Engineering topics

Davis, S. H.

Publications and source records attributed to Davis, S. H..

At least 37 records · Page 2

NASA NTRS1988

Directional solidification with heat losses

The upward directional solidification of a dilute binary alloy in a tall, thin, two-dimensional slot is considered. Heat losses from the sidewalls produce curved isotherms, interface deformations, and melt convection. An asymptotic approach is used which relates the small heat loss to the thinness of the solidification cell, and solutions are obtained for the resulting melt convection, interface deflection, and the distribution of heat and solute. The model is compared to the numerical results of Chang and Brown (1983) which exclude the effects of solute buoyancy and thermodynamic equilibrium at the interface. The radial segregation at the interface (consistent with both interface shapes and temperature fields) is computed, and it is found that the radial segregation is independent of interfacial shapes; the radial segregation cannot be calculated from only a knowledge of the interface shape.

Brattkus, K.↗

NASA NTRS1988

Flow-induced morphological instabilities - The rotating disc

The morphological stability of a rotating and solidifying disk is investigated under the assumption that delta, the thickness of the viscous boundary layer, is much larger than delta(c), the thickness of the solute boundary layer. It is found that axisymmetric disturbances with wavelengths comparable to delta respond to nonparallel flow effects and have stability characteristics quite different from disturbances in a parallel flow. These long waves are unstable because of the nonparallel flow and would decay without it. This analysis thus identifies a new mechanism of morphological change induced by flow.

Brattkus, K.↗

NASA NTRS1987

Anisotropic interface kinetics and tilted cells in unidirectional solidification

A nonlinear evolution equation is derived which governs the cellular structure of a binary alloy with a small segregation coefficient, including the effects of anisotropic interface kinetics. This equation, applicable to long-wave instabilities of a planar interface, describes the spatial pattern of the growing disturbances. The presence of anisotropy causes the cells to grow at an angle to the normal of the planar front. This transition to a cellular morphology is shown to be a subcritical instability.

Young, G. W.↗

NASA NTRS1987

Directional solidification in an imperfect furnace

The upward directional solidification of a binary alloy in which the rejected solute is more dense than the solvent is considered. The system is stably stratified both thermally and solutally. If heat is lost through the sidewalls, horizontal thermal gradients drive a steady double-diffusive convection. Solidification cells with small aspect ratios (width/length) A are considered, and asymptotic solutions to the steady double-diffusive system are obtained as A tends to 0 under the assumption heat losses are also small. When the thermal Grashof number is large, buoyancy boundary layers are at the sidewalls. The shape of the crystal-melt interface is determined by the coupled effects of local thermodynamic equilibrium, diffusion and convection.

Brattkus, K.↗

NASA NTRS1987

Crystal growing from the melt

The mechanical and electrical properties of crystals produced by a unidirectional process depend strongly on the temperature and flow fields since these control the concentration of solute at the melt-crystal interface. The solute gradient there drives morphological instabilities that lead to cellular or dendritic interfaces. In the presentation several features of flow-solidification interactions will be discussed. These will include the effects of convection driven by density changes and buoyancy and the imposition of forced flow.

Davis, S. H.↗

NASA NTRS1985

Instability of capillary jets with thermocapillarity

Long axisymmetric liquid zones are subject to axial temperature gradients which induce steady viscous flows driven by thermocapillarity. The approximately parallel flow in a cylindrical zone is examined for linearized instabilities. Capillary, surface-wave and thermal modes are found. Capillary breakup can be retarded or even suppressed for small Prandtl number and large Biot number B, which measures heat transfer from the liquid to the surrounding atmosphere. In the limiting case B approaches infinity the zone becomes an isothermal jet subject to axial 'wind stress' on its interface. It is then possible to suppress capillary breakup entirely so that one can maintain long coherent jets.

Xu, J.-J.↗

NASA NTRS1985

Thermocapillary Flows and Their Stability: Effects of Surface Layers and Contamination

The objective is to study quantitatively thermocapillary flows in two-dimensional and axisymmetric geometries in order to learn the impact of such flows on float-zone refining configurations. The work begins with the analytical study of steady flows in slots and zones to obtain predictions of surface curvature, flow and heat transport. It then examines the instability of such flows. Three new instability mechanisms have been identified and the results show that thermocapillary flows of high Prandtl number fluid become convectively unstable while those of low Prandtl number fluid become hydrodynamically unstable. The work includes numerical simulations of steady, high Marangoni number flows in unit aspect ratio boxes and asymptotic solutions in large boxes. Furthermore, the effect of surface contamination on the steady thermocapillary flows was examined. This fundamental study focused on fluid dynamical systems used to understand events in the flow of melts in float-zone geometries both on Earth and in microgravity environments.

Davis, S. H.↗

NASA NTRS1984

Convective thermocapillary instabilities in liquid bridges

A steady shear flow is generated in an axisymmetric liquid bridge surrounded by a passive gas through the imposition of a temperature gradient along the bridge and the driving of the motion by thermocapillarity. This dynamic state is susceptible to convective instabilities, which can lead to propagating hydrothermal waves that feed on the underlying temperature gradients. The convective instabilities of axisymmetric return flow are presently given as functions of the liquid's Prandtl number and the surface Biot number of the interface.

