Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convection diffusion 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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Gravitational effects on chemically reacting laminar boundary layer flows over a horizontal flat plate

A theoretical study of the chemically reacting laminar boundary layer flow over a horizontal flat plate with gravitationally induced buoyant force is presented. A diffusion flame sheet model was used to describe the combustion process. The effects of gravity on the purely force convection flow can be characterized by a dimensionless coordinate quantity, which is involved in the generation of the governing equations. A numerical solution of the zero and first order governing equations subject to the appropriate physical boundary conditions was obtained. It is shown that the cross stream buoyancy induced body force acts effectively to produce a streamwise pressure gradient in the fluid adjacent to the plate surface. It is concluded that buoyancy plays an important role in boundary layer diffusion flames.

Lavid, M.↗
NASA NTRS1991

Analysis of a dusty wall jet

An analysis is given for the entrainment of dust into a turbulent radial wall jet. Equations are solved based on incompressible flow of a radial wall jet into which dust is entrained from the wall and transported by turbulent diffusion and convection throughout the flow. It is shown that the resulting concentration of dust particles in the flow depends on the difference between the applied shear stress at the surface and the maximum level of shear stress that the surface can withstand (varies as rho(sub d)a(sub g)D) i.e., the pressure due to the weight of a single layer of dust. The analysis is expected to have application to the downflow that results from helicopter and VTOL aircraft.

Lim, Hock-Bin↗
NASA NTRS1985

The modulation features of the long-period cosmic ray variations in connection with the sign change of the general magnetic field of the Sun

On the basis of the model and experimental investigations, the spatial distribution of cosmic ray anisotropy for the different epochs of solar activity is studied. A solution is offered to the anisotropic diffusion equation with regard to the electromagnetic conditions for the periods of minimum and maximum solar activity and cosmic ray particle drift in a regular interplanetary magnetic field. It is shown that the long period changes amplitude and phase of the diurnal variations of cosmic rays is limited not only by convection and diffusion of particles but also by the drift effect before and after the sing change of the general magnetic field of the Sun. The calculated model is compared with the results obtained on the basis of an analysis of the experimental data from the neutron super monitor station, and it is shown that for the periods when the lines of magnetic force of the Sun come from the Northern Hemisphere the phase of the first harmonic diurnal variation is shifted forwards to an earlier time.

Iskra, K.↗
NASA NTRS1996

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗
NASA NTRS1997

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Bune, Andris V.↗
NASA NTRS1980

Velocity and concentration distribution in a Stefan diffusion tube

Numerical solutions for the diffusion- and gravity-driven flow in a cylindrical Stefan tube were obtained from the coupled diffusion and Navier-Stokes equations of Peclet numbers 0.3, 1 and 5. Distributions of binary component concentrations and velocities were calculated. The mass average velocity is parabolic in nature, except at high Peclet numbers. The solvent is not stagnant but recirculates, even in the absence of gravity. Radial concentration gradients develop which act convectively destabilizing. Consequences for the deduction of diffusion coefficients from Stefan tube experiments are discussed.

Markham, B. L.↗
NASA NTRS1994

Incorporating interfacial phenomena in solidification models

A general methodology is available for the incorporation of microscopic interfacial phenomena in macroscopic solidification models that include diffusion and convection. The method is derived from a formal averaging procedure and a multiphase approach, and relies on the presence of interfacial integrals in the macroscopic transport equations. In a wider engineering context, these techniques are not new, but their application in the analysis and modeling of solidification processes has largely been overlooked. This article describes the techniques and demonstrates their utility in two examples in which microscopic interfacial phenomena are of great importance.

