DIFFUSION APPROXIMATION FOR THERMAL RADIATION IN GASES WITH JUMP BOUNDARY CONDITION
Radiative diffusion in a nongray gas with jump boundary conditions
THERMAL RADIATION↗
SEARCH · Engineering Papers
Results for “Approximate boundary”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Diffusion approximation for thermal radiation in gases with jump boundary condition.
Radiative diffusion in nongray gas with jump boundary condition
THERMAL RADIATION↗
An approximate method for estimating the incompressible laminar boundary-layer characteristics on a flat plate in slipping flow
Explore the source record for details and available documents.
Donaldson, Coleman Dup↗
Approximate formulas for the computation of turbulent boundary-layer momentum thicknesses in compressible flows
Explore the source record for details and available documents.
Tetervin, Neal↗
Evaluation of some control-volume techniques for analysis of shock-boundary layer interactions in supersonic inlets
Various control-volume models used to analyze the shock boundary layer bleed interaction were investigated. The bleed assumptions of the models and their influence on the analytical solutions are discussed. The results of the analysis using these models are compared with experimental boundary-layer data taken in a supersonic inlet. The experimental Mach number upstream of the interaction was 1.66, and the oblique-shock pressure ratio was 1.33. The boundary layer data included bleed flow rates up to approximately 0.6 of the upstream boundary layer mass flow rate. The first model assumed the bleed was removed from the control volume with a momentum that was characterized by a pressure intermediate between the upstream and downstream pressures. The second model assumed the control volume was bounded by a streamline dividing the bleed and residual flows and eliminated the need to specify the momentum of the bleed flow. Comparison of the results using the models showed that specifying the bleed pressure in one model was equivalent to specifying the pressure along the dividing streamline in the other.
Hingst, W. R.↗
Finite Element Prediction of Acoustic Scattering and Radiation from Submerged Elastic Structures
A finite element formulation is derived for the scattering and radiation of acoustic waves from submerged elastic structures. The formulation uses as fundamental unknowns the displacement in the structure and a velocity potential in the field. Symmetric coefficient matrices result. The outer boundary of the fluid region is terminated with an approximate local wave-absorbing boundary condition which assumes that outgoing waves are locally planar. The finite element model is capable of predicting only the near-field acoustic pressures. Far-field sound pressure levels may be determined by integrating the surface pressures and velocities over the wet boundary of the structure using the Helmholtz integral. Comparison of finite element results with analytic results show excellent agreement. The coupled fluid-structure problem may be solved with general purpose finite element codes by using an analogy between the equations of elasticity and the wave equation of linear acoustics.
Everstine, G. C.↗
Investigation at Mach Number 1.88 of Half of a Conical-spike Diffuser Mounted as a Side Inlet with Boundary-layer Control / H. Fred Goelzer and Edgar M. Cortright, Jr
Experimental investigation was conducted at Mach number 1.88 to determine performance characteristics of half a 50 degree-conical-spike inlet mounted on a flat plate. Initial boundary layer was removed up-stream of inlet by a ram-type scoop of variable height. Initial boundary-layer thickness was also varied. With complete removal of initial boundary layer, total-pressure recovery of approximately 70 percent. Several alternative boundary-layer-removal systems were investigated which decreased the adverse effect of operating the ram scoop sub-critically.
