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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Using High-Order Methods on Lower-Order Geometries

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.

Casper, Jay↗
NASA NTRS1993

Statistics of Experiments on Cluster Formation and Transport in a Gravitational Field

Metastable state relaxation in a gravitational field is investigated in the case of non-critical binary solutions. A relaxation description is presented in terms of the time-dependent Ginzburg-Landau formalism for a non-conserved order parameter. A new ansatz for solution of the corresponding partial nonlinear stochastic differential equation is discussed. It is proved that, for the supersaturated solution under consideration, the metastable state relaxation in a gravitational field leads to formation of solute concentration gradients due to the sedimentation of subcritical solute clusters. The pure discussion of the possible methods to compare theoretical results and experimental data related to solute sedimentation in a gravitational field is presented. It is shown that in order to describe these experiments it is necessary to deal both with the value of the solute concentration gradient and with its formation rate. The stochastic nature of the sedimentation process is shown.

Izmailov, Alexander F.↗
NASA NTRS1998

Effects of Suction on Swept-Wing Transition

Stability experiments are conducted in the Arizona State University Unsteady Wind Tunnel on a 45 deg swept airfoil. The pressure gradient is designed to provide purely crossflow-dominated transition; that is, the boundary layer is subcritical to Tollmien-Schlichting disturbances. The airfoil surface is hand polished to a 0.25 microns rms finish. Under these conditions, stationary crossflow disturbances grow to nonuniform amplitude due to submicron surface irregularities near the leading edge. Uniform stationary crossflow waves are produced by controlling the initial conditions with spanwise arrays of micron-sized roughness elements near the attachment line. Hot-wire measurements provide detailed maps of the crossflow wave structure, and accurate spectral decompositions isolate individual-mode growth rates for the fundamental and harmonic disturbances. Roughness spacing, roughness height, and Reynolds number are varied to investigate the growth of all amplified wavelengths. The measurements show early nonlinear mode interaction causing amplitude saturation well before transition. Comparisons with nonlinear parabolized stability equations calculations show excellent agreement in both the disturbance amplitude and the mode-shape profiles.

Saric, William S.↗
NASA NTRS1998

Transition in Turbine Flows

We have further developed our capabilities to analyze transition in turbine boundary layers from first principles by integrating the nonlinear parabolized stability equations (PSE) with improved initial and boundary conditions. With modified iteration schemes, we are able to proceed deeper into the transition region where skin friction coefficient and heat transfer coefficient significantly increase. Initial and boundary conditions at elevated turbulence levels can be derived by receptivity analysis. Test runs for ERCOFTAC test case T3A at 2.4\% turbulence level provide results in good agreement with the experimental data. The sharper minimum of the skin coefficient also shown by DNS results is likely due to the missing intermittency. The method has been applied to various experimentally studied turbine blades (UTRC, VKI, Zierke, Langston, Hippensteele, and others). The PSE results, though physically reasonable, do not agree as well as expected with the experimental findings. We have, therefore, performed an extensive search for the reasons of the seemingly systematic deviations. A first source of uncertainty has been found in the often insufficient documentation of the experiments (e.g. on blockage by end-wall boundary layers). However, variation of the relevant parameters does not lead to more satisfactory agreement. A second reason has been found in the "standard procedure" which considers a 2D flow at midspan and uses a panel code and subsequent boundary-layer code to obtain the laminar basic flow for the transition analysis. Comparison with the pressure distribution obtained with a 3D design code (RVC3D) shows significant three-dimensionality of the flow (e.g. in the UTRC experiments). The spanwise variation has been neglected in our original PSE code. To overcome this problem, we have developed the PSE/3D for fully 3D boundary layers to account for streamwise and spanwise variations. Since the design code does not provide the boundary-layer flow with sufficient resolution, we have generated the Euler solution and employed a 3D boundary-layer code to obtain the viscous basic flow. Although only the linear stability level of PSE/3D has been implemented so far, the discrepancies with the experiments change but do not disappear. We still find deviations between the computed and experimental variations of C(sub f), and St along the blade for laminar flow. The main reason can be seen by comparing the solution of the boundary-layer code with the viscous results of the design code. The conventional boundary-layer solution exhibits an asymptotic behavior appropriate in external aerodynamics but does not match the steep gradients of the inviscid flow through the passage and consequently provides biased results for C(sub f), and St. An attempt is currently being made to correct this deficiency. Before attempting to perform the transition analysis for the viscous flow provided by the design code, we have analyzed the implementation and "best possible" results. Code and results exhibit flaws that may negatively affect the design and are intolerable for transition analysis. Therefore, we have decided to develop a new code to obtain a reliable basis for stability and transition studies. We expect to report improved results by the time of the meeting.

