Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “heat 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 415 records · Page 23

Formation of the Aerosol of Space Origin in Earth's Atmosphere

The problem of formation of the aerosol of space origin in Earth s atmosphere is examined. Meteoroids of the mass range of 10-18-10-8 g are considered as a source of its origin. The lower bound of the mass range is chosen according to the data presented in literature, the upper bound is determined in accordance with the theory of Whipple s micrometeorites. Basing on the classical equations of deceleration and heating for small meteor bodies we have determined the maximal temperatures of the particles, and altitudes at which they reach critically low velocities, which can be called as velocities of stopping . As a condition for the transformation of a space particle into an aerosol one we have used the condition of non-reaching melting temperature of the meteoroid. The simplified equation of deceleration without earth gravity and barometric formula for the atmosphere density are used. In the equation of heat balance the energy loss for heating is neglected. The analytical solution of the simplified equations is used for the analysis.

Kozak, P. M.↗

Radiatively forced dispersion of the Mt. Pinatubo volcanic cloud and induced temperature perturbations in the stratosphere during the first few months following the eruption

A combined 3-dimensional circulation model and aerosol microphysical/transport model is used to simulate the dispersion of the Mt. Pinatubo volcanic cloud in the stratosphere for the first few months following the eruption. Radiative heating of the cloud due to upwelling infrared radiation from the troposphere is shown to be an important factor affecting the transport. Without cloud heating, cloud material stays mostly north of the equator, whereas with cloud heating, the cloud is transported southward across the equator within the first two weeks following the eruption. Generally the simulations agree with Total Ozone Mapping Spectrometer (TOMS), Advanced Very High Resolution Radiometer (AVHRR), and Stratospheric Aerosol and Gas Experiment (SAGE) satellite observations showing the latitude distribution of cloud material to be between about 20 deg S and 30 deg N within the first few months. Temperature perturbations in the stratosphere induced by the aerosol heating are generally 1-4 K, in the range of those observed.

Young, Richard E.↗

Two Dimensional Topology Optimization of Heat Exchangers with the Density and Level-Set Methods

We design heat exchangers using two topology optimization approaches: the density, i.e. volume fraction and level set methods. Our goal is to maximize the heat exchange between two fluids in separate channels while constraining the pressure drop across each channel. The heat exchanger is modeled with a coupled thermal-flow formulation. The flow is governed by an isothermal and incompressible Stokes-Brinkman equation and the heat transfer is governed by a convection-diffusion equation with high Peclet number. We solve one set of Stokes-Brinkman equations per fluid. Each Brinkman term in the flow equation serves to model the other phase as a solid, thereby preventing mixing. We first represent the solid and fluid phases using a volume fraction variable and apply a SIMP-like penalization in the Brinkman term to drive the optimization to a discrete design. The cost and constraint function derivatives are automatically calculated with the library pyadjoint and the optimization is performed by the Method of Moving Asymptotes. In a second optimization formulation, we use the level set approach to define the interface that separates the two fluids. Pyadjoint calculates the shape derivatives of the cost and constraint functions and the Hamilton-Jacobi advects the interface, allowing for topological changes. We present results in two dimensions and discuss the advantages and disadvantages of each approach.

42 ENGINEERING↗

Kinetic plasma processes occurring in the outer plasmasphere

One area of data analysis work that was begun under this contract is the fitting of the perpendicular velocity distributions of equatorially trapped ions with a Kappa function. This type of characterization of the trapped ions will be very useful for comparison with velocity distributions produced by the model. A second area of data analysis is to study data from consecutive passes when DE 1's apogee was near the magnetic equator and the spacecraft was often skimming along nearly the same L shell. In 1982 three such periods occurred in May, June, and July. For these consecutive events we have Kp histories, density measurements from a number of sources (Whistler data, DE SFR, ISEE SFR) and consecutive samples of ion pitch angle distributions along field lines. It is clear from this data how the pitch angle distributions evolve during a flux tube refilling event. Our modeling of the flow of plasma along closed field lines is following two basic tracks. The first is a study of the basic refilling process without the effect of wave-particle heating near the equator or the effect of large or abrupt field-aligned electric potential drops. This model includes the effects of Coulomb self-collisions and collisions with the O+ ions in the topside ionosphere. The second track is a study of the effects of wave produced pitch-angle scattering and perpendicular heating occurring near the magnetic equator, in connection with the development of large potential drops that result from electron heating and the development of density gradients.

