Showing papers on "Open-channel flow published in 1979"
TL;DR: In this article, a general approach for the estimation of the Darcy-Weisbach friction factor is presented and independent field data indicates that the method can be successfully applied to predict the resistance to uniform flow in gravel-bed rivers.
Abstract: The resistance to uniform flow in straight gravel-bed rivers is basically dependent on the flow geometry, the cross-sectional variation in roughness heights, and the roughness height of the graded gravel bed sediment. The effect of these factors on the resistance to flow is evaluated and a general approach for the estimation of the Darcy-Weisbach friction factor is presented. Independent field data indicates that the method can be successfully applied to predict the resistance to uniform flow in gravel-bed rivers.
423 citations
TL;DR: In this paper, measurements of the three fluctuating components of the velocity and two components of wall shear stress fluctuations have been made in a fully developed turbulent channel flow at Re=7700 using hot-film probes.
Abstract: Measurements of the three fluctuating components of the velocity and of the two components of the wall shear stress fluctuations have been made in a fully developed turbulent channel flow at Re=7700 using hot‐film probes. These measurements include rms values, skewness and flatness factors, and probability density functions. Although the wall region is emphasized here, information for the whole channel half‐width is also given.
330 citations
TL;DR: In this paper, the authors describe the application of a finite-difference calculation procedure to the problem of simulating the three-dimensional, turbulent flow in a strongly curved, open, 180° bend with straight inlet and outlet reaches.
Abstract: The paper describes the application of a finite-difference calculation procedure to the problem of simulating the three-dimensional, turbulent flow in a strongly curved, open, 180° bend with straight inlet and outlet reaches. The configuration can be considered to represent an element of a model meander, and the work presented here forms an important stage in efforts to simulate the flow in successive reverse-curvature bends. No restrictions other than the absence of flow separation and hydraulic jumps are imposed. Full account is taken of non-linear fluid-inertia and of turbulent diffusion terms. Effects of turbulence are represented by an eddy viscosity related to two parameters— the turbulent kinetic energy k and its rate of dissipation ϵ\N— for which related differential transport equations are solved. Predictions are presented for the transverse surface slope and velocity field in a configuration experimentally examined by Rozovskii. Agreement between predictions and experimental data is judged to be satisfactory on all major flow phenomena.
190 citations
TL;DR: In this paper, the equation of motion for the two phase flow within a bubble column, operated within the recirculation flow regime, has been solved, and the profile of liquid flow has been determined.
Abstract: The equation of motion for the two phase flow within a bubble column, operated within the recirculation flow regime, has been solved, and the profile of liquid flow has been determined. Nicklin's relation for the bubble flow regime has been extended to the recirculation flow regime.
Data analysis shows that the mean slip velocity between bubble and liquid is approximately constant and that the kinematic turbulent viscosity increases rapidly with increasing diameter of the column. These observations lead to the conclusion that scale-up has but little influence upon the mean gas holdup.
168 citations
TL;DR: In this article, the radial and axial distributions of mean velocity, turbulent intensities and kinetic energy as well as radial distributions of the turbulent shear stress in the initial region of a turbulent air jet issuing from a long round pipe into still air.
Abstract: This note presents measurements of radial and axial distributions of mean velocity, turbulent intensities and kinetic energy as well as radial distributions of the turbulent shear stress in the initial region of a turbulent air jet issuing from a long round pipe into still air. The pipe flow is transformed relatively smoothly into a jet flow. In the core subregion the mean centre-line velocity decreases slightly. The highest turbulence occurs at an axial distance of about 6d and radius of (0·7 to 0·8)d. On the axis the highest turbulent kinetic energy appears at a distance of (7·5 to 8·5)d. Normalized distributions of the turbulent quantities are in good agreement with known data on the developed region of jets issuing from short nozzles.
148 citations
TL;DR: In this paper, a general theory of minimum rate of energy dissipation for a class of open channel flows with or without the movement of sediment is proposed, which is derived from the Navier-Stoke's equations of motion for gradually varied open channel flow without sediment transport.
