but typically this is not worth the effort and just two or three repeat calculations are necessary. They also may be repeated every 5-10 time steps for unsteady calculations.

Banks, D. W.↗

Dynamics of Numerics & Spurious Behaviors in CFD Computations

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Yee, Helen C.↗

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Jothiprasad, Giridhar↗

Computer Modeling of the Earliest Cellular Structures and Functions

In the absence of extinct or extant record of protocells (the earliest ancestors of contemporary cells). the most direct way to test our understanding of the origin of cellular life is to construct laboratory models of protocells. Such efforts are currently underway in the NASA Astrobiology Program. They are accompanied by computational studies aimed at explaining self-organization of simple molecules into ordered structures and developing designs for molecules that perform proto-cellular functions. Many of these functions, such as import of nutrients, capture and storage of energy. and response to changes in the environment are carried out by proteins bound to membrane< We will discuss a series of large-scale, molecular-level computer simulations which demonstrate (a) how small proteins (peptides) organize themselves into ordered structures at water-membrane interfaces and insert into membranes, (b) how these peptides aggregate to form membrane-spanning structures (eg. channels), and (c) by what mechanisms such aggregates perform essential proto-cellular functions, such as proton transport of protons across cell walls, a key step in cellular bioenergetics. The simulations were performed using the molecular dynamics method, in which Newton's equations of motion for each item in the system are solved iteratively. The problems of interest required simulations on multi-nanosecond time scales, which corresponded to 10(exp 6)-10(exp 8) time steps.

Pohorille, Andrew↗

Analysis of three-dimensional unsteady flow around oscillating wings

A method based on the Navier-Stokes equations was developed for determining analytically the three-dimensional unsteady flow patterns around oscillating wings. The Helmholz vorticity transport equations were discretized in three-dimensional finite element form from a variational formulation and integrated numerically. At each time step of the numerical integration the velocity field was calculated from the representation of the three-dimensional wing by a system of optimized distribution of vortices in space. During the numerical integration of the vorticity transport equations the time-dependent boundary conditions on the wing were specified as external constraint conditions. Examples of obtained results describing the three-dimensional unsteady flow around a wing were presented.

Bratanow, T.↗

An analytical approach to airfoil icing

An analytical procedure has been developed to predict rime ice growth on unprotected airfoil sections and to evaluate the aerodynamic performance. A time stepping method is used in which: (1) water droplet trajectories are calculated, (2) a rime ice shape determined, (3) the flowfield around the iced airfoil is recalculated, and (4) the build-up process iterated upon until the desired icing time is reached. The performance of the iced airfoil shapes are then determined from existing analytic methods. Rime ice shapes determined in the NASA Lewis Icing Research Tunnel on a modified NACA 64 series airfoil agree well with the shapes predicted by the analytical method. Measured and predicted increases in drag due to the rime ice also agree favorably. A simplified scaling analysis is also presented and verified which provides the duplication of full scale results of rime ice accretions in small scale model tests.

Bragg, M. B.↗

The matrix exponential in transient structural analysis

The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.

Minnetyan, Levon↗

General Flow-Solver Code for Turbomachinery Applications

Phantom is a computer code intended primarily for real-fluid turbomachinery problems. It is based on Corsair, an ideal-gas turbomachinery code, developed by the same authors, which evolved from the ROTOR codes from NASA Ames. Phantom is applicable to real and ideal fluids, both compressible and incompressible, flowing at subsonic, transonic, and supersonic speeds. It utilizes structured, overset, O- and H-type zonal grids to discretize flow fields and represent relative motions of components. Values on grid boundaries are updated at each time step by bilinear interpolation from adjacent grids. Inviscid fluxes are calculated to third-order spatial accuracy using Roe s scheme. Viscous fluxes are calculated using second-order-accurate central differences. The code is second-order accurate in time. Turbulence is represented by a modified Baldwin-Lomax algebraic model. The code offers two options for determining properties of fluids: One is based on equations of state, thermodynamic departure functions, and corresponding state principles. The other, which is more efficient, is based on splines generated from tables of properties of real fluids. Phantom currently contains fluid-property routines for water, hydrogen, oxygen, nitrogen, kerosene, methane, and carbon monoxide as well as ideal gases.

