Effect of fluid motion on free surface shape under reduced gravity.
Velocity, Bond number and Weber number effects on liquid free surface shape and meniscus height under reduced gravity
FLOW VELOCITY↗
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A free surface vortex method with weak viscous effects
The advantage of vortex methods for inviscid flows of several fluids separated by interfaces is that problems of this kind may be posed and solved numerically entirely on the interface surface. For free surface problems, where one of the fluids has negligible inertia, a small amount of viscosity produces a thin, weak rotational layer adjacent to the potential flow vortex sheet. Here, a method is described for including this weak viscous effect as a modification of the boundary conditions for the potential part of the flow, thus allowing this slightly viscous flow to be formulated as a vortex method on the free surface. This is important for unsupported free drops where the viscosity at the free surface is the only source of damping for oscillations, and for gas-filled bubbles, where it provides both drag and damping. Small applied shear stresses from aerodynamic, electrostatic, or other sources may be included provided they are of the same order as the potential flow shear stress or smaller.
Lundgren, T. S.↗
Application of turbulence modeling to predict surface heat transfer in stagnation flow region of circular cylinder
A theoretical analysis and numerical calculations for the turbulent flow field and for the effect of free-stream turbulence on the surface heat transfer rate of a stagnation flow are presented. The emphasis is on the modeling of turbulence and its augmentation of surface heat transfer rate. The flow field considered is the region near the forward stagnation point of a circular cylinder in a uniform turbulent mean flow. The free stream is steady and incompressible with a Reynolds number of the order of 10 to the 5th power and turbulence intensity of less than 5 percent. For this analysis, the flow field is divided into three regions: (1) a uniform free-stream region where the turbulence is homogeneous and isotropic; (2) an external viscid flow region where the turbulence is distorted by the variation of the mean flow velocity; and, (3) an anisotropic turbulent boundary layer region over the cylinder surface. The turbulence modeling techniques used are the kappa-epsilon two-equation model in the external flow region and the time-averaged turbulence transport equation in the boundary layer region. The turbulence double correlations, the mean velocity, and the mean temperature within the boundary layer are solved numerically from the transport equations. The surface heat transfer rate is calculated as functions of the free-stream turbulence longitudinal microlength scale, the turbulence intensity, and the Reynolds number.
Wang, Chi R.↗
Heat flow and convection demonstration experiments aboard Apollo 14.
A group of experiments was conducted by Apollo 14 astronaut Stuart A. Roosa during the lunar flyback on Feb. 7, 1971, to obtain information on heat flow and convection in gases and liquids in an environment of less than 0.000001 g gravity. Flow observations and thermal data have shown that: (1) there are, as expected, convective motions caused by surface tension gradients in a plane liquid layer with a free upper surface; (2) heat flow in enclosed liquids and gases occurs mainly by diffusive heat conduction; and (3) some convective processes, whose characteristics are not fully known, add to the heat transfer.
Grodzka, P. G.↗
Heat flow and convection demonstration (Apollo 14)
Apollo 14 Astronaut Stuart A. Roosa conducted a group of experiments during the lunar flyback on February 7, 1971, to obtain information on heat flow and convection in gases and liquids in an environment of less than 0.000001 g. Flow observations and thermal data have shown that: (1) as expected, there are convective motions caused by surface tension gradients in a plane liquid layer with a free upper surface; (2) heat flow in enclosed liquids and gases occurs mainly by diffusive heat conduction; and (3) some convective processes, whose characteristics are not fully known, add to the heat transfer. The raw data are presented, and the analysis approach is given.
Bannister, T. C.↗
Numerical algorithms for water waves with background flow over obstacles and topography
Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).
Ambrose, David M.↗
Water Tunnel Flow Visualization Study Through Poststall of 12 Novel Planform Shapes
To determine the flow field characteristics of 12 planform geometries, a flow visualization investigation was conducted in the Langley 16- by 24-Inch Water Tunnel. Concepts studied included flat plate representations of diamond wings, twin bodies, double wings, cutout wing configurations, and serrated forebodies. The off-surface flow patterns were identified by injecting colored dyes from the model surface into the free-stream flow. These dyes generally were injected so that the localized vortical flow patterns were visualized. Photographs were obtained for angles of attack ranging from 10' to 50', and all investigations were conducted at a test section speed of 0.25 ft per sec. Results from the investigation indicate that the formation of strong vortices on highly swept forebodies can improve poststall lift characteristics; however, the asymmetric bursting of these vortices could produce substantial control problems. A wing cutout was found to significantly alter the position of the forebody vortex on the wing by shifting the vortex inboard. Serrated forebodies were found to effectively generate multiple vortices over the configuration. Vortices from 65' swept forebody serrations tended to roll together, while vortices from 40' swept serrations were more effective in generating additional lift caused by their more independent nature.
Gatlin, Gregory M.↗
Time-dependent thermocapillary convection in a Cartesian cavity - Numerical results for a moderate Prandtl number fluid
The present numerical simulation explores a thermal-convective mechanism for oscillatory thermocapillary convection in a shallow Cartesian cavity for a Prandtl number 6.78 fluid. The computer program developed for this simulation integrates the two-dimensional, time-dependent Navier-Stokes equations and the energy equation by a time-accurate method on a stretched, staggered mesh. Flat free surfaces are assumed. The instability is shown to depend upon temporal coupling between large scale thermal structures within the flow field and the temperature sensitive free surface. A primary result of this study is the development of a stability diagram presenting the critical Marangoni number separating steady from the time-dependent flow states as a function of aspect ratio for the range of values between 2.3 and 3.8. Within this range, a minimum critical aspect ratio near 2.3 and a minimum critical Marangoni number near 20,000 are predicted below which steady convection is found.
