Fluid Dynamics Commons^™

Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

We study the fully three-dimensional Stokes flow within a geometry consisting of two infinite cones with coincident apices. The Stokes approximation is valid near the apex and we consider the dominant flow features as it is approached. The cones are assumed to be stationary and the flow to be driven by an arbitrary far-field disturbance. We express the flow quantities in terms of eigenfunction expansions and allow for the first time for nonaxisymmetric flow regimes through an azimuthal wave number. The eigenvalue problem is solved numerically for successive wave numbers. Both real and complex sequences of eigenvalues are found, their …

Hydrodynamic And Magnetohydrodynamic Computations Inside A Rotating Sphere, P. D. Mininni, D. C. Montgomery, L. Turner

Dartmouth Scholarship

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar–Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest …

Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

This paper considers the low-Reynolds-number flow of an incompressible fluid contained in the gap between two coaxial cones with coincident apices and bounded by a spherical lid. The two cones and the lid are allowed to rotate independently about their common axis, generating a swirling motion. The swirl induces a secondary, meridional circulation through inertial effects. For specific configurations complex eigenmodes representing an infinite sequence of eddies, analogous to those found in two-dimensional corner flows and some three-dimensional geometries, form a component of this secondary circulation. When the cones rotate these eigenmodes, arising from the geometry, compete with the forced …

Capillary-Driven Flows Along Rounded Interior Corners, Yongkang Chen, Mark M. Weislogel, Cory L. Nardin

Mechanical and Materials Engineering Faculty Publications and Presentations

The problem of low-gravity isothermal capillary flow along interior corners that are rounded is revisited analytically in this work. By careful selection of geometric length scales and through the introduction of a new geometric scaling parameter Tc, the Navier–Stokes equation is reduced to a convenient∼O(1) form for both analytic and numeric solutions for all values of corner half-angle α and corner roundedness ratio λ for perfectly wetting fluids. The scaling and analysis of the problem captures much of the intricate geometric dependence of the viscous resistance and significantly reduces the reliance on numerical data compared with several previous solution methods …

Viscoelastic Flow In Rotating Curved Pipes, Yitung Chen, Huajun Chen, Jinsuo Zhang, Benzhao Zhang

Mechanical Engineering Faculty Research

Fully developed viscoelastic flows in rotating curved pipes with circular cross section are investigated theoretically and numerically employing the Oldroyd-B fluid model. Based on Dean’s approximation, a perturbation solution up to the secondary order is obtained. The governing equations are also solved numerically by the finite volume method. The theoretical and numerical solutions agree with each other very well. The results indicate that the rotation, as well as the curvature and elasticity, plays an important role in affecting the friction factor, the secondary flow pattern and intensity. The co-rotation enhances effects of curvature and elasticity on the secondary flow. For …

Computational Aerodynamics Study Of Ahmed Body Car Model, Rajat Trehan

Mechanical & Aerospace Engineering Theses & Dissertations

Vehicle Aerodynamics has been the focus of study by researchers for centuries. This interest can be owed to increasing demand on fuel efficiency, vehicle top speed and acceleration performance. Interior aerodynamics, such as engine cooling, air conditioning, wind noise, stability, and cross wind sensitivity play key role in customer satisfaction. Hence a complete understanding of flow around the vehicle is prerequisite to achieve any of the above parameters. Aerodynamic development of motor vehicle is expensive. Much capital must be invested in test facilities such as wind tunnels and climate tunnels. The models are costly and at the beginning of a …

Assessing The Potential For Improved Scramjet Performance Through Application Of Electromagnetic Flow Control, Martin F. Lindsey

Theses and Dissertations

Hypersonic flight using scramjet propulsion bridges the gap between turbojets and rockets. Recent efforts focus on magnetogasdynamic (MGD) flow control to mitigate the problems of high thermomechanical loads and low efficiencies associated with scramjets. This research is the first flight-scale, three-dimensional computational analysis of a realistic scramjet to assess how MGD flow control improves scramjet performance. Developing a quasi-one dimensional design tool culminated in the first open source scramjet geometry. This geometry was tested with the Air Force Research Laboratory's electromagnetic computational code. To increase fidelity, an algorithm was developed to incorporate thermochemistry, resulting in the only open-source model of …

Development Of A Three-Dimensional Air Blast Propagation Model Based Upon The Weighted Average Flux Method, Stephen R. Mchale

Theses and Dissertations

Accurate numerical modeling of complex, multi-dimensional shock propagation is needed for many Department of Defense applications. A three-dimensional code, based upon E.F. Toro's weighted average flux (WAF) method has been developed, tested, and validated. Code development begins with the introduction and application of all techniques in a single dimension. First-order accuracy is achieved via Godunov's scheme using an exact Riemann solver. Adaptive techniques, which employ approximate solutions, are implemented to improve computational efficiency. The WAF method produces second-order accurate solutions, but introduces spurious oscillations near shocks and contact discontinuities. Total variation diminishing (TVD) flux and weight limiting schemes are added …

