Showing papers on "Pipe flow published in 1995"

A numerical study of turbulent supersonic isothermal-wall channel flow

Abstract: A study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation Mach numbers, based on the bulk velocity and sound speed at the walls, of 15 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel half-width, are of the order of 3000 Because of the relatively low Reynolds number, all of the relevant scales of motion can be captured, and no subgrid-scale or turbulence model is needed The isothermal boundary conditions give rise to a flow that is strongly influenced by wall-normal gradients of mean density and temperature These gradients are found to cause an enhanced streamwise coherence of the near-wall streaks, but not to seriously invalidate Morkovin's hypothesis : the magnitude of fluctuations of total temperature and especially pressure are much less than their mean values, and consequently the dominant compressibility effect is that due to mean property variations The Van Driest transformation is found to be very successful at both Mach numbers, and when properly scaled, statistics are found to agree well with data from incompressible channel flow results

Transition to turbulence in constant-mass-flux pipe flow

Abstract: We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number ( Re ) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re . This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.

LDA measurements in the near-wall region of a turbulent pipe flow

Abstract: This paper presents laser-Doppler measurements of the mean velocity and statistical moments of turbulent velocity fluctuations in the near-wall region of a fully developed pipe flow at low Reynolds numbers. A refractive-index-matched fluid was used in a Duran-glass test section to permit access to the near-wall region without distortion of the laser beams. All measurements were corrected for the influence of the finite size of measuring control volume. Measurements of long-time statistical averages of all three fluctuating velocity components in the near-wall region are presented. It is shown that the turbulence intensities in the wall region do not scale with inner variables. However, the limiting behaviour of the intensity components very close to the wall show only small variations with the Reynolds number. Measurements of higher-order statistical moments, the skewness and flatness factors, of axial and tangential velocity components confirm the limiting behaviour of these quantities obtained from direct numerical simulations of turbulent channel flow. The comparison of measured data with those obtained from direct numerical simulations reveals that noticeable discrepancies exist between them only with regard to the flatness factor of the radial velocity component near the wall. The measured v’ flatness factor does not show the steep rise close to the wall indicated by numerical simulations. Analysis of the measured data in the near-wall region reveals significant discrepancies between the present LDA measurements and experimental results obtained using the hot-wire anemometry.

Transient, turbulent, smooth pipe friction

Abstract: Two of the most promising analytical models of unsteady friction in turbulent pipe flows are based on sharply contrasting hypotheses. One uses the history of the flow; the other uses instantaneous conditions. The purposes of this paper are to present an analysis using the former approach and to indicate how to determine which of the two methods is appropriate. A weighting function model of transient friction is developed for flows in smooth pipes by assuming the turbulent viscosity to vary linearly within a thick shear layer surrounding a core of uniform velocity and is thus applicable to flows at high Reynolds number. In the case of low Reynolds number turbulent flows and short time intervals, the predicted skin friction is identical to an earlier model developed by Vardy et al (1993). In the case of laminar flows, it gives results equivalent to those of Zielke (1966, 1968). The predictions are compared with analytical results for the special case of flows with uniform acceleration. It is this case that ...

Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows

Abstract: In this work, we investigate the effect of the introduction of a stress diffusive term into the classical Oldroyd-B constitutive equation on the numerical stability of time-dependent viscoelastic flow calculations. The channel Poiseuille flow at Re ⪢ 1 and O(1) We is chosen as a test problem. Through a linear stability analysis, we demonstrate that the introduction of a small amount of (dimensionless) diffusivity, typically of the order 10−3, does not affect the critical eigenmodes of the viscoelastic Orr-Sommerfeld problem appreciably. However, a diffusive term of that magnitude is shown to have a significant influence on the singular eigenmodes of the classical Oldroyd-B model, associated with the continuum spectra. A finite amplitude perturbation is constructed as a linear superposition of the eigenvectors corresponding to the most unstable eigenvalues of the problem. This is superimposed on the steady Poiseuille flow solution to provide the initial conditions for time-dependent simulations. The numerical algorithm involves a fully spectral spatial discretization and a semi-implicit second order integration in time. For the Oldroyd-B fluid, depending on the magnitude of the initial perturbation, numerical instabilities set in at relatively short times while the components of the conformation tensor increase monotonically in magnitude with time. Introduction of a diffusive term into this model is shown to stabilize the calculations remarkably, and for a three-dimensional simulation with Re = 5000 and We = 1, no instabilities were observed even at very large times. The effect of the magnitude of the diffusivity on the stability and the flow dynamics is addressed through a direct comparison of the results with those obtained for the Oldroyd-B model.