BOUNDARY LAYER CONTROL-INTERNAL AERODYNAMICS↗
Evaluation of the anisotropic grain boundaries and surfaces of α -U via molecular dynamics
Alloys based on uranium-zirconium are gaining renewed interest as fuels for the Versatile Test Reactor and a number of microreactor designs. Implementing metallic fuel in reactors creates the need for robust descriptive and predictive fuel performance modeling. Here, the current state of metallic fuel performance modeling relies on empirical equations derived from historical experiments, which may be unreliable when applied outside of their temperature, power, and composition phase space. One area where such data is lacking is the irradiation behavior of alpha -U, specifically tearing and porosity formation at the early stages of irradiation. While grain boundaries likely play a key role in this fuel behavior, relatively little is known about grain boundaries in alpha-U. Thus, we evaluate the grain boundary, surface energy, and work of adhesion of alpha -U utilizing molecular dynamics. Symmetric tilt grain boundaries (STGBs) are analyzed with the tilt plane oriented along each major crystallographic axis, for a total of eighty unique grain boundaries. The effect of temperature, tilt plane, and misorientation angle on interfacial energies are analyzed. The interfacial energies typically increase with temperature and there is significant variance as a function of misorientation angle, irrespective of the tilt plane. At 500 K, the average surface energy (1.23 J/m 2 ) is approximately 1.5 times the grain boundary energy (0.79 J/m 2 ), and the work of adhesion is approximately twice the grain boundary energy (1.68 J/m 2 ). Orientations for the likely formation of twins and likely failure planes are identified.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
A three-dimensional axisymmetric calculation procedure for turbulent flows in a radial vaneless diffuser
An analytical model is proposed to calculate the three-dimensional axisymmetric turbulent flowfield in a radial vneless diffuser. The model assumes that the radial and tangential boundary layer profiles are approximated by power law profiles. Then, using the integrated radial and tangential momentum and continuity equations for the boundary layer and corresponding inviscid equations for the core flow, there results six ordinary differential equation in six unknowns which are easily solved using a Runge-Kutta technique. A model is also proposed for fully developed flow. The results using this technique were compared with the results from a three-dimensional viscous, axisymmetric duct code and with experimental data and good quantitative agreement was obtained.
Schumann, L. F.↗
A compact solution to computational acoustics
This paper demonstrates that the linearized, dimensional Euler equations for acoustic computation can be accurately solved as a set of decoupled first-order wave equations, and that if ordered properly, this system of simple waves has unambiguous, easily implemented boundary conditions, allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions. Thus, the task of designing a complex multi-dimensional scheme with approximate far-field boundary conditions reduces to the design of higher order schemes for the one-dimensional simple wave equation. A compact finite-difference scheme and a characteristically exact but numerically n(th) order accurate boundary condition are introduced for solving the first order wave equation. Spanning a three-point two-level stencil, this low-dispersion implicit scheme has a third order spatial accuracy when used on nonuniform meshes, fourth order accurate on uniform meshes, and a temporal accuracy of second order due to the choice of trapezoidal integration for algorithmic simplicity. The robustness and accuracy of the scheme are demonstrated through a series of numerical experiments and comparisons with published results. When tested on the one-dimensional wave equation on a uniform grid, this scheme allows a Gaussian wave packet to pass through any finite domain with low numerical dispersion characteristic of a spatially fourth-order scheme and reflections at numerical boundaries maintained below truncation error. On highly stretched and irregular grids, only mild dispersions are found in the solution while solutions by other methods fail or are severely distorted. Yet, this scheme is no more sophisticated to solve or implement than the Crank-Nicolson scheme. This scheme has been tested on four categories of the ICASE/LaRC benchmark problems, which include propagation of acoustic and convective waves in Cartesian and cylindrical domains, reflection of acoustic wave at stationary/moving boundaries, and sound generation by gust-blade interaction.
Fung, K.-Y.↗
Measurements in the near-wall region of a relaxing three-dimensional low speed turbulent air boundary layer
An experimental investigation was conducted at selected locations of the near-wall region of a three dimensional turbulent air boundary layer relaxing in a nominally zero external pressure gradient behind a transverse hump (in the form of a 30 deg swept, 5-foot chord wing-type model) faired into the side wall of a low speed wind tunnel. Wall shear stresses measured with a flush-mounted hot-film gage and a sublayer fence were in very good agreement with experimental data obtained with two Preston probes. With the upstream unit Reynolds number held constant at 325,000/ft. approximately one-fourth of the boundary layer thickness adjacent to the wall was surveyed with a single rotated hot-wire probe mounted on a specially designed minimum interference traverse mechanism. The boundary layer (approximately 3.5 in thick near the first survey station where the length Reynolds number was 5.5 million) had a maximum crossflow velocity ratio of 0.145 and a maximum crossflow angle of 21.875 deg close to the wall.