Low Magnetic Prandtl Number Dynamos With Helical Forcing, Pablo D. Mininni, David C. Montgomery

Dartmouth Scholarship

We present direct numerical simulations of dynamo action in a forced Roberts flow. The behavior of the dynamo is followed as the mechanical Reynolds number is increased, starting from the laminar case until a turbulent regime is reached. The critical magnetic Reynolds for dynamo action is found, and in the turbulent flow it is observed to be nearly independent on the magnetic Prandtl number in the range from ∼0.3 to ∼0.1. Also the dependence of this threshold with the amount of mechanical helicity in the flow is studied. For the different regimes found, the configuration of the magnetic and velocity …

The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom

Articles

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. Neutral curves associated with each instability can be constructed but it has been suggested that these curves do not cross but rather posses `kinks'. Our work is based in the small gap, large wavenumber limit and considers the simultaneous onset of Taylor …

Flow Patterns In A Two-Roll Mill, Christopher Hills

Articles

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …

Capillary Flow In Interior Corners: The Infinite Column, Mark M. Weislogel

Mechanical and Materials Engineering Faculty Publications and Presentations

Capillary flow of a sinusoidally perturbed liquid column in an interior corner of infinite extent is solved using lubrication theory. Due primarily to the length scales selected to nondimensionalize the momentum equation, an analytic time scale governing the settling of the perturbation is determined. The time scale, which is shown to be independent of a steady base state flow, proves useful in rapidly predicting transients for surface settling in certain liquid-bearing tanks of spacecraft employing interior corners for fluids management purposes. The asymptotic analysis is extended to address flows along interior corners whose faces are slightly nonplanar. The generalized formulation …

Velocity Field Distributions Due To Ideal Line Vortices, Thomas D. Levi, David C. Montgomery

Dartmouth Scholarship

We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We focus on “nearest-neighbor” contributions that result from vortices that fall (randomly) very close to the spatial points where the velocity is being sampled. We confirm that these events lead to a non-Gaussian high-velocity “tail” on an otherwise Gaussian distribution function for the Eulerian velocity field. We also investigate the behavior of distributions that do not have equilibrium mean-field probability distributions that are uniform inside the …

Capillary Surfaces In An Exotic Container: Results From Space Experiments, Paul Concus, Robert Finn, Mark M. Weislogel

Mechanical and Materials Engineering Faculty Publications and Presentations

Experimental results from the Interface Configuration Experiment (ICE) performed aboard the Space Shuttle and the Mir Space Station are reported. The experiment concerns fluid interfaces in certain ‘exotic’ containers in a low-gravity environment. These containers are rotationally symmetric and have the property that for given contact angle and liquid volume, a continuum of distinct rotationally symmetric equilibrium configurations can appear, all of which have the same mechanical energy. These symmetric equilibrium configurations are unstable, in that deformations that are not rotationally symmetric can be shown mathematically to yield configurations with lower energy. It is found experimentally, in confirmation of mathematical …

A Direct Numerical Simulation Of Vortex Breakdown Induced Tail Buffet, Steven James Massey

Mechanical & Aerospace Engineering Theses & Dissertations

A simulation of tail buffet is presented for a delta wing-vertical tail configuration. Flow conditions are chosen such that the wing primary-vortex cores experience vortex breakdown and the resulting turbulent wake flow impinges on the vertical tail. The dimensions and material properties of the vertical tail are chosen such that the deflections are large enough to insure interaction with the flow, and the natural frequencies are high enough to facilitate a practical computational solution. This multidisciplinary problem is solved sequentially for the fiuid flow, the elastic deformations and the grid displacements. The fluid flow is simulated by time accurately solving …

Simulation Of Vertical Tail Buffet In Internal Vortex Breakdown Flows, Mark William Flanagan

Mechanical & Aerospace Engineering Theses & Dissertations

Computational simulation of vertical tail buffet in an internal vortex breakdown flow is considered. The fiuid-flow problem is formulated using the full, compressible, unsteady Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite volume scheme. The fluid-flow problem is solved in a configured circular duct using quasi-axisymmetric assumptions to simplify the flow equations. A plate is placed transverse to the incoming flow. Solution of the flow in the duct is performed with and without a rigid plate, and with and without an elastic plate. The elastic response of the plate is calculated assuming that it is a cantilever …

Application Of Sensitivity Analysis To The Euler Equations, Vamshi Mohan Korivi

Mechanical & Aerospace Engineering Theses & Dissertations

An approximation method is presented for efficiently predicting the changes which occur in a steady-state numerical solution of the Euler equations as a consequence of a small change in the geometric shape of the domain. The method is extended to develop a general procedure for calculating aerodynamic sensitivity derivatives with respect to variations of geometric shape. The techniques are implemented using an upwind cell centered finite volume formulation, and are applied to two test cases, (1) a subsonic nozzle (M_∞ = 0.85), and (2) a supersonic inlet (M_∞ = 2.0). Conventional numerical solutions are first obtained for flow …

