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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↗

NASA NTRS1994

Dynamics of hard sphere colloidal dispersions

Our objective is to perform on homogeneous, fully equilibrated dispersions the full set of experiments characterizing the transition from fluid to solid and the properties of the crystalline and glassy solid. These include measurements quantifying the nucleation and growth of crystallites, the structure of the initial fluid and the fully crystalline solid, and Brownian motion of particles within the crystal, and the elasticity of the crystal and the glass. Experiments are being built and tested for ideal microgravity environment. Here we describe the ground based effort, which exploits a fluidized bed to create a homogeneous, steady dispersion for the studies. The differences between the microgravity environment and the fluidized bed is gauged by the Peclet number Pe, which measures the rate of convection/sedimentation relative to Brownian motion. We have designed our experiment to accomplish three types of measurements on hard sphere suspensions in a fluidized bed: the static scattering intensity as a function of angle to determine the structure factor, the temporal autocorrelation function at all scattering angles to probe the dynamics, and the amplitude of the response to an oscillatory forcing to deduce the low frequency viscoelasticity. Thus the scattering instrument and the colloidal dispersion were chosen such as that the important features of each physical property lie within the detectable range for each measurement.

Zhu, J. X.↗

NASA NTRS1994

Penetration below a convective zone

Two-dimensional numerical simulations are used to investigate how fully compressible nonlinear convection penetrates into a stably stratified zone beneath a stellar convection zone. Estimates are obtained of the extent of penetration as the relative stability S of the stable to the unstable zone is varied over a broad range. The model deals with a perfect gas possessing a constant dynamic viscosity. The dynamics is dominated by downward-directed plumes which can extend far into the stable material and which can lead to the excitation of a broad spectrum of internal gravity waves in the lower stable zone. The convection is highly time dependent, with the close coupling between the lateral swaying of the plumes and the internal gravity waves they generate serving to modulate the strength of the convection. The depth of penetration delta, determined by the position where the time-averaged kinetic flux has its first zero in the stable layer, is controlled by a balance between the kinetic energy carried into the stable layer by the plumes and the buoyancy braking they experience there. A passive scalar is introduced into the unstable layer to evaluate the transport of chemical species downward. Such a tracer is effectively mixed within a few convective overturning times down to a depth of delta within the stable layer. Analytical estimates based on simple scaling laws are used to interpret the variation of delta with S, showing that it first involves an interval of adiabatic penetration if the local Peclet number of the convection exceeds unity, followed by a further thermal adjustment layer, the depths of each interval scaling in turn as S(exp -1) and S(exp -1/4). These estimates are in accord with the penetration results from the simulations.

Hurlburt, Neal E.↗

NASA NTRS1990

Direct Numerical Simulations of Turbulent Convection: Variable Gravity and Uniform Rotation - Part 1

Turbulent convection may have played a major role in determining the structure and evolution of the primordial solar nebula, but current, incomplete models of convection and turbulence give very different results and remain largely untested in the absence of detailed astronomical observations. Numerical simulations provide an 'experimental' database for comparison with these models, and, to this end, direct numerical simulations of turbulent convection were performed with modifications intended to mimic some of the unique physical features of thin accretion disks, such as the primordial solar nebula: internal heating, a gravitational acceleration that is linearly proportional to the distance from midplane of the nebula, and rapid rotation. Peclet numbers in the simulations are comparable to those in solar nebula models; Rossby numbers in the simulations are an order of magnitude larger than those in solar nebula models because of the unrealistically high Prandtl and low, Reynolds numbers required to resolve all scales of the convective flow. We find that, despite the loss of buoyancy at midplane, turbulent motions easily penetrate the midplane region with little loss of intensity, providing efficient transport of heat and turbulent kinetic energy throughout the interior. A simple mixing length model modified to include rotation is found to give convective heat fluxes for the interior flow in rough agreement with the numerical simulations. We discuss these preliminary results with regard to assumptions about heating distributions and convective heat fluxes made in standard solar nebula models. More definitive comparisons with solar nebula modelling will become possible when more realistic effects of shear, density, stratification, and compression are included.

