Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Conservation equations”

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 343 records · Page 19

Numerical simulations of loops heated to solar flare temperatures. III - Asymmetrical heating

A numerical model is defined for asymmetric full solar flare loop heating and comparisons are made with observational data. The Dynamic Flux Tube Model is used to describe the heating process in terms of one-dimensional, two fluid conservation equations of mass, energy and momentum. An adaptive grid allows for the downward movement of the transition region caused by an advancing conduction front. A loop 20,000 km long is considered, along with a flare heating system and the hydrodynamic evolution of the loop. The model was applied to generating line profiles and spatial X-ray and UV line distributions, which were compared with SMM, P78-1 and Hintori data for Fe, Ca and Mg spectra. Little agreement was obtained, and it is suggested that flares be treated as multi-loop phenomena. Finally, it is concluded that chromospheric evaporation is not an effective mechanism for generating the soft X-ray bursts associated with flares.

Cheng, C.-C.↗

Drag characteristics of unsteady, perturbed boundary layer flows

A series of time-dependent numerical computations have been performed for the flow of an unsteady boundary layer over an embedded cavity, which is aligned normal to the flow direction. The unsteady flow is the result of the imposition of a Stuart vortex, at the inflow boundary of the computational domain, onto an otherwise unperturbed two-dimensional laminar boundary layer flow. This produces a strongly vortical, but spatially monochromatic, motion at inflow which is allowed to evolve downstream through the time-dependent numerical solution of appropriate conservation equations. As the imposed vortex evolves over the solid boundary, a weaker induced vortical motion is produced and together these perturbing motions interact with the fluid motion in the embedded cavity. An analysis of the pertinent dynamic variables as well as the time-dependent drag characteristics for this type of non-planar geometry is performed; with particular emphasis on the relative contribution of both pressure drag and frictional drag at various times in the evolution process.

Gatski, T. B.↗

The sensitivity of a general circulation model to Saharan dust heating

Evidence is accumulating that tropospheric aerosols, such as Saharan dust, can significantly influence weather and climate. The Climate Model of the Goddard Laboratory for Atmospheric Sciences is presently used to assess the possible effects of Saharan dust on the weather and climate of North Africa and the tropical Atlantic Ocean. The three-dimensional model solves the conservation equations for the horizontal wind vector, potential temperature, water vapor mixing ratio, and surface pressure. Parameterizations are included for turbulent exchange at the earth surface, cumulus convection, large scale saturation, diurnally varying solar radiation, and terrestrial radiation. Realistic simulations are thereby produced for many aspects of the observed climate.

Randall, D.↗

Tone excited jets. V - A theoretical model and comparison with experiment

A mathematical model of tone-excited jets is developed which consists of two major components: a mathematical description of the process by which the intrinsic instability waves of the jet are excited by the upstream tones; and the modeling of the nonlinear interaction between the mean flow of the jet, the excited large-scale instability waves or turbulence structure, and the fine scale turbulence. It is assumed that each of these jet flow components can be characterized by a few parameters, which are then related by conservation equations that are supplemented by closure models. This quasi-linear model's results are compared with experimental measurements, and good agreement is obtained over a wide range of excitation frequencies and excitation levels.

Tam, C. K. W.↗

Fluid flow and fuel-air mixing in a motored two-dimensional Wankel rotary engine

The implicit-factored method of Beam and Warming was employed to obtain numerical solutions to the conservation equations of mass, species, momentum, and energy to study the unsteady, multidimensional flow and mixing of fuel and air inside the combustion chambers of a two-dimensional Wankel rotary engine under motored conditions. The effects of the following engine design and operating parameters on fluid flow and fuel-air mixing during the intake and compression cycles were studied: engine speed, angle of gaseous fuel injection during compression cycle, and speed of the fuel leaving fuel injector.

Shih, T. I.-P.↗

Initiation of breakdown in slender compressible vortices

The onset of vortex breakdown in compressible flows is investigated analytically for the case in which the flow is axially symmetric, the vortex is isolated, its axis is parallel to the main flow, and the vortex radius is small compared to the breakdown length. The conservation equations for mass, momentum, and energy are formulated and solved numerically using a finite-difference scheme, as described by Krause (1985); numerical results are presented in graphs and briefly characterized.

Krause, E.↗

Numerical calculations of turbulent reacting flow in a gas-turbine combustor

A numerical study for confined, axisymmetrical, turbulent diffusion flames is presented. Local mean gas properties are predicted by solving the appropriate conservation equations in the finite difference form with the corresponding boundary conditions. The k-epsilon two-equation turbulence model is employed to describe the turbulent nature of the flow. A two-step kinetic model is assumed to govern the reaction mechanism. The finite reaction rate is the smaller of an Arrhenius type of reaction rate and a modified version of eddy-breakup model. Reasonable agreement is observed between calculations and measurements, but to obtain better agreement, more work is needed on improvements of the above mathematical models. However, the present numerical study offers an improvement in the analysis and design of the gas turbine combustors.

Lin, Chin-Shun↗

Thermodynamics and combustion modeling

Modeling fluid phase phenomena blends the conservation equations of continuum mechanics with the property equations of thermodynamics. The thermodynamic contribution becomes especially important when the phenomena involve chemical reactions as they do in combustion systems. The successful study of combustion processes requires (1) the availability of accurate thermodynamic properties for both the reactants and the products of reaction and (2) the computational capabilities to use the properties. A discussion is given of some aspects of the problem of estimating accurate thermodynamic properties both for reactants and products of reaction. Also, some examples of the use of thermodynamic properties for modeling chemically reacting systems are presented. These examples include one-dimensional flow systems and the internal combustion engine.