Effects of boundary conditions on non-Darcian heat transfer through porous media and experimental comparisons

Abstract: The present work centers around the numerical simulation of forced convective incompressible flow through porous beds. Inertial as well as viscous effects are considered in the momentum equation. The mathematical model for energy transport was based on the two-phase equation model, which does not employ local thermal equilibrium assumption between the fluid and the solid phases. The transport processes for two different types of boundary conditions are studied. The analysis was performed in terms of nondimensional parameters that successfully cast together all the pertinent influencing effects. Comparisons were made between our numerical findings and experimental results. Overall, the comparisons that were made for the constant wall heat flux boundary condition display good agreement.

Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method

Abstract: In this paper, a general class of viscoelastic model is used to investigate numerically the pattern and strength of the secondary flows in rectangular pipes as well as the influence of material parameters on them. To solve the coupled governing equation system, an implicit finite volume method based on the SIMPLEST algorithm, which is applicable for both time-dependent and steady-state flow computations, has been developed and extended for viscoelastic flow computations by applying the decoupled techniques. The main feature of the method is to split the solution process into a series of steps in which the continuity of the flow field is enforced by solving a Poisson's equation for the pressure, and at the end of the steps, both the pressure and velocity fields are made to satisfy one and the same momentum equation. For viscoelastic flow computations, artificial diffusion terms are introduced on both sides of the discretized constitutive equations to improve numerical stability. It is found that there are in total two vortices in each quadrant of the pipe at different aspect ratios (from 1 to 16), and at each ratio the pattern of secondary flows takes the same form for different material parameters, but their strength is very sensitive to the viscoelastic material parameters. Numerical results indicate that the presence of secondary flow strongly depends on the primary flow rate and the elasticity of the fluid, namely, the first and the second normal stress differences as well as their functional departure from the constant multiple viscosity.

Effects of Two-Dimensionality on Pipe Transients Modeling

Abstract: The paper discusses the rapid damping of pressure peaks in a water-hammer phenomenon after the end of a complete valve-closure maneuver. This effect is due to flow characteristics not considered when one-dimensional models are employed. Such an effect is linked to the cross-sectional velocity profiles, and therefore to the intrinsic two-dimensionality of the flow field. Applying a 2-D model, recently proposed in the literature, to expand the limited experimental data available with numerical results, useful information on the evolution of the velocity profiles during a transient has been obtained. Starting from an in-depth inspection of the terms in the momentum equation, an additional term is introduced to model the effects of the flow-field two-dimensionality in a 1-D formulation. Finally, the adequacy of a relationship previously proposed by the writers to evaluate the additional term is specifically showed for fast transients in the field of low-Reynolds-number flows when no cavitation occurs, even if its validity has been proven elsewhere for rather different conditions.

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

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

Parallel finite element simulation of 3d incompressible flows: fluid-structure interactions

Abstract: SUMMARY Massively parallel finite element computations of 3D, unsteady incompressible flows, including those involving fluid-structure interactions, are presented. The computations with time-varying spatial domains are based on the deforming spatial domaidstabilized spacetime (DSD/SST) finite element formulation. The capability to solve 3D problems involving fluid-structure interactions is demonstrated by investigating the dynamics of a flexible cantilevered pipe conveying fluid. Computations of flow past a stationary rectangular wing at Reynolds number 1000, 2500 and lo7 reveal interesting flow patterns. In these computations, at each time step approximately 3 x lo6 non-linear equations are solved to update the flow field. Also, preliminary results are presented for flow past a wing in flapping motion. In this case a specially designed mesh moving scheme is employed to eliminate the need for remeshing. All these computations are canied out on the Amy High Performance Computing Research Center supercomputers CM-200 and CM-5, with major speed-ups compared with traditional supercomputers. The coupled equation systems arising from the finite element discretizations of these large-scale problems are solved iteratively with diagonal preconditioners. In some cases, to reduce the memory requirements even further, these iterations are carried out with a matrix-fiee strategy. The finite element formulations and their parallel implementations assume unstructured meshes.

A Modified Low-Reynolds-Number Turbulence Model Applicable to Recirculating Flow in Pipe Expansion

Abstract: A modified low-Reynolds-number k-e turbulence model is developed in this work. The performance of the proposed model is assessed through testing with fully developed pipe flows and recirculating flow in pipe expansion. Attention is specifically focused on the flow region around the reattachment point. It is shown that the proposed model is capable of correctly predicting the near-wall limiting flow behavior while avoiding occurrence of the singular difficulty near the reattachment point as applying to the recirculating flow in sudden-expansion pipe.