Dorney, Daniel↗

Conical Euler analysis and active roll suppression for unsteady vortical flows about rolling delta wings

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling, highly swept delta wings undergoing either forced motions or free-to-roll motions that include active roll suppression. The flow solver of the code involves a multistage, Runge-Kutta time-stepping scheme that uses a cell-centered, finite-volume, spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free to-roll case by simultaneously integrating in time the rigid-body equation of motion with the governing flow equations. Results are presented for a delta wing with a 75 deg swept, sharp leading edge at a free-stream Mach number of 1.2 and at 10 deg, 20 deg, and 30 deg angle of attack alpha. At the lower angles of attack (10 and 20 deg), forced-harmonic analyses indicate that the rolling-moment coefficients provide a positive damping, which is verified by free-to-roll calculations. In contrast, at the higher angle of attack (30 deg), a forced-harmonic analysis indicates that the rolling-moment coefficient provides negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation, which is characteristic of highly swept delta wings. This limit cycle oscillation may be actively suppressed through the use of a rate-feedback control law and antisymmetrically deflected leading-edge flaps. Descriptions of the conical Euler flow solver and the free-to roll analysis are included in this report. Results are presented that demonstrate how the systematic analysis of the forced response of the delta wing can be used to predict the stable, neutrally stable, and unstable free response of the delta wing. These results also give insight into the flow physics associated with unsteady vortical flows about delta wings undergoing forced motions and free-to-roll motions, including the active suppression of the wing-rock type phenomenon. The conical Euler methodology developed is directly extend able to three-dimensional calculations.

Lee-Rausch, Elizabeth M.↗

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Towne, Charles E.↗

Real-Time Visualization of an HPF-based CFD Simulation

Current time-dependent CFD simulations produce very large multi-dimensional data sets at each time step. The visual analysis of computational results are traditionally performed by post processing the static data on graphics workstations. We present results from an alternate approach in which we analyze the simulation data in situ on each processing node at the time of simulation. The locally analyzed results, usually more economical and in a reduced form, are then combined and sent back for visualization on a graphics workstation.

Kremenetsky, Mark↗

Sensitivities of Modeled Tropical Cyclones to Surface Friction and the Coriolis Parameter

In this investigation the sensitivities of a 2-D tropical cyclone (TC) model to surface frictional coefficient and the Coriolis parameter are studied and their implication is discussed. The model used is an axisymmetric version of the latest version of the Goddard cloud ensemble model. The model has stretched vertical grids with 33 levels varying from 30 m near the bottom to 1140 m near the top. The vertical domain is about 21 km. The horizontal domain covers a radius of 962 km (770 grids) with a grid size of 1.25 km. The time step is 10 seconds. An open lateral boundary condition is used. The sea surface temperature is specified at 29C. Unless specified otherwise, the Coriolis parameter is set at its value at 15 deg N. The Newtonian cooling is used with a time scale of 12 hours. The reference vertical temperature profile used in the Newtonian cooling is that of Jordan. The Newtonian cooling models not only the effect of radiative processes but also the effect of processes with scale larger than that of TC. Our experiments showed that if the Newtonian cooling is replaced by a radiation package, the simulated TC is much weaker. The initial condition has a temperature uniform in the radial direction and its vertical profile is that of Jordan. The initial winds are a weak Rankin vortex in the tangential winds superimposed on a resting atmosphere. The initial sea level pressure is set at 1015 hPa everywhere. Since there is no surface pressure perturbation, the initial condition is not in gradient balance. This initial condition is enough to lead to cyclogenesis, but the initial stage (say, the first 24 hrs) is not considered to resemble anything observed. The control experiment reaches quasi-equilibration after about 10 days with an eye wall extending from 15 to 25 km radius, reasonable comparing with the observations. The maximum surface wind of more than 70 m/s is located at about 18 km radius. The minimum sea level pressure on day 10 is about 886 hPa. Thus the overall simulation is considered successful and the model is considered adequate for our investigation.

Chao, Winston C.↗

Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations

Although the Navier-Stokes equations describe most flows of interest in aerodynamics, the inviscid conservation law equations may be used for small regions with viscous forces. Thus, Euler equations and several time-accurate finite difference procedures, explicit and implicit, are discussed. Although implicit techniques require more computational work, they permit larger time steps to be taken without instability. It is noted that the Jacobian matrices for Euler equations in conservation-law form have certain eigenvalue-eigenvector properties which may be used to construct conservative-form coefficient matrices. This reduces the computation time of several implicit and semiimplicit schemes. Extensions of the basic approach to other areas are suggested.

Steger, J. L.↗