SEARCH · Engineering Papers

Results for “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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,369 records · Page 76

All sources NASA NTRS DOE OSTI

NASA NTRS1979

A calculation procedure for viscous flow in turbomachines, volume 1

A method for analyzing the nonadiabatic viscous flow through turbomachine rotors is presented. The field analysis is based upon the numerical integration of the full incompressible stream function vorticity form of the Navier-Stokes equations, together with the energy equation, over the rotor blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. A numerical scheme is used to carry out the necessary integration of the elliptic governing equations. The flow characteristics within the rotor of a radial inflow turbine are investigated over a wide range of operating conditions. The calculated results are compared to existing experimental data. The flow in a radial compressor is analyzed in order to study the behavior of viscous flow in diffusing cascades. The results are compared qualitatively to known experimental trends. The solution obtained provides insight into the flow phenomena in this type of turbomachine. It is concluded that the method of analysis is quite general and gives a good representation of the actual flow behavior within turbomachine passages.

Khalil, I.↗

NASA NTRS1982

Analytical calculation of a single jet in crossflow and comparison with experiment

A series of calculations of a jet in crossflow using a three-dimensional finite difference model of the Navier-Stokes equations were made on a series of progressively finer grids. With a reasonable number of grid point (40x30x20), calculated jet penetration and mixing characteristics were found to compare favorably with the experimental measurements of Crabb, Durao and Whitelaw. The calculated results were grid dependent (i.e., numerical or false diffusion was present in the result). A finer grid calculation indicated that turbulence model deficiencies may become more noticeable in the calculated results as the magnitude of numerical diffusion is reduced.

Clauss, R. W.↗

NASA NTRS1988

A new approach to the oxidational theory of mild wear

The wear and friction of 316 stainless steel was investigated in relation to oxidation at the real area of contact. An approach describing the oxidation characteristics of mild wear in terms of linear oxidation kinetics is presented. Linear oxidation kinetics more closely approaches the physical conditions involved where oxide growth on asperities is continuously interrupted by spalling and removal. The mild wear rate may now be described mathematically by two empirical equations in terms of the operational variables and the oxidational constants without using the critical oxide thickness, which is dependent on asperity size, shape and temperature, and is difficult to measure. The resulting activation energy for oxidational wear was significantly lower than that for static oxidation governed by diffusion controlled kinetics.

Hong, H.↗

NASA NTRS1991

Re-ionization and decaying dark matter

Gunn-Peterson tests suggest that the Universe was reionized after the standard recombination epoch. A systematic treatment is presented of the ionization process by deriving the Boltzmann equations appropriate to this regime. A compact solution for the photon spectrum is found in terms of the ionization ratio. These equations are then solved numerically for the Decaying Dark Matter scenario, wherein neutrinos with mass of order 30 eV radiatively decay producing photons which ionize the intergalactic medium. It was found that the neutrino mass and lifetime are severely constrained by Gunn-Peterson tests, observations of the diffuse photon spectrum in the ultraviolet regime, and the Hubble parameter.

Dodelson, Scott↗

NASA NTRS1993

Why does preferential diffusion strongly affect premixed turbulent combustion?

Combustion of premixed reactants in a turbulent flow is a classical but unresolved problem. The key problem is to explain the following data: the maximal turbulent and laminar burning velocities u(sub t) and u(sub L) occur at different equivalence ratios Phi. It is known that the equivalence ratio varies along a curved flame if molecular diffusivity D(sub fuel) does not equal D(sub oxygen). However, the mean flame radius of curvature is much larger than the laminar flame thickness delta-L. Therefore, significant influence of preferential diffusion should occur only if the flame propagation speed varies with flame curvature. This conclusion agrees with Zel'dovich's long-standing idea about the important role of leading points of a flame. The main objective of this paper is to prove Zel'dovich's hypothesis. An equation for the mean flame surface area density (MFSAD) is employed for this purpose. The second objective of this paper is to suggest a different approach to the derivation of the equation for MFSAD. It is based on the pdf equation for the reaction progress variable C and the relation between the pdf and MFSAD. This treatment suggests an entirely different closure assumption.

