Numerical calculation of viscous compressible fluid flow around an oscillating rigid cylinder
Numerical calculation of viscous compressible flow around harmonic oscillating rigid cylinder
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Numerical calculation of viscous compressible flow around harmonic oscillating rigid cylinder
Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.
We solve the Einstein constraint equations for a first-order causal viscous relativistic hydrodynamic theory in the case of a conformal fluid. For such a theory, a direct application of the conformal method does not lead to a decoupling of the equations, even for constant-mean curvature initial data. We combine the conformal method applied to a background perfect fluid theory with a perturbative argument in order to obtain the result.
Fluid motion in a fuel tank produced during thrust oscillations can circulate sub-cooled hydrogen near the liquid-vapor interface resulting in increased condensation and ullage pressure collapse. The first objective of this study is to validate the capabilities of a Computational Fluid Dynamics (CFD) tool, CFD-ACE+, in modeling the fundamental interface transition physics occurring at the propellant surface. The second objective is to use the tool to assess the effects of thrust oscillations on surface dynamics. Our technical approach is to first verify the CFD code against known theoretical solutions, and then validate against existing experiments for small scale tanks and a range of transition regimes. A 2D axisymmetric, multi-phase model of gases, liquids, and solids is used to verify that CFD-ACE+ is capable of modeling fluid-structure interaction and system resonance in a typical thrust oscillation environment. Then, the 3D mode is studied with an assumed oscillatory body force to simulate the thrust oscillating effect. The study showed that CFD modeling can capture all of the transition physics from solid body motion to standing surface wave and to droplet ejection from liquid-gas interface. Unlike the analytical solutions established during the 1960 s, CFD modeling is not limited to the small amplitude regime. It can extend solutions to the nonlinear regime to determine the amplitude of surface waves after the onset of instability. The present simulation also demonstrated consistent trends from numerical experiments through variation of physical properties from low viscous fluid to high viscous fluids, and through variation of geometry and input forcing functions. A comparison of surface wave patterns under various forcing frequencies and amplitudes showed good agreement with experimental observations. It is concluded that thrust oscillations can cause droplet formation at the interface, which results in increased surface area and enhanced heat transfer between the liquid and gas phases as the ejected droplets travel well into the warmer gas region.
Incompressible viscous flow fields induced by initial vorticity distributions with bounded support or exponential decay in the far field are investigated. A numerical scheme for the solution of the vorticity distribution and the velocity field is presented with special emphasis on the treatment of the boundary data. The efficiency of the scheme is demonstrated. The present method has been applied to the study of the merging and collision of vortex rings.
Design of magnetically driven micro-swimmer with feasibility in propelling through viscous fluids on desired trajectories.
The principal result obtained in this report is a generalization of Taylor's formula for a simple eddy. The discussion of the properties of the eddy indicates that there is a slight analogy between the theory of eddies in a viscous fluid and the quantum theory of radiation. Another exact solution of the equations of motion of viscous fluid yields a result which reminds one of the well-known condition for instability in the case of a horizontally stratified atmosphere.
An inherent numerical problem associated with the fully explicit pseudospectral numerical simulation of the incompressible Navier-Stokes equation for viscous flows with no-slip walls is described. A semi-implicit scheme which circumvents this numerical difficulty is presented. In this algorithm the equation of continuity rather than the Poisson equation for pressure is solved directly. Pseudospectral formulation of the channel flow problem using Fourier series and Chebyshev polynomials expansions is given for this scheme. An example demonstrating the applicability of the method is given.
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Tidal disruptions are investigated in viscous-fluid planetesimals whose radius is small relative to the distance of closest (parabolic-orbit) approach to a planet. The planetesimal surface is in these conditions always ellipsoidal, facilitating treatment by coupled ODEs which are solvable with high accuracy. While the disrupted planetesimals evolve into needlelike ellipsoids, their density does not decrease. The validity of viscous fluid treatment holds for solid (ice or rock) planetesimals in cases where tidal stresses are greater than material strength, but integrity is maintained by self-gravity.