Abstract: A general theory of minimum rate of energy dissipation for a class of open channel flows with or without the movement of sediment is proposed in this paper. This theory states that the rate of energy dissipation is a minimum under steady equilibrium or gradually varied flow conditions. The theory is derived from the Navier-Stoke's equations of motion for gradually varied open channel flow without sediment transport. It applies to turbulent and laminar flows as long as the inertia forces due to the time-averaged velocity distribution is small compared with the forces due to gravity and shear. The theory in different degrees of generality can be used to explain the fluvial processes from the movement of sediment to the change of velocity, slope, roughness, channel geometry, pattern, and profile of a river under an eqiulibrium condition or during the process of self-adjustment to reach an equilibrium condition.
144 citations
TL;DR: In this paper, a steady normal flow theory was used to estimate the entrainment coefficient of the underflowing river in a Western Australian reservoir using field data gathered from a reservoir and a simple theory using the concept of a normal flow depth.
Abstract: Field data gathered from a Western Australian reservoir are used to obtain an estimate for the entrainment coefficient of the underflowing river. By the use of a steady normal flow theory, the entrainment coefficient is related to the flow and river channel characteristics. By combination with a general turbulent entrainment law, it is shown that the entrainment coefficient and dilution may be directly related to the physical characteristics of the river channel, and thus may be estimated without recourse to a field experiment. In order to determine the initial underflow depth and the location of the plunge line, a simple theory using the concept of a normal flow depth is used, the results of which compare favorably with observation.
126 citations
TL;DR: In this paper, a 41 m wide by 308 m long, open channel on a 0.052 slope, constructed of loose boulders and through which flows up to 140 m3/s are passed, is described.
Abstract: Experience is described of a 41 m wide by 308 m long, open channel on a 0.052 slope, constructed of loose boulders and through which flows up to 140 m3/s are passed. A new expression for the Darcy ...
124 citations
TL;DR: In this paper, strong external disturbances were introduced into a mixing layer in order to test the formation of the quasi-two-dimensional coherent eddies and their survival under less than ideal conditions.
Abstract: Strong external disturbances were introduced into a mixing layer in order to test the formation of the quasi two-dimensional coherent eddies and their survival under less than ideal conditions. Velocity and temperature correlation measurements, flow visualization, and the simultaneous use of a large number of sensors suggest that these eddies are very stable in the range of Reynolds numbers considered and they persevere in spite of the external buffeting imposed. Some measurements were carried out in a mixing layer between two parallel streams and some in a mixing layer entraining quiescent surrounding fluid. In both cases the large eddies could be described. as vortex rolls spanning the test section; these rolls may be contorted and sometimes skewed, but they are basically two-dimensional.
123 citations
TL;DR: In this article, high viscous material which are Newtonian in shear but also highly elastic are used to examine the kinematics and stability of die entry flows, and the influence of elasticity on the secondary flow in the absence of shear thinning and inertial effects is identified.
Abstract: Highly viscous material which are Newtonian in shear but also highly elastic are used to examine the kinematics and stability of die entry flows. Flow properties, which include the shear and first normal stress difference are measured at die entry flow conditions with an R16 Weissenberg Rheogoniometer. Four flow regimes are identified: vortex growth flow, asymmetric flow, rotating flow, and helical flow. The size of the secondary flow cell in vortex growth flow is successfully correlated with the fundamental fluid properties and contraction ratio. The influence of elasticity on the secondary flow in the absence of shear thinning and inertial effects is identified. The nature of the flow instability is clearly identified, its source is specified, and the conditions for its onset are quantified. A motion picture film has been made to illustrate the flow phenomena observed.
TL;DR: In this article, the axisymmetric flow of an incompressible fluid through a pipe (of radius a) suffering a severe constriction is studied for large Reynolds numbers R, the features of symmetric channel flows being virtually the same.
Abstract: The axisymmetric flow of an incompressible fluid through a pipe (of radius a) suffering a severe constriction is studied for large Reynolds numbers R, the features of symmetric channel flows being virtually the same. Here ‘severe’ refers to a constriction whose typical dimensions are finite, and the oncoming velocity profile is taken to be of a realistic type, i.e. with no slip at the wall. The study adopts (Kirchhoff) free-streamline theory, which, for the mostly inviscid description, affords a rational basis consistent with viscous separation. The major (triple-deck) separation takes place on the constriction surface and is followed by a downstream eddy of length O(aR). Another, less familiar, separation is predicted to occur at a distance 0.087a In R + O(a) ahead of the finite obstacle. Free-streamline solutions are found in the two main extremes of moderately severe and very severe constriction. In both extremes, and in any slowly varying constriction, the major separation is sited near the maximum constriction point. The upstream separation point is also derived, to O(a) accuracy in each case. The upstream separation can be suppressed, however, if the constriction has no definite starting point and decaysslowly upstream, but then the upstream flow response extends over a much increased distance. Comparisons with Navier-Stokes solutions and with experiments tend to favour the predictions of the free-streamline theory.
