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This poster will be presented at the DOE Office of Electricity Peer Review in August. The attendees will be researchers funded by the program.
Laminar two-phase boundary layer flow in film boiling, obtaining asymptotic solutions for low and high subcooled liquids
Thermal convection driven by uniform volumetric energy sources was studied in a horizontal fluid layer bounded from above by a rigid, isothermal surface and from below by a rigid, zero heat-flux surface. The side walls of the fluid domain were assumed to be rigid and perfectly insulating. The computations were formally restricted to two-dimensional laminar convection but were carried out for a range of Rayleigh numbers which spans the regimes of laminar and turbulent flow. The results of the computations consists of streamline and isotherm patterns, horizontally averaged temperature distributions, and horizontally averaged Nusselt numbers at the upper surface. Flow and temperature fields do not exhibit a steady state, but horizontally averaged Nusselt numbers reach limiting, quasi-steady values for all Rayleigh numbers considered. Correlations of the Nusselt number in terms of the Rayleigh and Prandtl numbers were determined.
An experimental investigation was conducted on methane, laminar-jet, diffusion flames with coaxial, forced-air flow to examine flame shapes in zero-gravity and in situations where buoyancy aids (normal-gravity flames) or hinders (inverted-gravity flames) the flow velocities. Fuel nozzles ranged in size from 0.051 to 0.305 cm inside radius, while the coaxial, convergent, air nozzle had a 1.4 cm inside radius at the fuel exit plane. Fuel flows ranged from 1.55 to 10.3 cu cm/sec and air flows from 0 to 597 cu cm/sec. A computer program developed under a previous government contract was used to calculate the characteristic dimensions of normal and zero-gravity flames only. The results include a comparison between the experimental data and the computed axial flame lengths for normal gravity and zero gravity which showed good agreement. Inverted-gravity flame width was correlated with the ratio of fuel nozzle radius to average fuel velocity. Flame extinguishment upon entry into weightlessness was studied, and it was found that relatively low forced-air velocities (approximately 10 cm/sec) are sufficient to sustain methane flame combustion in zero gravity. Flame color is also discussed.
The problem of buoyancy driven flow in a vertical, rectangular cavity whose vertical sides are at different temperatures and whose horizontal sides are insulated is addressed. An application of the dynamic A.D.I. method to obtain numerical solutions to this problem is described. For large non-dimensional temperature differences characterized by the Rayleigh number the flow patterns develop strong boundary layers. These boundary layers are resolved by applying the D.A.D.I. method to the discretization of this problem on a non-uniform grid.
The results of two lines of research aimed at calculating the structure of the flows driven by buoyancy in small-scale crystal growth systems and at understanding the coupling between these flows, the shape of the solidification interface, and dopant segregation in the crystal are reviewed. First, finite-element methods are combined with computer-aided methods for detecting multiple steady solutions to analyze the structure of the buoyancy-driven axisymmetric flows in a vertical cylinder heated from below. This system exhibits onset of convection, multiple steady flows, and loss of the primary stable flow beyond a critical value of the Rayleigh number. Second, results are presented for calculations of convection, melt/solid interface shape, and dopant segregation within a vertical ampoule with thermal boundary conditions that represent a prototype of the vertical Bridgman growth system.
The problem of buoyancy driven flow in a vertical, rectangular cavity whose vertical sides are at different temperatures and whose horizontal sides are insulated is addressed. An application of the dynamic A.D.I. method to obtain numerical solutions to this problem is described. For large non-dimensional temperature differences characterized by the Rayleigh number the flow patterns develop strong boundary layers. These boundary layers are resolved by applying the D.A.D.I. method to the discretization of this problem on a non-uniform grid. Previously announced in STAR as N83-25433
A Petrov-Galerkin finite element method is presented for calculation of the steady, axisymmetric thermosolutal convection and interface morphology in a model for vertical Bridgman crystal growth of nondilute binary alloys. The Petrov-Galerkin method is based on the formulation for biquadratic elements developed by Heinrich and Zienkiewicz and is introduced into the calculation of the velocity, temperature and concentration fields. The algebraic system is solved simultaneously for the field variables and interface shape by Newton's method. The results of the Petrov-Galerkin method are compared critically with those of Galerkin's method using the same finite element grids. Significant improvements in accuracy are found with the Petrov-Galerkin method only when the mesh is refined and when the formulation of the residual equations is modified to account for the mixed boundary conditions that arise at the solidification interface. Calculations for alloys with stable and unstable solute gradients show the occurrence of classical flow transitions and morphological instabilities in the solidification system.