Linear stability analysis of viscoelastic Poiseuille flow using an Arnoldi-based orthogonalization algorithm

Abstract: An algorithm to compute the extremal eigenvalues of a non-Hermitian matrix, based on Arnoldi-orthogonalization, is employed in the linear stability analysis of the viscoelastic Poiseuille flow at high Reynolds numbers. It is shown that this algorithm is both computationally efficient and accurate in reproducing the most unstable modes in the pseudo-spectrally discretized eigenspectrum of the original problem. The Upper Convected Maxwell (UCM), Oldroyd-B and Chilcott-Rallison models are considered for the linear stability analysis of the high Reynolds number viscoelastic Poiseuille flow. Results for the UCM model show a large destabilization of the flow compared to the Newtonian limit, even for low values of flow elasticity, ϵ = We / Re , of the order 10 −3 , realized at high Reynolds numbers for O (1) We. These results agree qualitatively with those reported by Porteus and Denn, although some quantitative differences exist, especially at high values of elasticity. Furthermore, it is shown that the number of spectral modes necessary to obtain converged results increases substantially as the flow elasticity is increased. A comparison of the linear stability characteristics of the Oldroyd-B and the UCM models has revealed that the presence of a non-zero solvent viscosity has a pronounced stabilizing effect on the flow. Further stabilization occurs through the introduction of a finite molecular extensibility in the Chilcott-Rallison model.

Comparison of the Rotating Cylinder and Pipe Flow Tests for Flow-Sensitive Carbon Dioxide Corrosion

Abstract: The effects of various hydrodynamic parameters on the corrosion rate of low-carbon steel in carbon dioxide (CO2) environments were studied. Two different flow geometries, rotating cylinder (RC) and pipe flow, were studied simultaneously in the same electrolyte within a glass loop. Comparisons were made over a wide range of parameters: temperature (T) = 20°C to 80°C, pH = 4 to 6, CO2 partial pressure (PCO2) = 0 bar to 1 bar (0 kPa to 100 kPa), velocity (υ) = 0 m/s to 13 m/s. The hydrodynamic conditions studied covered the range from static to highly turbulent flow. The corrosion process was monitored using polarization resistance, potentiodynamic sweep, and electrochemical impedance methods. The comparison of the two flow geometries was carried out in terms of hydrodynamics, mass transfer, and CO2 corrosion. The measured mass transfer rates agreed well with published correlations for the RC and straight pipe (SP) flow. In the case of CO2 corrosion, it was possible to achieve good agreement between...

Calculation of Numerical Uncertainty Using Richardson Extrapolation: Application to Some Simple Turbulent Flow Calculations

Abstract: Richardson extrapolation has been applied to turbulent pipe flow and turbulent flow past a backward facing step. A commercial CFD code is used for this purpose. It is found that the application of the method is not straightforward and some aspects need careful consideration. Some of the problems are elucidated. The particular code used for the present application employs a hybrid scheme, and it does not give monotonic convergence for all the variables in all regions as the grid is refined. The flow regions and the variables which converge monotonically in these regions should be identified first before the method is applied. When this is done Richardson extrapolation gives good results in calculating the apparent order of the numerical procedure used, as well as obtaining grid independent results with which discretization error bounds can be calculated as measures of numerical uncertainty. Even in cases where it does not work, the method can be used as an error indicator for some obscured user mistakes. This paper also demonstrates several shortcomings of using commercial CFD codes. The present findings should help the users of CFD software in general, to quantify discretization errors in their calculations.

Chemical fingerprints of hydrological compartments and flow paths at La Cuenca, Western Amazonia

Abstract: A forested first-order catchment in western Amazonia was monitored for 2 years to determine the chemical fingerprints of precipitation, throughfall, overland flow, pipe flow, soil water, groundwater, and streamflow. We used five tracers (hydrogen, calcium, magnesium, potassium, and silica) to distinguish “fast” flow paths mainly influenced by the biological subsystem from “slow” flow paths in the geochemical subsystem. The former comprise throughfall, overland flow, and pipe flow and are characterized by a high potassium/silica ratio; the latter are represented by soil water and groundwater, which have a low potassium/silica ratio. Soil water and groundwater differ with respect to calcium and magnesium. The groundwater-controlled streamflow chemistry is strongly modified by contributions from fast flow paths during precipitation events. The high potassium/silica ratio of these flow paths suggests that the storm flow response at La Cuenca is dominated by event water.