Beckermann, Christoph↗
NASA NTRS1999

Analogies Between Colloidal Sedimentation and Turbulent Convection at High Prandtl Numbers

A new set of coarse-grained equations of motion is proposed to describe concentration and velocity fluctuations in a dilute sedimenting suspension of non-Brownian particles. With these equations, colloidal sedimentation is found to be analogous to turbulent convection at high Prandtl numbers. Using Kraichnan's mixing-length theory, we obtain scaling relations for the diffusive dissipation length delta(sub theta), the velocity variance delta u, and the concentration variance delta phi. The obtained scaling laws over varying particle radius alpha and volume fraction phi(sub ) are in excellent agreement with the recent experiment by Segre, Herbolzheimer, and Chaikin. The analogy between colloidal sedimentation and turbulent convection gives a simple interpretation for the existence of a velocity cut-off length, which prevents hydrodynamic dispersion coefficients from being divergent. It also provides a coherent framework for the study of sedimentation dynamics in different colloidal systems.

Tong, P.↗
NASA NTRS1981

State of the art in subgrid scale modeling

The present state of the art in subgrid scale modeling for large eddy simulation is reviewed. It is found that the eddy viscosity models are sufficient for simulating homogeneous flows but are probably insufficient for inhomogeneous shear flows. One- and two-equation subgrid scale models probably will not be of great value in subgrid scale modeling, and full Reynolds stress models may be required. In the latter, the convection and diffusion terms are expected to be of greater importance than they are in time-average modeling, but the pressure redistribution terms may be of less importance. A scale similarity model may provide an alternative.

Ferziger, J. H.↗
NASA NTRS1985

The equilibrium structure of thin magnetic flux tubes. I

A model atmosphere within a thin magnetic flux tube that is embedded in an arbitrarily stratified medium is presently constructed by solving the radiative transfer equation in the two-stream approximation for gray opacity, under the assumption that the magnetic field is sufficiently strong to warrant the neglect of both thermal conduction and convective diffusion; energy inside the flux tube therefore being transported solely by radiation. The structure of the internal atmosphere is determined on the basis of the hydrostatic and radiative equilibrium conditions of the tube embedded in an external atmosphere. The gas temperature along the axis of the tube is computed, and the geometry of the flux tube is determined on the basis of magnetic flux conservation and total pressure equilibrium.

Ferrari, A.↗
NASA NTRS1995

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

Vadyak, Joseph↗
NASA NTRS1976

Solutions of the Navier-Stokes equations for vortex breakdown

A numerical investigation of vortex breakdown has been undertaken in an attempt to understand its properties, and the mechanisms responsible for it. Solutions of the full steady axisymmetric Navier-Stokes equations for breakdown in an unconfined viscous vortex have been obtained for core Reynolds numbers up to 200, for a two-parameter family of assumed upstream velocity distributions. Diffusion and convection of vorticity away from the vortex core, and the strong coupling between the circumferential and axial velocity fields in highly-swirling flows, are shown to lead to stagnation and reversal of the axial flow near the axis. The various theories of vortex breakdown are considered in light of the present numerical solutions.

Grabowski, W. J.↗
NASA NTRS1978

Numerical method for boundary layers with blowing - The exponential box scheme

The paper describes a new numerical scheme based on exponential difference operator concepts combined with Keller's (1968) box scheme approach to produce a stable second-order accurate finite-difference scheme for convection-diffusion problems arising in boundary layer flows in the presence of massive injection through a porous surface. The technique is demonstrated by application to the self-similar boundary layer equations with massive blowing at the surface.

El-Mistikawy, T. M.↗
NASA NTRS1993

Flux-difference split parabolized Navier-Stokes algorithm for non-equilibrium chemically reacting flows

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rather than the steady Riemann problem, is solved. The algorithm allows either a second or an approximately third-order accurate upwind treatment of the convection terms by employing the unsteady approximate Riemann solver of Roe. The source terms of the species transport equations are treated in either an explicit or implicit manner, and the species diffusion terms are modeled with either a Fickian or a multicomponent model. A validation of the algorithm is performed by comparing computational results with the 2-D Mach 14, 15 degree compression-corner data of Holden. The three-dimensional capability of the algorithm is demonstrated by computing Mach 2.7 flow over a swept wedge scramjet fuel injector, and three-dimensional reacting flow capability is demonstrated by a computing a shock-jet interaction concept for mixing and combustion enhancement.