Wilson, Gordon R.↗

Thermal-Hydraulic Analysis of the AFIP-7 Irradiation Test in the Advanced Test Reactor - Oxide Growth Prediction and Correlation

Knowing the thickness of the oxide layer on the surface of aluminum fuel cladding is vitally important for predicting fuel temperature due to the low thermal conductivity of the oxide layer. Several correlation models for predicting oxide growth can be found in the literature. In previous research, the correlations were combined with heat transfer simulations in Abaqus, a finite element analysis code, to forecast the oxide growth. However, this approach requires heat transfer coefficients for modeling heat exchanges with the external flow field, and such coefficients were obtained through empirical equations. Since different empirical equations yield varying heat transfer coefficients, the cladding temperature and predicted oxide thickness both carry a high degree of uncertainty. Here, this research develops a new approach that integrates the fluid flow, fluid and solid heat transfer, and oxide growth correlation(s) into a single computational fluid dynamics model. We demonstrate this approach’s ability to predict oxide development on the AFIP-7 plates during two Advanced Test Reactor (ATR) irradiation cycles. The projected oxide thickness falls within the experimental measurements taken during post irradiation examination.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Heat transfer in pipes

The heat transfer from hot water to a cold copper pipe in laminar and turbulent flow condition is determined. The mean flow through velocity in the pipe, relative test length and initial temperature in the vessel were varied extensively during tests. Measurements confirm Nusselt's theory for large test lengths in laminar range. A new equation is derived for heat transfer for large starting lengths which agrees satisfactorily with measurements for large starting lengths. Test results are compared with the new Prandtl equation for heat transfer and correlated well. Test material for 200- and to 400-diameter test length is represented at four different vessel temperatures.

Burbach, T.↗

A Method for Calculating the Heat Required for Windshield Thermal Ice Prevention Based on Extensive Flight Tests in Natural Icing Conditions

An equation is presented for calculating the heat flow required from the surface of an internally heated windshield in order to prevent the formation of ice accretions during flight in specified icing conditions. To ascertain the validity of the equation, comparison is made between calculated values of the heat required and measured values obtained for test windshields in actual flights in icing conditions. The test windshields were internally heated and provided data applicable to two common types of windshield configurations; namely the V-type and the type installed flush with the fuselage contours. These windshields were installed on a twin-engine cargo airplane and the icing flights were conducted over a large area of the United States during the winters of 1945-46 and 1946-47. In addition to the internally heated windshield investigation, some test data were obtained for a windshield ice-prevention system in which heated air was discharged into the windshield boundary layer. The general conclusions resulting from this investigation are as follows: 1) The amount of heat required for the prevention of ice accretions on both flush- and V-type windshields during flight in specified icing conditions can be calculated with a degree of accuracy suitable for design purposes. 2) A heat flow of 2000 to 2500 Btu per hour per square foot is required for complete and continuous protection of a V-type windshield in fight at speeds up to 300 miles per hour in a moderate cumulus icing condition. For the same degree of protection and the same speed range, a value of 1000 Btu per hour per square foot suffices in a moderate stratus icing condition. 3) A heat supply of 1000 Btu per hour per square foot is adequate for a flush windshield located well aft of the fuselage stagnation region, at speeds up to 300 miles per hour, for flight in both stratus and moderate cumulus icing conditions. 4) The external air discharge system of windshield thermal ice prevention is thermally inefficient and requires a heat supply approximately 20 times that required for an internal system having the same performance.

