Showing papers on "Pipe flow published in 1996"

Two-layer approximate boundary conditions for large-eddy simulations

Abstract: A new method to model the effect of the solid boundaries on the rest of the flowfield in large-eddy simulations is proposed The filtered Navier-Stokes equations are solved up to the first computational point From there to the wall, a simplified set of equations is solved, and an estimate of the instantaneous wall shear stress required to impose boundary conditions is obtained Computations performed for the plane channel, square duct, and the rotating channel flow cases gave improved results compared with existing models The additional computing time required by the model is on the order of 10-15% of the overall computing time The mean flow quantities and low-order statistics, which are of primary interest in engineering calculations, are in very good agreement with the reference data available in the literature

Topology of fine-scale motions in turbulent channel flow

Abstract: An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

Boundary conditions for the lattice Boltzmann method

Abstract: When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints for density and momentum along the boundaries of the lattice. These constraints uniquely determine the three‐dimensional (3‐D) mass distribution for boundary nodes only when the number of external (inward‐pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3‐D body‐centered‐cubic lattices are presented for Poiseuille flow, porous‐plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two‐dimensional (2‐D) Poiseuille and Couette flows persists even when the mean free path between collisions is large, but that of the 3‐D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3‐D low‐Reynolds‐number flow.

Chemical engineering fluid mechanics

Abstract: Basic concepts dimensional analysis and scale-up fluid properties in perspective fluid statics conservation principles pipe flow internal flow applications pumps and compressors compressible flows flow measurement and control externalflows fluid-solid separations by free settling flow in porous media fluidization and sedimentation two-phase flow appendices.

The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a Straight Cooling Channel

Abstract: The local aerodynamic and heat transfer performance were measured in a rib-roughened square duct as a function of the rib pitch to height ratio. The blockage ratio of these square obstacles was 10 or 20 percent depending on whether they were placed on one single (1s) or on two opposite walls (2s). The Reynolds number, based on the channel mean velocity and hydraulic diameter, was fixed at 30,000. The aerodynamic description of the flow field was based on local pressure distributions along the ribbed and adjacent smooth walls as well as on two-dimensional LDV explorations in the channel symmetry plane and in two planes parallel to the ribbed wall(s). Local heat transfer distributions were obtained on the floor, between the ribs, and on the adjacent smooth side wall. Averaged parameters, such as friction factor and averaged heat transfer enhancement factor, were calculated from the local results and compared to correlations given in literature. This contribution showed that simple correlations derived from the law of the wall similarity and from the Reynolds analogy could not be applied for the present rib height-to-channel hydraulic diameter ratio (e/D h = 0.1). The strong secondary flows resulted in a three-dimensional flow field with high gradients in the local heat transfer distributions on the smooth side walls.

Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows

Abstract: The motion of dense particles in a turbulent gas flow has been studied by means of numerical simulations. The single‐phase turbulent pipe flow was modelled using Direct Numerical Simulation and Large Eddy Simulation. At tube Reynolds numbers of 5300, 18300 and 42000 particles with dimensionless relaxation times ranging from 5 to 104 were released. Assuming the system to be dilute, the characteristics of particle dispersion, deposition and concentration distribution were studied under various conditions of gravity and lift. This study shows that for small particles the deposition process is governed by the properties of the near‐wall layer where the wall‐normal turbulence intensity is low, while for large inertial particles turbulent dispersion determines the chances for particles to hit the tube wall. The motion of the latter particles appears to scale properly with the Lagrangian integral time scale of the turbulence. Furthermore we demonstrated the segregation of particles towards the wall, as a result of particle‐turbulence interaction.

Electrorheological Dampers, Part I: Analysis and Design

Abstract: Electrorheological (ER) materials are suspensions of specialized, micron-sized particles in nonconducting oils. When electric fields are applied to ER materials, they exhibit dramatic changes (within milli-seconds) in material properties. Pre-yield, yielding, and post-yield mechanisms are all influenced by the electric field. Namely, an applied electric field dramatically increases the stiffness and energy dissipation properties of these materials. A previously known cubic equation which describes the flow of fluids with a yield stress through a rectangular duct can be applied to annular flow, provided that certain conditions on the material properties are satisfied. An analytic solution and a uniform approximation to the solution, for the rectangular duct Poiseuille flow case is presented. A numerical method is required to solve the flow in annular geometries. The approximation for rectangular ducts is extended to deal with the annular duct case.

Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step

Abstract: A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds number Re = 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up to Re = 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 [les ] Re [les ] 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.

A numerical simulation of unsteady flow in a two-dimensional collapsible channel

Abstract: The collapse of a compressed elastic tube conveying a flow occurs in several physiological applications and has become a problem of considerable interest. Laboratory experiments on a finite length of collapsible tube reveal a rich variety of self-excited oscillations, indicating that the system is a complex, nonlinear dynamical system. Following our previous study on steady flow in a two-dimensional model of the collapsible tube problem (Luo & Pedley 1995), we here investigate the instability of the steady solution, and details of the resulting oscillations when it is unstable, by studying the time-dependent problem. For this purpose, we have developed a time-dependent simulation of the coupled flow – membrane problem, using the Spine method to treat the moving boundary and a second-order time integration scheme with variable time increments.It is found that the steady solutions become unstable as tension falls below a certain value, say Tu, which decreases as the Reynolds number increases. As a consequence, steady flow gives way to self-excited oscillations, which become increasingly complicated as tension is decreased from Tu. A sequence of bifurcations going through regular oscillations to irregular oscillations is found, showing some interesting dynamic features similar to those observed in experiments. In addition, vorticity waves are found downstream of the elastic section, with associated recirculating eddies which sometimes split into two. These are similar to the vorticity waves found previously for flow past prescribed, time-dependent indentations. It is speculated that the mechanism of the oscillation is crucially dependent on the details of energy dissipation and flow separation at the indentation.As tension is reduced even further, the membrane is sucked underneath the downstream rigid wall and, although this causes the numerical scheme to break down, it in fact agrees with another experimental observation for flow in thin tubes.

An experimental study of particle migration in pipe flow of viscoelastic fluids

Abstract: This paper reports experiments on particle migration in viscoelastic fluids used in hydraulic fracturing. It is found that particle migration in such fluids is controlled by the elastic properties of the suspending fluid and the shear rate gradient. In fluids with low but measurable normal stresses and dominant shear‐thinning properties, particles migrate to regions of lower shear rate. Migration is fast initially, but slows down rapidly over a short distance. For these fluids the bulk migration velocity correlates with the product of the Weissenberg number and the mean shear rate gradient. In contrast, highly elastic fluids with relaxation times well above one second and shear‐thickening properties at low shear rates, flow with a central plug region or slip at the wall, producing little or no migration.

Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium

Abstract: In this paper analytical solutions for the steady fully developed laminar fluid flow in the parallel-plate and cylindrical channels partially filled with a porous medium and partially with a clear fluid are presented. The Brinkman-extended Darcy equation is utilized to model the flow in a porous region. The solutions account for the boundary effects and for the stress jump boundary condition at the interface recently suggested by Ochoa-Tapia and Whitaker. The dependence of the velocity on the Darcy number and on the adjustable coefficient in the stress jump boundary condition is investigated. It is shown that accounting for a jump in the shear stress at the interface essentially influences velocity profiles.

Measurement of fully-developed turbulent pipe flow with digital particle image velocimetry

Abstract: A new and unique high-resolution image acquisition system for digital particle image velocimetry (DPIV) in turbulent flows is used for the measurement of fully-developed turbulent pipe flow at a Reynolds number of 5300. The flow conditions of the pipe flow match those of a direct numerical simulation (DNS) and of measurements with conventional (viz., photographic) PIV and with laser-Doppler velocimetry (LDV). This experiment allows a direct and detailed comparison of the conventional and digital implementations of the PIV method for a non-trivial unsteady flow. The results for the turbulence statistics and power spectra show that the level of accuracy for DPIV is comparable to that of conventional PIV, despite a considerable difference in the interrogation pixel resolution, i.e. 32 × 32 (DPIV) versus 256 × 256 (PIV). This result is in agreement with an earlier analytical prediction for the measurement accuracy. One of the advantages of DPIV over conventional PIV is that the interrogation of the DPIV images takes only a fraction of the time needed for the interrogation of the PIV photographs.

