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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

Balachandar, S.↗
NASA NTRS1998

Inlet-Compressor Analysis Using Coupled CFD Codes

Propulsion performance and operability are key factors in the development of a successful aircraft. For high-speed supersonic aircraft, mixed-compression inlets offer high performance but are susceptible to an instability referred to as unstart. An unstart occurs when a disturbance originating in the atmosphere or the engine causes the shock system to be expelled from the inlet. This event can have adverse effects on control of the aircraft, which is unacceptable for a passenger plane such as the high speed civil transport (HSCT). The ability to predict the transient response of such inlets to flow perturbations is, therefore, important to the proper design of the inlet and the control measures used to prevent unstart. Computational fluid dynamics (CFD) is having an increasing role in the analysis of individual propulsion components. isolated inlet studies are relatively easy to perform, but a major uncertainty is the boundary condition used at the inlet exit to represent the engine - the so-called compressor face boundary condition. A one-dimensional (I-D) Euler inlet simulation (ref. 1) showed that the predicted inlet unstart tolerance to free-stream pressure perturbations can vary by as much as a factor of about six, depending on the boundary condition used. Obviously, a thorough understanding of dynamic interactions between inlets and compressors/fans is required to provide the proper boundary condition.

Cole, Gary↗
NASA NTRS1995

Review of Combustion-acoustic Instabilities

Combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system. The problem of combustion-acoustic instability is a concern in many devices for various reasons, as each device may have a unique mechanism causing unsteady heat release rates and many have unique boundary conditions. To accurately predict and quantify combustion-acoustic stabilities, the unsteady heat release rate and boundary conditions need to be accurately determined. The present review brings together work performed on a variety of practical combustion devices. Many theoretical and experimental investigations of the unsteady heat release rate have been performed, some based on perturbations in the fuel delivery system particularly for rocket instabilities, while others are based on hydrodynamic processes as in ramjet dump combustors. The boundary conditions for rocket engines have been analyzed and measured extensively. However, less work has been done to measure acoustic boundary conditions in many other combustion systems.

Oyediran, Ayo↗
NASA NTRS1993

A method for the modelling of porous and solid wind tunnel walls in computational fluid dynamics codes

Porous wall wind tunnels have been used for several decades and have proven effective in reducing wall interference effects in both low speed and transonic testing. They allow for testing through Mach 1, reduce blockage effects and reduce shock wave reflections in the test section. Their usefulness in developing computational fluid dynamics (CFD) codes has been limited, however, by the difficulties associated with modelling the effect of a porous wall in CFD codes. Previous approaches to modelling porous wall effects have depended either upon a simplified linear boundary condition, which has proven inadequate, or upon detailed measurements of the normal velocity near the wall, which require extensive wind tunnel time. The current work was initiated in an effort to find a simple, accurate method of modelling a porous wall boundary condition in CFD codes. The development of such a method would allow data from porous wall wind tunnels to be used more readily in validating CFD codes. This would be beneficial when transonic validations are desired, or when large models are used to achieve high Reynolds numbers in testing. A computational and experimental study was undertaken to investigate a new method of modelling solid and porous wall boundary conditions in CFD codes. The method utilized experimental measurements at the walls to develop a flow field solution based on the method of singularities. This flow field solution was then imposed as a pressure boundary condition in a CFD simulation of the internal flow field. The effectiveness of this method in describing the effect of porosity changes on the wall was investigated. Also, the effectiveness of this method when only sparse experimental measurements were available has been investigated. The current work demonstrated this approach for low speed flows and compared the results with experimental data obtained from a heavily instrumented variable porosity test section. The approach developed was simple, computationally inexpensive, and did not require extensive or intrusive measurements of the boundary conditions during the wind tunnel test. It may be applied to both solid and porous wall wind tunnel tests.

Beutner, Thomas John↗
NASA NTRS1986

Application of a low order panel method to complex three-dimensional internal flow problems

An evaluation of the ability of a low order panel method to predict complex three-dimensional internal flow fields was made. The computer code VSAERO was used as a basis for the evaluation. Guidelines for modeling internal flow geometries were determined and the effects of varying the boundary conditions and the use of numerical approximations on the solutions accuracy were studied. Several test cases were run and the results were compared with theoretical or experimental results. Modeling an internal flow geometry as a closed box with normal velocities specified on an inlet and exit face provided accurate results and gave the user control over the boundary conditions. The values of the boundary conditions greatly influenced the amount of leakage an internal flow geometry suffered and could be adjusted to eliminate leakage. The use of the far-field approximation to reduce computation time influenced the accuracy of a solution and was coupled with the values of the boundary conditions needed to eliminate leakage. The error induced in the influence coefficients by using the far-field approximation was found to be dependent on the type of influence coefficient, the far-field radius, and the aspect ratio of the panels.

