Diffusion approximation for thermal radiation in gases with jump boundary condition.
Radiative diffusion in nongray gas with jump boundary condition
THERMAL RADIATION↗
SEARCH · Engineering Papers
Results for “BOUNDARY CONDITIONS”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Numerical analysis of laplace's equation with nonlinear boundary conditions
Numerical analysis of Laplace equation with nonlinear boundary conditions
NUMERICAL ANALYSIS↗
Boundary conditions and iterative procedures for plasma sheath problems
Boundary conditions and iterative procedures for plasma sheath problems
Parker, L. W.↗
Boundary conditions and iterative procedures for plasma sheath problems
Boundary conditions and iterative procedures for plasma sheath problems, using matrix equation to represent differenced Poisson equation
Parker, L. W.↗
A Simple Derivation of the Acoustic Boundary Condition in the Presence of Flow
In modeling the noise propagation in a duct of a ducted fan engine, the authors needed the boundary condition satisfied by the acoustic pressure on a lined duct wall in the presence of flow. The results, in the form used by the authors, was derived by M.K. Myers, who presented a formal derivation of a related results by K. Taylor. Here, a brief and simple derivation of the acoustic boundary condition of Myers is given. The main difference in the derivation from that by Myers is that the Gaussian coordinate system (q(exp 1, q(exp 2), q(exp 3)(q(exp 1, q(exp 2), t)) is used to specify the instantaneous position, i.e. Lagrangian variable, of the point on the mean position of the wall with curvilinear (Gaussian) coordinates (q(exp 1), q(exp 2)). Myers uses a locally orthogonal coordinate system which is somewhat less specific than what is used here.
Farassat, F.↗
Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures
Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations, such as high power microwave or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary conditions is best suited for large aspect ratios, while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
On the Boundary Conditions at an Oscillating Contact Line: A Physical/Numerical Experimental Program
We will pursue an improved physical understanding and mathematical model for the boundary condition at an oscillating contact line at high Reynolds number. We expect that the body force is locally unimportant for earth-based systems, and that the local behavior may dominate the mechanics of partially-filled reservoirs in the microgravity environment. One important space-based application for this contact-line study is for Faraday-waves. Oscillations in the direction of gravity (or acceleration) can dominate the fluid motion during take-off and reentry with large steady-state accelerations and in orbit, where fluctuations on the order of 10(exp -4)g occur about a zero mean. Our experience with Faraday waves has shown them to be 'cleaner' than those produced by vertical or horizontal oscillation of walls. They are easier to model analytically or computationally, and they do not have strong vortex formation at the bottom of the plate. Hence many, if not most, of the experiments will be performed in this manner. The importance of contact lines in the microgravity environment is well established. We will compare high resolution measurements of the velocity field (lO micro-m resolution) using particle-tracking and particle-image velocimetry as the fluid/fluid interface is approached from the lower fluid. The spatial gradients in the deviation provide additional means to determine an improved boundary condition and a measure of the slip region. Dissipation, the size of the eddy near the contact line, and hysteresis will be measured and compare to linear and nonlinear models of viscous and irrotational but dissipative models.
Perlin, Marc↗
A Simple Derivation of the Acoustic Boundary Condition in the Presence of Flow
In modelling the noise propagation in a duct of a ducted fan engine, the authors needed the boundary condition satisfied by the acoustic pressure on a lined duct wall in the presence of flow. The result in the form used by the authors was derived by M. K. Myers who presented a formal derivation of a related result by K. Taylor. A good review of the subject can be found in reference. Here, a brief and simple derivation of the acoustic boundary condition of Myers is given. The main difference in the derivation from that in reference is that the Gaussian co-ordinate system (q(sup 1), q(sup 2), q(sup 3)(q(sup 1), q(sup 2), t)) is used to specify the instantaneous position, i.e., Lagrangian variable, of the point on the mean position of the wall with curvilinear (Gaussian) co-ordinates (q(sup 1), q(sup 2)). Myers uses a locally orthogonal coordinate system which is somewhat less specific than what is used here.