Cabot, W.↗

NASA NTRS1996

Nonlinear Response of Layer Growth Dynamics in the Mixed Kinetics-Bulk-Transport Regime

In situ high-resolution interferometry on horizontal facets of the protein lysozyme reveal that the local growth rate R, vicinal slope p, and tangential (step) velocity v fluctuate by up to 80% of their average values. The time scale of these fluctuations, which occur under steady bulk transport conditions through the formation and decay of step bunches (macrosteps), is of the order of 10 min. The fluctuation amplitude of R increases with growth rate (supersaturation) and crystal size, while the amplitude of the v and p fluctuations changes relatively little. Based on a stability analysis for equidistant step trains in the mixed transport-interface-kinetics regime, we argue that the fluctuations originate from the coupling of bulk transport with nonlinear interface kinetics. Furthermore, step bunches moving across the interface in the direction of or opposite to the buoyancy-driven convective flow increase or decrease in height, respectively. This is in agreement with analytical treatments of the interaction of moving steps with solution flow. Major excursions in growth rate are associated with the formation of lattice defects (striations). We show that, in general, the system-dependent kinetic Peclet number, Pe(sub k) , i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe(sub k) can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities under steady bulk nutrient crystallization conditions.

Vekilov, Peter G.↗

NASA NTRS2000

The Dynamics of Miscible Interfaces: A Space Flight Experiment

Experiments as well as accompanying simulations are described that serve in preparation of a space flight experiment to study the dynamics of miscible interfaces. The investigation specifically addresses the importance of both nonsolenoidal effects as well as nonconventional Korteweg stresses in flows that give rise to steep but finite concentration gradients. The investigation focuses on the flow in which a less viscous fluid displaces one of higher viscosity and different density within a narrow capillary tube. The fluids are miscible in all proportions. An intruding finger forms that occupies a fraction of the total tube diameter. Depending on the flow conditions, as expressed by the Peclet number, a dimensionless viscosity ratio, and a gravity parameter, this fraction can vary between approximately 0.9 and 0.2. For large Pe values, a quasi-steady finger forms, which persists for a time of O(Pe) before it starts to decay, and Poiseuille flow and Taylor dispersion are approached asymptotically. Depending on the specific flow conditions, we observe a variety of topologically different streamline patterns, among them some that leak fluid from the finger tip. For small Pe values, the flow decays from the start and asymptotically reaches Taylor dispersion after a time of O(Pe). Comparisons between experiments and numerical simulations based on the 'conventional' assumption of solenoidal velocity fields and without Korteweg stresses yield poor agreement as far as the Pe value is concerned that distinguishes these two regimes. As one possibility, we attribute this lack of agreement to the disregard of these terms. An attempt is made to use scaling arguments in order to evaluate the importance of the Korteweg stresses and of the assumption of solenoidality. While these effects should be strongest in absolute terms when steep concentration fronts exist, i.e., at large Pe, they may be relatively most important at lower values of Pe. We subsequently compare these conventional simulations to more complete simulations that account for nonvanishing divergence as well as Korteweg stresses. While the exact value of the relevant stress coefficients are not known, ballpark numbers do exist, and their use in the simulations indicates that these stresses may indeed be important. We plan to evaluate these issues in detail by means of comparing a space experiment with corresponding simulations, in order to extract more accurate Korteweg stress coefficients, and to confirm or deny the importance of such stresses.

Maxworthy, Tony↗

NASA NTRS2001

The Dynamics of Miscible Fluids: A Space Flight Experiment (MIDAS)

We propose a space flight experiment to study the dynamics of miscible interfaces. A less viscous fluid displaces one of higher viscosity within a tube. The two fluids are miscible in all proportions. An intruding "finger" forms that occupies a fraction of the tube. As time progresses diffusion at the interface combined with flow induced straining between the two fluids modifies the concentration and velocity distributions within the whole tube. Also, under such circumstances it has been proposed that the interfacial stresses could depend on the local concentration gradients (Korteweg stresses) and that the divergence of the velocity need not be zero, even though the flow is incompressible. We have obtained reasonable agreement for the tip velocity between numerical simulations (that ignored the Korteweg stress and divergence effects) and physical experiments only at high Peclet Numbers. However at moderate to low Pe agreement was poor. As one possibility we attributed this lack of agreement to the disregard of these effects. We propose a space experiment to measure the finger shape, tip velocity, and the velocity and concentration fields. From intercomparisons between the experiment and the calculations we can then extract values for the coefficients of the Korteweg stress terms and confirm or deny the importance of these stresses.

Maxworthy, T.↗

NASA NTRS2003

Free Dendritic Growth of Succinonitrile-Acetone Alloys with Thermosolutal Melt Convection

A stagnant film model of the effects of thermosolutal convection on free dendritic growth of alloys is developed, and its predictions are compared to available earth-based experimental data for succinonitrileacetone alloys. It is found that the convection model gives excellent agreement with the measured dendrite tip velocities and radii for low solute concentrations. However, at higher solute concentrations the present predictions show some deviations from the measured data, and the measured (thermal) Peclet numbers tend to fall even below the predictions from diffusion theory. Furthermore, the measured selection parameter (sigma*) is significantly above the expected value of 0.02 and exhibits strong scatter. It is shown that convection is not responsible for these discrepancies. Some of the deviations between the predicted and measured data at higher supercoolings could be caused by measurement difficulties. The systematic disagreement in the selection parameter for higher solute concentrations and all supercoolings examined, indicates that the theory for the selection of the dendrite tip operating state in alloys may need to be reexamined.