Herbert, Thorwald↗
NASA NTRS1998

Computational Modeling of Semiconductor Dynamics at Femtosecond Time Scales

The Interchange No. NCC2-5149 deals with the emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. To build such devices and subsystems, one needs to model the entire chip. PICs are useful for building components for integrated optical transmitters, integrated optical receivers, optical data storage systems, optical interconnects, and optical computers. For example, the current commercial rate for optical data transmission is 2.5 gigabits per second, whereas the use of shorter pulses to improve optical transmission rates would yield an increase of 400 to 1000 times. The improved optical data transmitters would be used in telecommunications networks and computer local-area networks. Also, these components can be applied to activities in space, such as satellite to satellite communications, when the data transmissions are made at optical frequencies. The research project consisted of developing accurate computer modeling of electromagnetic wave propagation in semiconductors. Such modeling is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Presently, there are no computer codes that could provide this modeling. Current codes do not solve the full vector, nonlinear, Maxwell's equations, which are required for these short pulses and also current codes do not solve the semiconductor Bloch equations, which are required to accurately describe the material's interaction with femtosecond pulses. The research performed under NCC2-5149 solves the combined Maxwell's and Bloch's equations.

Agrawal, Govind P.↗
NASA NTRS1997

Sliding Mode Control of a Slewing Flexible Beam

An output feedback sliding mode controller (SMC) is proposed to minimize the effects of vibrations of slewing flexible manipulators. A spline trajectory is used to generate ideal position and velocity commands. Constrained nonlinear optimization techniques are used to both calibrate nonlinear models and determine optimized gains to produce a rest-to-rest, residual vibration-free maneuver. Vibration-free maneuvers are important for current and future NASA space missions. This study required the development of the nonlinear dynamic system equations of motion; robust control law design; numerical implementation; system identification; and verification using the Sandia National Laboratories flexible robot testbed. Results are shown for a slewing flexible beam.

Wilson, David G.↗
NASA NTRS2001

Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.

Pelaez, Juan↗
NASA NTRS2001

Sound Emission of Rotor Induced Deformations of Generator Casings

The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.

Polifke, W.↗
NASA NTRS1996

Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials

There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.

Goorjian, Peter M.↗
NASA NTRS2002

Interannual Variability of Martian Global Dust Storms: Simulations with a Low-Order Model of the General Circulation

We present simulations of the interannual variability of martian global dust storms (GDSs) with a simplified low-order model (LOM) of the general circulation. The simplified model allows one to conduct computationally fast long-term simulations of the martian climate system. The LOM is constructed by Galerkin projection of a 2D (zonally averaged) general circulation model (GCM) onto a truncated set of basis functions. The resulting LOM consists of 12 coupled nonlinear ordinary differential equations describing atmospheric dynamics and dust transport within the Hadley cell. The forcing of the model is described by simplified physics based on Newtonian cooling and Rayleigh friction. The atmosphere and surface are coupled: atmospheric heating depends on the dustiness of the atmosphere, and the surface dust source depends on the strength of the atmospheric winds. Parameters of the model are tuned to fit the output of the NASA AMES GCM and the fit is generally very good. Interannual variability of GDSs is possible in the IBM, but only when stochastic forcing is added to the model. The stochastic forcing could be provided by transient weather systems or some surface process such as redistribution of the sand particles in storm generating zones on the surface. The results are sensitive to the value of the saltation threshold, which hints at a possible feedback between saltation threshold and dust storm activity. According to this hypothesis, erodable material builds up its a result of a local process, whose effect is to lower the saltation threshold until a GDS occurs. The saltation threshold adjusts its value so that dust storms are barely able to occur.

Pankine, A. A.↗
NASA NTRS1947

The Elasto-Plastic Stability of Plates

This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.

