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NASA NTRS1989

Stereo image visualization of numerically simulated turbulence

Stereo imaging techniques are used in the current study to analyze the results of a direct Navier-Stokes simulation of a turbulent boundary layer. Coherent structures embedded within the unsteady, highly three-dimensional turbulent flow fields are significantly enhanced through the use of stereo computer graphic renderings. In the paper, the geometrical foundations of two different methods for generating stereo images are reviewed. Sufficient detail is provided to enable readers to code stereo display algorithms from scratch. The effects of varying the geometric parameters of the stereo algorithm are demonstrated. Sample image pairs from animations of the turbulence numerical simulation are presented in color. Stereo imagery, especially when used with time-evolving data, provides new insight into the physical processes responsible for the generation an maintenance of turbulence within boundary layers.

Robinson, Stephen K.↗

NASA NTRS1994

Numerical Simulations of Drop Collisions

Three-dimensional simulations of the off-axis collisions of two drops are presented. The full Navier-Stokes equations are solved by a Front-Tracking/Finite-Difference method that allows a fully deformable fluid interface and the inclusion of surface tension. The drops are accelerated towards each other by a body force that is turned off before the drops collide. Depending on whether the interface between the drops is ruptured or not, the drops either bounce or coalesce. For drops that coalesce, the impact parameter, which measures how far the drops are off the symmetry line, determines the eventual outcome of the collision. For low impact parameters, the drops coalesce permanently, but for higher impact parameters, a grazing collision, where the drops coalesce and then stretch apart again is observed. The results are in agreement with experimental observations.

Nobari, M. R. H.↗

NASA NTRS2012

Adhesion of Mineral and Soot Aerosols can Strongly Affect their Scattering and Absorption Properties

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

Mishchenko, Michael I.↗

NASA NTRS2013

ISSM: Ice Sheet System Model

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Larour, Eric↗

NASA NTRS1972

On the numerical solution of two-dimensional, laminar compressible flows with imbedded shock waves.

The complete, time-dependent Navier-Stokes equations are expressed in conservation form and solved by employing an explicit finite difference numerical technique which incorporates artificial viscosity terms of the form first suggested by Rusanov for numerical stability in the vicinity of shock waves. Surface boundary conditions are developed in a consistent and unique manner through the use of a physically oriented extrapolation procedure. From numerical experimentation an extended range for the explicit stability parameter is established. Also employed is an additional convergence parameter which relates incremental spatial steps. Convergence of the transient solution to a steady state flow was obtained after 400 to 500 time steps.

Goodrich, W. D.↗

NASA NTRS1987

Enhancements to Program LAURA for computation of three-dimensional hypersonic flow

Changes to Program Laura (Langley Aerothermodynamic Upwind Relaxation Algorithm) are presented which enhance both stability and accuracy of the algorithm. A discussion of iteration/sweeping strategies and their relation to computer architectures is included to best exploit the capabilities of serial, vector, and parallel processor machines. Test cases for Mach 10 perfect gas flow and Mach 32 real gas flow in chemical nonequilibrium over a blunt, raked elliptic cone using the thin-layer Navier-Stokes equations are presented in order to demonstrate the current improved capabilities. Algorithm changes include the use of volume averaging, application of a symmetric total variation diminishing (TVD) scheme, and stronger interaction between the grid/shock alignment routine and the relaxation algorithm. Good comparisons with heat transfer and pitching moment data at three different angles of attack for the Mach 10 tests serve to further validate the present algorithm. Parameters are defined which control the coupling of the specie continuity equations with the solution of the mixture conservation equations. A discussion of the consequences involved in the choice of strong versus weak coupling is presented, and a sample nonequilibrium calculation on a fine grid over a full scale model of the Aeroassist Flight Experiment (AFE) demonstrates current capabilities.

Gnoffo, Peter A.↗

NASA NTRS1999

A fluid--structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery

A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.