Kuznetsov, Vadim R.↗

NASA NTRS1995

Effects of pressure gradients on turbulent premixed flames

The influence of a constant acceleration on a turbulent premixed flame is studied by direct numerical simulation. This acceleration induces a mean pressure gradient across the flame brush, leading to a modification of the turbulent flame structure due to differential buoyancy mechanisms between heavy cold fresh and light hot burnt gases. Such a pressure gradient may be encountered in practical applications in ducted flames. A favorable pressure gradient, i.e. the pressure decreases from unburnt to burnt gases, is found to decrease the flame wrinkling, the flame brush thickness, and the turbulent flame speed. A favorable pressure gradient also promotes counter-gradient turbulent transport. On the other hand, adverse pressure gradients tend to increase the flame brush thickness and turbulent flame speed, and promote classical gradient turbulent transport. The balance equation for the turbulent flux of the Favre averaged progress variable is also analyzed. The first results show that the fluctuating pressure term, cannot be neglected as generally assumed in models. Simple models assuming that a high mean pressure gradient may only be balanced by the cross-dissipation term seem too approximate. This analysis has to be continued to compare simulation data and closure schemes proposed for the transport equation. The analysis developed by Veynante et al.(1995) has been extended to imposed acceleration and mean pressure gradients. A simple model for the turbulent flux is proposed and validated from simulation data. Then, a modified criterion is derived to delineate between counter-gradient and gradient turbulent diffusion. In fact, counter-gradient diffusion may occur in most practical applications, especially for ducted flames.

Veynante, D.↗

NASA NTRS2001

Rheology of Diabase: Implications for Tectonics on Venus and Mars

Two important goals of our experimental investigation of the rheological behavior of diabase rocks were: (1) to determine flow laws describing their creep behavior over wide ranges of temperature, stress and strain rate and (2) to develop an understanding of the physical mechanisms by which these rocks flow under laboratory conditions. With this basis, a primary objective then was to construct constitutive equations that can be used to extrapolate from laboratory to planetary conditions. We specifically studied the rheological properties of both natural rock samples and synthetic aggregates. The former provided constraints for geologic systems, while the latter defined the relative contributions of the constituent mineral phases and avoided the influence of glass/melt found in natural samples. In addition, partially molten samples of crustal rock composition were deformed in shear to large strains (greater than 200%) important in crustal environments. The results of this research yielded essential rheological properties essential for models of crustal deformation on terrestrial planets, specifically Venus and Mars, as well as on the geodynamical evolution of these planets. Over the past three years, we also completed our investigation of the creep behavior of water ice with applications to the glaciers, ice sheets and icy satellites. Constitutive equations were determined that describe flow over a wide ranged of stress, strain rate, grain size and temperature. In the case of ice, three creep regimes were delineate. Extrapolation demonstrates that dislocation glide and grain boundary sliding processes dominate flow in ice I under planetary conditions and that diffusion creep is not an important deformation mechanism either in the laboratory or on icy satellites. These results have already been incorporated by other investigators into models describing, for example, the thickness and stability of the ice shell on Europa and to unravel long-standing discrepancies between field observations on glaciers and laboratory results.

Kohlstedt, David L.↗

NASA NTRS1977

Field-aligned currents and ionospheric electric fields

It is shown that the observed distribution of the ionospheric electric field can be deduced from an equation combining Ohm's law with the current continuity equation by using the 'observed' distribution of field-aligned currents as the boundary condition for two models of the ionosphere. The first model has one conductive annular ring representing the quiet-time auroral precipitation belt; the second has two conductive annular rings that simulate the discrete and diffuse auroral regions. An analysis is performed to determine how well the electric-field distribution can be reproduced. The results indicate that the first model reproduces the Sq(p)-type distribution, the second model reproduces reasonably well a substorm-type potential and ionospheric current patterns together with the Harang discontinuity, and that the distribution of field-aligned currents is the same for both models.

