Showing papers on "Open-channel flow published in 1975"

Progress in the development of a Reynolds-stress turbulence closure

Abstract: The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate E. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows. Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.

Engineering Fluid Mechanics

Abstract: PREFACE. CHAPTER 1 Introduction. 1.1 Liquids and Gases. 1.2 The Continuum Assumption. 1.3 Dimensions, Units, and Resources. 1.4 Topics in Dimensional Analysis. 1.5 Engineering Analysis. 1.6 Applications and Connections. CHAPTER 2 Fluid Properties. 2.1 Properties Involving Mass and Weight. 2.2 Ideal Gas Law. 2.3 Properties Involving Thermal Energy. 2.4 Viscosity. 2.5 Bulk Modulus of Elasticity. 2.6 Surface Tension. 2.7 Vapor Pressure. 2.8 Summary. CHAPTER 3 Fluid Statics. 3.1 Pressure. 3.2 Pressure Variation with Elevation. 3.3 Pressure Measurements. 3.4 Forces on Plane Surfaces (Panels). 3.5 Forces on Curved Surfaces. 3.6 Buoyancy. 3.7 Stability of Immersed and Floating Bodies. 3.8 Summary. CHAPTER 4 Flowing Fluids and Pressure Variation. 4.1 Descriptions of Fluid Motion. 4.2 Acceleration. 4.3 Euler's Equation. 4.4 Pressure Distribution in Rotating Flows. 4.5 The Bernoulli Equation Along a Streamline. 4.6 Rotation and Vorticity. 4.7 The Bernoulli Equation in Irrotational Flow. 4.8 Separation. 4.9 Summary. CHAPTER 5 Control Volume Approach and Continuity Equation. 5.1 Rate of Flow. 5.2 Control Volume Approach. 5.3 Continuity Equation. 5.4 Cavitation. 5.5 Differential Form of the Continuity Equation. 5.6 Summary. CHAPTER 6 Momentum Equation. 6.1 Momentum Equation: Derivation. 6.2 Momentum Equation: Interpretation. 6.3 Common Applications. 6.4 Additional Applications. 6.5 Moment-of-Momentum Equation. 6.6 Navier-Stokes Equation. 6.7 Summary. CHAPTER 7 The Energy Equation. 7.1 Energy, Work, and Power. 7.2 Energy Equation: General Form. 7.3 Energy Equation: Pipe Flow. 7.4 Power Equation. 7.5 Contrasting the Bernoulli Equation and the Energy Equation. 7.6 Transitions. 7.7 Hydraulic and Energy Grade Lines. 7.8 Summary. CHAPTER 8 Dimensional Analysis and Similitude. 8.1 Need for Dimensional Analysis. 8.2 Buckingham Theorem. 8.3 Dimensional Analysis. 8.4 Common-Groups. 8.5 Similitude. 8.6 Model Studies for Flows Without Free-Surface Effects. 8.7 Model-Prototype Performance. 8.8 Approximate Similitude at High Reynolds Numbers. 8.9 Free-Surface Model Studies. 8.10 Summary. CHAPTER 9 Surface Resistance. 9.1 Surface Resistance with Uniform Laminar Flow. 9.2 Qualitative Description of the Boundary Layer. 9.3 Laminar Boundary Layer. 9.4 Boundary Layer Transition. 9.5 Turbulent Boundary Layer. 9.6 Pressure Gradient Effects on Boundary Layers. 9.7 Summary. CHAPTER 10 Flow in Conduits. 10.1 Classifying Flow. 10.2 Specifying Pipe Sizes. 10.3 Pipe Head Loss. 10.4 Stress Distributions in Pipe Flow. 10.5 Laminar Flow in a Round Tube. 10.6 Turbulent Flow and the Moody Diagram. 10.7 Solving Turbulent Flow Problems. 10.8 Combined Head Loss 10.9 Nonround Conduits. 10.10 Pumps and Systems of Pipes. 10.11 Summary. CHAPTER 11 Drag and Lift. 11.1 Relating Lift and Drag to Stress Distributions. 11.2 Calculating Drag Force. 11.3 Drag of Axisymmetric and 3D Bodies. 11.4 Terminal Velocity. 11.5 Vortex Shedding. 11.6 Reducing Drag by Streamlining. 11.7 Drag in Compressible Flow. 11.8 Theory of Lift. 11.9 Lift and Drag on Airfoils. 11.10 Lift and Drag on Road Vehicles. 11.11 Summary. CHAPTER 12 Compressible Flow. 12.1 Wave Propagation in Compressible Fluids. 12.2 Mach Number Relationships. 12.3 Normal Shock Waves. 12.4 Isentropic Compressible Flow Through a Duct with Varying Area. 12.5 Summary. CHAPTER 13 Flow Measurements. 13.1 Measuring Velocity and Pressure 13.2 Measuring Flow Rate (Discharge). 13.3 Measurement in Compressible Flow. 13.4 Accuracy of Measurements. 13.5 Summary. CHAPTER 14 Turbomachinery. 14.1 Propellers. 14.2 Axial-Flow Pumps. 14.3 Radial-Flow Machines. 14.4 Specific Speed. 14.5 Suction Limitations of Pumps. 14.6 Viscous Effects. 14.7 Centrifugal Compressors. 14.8 Turbines. 14.9 Summary. CHAPTER 15 Flow in Open Channels. 15.1 Description of Open-Channel Flow. 15.2 Energy Equation for Steady Open-Channel Flow. 15.3 Steady Uniform Flow. 15.4 Steady Nonuniform Flow. 15.5 Rapidly Varied Flow. 15.6 Hydraulic Jump. 15.7 Gradually Varied Flow. 15.8 Summary. Appendix A-1. Answers A-11. Index I-1.

