Showing papers on "Fluid dynamics published in 1995"

Computational fluid dynamics : the basics with applications

Abstract: Part I*Basic Thoughts and Equations 1 Philosophy of Computational Fluid Dynamics 2 The Governing Equations of Fluid Dynamics Their Derivation, A Discussion of Their Physical Meaning, and A Presentation of Forms Particularly Suitable to CFD 3 Mathematical Behavior of Partial Differential Equations The Impact on Computational Fluid Dynamics Part II*Basics of the Numerics 4 Basic Aspects of Discretization 5 Grids and Meshes, With Appropriate Transformations 6 Some Simple CFD Techniques A Beginning Part III*Some Applications 7 Numerical Solutions of Quasi-One-Dimensional Nozzle Flows 8 Numerical Solution of A Two-Dimensional Supersonic Flow Prandtl-Meyer Expansion Wave 9 Incompressible Couette Flow Numerical Solution by Means of an Implicit Method and the Pressure Correction Method 10 Incompressible, Inviscid Slow Over a Circular Cylinder Solution by the Technique Relaxation Part IV*Other Topics 11 Some Advanced Topics in Modern CFD A Discussion 12 The Future of Computational Fluid Dynamics Appendixes A Thomas's Algorithm for the Solution of A Tridiagonal System of Equations References

Topographic Effects in Stratified Flows

Abstract: 1. Background 2. The flow of a homogeneous layer with a free surface 3. Two-layer flows 4. Waves in stratified fluids 5. Stratified flow over two-dimensional obstacles 6. Stratified flow past three-dimensional topography 7. Applications to practical modelling of flow over complex terrain.

Single-Phase Liquid Jet Impingement Heat Transfer

Abstract: Publisher Summary Impinging liquid jets have been demonstrated to be an effective means of providing high heat or mass transfer rates in industrial transport processes. This chapter summarizes the available analytical and experimental work in the area with the objective of correlating the research findings. Significant progress has been made in understanding the fundamentals of heat, mass, and momentum transport in these systems. This chapter suggests that, there is considerable need for further research in liquid jet array applications, both in submerged and free-surface jet configurations. Cross-flow effects in these systems, which have been quite well characterized for submerged jets, have received only superficial treatment for free-surface jets. The physical phenomena are highly complex, requiring careful experimental investigation.

Fluid Dynamics for Physicists

Abstract: It is over three hundred and fifty years since Torricelli discovered the law obeyed by fountains, yet fluid dynamics remains an active and important branch of physics. This book provides an accessible and comprehensive account of the subject, emphasising throughout the fundamental physical principles, and stressing the connections with other branches of physics. Beginning with a gentle introduction, the book goes on to cover Bernouilli's theorem, compressible flow, potential flow, surface waves, viscosity, vorticity dynamics, thermal convection and instabilities, turbulence, non-Newtonian fluids and the propagation and attenuation of sound in gases. Undergraduate or graduate students in physics or engineering who are taking courses in fluid dynamics will find this book invaluable, but it will also be of great interest to anyone who wants to find out more about this fascinating subject.

Fluid Dynamics for Physicists

Abstract: It is over three hundred and fifty years since Torricelli discovered the law obeyed by fountains, yet fluid dynamics remains an active and important branch of physics. This book provides an accessible and comprehensive account of the subject, emphasising throughout the fundamental physical principles, and stressing the connections with other branches of physics. Beginning with a gentle introduction, the book goes on to cover Bernouilli's theorem, compressible flow, potential flow, surface waves, viscosity, vorticity dynamics, thermal convection and instabilities, turbulence, non-Newtonian fluids and the propagation and attenuation of sound in gases. Undergraduate or graduate students in physics or engineering who are taking courses in fluid dynamics will find this book invaluable, but it will also be of great interest to anyone who wants to find out more about this fascinating subject.