Yasuhara, F.↗

NASA NTRS1981

A numerical model study of long-term planetary wave predictability

A numerical model was developed to study planetary wave behavior over periods up to 4 months under the influences of stochastic and diffusive forcing by synoptic scale motions and of sea surface temperature anomalies. The model is suitable for Monte Carlo experiments which provide ensemble mean and variance predictions and permit the response to heating anomalies to be partly separated from random variability. The model incorporates the linear-balanced dynamical equations for wind at two tropospheric levels and temperature at one level. The model atmosphere is forced by semiempirical January heating linearly dependent on local air temperature. Topography and the lower boundary layer are represented by vertical motion and drag functions, respectively, of the lower level wind. The linear phase speeds of Rossby waves are modified to reflect the effect of the stratosphere.

Wobus, R. L.↗

NASA NTRS1984

On the theory of cosmic-ray-mediated shocks with variable compression ratio

Cosmic-ray-mediated shocks may accelerate enough cosmic rays to high enough energies that they escape the shock, carrying an appreciable amount of energy before being convected to downstream infinity. Under such conditions, it is noted, the overall compression ratio cannot be determined from the conservation equations as in conventional hydrodynamic treatments, and the standard equations for shock acceleration admit arbitrarily high compression ratios. A procedure is outlined for obtaining the structure of high Mach number, cosmic-ray-mediated shocks, including their overall compresion ratio, around a low Mach number viscous subshock. Analytic solutions are obtained by quardrature for an energy-dependent diffusion coefficient in the limit of extreme sensitivity to energy, which, unlike previous solutions, include the finite thermal pressure of the preshock gas.

Eichler, D.↗

NASA NTRS1977

Studies of silicon pn junction solar cells

Modifications of the basic Shockley equations that result from the random and nonrandom spatial variations of the chemical composition of a semiconductor were developed. These modifications underlie the existence of the extensive emitter recombination current that limits the voltage over the open circuit of solar cells. The measurement of parameters, series resistance and the base diffusion length is discussed. Two methods are presented for establishing the energy bandgap narrowing in the heavily-doped emitter region. Corrections that can be important in the application of one of these methods to small test cells are examined. Oxide-charge-induced high-low-junction emitter (OCI-HLE) test cells which exhibit considerably higher voltage over the open circuit than was previously seen in n-on-p solar cells are described.

Lindholm, F. A.↗

NASA NTRS1981

High power densities from high-temperature material interactions

Thermionic energy conversion (TEC) and metallic-fluid heat pipes (MFHPs), offering unique advantages in terrestrial and space energy processing by virtue of operating on working-fluid vaporization/condensation cycles that accept great thermal power densities at high temperatures, share complex materials problems. Simplified equations are presented that verify and solve such problems, suggesting the possibility of cost-effective applications in the near term for TEC and MFHP devices. Among the problems discussed are: the limitation of alkali-metal corrosion, protection against hot external gases, external and internal vaporization, interfacial reactions and diffusion, expansion coefficient matching, and creep deformation.

Morris, J. F.↗

NASA NTRS1986

Inverse design of axisymmetric flow passages using compressible viscous flow theory

A study reported by Yang and Hudson (1971) was extended by Nelson (1971), who presented a method of inverse design for axisymmetric diffusers. The diffusers obtained with the aid of this method were found to function well under certain conditions, while, for other cases, a modification of the analytical design procedure was required. An outline is provided of the method of inverse solution in simple axisymmetric internal flow passages. Attention is given to governing equations, the method of solution, and examples which illustrate the feasibility of the design procedure. The discussed method, which is based on viscous compressible flow theory, has some limitations. However, it is expected to yield good designs in many practical cases in which the existing design must be modified.

