Showing papers on "Pipe flow published in 1986"

On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow

Abstract: A series of large-eddy simulations of plane Poiseuille flow are discussed. The subgrid-scale motions are represented by an eddy viscosity related to the flow deformation — the ‘Smagorinsky’ model. The resolution of the computational mesh is varied independently of the value of the coefficient Cs which determines the magnitude of this subgrid eddy viscosity. To ensure that results are from a statistically steady state unrealistic initial conditions are used and sufficient time is allowed for the flow to become independent of the initial conditions. In keeping with previous work it is found that for large Cs the resolved-scale motions are damped out; however, this critical value of Cs is found to depend on the mesh resolution. Only with a fine mesh does the value of Cs previously found to be appropriate for homogeneous turbulence (≈ 0.2) give simulations with sustained resolved-scale motions. The ratio l0/δ of the channel width 2δ to the scale of the ‘Smagorinsky’ mixing length, l0 = CsΔ where Δ is a typical mesh spacing), is found to be the key parameter determining the ‘turbulent’ eddy-viscosity ‘Reynolds number’ of the resolved-scale motions. A fixed value of 10 is regarded as determining the separation of scales into resolved and subgrid. The value of l0 is regarded as a measure of numerical resolution and values of Cs less than about 0.2 correspond to inadequate resolution.

Surfactant systems for drag reduction: physico-chemical properties and rheological behaviour

Abstract: The first part of the work presents an overview of the physical chemistry of surfactants which in aqueous solutions reduce the frictional loss in turbulent pipe flow. It is shown that these surfactants form rodlike micelles above a characteristic concentraionc t. The experimental evidence for rodlike micelles are reviewed and the prerequisites that the surfactant system must fulfill in order to form rodlike micelles are given. It is demonstrated by electrical conductivity measurements that the critical concentration for the formation of spherical micelles shows little temperature dependence, whereasc t increases very rapidly with temperature. The length of the rodlike micelles, as determined by electric birefringence, decreases with rising temperature and increases with rising surfactant concentration. The dynamic processes in these micellar systems at rest and the influence of additives such as electrolytes and short chain alcohols are discussed. In the second part, the rheological behaviour of these surfactant solutions under laminar and turbulent flow conditions are investigated. Viscosity measurements in laminar pipe and Couette flow show the build-up of a shear induced viscoelastic state, SIS, from normal Newtonian fluid flow. A complete alignment of the rodlike micelles in the flow direction in the SIS was verified by flow birefringence. In turbulent pipe flow, drag reduction occurs in these surfactant systems as soon as rodlike micelles are present in the solution. The extent and type of drag reduction, i.e. the shape of the friction factor versus Reynolds number curve, depends directly on the size, number and surface charge of the rodlike micelles. The friction factor curve of each surfactant investigated changes in the same characteristic way as a function of temperature. For each surfactant, independent of concentration, an upper absolute temperature limit,T L, for drag reduction exists which is caused by the micellar dynamics.T L is influenced by the hydrophobic chain length and the counter-ion of the surfactant system. A first attempt is made to explain the drag reduction of surfactants by combining the results of these rheological measurements with the physico-chemical properties of the micellar systems.

Numerical investigation of incompressible flow in grooved channels. Part 1. Stability and self-sustained oscillations

Abstract: Incompressible moderate-Reynolds-number flow in periodically grooved channels is investigated by direct numerical simulation using the spectral element method. For Reynolds numbers less than a critical value Rc the flow is found to approach a stable steady state, comprising an ‘outer’ channel flow, a shear layer at the groove lip, and a weak re-circulating vortex in the groove proper. The linear stability of this flow is then analysed, and it is found that the least stable modes closely resemble Tollmien–Schlichting channel waves, forced by Kelvin–Helmholtz shear-layer instability at the cavity edge. A theory for frequency prediction based on the Orr–Sommerfeld dispersion relation is presented, and verified by variation of the geometric parameters of the problem. The accuracy of the theory, and the fact that it predicts many qualitative features of low-speed groove experiments, suggests that the frequency-selection process in these flows is largely governed by the outer, more stable flow (here a channel), in contrast to most current theories based solely on shear-layer considerations. The instability of the linear mode for R > Rc is shown to result in self-sustained flow oscillations (at frequencies only slightly shifted from the originating linear modes), which again resemble (finite-amplitude) Tollmien-Schlichting modes driven by an unstable groove vortex sheet. Analysis of the amplitude dependence of the oscillations on degree of criticality reveals the transition to oscillatory flow to be a regular Hopf bifurcation.