ICE FORMATION↗

Estimation of instantaneous heat transfer coefficients for a direct-injection stratified-charge rotary engine

The main objective of this report was to derive equations to estimate heat transfer coefficients in both the combustion chamber and coolant pasage of a rotary engine. This was accomplished by making detailed temperature and pressure measurements in a direct-injection stratified-charge rotary engine under a range of conditions. For each sppecific measurement point, the local physical properties of the fluids were calculated. Then an empirical correlation of the coefficients was derived by using a multiple regression program. This correlation expresses the Nusselt number as a function of the Prandtl number and Reynolds number.

Lee, C. M.↗

Improved Heat-Transfer Calculations for Hypersonic Flow

Lewis number corrected for extremely high airspeeds. Algorithm calculates improved, variable value of Lewis number, factor in equation for heat-transfer coefficient at stagnation point of body in hypersonic flow mach numbers of approximately 25. New algorithm improves accuracy of calculations of heat generated by hot air acting on moving body.

Greenschlag, S. N.↗

Incompressible Navier-Stokes Computations with Heat Transfer

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

Kiris, Cetin↗

Two-dimensional numerical modeling and solution of convection heat transfer in turbulent He II

Numerical schemes are employed to investigate heat transfer in the turbulent flow of He II. FEM is used to solve a set of equations governing the heat transfer and hydrodynamics of He II in the turbulent regime. Numerical results are compared with available experimental data and interpreted in terms of conventional heat transfer parameters such as the Prandtl number, the Peclet number, and the Nusselt number. Within the prescribed Reynolds number domain, the Gorter-Mellink thermal counterflow mechanism becomes less significant, and He II acts like an ordinary fluid. The convection heat transfer characteristics of He II in the highly turbulent regime can be successfully described by using the conventional turbulence and heat transfer theories.

Zhang, Burt X.↗

Eight-moment approximation solar wind models

Heat conduction from the corona is important in the solar wind energy budget. Until now all hydrodynamic solar wind models have been using the collisionally dominated gas approximation for the heat conductive flux. Observations of the solar wind show particle distribution functions which deviate significantly from a Maxwellian, and it is clear that the solar wind plasma is far from collisionally dominated. We have developed a numerical model for the solar wind which solves the full equation for the heat conductive flux together with the conservation equations for mass, momentum, and energy. The equations are obtained by taking moments of the Boltzmann equation, using an 8-moment approximation for the distribution function. For low-density solar winds the 8-moment approximation models give results which differ significantly from the results obtained in models assuming the gas to be collisionally dominated. The two models give more or less the same results in high density solar winds.

Olsen, Espen Lyngdal↗

A parameter study of the two-fluid solar wind

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

Sandbaek, Ornulf↗

Thermal interaction between an impinging hot jet and a conducting solid surface

Powered-lift aircraft may produce severe high-temperature environments which are potentially damaging to a landing surface or the aircraft. The interaction betweean the high temperature flow field and a nonadiabatic landing surface is analyzed with a coupled computational fluid dynamics/solid thermal conduction computer code, HOTJET. The HOTJET code couples time-accurate, implicit, factored solution schemes for the governing fluid dynamics equations (Reynolds-averaged Navier-Stokes equations) to the unsteady thermal conduction equation, which governs heat flux within a solid. HOTJET is validated against exact solutions to the thermal conduction and Navier-Stokes equations. First-of-a-kind results are included which show the impact of surface material properties on the fluid physics and the coupled fluid/material thermal fields.

Abeloff, P. A.↗

The design of fins for air-cooled cylinders

An analysis was made to determine the proportions of fins made of aluminum, copper, magnesium, and steel necessary to dissipate maximum quantities of heat for different fin widths, fin weights, and air-flow conditions. The analysis also concerns the determination of the optimum fin proportions when specified limits are placed on the fin dimensions. The calculation of the heat flow in the fins is based on experimentally verified, theoretical equations. The surface heat-transfer coefficients used with this equation were taken from previously reported experiments. In addition to the presentation of fin-design information, this investigation shows that optimum fin dimensions are inappreciably affected by the differences in air flow that are obtained with different air-flow arrangements or by small changes in the length of the air-flow path.

Biermann, Arnold E↗