Xu, J.-J.↗

NASA NTRS1984

Thermocapillary flows and their stability: Effects of surface layers and combination

The theoretical analysis of the fluid mechanics and heat transfer of motions driven by surface tension gradients (Marangoni convection) was researched. Convection accompanying the process of growing high quality single crystals from the melt in a micro-g environment was examined. The geometries considered include two dimensional liquid filled slots and axisymmetric float-zone configurations.

Davis, S. H.↗

NASA NTRS1984

On the stability of the decelerating laminar boundary layer

The stability of a decelerating boundary-layer flow is investigated experimentally and numerically. Experimentally, a flat plate having a Blasius boundary layer is decelerated in an 18 m towing tank. The boundary layer becomes unstable to two-dimensional waves, which break down into three-dimensional patterns, hairpin vortices, and finally turbulent bursts when the vortices lift off the wall. The unsteady boundary-layer equations are solved numerically to generate instantaneous velocity profiles for a range of boundary and initial conditions. A quasi-steady approximation is invoked and the stability of local velocity profiles is determined by solving the Orr-Sommerfeld equation using Chebyshev matrix methods. Comparisons are made between the numerical predictions and the experimentally observed instabilities.

Gad-El-hak, M.↗

NASA NTRS1983

Liquid bridges with thermocapillarity

An axisymmetric liquid bridge is subjected to an axial temperature gradient. Thermal variations in surface tension drive a motion that is described using lubrication theory for slender bridges. At leading order in aspect ratio, a class of similarity solutions is obtained valid in the core region away from the endwalls of the bridge. These solutions describe the flows, temperature fields, and interfacial shapes of bridges that may sustain substantial interfacial deflections.

Xu, J.-J.↗

NASA NTRS1983

Viscous thermocapillary convection at high Marangoni number

A liquid, contained in a quarter plane, undergoes steady motion due to thermocapillary forcing on its upper boundary, a free surface separating the liquid from a passive gas. The rigid vertical sidewall has a strip whose temperature is elevated compared with the liquid at infinity. A boudnary-layer analysis is performed that is valid for large Marangoni numbers M and Prandtl numbers P. It is found that the Nusselt number N for the horizontal heat transport satisfies N proportional to min (M to the 1 2/7/power, M to the 1 1/5/power, M to the 1 1/10/power) Generalizations are discussed.

Cowley, S. J.↗

NASA NTRS1983

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.↗

NASA NTRS1982

Thermocapillary flows and their stability: Effects of surface layers and contamination

The fluid mechanics and heat transfer of motions driven by surface tension gradients (Marangoni convection) were analyzed theoretically to obtain an understanding of the convection accompanying the process of growing high quality single crystals from the melt in a mu-g environment. The geometries considered include two dimensional liquid filled slots and axisymmetric float zone configurations.

Davis, S. H.↗

NASA NTRS1982

Steady thermocapillary flows in two-dimensional slots

Liquid in a slot flows owing to a temperature gradient applied along its free surface. The thermal variation of surface tension induces a steady viscous flow directed on the surface from hot to cold, and recirculating below. For small aspect ratios A, giving flow in thin, two-dimensional slots, an asymptotic theory valid for A yields to 0 is used to obtain the fluid and thermal fields as well as the interfacial shapes. Solutions are obtained for both fixed lines and fixed angles at the contact between the interface and the solid side walls.

Sen, A. K.↗

NASA NTRS1982

The instability of sheared liquid layers

The critical values of the Reynolds number (Rc) above which unstable travelling waves exist in a steady shear flow are calculated with the inclusion of a term in the normal stress boundary condition omitted by Miles (1960). Results show a value of Rc = 34.2, compared to Miles' value of 203, for the case of a zero-surface tension interface. The critical wavenumber, critical phase speed, and Rc are calculated as functions of a nondimensional surface tension, and the mechanism of the instability is investigated by examining the disturbance energy equation. A long wave instability is found at small values of the Reynolds number when the shear flow has a parabolic velocity profile. In addition, these results are extended to larger values of the wavenumber by numerical methods, and the relation between this long wave instability and the profile curvature is examined.

Smith, M. K.↗

NASA NTRS1982

Nonlinear Marangoni convection in bounded layers. I - Circular cylindrical containers. II - Rectangular cylindrical containers

Liquid undergoing nonlinear Marangoni instability in a circular cylinder is examined, with attention given to roll-cell development and interaction. Surface deflections are neglected and the side walls are considered as adiabatic and impenetrable, allowing the liquid to freely slip. The nonlinear convective states are calculated and their stability is defined. The behavior and amplitude of cells forming in the liquid, heated from below, are modeled in order to derive all the transport properties. A new small parameter is formulated which is related to the critical Marangoni number of the infinite matrix expressing the eigenvalue expansion of the problem. The observed roll cell amplitudes and transport properties are shown to be available from simple eigenvalues, with double eigenvalues, indicating the existence of two roll-states as predicted by linear theory, nonlinear theory indicates transitions from one steady convective state to another.

Rosenblat, S.↗

NASA NTRS1982

Steady thermocapillary flows and their stability

Thermocapillarity can drive steady flows in float-zone configurations. These flows can become unstable and exhibit time-periodic oscillations. In order to obtain insight into such phenomena, studies are made of a simplified system consisting of liquid in a two-dimensional slot. Steady flows and their instabilities are examined.

Sen, A. K.↗