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NASA NTRS1975

Analysis of liquid-metal-jet impingement cooling in a corner region and for a row of jets

A conformal mapping method was used to analyze liquid-metal-jet impingement heat transfer. The jet flow region and energy equation are transformed to correspond to uniform flow in a parallel plate channel with nonuniform heat addition along a portion of one wall. The exact solution for the wall-temperature distribution was obtained in the transformed channel, and the results are mapped back into the physical plane. Two geometries are analyzed. One is for a single slot jet directed either into an interior corner formed by two flat plates, or over the external sides of the corner; the flat plates are uniformly heated, and the corner can have various included angles. The heat-transfer coefficient at the stagnation point at the apex of the plates is obtained as a function of the corner angle, and temperature distributions are calculated along the heated walls. The second geometry is an infinite row of uniformly spaced parallel slot jets impinging normally against a uniformly heated plate. The heat-transfer behavior is obtained as a function of the spacing between the jets. Results are given for several jet Peclet numbers from 5 to 50.

Siegel, R.↗

NASA NTRS1977

Further calculations based upon a theory of flame spread across solid fuels

A theory of flame spread above solid fuel beds of finite or infinite thickness is considered. Heat transfer ahead of the flame is allowed through both the solid and gas phases. The simplifying assumption of a surface reaction is made. Temperature profiles in both phases, concentration profiles in the gas phase, heat transfer at the surface, and flame spreading rates are determined. It is found that chemical kinetic parameters together with transport properties strongly influence the spreading rate. Heat transfer through the gas phase is the dominant mechanism for energy transfer ahead of the spreading flame over a wide range of Peclet numbers for the gas and solid phases.

Feng, C. C.↗

NASA NTRS1978

Tabulation and summary of thermodynamic effects data for developed cavitation on ogive-nosed bodies

Thermodynamic effects data for developed cavitation on zero and quarter caliber ogives in Freon 113 and water are tabulated and summarized. These data include temperature depression (delta T), flow coefficient (C sub Q), and various geometrical characteristics of the cavity. For the delta T tests, the free-stream temperature varied from 35 C to 95 C in Freon 113 and from 60 C to 125 C in water for a velocity range of 19.5 m/sec to 36.6 m/sec. Two correlations of the delta T data by the entrainment method are presented. These correlations involve different combinations of the Nusselt, Reynolds, Froude, Weber, and Peclet numbers and dimensionless cavity length.

Holl, J. W.↗

NASA NTRS1979

Stellar convection 2: A multi-mode numerical solution for convection in spheres

The convective flow of a self gravitating sphere of Boussinesq fluid for small Reynolds and Peclet numbers is numerically determined. The decomposition of the equations of motion into modes is reviewed and a relaxation method is developed and presented to compute the solutions to these equations. The stable equilibrium flow for a Rayleigh number of 10 to the 4th power and a Prandtl number of 10 is determined. The 2 and 3 dimensional spectra of the kinetic and thermal energies and the convective flux as a function of wavelengths are calculated in terms of modes. The anisotropy of the flow as a function of wavelength is defined.

Marcus, P. S.↗

NASA NTRS1982

Boundary integral equation method calculations of surface regression effects in flame spreading

A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.

Altenkirch, R. A.↗

NASA NTRS1986

The effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendrite

The Ivantsov (1947) analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite, an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change epsilon, and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero epsilon, but the effect is of order epsilon and hence is seen to be minor for most values of epsilon and dimensionless supercooling that occur in practice.

Mcfadden, G. B.↗

NASA NTRS1987

Vortex-scalar element calculations of a diffusion flame stabilized on a plane mixing layer

The vortex-scalar element method, a scheme which utilizes vortex elements to discretize the region of high vorticity and scalar elements to represent species or temperature fields, is utilized in the numerical simulations of a two-dimensional reacting mixing layer. Computations are performed for a diffusion flame at high Reynolds and Peclet numbers without resorting to turbulence models. In the nonreacting flow, the mean and fluctuation profiles of a conserved scalar show good agreement with experimental measurements. Results for the reacting flow indicate that for temperature independent kinetics, the chemical reaction begins immediately downstream of the splitter plate where mixing starts. Results for the reacting flow with Arrhenius kinetics show an ignition delay, which depends on reactant temperature, before significant chemical reaction occurs. Harmonic forcing changes the structure of the layer, and concomitantly the rates of mixing and reaction, in accordance with experimental results. Strong stretch within the braids in the nonequilibrium kinetics case causes local flame quenching due to the temperature drop associated with the large convective fluxes.