Squirt flow in fully saturated rocks

Abstract: We estimate velocity/frequency dispersion and attenuation in fully saturated rocks by employing the squirt‐flow mechanism of solid/fluid interaction. In this model, pore fluid is squeezed from thin soft cracks into the surrounding large pores. Information about the compliance of these soft cracks at low confining pressures is extracted from high‐pressure velocity data. The frequency dependence of squirt‐induced pressure in the soft cracks is linked with the porosity and permeability of the soft pore space, and the characteristic squirt‐flow length. These unknown parameters are combined into one expression that is assumed to be a fundamental rock property that does not depend on frequency. The appropriate value of this expression for a given rock can be found by matching our theoretical predictions with the experimental measurements of attenuation or velocity. The low‐frequency velocity limits, as given by our model, are identical to those predicted by Gassmann’s formula. The high‐frequency limits may sign...

Experiments on flow focusing in soluble porous media, with applications to melt extraction from the mantle

Abstract: We demonstrate finite structures formed as a consequence of the “reactive infiltration instability” (Chadam et al., 1986) in a series of laboratory and numerical experiments with growth of solution channels parallel to the fluid flow direction. Regions with initially high porosity have high ratios of fluid volume to soluble solid surface area and exhibit more rapid fluid flow at constant pressure, so that dissolution reactions in these regions produce a relatively rapid increase in porosity. As channels grow, large ones entrain flow laterally inward and extend rapidly. As a result, small channels are starved and disappear. The growth of large channels is an exponential function of time, as predicted by linear stability analysis for growth of infinitesimal perturbations in porosity. Our experiments demonstrate channel growth in the presence of an initial solution front and without an initial solution front where there is a gradient in the solubility of the solid matrix. In the gradient case, diffuse flow is unstable everywhere, channels can form and grow at any point, and channels may extend over the length scale of the gradient. As a consequence of the gradient results, we suggest that the reactive infiltration instability is important in the Earth's mantle, where partial melts in the mantle ascend adiabatically. Mantle peridotite becomes increasingly soluble as the melts decompress. Dissolution reactions between melts and peridotite will produce an increase in liquid mass and lead to formation of porous channels composed of dunite (>95% olivine). Replacive dunite is commonly observed in the mantle section of ophiolites. Focused flow of poly baric partial melts of ascending peridotite within dunite channels may explain the observed chemical disequilibrium between shallow, oceanic mantle peridotites and mid-oceanic ridge basalts (MORB). This hypothesis represents an important alternative to MORB extraction in fractures, since fractures may not form in weak, viscously deforming asthenospheric mantle. We also briefly consider the effects of crystallization, rather than dissolution reactions, on the morphology of porous flow via a second set of experiments where fluid becomes supersaturated in a solid phase. Formation of short-lived conduits parallel to the flow direction occurs rapidly, and then each conduit is eventually choked by interior crystallization; fluid flow then passes through the most permeable portion of the walls to form a new conduit. On long time scales and length scales, transient formation and destruction of conduits will result in random and diffuse flow. Where liquid cools as it rises through mantle tectosphere on a conductive geotherm, it will become saturated in pyroxene as well as olivine and decrease in mass. This process may produce a series of walled conduits, as in our experiments. Development of a low-porosity cap overlying high porosity conduits may create hydrostatic overpressure sufficient to cause fracture and magma transport to the surface in dikes.

