Showing papers on "Open-channel flow published in 1986"

Open‐channel Flow Measurements with a Laser Doppler Anemometer

Abstract: A powerful two‐color Laser Doppler Anemometer (LDA) system, with direct digital signal processing has been used to measure accurately the longitudinal and vertical velocity components in two‐dimensional, fully‐developed open‐channel flow over smooth beds. The law of the wall and the velocity defect law were re‐examined because the log‐law has been often applied to open channels without detailed verification. It was found that the log‐law can be applied strictly only to the near‐wall region. In this region, the von K´rm´n constant κ and the integral constant A are truly universal, having values of κ=0.412 and A=5.29 irrespective of the Reynolds and Froude number. As the Reynolds number becomes larger, the deviation from the log‐law cannot be neglected in the outer region. This deviation can be expressed well by Coles' wake function which involves a Reynolds‐number dependent parameter Π. The distributions of eddy viscosity and mixing length were evaluated and found to depend on Π. All the data including the...

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.

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.

Separated two‐phase flow and basaltic eruptions

Abstract: Fluid dynamical models of volcanic eruptions are usually made in the homogeneous approximation where gas and liquid are constrained to move at the same velocity. Basaltic eruptions exhibit the characteristics of separated flows, including transitions in their flow regime, from bubbly to slug flow in Strombolian eruptions and from bubbly to annular flow in Hawaiian ones. These regimes can be characterized by a parameter called the melt superficial velocity, or volume flux per unit cross section, which takes values between 10−3 and 10−2 m/s for bubbly and slug flow, and about 1 m/s for annular flow. We use two-phase flow equations to determine under which conditions the homogeneous approximation is not valid. In the bubbly regime, in which many bubbles rise through the moving liquid, there are large differences between the two-phase and homogeneous models, especially in the predictions of gas content and pressure. The homogeneous model is valid for viscous lavas such as dacites because viscosity impedes bubble motion. It is not valid for basaltic lavas if bubble sizes are greater than 1 cm, which is the case. Accordingly, basaltic eruptions should be characterized by lower gas contents and lower values of the exit pressure, and they rarely erupt in the mist and froth regimes, which are a feature of more viscous lavas. The two-phase flow framework allows for the treatment of different bubble populations, including vesicles due to exsolution by pressure release in the volcanic conduit and bubbles from the magma chamber. This yields information on poorly constrained parameters including the effective friction coefficient for the conduit, gas content, and bubble size in the chamber. We suggest that the observed flow transitions record changes in the amount and size of gas bubbles in the magma chamber at the conduit entry.

Effects of Suspended Sediment on the Open-Channel Velocity Distribution

Abstract: Experiments were performed in which suspended sediment concentration in open-channel bounded shear flow was varied systematically while flow depth, slope, and discharge were held essentially constant. The effect of variation in suspended sediment concentration on velocity profile characteristics was investigated. The experiments showed that the Karman coefficient was independent of changes in suspended sediment concentration, while the Coles wake strength coefficient was very sensitive to such changes. The thickness of the logarithmic part of the velocity profile decreased as sediment concentration increased. The logarithmic parts of velocity profiles in sediment-suspending flow were shifted downward relative to control profiles in comparable clear-water flows.

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.

Transonic, turbulent boundary-layer separation generated on an axisymmetric flow model

Abstract: Experimental data describing the transonic, turbulent, separated flow generated by an axisymmetric flow model are presented. The model consisted of a circular-arc bump affixed to a straight, circular cylinder aligned with the flow direction. Measurements of the mean velocity, turbulence intensity, and Reynolds shear-stress profiles were made in the separated flow. These data revealed dramatic changes in the shear-stress levels as the flow passed through the interaction to reattachment. Behavior of the turbulence reaction to the imposed pressure gradients was examined in terms of the mixing length and the excursions of the turbulence from equilibrium.

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.

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.

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.

Turbulent spots in plane Poiseuille flow-flow visualization

Abstract: The structure and spreading of turbulent spots in plane Poiseuille flow were studied through flow visualization, in the Reynolds number range 1100 to 2200 (based on centerline velocity and channel half‐height). The spot spreading half‐angle varied from 6° for the lowest Re to 12° for the highest Re. The propagation velocity of the rear laminar–turbulent interface was slightly above 50% of the centerline velocity. Spotsplitting, as reported in earlier studies, seems to occur only at low Re.

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...

Oscillating turbulent boundary layer with suspended sediments

Abstract: A dynamic boundary layer model with simultaneous interactions between constant, oscillatory, and turbulent flow; suspended sediments; and erosion is developed. The model appears to be verified as well as the existing data permits. In purely oscillatory flow most of the state variables appear to be associated with a turbulent kinetic energy maximum developing near the bottom and phase angle π/2 and propagating upward thereafter. The maximum horizontal sediment flux is approximately proportional to the third power of the maximum turbulent stress. A channel flow with constant pressure gradient may be strongly reduced by the presence of waves. The waves may also increase the suspended sediment concentration significantly.

