Showing papers on "Fluid dynamics published in 1981"

Numerical experiments in homogeneous turbulence

Abstract: The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.

Hydrodynamic instabilities and the transition to turbulence

Abstract: Strange attractors and turbulence.- Hydrodynamic stability and bifurcation.- Chaotic behavior and fluid dynamics.- Transition to turbulence in Rayleigh-Beenard convection.- Instabilities and transition in flow between concentric rotating cylinders.- Shear flow instabilities and transition.- Instabilities in geophysical fluid dynamics.- Instabilities and chaos in nonhydrodynamic systems.- Recent Progress.

Turbulent boundary layer at low Reynolds number

Abstract: The results of an experimental investigation of a turbulent boundary layer with zero‐pressure gradient directed toward extending the data base at low Reynolds numbers are presented. The data obtained are concerned primarily with mean‐velocity distributions, skin‐friction coefficients, and distributions of intensity of the longitudinal‐component of the turbulent‐velocity fluctuations for Reynolds numbers based on momentum thickness as low as 465. The validity, at low Reynolds numbers, of the semi‐empirical laws characterizing the inner and outer regions of the boundary layer is examined.

On the growth of turbulent regions in laminar boundary layers

Abstract: Turbulent spots evolving in a laminar boundary layer on a nominally zero pressure gradient flat plate are investigated. The plate is towed through an 18 m water channel, using a carriage that rides on a continuously replenished oil film giving a vibrationless tow. Turbulent spots are initiated using a solenoid valve that ejects a small amount of fluid through a minute hole on the working surface. A novel visualization technique that utilizes fluorescent dye excited by a sheet of laser light is employed. Some new aspects of the growth and entrainment of turbulent spots, especially with regard to lateral growth, are inferred from the present experiments. To supplement the information on lateral spreading, a turbulent wedge created by placing a roughness element in the laminar boundary layer is also studied both visually and with probe measurements. The present results show that, in addition to entrainment, another mechanism is needed to explain the lateral growth characteristics of a turbulent region in a laminar boundary layer. This mechanism, termed growth by destabilization, appears to be a result of the turbulence destabilizing the unstable laminar boundary layer in its vicinity. To further understand the growth mechanisms, the turbulence in the spot is modulated using drag-reducing additives and salinity stratification.

Acoustics as a branch of fluid mechanics

Abstract: This article gives a review of six areas of current activity and importance in aero-acoustics, including (i) the generation of sound and vorticity by vorticity and sound, respectively, (ii) the basis for, and consequences of, the application of a Kutta condition in unsteady leading- and trailing-edge flows, and (iii) the suppression or amplification of broadband hydrodynamic and acoustic fields in a jet under the influence of weak discrete tone forcing. The intention is also to promote acceptance once again of acoustics as a serious branch of fluid mechanics.

Rates of convergence for viscous splitting of the Navier-Stokes equations

Abstract: Viscous splitting algorithms are the underlying design principle for many numerical algorithms which solve the Navier-Stokes equations at high Reynolds number. In this work, error estimates for splitting algorithms are developed which are uniform in the viscosity v as it becomes small for either twoor three-dimensional fluid flow in all of space. In particular, it is proved that standard viscous splitting converges uniformly at the rate C^lAt, Strang-type splitting converges at the rate CP(At)2, and also that solutions of the Navier-Stokes and Euler equations differ by Cp in this case. Here C depends only on the time interval and the smoothness of the initial data. The subtlety in the analysis occurs in proving these estimates for fixed large time intervals for solutions of the Navier-Stokes equations in two space dimensions. The authors derive a new long-time estimate for the two-dimensional NavierStokes equations to achieve this. The results in three space dimensions are valid for appropriate short time intervals; this is consistent with the existing mathematical theory.