Ilyushin, A. A.↗
NASA NTRS2003

Modeling and Validation of a Propellant Mixer for Controller Design

A mixing chamber used in rocket engine testing at the NASA Stennis Space Center is modelled by a system of two nonlinear ordinary differential equations. The mixer is used to condition the thermodynamic properties of cryogenic liquid propellant by controlled injection of the same substance in the gaseous phase. The three inputs of the mixer are the positions of the valves regulating the liquid and gas flows at the inlets, and the position of the exit valve regulating the flow of conditioned propellant. Mixer operation during a test requires the regulation of its internal pressure, exit mass flow, and exit temperature. A mathematical model is developed to facilitate subsequent controller designs. The model must be simple enough to lend itself to subsequent feedback controller design, yet its accuracy must be tested against real data. For this reason, the model includes function calls to thermodynamic property data. Some structural properties of the resulting model that pertain to controller design, such as uniqueness of the equilibrium point, feedback linearizability and local stability are shown to hold under conditions having direct physical interpretation. The existence of fixed valve positions that attain a desired operating condition is also shown. Validation of the model against real data is likewise provided.

Richter, Hanz↗
NASA NTRS2004

Nonlinear Analysis of Bonded Composite Single-LAP Joints

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint

Oterkus, E.↗
NASA NTRS1997

A model for the kinetics of homotypic cellular aggregation under static conditions

We present the formulation and testing of a mathematical model for the kinetics of homotypic cellular aggregation. The model considers cellular aggregation under no-flow conditions as a two-step process. Individual cells and cell aggregates 1) move on the tissue culture surface and 2) collide with other cells (or aggregates). These collisions lead to the formation of intercellular bonds. The aggregation kinetics are described by a system of coupled, nonlinear ordinary differential equations, and the collision frequency kernel is derived by extending Smoluchowski's colloidal flocculation theory to cell migration and aggregation on a two-dimensional surface. Our results indicate that aggregation rates strongly depend upon the motility of cells and cell aggregates, the frequency of cell-cell collisions, and the strength of intercellular bonds. Model predictions agree well with data from homotypic lymphocyte aggregation experiments using Jurkat cells activated by 33B6, an antibody to the beta 1 integrin. Since cell migration speeds and all the other model parameters can be independently measured, the aggregation model provides a quantitative methodology by which we can accurately evaluate the adhesivity and aggregation behavior of cells.

Non-NASA Center↗
NASA NTRS2006

PAB3D: Its History in the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows

This is a review paper for PAB3D s history in the implementation of turbulence models for simulating jet and nozzle flows. We describe different turbulence models used in the simulation of subsonic and supersonic jet and nozzle flows. The time-averaged simulations use modified linear or nonlinear two-equation models to account for supersonic flow as well as high temperature mixing. Two multiscale-type turbulence models are used for unsteady flow simulations. These models require modifications to the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k-epsilon) model with a RANS/LES transition function, dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) formulation. All of these models are implemented in the three-dimensional Navier-Stokes code PAB3D. This paper discusses computational methods, code implementation, computed results for a wide range of nozzle configurations at various operating conditions, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions.

Abdol-Hamid, Khaled S.↗
NASA NTRS2010

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Li, Fei↗
NASA NTRS2013

DRE-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers

Nonlinear parabolized stability equations and secondary instability analyses are used to provide a computational assessment of the potential use of the discrete roughness elements (DRE) technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural laminar flow airfoil with a leading-edge sweep angle of 34.6deg, free-stream Mach number of 0.75 and chord Reynolds numbers of 17 x 10(exp 6), 24 x 10(exp 6) and 30 x 10(exp 6) suggest that DRE could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small wavelength stationary crossflow disturbances (i.e., DRE) also suppresses the growth of most amplified traveling crossflow disturbances.

Malik, Mujeeb↗
NASA NTRS2015

Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers

Nonlinear parabolized stability equations and secondary-instability analyses are used to provide a computational assessment of the potential use of the discrete-roughness-element technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural-laminar-flow airfoil with a leading-edge sweep angle of 34.6 deg, freestream Mach number of 0.75, and chord Reynolds numbers of 17 × 10(exp 6), 24 × 10(exp 6), and 30 × 10(exp 6) suggest that discrete roughness elements could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small-wavelength stationary crossflow disturbances (i.e., discrete roughness element) also suppresses the growth of most amplified traveling crossflow disturbances.

Malik, Mujeeb↗