Showing papers on "Pipe flow published in 1990"

On the space‐time characteristics of wall‐pressure fluctuations

Abstract: A database obtained by direct numerical simulation of turbulent channel flow was used to compute the three‐dimensional frequency/wave‐number spectrum of wall‐pressure fluctuations. The spectrum was used to deduce scaling laws for pressure fluctuations and to evaluate the similarity form for the power spectrum. The convection velocity as a function of frequency, wave number, and spatial and temporal separations was calculated and compared with the experimental data. The problem of artificial ‘‘acoustics’’ in numerical simulation of incompressible flows is discussed.

Flow of non-newtonian fluids in a pipe

Abstract: Measurements of mean axial velocity and of the three normal stresses have been obtained in fully developed pipe-flow with four concentrations of a polymer (sodium carboxymethyl cellulose) in aqueous solution and with water and viscous Newtonian fluids encompassing a range of Reynolds numbers from 240 to 111,000. The results quantify the delay in transition from laminar to turbulent flow caused by shear-thinning, the suppression of turbulent fluctuations particularly in the radial and tangential components of normal stress, and the drag reduction at the higher Reynolds numbers. They also confirm that the maximum drag reduction asymptote is appropriate to these shear-thinning solutions.

An improved k-e model for boundary layer flows

Abstract: An improvement of the k-e model has been made in conjunction with an accurate prediction of the near-wall limiting behaviour of turbulence and the final period of the decay law of free turbulence. The present improved k-e model has been extended to predict the effects of adverse pressure gradients on shear layers, which most previously proposed models failed to do correctly. The proposed model was tested by application to a turbulent pipe flow, a flat plate boundary layer, a relaminarising flow and a diffuser flow with a strong adverse pressure gradient. Agreement with the experiments was generally very satisfactory.

Internal flow field studies in a simulated cylindrical port rocket chamber

Abstract: The objective of these studies is to experimentally characterize the mean and fluctuating flow field that develops along the length of a simulated cylindrical port rocket chamber. Flow simulation was accomplished by injecting ambient temperature nitrogen uniformly along the walls of 10.2-cm (4-in.) diam, porous-tube chambers connected to a choked sonic nozzle. Experiments were conducted with chamber L/D ratios of 9.5 and 14.3, at injection Mach numbers and Reynolds numbers typical of rocket motor values. Maximum Reynolds numbers based on injection and centerline velocities were, respectively, 1.8 x 10 and 1.6 x 10. Mean and fluctuating speed and turbulent shear stresses were measured in the principle coordinate directions using three-element hot-wire anemometers. The data show that noticeable velocity fluctuations in the head-end region generally decrease in intensity, relative to centerline speed, over the first five port diameters. At this point, regular velocity oscillations appear near the wall, just prior to the transition to turbulent flow. The oscillation frequency characteristics suggest the occurrence of vortical disturbances which exhibit pairing as they move away from the wall. The downstream turbulence development is characterized by a slow spreading toward the centerline: peak values of turbulence intensity and shear stress occur a few tenths of a port radius from the wall and remain relatively constant. Mean velocity profiles prior to transition show fair agreement with those derived for a rotational inviscid flow injected normal to the surface. A slow transition from these profiles occurs downstream in the turbulent region. Two surprising features of the flow were the occurrence of both buoyant flow influences and flow spinning in forward regions of the chamber.

On near-wall turbulent flow modelling

Abstract: The behavior of various terms in the Reynolds-stress transport equations is evaluated in view results of near-wall turbulence characterizations which show that all components of the velocity-pressure gradient correlation vanish at the wall. A methodology for deriving an asymptotically correct model of the velocity-pressure gradient correlation is proposed, and a model capable of approaching the high-Reynolds number model for pressure distribution far from the wall is derived. A parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds number-dependent; with this modification, excellent agreement is obtained with measured and simulated near-wall turbulence statistics.

