Showing papers on "Pipe flow published in 1998"

Mean-flow scaling of turbulent pipe flow

Abstract: Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60 9×103). Von Karman's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600 5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow

Abstract: We propose the viscous Camassa-Holm equations as a closure approximation for the Reynolds-averaged equations of the incompressible Navier-Stokes fluid. This approximation is tested on turbulent channel and pipe flows with steady mean. Analytical solutions for the mean velocity and the Reynolds shear stress are consistent with experiments in most of the flow region.

Low-Diffusion Flux-Splitting Methods for Flows at All Speeds

Abstract: Methods for extending the advective upwind splitting method (AUSM) family of low-diffusion flux-splitting schemes to operate effectively at all flow speeds are developed. The extensions developed are designed for use with time-derivative preconditioning and are based on the idea that the speed of sound should cease to be an important scaling parameter for the diffusive contributions to the interface flux as the Mach number becomes small. Using this criterion, alternative definitions for the interface Mach numbers are developed, and methods for ensuring pressure-velocity coupling at low speeds are formulated. Results are presented for inviscid flows through a channel at various Mach numbers, developing viscous flow in a two-dimensional duct, driven-cavity flows at various Mach and Reynolds numbers, flow over a backward-facing step, and hydrogen-nitrogen mixing layers

Heat Transfer Characteristics in Partial Boiling, Fully Developed Boiling, and Significant Void Flow Regions of Subcooled Flow Boiling

Abstract: Subcooled flow boiling covers the region beginning from the location where the wall temperature exceeds the local liquid saturation temperature to the location where the thermodynamic quality reaches zero, corresponding to the saturated liquid state. Three locations in the subcooled flow have been identified by earlier investigators as the onset of nucleate boiling, the point of net vapor generation, and the location where x = 0 is attained from enthalpy balance equations. The heat transfer regions are identified as the single-phase heat transfer prior to ONB, partial boiling (PB), and fully developed boiling (FDB). A new region is identified here as the significant void flow (SVF) region. Available models for predicting the heat transfer coefficient in different regions are evaluated and new models are developed based on our current understanding

A New Equivalent Reynolds Number Model for Condensation in Smooth Tubes

Abstract: In 1959, Akers et al. developed an in-tube condensation model, which defines the all-liquid flow rate that provides the same heat transfer coefficient as an annular condensing flow. This liquid flow rate was expressed by an equivalents Reynolds number and used in a single-phase, turbulent flow equation to predict the condensation coefficient. However, the assumptions on which the equivalent Reynolds number is based are shown in the present work to be faulty. This results in the underprediction of many researchers' data. A new equivalent Reynolds number model, based on the heat-momentum analogy, is developed in this study. This model is then shown to predict the experimental Nusselt number of 1197 data points from 18 sources with an average deviation of 13.64 percent. The data are for tube internal diameters between 3.14 and 20 mm.

Suboptimal control of turbulent channel flow for drag reduction

Abstract: Two simple feedback control laws for drag reduction are derived by applying a suboptimal control theory to a turbulent channel flow. These new feedback control laws require pressure or shear-stress information only at the wall, and when applied to a turbulent channel flow at Re τ = 110, they result in 16-22% reduction in the skin-friction drag. More practical control laws requiring only the local distribution of the wall pressure or one component of the wall shear stress are also derived and are shown to work equally well

Laminar-turbulent transition in pipe flow for Newtonian and non-Newtonian fluids.

Abstract: A cylindrical pipe facility with a length of 32 m and a diameter of 40 mm has been designed. The natural transition Reynolds number, i.e. the Reynolds number at which transition occurs as a result of non-forced, natural disturbances, is approximately 60 000. In this facility we have studied the stability of cylindrical pipe flow to imposed disturbances. The disturbance consists of periodic suction and injection of fluid from a slit over the whole circumference in the pipe wall. The injection and suction are equal in magnitude and each distributed over half the circumference so that the disturbance is divergence free. The amplitude and frequency can be varied over a wide range.First, we consider a Newtonian fluid, water in our case. From the observations we compute the critical disturbance velocity, which is the smallest disturbance at a given Reynolds number for which transition occurs. For large wavenumbers, i.e. large frequencies, the dimensionless critical disturbance velocity scales according to Re−1, while for small wavenumbers, i.e. small frequencies, it scales as Re−2/3. The latter is in agreement with weak nonlinear stability theory. For Reynolds numbers above 30 000 multiple transition points are found which means that increasing the disturbance velocity at constant dimensionless wavenumber leads to the following course of events. First, the flow changes from laminar to turbulent at the critical disturbance velocity; subsequently at a higher value of the disturbance it returns back to laminar and at still larger disturbance velocities the flow again becomes turbulent.Secondly, we have carried out stability measurements for (non-Newtonian) dilute polymer solutions. The results show that the polymers reduce in general the natural transition Reynolds number. The cause of this reduction remains unclear, but a possible explanation may be related to a destabilizing effect of the elasticity on the developing boundary layers in the entry region of the flow. At the same time the polymers have a stabilizing effect with respect to the forced disturbances, namely the critical disturbance velocity for the polymer solutions is larger than for water. The stabilization is stronger for fresh polymer solutions and it is also larger when the polymers adopt a more extended conformation. A delay in transition has been only found for extended fresh polymers where delay means an increase of the critical Reynolds number, i.e. the number below which the flow remains laminar at any imposed disturbance.

