Showing papers on "Pipe flow published in 1991"

The minimal flow unit in near-wall turbulence

Abstract: Direct numerical simulations of unsteady channel flow were performed at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic (in x and z) array of identical structures. The goal is to isolate the basic flow unit, to study its morphology and dynamics, and to evaluate its contribution to turbulence in fully developed channels. For boxes wider than approximately 100 wall units in the spanwise direction, the flow is turbulent and the low-order turbulence statistics are in good agreement with experiments in the near-wall region. For a narrow range of widths below that threshold, the flow near only one wall remains turbulent, but its statistics are still in fairly good agreement with experimental data when scaled with the local wall stress. For narrower boxes only laminar solutions are found. In all cases, the elementary box contains a single low-velocity streak, consisting of a longitudinal strip on which a thin layer of spanwise vorticity is lifted away from the wall. A fundamental period of intermittency for the regeneration of turbulence is identified, and that process is observed to consist of the wrapping of the wall-layer vorticity around a single inclined longitudinal vortex.

Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylinders

Abstract: Two‐dimensional unsteady flows in complex geometries that are characterized by simple (low‐dimensional) dynamical behavior are considered. Detailed spectral element simulations are performed, and the proper orthogonal decomposition or POD (also called method of empirical eigenfunctions) is applied to the resulting data for two examples: the flow in a periodically grooved channel and the wake of an isolated circular cylinder. Low‐dimensional dynamical models for these systems are obtained using the empirically derived global eigenfunctions in the spectrally discretized Navier–Stokes equations. The short‐ and long‐term accuracy of the models is studied through simulation, continuation, and bifurcation analysis. Their ability to mimic the full simulations for Reynolds numbers (Re) beyond the values used for eigenfunction extraction is evaluated. In the case of the grooved channel, where the primary horizontal wave number of the flow is imposed from the channel periodicity and so remains unchanged with Re, the models extrapolate reasonably well over a range of Re values. In the case of the cylinder wake, however, due to the significant spatial wave number changes of the flow with the Re, the models are only valid in a small neighborhood of the decompositional Reynolds number.

Experimental study of turbulent swirling flow in a straight pipe.

Abstract: Swirling flow through a pipe is a highly complex turbulent flow and is still challenging to predict. An experimental investigation is performed to obtain systematic data about the flow and to understand its physics. A free-vortex-type swirling flow is introduced in a long straight circular pipe. The swirling component decays downstream as a result of wall friction. The velocity distributions are continuously changing as they approach fully developed parallel flow. The swirl intensity Ω, defined as a non-dimensional angular momentum flux, decays exponentially. The decay coefficients, however, are not constant as conventionally assumed, but depend on the swirl intensity. The wall shear stresses are measured by a direct method and, except in a short inlet region, are a function only of the swirl intensity and the Reynolds number. The velocity distributions and all Reynolds stress components are measured at various axial positions in the pipe. The structure of the tangential velocity profile is classified into three regions: core, annular and wall regions. The core region is characterized by a forced vortex motion and the flow is dependent upon the upstream conditions. In the annular region, the skewness of the velocity vector is noticeable and highly anisotropic so that the turbulent viscosity model does not work well here. The tangential velocity is expressed as a sum of free and forced vortex motion. In the wall region the skewness of the flow becomes weak, and the wall law modified by the Monin–Oboukhov formula is applicable. Data on the microscale and the spectrum are also presented and show quite different turbulence structures in the core and the outer regions.

The role of particle collisions in pneumatic transport

Abstract: We analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. The balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. (1984).

An Experimental Study of Entrainment Effects on the Heat Transfer From a Flat Surface to a Heated Circular Impinging Jet

Abstract: This paper reports on a study to investigate the effect of ambient air entrainment into a heated impinging jet on the heat transfer from a flat surface. It provides a well-characterized jet by using a long circular pipe to obtain fully developed pipe flow for the jet and a uniform heat flux surface thermal boundary condition by electrically heating a vacuum-deposited gold coating. The surface temperature distribution is measured using a liquid crystal.

Large eddy simulation of turbulence‐driven secondary flow in a square duct

Abstract: The fully developed turbulent flow in a straight duct of square cross section has been simulated using the large eddy simulation (LES) technique. A mixed spectral‐finite difference method has been used in conjunction with the Smagorinsky eddy‐viscosity model for the subgrid scales. The simulation was performed for a Reynolds number of 360 based on friction velocity (5810 based on bulk velocity) and duct width. The simulation correctly predicted the existence of secondary flows and their effects on the mean flow and turbulence statistics. The results are in good qualitative agreement with the experimental data available at much higher Reynolds numbers. It is observed that both the Reynolds normal and shear stresses equally contribute to the production of mean streamwise vorticity.