Ghoniem, Ahmed F.↗

NASA NTRS1987

CONDIF - A modified central-difference scheme for convective flows

The paper presents a method, called CONDIF, which modifies the CDS (central-difference scheme) by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems. CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid.

Runchal, Akshai K.↗

NASA NTRS1987

Fermi acceleration at shocks with arbitrary velocity profiles

Diffusive particle acceleration in modified shock fronts is considered. A method by means of which to obtain the resulting particle spectrum for an arbitrary flow profile is outlined; this method is based on a reformulation of the transport equation as a nonlinear first-order equation. Besides the shape of the flow profile, the spectral index of particles depends on the Peclet number of the shock. Results are given for some sample profiles.

Schneider, Peter↗

NASA NTRS1989

Simultaneous axial conduction in the fluid and the pipe wall for forced convective laminar flow with blowing and suction at the wall

Numerical solutions are reported for conjugate heat transfer in a porous pipe having an internal flow with blowing or suction at the inner surface of the pipe and constant heat flux at the outer surface. The effect of the simultaneous axial conduction through the wall and the fluid has been studied for the combined hydrodynamic and thermal entry lengths. The results show that the ratio of the thermal conductivities of the pipe wall to the fluid and the thickness of the pipe wall may become significant factors on the heat transfer when the Peclet number is small, especially for the case when fluid is injected into the pipe. It is also shown that the effect of axial wall conduction for the case of constant heat flux at the outer wall surface can be neglected when the wall thickness is small and the ratio of the conductivities of the wall to the fluid approaches unity.

Faghri, Amir↗

NASA NTRS1989

An algebraic model for the turbulent flux of a passive scalar

Direct numerical simulations of the unsteady incompressible Navier-Stokes equations have been performed in order to investigate the behavior of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow. For all orientations of the mean scalar gradient, the sum of the pressure-scalar gradient and velocity gradient-scalar gradient terms in the turbulent scalar flux balance equation are found to be approximately aligned with the scalar flux vector itself. The simulation results are used to obtain dimensionless model coefficients as a function of the turbulence Reynolds and Peclet numbers.

Rogers, Michael M.↗

NASA NTRS1990

Full numerical simulation of coflowing, axisymmetric jet diffusion flames

The near field of a non-premixed flame in a low speed, coflowing axisymmetric jet is investigated numerically using full simulation. The time-dependent governing equations are solved by a second-order, explicit finite difference scheme and a single-step, finite rate model is used to represent the chemistry. Steady laminar flame results show the correct dependence of flame height on Peclet number and reaction zone thickness on Damkoehler number. Forced simulations reveal a large difference in the instantaneous structure of scalar dissipation fields between nonbuoyant and buoyant cases. In the former, the scalar dissipation marks intense reaction zones, supporting the flamelet concept; however, results suggest that flamelet modeling assumptions need to be reexamined. In the latter, this correspondence breaks down, suggesting that modifications to the flamelet modeling approach are needed in buoyant turbulent diffusion flames.

Mahalingam, S.↗

NASA NTRS1990

The baroeffect and an appropriate momentum boundary condition

As disparate molecular weight gases isothermally diffuse between two ends of a capillary tube, they can support a pressure gradient. The magnitude of this pressure gradient depends critically on viscous wall stress and becomes a measure of the boundary condition. Here, a one-dimensional analytical model is proposed that allows for specular gas reflection from the wall. It explains anomalous (4/3) correction factors required previously to match experiment to baroeffect models. It predicts a new physical phenomenon, a surface-driven baroeffect for equal molecular weight gases. Diffusive slip contributions exceed the order of convective diffusion for Peclet number Pe less than 1 and approximately equal convective diffusion for Pe values between 1 and 4. For binary gases, this model further extends the baroeffect experiment as a means to find momentum accommodation coefficients, slip lengths, and external friction coefficients. A corrected binary diffusion coefficient is defined.