Measurements of turbulent flow in a channel at low Reynolds numbers

Abstract: Normal and streamwise components of the velocity fields of turbulent flow in a channel at low Reynolds numbers have been measured with laser-Doppler techniques. The experiments duplicate the conditions used in current direct numerical simulations of channel flow, and good, but not exact, agreement is found for single-point moments through fourth order. In order to eliminate LDV velocity bias and to measure velocity spectra, the mean time interval between LDV signals was adjusted to be much smaller than the smallest turbulence time scale. Spectra of the streamwise and normal components of velocity at locations spanning the channel are presented.

The influence of the wall on flow through pipes packed with spheres

Abstract: This paper presents the results of an experimental investigation that is a sequel to a previously published study of the flow of fluids through porous media whose matrices are composed of randomly packed spheres. The objective of the previous study was to accurately determine the ranges of the Reynolds number for which Darcy, Forchheimer and turbulent flow occur, and also the values of the controlling flow parameters - namely, the Kozeny-Carman constant for Darcy flow and the Ergun constants for Forchheimer and turbulent flow for porous beds that are infinite in extent; that is, practically speaking, for sufficiently large values of the dimension ratio, D/d, where D is a measure of the extent of the bed and d is the diameter of a single spherical particle of which porous matrix is composed. The porous media studied in the previous and present experiments were confined within circular cylinders (pipes), for which the dimension D is taken to be the diameter of the confining cylinder.

Separation and reattachment of non-newtonian fluid flows in a sudden expansion pipe

Abstract: In the current flow visualization studies, the role of non-Newtonian characteristics (such as shear-rate-dependent viscosity and viscoelasticity) on flow behavior across the sudden expansion step in a circular pipe is investigated over a wide range of Reynolds numbers including the turbulent flow. The expansion ratios tested are 2.000 and 2.667 and the range of the Reynolds number covered in the current flow visualization tests are 10–35 000 based on the inlet diameter. The reattachment lengths for the viscoelastic fluids in the laminar flow regime are found to be much shorter than those for the Newtonian fluid. In addition they decrease significantly with increasingly concentration of viscoelastic fluid at the same Reynolds number. However, in the turbulent flow regime, the reattachment length for the viscoelastic fluids is two or three times longer than those for water, and gradually increases with increasing concentration of viscoelastic solutions, resulting in 25 and 28 step-height distances for 500 ppm and 1000 ppm polyacrylamide solutions respectively. This may be because the elasticity in polyacrylamide solutions suppresses the eddy motion and controls separation and reattachment behavior in the sudden expansion pipe flow. The reattachment lengths for the purely viscous non-Newtonian fluids are found to be almost the same as those for water.

Instabilities of flow in a collapsed tube

Abstract: In a previous paper (Jensen & Pedley 1989) a model was analysed describing the effects of longitudinal wall tension and energy loss through flow separation on the existence and nature of steady flow in a finite length of externally pressurized, elastic-walled tube. The stability of these steady flows to small time-dependent perturbations is now determined. A linear analysis shows that the tube may be unstable to at least three different modes of oscillation, with frequencies in distinct bands, depending on the governing parameters ; neutral stability curves for each mode are calculated. The motion of the separation point at a constriction in the tube appears to play an important role in the mechanism of these oscillations. A weakly nonlinear analysis is used to examine the instabilities in a neighbourhood of their neutral curves and to investigate mode interactions. The existence of multiple independent oscillations indicates that very complex dynamical behaviour may occur.

Energy Relations in Transient Closed‐Conduit Flow

Abstract: When the rate of flow in a closed conduit is changed, large-scale conversions of mechanical energy often occur, particularly if the pipeline is carrying water or some other slightly compressible liquid. Mathematical expressions describing these transient energy transformations are motivated from first principles and derived by mathematical manipulation of the governing continuity and momentum equations. The resulting expression accounts for the kinetic energy of the fluid, the internal energy associated with fluid compressibility and pipeline elasticity effects, the energy dissipated by friction, and the work done at the ends of the conduit. The energy approach provides an integrated view of transient conditions in the pipeline and is thus a simple, efficient, and logically consistent way of comparing the transient response of different systems and solution techniques. In particular, compressibility effects are shown to be negligible when the ratio of the change in internal energy to the change in kinetic energy is much less than one. This rule helps to distinguish the “rigid water column” model of unsteady flow from the more complex water-hammer theory.