White, J. A.↗
NASA NTRS2005

Removal of organic contaminants by RO and NF membranes

Rejection characteristics of organic and inorganic compounds were examined for six reverse osmosis (RO) membranes and two nanofiltration (NF) membranes that are commercially available. A batch stirred-cell was employed to determine the membrane flux and the solute rejection for solutions at various concentrations and different pH conditions. The results show that for ionic solutes the degree of separation is influenced mainly by electrostatic exclusion, while for organic solutes the removal depends mainly upon the solute radius and molecular structure. In order to provide a better understanding of rejection mechanisms for the RO and NF membranes, the ratio of solute radius (r(i,s)) to effective membrane pore radius (r(p)) was employed to compare rejections. An empirical relation for the dependence of the rejection of organic compounds on the ratio r(i,s)/r(p) is presented. The rejection for organic compounds is over 75% when r(i,s)/r(p) is greater than 0.8. In addition, the rejection of organic compounds is examined using the extended Nernst-Planck equation coupled with a steric hindrance model. The transport of organic solutes is controlled mainly by diffusion for the compounds that have a high r(i,s)/r(p) ratio, while convection is dominant for compounds that have a small r(i,s)/r(p) ratio. c2005 Elsevier B.V. All rights reserved.

NASA Discipline Life Sciences Technologies↗
NASA NTRS1993

A numerical study of confined turbulent jets

A numerical investigation is reported of turbulent incompressible jets confined in two ducts, one cylindrical and the other conical with a 5 degree divergence. In each case, three Craya-Curtet numbers are considered which correspond, respectively, to flow situations with no moderate and strong recirculation. Turbulence closure is achieved by using the k-epsilon model and a recently proposed realizable Reynolds stress algebraic equation model that relates the Reynolds stresses explicitly to the quadratic terms of the mean velocity gradients and ensures the positiveness of each component of the turbulent kinetic energy. Calculations are carried out with a finite-volume procedure using boundary-fitted curvilinear coordinates. A second-order accurate, bounded convection scheme and sufficiently fine grids are used to prevent the solutions from being contaminated by numerical diffusion. The calculated results are compared extensively with the available experimental data. It is shown that the numerical methods presented are capable of capturing the essential flow features observed in the experiments and that the realizable Reynolds stress algebraic equation model performs much better than the k-epsilon model for this class of flows of great practical importance.

Zhu, J.↗
NASA NTRS2000

Design and Performance of McRas in SCMs and GEOS I/II GCMs

The design of a prognostic cloud scheme named McRAS (Microphysics of clouds with Relaxed Arakawa-Schubert Scheme) for general circulation models (GCMs) will be discussed. McRAS distinguishes three types of clouds: (1) convective, (2) stratiform, and (3) boundary-layer types. The convective clouds transform and merge into stratiform clouds on an hourly time-scale, while the boundary-layer clouds merge into the stratiform clouds instantly. The cloud condensate converts into precipitation following the auto-conversion equations of Sundqvist that contain a parametric adaptation for the Bergeron-Findeisen process of ice crystal growth and collection of cloud condensate by precipitation. All clouds convect, advect, as well as diffuse both horizontally and vertically with a fully interactive cloud-microphysics throughout the life-cycle of the cloud, while the optical properties of clouds are derived from the statistical distribution of hydrometeors and idealized cloud geometry. An evaluation of McRAS in a single column model (SCM) with the GATE Phase III and 5-ARN CART datasets has shown that together with the rest of the model physics, McRAS can simulate the observed temperature, humidity, and precipitation without many systematic errors. The time history and time mean incloud water and ice distribution, fractional cloudiness, cloud optical thickness, origin of precipitation in the convective anvil and towers, and the convective updraft and downdraft velocities and mass fluxes all show a realistic behavior. Performance of McRAS in GEOS 11 GCM shows several satisfactory features but some of the remaining deficiencies suggest need for additional research involving convective triggers and inhibitors, provision for continuously detraining updraft, a realistic scheme for cumulus gravity wave drag, and refinements to physical conditions for ascertaining cloud detrainment level.

Sud, Yogesh C.↗
NASA NTRS1997

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

Cockburn, Bernardo↗