Non-NASA Center↗

NASA NTRS1978

Numerical solution of the Navier-Stokes equations for super-sonic flows with strong shocks

The numerical solution of the full Navier-Stokes Equations for viscous flows with high Mach numbers and a strong detached bow shock was obtained. Two dimensional flows around a circular cylinder, and a circular cylinder with an aft-body in the form of a fairing, were considered. The solution of the compressible N.S. equations was accomplished by the method of finite differences. An implicit scheme of solution, the S.O.R., was used with the optimum acceleration parameters determined by trial and error. The tensor notation was used in writing the N-S Equations transformed into general curvilinear coordinates. The equations for the generation of the coordinate system were solved, followed by the solution of the N.S. equations, at the end of a set of given number of time steps. "Wiggles", constituted the one major problem that needed to be overcome. These oscillations give rise to quantities such as negative temperatures, which ultimately caused the computational program to break down. Certain dissipative finite-difference schemes damped these oscillations.

Devarayalu, K.↗

NASA NTRS1991

Prediction of internal performance for two-dimensional convergent-divergent nozzles

A three-dimensional code (PAB3D) has been under development to simulate underexpanded and overexpanded supersonic jet exhaust effects on a nonaxisymmetric nozzle/afterbody. The code is a multiblock/multizone technique solving the simplified Navier-Stokes equations. This method was applied to the solution of two nozzle configurations to verify the recent implementation of a nozzle performance calculation package. Static pressure distributions, discharge coefficient and thrust ratio quantities were calculated for on-design and off-design operating conditions for rectangular convergent-divergent nozzles with different throat designs. Approaches involved in computing the flows for these nozzles are presented. Computation of performance parameters were typically within 1 percent of experimental on-design and off-design data.

Carlson, John R.↗

NASA NTRS1991

Three-dimensional blade vortex interactions

A three-dimensional time dependent Navier-Stokes analysis was applied to the rotor blade vortex interaction problem. The numerical procedure is an iterative implicit procedure using three point central differences to represent spatial derivatives. A series of calculations were made to determine the time steps, pseudo-time steps, iterations, artificial dissipation level, etc. required to maintain a nondissipative vortex. Results show the chosen method to have excellent non-dissipative properties provided the correct parameters are chosen. This study was used to set parameters for both two- and three-dimensional blade vortex interaction studies. The case considered was the interaction between a vortex and a NACA0012 airfoil. The results showed the detailed physics during the interaction including the pressure pulse propagating from the blade. The simulated flow physics was qualitatively similar to that experimentally observed. The BVI phenomena is the result of the buildup and violent collapse of the shock waves and local supersonic pockets on the blade surfaces. The resulting pressure pulse build-up appears to be centered at the blade leading edge.

Davoudzadeh, Farhad↗

NASA NTRS2010

Aeroelastic Computations of a Compressor Stage Using the Harmonic Balance Method

The aeroelastic characteristics of a compressor stage were analyzed using a computational fluid dynamic (CFD) solver that uses the harmonic balance method to solve the governing equations. The three dimensional solver models the unsteady flow field due to blade vibration using the Reynolds-Averaged Navier-Stokes equations. The formulation enables the study of the effect of blade row interaction through the inclusion of coupling modes between blade rows. It also enables the study of nonlinear effects of high amplitude blade vibration by the inclusion of higher harmonics of the fundamental blade vibration frequency. In the present work, the solver is applied to study in detail the aeroelastic characteristics of a transonic compressor stage. Various parameters were included in the study: number of coupling modes, blade row axial spacing, and operating speeds. Only the first vibration mode is considered with amplitude of oscillation in the linear range. Both aeroelastic stability (flutter) of rotor blade and unsteady loading on the stator are calculated. The study showed that for the stage considered, the rotor aerodynamic damping is not influenced by the presence of the stator even when the axial spacing is reduced by nearly 25 percent. However, the study showed that blade row interaction effects become important for the unsteady loading on the stator when the axial spacing is reduced by the same amount.