Qualitative model for dynamic combustion

Abstract: A qualitative model for studying shock-wave chemistry interactions in combustion theory is introduced. The model which we study bears the analogous relationship to reacting gas flow as Burgers’ equation does to ordinary compressible fluid flow. When the corresponding physical assumptions of the Chapman–Jouget and von Neumann–Zeldovich–Doring theories are introduced in this model, explicit and completely analogous phenomena occur. Without any approximations, combustion profiles with finite reaction rate and finite diffusion are examined in detail. In the context of this model, the validity of the approximate theories mentioned above depends on the relative size of two critical parameters—the energy liberated by chemical reaction and a parameter which measures the ratio of the width of the shock layer to the reaction zone.

Collection efficiency of cyclone separators

Abstract: Based on terLinden's (A. J. terLinden, “Investigations into Cyclone Dust Collectors,” IME Proc., 160, 233, 1949) experimental observations, a three-region model is proposed for the fluid flow in a cyclone. Within each region, turbulence is assumed to promote mixing of the suspended particles. Incorporation of this mixing concept into the three-region model allows an analytic expression for the collection efficiency of the cyclone to be developed. The theoretical result is compared with data obtained in the high temperature, high pressure exhaust from a pressurized fluidized bed combustor.

Natural Convection in Undivided and Partially Divided Rectangular Enclosures

Abstract: / Heat transfer by natural convection in a two-dimensional rectangular enclosure fitted with partial vertical divisions is investigated experimentally. The horizontal walls of the enclosure are adiabatic while the vertical walls are maintained at different temperatures. The experiments are carrir8 out with water, n 3.5, for Rayleigh numbers in the range, 2.3 X 10 < RaL < 1.1 x 10 , and an aspect ratio, A = H/L = 1/2. The effect of the partial-vertical divisions on the fluid flow and temperature fields is investigated by dye-injection flow visualization and by thermocouple probes, respectively. The effect of the partitions on the heat transfer across the enclosure is also studied and correlations for the Nusselt number as a function of RaL and partition length are generated for both conducting and non-conducting partition materials. Partial divisions are found to have a significant effect on the heat transfer, especially when the divisions are adiabatic. The results also indicate that the partial divisions may have a stabilizing effect on the laminar-transitional flow on the heated vertical walls of the enclosure.

The equivalence of quasistatic flow in fluid‐saturated porous media and Biot’s slow wave in the limit of zero frequency

Abstract: We have established in a simple and straightforward fashion that the analysis of quasistatic flow in fluid‐saturated porous media due to Rice and Cleary is derivable from the low‐frequency limit of Biot’s slow compressional/diffusive mode. The single material parameter of the problem, the diffusivity, is simply related to the bulk and shear moduli and permeability of the skeletal frame and to the viscous and elastic properties of the constitutive media. Since this common theory treats fluid and solid displacements on an equal footing, it is the most general linearized description of the problem; other treatments are special cases. These latter include the rigid frame approximation used in the petroleum industry and the weak frame approximation used by De Gennes to describe the motion of polymer gels.

Transport equation for the joint probability density function of velocity and scalars in turbulent flow

Abstract: The transport equation for the joint probability density function of velocity and scalars is shown to provide a good basis for modeling turbulent reactive flows. As in the equation for the probability density function of the scalars alone, nonlinear reaction schemes can be treated without approximation. The advantage of considering the joint probability density function equation is that convection (by both the mean and fluctuating velocities) appears in closed form. Consequently, the gradient‐diffusion assumption for turbulent transport is avoided. Closure approximations are presented for the terms involving the fluctuating pressure and viscous and diffusive mixing. These models can be expected to be reliable since they are compatible with accurate and proven Reynolds‐stress models. The resulting modeled transport equation for the joint probability density function can be solved by the Monte‐Carlo method for inhomogeneous flows with complex reactions.