Peltier, L. J.↗
Numerical simulation of thermocapillary flow under zero and low gravity conditions
This paper discusses the numerical solution methods and results of steady and unsteady thermocapillary (surface-tension) and buoyancy driven flows in 2D cavities and liquid columns. The 2D cavity was assumed to be square with one free surface with a zero Capillary number (i.e., the free surface was constrained to be flat). A pseudospectral method was used to solve steady and unsteady surface tension-driven and mixed buoyancy-surface tension flows in a square cavity. For the liquid column a finite-difference scheme based on a Picard iteration was used to solve for the flow, temperature and free surface shape. The surface of the liquid column was allowed to deform and, as for the 2D cavity, the surface tension was assumed to depend on temperature.
Alexander, J. I. D.↗
Three-dimensional flow in radial turbomachinery and its impact on design
In the two papers on the 'Theory of Blade Design for Large Deflections' published in 1984, a new inverse design technique was presented for designing the shape of turbomachinery blades in three-dimensional flow. The technique involves the determination of the blade profile from the specification of a distribution of the product of the radius and the pitched averaged tangential velocity (i.e., r bar-V(sub theta), the mean swirl schedule) within the bladed region. This is in contrast to the conventional inverse design technique for turbomachinery blading in two dimensional flow in which the blade surface pressure or velocity distribution is specified and the blade profile determined as a result; this is feasible in two-dimensional flow because the streamlines along the blade surfaces are known a priori. However, in three-dimensional flow, the stream surface is free to deform within the blade passage so that the streamlines on the blade surfaces are not known a priori; thus it is difficult and not so useful to prescribe the blade surface pressure or velocity distribution and determine the resulting blade profile. It therefore seems logical to prescribe the swirl schedule within the bladed region for designing a turbomachinery blade profile in three-dimensional flow. Furthermore, specifying r bar-V(sub theta) has the following advantages: (1) it is related to the circulation around the blade (i.e., it is an aerodynamic quantity); (2) the work done or extracted is approximately proportional to the overall change in r bar-V(sub theta) across a given blade row (Euler turbine equation); and (3) the rate of change of r bar-V(sub theta) along the mean streamline at the blade is related to the pressure jump across the blade and therefore the blade loading. Since the publications of those two papers, the technique has been applied to the design of a low speed as well as a high speed radial inflow turbine (for turbocharger applications) both of which showed definite improvements in performance over that of wheels of conventional designs, the design study of a high pressure ratio radial inflow turbine with and without splitter blades.
Tan, Choon S.↗
Analysis of the weighted shifted boundary method for the Poisson and Stokes problems
The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.
Approximate domain boundaries↗
PROCEEDINGS OF THE SECOND INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS
Rarefied gas dynamics - molecular beams and surface interactions, free-molecular flow, fluid mechanics, kinetic theory
MOLECULAR FLOW↗
An experimental study of hypersonic rarefied flow over sharp cones
Hypersonic rarefied merged layer flow over sharp slender cones, using strong interaction theory and free molecular flow to analyze surface pressures
Horstman, C. C.↗
Manufacturing in space: Fluid dynamics numerical analysis
Thermocapillary convection in an air-jet Marangoni flow suppressing technique was numerically simulated for flow under various conditions of fluid properties, gravity, and temperature gradient. Results presented include computer generated plots of streamlines, velocities, and temperatures throughout the contained fluid flow, and plots of Marangoni flow velocities over the free surface.
Robertson, S. J.↗
Flow velocity measurements by image processing of optically activated tracers
A computerized flow visualization technique capable of quantifying the flow field automatically has been developed. This technique uses afterglowing effect of optically activated phosphorescent particles to retrieve vectorial information on each trace. By using this information, in conjunction with computer image processing, the flow field of a free surface transient vortex was investigated.
Gharib, M.↗
Screen test for cadmium and nickel plates
A new procedure is described which was recently developed to quantify loading uniformity of nickel and cadmium plates and to screen finished electrodes prior to cell assembly. The technique utilizes the initial solubility rates of the active material in a standard chemical deloading solution at fixed conditions. The method can provide a reproducible indication of plate loading uniformity in situations where high surface loading limits the free flow of deloading solution into the internal porosity of the sinter plate. A preliminary study indicates that 'good' cell performance is associated with higher deloading rates.
Phan, Angie H.↗
Screen test for cadmium and nickel plates as developed and used within the Aerospace Corporation
A new procedure described here was recently developed to quantify loading uniformity of nickel and cadmium plates and to screen finished electrodes prior to cell assembly. The technique utilizes the initial solubility rates of the active material in a standard chemical deloading solution at fixed conditions. The method can provide a reproducible indication of plate loading uniformity in situations where high surface loading limits the free flow of deloading solution into the internal porosity of the sinter plate. A preliminary study indicates that 'good' cell performance is associated with higher deloading rates.
Phan, A. H.↗
Control of Shock Loading from a Jet in a Flexible Structure's Presence
The control of shock noise or screech from a jet near a flexible structure is discussed. The pressure from the supersonic jet consists of a shock with spiral and flapping nonaxisymmetric modes superimposed on broadband response. This shock induces a nonlinear-nonstationary loading problem associated with acoustic wave generation and propagation coupled with structural vibration. Control of the shock is achieved by placing a ring at the nozzle lip oscillating at the shock fundamental frequency. The ring prevents the shock characteristics originating in the column of the shear layer from sustaining connection with the out-of-phase surface vibration. Shock-free flow is maintained over a large pressure ratio. The peak power spectral density of the pressure due to shock fundamental and harmonics is converted to broadband level. The experiment is motivated by consideration of aircraft structural fatigue and interior noise.
Maestrello, Lucio↗