Reddy, T. S. R.↗

NASA NTRS1975

An experimental and numerical investigation of shock-wave induced turbulent boundary-layer separation at hypersonic speeds

An experiment designed to test and guide computations of the interaction of an impinging shock wave with a turbulent boundary layer is described. Detailed mean flow-field and surface data are presented for two shock strengths which resulted in attached and separated flows, respectively. Numerical computations, employing the complete time-averaged Navier-Stokes equations along with algebraic eddy-viscosity and turbulent Prandtl number models to describe shear stress and heat flux, are used to illustrate the dependence of the computations on the particulars of the turbulence models. Models appropriate for zero-pressure-gradient flows predicted the overall features of the flow fields, but were deficient in predicting many of the details of the interaction regions. Improvements to the turbulence model parameters were sought through a combination of detailed data analysis and computer simulations which tested the sensitivity of the solutions to model parameter changes. Computer simulations using these improvements are presented and discussed.

Marvin, J. G.↗

NASA NTRS1990

Two- and three-dimensional blade vortex interactions

A three-dimensional time dependent Navier-Stokes analysis was applied to the rotor blade vortex interaction (BVI) problem. The numerical procedure is an iterative implicit procedure using three point central differences to represent spatial derivatives. A series of calculations were made to determine the time steps, pseudo-time steps, iterations, artificial dissipation level, etc. required to maintain a nondissipative vortex. Results show the chosen method to have excellent non-dissipative properties provided the correct parameters are chosen. This study was used to set parameters for both two- and three-dimensional blade vortex interaction studies. The two-dimensional study considered the interaction between a vortex and a NACA0012 airfoil. The results showed the detailed physics during the interaction including the pressure pulse propagating from the blade. The simulated flow physics was qualitatively similar to that experimentally observed. The 2-D BVI phenomena is the result of the buildup and violent collapse of the shock waves and local supersonic pockets on the blade surfaces. The resulting pressure pulse build-up appears to be centered at the blade leading edge. The three-dimensional interaction study considered the case of a vortex at 20 deg incidence to the blade leading edge. Although the qualitative results were similar to that of the two-dimensional interaction, details clearly showed the three-dimensional nature of the interaction process.

Davoudzadeh, F.↗

NASA NTRS1986

Diffusion flame extinction in slow convenctive flow under microgravity environment

A theoretical analysis is presented to study the extinction characteristics of a diffusion flame near the leading edge of a thin fuel plate in slow, forced convective flows in a microgravity environment. The mathematical model includes two-dimensional Navier-Stokes momentum, energy and species equations with one-step overall chemical reaction using second-order finite rate Arrhenius kinetics. Radiant heat loss on the fuel plate is applied in the model as it is the dominant mechanism for flame extinguishment in the small convective flow regime. A parametric study based on the variation of convective flow velocity, which varies the Damkohler number (Da), and the surface radiant heat loss parameter (S) simultaneously, is given. An extinction limit is found in the regime of slow convective flow when the rate of radiant heat loss from fuel surface outweighs the rate of heat generation due to combustion. The transition from existent envelope flame to extinguishment consists of gradual flame contraction in the opposed flow direction together with flame temperature reduction as the convective flow velocity decreases continuously until the extinction limit is reached. A case of flame structure subjected to surface radiant heat loss is also presented and discussed.

Chen, C. H.↗

NASA NTRS1986

Diffusion flame extinction in slow convection flow under microgravity environment

A theoretical analysis is presented to study the extinction characteristics of a diffusion flame near the leading edge of a thin fuel plate in slow, forced convective flows in a microgravity environment. The mathematical model includes two-dimensional Navier-Stokes momentum, energy and species equations with one-step overall chemical reaction using second-order finite rate Arrhenius kinetics. Radiant heat loss on the fuel plate is applied in the model as it is the dominant mechanism for flame extinguishment in the small convective flow regime. A parametric study based on the variation of convective flow velocity, which varies the Damkchler number (Da), and the surface radiant heat loss parameter (S) simultaneously, is given. An extinction limit is found in the regime of slow convective flow when the rate of radiant heat loss from fuel surface outweighs the rate of heat generation due to combustion. The transition from existent envelope flame to extinguishment consists of gradual flame contraction in the opposed flow direction together with flame temperature reduction as the convective flow velocity decreases continuously until the extinction limit is reached. A case of flame structure subjected to surface radiant heat loss is also presented and discussed.