Beckermann, Christoph↗

NASA NTRS2002

Solutal Convection Around Growing Protein Crystal and Diffusional Purification in Space

This work theoretically addressed two subjects: 1) onset of convection, 2) distribution of impurities. Onset of convection was considered analytically and numerically. Crystal growth was characterized by slow surface incorporation kinetics, i.e. growth kinetic coefficient beta (cm/s) small as compared to the typical bulk diffusion rate, D(sub 1)/h, where D(sub 1) is diffusivity of major crystallizing protein and h is the crystal size. Scaling type analysis predicted two laws on how the convection rate, v, essentially the Peclet number, Pe exactly equal to vh/D(sub 1), depends on dimensionless kinetic coefficient a exactly equal to beta h/D(sub 1). Namely: Pe = C(sub 2/5)(aRa(sup 2/5)) and Pe = C(sub 1) aRa. Here, Reynolds number Ra = rho(sub 1)(sup 0)gh(sup 3)(rho(sub p) - rho(sub w))/rho(sup p)rho(sub 1)vD(sub 1), v being solution viscosity. The constants C(sub 2/5), exactly equal to 0.28 and C(sub 1) exactly equal to 10(exp -2) found from the full scale computer simulation for a cylindrical crystal inside big cylindrical vessel. The linear boundary conditions connecting protein and impurity concentration at the interface with the flux to/from the interface was applied. No-slip condition for Navier-Shocker equations was employed. With these conditions, flow and concentration distributions were calculated. Validity of the Pe(Ra) dependencies follows for wide range of parameters for which numerical calculations have been accomplished and presented by various points.

Chernov, A. A.↗

NASA NTRS2003

Concentration and Velocity Gradients in Fluidized Beds

In this work we focus on the height dependence of particle concentration, average velocity components, fluctuations in these velocities and, with the flow turned off, the sedimentation velocity. The latter quantities are measured using Particle Imaging Velocimetry (PIV). The PIV technique uses a 1-megapixel camera to capture two time-displaced images of particles in the bed. The depth of field of the imaging system is approximately 0.5 cm. The camera images a region with characteristic length of 2.6 cm for the small particles and 4.7 cm. for the large particles. The local direction of particle flow is determined by calculating the correlation function for sub-regions of 32 x 32 pixels. The velocity vector map is created from this correlation function using the time between images (we use 15 to 30 ms). The software is sensitive variations of 1/64th of a pixel. We produce velocity maps at various heights, each consisting of 3844 velocities. We break this map into three vertical zones for increased height information. The concentration profile is measured using an expanded (1 cm diameter) linearly polarized HeNe Laser incident on the fluidized bed. A COHU camera (gamma=1, AGC off) with a lens and a polarizer images the transmitted linearly polarized light to minimize the effects of multiply scattered light. The intensity profile (640 X 480 pixels) is well described by a Gaussian fit and the height of the Gaussian is used to characterize the concentration. This value is compared to the heights found for known concentrations. The sedimentation velocity is estimated using by imaging a region near the bottom of the bed and using PIV to measure the velocity as a function of time. With a nearly uniform concentration profile, the time can be converted to height information. The stable fluidized beds are made from large pseudo-monodisperse particles (silica spheres with radii (250-300) microns and (425-500) microns) dispersed in a glycerin/water mix. The Peclet number is sufficiently large that Brownian motion of the particles can be ignored and the Reynolds number sufficiently small that particle inertia is negligible. A packed particle bed is used to randomize and disperse the flowing fluid introduced by a peristaltic pump. The bed itself is a rectangular glass cell 8 cm wide (x), 0.8 cm deep and a height of 30.5 cm (z). The depth of field of the camera is approximately 0.5 cm so depth information is averaged. Over flow fluid is returned to the reservoir making a closed loop system. In these experiments the particles form a sediment approximately 5.7 cm high with the pump off and expand to 22 cm with the pump on. For the smaller particles the pump velocity is .5 millimeters per second and 1.1 millimeters per second for the large particles. At this concentration the bed has a very well defined top where particle concentration rapidly drops to zero.

McClymer, James P.↗