TL;DR: In this paper, the effect of slip velocity at a membrane surface is studied in detail for a tubular membrane system, and a second-order perturbation solution of the equations of motion is found to be very satisfactory.
TL;DR: In this paper, the boundary layer equations in the inlet region and the Navier-Stokes equations with order-of-magnitude analysis in the filled region are solved using fourth-degree velocity profiles.
Abstract: The entrance region has been divided into two parts, the inlet region and the filled region. At the end of the inlet region, the boundary layers meet at the pipe axis but the velocity profiles are not yet similar. In the filled region, adjustment of the completely viscous profile takes place until the Poiseuille similar profile is attained at the end of it. The boundary-layer equations in the inlet region and the Navier-Stokes equations with order-of-magnitude analysis in the filled region are solved using fourth-degree velocity profiles. The total length of the entrance region so obtained is ξ = x/R Re = 0·150, whereas the boundary layers are observed to meet at approximately one-quarter of the entrance length, i.e. at ξ = 0·036. Experiments reported in the paper corroborate the analytical results.
TL;DR: In this article, a finite difference procedure was used to solve the governing equations in dimensionless form using air as the fluid, and several correlations developed to enable important performance characteristics to be estimated given the channel thickness, height, and surface temperatures.
TL;DR: In this article, the authors presented measurements of the fluctuating pressure recorded at a point 90° from the mean position of the forward stagnation point on a circular cylinder oscillating in a water flow.
Abstract: Measurements are presented of the fluctuating pressure recorded at a point 90° from the mean position of the forward stagnation point on a circular cylinder oscillating in a water flow. The aspect ratio of the cylinder was 9·5 and the turbulence level in the free-stream was 5·5%. The cylinder Reynolds number was 2·4 × 104 and the cylinder was forced to oscillate transverse to the main flow at amplitudes up to 1·33 cylinder diameters. The reduced velocity was varied over the range 3–18 and the experiments spanned the vortex-shedding lock-in range. Measurements of phase difference between pressure and displacement show that the maximum out-of-phase lift force occurs at an amplitude of about half a diameter. Good agreement is found between measurements on forced and freely oscillating cylinders. A simple potential-flow model gives reasonable predictions of the pressure fluctuations at the body frequency and at twice the body frequency at reduced velocities away from lock-in.
TL;DR: In this paper, the authors used asymptotic methods to analyse the flow in a narrow channel of a fluid with temperature-dependent viscosity and internal viscous dissipation.
Abstract: This paper uses asymptotic methods to analyse the flow in a narrow channel of a fluid with temperature-dependent viscosity and internal viscous dissipation. When the Nahme–Griffith number is large we show how the flow evolves from Poiseuille flow with a uniform temperature distribution to a plug flow with hot boundary layers on the walls. An asymptotic solution is obtained for the flow in the region of transition from Poiseuille to plug flow and an explicit equation is derived for the pressure gradient in terms of the local downstream co-ordinate in this transition region.
TL;DR: In this paper, the authors verified some of the important qualitative features of three-dimensional separation criteria proposed earlier by Maskell, Wang and others and compared the observed locations of laminar separation lines on a spheroid at various incidences.
Abstract: Surface streamline patterns on a spheroid have been examined at several angles of attack. Most of the tests were performed at low Reynolds numbers in a hydraulic flume using coloured dye to make the surface flow visible. A limited number of experiments was also carried out in a wind tunnel, using wool tufts, to study the influence of Reynolds number and turbulent separation. The study has verified some of the important qualitative features of three-dimensional separation criteria proposed earlier by Maskell, Wang and others. The observed locations of laminar separation lines on a spheroid at various incidences have been compared with the numerical solutions of Wang and show qualitative agreement. The quantitative differences are attributed largely to the significant viscous-inviscid flow interaction which is present, especially at large incidences.
TL;DR: In this article, an experimental study of two-dimensional flow over non-uniform roughness is reported in which artificial strip roughness was employed, the roughness elements were square in cross section and placed at different relative spacings.