Farassat, F.↗
Exactly and Easily Applying Experimental Boundary Conditions in Computational Structural Dynamics
Most experimental setups and environment specifications define acceleration loads on the component. However, Sierra Structural Dynamics cannot apply acceleration boundary conditions in modal transient analysis. Modal analysis of these systems and environments must be done through the application of a huge artificial force to a large fictitious point mass. Introducing a large mass into the analysis is a common source of numerical error. In this report we detail a mathematical procedure to directly apply acceleration boundary conditions in modal analyses without the requirement of adding a non-physical mass to the system. We prototype and demonstrate this procedure in Matlab and scope the work required to integrate this procedure into Sierra Structural Dynamics.
97 MATHEMATICS AND COMPUTING↗
Impacts of Sub‐Grid Topographic Representations on Surface Energy Balance and Boundary Conditions in the E3SM Land Model: A Case Study in Sierra Nevada
Abstract Sub‐grid topographic heterogeneity has large impacts on surface energy balance and land‐atmosphere interactions. However, the impacts of representing sub‐grid topographic effects in land surface models (LSMs) on surface energy balance and boundary conditions remain unclear. This study analyzed and evaluated the impacts of sub‐grid topographic representations on surface energy balance, turbulent heat flux, and scalar (co‐)variances in the Energy Exascale Earth System Model (E3SM) land model (ELM). Three sub‐grid topographic representations in ELM were compared: (a) the default sub‐grid structure (D), (b) the recently developed sub‐grid topographic structure (T), and (c) high spatial resolution (1KM). Additionally, two different solar radiation schemes in ELM were compared: (a) the default plane‐parallel radiative transfer scheme (PP) and (b) the parameterization scheme (TOP) that accounts for sub‐grid topographic effects on solar radiation. A series of offline simulations with the three grid discretization structures (D, T, and 1KM) and two schemes of solar radiation (TOP and PP) were carried out using the Sierra Nevada, California. 1KM simulations with TOP well capture the spatial heterogeneity of surface fluxes compared to Moderate Resolution Imaging Spectroradiometer remote sensing data. There are significant differences between TOP and PP in the 1‐km simulated surface energy balance, but the differences in mean values and standard deviations become small when aggregated to the grid scale (i.e., 0.5°). The T configuration better mimics the 1KM simulations with TOP than the D configuration and better captures the sub‐grid topographic effects on surface energy balance and boundary conditions. These results underline the importance of representing sub‐grid topographic heterogeneities in LSMs and motivate future research to understand the sub‐grid topographic effects on land‐atmosphere interactions over mountainous areas.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Analysis of laminated, composite, circular cylindrical shells with general boundary conditions
This report develops: (1) a refined approximate theory for the static and dynamic analyses of finite, laminated, composite, circular cylindrical shells with general boundary conditions; (2) an exact three-dimensional analysis of simply supported, laminated, composite, circular cylindrical shells, and (3) a thin-shell theory for laminated, composite, circular cylindrical shells. In the refined approximate theory the displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and transverse normal stress are included. A variational approach is followed to obtain the governing differential equations and boundary conditions. A general solution of the governing differential equations is also presented. The results obtained by using the refined approximate theory and the thin-shell theory are compared with the exact results for the case of free vibrations of simply supported, laminated, composite, circular cylindrical shells. The refined approximate theory is very accurate, even for thick shells with short nodal distances, whereas thin-shell theory is reasonably accurate only for thin shells at moderate nodal distances and wave number less than 2.
Srinivas, S.↗
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.
Carpenter, Mark H.↗
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.
Carpenter, Mark H.↗
Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation
It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.
42 ENGINEERING↗
Multicomponent Gas Diffusion and an Appropriate Momentum Boundary Condition
Multicomponent gas diffusion is reviewed with particular emphasis on gas flows near solid boundaries-the so-called Kramers-Kistemaker effect. The aim is to derive an appropriate momentum boundary condition which governs many gaseous species diffusing together. The many species' generalization of the traditional single gas condition, either as slip or stick (no-slip), is not obvious, particularly for technologically important cases of lower gas pressures and very dissimilar molecular weight gases. No convincing theoretical case exists for why two gases should interact with solid boundaries equally but in opposite flow directions, such that the total gas flow exactly vanishes. ln this way, the multicomponent no-slip boundary requires careful treatment The approaches discussed here generally adopt a microscopic model for gas-solid contact. The method has the advantage that the mathematics remain tractable and hence experimentally testable. Two new proposals are put forward, the first building in some molecular collision physics, the second drawing on a detailed view of surface diffusion which does not unphysically extrapolate bulk gas properties to govern the adsorbed molecules. The outcome is a better accounting of previously anomalous experiments. Models predict novel slip conditions appearing even for the case of equal molecular weight components. These approaches become particularly significant in view of a conceptual contradiction found to arise in previous derivations of the appropriate boundary conditions. The analogous case of three gases, one of which is uniformly distributed and hence non-diffusing, presents a further refinement which gives unexpected flow reversals near solid boundaries. This case is investigated alone and for aggregating gas species near their condensation point. In addition to predicting new physics, this investigation carries practical implications for controlling vapor diffusion in the growth of crystals used in medical diagnosis (e.g. mercuric iodide) and semiconductors.