Chen, Chiun-Hsun↗

NASA NTRS2016

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

To meet the flight control damping requirement, baffles of various configurations have been devised to increase the natural viscous damping and decrease the magnitude of the slosh forces and torques. In the design of slosh baffles, the most widely used damping equation is the one derived by Miles, which is based on the experiments of Keulegan and Carpenter. This equation has been used in predicting damping of the baffled tanks in different diameters ranging from 12 to 112 inches. The analytical expression of Miles equation is easy to use, especially in the design of complex baffle system. Previous investigations revealed that some experiments had shown good agreements with the prediction method of Miles, whereas other experiments have shown significant deviations. For example, damping from Miles equation differs from experimental measurements by as much as 100 percent over a range of tank diameters from 12 to 112 inches, oscillation amplitudes from 0.1 to 1.5 baffle widths, and baffle depths of 0.3 to 0.5 tank radius. Previously, much of this difference has been attributed to experimental scatter. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between Miles equation and experimental measurement, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use CFD technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. A well validated CFD solver, developed at NASA MSFC, Loci-STREAM-VOF, is applied to study vorticity field around the baffle and around the fluid interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data are then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (h/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Yang, H. Q.↗

NASA NTRS1985

Numerical simulation of vortex breakdown

The breakdown of an isolated axisymmetric vortex embedded in an unbounded uniform flow is examined by numerical integration of the complete Navier-Stokes equations for unsteady axisymmetric flow. Results show that if the vortex strength is small, the solution approaches a steady flow and the vortex is stable. If the strength is large enough, the solution remains unsteady and a recirculating zone will appear near the axis, its form and internal structure resembling those of the axisymmetric breakdown bubbles with multi-cells observed by Faler and Leibovich (1978). For apppropriate combinations of flow parameters, the flow reveals quasi-periodicity. Parallel calculations with the quasi-cylindrical approximation indicate that so far as predicting of breakdown is concerned, its results coincide quite well with the results mentioned above. Both show that the vortex breakdown has little concern with the Reynolds number or with the critical classification of the upstream flow, at least for the lower range of Reynolds numbers.

Shi, X.↗

NASA NTRS2001

Transition In Supersonic Flows With Corners

It is proposed to investigate the effect of sudden change in the slope of the surface on the stability and transition onset point in supersonic and hypersonic boundary layers. Since we can not use the linear stability theory in flows where there are discontinuities we have to solve the full Navier-Stokes equations to determine the amplification of the disturbances across the oblique shock which exists at the corner. We will use the Navier-Stokes code which was developed by Dr. Harold Atkins in the aerodynamic and acoustic methods branch. The code is developed using the higher order ENO scheme and is currently set up for two-dimensional flows. In the first year of our investigation, we will investigate the evolution of small amplitude two-dimensional disturbances and determine the N-factors for the most amplified disturbances. We will perform the analysis for the parameter similar to X-31 model and flight experiment conditions. From these computation we will infer what is the maximum amplification rate possible in quite environments without any tripping devices. In the second part of the investigation, we will perform nonlinear computations to determine what is the minimum amplitudes necessary to cause the transition at a designed location. In the third part, we have to determine what kind of trip devices necessary to excite the required disturbances. The principal investigator of this project is Dr. P. Balakumar, Associate Professor of Department of Aerospace Engineering, Old Dominion University. We will actively collaborate with research scientists in the Aero-Thermodynamics Branch at NASA/Langley Research Center. A half-time graduate student will also participate in the project.

Balakumar, P.↗