The attenuation of fluctuations in scalar concentrations through sampling tubes

Abstract: We present results of a laboratory investigation of the attenuation of humidity fluctuations in tubing. The purpose is to obtain simple formulations for use in turbulent flux measurement applications, where the measurement of a trace species may be remote from the sampling point so that the sample must be transported through a tube to the sensor. The laboratory data are compared to the attenuation predicted from Taylor's (1953 and 1954) formulations for the virtual longitudinal eddy diffusivity of a constituent introduced into a pipe, for both laminar and turbulent flow, by plotting the normalized half-power frequency against Reynolds number. Results were first obtained for fully developed equilibrium flow (both laminar and turbulent) through a straight tube. The following modifications were then studied: an intake section, a 90 o elbow bend, and curved tubes (bending through 90 o) with tube-radius to radius-of-curvature ratios of a/R = 0.034 and 0.081. The effect, if any, of these modifications is to increase the half-power frequency over that of the equivalent length of straight tubing. Applying this analysis to a situation where a sample is collected on a tower and transported to an instrument at the base of the tower, we ftnd that as long as the flow in the tube is turbulent, the attenuation in the tubing should not be a significant factor for introducing errors in flux measurements in the unstably stratified atmospheric surface layer.

Nonlinear dynamics of viscoelastic flow in axisymmetric abrupt contractions

Abstract: The steady-state and time-dependent flow transitions observed in a well-characterized viscoelastic fluid flowing through an abrupt axisymmetric contraction are characterized in terms of the Deborah number and contraction ratio by laser-Doppler velocimetry and flow visualization measurements. A sequence of flow transitions are identified that lead to time-periodic, quasi-periodic and aperiodic dynamics near the lip of the contraction and to the formation of an elastic vortex at the lip entrance. This lip vortex increases in intensity and expands outwards into the upstream tube as the Deborah number is increased, until a further flow instability leads to unsteady oscillations of the large elastic vortex. The values of the critical Deborah number for the onset of each of these transitions depends on the contraction ratio β, defined as the ratio of the radii of the large and small tubes. Time-dependent, three-dimensional flow near the contraction lip is observed only for contraction ratios 2 [les ] β [les ] 5, and the flow remains steady for higher contraction ratios. Rounding the corner of the 4:1 abrupt contraction leads to increased values of Deborah number for the onset of these flow transitions, but does not change the general structure of the transitions.

Experiments on transition to turbulence in oscillatory pipe flow

Abstract: A laser-Doppler velocimeter is used to analyse volume-cycled oscillatory flow of a Newtonian viscous fluid in a straight circular tube. The axial velocity is measured at radial positions across the diameter of the tube for a wide range of amplitude A = stroke distance/tube radius (2.4 [les ] A [les ] 21.6) and Womersley parameter (9 < α < 33). Transition to turbulence is detected during the decelerating phase of fluid motion for 500 < Rδ < 854, where Rδ = αA √2 is the Reynolds number based on Stokes-layer thickness. The turbulence is confined to an annular region which is a few times the Stokes-layer thickness near the wall. Hot-film anemometer measurements indicate the core flow remains stable when the boundary layer becomes turbulent for Rδ up to 1310.

Large‐scale computer simulation of fully developed turbulent channel flow with heat transfer

Abstract: Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.

Dynamical eigenfunction decomposition of turbulent channel flow

Abstract: The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loeve(K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re,= 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90% of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, posses viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher-order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.

High resolution measurement of turbulent structure in a channel with particle image velocimetry

Abstract: High resolution particle image velocimetry is used to measure the turbulent velocity field for fully developed flow (Re = 2,872) in an enclosed channel. Photographs of particle displacement are obtained in a plane that is parallel to the flow and perpendicular to the walls. These are analyzed to give simultaneous measurements of two components of the velocity at more than 10,000 points. Maps of velocity vectors, spanwise vorticity and Reynolds stress reveal structural aspects of the turbulence. In particular, internal shear layers are observed, in agreement with predictions of direct numerical simulation. Ensemble-averaging of a number of photographs yields statistical properties of the velocity in good agreement with laser-Doppler velocimeter measurements, and with direct numerical simulations.