Hebbar, K. S.↗
Low-speed Investigation of a Semisubmerged Air Scoop with and Without Boundary-layer Suction
A preliminary low-speed investigation has been made of an air scoop submerged one-half the inlet height in a depression on the surface of a simulated fuselage. Boundary-layer suction was used on the steep approach ramp to improve the internal flow. A 6-degree-included-angle diffuser with an area ratio of 1.9:1 was located behind the inlet in the model. Most of the tests were conducted with an initial turbulent boundary layer believed to approximate that which would occur on the forward part of a fuselage. A few tests were made with a boundary layer about 2.5 times the thickness of the original boundary layer to determine the effect of moving the inlet further rearward on the fuselage. The effects of suction-slot location and slot width were determined and a few tests with area suction were made. The maximum quantity of suction flow was about 15 percent of the inlet flow at an inlet-velocity ratio of 0.6.
Pierpont, P Kenneth↗
Structure of the low-latitude boundary layer
High temporal resolution observations of the frontside magnetopause and plasma boundary layer made with the fast plasma analyzer aboard the ISEE 1 and 2 spacecraft are reported. The data are found to be compatible with a boundary layer that is always attached to the magnetopause but where the layer thickness has a large-scale spatial modulation pattern which travels tailward past the spacecraft. Periods are included when the thickness is essentially zero and others when it is of the order of 1 earth radius. The duration of these periods is highly variable but is typically in the range of 2-5 min corresponding to a distance along the magnetopuase of approximately 3-8 earth radii. The observed boundary layer features include a steep density gradient at the magnetopause with an approximately constant boundary layer plasma density amounting to about 25% of the magnetosheath density, and a second abrupt density decrease at the inner edge of the layer.
Sckopke, N.↗
Neural operator prediction of linear instability waves in high-speed boundary layers
Here, we investigate if neural operators can predict the linear evolution of instability waves in high-speed boundary layers. To this end, we extend the design of the DeepOnet to ensure accurate and robust predictions, and also to perform data assimilation. In particular, we train DeepONet to take as inputs an upstream disturbance and a downstream location of interest, and to provide as output the perturbation field downstream in the boundary layer. DeepONet thus approximates the linearized and parabolized Navier-Stokes operator for this flow. For successful application to the high-speed boundary layer problem, we add sample weighting and Fourier input features to the regular DeepONet formulation. Once trained, the DeepOnet can perform fast and accurate predictions of the downstream disturbances within the range of training frequencies (inside the distribution). In addition, we show that DeepONet can solve the inverse problem, where downstream wall measurements are adopted as input, and a trained network can predict the upstream disturbances that led to these observations. This capability, along with the forward predictions, allows us to perform a full data assimilation cycle efficiently: starting from wall-pressure data, we predict the upstream disturbance using the inverse DeepONet and its evolution using the forward DeepONet. Finally, we introduce three new metrics to benchmark the training, evaluation and break-even cost of neural operators.
42 ENGINEERING↗
A state-trajectory control law for dc-to-dc converters
Mathematical representations of a state-plane switching boundary employed in a state-trajectory control law for dc-to-dc converters are derived. Several levels of approximation to the switching boundary equations are presented, together with an evaluation of the effects of nonideal operating characteristics of converter power stage components on the shape and location of the boundary and the behavior of a system controlled by it. Digital computer simulations of dc-to-dc converters operating in conjunction with each of these levels of control are presented and evaluated with respect to changes in transient and steady-state performance.
Burns, W. W., III↗
Analytic derivation and evaluation of a state-trajectory control law for dc-to-dc converters
Mathematical representations of a state-plane switching boundary employed in a state-trajectory control law for dc-to-dc converters are derived. Several levels of approximation to the switching boundary equations are presented, together with an evaluation of the effects of nonideal operating characteristics of converter power stage components on the shape and location of the boundary and the behavior of a system controlled by it. Digital computer simulations of dc-to-dc converters operating in conjunction with each of these levels of control are presented and evaluated with respect to changes in transient and steady-state performance.
Burns, W. W., III↗
An implicit-iterative solution of the heat conduction equation with a radiation boundary condition
For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.
Williams, S. D.↗
Analysis of the weighted shifted boundary method for the Poisson and Stokes problems
The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.
Approximate domain boundaries↗