Laminar secondary flows in curved rectangular ducts

Abstract: The occurrence of secondary flow in curved ducts due to the centrifugal forces can often significantly influence the flow rate. In the present work, the secondary flow of an incompressible viscous fluid in a curved duct is studied by using a finite-volume method. It is shown that as the Dean number is increased the secondary flow structure evolves into a double vortex pair for low-aspect-ratio ducts and roll cells for ducts of high aspect ratio. A stability diagram is obtained in the domain of curvature ratio and Reynolds number. It is found that for ducts of high curvature the onset of transition from single vortex pair to double vortex pair or roll cells depends on the Dean number and the curvature ratio, while for ducts of small curvature the onset can be characterized by the Dean number alone. A comparison with the available theoretical and experimental results indicates good agreement. A correlation for the friction factor as a function of the Dean number and aspect ratio is developed and is found to be in good agreement with the available experimental and computational results for a wide range of parameters.

Squeezing flow between parallel plates

Abstract: The flow between two parallel plates (rectangular or circular) approaching or receding from each other symmetrically is analysed. The Xavier-Stokes equations have been transformed into an ordinary differential equation using a similarity transformation and the resulting equations are solved numerically. Results for the velocity components, pressure distribution and shearing stress on the wall are presented. In the case of squeezing flow between two circular plates the load supporting capacity of the upper plate has been calculated.

Simple and accurate friction loss equation for plastic pipe.

Abstract: The Blasius equation which has been verified by many researchers and has been recently shown to work very well for small diameter plastic pipe can be combined with the Darcy-Weisbach equation to give a simple and accurate equation written in terms of flow rate, pipe length, and pipe diameter. It allows for correcting for viscosity changes, and is very accurate for flows resulting in Reynolds numbers less than 100,000. Unlike other commonly used empirical equations in a similar form, this equation is theoretically sound and dimensionally homogeneous.

Turbulent Premixed Hydrogen/Air Flames at High Reynolds Numbers

Abstract: Measurements of mean and fluctuating reaction progress variable and streamwise velocities are reported for turbulent premixed hydrogen/air flames burning at relatively high Reynolds numbers (up to 1800. based on streamwise r.m.s. velocity fluctuations and integral length scales). A round-jet geometry was used with the flame surrounded by a hot combustion-gas environment at atmospheric pressure. Mixing-limited combustion was achieved: values of r.m.s. velocity fluctuations, normalized by the laminar burning velocity (u/SL), exceeded 15 in some instances. Test conditions included fuel-equivalence ratios of 0.3-3.6 and burner exit Reynolds numbers (based on exit diameter) of 7000-40000 with fully-developed turbulent pipe flow at the burner exit. It was found that effects of diffusive-thermal (preferential-diffusion) phenomena were important, for both stable (fuel-equivalence ratios greater than 1.8) and unstable conditions, even at the present high Reynolds numbers; for example, flame surfaces were ...

