Search NASA⌕ Search

SEARCH · Search NASA

Results for “Continuity equation”

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.

At least 127 records · Page 7

Kinetic energy budgets in areas of intense convection

A kinetic energy budget analysis of the AVE-SESAME 1 period which coincided with the deadly Red River Valley tornado outbreak is presented. Horizontal flux convergence was found to be the major kinetic energy source to the region, while cross contour destruction was the major sink. Kinetic energy transformations were dominated by processes related to strong jet intrusion into the severe storm area. A kinetic energy budget of the AVE 6 period also is presented. The effects of inherent rawinsonde data errors on widely used basic kinematic parameters, including velocity divergence, vorticity advection, and kinematic vertical motion are described. In addition, an error analysis was performed in terms of the kinetic energy budget equation. Results obtained from downward integration of the continuity equation to obtain kinematic values of vertical motion are described. This alternate procedure shows promising results in severe storm situations.

Fuelberg, H. E.↗

Investigation of Convection and Pressure Treatment with Splitting Techniques

Treatment of convective and pressure fluxes in the Euler and Navier-Stokes equations using splitting formulas for convective velocity and pressure is investigated. Two schemes - controlled variation scheme (CVS) and advection upstream splitting method (AUSM) - are explored for their accuracy in resolving sharp gradients in flows involving moving or reflecting shock waves as well as a one-dimensional combusting flow with a strong heat release source term. For two-dimensional compressible flow computations, these two schemes are implemented in one of the pressure-based algorithms, whose very basis is the separate treatment of convective and pressure fluxes. For the convective fluxes in the momentum equations as well as the estimation of mass fluxes in the pressure correction equation (which is derived from the momentum and continuity equations) of the present algorithm, both first- and second-order (with minmod limiter) flux estimations are employed. Some issues resulting from the conventional use in pressure-based methods of a staggered grid, for the location of velocity components and pressure, are also addressed. Using the second-order fluxes, both CVS and AUSM type schemes exhibit sharp resolution. Overall, the combination of upwinding and splitting for the convective and pressure fluxes separately exhibits robust performance for a variety of flows and is particularly amenable for adoption in pressure-based methods.

Thakur, Siddharth↗

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 2: Constant property turbulent boundary layer flow with simultaneous mass transfer and pressure gradient

An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.

Boccio, J.↗

Approach to the origin of turbulence on the basis of two-point kinetic theory

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

Tsuge, S.↗

A theoretical study of the acoustic impedance of orifices in the presence of a steady grazing flow

Oscillatory fluid flow in the vicinity of a circular orifice with a steady grazing flow is analyzed. A simplified system of partial differential equations is obtained by starting with the momentum and continuity equations and by assuming that the flow can be represented as an oscillatory motion superimposed on the (known) steady flow. It is found that the equations are linear in the region where grazing-flow effects dominate; a solution and the resultant orifice impedance are given for this region. It is tentatively concluded that orifice resistance is directly proportional to grazing-flow velocity and that the orifice inductive end correction is not a function of grazing flow.

Rice, E. J.↗

Simulation of three-dimensional liquid sloshing flows using a strongly implicit calculation procedure

A coupled strongly implicit solution strategy for unsteady three-dimensional free surface flows has been developed based on an artificial compressibility formulation for the incompressible Navier-Stokes equations. A pseudotime term has been used in the continuity equation to permit time accurate calculations to be achieved. The scheme appears capable of tracking the free surface reasonably accurately inside a partially-filled spherical container undergoing a general rotating motion characteristic of that experienced by a spin-stabilized satellite. Five different free surface calculations have been presented. Some of the results exhibit an interesting Reynolds number dependent oscillatory behavior which is believed to be physical although no experimental results appears to be available for verification to date.

Chen, K.-H.↗

Statistically Reliable 'Atomistic' Simulation of Sub 100 nm MOSFETs

A 3D 'atomistic' simulation technique to study random impurity induced threshold voltage lowering and fluctuations in sub 0. 1 micron MOSFETs is presented. It allows statistical analysis of random impurity effects down to the individual impurity level-Efficient algorithms based on a single solution of Poisson's equation, followed by the solution of a simplified current continuity equation are used in the simulations.

Asenov, Asen↗

Efficient 3D 'Atomistic' Simulation Technique for Studying of Random Dopant Induced Threshold Voltage Lowering and Fluctuations in Decanano MOSFETs

A 3D 'atomistic' simulation technique to study random dopant induced threshold voltage lowering and fluctuations in sub 0.1 micron MOSFETs is presented. It allows statistical analysis of random impurity effects down to the individual impurity level. Efficient algorithms based on a single solution of Poisson's equation, followed by the solution of a simplified current continuity equation are used in the simulations.