Abstract: An experimental study of two-dimensional flow over non-uniform roughness is reported in which artificial strip roughness was employed. The roughness elements were square in cross section and placed at different relative spacings. A six-fold classification system is suggested based upon the ideas of Morris and Adachi. Resistance data from other investigators is also considered, and the variation of resistance coefficient with Reynolds number, relative spacing, and relative depth examined. The general resistance parameter, X, first introduced by Sayre and Albertson is found to be particularly helpful in synthesizing the various sets of resistance data. Logarithmic resistance equations involving X are validated over a wide range of roughness wavelength to height ratio. The relationship between roughness height and Nikuradse's equivalent sand roughness size is also examined.
TL;DR: In this paper, the effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall.
Abstract: The effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall. Uniform suction was introduced into a pipe flow with a Reynolds number of 17250 by means of a porous-walled section 2·2 diameters in length with very fine perforations. The effect of suction on the turbulent energy balance was then measured over the entire cross-section at four axial locations. The results indicate the following.
The amplitudes of the three principal velocity fluctuation components are reduced by suction, but to differing degrees. Moreover, the effects of suction on the amplitudes of these fluctuations develop at differing rates such that the x-wise components are first affected, then the r-wise and lastly the ϕ-wise components.The suction-induced perturbation in the turbulent structure propagates from the wall to the pipe centre-line with a velocity approximately equal to the friction velocity Uτ.Even with very small rates of fluid extraction the maxima of the terms in the turbulent energy balance occurring close to the wall are drastically reduced. Nevertheless there is no tendency for the location of these maxima to move towards the wall.The general reduction of the level of turbulent energy across the entire section is due to transport of this energy by the augmented mean radial velocity towards the wall, where it is dissipated since the boundary condition inhibits the passage of turbulent energy through the wall.
TL;DR: For every viscoelastic fluid studied in the contraction geometry, it was found that increasing the flow rate beyond a certain limit resulted in disturbance to the stable entry flow patterns described in Parts I and II as discussed by the authors.
Abstract: For every viscoelastic fluid studied in the contraction geometry, it was found that increasing the flow rate beyond a certain limit resulted in disturbance to the stable entry flow patterns described in Parts I and II. An examination of the development of the entry flow disturbances was carried out using still and cine photography. Still photographs are presented to illustrate the characteristics of the unstable flow patterns. The time varying nature of the flow has been recorded on a cine film Flow Patterns in Abrupt Entry Flow of Viscoelastic Fluids which is available for loan. Critical condition criteria for the onset of the periodic flow disturbances were obtained in terms of the fundamental fluid properties and are presented and compared with other suggested criteria for the onset of unstable entry flow of viscoelastic fluids.
TL;DR: In this paper, the authors have demonstrated the transport of longitudinal momentum from the main channel to the flood plain and demonstrated that the velocity profiles in the region affected by this interaction have been found to be similar if viewed with respect to the undisturbed flow in a flood plain.
Abstract: The experimental results presented in this paper have demonstrated the transport of longitudinal momentum from the main channel to the flood plain. This transport increases the bed shear stress in the flood plain and produces the opposite result on the main channel. The velocity profiles in the region affected by this interaction have been found to be similar if viewed with respect to the undisturbed flow in the flood plain. The velocity and length scales have been correlated with mainly the ratio of the depth of flow in the main channel to that in the flood plain. In the present experiments, the main channel was narrow and thus the interaction extended inwards to the center line of the main channel. For the concepts introduced in this paper to be used in solving practical problems, further experiments should be conducted with wider main channels including the effects of bed roughness.
TL;DR: In this article, the energy balance of spatially varied flows at the junction of a rectangular open channel and a side channel is investigated by a one-dimensional flow analysis of experimental data obtained from a laboratory channel system.
Abstract: The energy balance of spatially varied flows at the junction of a rectangular open channel and a side channel is investigated by a one-dimensional flow analysis of experimental data obtained from a laboratory channel system. By means of a large control volume enclosing the neighborhood of the junction and having the control surface located at the cross sections where the flow is unidirectional, the energy loss can be evaluated. The energy loss is then divided into two components: the boundary friction loss and the turbulent mixing loss. The turbulent mixing loss is found to be of the same order of magnitude as the boundary friction loss evaluated by Manning's formula. The loss coefficient is derived as a function of the ratio of lateral to total flow rate. An energy transfer process from the main channel flow to the lateral inflow or vice versa, which is implicit in the one-dimensional flow analysis, can be analyzed by means of the turbulent mixing loss coefficients. The result may be applied to the calculation of energy losses in the junction or in spatially varied flows with lateral inflow in an open channel flow analysis.