Continuum Deductions from Molecular Hydrodynamics

Abstract: Since a fluid is composed of molecules, one always has the option of calculating its static or dynamic properties by computing the motion of these constituents. For most purposes such a procedure is very inefficient, because it provides detailed information at molecular length scales, which are far beneath the usual realm of interest for continuum fluid mechanics. There are, however, situations where the microscopic details of a fluid flow are interesting if not crucial. For example, fluids in microscopic geometries or under high stress may exhibit deviations from the continuum equations, and one may wish to calculate such effects from first principles. Alternatively, in some problems the boundary conditions to be applied to the Navier-Stokes equations are not fully established or are unsatisfactory, as in the presence of moving contact lines or at the edge of a porous

Effect of three‐dimensionality on the lift and drag of nominally two‐dimensional cylinders

Abstract: It has been known for some time that two‐dimensional numerical simulations of flow over nominally two‐dimensional bluff bodies at Reynolds numbers for which the flow is intrinsically three dimensional, lead to inaccurate prediction of the lift and drag forces. In particular, for flow past a normal flat plate (International Symposium on Nonsteady Fluid Dynamics, edited by J. A. Miller and D. P. Telionis, 1990, pp. 455–464) and circular cylinders [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)], it has been noted that the drag coefficient computed from two‐dimensional simulations is significantly higher than what is obtained from experiments. Furthermore, it has been found that three‐dimensional simulations of flows lead to accurate prediction of drag [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)]. The underlying cause for this discrepancy is that the surface pressure distribution obtained from two‐dimensional simulations does not match up with that obtained from experiments and three‐dimensional simulations and a number of reasons have been put forward to explain this discrepancy. However, the details of the physical mechanisms that ultimately lead to the inaccurate prediction of surface pressure and consequently the lift and drag, are still not clear. In the present study, results of two‐dimensional and three‐dimensional simulations of flow past elliptic and circular cylinders have been systematically compared in an effort to pinpoint the exact cause for the inaccurate prediction of the lift and drag by two‐dimensional simulations. The overprediction of mean drag force in two‐dimensional simulations is directly traced to higher Reynolds stresses in the wake. It is also found that the discrepancy in the drag between two‐dimensional and three‐dimensional simulations is more pronounced for bluffer cylinders. Finally, the current study also provides a detailed view of how the fluctuation, which are associated with the Karman vortex shedding in the wake, affect the mean pressure distribution and the aerodynamic forces on the body.

Characterization of fluid flow velocity by optical Doppler tomography

Abstract: The spatial profiles of fluid flow velocity in transparent glass and turbid collagen conduits are measured by optical Doppler tomography (ODT). The flow velocity at a discrete user-specified spatial location in the conduit is determined by measurement of the Doppler shift of backscattered light from microspheres suspended in the flowing fluid. Experimental data and theoretical calculations are in excellent agreement. ODT is an accurate method for the characterization of high-resolution fluid flow velocity.

The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow

Abstract: This work determines the pressure–velocity relation of bubble flow in polygonal capillaries. The liquid pressure drop needed to drive a long bubble at a given velocity U is solved by an integral method. In this method, the pressure drop is shown to balance the drag of the bubble, which is determined by the films at the two ends of the bubble. Using the liquid-film results of Part 1 (Wong, Radke & Morris 1995), we find that the drag scales as Ca2/3 in the limit Ca → 0 (Ca μU/σ, where μ is the liquid viscosity and σ the surface tension). Thus, the pressure drop also scales as Ca2/3. The proportionality constant for six different polygonal capillaries is roughly the same and is about a third that for the circular capillary.The liquid in a polygonal capillary flows by pushing the bubble (plug flow) and by bypassing the bubble through corner channels (corner flow). The resistance to the plug flow comes mainly from the drag of the bubble. Thus, the plug flow obeys the nonlinear pressure–velocity relation of the bubble. Corner flow, however, is chiefly unidirectional because the bubble is long. The ratio of plug to corner flow varies with liquid flow rate Q (made dimensionless by σa2/μ, where a is the radius of the largest inscribed sphere). The two flows are equal at a critical flow rate Qc, whose value depends strongly on capillary geometry and bubble length. For the six polygonal capillaries studied, Qc [Lt ] 10−6. For Qc [Lt ] Q [Lt ] 1, the plug flow dominates, and the gradient in liquid pressure varies with Q2/3. For Q [Lt ] Qc, the corner flow dominates, and the pressure gradient varies linearly with Q. A transition at such low flow rates is unexpected and partly explains the complex rheology of foam flow in porous media.