Ashby, D. L.↗
NASA NTRS1993

An extended laser flash technique for thermal diffusivity measurement of high-temperature materials

Knowledge of thermal diffusivity data for high-temperature materials (solids and liquids) is very important in analyzing a number of processes, among them solidification, crystal growth, and welding. However, reliable thermal diffusivity versus temperature data, particularly those for high-temperature liquids, are still far from complete. The main measurement difficulties are due to the presence of convection and the requirement for a container. Fortunately, the availability of levitation techniques has made it possible to solve the containment problem. Based on the feasibility of the levitation technology, a new laser flash technique which is applicable to both levitated liquid and solid samples is being developed. At this point, the analysis for solid samples is near completion and highlights of the technique are presented here. The levitated solid sample which is assumed to be a sphere is subjected to a very short burst of high power radiant energy. The temperature of the irradiated surface area is elevated and a transient heat transfer process takes place within the sample. This containerless process is a two-dimensional unsteady heat conduction problem. Due to the nonlinearity of the radiative plus convective boundary condition, an analytic solution cannot be obtained. Two options are available at this point. Firstly, the radiation boundary condition can be linearized, which then accommodates a closed-form analytic solution. Comparison of the analytic curves for the temperature rise at different points to the experimentally-measured values will then provide the thermal diffusivity values. Secondly, one may set up an inverse conduction problem whereby experimentally obtained surface temperature history is used as the boundary conditions. The thermal diffusivity can then be elevated by minimizing the difference between the real heat flux boundary condition (radiation plus convection) and the measurements. Status of an experimental study directed at measuring the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloys are presented. Preliminary measurements showing surface temperature histories are discussed.

Shen, F.↗
NASA NTRS1981

Recent advances in the development of implicit schemes for the equations of fluid dynamics

Innovations and extensions of implicit schemes for equations of fluid dynamics are presented. The notation and theory for linear multistep methods are reviewed, and extensions of work by Beam and Warming (1979) include the implementation of one-leg methods, ADI methods for equations with mixed derivatives, flux vector splitting, the P-dimensional wave equation, and boundary conditions. Numerical experiments indicate that implicit treatment of the boundary conditions is necessary for unconditional stability, and the improvement and implementation of the boundary condition theory should improve the implicit algorithms for gas dynamic equations.

Warming, R. F.↗
NASA NTRS2000

Computation of Transonic Nozzle Sound Transmission and Rotor Problems by the Dispersion-Relation-Preserving Scheme

The transonic nozzle transmission problem and the open rotor noise radiation problem are solved computationally. Both are multiple length scales problems. For efficient and accurate numerical simulation, the multiple-size-mesh multiple-time-step Dispersion-Relation-Preserving scheme is used to calculate the time periodic solution. To ensure an accurate solution, high quality numerical boundary conditions are also needed. For the nozzle problem, a set of nonhomogeneous, outflow boundary conditions are required. The nonhomogeneous boundary conditions not only generate the incoming sound waves but also, at the same time, allow the reflected acoustic waves and entropy waves, if present, to exit the computation domain without reflection. For the open rotor problem, there is an apparent singularity at the axis of rotation. An analytic extension approach is developed to provide a high quality axis boundary treatment.

Tam, Christopher K. W.↗
NASA NTRS1993

Convection equation modeling: A non-iterative direct matrix solution algorithm for use with SINDA

The determination of the boundary conditions for a component-level analysis, applying discrete finite element and finite difference modeling techniques often requires an analysis of complex coupled phenomenon that cannot be described algebraically. For example, an analysis of the temperature field of a coldplate surface with an integral fluid loop requires a solution to the parabolic heat equation and also requires the boundary conditions that describe the local fluid temperature. However, the local fluid temperature is described by a convection equation that can only be solved with the knowledge of the locally-coupled coldplate temperatures. Generally speaking, it is not computationally efficient, and sometimes, not even possible to perform a direct, coupled phenomenon analysis of the component-level and boundary condition models within a single analysis code. An alternative is to perform a disjoint analysis, but transmit the necessary information between models during the simulation to provide an indirect coupling. For this approach to be effective, the component-level model retains full detail while the boundary condition model is simplified to provide a fast, first-order prediction of the phenomenon in question. Specifically for the present study, the coldplate structure is analyzed with a discrete, numerical model (SINDA) while the fluid loop convection equation is analyzed with a discrete, analytical model (direct matrix solution). This indirect coupling allows a satisfactory prediction of the boundary condition, while not subjugating the overall computational efficiency of the component-level analysis. In the present study a discussion of the complete analysis of the derivation and direct matrix solution algorithm of the convection equation is presented. Discretization is analyzed and discussed to extend of solution accuracy, stability and computation speed. Case studies considering a pulsed and harmonic inlet disturbance to the fluid loop are analyzed to assist in the discussion of numerical dissipation and accuracy. In addition, the issues of code melding or integration with standard class solvers such as SINDA are discussed to advise the user of the potential problems to be encountered.