A numerical study of the planar contraction flow of a viscoelastic fluid using the simpler algorithm

Abstract: A finite volume technique has been introduced in an attempt to simulate the planar 4:1 contraction flow of the Oldroyd B fluid on a non-uniform staggered grid system, which incorporates the SIMPLER algorithm in discretizing the momentum equations and the deferred correction method in discretizing the constitutive equations For some combinations of viscoelastic parameters, the size and shape of the corner vortex growth are shown to be in good qualitative agreement with those observed experimentally by others for constant viscosity viscoelastic fluids In general, however, they seem to be sensitive to the ratio of retardation time to relaxation time

Improving Zielke’s Method of Simulating Frequency-Dependent Friction in Laminar Liquid Pipe Flow

Abstract: Zielke’s technique of using a method of characteristics to simulate transient phenomena of a liquid transmission line is accurate, easy to apply to complicated systems and therefore, frequently used. However, it requires a very large amount of computation time and computer storage to simulate frequency-dependent friction in a transient liquid flow. Searching for a way to counteract these disadvantages, the authors took note of the fact that the weighting function, which is the root of the above problems, is given by exponential functions or other functions depending on dimensionless time. In order to perform mathematically equivalent calculation without approximations, they have developed a new method which requires much less computation time and computer storage than Zielke’s method. The calculation process is shown by a block diagram to facilitate visual understanding of the method.

Plane-Couette flow between smooth and rough walls

Abstract: A novel approach is utilized to acquire new experimental information on plane-Couette flow. To this end a rigid plate, functioning as the moving wall, is propelled through air by the carriage of a towing channel, and the fixed wall is a stationary bench. It is shown that, irrespective of the state of the walls, the critical Reynolds number, expressed in terms of relative wall velocity and wall spacing, is about 1,200. Findings support the notion of universality of turbulent flow structure in the wall region, but shed doubt on the conjecture of homogeneous shear-flow turbulence in the core.

Chaotic motions of a constrained pipe conveying fluid : comparison between simulation, analysis and experiment

Abstract: A refined analytical model is presented for the dynamics of a cantilevered pipe conveying fluid and constrained by motion limiting restraints

Cooling hole arrangements in jet engine components exposed to hot gas flow

Abstract: A jet engine component includes a body having a wall portion with an external surface exposed to hot gas flow and an internal surface exposed to a cooling air flow. The engine component incorporates an arrangement of cooling holes defined through the wall portion between the external and internal surfaces thereof to permit flow of cooling air from the hollow interior through the wall portion to the exterior of the component. Each cooling hole includes at least one flow inlet at the internal surface of the wall for receiving the cooling air flow, at least a pair of flow outlets at the external surface of the wall for discharging the cooling air flow, and at least a pair of flow branches extending through the wall portion and between the flow inlet and the flow outlets for permitting passage of the cooling air flow from the flow inlet to the flow outlets. In one V-shaped configuration, the flow branches merge and intersect with one another at the flow inlet. In another X-shaped configuration, there are a pair of flow inlets and the flow branches merge and intersect with one another at a location intermediate between and spaced from the flow inlets and outlets. The flow outlets are displaced preferably downstream of the flow inlet relative to the direction of gas flow past the external surface of the wall of the engine component.

A numerical study of the effects of spanwise rotation on turbulent channel flow

Abstract: The effects of spanwise rotation on the large‐scale structures in a turbulent channel flow are numerically simulated by integrating the filtered Navier–Stokes equations. A finite‐difference technique is used to retain the generality for complex geometries and developing flows to be considered in the future. The computed results are consistent with previous flow visualization data and measurements. It is seen that for the presently considered low Reynolds number, the flow significantly laminarizes on the stable side even for low rotation rates. Cellular spanwise structures are observed to develop as a result of the unstable interaction between mean shear and Coriolis forces. The statistics of these roll cells and the underlying turbulence are analyzed and presented in this paper. It is observed that the roll cells make a significant contribution to total turbulent quantities and also aid in the transport of underlying turbulence.