Developing flow and flow reversal in a vertical channel with asymmetric wall temperatures

Abstract: Etude numerique des effets de la poussee hydrostatique sur les parametres hydrodynamiques et thermiques dans l'ecoulement laminaire, vertical ascendant d'un gaz entre plaques paralleles

Numerical study of sink-flow boundary layers

Abstract: Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 x 10 to the -6th and 3.0 x 10 to the -6th, are presented. The three-dimensional, time-dependent Navier-Stokes equations are solved numerically, using a spectral method, with about one million degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones and Launder (1972) is observed. The two effects of the favorable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of R(theta) for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 x 10 to the -6th, corresponding to a Reynolds number R(theta) of about 330.

Fingering in Hele−Shaw cells

Abstract: A large class of explicit solutions for Hele-Shaw flow with a free surface is presented. The results are valid when surface-tension effects in the plane of the cell are negligible. Most of the solutions given produce fingers, both in channel flow and on a growing air bubble. Possible behaviour of these fingers is described, and a qualitative comparison with published experimental results is made.

The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields

Abstract: Several conditional sampling techniques are applied to a data base generated by large-eddy simulation of turbulent channel flow. It is shown that the bursting process is associated with well-organized horseshoe vortices inclined at about 45 deg. to the wall. These vortical structures are identified by examining the vortex lines of three-dimensional, ensemble averaged vorticity fields. Two distinct horseshoe-shaped vortices corresponding to the sweep and ejection events are detected. These vortices are associated with high Reynolds shear stress and hence make a significant contribution to turbulent energy production. The dependency of the ensemble averaged vortical structures on the detection criteria, and the question of whether this ensemble-averaged structure is an artifact of the ensemble averaging process are examined. The ensemble-averaged pattern of these vortical structures that emerge from the analysis could provide the basis for a hypothetical model of the organized structures of wall-bounded shear flows.

Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement

Abstract: Modulatory heat-transfer enhancement in grooved channels is investigated by direct numerical simulation of the Navier–Stokes and energy equations using the spectral element method. It is shown that oscillatory perturbation of the flow at the frequency of the least-stable mode of the linearized system results in subcritical resonant excitation and associated transport enhancement as the critical Reynolds number of the flow is approached. The Tollmien–Schlichting frequency theory that was presented in Part 1 of this paper is shown to accurately predict the optimal frequency for transport augmentation for small values of the modulatory amplitude, and the effect of the excited travelling-wave channel modes on the resulting temperature distribution is described. The importance of (non-trivial) geometry in the forced response of a flow is discussed, and grooved-channel flow is compared to (straight-channel) plane Poiseuille flow, for which no resonance excitation occurs owing to a zero projection of the forcing inhomogeneity on the dangerous modes of the system. For the particular grooved-channel geometry investigated, resonant oscillatory forcing at modulatory amplitudes as small as 20% of the mean flow results in a doubling of transport as measured by a time, space-averaged Nusselt number.