A Wall-Distance-Free k-ε Model With Enhanced Near-Wall Treatment

Abstract: We evaluate a wall-distance-free low-Re κ-e turbulence closure model which Incorporates an extra source term in the e transport equation designed to increase the level of e in nonequilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, including those involving separated flows regions. Two such cases are used here to test the model: one in the low speed flow regime, the other a supersonic one. Comparisons with experimental data and with an earlier version of the κ-e model, as well as with a variant of the κ-ω model (both also wall-distance-free) reveal that the proposed model enables improved prediction of adverse pressure gradient flows relative to more traditional κ-e models

Trajectory and entrainment of a round jet in crossflow

Abstract: This paper examines the trajectory and entrainment characteristics of a round jet in crossflow. A series of large eddy simulations was performed at Reynolds numbers of 1050 and 2100 and at jet to crossflow velocity ratios of 2.0 and 3.3. Trajectories, which are defined based on the mean streamlines on the centerplane, all collapse to a single curve far from the jet exit, and this curve can be represented with a power law fit. Within this power law region, entrainment of crossflow fluid is shown to be the primary mechanism by which the jet trajectory is determined. Upstream of the power law region, near the jet exit, jet trajectory varies from changes in pressure drag and from differences in the turbulence intensities in the incoming pipe flow.

Direct Numerical Simulation of a Fully Developed Turbulent Flow over a Wavy Wall

Abstract: Turbulent flow over a sinusoidal solid wavy surface was investigated by a direct numerical simulation using a spectral element technique. The train of waves has an amplitude to wavelength ratio of 0.05. For the flow conditions (Re=hUb/2ν= 3460) considered, adverse pressure gradients were large enough to cause flow separation. Numerical results compare favorably with those of Hudson's (1993) measurements. Instantaneous flow fields show a large variation of the flow pattern in the spanwise direction in the separated bubble at a given time. A surprising result is the discovery of occasional velocity bursts which originate in the separated region and extend over large distances away from the wavy wall. Turbulence in this region is very different from that near a flat wall in that it is associated with a shear layer which is formed by flow separation.

Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend

Abstract: The steady, turbulent flow in a circular-sectioned 90° bend with smooth walls has been investigated experimentally. The bend had a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. The longitudinal, circumferential and radial components of mean and fluctuating velocities, and the Reynolds stresses in the pipe cross section at several longitudinal stations were obtained with the technique of rotating a probe with an inclined hot wire at a Reynolds number of 6×104. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross section were illustrated. Moreover, other characteristics of the bend flow, such as deviation of the primary flow and intensity of the secondary flow, were presented. Simultaneously, discussions were given on the transition of phenomena in the longitudinal direction and the structures of turbulence in the 90° bend.

Three dimensional numerical simulations of viscoelastic flows through planar contractions