Coriolis-effect in mass flow metering

Abstract: The paper aims at a detailed description of the physical background, for the so-called Coriolis mass flow meter. It presents essentially an analysis of the (free) vibration modes of a fluid conveying straight pipe segment. Due to the inertial effects of the flowing fluid, mainly the Coriolis force, these modes deviate in shape (and in frequency) from those appearing in the absence of fluid motion. The effect of fluid inertia may, therefore, be exploited for the purpose of flow measurement. The analysis is performed under a simplifying approximation: The pipe is considered as a beam, the fluid as a moving string. This approximation leaves the fluid with only one degree of freedom, connected with its mean velocity, and eliminates an infinity of degrees of freedom of the pipe. Yet it keeps, the essential features of the phenomenon. The equations describing the vibrations are derived variationally, with the constraint of a common vibration amplitude of both fluid and pipe. The Lagrange multiplier associated with the constraint gives the interaction force between pipe and fluid. The modes are determined by a perturbation procedure, wherein the small (perturbation) parameter is related to the fluid velocity. The analysis shows, as main result, how the time delay between the vibrations of two appropriately chosen points of the pipe may serve to determine the mass flow rate of the fluid. Other aspects of the problem, like the precise role of the Coriolis force, are considered. The possible improvement of the used approximation is discussed.

Regional heat transfer in two-pass and three-pass passages with 180-deg sharp turns

Abstract: The heat transfer distributions for flow passing through two-pass (one-turn) and three-pass (two-turn) passages with 180-deg sharp turns are studied by using the analogous naphthalene mass transfer technique. Both passages have square cross section and length-to-height ratio of 8. The passage surface, including top wall, side walls, and partition walls, is divided into 26 segments for the two-pass passage and 40 segments for the three-pass passage. Mass transfer results are presented for each segment along with regional and overall averages. The very nonuniform mass transfer coefficients measured around a sharp 180-deg turn exhibit the effects of flow separation, reattachment, and impingement, in addition to secondary flows. Results for the three-pass passage indicate that heat transfer characteristics around the second turn are virtually the same as those around the first turn. This may imply that, in a multiple-pass passage, heat transfer at the first turn has already reached the thermally developed (periodic) condition. Over the entire two-pass passage, the heat transfer enhancement induced by the single-turn is about 45 to 65% of the fully developed values in a straight channel. Such as heat transfer enhancement decreases with an increase in Reynolds number. In addition, overall heat transfer of three-pass passage ismore » approximately 15% higher than that of the two-pass one. This 15% increase appears to be Reynolds number independent. The pressure loss induced by the sharp turns is found to be very significant. Within the present testing range, the pressure loss coefficient for both passages is Reynolds number dependent.« less

Viscoelastic Poiseuille flow through a curved channel: A new elastic instability

Abstract: The linear stability of the inertialess, pressure‐driven Poiseuille flow of an Oldroyd‐B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor–Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbance‐energy equation.

Secondary flows in straight ducts of rectangular cross section

Abstract: In this paper we consider the “elastic effects” that a non-Newtonian fluid, a solution of 2% viscarin in water, can exhibit in fully developed laminar flow in straight ducts of rectangular cross section. The elastic effects associated with the nonlinear properties of constitutive equations are modelled by the CEF-equation. Our main concern is the nature and magnitude of the secondary flows, determined both by numerical and experimental means. In contrast to earlier work, where a perturbation method has been used, the full non-linear equations are solved numerically by a finite volume method. It is shown that two vortices in each quadrant are observed for unity and moderate aspect ratios whereas three vortices are observed for the large aspect ratio of 16. The effect of secondary flow on pressure drop is calculated using both the generalized Newtonian model and the CEF-model. At low flow rates the effect is small but significant effects are observed at high flow rates. This is partly verified through measurements of pressure drop. Calculated velocity fields are compared to data obtained by laser velocimetry and show general agreement within experimental uncertainty.

Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics

Abstract: The nonlinear, three-dimensional Euler equations can be reduced to a simple linear equation when the flow has helical symmetry and when the flow consists of a rigidly rotating basic part plus a Beltrami disturbance part (with vorticity proportional to velocity or a slight generalization of this). Solutions to this linear equation represent steadily rotating, non-axisymmetric waves of arbitrary amplitude. Exact solutions can be constructed in the case of flow in a straight pipe of circular cross-section. Analogous results are obtained for the incompressible, non-dissipative equations of magnetohydrodynamics. In addition to a rigidly rotating basic flow, there may exist a toroidal magnetic field varying linearly with radius.

Turbulent Flow in a Channel With a Wavy Wall

Abstract: A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations, together with a two-layer turbulence model, has been used to describe steady flow in a two-dimensional channel with a wavy wall. Comparisons of calculations with experiments demonstrate the effects of alternating pressure gradients induced by alternating surface curvatures, and multiple separations and reattachments. The numerical method and the turbulence model are shown to capture the overall features of such a flow, including the breakdown of the logarithmic law of the wall in strong pressure gradients and in separated flow.