Asenov, Asen↗

Random Dopant Induced Threshold Voltage Lowering and Fluctuations in Sub-0.1 (micron)meter MOSFET's: A 3-D 'Atomistic' Simulation Study

A three-dimensional (3-D) "atomistic" simulation study of random dopant induced threshold voltage lowering and fluctuations in sub-0.1 microns MOSFET's is presented. For the first time a systematic analysis of random dopant effects down to an individual dopant level was carried out in 3-D on a scale sufficient to provide quantitative statistical predictions. Efficient algorithms based on a single multigrid solution of the Poisson equation followed by the solution of a simplified current continuity equation are used in the simulations. The effects of various MOSFET design parameters, including the channel length and width, oxide thickness and channel doping, on the threshold voltage lowering and fluctuations are studied using typical samples of 200 atomistically different MOSFET's. The atomistic results for the threshold voltage fluctuations were compared with two analytical models based on dopant number fluctuations. Although the analytical models predict the general trends in the threshold voltage fluctuations, they fail to describe quantitatively the magnitude of the fluctuations. The distribution of the atomistically calculated threshold voltage and its correlation with the number of dopants in the channel of the MOSFET's was analyzed based on a sample of 2500 microscopically different devices. The detailed analysis shows that the threshold voltage fluctuations are determined not only by the fluctuation in the dopant number, but also in the dopant position.

Asenov, Asen↗

The effect of microscopic turbulence on magnetosphere-ionosphere coupling

The effect of turbulence on the coupling of the magnetosphere and ionosphere has been investigated by including an effective collision frequency in the electron equation of motion. When this term is combined with the continuity equation, the ion equation of motion and Maxwell's equations, a dispersion relation for the kinetic Alfven wave including effective collisions is found. The wave-particle interaction leads to a strong damping of the wave. Inclusion of the effects of plasma sheet kinetics yields a scale size transverse to the magnetic field which corresponds to the size of visual auroral arcs.

Lysak, R. L.↗

A numerical model of magnetosphere-ionosphere coupling Preliminary results

A three-dimensional simulation model was developed to study magnetosphere-ionosphere coupling in the auroral region. One-fluid MHD equations are adopted to model the magnetosphere, and current density continuity equations were solved consistently to model the ionosphere. In the preliminary simulation runs described here, the electrodynamics of region 1 field-aligned currents were modeled. Initially, the electric field is taken to be in the magnetospheric equatorial plane. Alfven waves then propagate down to the ionosphere, accompanying a field-aligned current and exciting the electrostatic potential in the ionosphere by electrodynamic coupling. The results of the preliminary runs directly correspond with the fundamental characteristics of global magnetosphere-ionosphere coupling. These characteristics include an ionospheric electrostatic potential which varies in its development in time, depending upon the ratio of ionospheric resistance to magnetospheric impedance, the flowing of field-aligned currents into the ionosphere on the dawnside and out on the duskside, and the distribution along the geomagnetic field of the amplitude of the field-aligned current density in proportion to the field intensity.

Watanabe, K.↗

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Cai, Z.↗

Descending Layer Variability Over Arecibo

Descending layers of ionization over Arecibo exhibit very diverse behavior from night to night that does not appear to be strongly correlated to geomagnetic activity, solar forcing, or average semidiurnal tidal winds. On some nights, three or more distinct layers are observed to form near 170 km over timescales of approx. 2 hours. Rather than descending smoothly over periods of several hours, these layers stall, abruptly disappear, or even reverse direction in the midst of their descent. The time scales for their disappearance are examined and compared to loss rates arising from diffusion and recombination. Diffusion alone is found to be too slow to account for the observations, but recombination is fast enough provided that the convergent wind shear that forms the layer is relatively weak coincident with their disappearance. The continuity equation is solved in conjunction with a time sequence of radar profiles to estimate the vertical drift and horizontal neutral wind consistent with the observed behavior. The resultant wind field is northward, has an average speed of approx. 80 m/ s, and varies significantly near the altitude where the layers are observed. These inferred winds are consistent with the presence of the observed layers, and their magnitudes as obtained from the classical continuity and momentum equations are reasonable for this altitude range.

Earle, G. D.↗

A composite velocity procedure for the compressible Navier-Stokes equations

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Khosla, P. K.↗

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗

Prediction of vortical flows on wings using incompressible Navier-Stokes equations

Numerical solutions to the incompressible Navier-Stokes equations are in greater demand than ever before as the field of computational fluid dynamics (CFD) increases its impact as an engineering tool. An implicit upwind-relation finite-difference scheme is developed for solving unsteady incompressible Navier-Stokes equations incorporating an artificial time derivative of the pressure to the continuity equation. The essential features observed in experiments for complicated vortical flows past three round-edged low-aspect-ratio wings at high angles of attack are reproduced both qualitatively and quantitatively.

Hsu, C.-H.↗