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At least 397 records · Page 22

Compressible laminar boundary layers with large acceleration and cooling

The paper extends an approximate prediction method involving the integral form of the momentum equation to deduce the flow quantities of interest when compressibility effects become important and heat transfer may occur. The approximate method is applicable to a two-dimensional laminar boundary layer on an impermeable surface of negligible curvature for a specified integral momentum equation. The proposed approximate method involves the use of similar solutions in conjunction with the integral momentum equation for isentropic freestream flow of a perfect gas by assuming that viscosity is proportional to stagnation condition and Prandtl number is unity. The study pertains to larger values of acceleration (acceleration parameter to 20 rather than 2) than previously considered to account for rapidly accelerating flows such as in supersonic nozzles. A discussion of some applications confirms the advantages of the method in establishing better confidence in the predictions.

Back, L. H.↗

Computer program for obtaining thermodynamic and transport properties of air and products of combustion of ASTM-A-1 fuel and air

A computer program for determining desired thermodynamic and transport property values by means of a three-dimensional (pressure, fuel-air ratio, and either enthalpy or temperature) interpolation routine was developed. The program calculates temperature (or enthalpy), molecular weight, viscosity, specific heat at constant pressure, thermal conductivity, isentropic exponent (equal to the specific heat ratio at conditions where gases do not react), Prandtl number, and entropy for air and a combustion gas mixture of ASTM-A-1 fuel and air over fuel-air ratios from zero to stoichiometric, pressures from 1 to 40 atm, and temperatures from 250 to 2800 K.

Hippensteele, S. A.↗

Effect of wall temperature on a supersonic turbulent boundary layer

Measurement of mean flow profiles in a fully developed Mach 3 turbulent boundary layer with negligible pressure gradient is reported. Data were acquired at several streamwise locations for wall-to-total temperature ratios of 0.94, 0.71, and 0.54. The results demonstrate that the velocity defect formulation of the law-of-the-wake, which successfully correlates compressible, adiabatic boundary layers, is also valid for nonadiabatic flows. It is also shown that for adiabatic walls, the linear Crocco relation between total temperature and velocity does not provide a valid test of the nature of the boundary-layer flow for practical cases where the Prandtl number departs from unity. Finally, the turbulent shear stress, mixing length, and eddy viscosity were extracted from the 'time-averaged' conservation equations using the measured mean flow profiles and found to be insensitive to wall temperature. In particular, the latter properties are in good agreement with earlier compressible, adiabatic correlations of turbulent transport properties.

Laderman, A. J.↗

Numerical solution of two-dimensional turbulent blunt body flows with an impinging shock

An implicit finite-difference method has been developed to compute two-dimensional, turbulent, blunt body flows with an impinging shock wave. The full time-averaged Navier-Stokes equations are solved with algebraic eddy viscosity and turbulent Prandtl number models employed for shear stress and heat flux. The irregular-shaped bow shock is treated as a discontinuity across which the Rankine-Hugoniot equations are applied. A Type III turbulent shock interference flow field has been computed and the numerical results compare favorably with existing experimental data. In addition, comparisons are made between the present implicit code and a previous explicit code.

Tannehill, J. C.↗

Thermal response behavior of boundary-layer flows

This paper presents an approximate, but general, analysis for the thermal response behavior of incompressible, constant property, laminar boundary layer flow over a smooth object of arbitrary shape. It encompasses the classic time-dependent Leveque problem as its special case. Comparisons with available data show that, for fluids with Prandtl number of the order of unity or larger, this analytical solution is able to provide reasonably accurate results for most engineering applications. Under certain restrictive conditions, it can also be used to predict the thermal response of a compressible boundary layer flow.

Lin, F. N.↗

Solid Convection in the Terrestrial Planets; Workshop, NASA Ames Research Center, Moffett Field, Calif., December 12, 13, 1977, Review Papers and Contributions

Review papers and specific contributions on the subject of convection in the solid interiors of the terrestrial planets and planetary evolution are presented. Geophysical observations of solid-state convection in the terrestrial planets are reviewed, along with the theory of convection in a layer with a high Prandtl number and numerical approaches to the calculation of convection in planetary interiors. Other papers treat the formation, history and energetics of terrestrial planet cores, the effects of convection on lunar thermal history and the relation between the height of mountains on Venus and the creep properties of Venusian rocks.