On the stability of an axisymmetric rotating flow in a pipe

Abstract: The linear stability of an inviscid, axisymmetric and rotating columnar flow in a finite length pipe is studied. A well posed model of the unsteady motion of swirling flows with compatible boundary conditions that may reflect the physical situation is formulated. A linearized set of equations for the development of infinitesimal axially‐symmetric disturbances imposed on a base rotating columnar flow is derived. Then, a general mode of axisymmetric disturbances, that is not limited to the axial‐Fourier mode, is introduced and an eigenvalue problem is obtained. Benjamin’s critical state concept is extended to the case of a rotating flow in a finite length pipe. It is found that a neutral mode of disturbance exists at the critical state. In the case of a solid body rotating flow with a uniform axial velocity component, analytical solution of the eigenvalue problem is found. It is demonstrated that the flow changes its stability characteristics as the swirl changes around the critical level. When the flow is ...

Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows

Abstract: A novel method is proposed that allows accurate estimates of the local wall shear stress from near-wall mean velocity data in fully developed pipe and channel flows DNS databases are used to demonstrate the accuracy of the method and to provide the reliability requirements on the experimental data To demonstrate the applicability of the method, near-wall LDA measurements in turbulent pipe and channel flows were performed The estimated wall shear stress is shown to be accurate to within 1% Streamwise mean velocity and turbulence intensity profiles normalized with the wall friction velocity at several Reynolds numbers are presented

Local Heat Transfer in Rotating Smooth and Ribbed Two-Pass Square Channels With Three Channel Orientations

Abstract: This paper presents experimental heat transfer results in a two-pass square channel with smooth and ribbed surfaces. The ribs are placed in a staggered half-V fashion with the rotation orthogonal to the channel axis. The channel orientation varies with respect to the rotation plane. A change in the channel orientation about the rotating frame causes a change in the secondary flow structure and associated flow and turbulence distribution. Consequently, the heat transfer coefficient from the individual surfaces of the two-pass square channel changes. The effects of rotation number on local Nusselt number ratio distributions are presented. Heat transfer coefficients with ribbed surfaces show different characteristics in rotation number dependency from those with smooth surfaces. Results show that staggered half-V ribs mostly have higher heat transfer coefficients than those with 90 and 60 deg continuous ribs. 16 refs., 10 figs.

Flow of a yield stress fluid in a long domain. Application to flow on an inclined plane

Abstract: Complex isochoric flows in a domain of space that is long compared to its width are studied for a viscoplastic and perfectly rigid Herschel–Bulkley model. It is argued here that no continuous yield surface can exist along the flow direction in these either confined or open channel flows. A similarity analysis is performed that shows that normal stresses cannot be neglected. For open channel flows the influence of normal stresses can be estimated through comparison of the yield stress value to the hydrostatic pressure value at the channel bed. Generalized Barre de Saint Venant one‐dimensional equations are obtained. The influence of the yield stress value on wave velocity and on gradually varied flows and critical depth has been deduced.

Pipe flow of a thixotropic liquid

Abstract: Detailed measurements of mean velocity and velocity fluctuation levels (axial, tangential and radial) have been carried out using a laser Doppler anemometer for fully developed pipe flow of an aqueous solution of Laponite, a synthetic clay. The equilibrium rheological structure of this thixotropic liquid is well characterised by the Herschel-Bulkley model. Velocity profiles calculated for a Herschel-Bulkley fluid prove to be a very accurate representation of the measurements for laminar flow at reynolds numbers below about 1500. The measured profiles develop an unexplained asymmetry for higher Reynolds numbers until the flow undergoes transition to turbulence. The fluid is drag reducing under turbulent flow conditions with relative levels of tangential and radial turbulence intensity suppressed in comparison with water whilst the axial turbulence intensity is little different. Under all flow conditions it is evident that the fluid rheology is far from structural equilibrium, with values for the apparent yield stress and effective viscosity determined from near-wall velocity measurements considerably below those obtained from a rheometer.