A Theoretical Analysis of Viscous Crossflow

Abstract: A theory predicting fluid flow in a stratified reservoir considering the affects of viscous crossflow is presented. In theory, the equations describing flow are applicable to an arbitrary number of layers, arbitrary initial and injection number of layers, arbitrary initial and injection conditions, arbitrary phase properties affecting flow, and encompasses fractional flow theory applied to water-oil displacements as well as enhanced oil recovery processes. At present the development is restricted to thw phases and two components in the injected phase with no partitioning of material between phases. 29 refs.

Molecular Transport Effects in Turbulent Diffusion Flames at Moderate Reynolds Number

Abstract: : In flames molecular diffusivities are enhanced by the high temperatures and can be of the same order as turbulent diffusivities in flames of moderate Reynolds number. A perturbation analysis is used to quantify effects in a hydrogen/air diffusion flame which arise from differential molecular diffusivities. The analysis uses perturbations about the equal diffusivity, adiabatic, equilibrium theory commonly used and yields solutions for the average and higher moments for the departures in normalized element mass fractions and enthalpy. The results are compared with the laser-Raman measurements of Drake et al. in a relatively low Reynolds number flame. Generally the agreement is excellent. (Author)

Effect of fluid flow on macrosegregation in axi-symmetric ingots

Abstract: A combined theoretical and experimental study of steady-state fluid flow, heat flow and segregation in axi-symmetric ingot production is presented, with specific applications in continuous casting and ESR. The fluid flow-segregation model involves the coupling of convective heat and fluid flow in the fully liquid metal pool ahead of the liquidus isotherm to the interdendritic fluid flow responsible for macrosegregation in the “mushy” zone of ingots solidifying under axi-symmetric conditions. Experiments on low-temperature Sn-Pb alloys verify the solidification model.

Numerical investigation of turbulent channel flow

Abstract: Fully developed turbulent channel flow was simulated numerically at Reynolds number 13800, based on centerline velocity and channel halt width. The large-scale flow field was obtained by directly integrating the filtered, three dimensional, time dependent, Navier-Stokes equations. The small-scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC IV computer with up to 516,096 grid points. The computed flow field was used to study the statistical properties of the flow as well as its time dependent features. The agreement of the computed mean velocity profile, turbulence statistics, and detailed flow structures with experimental data is good. The resolvable portion of the statistical correlations appearing in the Reynolds stress equations are calculated. Particular attention is given to the examination of the flow structure in the vicinity of the wall.

Modeling the flow of viscoelastic fluids through porous media

Abstract: A tube with sinusoidal axial variations in diameter has been used as a first step toward modeling the flow channels of a porous medium in such a way that appreciable Lagrangian unsteadiness is present. Experiments with dilute aqueous solutions of a polyacrylamide (Dow Separan AP-30) show that the Lagragian unsteadiness gives rise to an increase in resistance to flow through the sinusoidal channel relative to that predicted for a purely viscous fluid. The increase in pressure drop can occur as a consequence of fluid elasticity, without any observable secondary flow. At sufficiently high flow rates, secondary flow appears. 20 references.

Mathematical Model of Shallow Water Flow over Porous Media

Abstract: A conjunctive mathematical model for a surface-subsurface flow system is developed. The unsteady surface flow is explored by a set of one-dimensional dynamic wave equations for shallow water, which are solved by using a four-point implicit finite-difference scheme. The transient subsurface flow is two-dimensional, with potential gradients in the vertical direction as well as the surface flow direction. The porous medium may be saturated or unsaturated or both, and it can be nonhomogeneous and anisotropic. The subsurface flow equation is solved by employing a successive line over-relaxation implicit finite-difference scheme. The surface and subsurface flow components are coupled at the ground surface considering the mass conservation and pressure relationships. The model is verified by using existing experimental data and analytical solutions for special cases.

Rotary thermodynamic apparatus and method

Abstract: Rotary thermodynamic compression and refrigeration apparatus and methods in which the mechanical impedance and/or thermodynamic impedance of the system are controlled in order to obtain stable operation. By controlling these impedances, the overall pressure drop of the fluid flow in the system is made to increase with increasing fluid flow rate, thus ensuring stable operation.