01 Jan 1979
TL;DR: In this paper, numerical solutions of the time-averaged Navier-Stokes equations employing a simple eddy-viscosity model have been obtained for three dimensional turbulent flow fields at supersonic speeds.
Abstract: Numerical solutions of the time-averaged Navier-Stokes equations employing a simple eddy-viscosity model have been obtained for three dimensional turbulent flow fields at supersonic speeds. The computer results are compared with a series of experimental test flows describing the interaction of a swept shock wave with a turbulent boundary layer for various shock-wave strengths. Very good agreement is obtained between the computed and experimental surface and flow-field results. The computed flow fields are examined in detail to investigate the physics of this type of flow field. Questions concerning the existence of a vortex and the relationship between converging surface oil streaks and the resulting flow field are addressed.
TL;DR: In this paper, the distribution of velocity and boundary shear stress in a rectangular flume has been examined experimentally, and the influence of varying the bed roughness and aspect ratio assessed.
Abstract: The distribution of velocity and boundary shear stress in a rectangular flume has been examined experimentally, and the influence of varying the bed roughness and aspect ratio assessed. The resistance of the channel bed was varied by means of artificial strip roughness elements, and measurements made of the wall and bed shear stresses. Dimensionless plots of both shear stress and shear force parameters are presented for different bed roughnesses and aspect ratios, and these serve to illustrate the complex way in which such parameters vary. The definition of a wide channel is also examined, and a graph giving the limiting aspect ratio for different roughness conditions is presented. The boundary shear stress distributions and isovel patterns are used to examine one of the standard side-wall correction procedures. One of the basic assumptions underlying the procedure is found to be untenable due to the cross channel transfer of linear momentum.
TL;DR: In this article, the authors examined the effect of the superimposed oscillations upon the flow with particular attention to the flow rate and found that the flow appears to be dominated by a shear-thinning effect.
Abstract: In the present communication, the flow of liquids through a straight pipe which is oscillating longitudinally about a mean position is examined. The basic flow is generated by a constant pressure gradient and the effect of the superimposed oscillations upon the flow is analyzed with particular attention to the flow rate. In the viscous case as well as for an elastic fluid with constant viscosity, no variation in the flow rate is present. This is in agreement with the theoretical analysis. Nevertheless, for viscoelastic fluids, increases in the flow rate of up to twenty times are possible when compared to purely rectilinear flow. This effect is examined for various viscoelastic fluids and relations are found with that basic properties of such fluids. The complex flow situation is analyzed using flow visualization techniques. As a result, the flow appears to be dominated by a shear-thinning effect. A numerical solution using a power-law fluid predicts increases in flow rate which agree qualitatively with the experimental data but are quantitatively different. It is therefore concluded that a more general model must be used for agreement between experiments and theory. In the light of the experimental results, applications are being presently undertaken for the flow of polymer melts in situations of industrial interest.
01 Jan 1979
TL;DR: Theoretical and experimental studies on a turbulent flow in a two-dimensional channel of aspect ratio 1:16 in which a square obstacle of half the channel height was located are reported in this paper.
Abstract: Theoretical and experimental studies are reported on a turbulent flow in a two-dimensional channel of aspect ratio 1:16 in which a square obstacle of half the channel height was located. A one dimensional laser-Doppler anemometer was used to measure the mean longitudinal velocity distribution and the rms values of the longitudinal velocity fluctuations. The measurements were carried out along the channel center from 20 channel heights upstream of the obstacle to 33 channel heights downstream. Flow visualization techniques were employed to observe the regions not covered by the LDA measurements. The governing partial differential equations were solved numerically, and results are described in the theoretical part of the paper. In the separated flow region, the Reynolds equations were solved using the two-equation k − ϵ turbulence model, and in the region downstream of the separation, the boundary-layer equations were solved with both k − ϵ and the three-equation \(k-\varepsilon -\bar{u}\bar{v}\) turbulence model. The calculations are compared with the measurements and demonstrate clearly that for turbulent flows with separation, the present state of turbulence modelling results in inaccurate predictions. Calculated values are presented for the increase in heat transfer rates and the pressure drop due to the obstruction.