Zeleznik, Frank J.↗

Research in computational fluid dynamics

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Murman, Earll M.↗

An exact energy corollary for homentropic flow

An exact conservation equation is developed which generalizes the familiar acoustic energy equation. The new relation is valid for arbitrary homentropic disturbances to a homentropic steady flow. It is suggested by a derivation of the acoustic energy equation by means of a regular perturbation expansion of the general energy equation for an ideal compressible fluid. A perturbation energy density and flux are defined and are identified as the exact physical quantities whose leading order representations are the usual acoustic energy density and flux.

Myers, M. K.↗

A new PNS code for chemical nonequilibrium flows

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic laminar flow of a multicomponent, chemically reacting mixture of thermally perfect gases over two-dimensional and axisymmetric bodies. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, space-marching finite-difference method. The conditions for well-posedness of the space-marching method have been derived from an eigenvalue analysis of the governing equations. The code has been used to compute hypersonic laminar flow of chemically reacting air over wedges and cones. The results of these computations are in good agreement with the results of reacting boundary-layer calculations.

Prabhu, D. K.↗

Initiation of breakdown in slender compressible vortices

The initiation of the breakdown process for axially symmetric compressible flows is investigated using a numerical solution of the conservation equations for mass, momentum, and energy. The vortex is isolated, with its axis parallel to the direction of the main stream, and the core radius is small compared to the breakdown length. Computations for several flowfields indicate that the breakdown of the solution is shifted further downstream with increasing Mach number until breakdown is no longer observed. In the subsonic case, the influence of the initial temperature distribution on the breakdown length of the solution is more pronounced than in the supersonic case, with heating of the core enhancing breakdown, and cooling delaying it. The breakdown of the solution is seen to always occur for nonvanishing axial velocity components.

Krause, E.↗

A new PNS code for three-dimensional chemically reacting flows

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous, chemically reacting flow fields around three-dimensional bodies. The flow medium is assumed to be a multicomponent mixture of thermally perfect but calorically imperfect gases. The new PNS code solves the gasdynamic and species conservation equations in a coupled manner using a noniterative, implicit, approximately-factored, finite-difference algorithm. The space-marching method is made well-posed by special treatment of the streamwise pressure gradient term. The code has been used to compute hypersonic laminar flow of chemically reacting air over cones at angles of attack. The results of the computations are compared with the results of reacting boundary-layer computations and show excellent agreement.

Prabhu, D. K.↗

Numerical computation of space shuttle orbiter flow field

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic, viscous chemically reacting flow fields around 3-D bodies. The flow medium is assumed to be a multicomponent mixture of thermally perfect but calorically imperfect gases. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, approximately factored, finite difference algorithm. The space-marching method is made well-posed by special treatment of the streamwise pressure gradient term. The code has been used to compute hypersonic laminar flow of chemically reacting air over cones at angle of attack. The results of the computations are compared with the results of reacting boundary-layer computations and show excellent agreement.

Tannehill, John C.↗

Two-temperature interpretation of dissociation rate data for N2 and O2

The existing experimental data on dissociation of nitrogen and oxygen obtained using shock-tubes during the 1960's and 1970's are reinterpreted using the two-temperature thermo-chemical model developed recently in order to determine the rate coefficients consistent with the model. In this model, the vibrational-electronic temperature is calculated by integrating a separate conservation equation accounting for the suppression of vibrational energy during dissociation due to preferential removal of high vibrational states. The rate coefficient is assumed to be a function of the geometrically-averaged temperature between the translational-rotational temperature and the vibrational-electronic temperature. By comparing the computed overall and species densities with the experimental data, the rate coefficient values most consistent with the model, and their ranges of uncertainty, are deduced for dissociation of N2 through collisions with N2 or N, and for O2 through collisions with O2, O or N2. It is seen that a single set of such rate coefficients fit all existing experimental data closely. According to the two-temperature model, density and species density are insensitive to the rate coefficients, and so the rate coefficients so determined are uncertain to within a factor of at least 1.5.

Park, Chul↗

Temporal and spatial adaptive algorithm for reacting flows

A numerical integration scheme for quasi-one-dimensional unsteady flows with finite-rate chemistry is developed and demonstrated. The governing Euler and species-conservation equations are derived; the integration method and the spatial and temporal grid embedding techniques are explained; and results for sample problems involving stream-tube flow with one dissociating gas, shock-tube flow with one dissociating gas, and diverging-channel flow with multiple reactions are presented in extensive graphs and briefly characterized. Accuracy comparable to that of globally fine grid solutions is obtained with significant savings in CPU time.

Pervaiz, Mehtab M.↗

Numerical study of multicomponent droplet vaporization at near critical conditions

A comprehensive numerical analysis of multicomponent droplet vaporization at near critical conditions has been carried out. The model is based on the full time-dependent conservation equations and accommodates various important high-pressure phenomena. As an example, the case involving a two-component (n-pentane and n-octane) fuel droplet in nitrogen gas is studied. The influences of transient effects, surface regression, ambient gas solubility, and phase-equilibrium relations on vaporization mechanisms are examined in detail.

Hsieh, Kwang-Chung↗

A mixed finite difference/Galerkin method for three-dimensional Rayleigh-Benard convection

A fast and accurate numerical method, for nonlinear conservation equation systems whose solutions are periodic in two of the three spatial dimensions, is presently implemented for the case of Rayleigh-Benard convection between two rigid parallel plates in the parameter region where steady, three-dimensional convection is known to be stable. High-order streamfunctions secure the reduction of the system of five partial differential equations to a system of only three. Numerical experiments are presented which verify both the expected convergence rates and the absolute accuracy of the method.

Buell, Jeffrey C.↗