Origin of high kurtosis levels in the viscous sublayer : direct numerical simulation and experiment

Abstract: In the literature, a major discrepancy is reported between the value of the kurtosis for the normal velocity fluctuations close to the wall as found from direct numerical simulations and obtained from experiments. The origin of these high kurtosis levels is analyzed with help of a direct numerical simulation of a turbulent channel flow. In addition, a detailed analysis of LDV measurements in the near‐wall region of a turbulent pipe flow is made with the results of the DNS as a starting point. In both data sets, i.e. DNS and experiments, similar velocity events were found that contribute to the high kurtosis level. The dynamics of these events can be associated with the regeneration process of streamwise vortices as described by Brooke and Hanratty [Phys. Fluids A 5, 1011 (1993)]. Based on this evidence, we conclude that the high kurtosis is of a truly physical nature. It is caused by very strong events that appear only in the near‐wall region and that are rare in time as well as in space. The very rare ap...

Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence

Abstract: A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds-number-dependency of its peak value. The following canonical flow geometries are considered: an incompressible turbulent boundary layer under zero pressure gradient, a fully developed two-dimensional channel and a cylindrical pipe flow. Data were collected from 47 independent experimental and numerical studies, which cover a Reynolds number range of Rθ=U∞θ/v=300−20,920 for the boundary layer with θ the momentum thickness and R+=u*R/v=100-4,300 for the internal flows with R the pipe radius or the channel half-width. It is found that the peak value of the rms-value normalised by the friction velocity, u*, is within statistical errors independent of the Reynolds number. The most probable value for this parameter was found to be 2.71±0.14 and 2.70±0.09 for the case of a boundary layer and an internal flow, respectively. The present survey also includes some data of the streamwise velocity fluctuations measured over a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and this property of the normalised peak value may for instance be exploited to estimate the wall shear stress from the streamwise velocity fluctuations. We also consider the skewness of the streamwise velocity fluctuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the equations of the third-order moment of velocity fluctuations. These results for the peak value of the rms of the streamwise velocity fluctuations and also the coincidence of this peak with the zero value of the third moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furthermore, these results can be also used as a requirement which turbulence models for the second and triple velocity correlations should satisfy.

On the instability of pipe Poiseuille flow

Abstract: Stability of the flow of incompressible viscous fluid in a circular pipe is studied numerically. A perturbation consisting of finite‐amplitude two‐dimensional and infinitesimal three‐dimensional parts is imposed on the basic flow. The temporal evolution of the perturbation is analyzed by direct numerical calculation of the Navier–Stokes equations. The two‐dimensional disturbances are independent of the streamwise coordinate and initially take the form of streamwise rolls. It is shown that the nonlinear development of two‐dimensional perturbations results in substantial spanwise modulation of the streamwise velocity component manifesting itself as a formation of streaks and the occurrence of inflection points. The modulated mean flow is found to be highly unstable to the three‐dimensional perturbations which are localized spatially near these points. An instability mechanism that includes the modulation of the flow by growing two‐dimensional disturbances and the inflectional instability of the modulated flow to three‐dimensional perturbations is proposed.

Improving curved subsonic diffuser performance with vortex generators

Abstract: The objective of this research was to use vortex generators to reduce total pressure distortion (ie, total pressure nonuniformity) and improve total pressure recovery within a curved subsonic diffuser In this study more than 20 configurations of both co- and counter-rotating arrays of vortex generators were tested in a diffusing S duct Surface static pressure, surface flow visualization, and exit plane total pressure and transverse velocity data were acquired The aerodynamic performance of each configuration was assessed by calculating total pressure recovery and spatial distortion elements The best configuration tested reduced distortion by more than 50% while improving total pressure recovery by 05% The results indicate that the mechanism responsible for improved aerodynamic performance is not boundary-layer re-energization from shed axial vortices but rather the suppression of detrimental secondary flows by redirecting the flow

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 af , the gravitational to frictional pressure gradient ratio R gf and the inflow-directional to accelerational pressure gradient ratio R 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 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 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 the fluid properties and inflow rate; whereas R 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. For laminar flow, wall friction increases due to inflow but decreases due to outflow. For turbulent flow, inflow reduces the wall friction, while outflow increases the wall friction. New wall friction factor correlations for wellbore flows have been developed, which can be applied to determine the wall friction shear and the frictional pressure drop for either inflow (production well) or outflow (injection well) and for either laminar or turbulent flow regime. Calculation results show that the accelerational pressure drop may or may not be important compared to the frictional component depending on the specific pipe geometry, fluid properties and flow conditions. 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.