The dynamics of magma-mixing during flow in volcanic conduits

Abstract: The production of mixed magmas (streaky pumice) during flow in a volcanic conduit has been modelled in the laboratory by studying the flow of two miscible fluids of differing viscosity passing concentrically through a vertical pipe. In the experiments reported in this paper, the outermost fluid is the more viscous, as would be the case when two magmas are simultaneously tapped from a zoned chamber in which silicic magma overlies mafic magma. At a Reynolds number (Re) which is much less than that required for turbulence in isoviscous pipe flow, the interface between two liquids of different viscosity can become unstable. Growth of the instability and mixing proceed when Re, based on the properties of the inner, less viscous fluid (Re i), is greater than approximately 3 if between 10% and 90% of the flowing fluid is composed of the more viscous fluid. Outside this range of flow rate ratios, higher Re i and viscosity ratios are required to ensure mixing. When the viscosity ratio U≤10 the unstable flow takes the form of an asymmetric, sinusoidal wave and at higher viscosity ratios axisymmetric, bead-like waves are the dominant instability. Entrainment across the boundaries of these wavy interfaces results in the production of streaky mixtures of the two liquids. The degree of mixing increases with Re 1, U and distance downstream. Application of experimental results to magmatic situations shows that mixing will be possible in eruptions which tap layers of different viscosity from a stratified chamber. If a volcanic feeder is allowed to become lined by silicic magma before a mafic magma layer is drawn up from the chamber then a mixed pumice (or lava) sequence will ensue. Alternatively, if draw-up occurs when the feeder is still propagating away from the chamber, the slower flowing silicic magma may be overtaken by the faster flowing mafic magma. The advancing conduit will then have mafic or hybrid chilled margins enclosing a silicic interior, i.e. the usual arrangement in composite dykes and sills. Simultaneous tapping of silicic and underlying mafic magmas from a chamber can thus lead to magma mixing and to the emplacement of either mixed pumice sequences or composite intrusions, depending on the history of magma withdrawal and the dynamics of flow in the conduit.

Laboratory Studies of Gas Flow Through a Single Natural Fracture

Abstract: The relationship between the aperture and gas conductivity of a single natural fracture was investigated in the laboratory. Fracture conductivity was evaluated as a function of both the applied fluid pressure gradient and average fracture aperture, the latter ranging from 600 to 200 μm. Fracture apertures were determined independently on the basis of both fracture deformation and fracture volume measurements. Flow generally occurred in the linear and transitional flow regime between linear and fully nonlinear flow. The transition was found to be smooth and well described by an equation of the form: −(dp/dx) = av + bv2, where dp/dx is the pressure gradient and v is the fluid velocity. The linear and nonlinear fracture conductivities were found to be functions of the aperture and surface roughness of the fracture in agreement with existing empirical equations. A new physical model for fracture flow is also formulated based on an analogy to pipe flow.

Flow visualization in parallel-plate ducts with corrugated walls

Abstract: For flow visualization o-cresolphthalein was found to be superior to thymol blue as an electrode-activated pH indicator because its slower reverse reaction results in better colour retention; its poor solubility was overcome by using a 50:50 water-ethanol mixture.The method revealed unknown flow patterns in plate heat-exchanger configurations with the corrugations on opposite walls abutting. The main flow is along the furrows on each wall. The interaction between these criss-crossing flows causes spiralling in the flow along a furrow. At angles between corrugations and the duct axis of at least up to 45°, the furrow flow is reflected only at the sidewalls of the duct, whereas at high angles, e.g. at 80°, there are intermediate ‘reflections’ at the nodes where the crests of opposite walls meet.

Numerical simulation of unsteady, viscous, high-angle-of-attack flows using a partially flux-split algorithm

Abstract: Viscous separated flow surrounding a hemisphere-cylinder body at angles of attack ranging up to 19 deg in transonic flow has been computed using an implicit, approximately-factored, partially flux-split algorithm. The resulting flowfield structures, including the vortical flow on the leeward side of the body and the three-dimensional separation patterns, have been investigated. The computed results show good qualitative and quantitative agreement with experimental data. Furthermore, visualization of the flowfield patterns has yielded insight into the behavior of the three-dimensional separated flow.

Developing Turbulent Flow in a U-Bend of Circular Cross-Section: Measurement and Computation

Abstract: Laser-Doppler measurements of the longitudinal and circumferential velocity components are reported for developing turbulent flow in a strongly curved 180 deg pipe and its downstream tangent. In the bend, the mean longitudinal velocity component changes little after θ = 90 deg, but the circumferential component never achieves a fully-developed state. Similar behavior is observed in the normal stresses, with large levels of flow anisotropy arising everywhere in the bend and downstream tangent. Between θ = 90 deg and X/D = 5, the circumferential velocity profiles display reversals of the secondary flow which are essentially independent of the Reynolds number. Predictions of the flow development are presented based on a “semi-elliptic” truncation of the Reynolds equations in the main part of the flow with the standard k-e effective viscosity model used to approximate the turbulent stress field. In the immediate vicinity of the wall a simpler treatment, PSL, is adopted that allows the inclusion of the very fine mesh needed to resolve the viscous sublayer without excessive computer storage. The calculated behavior displays reasonably good agreement with the measurements in the bend, including the secondary flow reversals. Downstream of the bend, however, the rate of recovery of the flow is too slow, which points to the same weakness in the turbulence model as found in the recovery region of the flow over a backward-facing step.

