SEARCH · Search NASA

Results for “ENERGY 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 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1974

Liquefaction dynamics of n-octadecane in cylindrical coordinates

The study presents one method of mathematically modeling the effects of gravity-induced free convection upon the melting phenomena of a finite paraffin slab. The theoretical model is based on the numerical computer solution of the solid phase and liquid phase energy equations, coupled with an imposed ideal-viscous flow approximation. An implicit alternating-direction technique is used as the finite-difference approximation for the basic energy equations in the numerical solution. The theoretical predictions are compared to experimental data from an annular test cell, in which n-octadecane, C18H38, was used as the test material. The results show that the model is a good first approximation to the solution of solid-liquid phase change involving gravity-induced free convection.

Bain, R. L.↗

NASA NTRS1990

Filtering analysis of a direct numerical simulation of the turbulent Rayleigh-Benard problem

A filtering analysis of a turbulent flow was developed which provides details of the path of the kinetic energy of the flow from its creation via thermal production to its dissipation. A low-pass spatial filter is used to split the velocity and the temperature field into a filtered component (composed mainly of scales larger than a specific size, nominally the filter width) and a fluctuation component (scales smaller than a specific size). Variables derived from these fields can fall into one of the above two ranges or be composed of a mixture of scales dominated by scales near the specific size. The filter is used to split the kinetic energy equation into three equations corresponding to the three scale ranges described above. The data from a direct simulation of the Rayleigh-Benard problem for conditions where the flow is turbulent are used to calculate the individual terms in the three kinetic energy equations. This is done for a range of filter widths. These results are used to study the spatial location and the scale range of the thermal energy production, the cascading of kinetic energy, the diffusion of kinetic energy, and the energy dissipation. These results are used to evaluate two subgrid models typically used in large-eddy simulations of turbulence. Subgrid models attempt to model the energy below the filter width that is removed by a low-pass filter.

Eidson, T. M.↗

NASA NTRS1981

A study of the viscous and nonadiabatic flow in radial turbines

A method for analyzing the viscous nonadiabatic flow within turbomachine rotors is presented. The field analysis is based upon the numerical integration of the incompressible Navier-Stokes equations together with the energy equation over the rotors 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. Effects of turbulence are modeled with two equations; one expressing the development of the turbulence kinetic energy and the other its dissipation rate. The method of analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.

Khalil, I.↗

NASA NTRS2007

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Amar, Adam J.↗

NASA NTRS1992

Three-dimensional MHD modeling of magnetotail dynamics for different polytropic indices

The paper analyzes the 3D resistive tearing instability in a magnetotail configuration by means of a resistive MHD code for various forms of the energy equation, including ohmic and compressional heating. A complete derivation of the set of MHD equations from a kinetic formalism is presented, with all simplifying assumptions noted. Emphasis is placed on the changes in magnetotail evolution caused by a variation of the assumed value of the polytropic exponent gamma, representing the ratio of specific heat in the energy equation which closes the set of MHD equations. Within the gamma range of 2/3-4, a tearing mode is found to develop in all cases. Certain properties, such as the formation and ejection of a plasmoid, associated with the formation of the reversal region of the north-south component of the magnetic field, and strong earthward and tailward flow fields prevail as qualitative features independent of the value of gamma chosen. Ohmic dissipation is found to be the major source of the heating, while adiabatic or nonadiabatic compression may contribute primarily in the closed field region earthward of the reconnection site.

Hesse, Michael↗

NASA NTRS1999

Diffusion, Fluxes, Friction Forces, and Joule Heating in Two-Temperature Multicomponent Magnetohydrodynamics

The relationship between Joule heating, diffusion fluxes, and friction forces has been studied for both total and electron thermal energy equations, using general expressions for multicomponent diffusion in two-temperature plasmas with the velocity dependent Lorentz force acting on charged species in a magnetic field. It is shown that the derivation of Joule heating terms requires both diffusion fluxes and friction between species which represents the resistance experienced by the species moving at different relative velocities. It is also shown that the familiar Joule heating term in the electron thermal energy equation includes artificial effects produced by switching the convective velocity from the species velocity to the mass-weighted velocity, and thus should not be ignored even when there is no net energy dissipation.

Chang, C. H.↗

NASA NTRS1993

Large eddy simulation of shock turbulence interaction

A nonconservative formulation of the energy equation (solving for internal energy) was used to perform large eddy simulations of compressible turbulence in Moin et al. due to its simplicity in implementing SGS models compared to the conservative formulation (solving for total energy). In problems with shocks in the domain, however, the total energy formulation is preferred due to its conservative nature. A conservative set of equations for the LES were derived from the nonconservative equations derived by Moin et al. Performance of the conservative formulation was compared with the experiment on decaying grid-generated turbulence as well as with the filtered DNS field. Various shock-capturing schemes were tested, and an ENO shock-capturing scheme of Shu and Osher was chosen for the simulation of shock/turbulence interaction. The scheme was tested and validated against the data base generated by DNS of weak shock waves. The results obtained with the essentially nonoscillatory (ENO) scheme were within 5 percent from the DNS results, and used less than 25 percent of the CPU time used in the DNS.