H theorems in statistical fluid dynamics

Abstract: It is demonstrated that the second-order Markovian closures frequently used in turbulence theory imply an H theorem for inviscid flow with an ultraviolet spectral cut-off. That is, from the inviscid closure equations, it follows that a certain functional of the energy spectrum (namely entropy) increases monotonically in time to a maximum value at absolute equilibrium. This is shown explicitly for isotropic homogeneous flow in dimensions d>or=2, and then a generalised theorem which covers a wide class of systems of current interest is presented. It is shown that the H theorem for closure can be derived from a Gibbs-type H theorem for the exact non-dissipative dynamics.

Surface and buoyancy driven free convection

Abstract: A system of two interfacing immiscible fluids subject to an imposed temperature difference in a gravity field is considered. The fluids, the gravity level, the temperature difference and the extension of the interface are arbitrary. An order of magnitude analysis is applied to determine: (i) the types of flow regimes that can be attained in natural, Marangoni or combined free convection; (ii) how the problem's data identify which type of free convection and of flow regime prevails in each specific case.

Conformal Mapping for Channel Junction Flow

Abstract: An analysis of the flow behavior at rectangular channel junctions with combining flow using the conformal mapping technique has been presented. Equations for the location of the stagnation point and the free-streamline for different flow conditions at rectangular channel junctions have been developed. These equations have been solved numerically by using Simpsons rule. It is observed that for each channel junction there is a unique value of discharge ratio corresponding to which the stagnation point coincides with the upstream corner of the junction. The value of the discharge ratio depends on the junction angle as well as on the bed-widths of the channels. It is also indicated that the zone of stagnant fluid between the free-streamline and the channel boundary depends on the junction angle and the location of the stagnation point.

The infinitesimal group of the Navier-Stokes equations

Abstract: The Navier-Stokes equations for an incompressible viscous fluid admit time translation, time dependent change of the pressure origin, a scale change, rotation of axes, and time dependent spatial translation. No other transformations appear if dependence on derivatives is allowed.

Carbon dioxide in igneous petrogenesis: II. Fluid dynamics of mantle metasomatism

Abstract: Petrographic, fluid inclusion, geochemical and isotopic evidence from xenoliths in alkali basalts suggests that low-viscosity fluids rich in O-H-C, dissolved silicates and especially the incompatible elements may ascend, decompress and precipitate crystalline phases and/or induce partial fusion in the upper mantle. Such mantle metasomatic fluids (MMF) may be important in generating isotopic heterogeneity and in transporting and focusing mantle heat. In order to model the movement of MMF, the ordinary differential equations governing the variation ofP, T, ascent velocity and fluid density of a compressible, viscous, single-phase (H2O or CO2) non-reacting fluid ascending through a vertical crack of constant width have been solved. A large number of numerical simulations were carried out in which the significant factors affecting flow behavior (thermodynamic and transport fluid properties, roughness and width of cracks, geothermal gradient, initial conditions, etc.) were systematically varied. The calculations show that: (1) MMF tends to move at uniform rates following a short period of rapid initial acceleration, (2) MMF ascends nearly isothermally, (3) MMF acts as an efficient heat transfer agent; numerical experiments show that transport of heat into regions undergoing metasomatism can lead to partial fusion. The heat transported by movement of MMF averaged over the age of the Earth is sufficient to generate about 0.1 km3 of basaltic magma per year, which is approximately equal to the production rate of alkaline magma. If an intense period of mantle degassing occured early in the history of the Earth, the transport of heat and mass (K, U, Rb, LREE) by migrating fluids might have been important.

A note on Poisson’s equation for pressure in a turbulent flow

Abstract: It is shown that the ’’forcing function’’ (the right‐hand side) of Poisson’s equation for the mean or fluctuating pressure in a turbulent flow can be divided into two parts, one related to the square of the rate of strain and the other to the square of the vorticity.