Cassen, P.↗

Thermodynamic and transport combustion properties of hydrocarbons with air. Part 1: Properties in SI units

Thermodynamic and transport combustion properties were calculated for a wide range of conditions for the reaction of hydrocarbons with air. Three hydrogen-carbon atom ratios (H/C = 1.7, 2.0, 2.1) were selected to represent the range of aircraft fuels. For each of these H/C ratios, combustion properties were calculated for the following conditions: Equivalence ratio: 0, 0.25, 0.5, 0.75, 1.0, 1.25 Water - dry air mass ratio: 0, 0.03 Pressure, kPa: 1.01325, 10.1325, 101.325, 1013.25, 5066.25 (or in atm: 0.01, 0.1, 1, 10, 50) Temperature, K: every 10 degrees from 200 to 900 K; every 50 degrees from 900 to 3000 K Temperature, R: every 20 degrees from 360 to 1600 R; very 100 degrees from 1600 to 5400 R. The properties presented are composition, density, molecular weight, enthalphy, entropy, specific heat at constant pressure, volume derivatives, isentropic exponent, velocity of sound, viscosity, thermal conductivity, and Prandtl number. Property tables are based on composites that were calculated by assuming both: (1) chemical equilibrium (for both homogeneous and heterogeneous phases) and (2) constant compositions for all temperatures. Properties in SI units are presented in this report for the Kelvin temperature schedules.

Gordon, S.↗

Baroclinic instability of a rotating Hadley cell

The stability of a thin fluid layer between two rotating plates which are subjected to a horizontal temperature gradient is investigated. The solution for the stationary basic state is obtained in a closed form. It is pointed out that this solution identifies Ekman and thermal layers adjacent to the plates and interior temperature and velocity fields which are almost linear functions of height. The stability of that basic state with respect to infinitesimal zonal waves is then analyzed via the solution of the complete viscous linear equations for the perturbations. The character of the growth rates is found to be similar to those of the classical baroclinic waves. It is also found that the region of stability depends on the Prandtl number, the vertical stratification parameter, and both the meridional and zonal wavenumbers. The flow is generally unstable for small enough Ekman numbers and for Rossby numbers less than 10.

Antar, B. N.↗

Transport properties of oxygen

Tables of viscosity, thermal conductivity, and thermal diffusivity of oxygen as a function of temperature and pressure from the triple point to 320 K and at pressures to 100 MPa are presented. Auxiliary tables in engineering units are also given. Viscosity and thermal conductivity are calculated from published correlations. Density and specific heat at constant pressure, required to calculate thermal diffusivity, are obtained from an equation of state. The Prandtl number can be obtained quite easily from the values tabulated.

Roder, H. M.↗

Convection effects at solid-liquid interfaces: Influence of gravity

The stability of the flow between two vertical, infinite, rigid, coaxial cylinders held at different temperatures is analyzed by linear stability theory. For a Prandtl number of 22.8 and a radius ratio of 0.02, the flow is unstable to an axisymmetric perturbation at a critical Grashof number of 2150; the wave speed of the instability is comparable to the maximum velocity of the unperturbed flow. When the rigid outer cylinder-fluid interface is replaced by a crystal-melt interface which can change shape, two new modes of instability occur at lower Grashof numbers.

Glicksman, M. E.↗

Time-dependent solutions of multimode convection equations

Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Numerical studies dealing with two or three modes with triad interactions are discussed. Rich time dependence was found in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favorably. Except at the highest Rayleigh number considered (10,000,000), the theoretical Nusselt numbers agree well with experiment.

Toomre, J.↗

Character and stability of axisymmetric thermal convection in spheres and spherical shells

The influence of shell size and mode of heating on the behavior and stability of axisymmetric, infinite Prandtl number convection in a spherical geometry is studied. Heating from within and below features convection onset governed by a self-adjoint system of equations and boundary conditions. For heating only from within or from below, linearized equations and boundary conditions are non-self-adjoint. Identification of the parameter which initiates the departure from self-adjointness, together with the properties of the self-adjoint solution, provide a basis for calculating the heat transfer characteristics of the non-self-adjoint situations. The investigations are an effort to develop a model for heat transfer in planetary interiors. Further development of the technique by modifying the Galerkin method by the introduction of diagonal mode truncation is suggested to permit the consideration of higher values of the Rayleigh numbers, i.e., those more commensurate with terrestrial planet mantles.

Zebib, A.↗

A model of mean zonal flows in the major planets

The linear theory of deep zonal flows developed by Busse (1976) for the origins of deep motions of the atmospheres of Jupiter and Saturn is extended into the nonlinear regime. Relationships for the relative magnitudes of convective heat and momentum transports are formulated. A perturbation approach is taken to the problem, with the amplitude of the convection serving as the small parameter, and the basic equations being expanded in terms of the Prandtl number. The Boussinesq approximation is employed, together with an assumption of a low Rossby number for the Jovian and Saturn atmospheres. Differences in the amplitude of the Jovian equatorial jet relative to that of Saturn are explored in terms of a low equatorial convective heat flux on Jupiter.