Abstract: We present in this paper a fully three dimensional (3D) convergent numerical study of planar viscoelastic contraction flows. A 3D finite volume method (FVM) with the primary variable elastic viscous split stress (EVSS) formulation is employed, and a very efficient 3D block solver coupled with block correction is developed to speed up the convergence rate. Full 3D simulations of viscoelastic flows in 4:1 planar abrupt contractions are carried out using experimental conditions. Upstream vortex patterns comparable with the existing flow visualisation observations are captured using the upper convected Maxwell model for a Boger fluid and the Phan-Thien–Tanner model for a shear thinning fluid. Comprehensive comparisons between numerical simulation results and data measured in the dynamic fields in a 4:1 planar abrupt contraction are made, and the results indicate that the experimental measurements can be quantitatively reproduced if the fluid is well characterised by an appropriate viscoelastic model. It is confirmed numerically that the shear thinning of the fluid reduces the intensity of the singularity of viscoelastic flow near the re-entrant corner. With the Oldroyd-B model, by extensive computations on successively refined meshes with the minimum dimensionless size being 0.16–0.014 on the contraction plane in 2D configuration, it is revealed that, although the asymptotic flow behavior near the re-entrant corner and the build-up of the overall pressure and extensional stresses as well as the kinematic behavior along the centreline are insensitive to mesh refinement, completely different vortex activities may be predicted if the mesh is not sufficiently fine. It is verified numerically that, depending on the flow inertia and rheological properties of fluids, both the lip vortex mechanism and the corner vortex mechanism may be responsible for the vortex activities of viscoelastic fluids in 4:1 planar contraction flow, and the elasticity number E and Mach number M of the flow can be used to determine the vortex mechanism approximately. It is clear that the development process of the vortex activities could be underestimated with 2D simplification, and overpredicted with the creeping flow assumption, particularly when Re>0.5. Therefore, in planar contraction flow analyses, numerical artifacts may be produced with a coarse mesh, and 2D flow simulation is only a good approximation to the fully 3D flow if the upstream aspect ratio W/H in the experiment is at least 10.

Particle Deposition with Thermophoresis in Laminar and Turbulent Duct Flows

Abstract: A numerical simulation procedure for studying deposition of aerosol particles in duct flows including the effect of thermal force under laminar and turbulent flow conditions is developed. An improved model for thermophoretic force acting on small particles is presented. Perturbation based analytical expressions for velocity and temperature profiles are used in the analysis for the laminar duct flow. The Reynolds stress transport model (RSM) of the FLUENT code is used to evaluate the mean flow and temperature fields for the turbulent duct flow case. The instantaneous fluctuation velocity field is generated by the continuous filtered white noise model. Effects of Brownian diffusion, thermophoresis, lift force, and gravity are included in the computation. Ensembles of particle trajectories are generated and statistically analyzed. Particle dispersion from a point source in the presence of a temperature gradient field in laminar and turbulent duct flows is studied. For an initially uniform concentrat...

Perspective: Flow at High Reynolds Number and Over Rough Surfaces—Achilles Heel of CFD

Abstract: The law of the wall and related correlations underpin much of current computational fluid dynamics (CFD) software, either directly through use of so-called wall functions or indirectly in near-wall turbulence models. The correlations for near-wall flow become crucial in solution of two problems of great practical importance, namely, in prediction of flow at high Reynolds numbers and in modeling the effects of surface roughness. Although the two problems may appear vastly different from a physical point of view, they share common numerical features. Some results from the 'super-pipe' experiment at Princeton University are analyzed along with those of previous experiments on the boundary layer on an axisymmetric body to identify features of near-wall flow at high Reynolds numbers that are useful in modeling. The study is complemented by a review of some computations in simple and complex flows to reveal the strengths and weaknesses of turbulence models used in modern CFD methods. Similarly, principal results of classical experiments on the effects of sand-grain roughness are reviewed, along with various models proposed to account for these effects in numerical solutions

Darcian, Transitional, and Turbulent Flow through Porous Media

Abstract: The study of flow through media consisting of large-sized grains is important in a number of civil engineering applications. Employing the square root of permeability as the characteristic length in defining friction factor and Reynolds number, theoretical curves, relating friction factor and Reynolds number—similar to the Moody diagram used in pipe flow to estimate the friction factor—have been developed using the ratio of characteristic length \id and square root of permeability √\ik as the third parameter. The existing experimental data on flow through porous media have been sorted based on the \id/√\ik ratio and are used to verify the theory developed. The agreement is good. From the set of theoretical curves so obtained, the Reynolds number at which the friction factor–Reynolds number relationship deviates from Darcy’s law and the Reynolds number at which turbulent flow is fully established are identified. Empirical equations for these Reynolds numbers in terms of media parameters have been obtained. The factors affecting linear parameter \ia and nonlinear parameter \ib have been brought out. The empirical power law applicable for high Reynolds number flows is given a theoretical justification.

Drag reduction of turbulent pipe flows by circular-wall oscillation

Abstract: An experimental study on turbulent pipe flows was conducted with a view to reduce their friction drag by oscillating a section of the pipe in a circumferential direction. The results indicated that the friction factor of the pipe is reduced by as much as 25% as a result of active manipulation of near-wall turbulence structure by circular-wall oscillation. An increase in the bulk velocity was clearly shown when the pipe was oscillated at a constant head, supporting the measured drag reduction in the present experiment. The percentage reduction in pipe friction was found to be better scaled with the nondimensional velocity of the oscillating wall than with its nondimensional period, confirming a suggestion that the drag reduction seem to be resulted from the realignment of longitudinal vortices into a circumferential direction by the wall oscillation.