Exact solutions for some simple flows of an Oldroyd-B fluid

Abstract: We present two simple but elegant solutions for the flow of an Oldroyd-B fluid. First, we consider the flow past an infinite porous plate and find that the problem admits an asymptotically decaying solution in the case of suction at the plate, and that in the case of blowing it admits no such solution. Second, we study the longitudinal and torsional oscillations of an infinitely long rod of finite radius. The solutions are found in terms of Bessel functions.

Lattice Boltzmann simulation of solid particles suspended in fluid

Abstract: The lattice Boltzmann method, an alternative approach to solving a fluid flow system, is used to analyze the dynamics of particles suspended in fluid. The interaction rule between the fluid and the suspended particles is developed for real suspensions where the particle boundaries are treated as no-slip impermeable surfaces. This method correctly and accurately determines the dynamics of single particles and multi-particles suspended in the fluid. With this method, computational time scales linearly with the number of suspensions,N, a significant advantage over other computational techniques which solve the continuum mechanics equations, where the computational time scales asN 3. Also, this method solves the full momentum equations, including the inertia terms, and therefore is not limited to low particle Reynolds number.

Magnetic and electric fields associated with changes in high pore pressure in fault zones : Application to the Loma Prieta ULF emissions

Abstract: We determined the electric and magnetic fields generated during failure of faults containing sealed compartments with pore pressures ranging from hydrostatic to lithostatic levels. Exhumed fault studies and strain measurement data limit the possible size of these compartments to less than 1 km in extent. Rupture of seals between compartments produces rapid pore pressure changes and fluid flow and may create fractures that propagate away from the high-pressure compartment, along the fault face. Nonuniform fluid flow results from pressure decrease in the fracture from crack-generated dilatancy, partial blockage by silica deposition, and clearing as pressure increases. A direct consequence of this unsteady fluid flow may be associated transient magnetic signals caused by electrokinetic, piezomagnetic, and magnetohydrodynamic effects. Models of these processes for fault geometries with 1-km-high pressure compartments show that electrokinetic effects are several orders of magnitude larger than the other mechanisms. The electrokinetic signals produced by this unsteady flow are comparable in magnitude and frequency to the magnetic signals observed prior to the ML 7.1 Loma Prieta earthquake of October 18, 1989, provided fracture lengths are less than 200 m.

Dispersive Transport Dynamics in a Strongly Coupled Groundwater-Brine Flow System

Abstract: Many problems in subsurface hydrology involve the flow and transport of solutes that affect liquid density. When density variations are large (>5%), the flow and transport are strongly coupled. Density variations in excess of 20% occur in salt dome and bedded-salt formations which are currently being considered for radioactive waste repositories. The widely varying results of prior numerical simulation efforts of salt dome groundwater-brine flow problems have underscored the difficulty of solving strongly coupled flow and transport equations. We have implemented a standard model for hydrodynamic dispersion in our general purpose integral finite difference simulator, TOUGH2. The residual formulation used in TOUGH2 is efficient for the strongly coupled flow problem and allows the simulation to reach a verifiable steady state. We use the model to solve two classic coupled flow problems as verification. We then apply the model to a salt dome flow problem patterned after the conditions present at the Gorleben salt dome, Germany, a potential site for high-level nuclear waste disposal. Our transient simulations reveal the presence of two flow regimes: (1) recirculating and (2) swept forward. The flow dynamics are highly sensitive to the strength of molecular diffusion, with recirculating flows arising for large values of molecular diffusivity. For pure hydrodynamic dispersion with parameters approximating those at Gorleben, we find a swept-forward flow field at steady state rather than the recirculating flows found in previous investigations. The time to steady state is very sensitive to the initial conditions, with long time periods required to sweep out an initial brine pool in the lower region of the domain. Dimensional analysis is used to demonstrate the tendency toward brine recirculation. An analysis based on a dispersion timescale explains the observed long time to steady state when the initial condition has a brine pool in the lower part of the system. The nonlinearity of the equations and the competing effects of dispersion and gravity make this variable-density problem a challenge for any numerical simulation method.