Turbulence Modeling of Flood Plain Flows

Abstract: A numerical model capable of predicting flow characteristics in a compound channel is described. The model solves the continuity and momentum equations along with the transport equations of kinetic energy of turbulence and the dissipation rate. Closure is achieved with the aid of algebraic relations for turbulence stresses. The model is capable of treating compound channels formed by regular geometrical sections of main channel and flood plain segments. The width of the main channel, the width of the total section, the depth of flow in flood plain, the total depth, channel slope and boundary roughness of main channel section and flood plain section can all be varied. The model predictions of total flow rate, shear stress distributions around the wetted perimeter, and the percentage of flow and shear force carried by the different sections were compared with published experimental data. Reasonable agreement between data and predictions was obtained.

SCRAPED SURFACE HEAT EXCHANGERS.: A literature survey of flow patterns, mixing effects, residence time distribution, heat transfer and power requirements.

Abstract: In this literature survey flow patterns, mixing effects, heat transfer and power required for rotation in scraped surface heat exchangers (SSHE) are thoroughly discussed, with the emphasis on assumptions and results, while the principal design of different SSHEs are only briefly discussed. The flow patterns control the desired radial mixing and the undesired axial mixing. the flow in a SSHE can be regarded as the sum of an axial flow and a rotational flow. the axial flow is laminar and the rotational flow is laminar or vortical. With laminar flow the radial mixing is poor, which causes poor heat transfer and allows the axial flow profile to control the residence time distribution. the precise onset of vortical flow in a SSHE is hard to predict. the vortical flow makes the radial mixing very efficient, giving good heat transfer and perhaps plug flow behavior. However, vortical flow also causes axial mixing which reduces the apparent heat transfer coefficient and increases the residence time distribution. The power required to rotate the shaft and blades is mainly determined by the design of the blades.

Flow and Bed Profile in Meandering Sand-Silt Rivers

Abstract: Mathematical models for defining three-dimensional flow and bed topography in sinuous channels with suspendable bed material are presented. It is shown theoretically that the secondary flow in sinuous channels shows a reduction in its magnitude below that of a uniformly-curved channel, and also displays a phase-lag relative to the channel plan-form. The model for bed topography is derived by considering the sediment balance for bed load and suspended load, the transport rate and direction, all of which are governed by the three-dimensional flow. A laboratory test supports the model. The present study has made it possible to predict the large-scale bed topography of meandering sand-silt rivers, including such features as the magnitude and the location of local scour and point-bar deposits.

Structure of 3‐D Flow in Rectangular Open Channels

Abstract: A parameter estimation method has been developed for a system of three‐dimensional mathematical model of flow in open channels, which does not require (primary flow) velocity data. It has broadened the applicability and effectiveness of the model in scientific investigations into the complex interaction among the primary and secondary flows, shear stress distribution, channel characteristics (roughness, slope, and geometry), and other related variables governing all transport processes in open channels. The method was applied to a study of 3‐D structure of flow in rectangular open channels. The interaction among the primary and secondary flows and the shear stress distribution was investigated under various values of Manning's n, width‐to‐depth ratio and slope of the channels. The result has answered quantitatively many questions which arise in open channel hydraulics.

High-speed separation of large (> 1. mu. m) particles by steric field-flow fractionation

Abstract: It is postulated, based on known elements of the steric field-flow fractionation mechanism, that separation speed can be increased without resolution loss by increasing the channel flow rate and simultaneously increasing the sedimentation field strength. The validity of this approach was confirmed in a general way by two series of runs, one with increasing flow at constant field strength (7 g) and one with increasing field strength at constant flow (21 mL/min). The limits of this approach were searched for (but not found) in a special high-flow set of experiments run at 38 mL/min. With a field strength of 343 g, seven different sizes of latex particles (2-45 ..mu..m diameter) were base-line resolved in about 3.5 min from the start-up of the centrifuge and 3.0 min from the initiation of flow.

The entrainment of high-viscosity magma into low-viscosity magma in eruption conduits

Abstract: We report experiments on the flow of two fluids of contrasting viscosity through a pipe in which low-viscosity fluid occupies the center of the pipe. The volume flux of the low-viscosity fluid in the pipe increased during an experiment but did not reach 100% in most cases. The transition from high- to low-viscosity-dominated outflow involved a drop in pressure gradient and an increase in flow rate due to reduced viscous resistance in the pipe. Initially, the central flow was thin and parallel-sided, but as its diameter increased the flow became unstable. A sequence of instabilities was observed during the course of each experiment, both in time and as a function of height in the pipe. In the most commonly observed instability the central flow adopted a helical geometry. The transition from parallel-sided to unstable flow first appeared at the top of the pipe and propagated downwards against the flow. Axisymmetric instabilities originating at the pipe entrance were also observed. All forms of instability exhibited entrainment of viscous fluid into the faster moving central flow. Entrainment was extensive early in the existence of the central flow, but later on the volume flux of lower-viscosity fluid in the central flow rose more rapidly than the rate of entrainment and the proportion of lower-viscosity fluid increased with time. These compositional changes determined the viscosity of the central flow which was found to control its diameter and velocity. In banded pumice deposits, silicic pumice without mafic component is commonly erupted alongside banded pumice blocks. We infer that banded pumice may correspond to the central flow in our experiments, i. e., that viscous magma has been incorporated into less viscous melt, and that pure acid pumice is derived from the outer flow. Changes in eruption style may be caused by variations in pressure gradient and flow rate due to changes in the viscosity of the melt in the conduit. Varied mafic/silicic proportions and degree of mixing in magmatic associations are controlled by the bulk volume erupted, discharge rate, initial temperature difference and aspect ratio of the conduit.

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.