Second Law Analysis of Laminar Viscous Flow Through a Duct Subjected to Constant Wall Temperature

Abstract: Entropy generation for a fully developed laminar viscous flow in a duct subjected to constant wall temperature is investigated analytically. The temperature dependence on the viscosity is taken into consideration in the analysis. The ratio of the pumping power to the total heat flux decreases considerably and the entropy generation increases along the duct length for viscous fluids. The variation of total exergy loss due to both the entropy generation and the pumping process is studied along the duct length as well as varying the fluid inlet temperature for fixed duct length. For low heat transfer conditions the entropy generation due to viscous friction becomes dominant and the dependence of viscosity with the temperature becomes essentially important to be considered in order to determine the entropy generation accurately

Methods to Set Up and Investigate Low Reynolds Number, Fully Developed Turbulent Plane Channel Flows

Abstract: The tripping of fully developed turbulent plane channel flow was studied at low Reynolds number, yielding unique flow properties independent of the initial conditions. The LDA measuring technique was used to obtain reliable mean velocities, rms values of turbulent velocity fluctuations and skewness and flatness factors over the entire cross-section with emphasis on the near-wall region. The experimental results were compared with the data obtained from direct numerical simulations available in the literature. The analysis of the data indicates the important role of the upstream conditions on the flow development. It is shown that the fully developed turbulent state at low Reynolds number can be reached only by significant tripping of the flow at the inlet of the channel. Effects related to the finite size of the LDA measuring control volume and an inaccuracy in the estimation of the wall shear stress from near-wall velocity measurements are discussed in detail since these can yield systematic discrepancies between the measured and simulated results.

The onset of turbulence in physiological pulsatile flow in a straight tube

Abstract: An empirical correlation for the onset of turbulence in physiological pulsatile flow is presented. We pumped three different test fluids of kinematic viscosity 0.008–0.035 cm2/s through four straight tubes 0.4–3.0 cm in diameter. A Scotch yoke mechanism provided an oscillatory sine wave flow component of known stroke volume and frequency. We adjusted the mean flow independently until we detected signal instabilities from hot film wall shear stress probes. The critical peak Reynolds number was found to correlate with the Womersley parameter and the Strouhal number as a power law function with a root-mean-square (rms) error of 15.2%. Experimental measurements of the laminar velocity profile are compared to theoretical predictions from Poiseuille’s law and Womersley’s solution.

Pressure loss equations for laminar and turbulent non-newtonian pipe flow

Abstract: The equations that define Newtonian pipe flow are well established and used routinely by engineers and scientists throughout the world. The same cannot be said for non-Newtonian flows, which have a higher degree of complexity. This paper presents a coherent set of equations for the laminar and turbulent flow of Herschel-Bulkley fluids. These equations are consistent with those used for Newtonian fluids and previous work on the behavior of generalized non-Newtonian fluids. A numerical model for non-Newtonian flows is discussed and has been compared with experimental measurements from different sources. This model has been used to run a series of simulations to find the coefficients required for a new turbulent friction factor correlation. A new Reynolds number has been defined that represents the conditions in turbulent flows more realistically than the existing Metzner-Reed Reynolds number.

Transition of unsteady velocity profiles with reverse flow

Abstract: This paper deals with the stability and transition to turbulence of wall-bounded unsteady velocity profiles with reverse flow. Such flows occur, for example, during unsteady boundary layer separation and in oscillating pipe flow. The main focus is on results from experiments in time-developing flow in a long pipe, which is decelerated rapidly. The flow is generated by the controlled motion of a piston. We obtain analytical solutions for laminar flow in the pipe and in a two-dimensional channel for arbitrary piston motions. By changing the piston speed and the length of piston travel we cover a range of values of Reynolds number and boundary layer thickness. The velocity profiles during the decay of the flow are unsteady with reverse flow near the wall, and are highly unstable due to their inflectional nature. In the pipe, we observe from flow visualization that the flow becomes unstable with the formation of what appears to be a helical vortex. The wavelength of the instability [simeq R: similar, equals]3[delta] where [delta] is the average boundary layer thickness, the average being taken over the time the flow is unstable. The time of formation of the vortices scales with the average convective time scale and is [simeq R: similar, equals]39/([Delta]u/[delta]), where [Delta]u=(umax[minus sign]umin) and umax, umin and [delta] are the maximum velocity, minimum velocity and boundary layer thickness respectively at each instant of time. The time to transition to turbulence is [simeq R: similar, equals]33/([Delta]u/[delta]). Quasi-steady linear stability analysis of the velocity profiles brings out two important results. First that the stability characteristics of velocity profiles with reverse flow near the wall collapse when scaled with the above variables. Second that the wavenumber corresponding to maximum growth does not change much during the instability even though the velocity profile does change substantially. Using the results from the experiments and the stability analysis, we are able to explain many aspects of transition in oscillating pipe flow. We postulate that unsteady boundary layer separation at high Reynolds numbers is probably related to instability of the reverse flow region.