Infusion pump, treatment fluid bag therefor, and method for the use thereof

Abstract: An infusion pump for infusing a medical treatment fluid intravenously to a patient includes a collapsible treatment fluid bag juxtaposed with an inflatable drive fluid bladder confined between a pair of opposing containment members which cause the bladder to impinge against the bag as the bladder is inflated A drive fluid pump controllably inflates the bladder, thereby displacing treatment fluid from the bag into an outlet tube affixed thereto which conveys the treatment fluid to the patient where it is received intravenously The treatment fluid flow rate through the tube is controlled by increasing or decreasing the drive fluid pump output and consequently the pressure in the bladder in response to a pressure sensor in fluid communication with the bladder Alternatively, the treatment fluid flow rate is adjusted by opening or closing the outlet tube by means of an occluder or restrictor positioned along the tube

Fluid Flow in Fault Zones: Analysis of the Interplay of Convective Circulation and Topographically Driven Groundwater Flow

Abstract: High-permeability faults, acting as preferential pathways for fluid migration, are important geological structures for fluid, energy, and solute transport. This paper examines the interaction of thermally driven convective circulation in a steeply dipping fault zone and groundwater flow through the surrounding country rock that is driven by a regional topographic gradient. We consider a geometry where a fault zone with a homogeneous, isotropic permeability is located beneath a narrow valley in a region with substantial topographic relief. System behavior is best characterized in terms of the large-scale permeabilities of the country rock and the fault zone. Using three-dimensional numerical simulations, we map in permeability space four fluid flow and heat transfer regimes within a fault zone: conductive, advective, steady convective, and unsteady convective. The patterns of fluid flow and/or heat transfer are substantially different in each of these regimes. Maximum discharge temperatures can also be plotted in permeability space; the maximum discharge temperature in the advective regime is in general lower than that in the steady convective regime. A higher basal heat flux expands the convective regime in permeability space, as does a greater fault depth. Higher topographic relief on the regional water table compresses the convective regime, with the advective regime suppressing convective circulation at lower country rock permeabilities. If convective cells with aspect ratios close to 1 cannot form, the steady convective regime is smaller in permeability space, and the boundary between steady and unsteady convection occurs at lower values of fault zone permeability. At low country rock permeabilities a water table gradient along the surface trace of the fault of approximately 0.3% suppresses convective cells; at higher country rock permeabilities, convection can be suppressed by smaller gradients on the water table.

Applicability of the Reynolds Equation for modeling fluid flow between rough surfaces

Abstract: Predictions of the Reynolds equation for flow between rough-walled surfaces have been compared to a more exact calculation of Navier-Stokes flow based on a lattice-gas automaton method. Two-dimensional channels were constructed with an idealized sinusoidal roughness on each wall. Flow in the channels was studied by both methods for various amplitude to wavelength ratios of the roughness, surface separations, relative alignment or phase of the sinusoids, and Reynolds numbers. The Reynolds equation overestimates fluid velocity as the surfaces are placed together or the amplitude of the roughness increases relative to its wavelength.

Traffic jams, granular flow, and soliton selection

Abstract: The flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow. In a certain range of traffic density, steady flow becomes unstable against the growth of a cluster, or ``phantom'' traffic jam, which moves at a slower speed than the otherwise homogeneous flow. We show that near the onset of this instability, traffic flow is described by a perturbed Korteweg--de Vries (KdV) equation. The traffic jam can be identified with a soliton solution of the KdV equation. The perturbation terms select a unique member of the continuous family of KdV solitons. These results may also apply to the dynamics of granular relaxation.