Variable damping achieved without problems of containing viscous fluids. Eddy-current damping obtained by moving copper or aluminum conductors through magnetic fields. Position of magnet carrier determines amount of field engagement and, therefore, amount of damping. Three advantages of concept: Magnitudes of stiffness and damping continously varied from maximum to zero without bringing rotor or shaft to stop; used in rotating machines not having viscous fluids available such as lubricating oils; produces sizable damping forces in machines that pump liquid hydrogen at - 246 degrees C and liquid oxygen at - 183 degrees C and are compact in size.
We investigate non-linear instabilities stemming from superluminal propagation of information in Israel-Stewart-like models of relativistic viscous fluid dynamics. In relativity, the characteristic speed of propagation of information, $w$, and the speed of the fluid, $v$, allow us to differentiate between regimes of the hydrodynamic equations that are acausal but stable ($w>1$), unstable ($v^{2} w^{2} \geq 1$), and covariantly ill-posed ($w^{2} \leq 0$). As an analytical benchmark, we present a new solution that illustrates these distinct regimes. We compare this analytical solution to the result of a numerical relativistic viscous fluid dynamics solver, and confirm that the analytical result can be recovered numerically in the stable regime, whether causal or acausal. The onset of numerical instabilities is further found to occur in the regime predicted by the analytical solution.
Solids are often assumed to behave as viscous fluids under high-strain rates. This behavior has been studied experimentally in metals but largely unexplored in brittle ceramic materials. Here, in this study, we present a technique for measuring the viscosity of MgO using time-resolved velocimetry to track the growth rate of a perturbation caused by the Richtmyer-Meshkov instability at the OMEGA EP laser facility. To interpret the results, we use an in-house Eulerian hydrocode to simulate our experiments and model the plastic deformation of solid MgO as a viscous fluid. Results indicate that MgO has a surprisingly low upper bound to its effective viscosity of ∼10 2 Pa s at 175 ± 15 GPa, ∼3500K, and 10 6 −10 7 s −1 strain rate.
Placing firmer constraints on the emplacement timescales of visible volcanic features is essential to obtaining a better understanding of the resurfacing history of Venus. Fig. 1 shows a Magellan radar image and topography for a putative venusian lava dome. 175 such domes have been identified, having diameters that range from 19 - 94 km, and estimated thicknesses as great as 4 km [1-2]. These domes are thought to be volcanic in origin [3], having formed by the flow of a viscous fluid (i.e., lava) onto the surface. Among the unanswered questions surrounding the formation of Venus steep-sided domes are their emplacement duration, composition, and the rheology of the lava. Rheologically speaking, maintenance of extremely thick, 1-4 km flows necessitates higher viscosity lavas, while the domes' smooth upper surfaces imply the presence of lower viscosity lavas [2-3]. Further, numerous quantitative issues, such as the nature and duration of lava supply, how long the conduit remained open and capable of supplying lava, the volumetric flow rate, and the role of rigid crust in influencing flow and final morphology all have implications for subsurface magma ascent and local surface stress conditions. The surface of Jupiter's icy moon Europa exhibits many putative cryovolcanic constructs [5-7], and previous workers have suggested that domical positive relief features imaged by the Galileo spacecraft may be volcanic in origin [5,7-8] (Fig. 2). Though often smaller than Venus domes, if emplaced as a viscous fluid, formation mechanisms for europan domes may be similar to those of venusian domes [7]. Models for the emplacement of venusian lava domes (e.g. [9-10]) have been previously applied to the formation of putative cryolava domes on Europa [7].
Condition for swirling flow stability in circular magnetic field - mathematical analysis
Free laminar boundary layer flow between parallel streams of different magnetic fields and temperatures for incompressible viscous fluid
Data on experimental verification of Iberall's analysis applies to such problems as pressure sensing, pneumatic control circuits with bellows, measuring irregular shaped volumes, and transmitting fluid power by pulsating flow.
Mathematical models for investigating stability of thermally stratified shear flow in atmosphere