The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown

Abstract: The evolution of a perturbed vortex in a pipe to axisymmetric vortex breakdown is studied through numerical computations. These unique simulations are guided by a recent rigorous theory on this subject presented by Wang & Rusak (1997a). Using the unsteady and axisymmetric Euler equations, the nonlinear dynamics of both small- and large-amplitude disturbances in a swirling flow are described and the transition to axisymmetric breakdown is demonstrated. The simulations clarify the relation between our linear stability analyses of swirling flows (Wang & Rusak 1996a, b) and the time-asymptotic behaviour of the flow as described by steady-state solutions of the problem presented in Wang & Rusak (1997a). The numerical calculations support the theoretical predictions and shed light on the mechanism leading to the breakdown process in swirling flows. It has also been demonstrated that the fundamental characteristics which lead to vortex instability and breakdown in high-Reynolds-number flows may be calculated from considerations of a single, reduced-order, nonlinear ordinary differential equation, representing a columnar flow problem. Necessary and sufficient criteria for the onset of vortex breakdown in a Burgers vortex are presented.

Steady flow in a helically symmetric pipe

Abstract: Fully developed flow in an infinite helically coiled pipe is studied, motivated by physiological applications. Most of the bends in the mammalian arterial system curve in a genuinely three-dimensional way, so that the arterial centreline has not only curvature but torsion and can be modelled by a helix. Flow in a helically symmetric pipe generalizes related problems in axisymmetry (Dean flow) and two-dimensionality, but the geometry ensures that even irrotational flow has a cross-pipe component. Fully developed helical flows driven by a steady pressure gradient are studied analytically and numerically. Varying the radius and pitch of the helical pipe, the effects of curvature and torsion on the flow are investigated.

Stokes flow in an elastic tube—a large-displacement fluid-structure interaction problem

Abstract: SUMMARY Viscous flow in elastic (collapsible) tubes is a large-displacement fluid-structure interaction problem frequently encountered in biomechanics. This paper presents a robust and rapidly converging procedure for the solution of the steady three-dimensional Stokes equations, coupled to the geometrically non-linear shell equations which describe the large deformations of the tube wall. The fluid and solid equations are coupled in a segregated method whose slow convergence is accelerated by an extrapolation procedure based on the scheme’s asymptotic convergence behaviour. A displacement control technique is developed to handle the system’s snap-through behaviour. Finally, results for the tube’s post-buckling deformation and for the flow in the strongly collapsed tube are shown. © 1998 John Wiley & Sons, Ltd.

General wellbore flow model for horizontal, vertical, and slanted well completions

Abstract: A general wellbore flow model, which incorporates not only frictional, accelerational, and gravitational pressure drops, but also the pressure drop caused by inflow, is presented in this paper. The new wellbore model is readily applicable to different wellbore perforation patterns and well completions, and can be easily incorporated in reservoir simulators or analytical reservoir inflow models. Three dimensionless numbers, the accelerational to frictional pressure gradient ratio R{sub af}, the gravitational to frictional pressure gradient ratio R{sub gf}, and the inflow-directional to accelerational pressure gradient ratio R{sub da}, have been introduced to quantitatively describe the relative importance of different pressure gradient components. For fluid flow in a production well, it is expected that there exist three different flow regions along the wellbore, the laminar flow region, the partially-developed turbulent flow region, and the fully-developed turbulent flow region. For wellbore flow with uniform influx, R{sub af} in the laminar flow region is a constant which is only dependent on fluid properties, inflow rate and pipe ID, but independent of axial location and pipe roughness; R{sub af} in the fully-developed turbulent flow region is related to the axial location and pipe geometry (pipe ID and pipe roughness) and may be independent of themore » fluid properties and inflow rate; whereas R{sub af} in the partially- developed turbulent flow region depends on location, pipe geometry, fluid properties and inflow rate. It is found that the influence of either inflow or outflow depends on the flow regime present in the wellbore. It is recommended that the new wellbore flow model be included in wellbore-reservoir coupling models to achieve more accurate predictions of pressure drop and inflow distribution along the wellbore as well as the well production or injection rates.« less