Ntone, F.↗

NASA NTRS1989

Computation of aircraft component flow fields at transonic Mach numbers using a three-dimensional Navier-Stokes algorithm

A computer analysis was developed for calculating steady (or unsteady) three-dimensional aircraft component flow fields. This algorithm, called ENS3D, can compute the flow field for the following configurations: diffuser duct/thrust nozzle, isolated wing, isolated fuselage, wing/fuselage with or without integrated inlet and exhaust, nacelle/inlet, nacelle (fuselage) afterbody/exhaust jet, complete transport engine installation, and multicomponent configurations using zonal grid generation technique. Solutions can be obtained for subsonic, transonic, or hypersonic freestream speeds. The algorithm can solve either the Euler equations for inviscid flow, the thin shear layer Navier-Stokes equations for viscous flow, or the full Navier-Stokes equations for viscous flow. The flow field solution is determined on a body-fitted computational grid. A fully-implicit alternating direction implicit method is employed for the solution of the finite difference equations. For viscous computations, either a two layer eddy-viscosity turbulence model or the k-epsilon two equation transport model can be used to achieve mathematical closure.

Shrewsbury, George D.↗

NASA NTRS1994

Modeling the effect of water on mantle rheology

To study the thermal history of the Earth we use a parameterized model of mantle convection. This model includes a mathematical description of de- and regassing processes of water from the Earth's mantle. The rates of this processes are considered to be directly proportional to the seafloor spreading rate. The kinematic viscosity of the mantle depends on the temperature/pressure as well as on the volatile content. Dissolved volatiles such as water weaken the minerals by reducing their activation energy for solid state creep. Karato and Toriumi showed a power law dependence between creep rate and water fugacity derived from experimental results. Therefore, we use such flow parameters of diffusion creep in olivine under wet and dry conditions to calculate the mantle viscosity as a function of the water content. Because the creep rate is proportional to the concentration of water-related point deflects we assume that the water fugacity is proportional to the water weight fraction. An equation for the steady-state strain rate under wet conditions is established. To assess the unknown constant K in this equation, we use flow law parameters given by Karato and Wu as well as the results of McGovern and Schubert.

Bounama, CH.↗

NASA NTRS2000

Modeling of a Non-Dilute Alloy Solidification Under Terrestrial and Microgravity Conditions

A general finite element model of non-dilute alloy solidification was used to simulate growth of HgCdTe from the melt. 2-D and 3-D models with and without Oberbeck-Boussinesq (O-B) approximation were used. Verification of the 3-D model was based on experimental data. The location and the shape of the interface were determined using melting temperatures obtained from the HgCdTe liquidus curve. Double-diffusive convection in the melt is caused by radial temperature gradients and by rejection at the solid-melt interface of the heavier HgTe-rich solute. Because of these complicating factors, dimensional rather than non-dimensional modeling was performed. Models based on complete set of Navier-Stokes equations for compressible media are superior to the O-B approximation in microgravity, because they provide more accurate estimation of convection.

Bune, Andris V.↗

NASA NTRS2000

Hierarchical Statistical 3D ' Atomistic' Simulation of Decanano MOSFETs: Drift-Diffusion, Hydrodynamic and Quantum Mechanical Approaches

When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.

Asenov, Asen↗

NASA NTRS1978

Analysis of turbulent free jet hydrogen-air diffusion flames with finite chemical reaction rates

The nonequilibrium flow field resulting from the turbulent mixing and combustion of a supersonic axisymmetric hydrogen jet in a supersonic parallel coflowing air stream is analyzed. Effective turbulent transport properties are determined using the (K-epsilon) model. The finite-rate chemistry model considers eight reactions between six chemical species, H, O, H2O, OH, O2, and H2. The governing set of nonlinear partial differential equations is solved by an implicit finite-difference procedure. Radial distributions are obtained at two downstream locations of variables such as turbulent kinetic energy, turbulent dissipation rate, turbulent scale length, and viscosity. The results show that these variables attain peak values at the axis of symmetry. Computed distributions of velocity, temperature, and mass fraction are also given. A direct analytical approach to account for the effect of species concentration fluctuations on the mean production rate of species (the phenomenon of unmixedness) is also presented. However, the use of the method does not seem justified in view of the excessive computer time required to solve the resulting system of equations.

Sislian, J. P.↗