Busse, F. H.↗

Instabilities of dynamic thermocapillary liquid layers. I Convective instabilities

A steady shear flow is set up in a planar liquid layer bounded below by a rigid plate, and above by an interface with a passive gas, by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. The thermal-convective instabilities to which this dynamic state is susceptible include stationary longitudinal rolls involving the classical Marangoni instability, and unsteady hydrothermal waves, whose new instability mechanism derives its energy from the horizontal temperature gradients. The thermal stability characteristics for liquid layers with and without return flow profiles are presently given as functions of the Prandtl number for the liquid and the Biot number for the interface, and comparisons are made with available experimental observations.

Smith, M. K.↗

Ground based studies for the space processing of lead-tin-telluride

This paper summarizes the results of a series of studies dealing with crystal growth from the melt and in particular, the growth of the narrow bandgap semiconductor PbSnTe by the Bridgman technique. Theoretical calculations have shown that for low Prandtl number fluids such as semiconductors, convection has no effect on the temperature field in the melt but has a significant effect on the compositional field. They also show that convective flow will exist in a Bridgman growth system on earth, even in the 'thermally stable' configuration. Measurements of the specific heat have been made up to temperatures of 722 C. The thermal diffusivity has been measured up to 1010 C which includes values for the melt. The interdiffusion coefficients for PbTe and SnTe in the melt have been determined. A technique has been developed and tested which provides a vacuum tight quartz ampoule with electrical feedthroughs for interface demarcation studies during the Bridgman growth. Analysis of crystals grown has indicated that the PbSnTe system is solutally unstable and the distribution of SnTe in the crystal, after an anomalous first to freeze region, follows that predicted by Pfann for convection controlled growth. Studies of the amount of supercooling in PbSnTe indicate that this may explain an anomalous composition distribution in the first to freeze region of an unseeded growth.

Crouch, R. K.↗

Deposit formation and heat transfer in hydrocarbon rocket fuels

An experimental research program was undertaken to investigate the thermal stability and heat transfer characteristics of several hydrocarbon fuels under conditions that simulate high-pressure, rocket engine cooling systems. The rates of carbon deposition in heated copper and nickel-plated copper tubes were determined for RP-1, propane, and natural gas using a continuous flow test apparatus which permitted independent variation and evaluation of the effect on deposit formation of wall temperature, fuel pressure, and fuel velocity. In addition, the effects of fuel additives and contaminants, cryogenic fuel temperatures, and extended duration testing with intermittent operation were examined. Parametric tests to map the thermal stability characteristics of RP-1, commercial-grade propane, and natural gas were conducted at pressures of 6.9 to 13.8 MPa, bulk fuel velocities of 30 to 90 m/s, and tube wall temperatures in the range of 230 to 810 K. Also, tests were run in which propane and natural gas fuels were chilled to 230 and 160 K, respectively. Corrosion of the copper tube surface was detected for all fuels tested. Plating the inside of the copper tubes with nickel reduced deposit formation and eliminated tube corrosion in most cases. The lowest rates of carbon deposition were obtained for natural gas, and the highest rates were obtained for propane. For all fuels tested, the forced-convection heat transfer film coefficients were satisfactorily correlated using a Nusselt-Reynolds-Prandtl number equation.

Giovanetti, A. J.↗

Multiple buoyancy driven flows in a vertical cylinder heated from below

The structure of axisymmetric buoyancy-driven convection in a vertical cylinder heated from below is probed by finite element solution of the Boussinesq equations coupled with computed-implemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with Prandtl number of one and for cylinders with aspect ratio (Lambda) (defined as the height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curve for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous evolution of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shear-free sidewalls. The smooth transitions in flow structure with Rayleigh number and lambda are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Lambda or = Lambda * approximately 0.80 or by a limit point for Lambda Lambda *. The transition between these two modes may be described by the theory of multiple limit point bifurcation.

Yamaguchi, Y.↗

Deposit formation and heat transfer in hydrocarbon rocket fuels

An experimental research program was undertaken to investigate the thermal stability and heat transfer characteristics of several hydrocarbon fuels under conditions that simulate high-pressure, rocket engine cooling systems. The rates of carbon deposition in heated copper and nickel-plated copper tubes were determined for RP-1, propane, and natural gas using a continuous flow test apparatus which permitted independent variation and evaluation of the effect on deposit formation of wall temperature, fuel pressure, and fuel velocity. In addition, the effects of fuel additives and contaminants, cryogenic fuel temperatures, and extended duration testing with intermittent operation were examined. Corrosion of the copper tube surface was detected for all fuels tested; however, plating the insides of the tubes with nickel reduced deposit formation and eliminated corrosion in most cases. The lowest rates of carbon deposition were obtained for natural gas, and the highest rates were obtained for propane. Forced-convection heat transfer film coefficients were satisfactorily correlated using a Nusselt-Reynolds-Prandtl number equation for all the fuels tested.

Giovanetti, A. J.↗