A numerical analysis of transient combined heat and mass transfer across a rectangular cavity is performed by a numerical method based on the SIMPLE algorithm. The physical parameters are selected to represent a range of possible crystal growth in solutions. Numerical results are compared with available experimental data to confirm the accuracy of the results. Good qualitative agreements are obtained for the average mass transfer rate across the cavity. Also, qualitative agreements are observed for the global development of thermal and solute fields. It is found that the thermal and solute fields become highly oscillatory when the thermal and solute Grashof numbers are large. Oscillations are probably caused by a number of different instability mechanisms. By reducing the gravity some of these instabilities were made to disappear at the lower Grashof numbers. Transient temperature and solute distribution near the crystal growing surface are highly non-uniform at the higher Grashof numbers. These non-uniformities are less severe in the reduced gravity environments but still exist. The effects of convection on the rate of average mass transfer are more than one order of magnitude higher than those of conduction in the range of Grashof numbers studied. Dependency of mass transfer rate on the Grashof number indicates that the convection effects many not be negligible even in the microgravity environments for the range of parameters investigated.
A numerical analysis of transient heat and solute transport across a rectangular cavity with combined horizontal temperature and concentration gradients is performed by a numerical method based on the SIMPLE. Numerical results show that the average Nusselt and Sherwood numbers both decrease markedly when the solutal and thermal buoyancy forces act in the opposite directions. When the solutal and thermal buoyancy forces act in the same directions, however, the average Sherwood number increases significantly and yet the average Nusselt number decreases slightly.
The multicellular flow between two vertical parallel plates is numerically simulated using a time-splitting pseudospectral method. The steady flow of air and the time-periodic flow of oil are investigated, and descriptions of these flows using both physical and spectral approaches are presented. The time dependence of the flow and temperature fields of oil are shown, and the dynamics of the process is discussed. The spectral transfer of energy among the axial modes comprising the flow is explored. The three-dimensional linear stabiltiy of the multicellular air flow is parametrically studied. The domain of stable two-dimensional cellular motion is found to be constrained by the Eckhaus instability and by two types of monotone instability. The two-dimensional multicellular flow is unstable above a Grashof number of about 8550.
A numerical analysis is performed on thermocapillary buoyancy convection induced by phase change in a liquid droplet. A finite-difference code is developed using an alternating-direction implicit (ADI) scheme. The intercoupling relation between thermocapillary force, buoyancy force, fluid property, heat transfer, and phase change, along with their effects on the induced flow patterns, are disclosed. The flow is classified into three types: thermocapillary, buoyancy, and combined convection. Among the three mechanisms, the combined convection simulates the experimental observations quite well, and the basic mechanism of the observed convection inside evaporating sessile drops is thus identified. It is disclosed that evaporation initiates unstable convection, while condensation always brings about a stable density distribution which eventually damps out all fluid disturbances. Another numerical model is presented to study the effect of boundary recession due to evaporation, and the 'peeling-off' effect (the removal of the surface layer of fluid by evaporation) is shown to be relevant.
A numerical analysis of transient combined heat and mass transfer across a rectangular cavity is performed. The physical parameters are selected to represent a range of possible crystal growth in solutions. Good agreements with measurement data are observed. It is found that the thermal and solute fields become highly oscillatory when the thermal and solute Grashof numbers are large.
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The paper presents a critical comment on the work of Henkes and Hoogendoorn. In particular, it is argued that the model of To and Humphrey (TH) (1986) has been implemented incorrectly, rendering invalid the conclusion that the TH model considerably deviates from the other models evaluated. In their response to the criticism, the authors present arguments in support of the correctness of their implementation of the TH model and of the validity of the conclusions reached in their work.
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Explore the source record for details and available documents.