Response of a turbulent boundary layer to sinusoidal free-stream unsteadiness

Abstract: In this paper, selected findings of a detailed experimental investigation are reported concerning the effects of forced free-stream unsteadiness on a turbulent boundary layer. The forced unsteadiness was sinusoidal and was superimposed locally on an otherwise-steady mainstream, beyond a turbulent boundary layer which had developed under constant-pressure conditions. Within the region over which free-stream unsteadiness was induced, the sinusoidal variation in pressure gradient was between extremes of zero and a positive value, with a positive average level. The local response of the boundary layer to these free-stream effects was studied through simultaneous measurements of the u- and v-components of the velocity fieldAlthough extensive studies of unsteady, turbulent, fully-developed pipe and channel flow have been carried out, the problem of a developing turbulent boundary layer and its response to forced free-stream unsteadiness has received comparatively little attention. The present study is intended to redress this imbalance and, when contrasted with other studies of unsteady turbulent boundary layers, is unique in that: (i) it features an appreciable amplitude of mainstream modulation at a large number of frequencies of forced unsteadiness, (ii) its measurements are both detailed and of high spatial resolution, so that the near-wall behaviour of the flow can be discerned, and (iii) it allows local modulation of the mainstream beyond a turbulent boundary layer which has developed under the well-known conditions of steady, two-dimensional, constant-pressure flowResults are reported which allow comparison of the behaviour of boundary layers under the same mean external conditions, but with different time dependence in their free-stream velocities. These time dependences correspond to: (i) steady flow, (ii) quasi-steadily varying flow, and (iii) unsteady flow at different frequencies of mainstream unsteadiness. Experimental results focus upon the time-averaged nature of the flow; they indicate that the mean structure of the turbulent boundary layer is sufficiently robust that the imposition of free-stream unsteadiness results only in minor differences relative to the mean character of the steady flow, even at frequencies for which the momentary condition of the flow departs substantially from its quasi-steady state. Mean levels of turbulence production are likewise unaffected by free-stream unsteadiness and temporal production of turbulence appears to result only from modulation of the motions which contribute to turbulence production as a time-averaged measure.

Mathematical modeling and analysis of heat pipe start-up from the frozen state

Abstract: The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Analysis of Transient Pressures in Bubbly, Homogeneous, Gas-Liquid Mixtures

Abstract: Flow of a gas-liquid mixture in a piping system may be treated as a pseudo-fluid flow if the mixture is homogeneous and the void fraction is small. The governing equations for such flows are a set of nonlinear partial differential equations with pressure dependent coefficients. Shocks may be produced during transient state conditions. For numerical integration of these equations, two second-order explicit finite-difference shemes are introduced

Unsteady flows in a semi-infinite expanding pipe with injection through wall

Abstract: A theoretical analysis of the unsteady incompressible laminar flow in a semi-infinite porous circular pipe with injection or suction through the pipe wall whose radius varies with time is presented. The present analysis simulates the flow field by the burning of inner surface of cylindrical grain in a solid rocket motor, in which the burning surface regresses with time. An exact similar solution of fully non-linear form of the Navier-Stokes equation is calculated numerically. The flow field can be subjected to expanding coefficient of pipe wall α(=aa/ν) and injection parameter R=aV/ν. The properties of flow such as velocity components are represented as functions of expanding coefficient and injection parameter. Concludingly, the effect of burning surface regression on the flow field in combustion chamber of a solid rocket motor is so little that it may be negligible.

Reynolds stress and the physics of turbulent momentum transport

Abstract: The nature of the momentum transport processes responsible for the Reynolds shear stress is investigated using several ensembles of fluid particle paths obtained from a direct numerical simulation of turbulent channel flow. It is found that the Reynolds stress can be viewed as arising from two fundamentally different mechanisms. The more significant entails transport in the manner described by Prandtl in which momentum is carried unchanged from one point to another by the random displacement of fluid particles. One-point models, such as the gradient law are found to be inherently unsuitable for representing this process. However, a potentially useful non-local approximation to displacement transport, depending on the global distribution of the mean velocity gradient, may be developed as a natural consequence of its definition. A second important transport mechanism involves fluid particles experiencing systematic accelerations and decelerations. Close to the wall this results in a reduction in Reynolds stress due to the slowing of sweep-type motions. Further away Reynolds stress is produced in spiralling motions, where particles accelerate or decelerate while changing direction. Both transport mechanisms appear to be closely associated with the dynamics of vortical structures in the wall region.