Noever, David A.↗

NASA NTRS1992

Oscillating-flow regenerator test rig: Woven screen and metal felt results

We present correlating expressions, in terms of Reynolds or Peclet numbers, for friction factors, Nusselt numbers, enhanced axial conduction ratios, and overall heat flux ratios in four porous regenerator samples representative of stirling cycle regenerators: two woven screen samples and two random wire samples. Error estimates and comparison of data with others suggest our correlations are reliable, but we need to test more samples over a range of porosities before our results will become generally useful.

Gedeon, D.↗

NASA NTRS1992

Physical effects at the cellular level under altered gravity conditions

Several modifications of differentiated functions of animal cells cultivated in vitro have been reported when cultures have been exposed to increased or decreased inertial acceleration fields by centrifugation, clinorotation, and orbital space flight. Variables modified by clinorotation conditions include inertial acceleration, convection, hydrostatic pressure, sedimentation, and shear stress, which also affect transport processes in the extracellular chemical environment. Autocrine, paracrine and endocrine substances, to which cells are responsive via specific receptors, are usually transported in vitro (and possibly in certain embryos) by convection and in vivo by a circulatory system or ciliary action. Increased inertial acceleration increases convective flow, while microgravity nearly abolishes it. In the latter case the extracellular transport of macromolecules is governed by diffusion. By making certain assumptions it is possible to calculate the Peclet number, the ratio of convective transport to diffusive transport. Some, but not all, responses of cells in vitro to modified inertial environments could be manifestations of modified extracellular convective flow.

Todd, Paul↗

NASA NTRS1992

Morphological instability of a thermophoretically growing deposit

The stability of the planar interface of a structureless solid growing from a depositing component dilute in a carrier fluid is studied when the main solute transport mechanism is thermal (Soret) diffusion. A linear stability analysis, carried out in the limit of low growth Peclet number, leads to a dispersion relation which shows that the planar front is unstable either when the thermal diffusion factor of the condensing component is positive and the latent heat release is small or when the thermal diffusion factor is negative and the solid grows over a thermally-insulating substrate. Furthermore, the influence of interfacial energy effects and constitutional supersaturation in the vicinity of the moving interface is analyzed in the limit of very small Schmidt numbers (small solute Fickian diffusion). The analysis is relevant to physical vapor deposition of very massive species on cold surfaces, as in recent experiments of organic solid film growth under microgravity conditions.

Castillo, Jose L.↗

NASA NTRS1992

Flow-induced gelation of living (micellar) polymers

The effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution is considered. A kinetic equation is introduced for the time-dependent concentration of aggregates of length L, consisting of 'bimolecular' combination processes L + L-prime yield (L + L-prime) and unimolecular fragmentations L yield L + (L - L-prime). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear-induced coalesence of emulsions, and the latter by incorporating the tension-deformation effects due to flow. Steady-state solutions to the kinetic equation are obtained, with the corresponding mean micellar size evaluated as a function of the Peclet number P (i.e., the dimensionless ratio of the flow rate and the rotational diffusion coefficient). For sufficiently dilute solutions, only a weak dependence of the micellar size on P is found. In the semidilute regime, however, an apparent divergence in the micellar size at P of about 1 suggests a flow-induced first-order gelation phenomenon.

Bruinsma, Robijn↗

NASA NTRS1993

Thermocapillary migration of a small chain of bubbles

The quasistatic thermocapillary migration of a chain of two or three spherical bubbles in an unbounded fluid possessing a uniform temperature gradient is investigated in the limit of vanishing Reynolds and Peclet numbers. The line of bubble centers is permitted to be either parallel or perpendicular to the direction of the undisturbed temperature gradient. The governing equations are solved by a truncated-series, boundary-collocation technique. Results are presented which demonstrate the impact of the presence of other bubbles on a test bubble. In the three-bubble case, a simple pairwise-additive approximation is constructed from the reflections solution, and found to perform well except when the bubbles are close to each other. Also, features of the flow topology in the fluid are explored. Separated reverse flow wakes are found in the axisymmetric problem, and other interesting structures are noted for the case in which the line of centers is perpendicular to the applied temperature gradient. The observed flow structure is shown to be the result of superposition of simpler basic flows.

Wei, Huailiang↗