Coupled turbulent flow, heat, and solute transport in continuous casting processes

Abstract: A fully coupled fluid flow, heat, and solute transport model was developed to analyze turbulent flow, solidification, and evolution of macrosegregation in a continuous billet caster. Transport equations of total mass, momentum, energy, and species for a binary iron-carbon alloy system were solved using a continuum model, wherein the equations are valid for the solid, liquid, and mushy zones in the casting. A modified version of the low-Reynolds numberk-e model was adopted to incorporate turbulence effects on transport processes in the system. A control-volume-based finite-difference procedure was employed to solve the conservation equations associated with appropriate boundary conditions. Because of high nonlinearity in the system of equations, a number of techniques were used to accelerate the convergence process. The effects of the parameters such as casting speed, steel grade, nozzle configuration on flow pattern, solidification profile, and carbon segregation were investigated. From the computed flow pattern, the trajectory of inclusion particles, as well as the density distribution of the particles, was calculated. Some of the computed results were compared with available experimental measurements, and reasonable agreements were obtained.

Computational study of heat transfer and gas dynamics in the pulsed laser evaporation of metals

Abstract: Pulsed laser irradiation of nanosecond duration is used in a variety of applications, including laser deposition of thin films and micromachining. Of fundamental interest is the prediction of the evaporative material removal rates, as well as the velocity, density, and temperature distributions of the ejected particles as functions of the laser‐beam pulse energy, temporal distribution, and irradiance density on the target material surface. In order to address these issues, the present work establishes a new computational approach for the thorough treatment of the heat transfer and fluid flow phenomena in pulsed laser processing of metals. The heat conduction in the solid substrate and the liquid melt is solved by a one‐dimensional transient heat transfer model. The ejected high‐pressure vapor generates shock waves against the ambient background pressure. The compressible gas dynamics is computed numerically by solving the system of Euler equations for mass, momentum, and energy, supplemented by an isentropic gas equation of state. The aluminum, copper, and gold targets considered were subjected to pulsed ultraviolet excimer laser irradiation of nanosecond duration. Results are given for the temperature distribution, evaporation rate, and melting depth in the target, as well as the pressure, velocity, and temperature distributions in the vapor phase.

Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe

Abstract: The flow of a fluid-solid mixture is very complicated and may depend on many variables, such as the physical properties of each phase and the size and shape of the solid particles. One approach to the study of these flows is to model the mixture as a non-Newtonian fluid. Much effort has been put into analyzing various transport processes in non-Newtonian fluids, such as coal slurries. Heat transfer plays an important role in the handling and processing of these fluids. In this paper, the fully developed flow of an incompressible, thermodynamically compatible fluid of grade three in a pipe is studied. The temperature of the pipe is assumed to be higher than the temperature of the fluid and the shear viscosity of the fluid is assumed to be a function of the temperature.

The law of the wall in turbulent flow

Abstract: The `law of the wall' for the inner part of a turbulent shear flow over a solid surface is one of the cornerstones of fluid dynamics, and one of the very few pieces of turbulence theory whose results include a simple analytic function for the mean velocity distribution, the logarithmic law Various aspects of the law have recently been questioned, and this paper is a summary of the present position Although the law of the wall for velocity has apparently been confirmed by experiment well outside its original range, the law of the wall for temperature seems to apply only to very simple flows Since the two laws are derived by closely analogous arguments this throws suspicion on the law of the wall for velocity Analysis of simulation data, for all the Reynolds stresses including the shear stress, shows that law-of-the-wall scaling fails spectacularly in the viscous wall region, even when the logarithmic law is relatively well behaved Virtually all turbulence models are calibrated to reproduce the law of the wall in simple flows, and we discuss whether, in practice or in principle, their range of validity is larger than that of the law of the wall itself: the present answer is that it is not; so that when the law of the wall (or the mixing-length formula) fails, current Reynolds-averaged turbulence models are likely to fail too