Laminar compressible flow in a tube

Abstract: A two-dimensional solution for the velocity and pressure distributions in steady, laminar, isothermal flow of an ideal gas in a long tube is obtained as a double perturbation expension in β, the radius to length ratio, and e, the relative pressure drop. It is found that simple approximations estimate the exact flow rate-pressure drop relationship accurately.

Studies of the wall shear stress in a turbulent pulsating pipe flow

Abstract: Measurements are presented of the time variation of the wall shear stress caused by the imposition of a sinusoidal oscillation on a turbulent pipe flow. The amplitude of the oscillation is small enough that a linear response is obtained and the dimensionless frequency, ω+ = ων/u*2, is large compared with that studied by most previous investigators. The most striking feature of the results is a relaxation effect, similar to that observed for flow over a wavy surface, whereby the phase angle characterizing the temporal variation of the wall shear stress undergoes a sharp change over a rather narrow range of ω+. At ω+ larger than the median frequency of the turbulence there appears to be an interaction between the imposed flow oscillation and the turbulence fluctuations in the viscous sublayer, which is not described by present theories of turbulence.

A study of recirculating flow computation using body-fitted coordinates: consistency aspects and mesh skewness

Abstract: A study of the computation of recirculating flows using body-fitted coordinates has been conducted with a numerical algorithm developed previously. Both the consistent treatment of the continuity equation and the effects of the grid skewness on the calculated flow field have been investigated. A more consilient method has been developed that formally satisfies the conservation laws more closely, allowing the mass residual to be driven to lower levels on highly irregular grids. The new method can also be more effective in numerically damping out disturbances in the flow field as the solution progresses. Since the computed flow fields arc found to be quite insensitive to the final level of the residuals, the residuals are not a good indicator of the level of convergence; the kinetic energy of the flow field serves as a useful alternative. It is found that the effects of the excessive local mesh skewness on the overall ac~ curacy of the calculated solution are quite tolerable. This finding demonstrates the d...

On transition of the pulsatile pipe flow

Abstract: Transition in a pipe flow with a superimposed sinusoidal modulation has been studied in a straight circular water pipe using laser-Doppler anemometer (LDA) techniques. This study has determined the stability–transition boundary in the three-dimensional parameter space defined by the mean and modulation Reynolds numbers Rem, Remω and the frequency parameter λ. Furthermore, it documents the mean passage frequency Fp of ‘turbulent plugs’ as functions of Rem’ Remω and λ. This study also delineates the conditions when plugs occur randomly in time (as in the steady flow) or phase-locked with the excitation. The periodic flow requires a new definition of the transitional Reynolds number Rer, identified on the basis of the rate of change of Fp with Rem. The extent of increase or decrease in Rer from the corresponding steady flow value depends on λ and Remω. At any Rem and Remω, maximum stabilization occurs at λ ≈ 5. With increasing Remω, the ‘stabilization bandwidth’ of modulation frequencies increases and then abruptly decreases after levelling off. The maximum stabilization bandwidth depends strongly on Rem, decreasing with increasing Rem. Previously reported observations of turbulence during deceleration, followed by a relaminarization during acceleration, can be explained in terms of a new phenomenon: namely, periodic modulation produces longitudinally periodic cells of turbulent fluid ‘plugs’ which differ in structural details from ‘puffs’ or ‘slugs’ in steady transitional pipe flows and are called patches. The length of a patch could be increased continuously from zero to the entire pipe length by increasing Rem. This tends to question the concept that all turbulent plugs (and even the fully-turbulent pipe flow) consists of many identical elementary plugs as basic ‘building blocks’.