Schrage, Dean S.↗
NASA NTRS2017

A Method to Predict Magnetopause Expansion in Radial IMF Events by MHD Simulations

This paper presents a method for taking into account changes of solar wind parameters in the foreshock using global MHD simulations. We simulate four events with very distant subsolar magnetopause crossings that occurred during quasi-radial interplanetary magnetic field (IMF) intervals lasting from one to several hours. Using previous statistical results, we suggest that the density and velocity in the foreshock cavity decrease to approx. 60% and approx. 94% of the ambient solar wind values when the IMF cone angle falls below 50 deg. This diminishes the solar wind dynamic pressure to 53% and causes a corresponding magnetospheric expansion. We change the upstream solar wind parameters in a global MHD model to take these foreshock effects into account. We demonstrate that the modified model predicts magnetopause distances during radial IMF intervals close to those observed by THEMIS. The strong total pressure decrease in the data seems to be a local, rather than a global, phenomenon. Although the simulations with decreased solar wind pressure generally reproduce the observed total pressure in the magnetosheath well, the total pressure in the magnetosphere often agrees better with results for nonmodified boundary conditions. The last result reveals a limitation of our method: we changed the boundary conditions along the whole inflow boundary, although a more correct approach would be to vary parameters only in the foreshock. A model with the suggested global modification of the boundary conditions better predicts the location of part of the magnetopause behind the foreshock but may fail in predicting the rest of the magnetopause.

Samsonov, A. A.↗
NASA NTRS2017

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Hu, Fang↗
DOE OSTI2022

Boundary theory of the X-cube model in the continuum

We study the boundary theory of the Z N X-cube model using a continuum perspective, from which the exchange statistics of a subset of bulk excitations can be recovered. We discuss various gapped boundary conditions that either preserve or break the translation/rotation symmetries on the boundary, and further present the corresponding ground state degeneracies on T 2 × I. The low-energy physics is highly sensitive to the boundary conditions: even the extensive part of the ground state degeneracy can vary when different sets of boundary conditions are chosen on the two boundaries. Here, we also examine the anomaly inflow of the boundary theory and find that the X-cube model is not the unique (3 + 1)-dimensional theory that cancels the 't Hooft anomaly of the boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1976

Buckling of Cylindrical Panels Under Axial Compression

This paper investigates the effects of boundary conditions and panel width on the axially compressive buckling behavior of unstiffened, isotropic, circular cylindrical panels. Numerical results are presented for eight different sets of boundary conditions along the straight edges of the panels. For all sets of boundary conditions except one (SSI), the results show that the panel buckling loads monotonically approach the complete cylinder buckling load from above as the panel width is increased. Low buckling loads, sometimes less than half the complete cylinder buckling load, are found for simply supported panels with free in-plane edge displacements (SSI). The SSI buckling loads are below the complete cylinder load even for '360deg panels'. It is also observed that the prevention of circumferential edge displacement is the most important in-plane boundary condition from the point of view of increasing the buckling load, and that the prevention of edge rotation (i.e. clamping) in the circumferential direction also significantly increases the buckling load. Parametric studies are also performed to determine the effects of variations in panel length and thickness on the buckling loads.

Sobel, L. H.↗
NASA NTRS1986

Continuum calculations of continental deformation in transcurrent environments

A thin viscous sheet approximation is used to investigate continental deformation near a strike-slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Exact and approximate analytic solutions for a region with a sinusoidal strike-slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across-strike length scale of the deformation is approximately 1/4pi x sq rt n times the dominant wavelength of the imposed strike-slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large-scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific-North America plate boundary in California.

Sonder, L. J.↗
NASA NTRS1993

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Carpenter, Mark H.↗
NASA NTRS1979

Nonequilibrium viscous flow over Jovian entry probes at high altitudes

The viscous chemical nonequilibrium flow around a Jovian entry body is investigated at high altitudes using two different methods. First method is only for the stagnation region and integrates the full Navier-Stokes equations from the body surface to the freestream. The second method uses viscous shock layer equations between the body surface and the shock. Due to low Reynolds numbers, both methods use surface slip boundary conditions and the second method also uses shock slip boundary conditions. The results of the two methods are compared at the stagnation point. It is found that the entire shock layer is under chemical nonequilibrium at higher altitudes and that the slip boundary conditions are important at these altitudes.

Kumar, A.↗
NASA NTRS1973

Iterative methods for plasma sheath calculations: Application to spherical probe

The computer cost of a Poisson-Vlasov iteration procedure for the numerical solution of a steady-state collisionless plasma-sheath problem depends on: (1) the nature of the chosen iterative algorithm, (2) the position of the outer boundary of the grid, and (3) the nature of the boundary condition applied to simulate a condition at infinity (as in three-dimensional probe or satellite-wake problems). Two iterative algorithms, in conjunction with three types of boundary conditions, are analyzed theoretically and applied to the computation of current-voltage characteristics of a spherical electrostatic probe. The first algorithm was commonly used by physicists, and its computer costs depend primarily on the boundary conditions and are only slightly affected by the mesh interval. The second algorithm is not commonly used, and its costs depend primarily on the mesh interval and slightly on the boundary conditions.

Parker, L. W.↗
NASA NTRS1988

Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

It has previously been shown that the no-slip boundary conditions leads to a singularity at a moving contact line and that this presumes some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition, the length of the slip region becomes a property of the fluid flow.

Durbin, P. A.↗