The damping of sound by wall turbulent shear layers

Abstract: A frequency‐dependent model is proposed for the eddy viscosity controlling the momentum and thermal wall boundary layers formed when an acoustic wave interacts with a low Mach number turbulent boundary layer whose thickness is much smaller than the acoustic wavelength. This is used to determine the effective acoustic admittance of the boundary layer, and to predict the attenuation of sound reflecting from a plane wall boundary layer, and low‐frequency sound propagating in fully developed turbulent pipe flow. The predictions are shown to compare well with a recent experimental study of acoustic attenuation in pipe flows.

Pipe viscometry of foams

Abstract: This paper describes a method for extracting useful information from small‐scale pipe viscometer measurements of foam rheology. The rheology of a foamed polymer solution at a given temperature, pressure, and quality was determined in pipes of five diameters. The flow curves showed a marked dependence on the diameter of the pipe. The concept of apparent slip could be used to explain the phenomenon. The classical slip correction of Mooney was not applicable, but the method developed by Jastrzebski (based on the previous work of Oldroyd) provided a consistent means of apparent slip correction. The geometric interpretation of the two slip correction methods revealed the possible reason for the difference of their performance. The slip corrected measurements were interpreted in the framework of the volume equalization principle.

Stability of the viscous flow of a fluid through a flexible tube

Abstract: The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Unsteady axial viscoelastic pipe flows

Abstract: The main objective of this work is to examine in detail basic unsteady pipe flows and to investigate any new physical phenomena. We take the viscoelastic upper-convected Maxwell fluid as our non-Newtonian model and consider the flow of such a fluid in pipes of uniform circular cross-section in the following three cases: 1. (a) when the pressure gradient varies exponentially with time; 2. (b) when the pressure gradient is pulsating; 3. (c) a starting flow under a constant pressure gradient. In the first problem we looked separately at the pressure gradient rising exponentially with time and falling exponentially with time, i.e. the pressure gradient is proportional to e±α2τ. The behaviour of the flow field depends to a large extent on β where β2 = α2(1 ± Hα2) with H being the quotient of the Weissenberg and Reynolds numbers. In both cases for small |βη|, η being the radial distance from the axis, the velocity profiles are seen to be parabolic. However, for large |βη| the flows are vastly different. In the case of increasing pressure gradient the flow depicts boundary-layer characteristics while for decreasing pressure gradient the velocity depends on the wall distance. The case of a pulsating pressure gradient is investigated in the second problem. Here the pressure gradient is proportional to cos nτ. Again the flow depends to a large extent on a parameter β (β2 = in − n2H). For small values of |βη| the velocity profile is parabolic. However, it is found that, unlike Newtonian fluids, the velocity distribution for the upper-convected Maxwell fluid is not in phase with the exciting pressure distribution. In the case of large |βη| the solution displays a boundary-layer characteristic and the phase of the motion far from the wall is shifted by half a period. The final problem examines a flow that is initially at rest and then set in motion by a constant pressure gradient. A closed form solution has been obtained with the aid of a Fourier-Bessel series. The variation of the velocity across the pipe has been sketched and comparison made with the classical solution.

A tentative approach to the direct simulation of drag reduction by polymers

Abstract: An efficient technique for drag reduction uses dilute solutions of a few p.p.m. of polymers. A possible reduction in drag of up to 80% is achieved. Several experimental observations have been made which tend to indicate that the polymers modify the turbulence structures within the buffer layer. Flow visualisations have shown that the changes consist of a weakening of the strength of the streamwise vortices. Existing literature reveals no attempts of numerical simulation of this phenomenon. In this paper an approach is pursued by using a constitutive equation which relates the elongation viscosity to the local properties of the flow. According to this model this viscosity is large in zones where the amount of strain rate is greater than the amount of vorticity, and is zero when the vorticity exceeds the strain rate. Simulations have been performed in a “minimal channel” to give good resolution with a limited number of grid points. The accuracy of the method is tested by comparison with the results of other techniques. For simulations with polymers, quantitative comparisons cannot be made, but the results reproduce the qualitative outputs of the experiments. The mean streamwise velocity is modified in the buffer layer; the peak of the streamwise turbulent intensity, in wall units, increases and its maximum moves far from the wall; and the vertical turbulent intensity is largely reduced in the wall region. An interesting outcome from both the simulation and the experiments is that the strength of the longitudinal vortices is reduced when the polymers are present.

Fluid flow control devices

Abstract: A fluid flow control device, comprising a flow surface over which a fluid flows, a flow effect means located on the flow surface and operated by pressure such that the flow effect means improves the flow characteristics of the flow surface, pressure supply means to operate the flow effect means and at least one microelectromechanical system ("MEMS") valve means which controls the flow effect means by controlling the supply of pressure to the flow effect means from the pressure supply means.