A Model for Adhesive Failure of Viscoelastic Fluids During Flow

Abstract: Slip of a polymer as it flows through a conduit has been modeled by applying the concept of junctions at the conduit/polymer interface as well as in the bulk of the polymer fluid. This model has been combined with a kinetic equation describing a reaction, to which activation rate theory applies, between bonded and free macromolecules at the interface. The result is a prediction of the temperature dependence of wall slip velocities. The prediction was found to be consistent with published data for an ethylene‐propylene copolymer. It was also found that at constant temperature a power‐law relation provides a good description of the dependence of wall slip velocity on wall shear stress.

Aspects of the equilibrium puff in transitional pipe flow

Abstract: In the transitional pipe flow-visualization studies presently undertaken to investigate the self-sustenance mechanism of a turbulent equilibrium puff, the upstream laminar fluid continuously enters the relatively more slowly moving turbulent puff around the pipe center. The passage of this high speed laminar plug flow past the slower fluid residing near the wall at the upstream interface leads to the shedding of a train of three-dimensional, wake-like vortices near the wall. The prominent feature of the decay region is a series of longitudinal vortices that appear to be undergoing stretching.

Some observations on the evolution of shear layer instabilities in laminar flow through axisymmetric sudden expansions

Abstract: The laminar flow in an axisymmetric sudden expansion has been studied experimentally. Using a nominal diameter ratio of 0.5 and well‐defined inlet velocity profile conditions, data are presented that, for the first time, demonstrate clearly that the onset of shear layer instabilities is dependent on the inlet velocity profile. The reattachment length of the shear layer (normalized by the expansion step height) as a function of the inlet Reynolds number is linear with slopes of 0.096 and 0.068 for upstream velocity profile conditions of Poiseuille and nominal plug flow, respectively.

New concepts in molecular gas flow

Abstract: This paper will outline several new concepts dealing with molecular flow calculations. One is a simple equation for calculating the ‘‘Clausing’’ transmission probability through circular tubes. A technique will also be demonstrated for developing similar expressions for the short‐tube probability of other tube cross sections. Tube conductance will then be compared to transmission probabilities in terms of exit losses, entrance losses, and changes from random gas flow to fully developed tube flow. A format will be presented which assists in converting between short‐tube conductance and probabilities. Finally, a correction term is added to Oatley’s probability combining equation to compensate for ‘‘beaming’’ effects. This term reduces the normal maximum error for circular tube calculations from 3.7% to 0.28%.

COMPARISON of FRICTION FACTOR EQUATIONS FOR NON‐NEWTONIAN FLUIDS IN PIPE FLOW1

Abstract: The pressure drop, due to friction, in pipe flow of non-Newtonian fluids can be estimated if the friction factor is known. For laminar flow, the friction factor for power law, Bingham plastic and Herschel-Bulkely fluids can be obtained from a single theoretical relationship. However, a number of different relationships have been developed for turbulent flow. This paper presents a summary and comparison of these relationships. Friction factor predictions were found to differ significantly depending on the flow behavior index, Reynolds number and Hedstrom number. Generally, the spread of predictions increased as the fluid deviated from Newtonian behavior. Significant errors can be made when using relationships based on fluids without a yield stress to predict friction factors for fluids having a yield stress.

Theoretical investigation of laser-sustained argon plasmas

Abstract: A theoretical model has been developed for laser‐sustained argon plasmas in a forced convective axisymmetric pipe flow. The two‐dimensional model based on Navier–Stokes equations was solved using a finite difference algorithm, and included geometric optics, temperature‐dependent thermodynamic, transport, and optical properties, as well as radiation‐induced thermal conductivity. The results showed good agreement with existing experimental data on temperature distribution, shape, and size of the plasma. The calculated velocity distribution revealed the complexity of the flow field and indicated that the constant axial mass flux (product of axial velocity and density) assumption adopted by existing one‐dimensional and semi‐two‐dimensional models is not adequate. The radiation transfer was found to have a significant influence on the predicted temperature distribution and peak temperature of laser‐sustained plasmas.