Noever, David A.↗
Dependence of Lamellar Eutectic Growth with Convection on Boundary Conditions and Geometric Confinement: A Phase-Field Lattice-Boltzmann Study
Simulating eutectic growth with convection is challenging because of the enormous computing demand resulting from the required domain size compared with the eutectic scale. In this study, a phase-field lattice-Boltzmann approach was employed to reproduce the eutectic growth with convection (both natural and forced). To enable and accelerate large-scale simulations, a parallel-adaptive mesh refinement algorithm was developed to combine with this numerical approach. The effects of the boundary conditions and the geometric confinement on the eutectic growth with convection were systematically investigated in the Al-Cu eutectic alloy. Results showed that both boundary conditions and the geometric confinement altered the eutectic evolution by affecting the distributions of the solute and velocity ahead of the eutectic solid/liquid interface. As the first attempt to explore the two factors on the eutectic growth with convection, our thorough investigation lays a foundation for modeling the coupled convection–solute eutectic evolution.
36 MATERIALS SCIENCE↗
Development of an Experimental Data Base to Validate Compressor-Face Boundary Conditions Used in Unsteady Inlet Flow Computations
The ability to predict the dynamics of integrated inlet/compressor systems is an important part of designing high-speed propulsion systems. The boundaries of the performance envelope are often defined by undesirable transient phenomena in the inlet (unstart, buzz, etc.) in response to disturbances originated either in the engine or in the atmosphere. Stability margins used to compensate for the inability to accurately predict such processes lead to weight and performance penalties, which translate into a reduction in vehicle range. The prediction of transients in an inlet/compressor system requires either the coupling of two complex, unsteady codes (one for the inlet and one for the engine) or else a reliable characterization of the inlet/compressor interface, by specifying a boundary condition. In the context of engineering development programs, only the second option is viable economically. Computations of unsteady inlet flows invariably rely on simple compressor-face boundary conditions (CFBC's). Currently, customary conditions include choked flow, constant static pressure, constant axial velocity, constant Mach number or constant mass flow per unit area. These conditions are straightforward extensions of practices that are valid for and work well with steady inlet flows. Unfortunately, it is not at all likely that any flow property would stay constant during a complex system transient. At the start of this effort, no experimental observation existed that could be used to formulate of verify any of the CFBC'S. This lack of hard information represented a risk for a development program that has been recognized to be unacceptably large. The goal of the present effort was to generate such data. Disturbances reaching the compressor face in flight may have complex spatial structures and temporal histories. Small amplitude disturbances may be decomposed into acoustic, vorticity and entropy contributions that are uncoupled if the undisturbed flow is uniform. This study is focused on the response of an inlet/compressor system to acoustic disturbances. From the viewpoint of inlet computations, acoustic disturbances are clearly the most important, since they are the only ones capable of moving upstream. Convective and entropy disturbances may also produce upstream-moving acoustic waves, but such processes are outside the scope of the present study.
Sajben, Miklos↗
Stability analysis of intermediate boundary conditions in approximate factorization schemes
In many cases, approximate factorization schemes have provided a significant increase in efficiency over previously used solution methods in certain problems. The present investigation is concerned with the importance of intermediate boundary conditions in approximate factorization schemes, taking into account a specific example regarding a boundary-induced stability restriction in a scheme for the transonic full-potential equation. The considered scheme has been discussed by Holst (1979). Holst's scheme is a variation of the AF2 schemes described by Ballhaus and Steger (1975). The application of the AF2 scheme to the two-dimensional Laplace equation in a rectangle is studied giving attention to the stability of the scheme in connection with various boundary conditions for the intermediate variable.
South, J. C., Jr.↗