Lee, Sangsan↗

NASA NTRS1978

The Martian ionosphere in light of the Viking observations

A theoretical model has been constructed in which the ion density and the ion and electron temperature distributions are calculated by solving the coupled continuity-momentum equations and the coupled energy equations. The latest experimental results from the Viking 1 and 2 landers are used to vary some of the parameters in the model in order to obtain agreement between the theoretical and experimental results. It is found that solar EUV radiation alone is not able to maintain the observed high ion temperatures. It was also established that the energy coupling between the electron and ion gas is insufficient to account for the measured ion temperatures even in the presence of very large electron temperatures. Direct heat input to the ion gas, probably due to solar wind-ionosphere interactions, can result in ion temperature values in reasonable agreement with the observations. The ion densities calculated with the present model agree well with the Viking observations in the chemically controlled region, but at higher altitudes, dynamic transport processes need to be invoked to achieve consistency among the observed and calculated temperature and density values.

Chen, R. H.↗

NASA NTRS1975

A numerical investigation of severe thunderstorm gust fronts

A numerical model was developed to simulate the evolution and structure of severe thunderstorm gust fronts. The model is a non-hydrostatic, fine resolution, cross-sectional primitive equation model. Two-dimensional horizontal and vertical equations of motion, the continuity equation, and the thermodynamic energy equation were utilized. It was shown that two dominant factors influencing gust front configuration are surface friction and the solenoidal field coincident with the front. It is suggested that solenoidal accelerations oppose the deceleration of surface friction. After a downdraft is initiated in the model, these opposing tendencies soon reach a balance and the gust front achieves a quasi-steady configuration. Thus, the experiments indicate that surface friction does not induce a cycle of front formation and collapse. In addition, the effect of evaporative cooling in producing a vigorous downdraft was parameterized by a local cooling function. Greater cooling in the downdraft results in a more intense gust front that exhibits stronger wind maximums and greater shears. The ambient air stability was shown to be an important factor influencing the depth of the cold outflow.

Mitchell, K. E.↗

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 NTRS1980

A calculation procedure for viscous flow in turbomachines, volume 3

A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.

Khalil, I.↗

NASA NTRS1979

Marangoni bubble motion in zero gravity

It is shown experimentally that the Marangoni phenomenon is a primary mechanism for the movement of a gas bubble in a nonisothermal liquid in a low-gravity environment. In such two-phase flow systems, local variations in bubble surface tension are caused by a temperature gradient in the liquid. Shearing stresses thus generated at the bubble surface lead to convection in both media, as a result of which the bubble begins to move. A mathematical model consisting of the Navier-Stokes equations and the thermal energy equations, along with the appropriate boundary conditions for both media, is proposed.

Thompson, R. L.↗

NASA NTRS1980

A magnetohydrodynamic model for corotating interplanetary structures

A model is developed which treats interplanetary structures as a small-scale incompressible Alfvenic fluctuation superposed on a large-scale background flow, and uses the complete magnetohydrodynamic equations and the full energy equation to describe the interplanetary structures. For steady-state corotating structures the model assumes the background flow to be field aligned, and the nonlinear system is treated as being composed of two subsets: one dealing with the expansion of the solar wind in stream tubes, the other with the interaction between neighboring stream tubes. The expansion subset has a singularity at Parker's critical radius, and the interaction subset has a singularity at the Alfvenic point. Concerning the region where the flow velocity is super-Alfvenic, the characteristic equation is derived, and a general method of numerical solution for the three-dimensional problems based on the characteristics theory is discussed. In addition, a viscous WKB solution of the microscale system is presented.

Whang, Y. C.↗

NASA NTRS1981

Canonical orbital elements in terms of an arbitrary independent variable

Within the framework of the Hamiltonian mechanics in the extended phase space, a set of canonical elements of the Delaunay type is developed in terms of an arbitary independent angular variable. Application to the four classical anomalies - eccentric, true, elliptic, and mean - is presented. Particular attention is given to the generalized time equation and its conjugate energy equation.

Bond, V. R.↗

NASA NTRS1981

A normative price for energy from an electricity generation system: An Owner-dependent Methodology for Energy Generation (system) Assessment (OMEGA). Volume 2: Derivation of system energy price equations

The methodology presented is a derivation of the utility owned solar electric systems model. The net present value of the system is determined by consideration of all financial benefits and costs including a specified return on investment. Life cycle costs, life cycle revenues, and residual system values are obtained. Break-even values of system parameters are estimated by setting the net present value to zero.

Chamberlain, R. G.↗

NASA NTRS1986

Lower mass limit of an evolving interstellar cloud and chemistry in an evolving oscillatory cloud

Simultaneous solution of the equation of motion, equation of state and energy equation including heating and cooling processes for interstellar medium gives for a collapsing cloud a lower mass limit which is significantly smaller than the Jeans mass for the same initial density. The clouds with higher mass than this limiting mass collapse whereas clouds with smaller than critical mass pass through a maximum central density giving apparently similar clouds (i.e., same Av, size and central density) at two different phases of its evolution (i.e., with different life time). Preliminary results of chemistry in such an evolving oscillatory cloud show significant difference in abundances of some of the molecules in two physically similar clouds with different life times. The problems of depletion and short life time of evolving clouds appear to be less severe in such an oscillatory cloud.

Tarafdar, S. P.↗

NASA NTRS1987

Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow

An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.

Braun, M. J.↗

NASA NTRS1998

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

Majumdar, Alok↗