Use Of A Generalized Set Of Variables In Fluid Flow Calculations, Pawel Chwalowski

Mechanical & Aerospace Engineering Theses & Dissertations

In fluid flow calculations, a set of generalized field variables is used to replace the more conventional choice of either the conserved variables, or the primitive variables. This generalized set of variables represents an infinite number of possible choices for the specific set of field variables. For algorithms of both the implicit and explicit type, the resulting effect of a change in field variables on a steady-state flow solution is in general relatively small. However, for implicit algorithms, a consistent linearization with respect to the new variables results in dramatic changes in the overall matrix conditioning of the linear systems …

Navier-Stokes Analysis Of Cold Gas Scramjet Nozzle-Afterbody Flowfields, Walter C. Engelund

Mechanical & Aerospace Engineering Theses & Dissertations

The recent renewal of interest in hypersonic aerodynamics, brought about largely in part due to the development of the National Aerospace Plane (NASP), is resulting in an increased reliance on computational fluid dynamics for flowfield data in this flight regime. The design of the nozzle-afterbody section for a hypersonic transport such as the NASP is currently underway, and is being conducted using both computational fluid dynamics and cold, non-reacting, simulant gas experimental models. In this study, a computational analysis is conducted for the flow through a scramjet nozzle-afterbody test section.

Computations have been performed for a cold gas simulation of …

Domain Decomposition For Multigrid, Finite Volume Flow Solvers, Victor Robert Lessard

Mechanical & Aerospace Engineering Theses & Dissertations

Computing the flow fields about three-dimensional complex configurations accurately becomes a difficult task, if it is attempted to generate a single, body fitted grid with proper clustering. The domain decomposition methods, which divide the computational domain into less complex subdomains, are extensively used to decrease the grid generation workload. A domain decomposition technique also allows the use of different solution methods for different subdomains. The objective of this work is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multigrid, finite volume solution algorithms. A computer code, given the name MaGGiE, …

The Development Of A Microprocessor Controlled Linearly Actuated Valve Assembly, Raymond H. Wall

Mechanical & Aerospace Engineering Theses & Dissertations

The development of a proportional fluid control valve/assembly is presented. This electro-mechanical system is needed for space applications to replace the current proportional flow controllers that use bulky hydraulic or pneumatic actuation systems. The flow is controlled by a microprocessor system that monitors the control parameters of upstream pressure and requested volumetric flow rate. The microprocessor achieves the ·proper valve stem displacement by means of a digital linear actuator. A linear displacement sensor is used to measure the valve stem position. 'Ibis displacement is monitored by the microprocessor system as a feedback signal to close the control loop. With an …

Influence Of Las Vegas Wash Density Current On Nutrient Availability And Phytoplankton Growth In Lake Mead, John R. Baker, Larry J. Paulson

Publications (WR)

Density currents are commonly formed in reservoirs because of temperature or salinity induced density differences between inflowing and receiving waters. Anderson and Pritchard (1951) were among the first to demonstrate this in their investigations of density currents in Lake Mead. They found that the Colorado River formed an underflow in Lake Mead during the winter, an overflow in the spring and an interflow in the summer and fall. Wunderlich and Elder (1973) have since described the hydromechanics of these types of flow patterns, and density currents have been reported for several other large reservoirs (Carmack et al. 1979, Johnson and …

Partial Chemical Equilibrium In Fluid Dynamics, John D. Ramshaw

Physics Faculty Publications and Presentations

An analysis is given for the flow of a multicomponent fluid in which an arbitrary number of chemical reactions may occur, some of which are in equilibrium while the others proceed kinetically. The primitive equations describing this situation are inconvenient to use because the progress rates ω [subscript s] for the equilibrium reactions are determined implicitly by the associated equilibrium constraint conditions. Two alternative equivalent equation systems that are more pleasant to deal with are derived. In the first system, the ω [subscript s] are eliminated by replacing the transport equations for the chemical species involved in the equilibrium reactions …

An Experimental Investigation Of The Vortex Sink Rate Sensors, Nelson L. Lu

Mechanical & Aerospace Engineering Theses & Dissertations

The vortex sink rate sensor device consists basically of an ideal sink flow between two coaxial disks. A sink tube was located at the center of one disk. The vortex was created by the rotation of the unit about its axis of symmetry. Five inch and 10 inch diameter of porous couplers were used for the air chamber here in this investigation. Several slenderness parameters, i.e., the ratio of the sink tube diameter to the height of the air chamber ^ro/n were conducted. Two probes were used to measure the static pressure and stagnation pressure respectively at various positions …

A Numerical Solution To The Problem Of Rotation Near The Ground, David D. Chen

Mechanical & Aerospace Engineering Theses & Dissertations

No abstract.

Asymptotic Behavior Of Fluid Jets, Ronald Walter Godfrey

All Master's Theses

In this paper we shall consider the steady-state, two dimensional, irrotational flow of an inviscid, incompressible fluid under gravity.