On displacement-thickness, wall-layer and mid-flow scales in turbulent boundary layers, and slugs of vorticity in channel and pipe flows

Abstract: This theoretical study is motivated by the experimental observations ( a ) on the thickening of a turbulent boundary layer compared with its laminar counterpart, ( b ) on the erupting tongue of fluid that forms the leading edge of a turbulent spot in a boundary layer, ( c ) on the wall-layer and mid-flow scales, and ( d ) on the slugs of vorticity that occur in the middle of turbulent channel and pipe flows. It appears that no previous rational explanation has been put forward for these experimental observations. The present tentative suggestions for ( a ), ( b ) and ( d ) centre on the existence of small-deficit fast-travelling zones of concentrated vorticity governed by the nonlinear Euler equations to leading order at high Reynolds numbers Re but crucially influenced by viscosity nevertheless. In the boundary-layer case these zones travel outside the original boundary layer and hence act to increase the effective boundary-layer thickness. The structure of such zones and their scales, governing equations and amplitude dependence are discussed for assumed planar boundary layers and channel flows and for three-dimensional pipe flows in turn. Allied with this, the theory addresses the closure of the amplitude-dependent neutral curve at high Reynolds numbers, the connection with other Euler-type flows and the possibility of delay in sublayer bursting, as well as aiming to give some guidance on nonlinear aspects of unsteady two- and three-dimensional computations for Euler and related flows. The aspects in ( c ) above, concerning the turbulent scales both of the thin wall layer ( O ( Re -1 In Re ), from a renormalizing and scale-cascade argument) and of the thicker mid-flow zone (containing the Kolmogorov microscale O ( Re -3/4 )) which lies between that layer and the extensive small-deficit outer zone, are also discussed tentatively in terms of their dynamics, leading to apparently good agreement with turbulent-flow experiments and empirical models, for those scales. Other qualitative comparisons are presented.

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

Abstract: Calculation methods for turbulent duct flows are generalised for ducts with arbitrary cross sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered in the present study.

Anomalous flow patterns in viscoelastic entry flow through a planar contraction

Abstract: This paper adds further experimental evidence to demonstrate that the flow characteristics in planar contraction flows of shear-thinning aqueous polyacrylamide solutions are far more complex than initially supposed, with anomalous flow phenomena appearing in the unstable flow regime. It is confirmed that a lip vortex occurs at the re-entrant corner and it appears at lower flow rates with an increase in contraction ratio.

Gate Vibrations due to Unstable Flow Separation

Abstract: The unsteady load and vibration behavior of vertical‐lift gates was investigated for different gate‐bottom geometries and disharge conditions in an open channel and at a conduit inlet. In all cases, vibrations occurred in specific ranges of a dimensionless velocity parameter whenever the flow fluctuated between complete separation and reattachment at the gate bottom. The excitation mechanism was attributed to the combined effect of shear‐layer instabilities and motion‐induced vortices shed at the leading edge of the gate bottom. Many puzzling features of in‐flow and cross‐flow vibration of gates with flow underneath can thus be clarified. In addition, it is shown that the slope of the mean lift curve acting on the gate bottom provides an effective means of predicting with reasonable accuracy the critical range of gate openings with respect to potential gate vibration. The prediction method is illustrated in a practical case.

Studies of Detonation Quenching by Water Sprays

Abstract: Methods designed to quench a detonation wave in a pipe usually rely on some passive device which often presents an unacceptable impedance to the normal pipe flow. One method which overcomes this problem is a triggered water spray barrier, the principles of which are examined in the present study. Experimental data on detonation quenching were obtained in a vertical tube, 76 mm diameter, fitted with various spray generators. The empirical relations of Ranger and Nicholls were then used to calculate the rate at which water is stripped from a droplet in the shock flow field to form a micromist, thus enabling the energy loss from the wavefront in heating and vapourising the micromist to be found. Application of the Shchelkin criterion to the quenching mechanism shows that a 20% energy loss is required from the wavefront. This requirement is met at distances ranging from 0.2 to 1.0 cell lengths which is in reasonable agreement with the expected position of the CJ plane.