Analysis of Flow through Vegetation

Abstract: The Manning n value is quantitatively evaluated for flow in heavily vegetated channels. Momentum analysis shows that the composite n value as a function of flow depth is dependent on the bottom roughness and the density of vegetation. In some cases, the vegetation density can be evaluated directly from physical measurements of the vegetation. However, in most situations, it must be evaluated indirectly from limited field data. The results show that the n value increases in proportion to two-thirds power of the hydraulic radius for conditions where the vegetation density is a constant over the flow depth. Field application of the flow resistance model are described for projects concerned with flood routing, backwater computations, extension of rating curves, channel improvement work, and erosion control.

Transition to turbulence in oscillating pipe flow

Abstract: Published results on transition in a Stokes layer indicate a wide range of transition Reynolds numbers. As thermal effects in a resonance tube (Merkli & Thomann 1975) depend on the state of the boundary layer, the transition Reynolds number was determined, and a critical Reynolds number Ac ≈ 400 was found. The observations were made with hot wires and with flow visualization by means of smoke, and provide new details on turbulence in a Stokes layer. With this knowledge an explanation of the large discrepancies between some stability theories and the experiments is suggested. The main point is that turbulence occurs in the form of periodic bursts which are followed by relaminarimtion in the same cycle and do not lead to turbulent flow during the whole cycle.A further, unexpected result of the present investigation is the discovery of vortex patterns superimposed on the normal laminar acoustic motion.

On transition in a pipe. Part 2. The equilibrium puff

Abstract: Conditionally sampled hot-wire measurements were taken in a pipe at low Reynolds numbers (2700 > Re > 2000) corresponding to the onset of turbulence as a result of a large perturbation in the flow. This type of transition gives rise to a turbulent puff which maintains itself indefinitely at around Re = 2200. The structure of puffs was investigated in some detail and was found to be very different from the structure of fully developed turbulent pipe flow. Nevertheless, it is independent of the character of the disturbance which created it. The purpose of the study was to gain some insight into the mechanism of transition in a pipe.

Prediction of turbulent flow in curved pipes

Abstract: A finite-difference procedure is employed to predict the development of turbulent flow in curved pipes. The turbulence model used involves the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. The predicted total-velocity contours for the developing flow in a 180° bend are compared with the experimental data. Predictions of fully developed velocity profiles for long helically wound pipes are also presented and compared with experimental measurements.

Turbulence of open channel flow over smooth and rough beds

Abstract: In the last decade a broad knowledge of dynamics of wall turbulence in water flow has been obtained through development of a hot-film anemometer or a hydrogen-bubble method. One of the headmost studies in this field was done by a group of Stanford University1) under the direction of Kline who looked for the mechanism of turbulence production by means of flow visualization with the hydrogen-bubble method. Several experimental works done by use of both flow visualization and point measurements have recently brought to light turbulence characteristics of the shear flow, with aid of improved methods of data analysis. Turbulence measurments of open-channel shear flow over a smooth or rough bed were vigorously done by Raichlen2), McQuivey et al.3), Ishii et a1.4) and Imamoto5) by making use of singlesensor hot-film anemometer. It is very interesting in practice to investigate how the structure of turbulence would be influenced by hydraulic parameters such as Reynolds

Entry flow in a curved pipe

Abstract: A secondary flow is set up when a fluid flows through a stationary curved pipe. The fluid in the middle of the pipe moves outwards and that near the wall inwards. Dean showed that the dynamical similarity of this fully developed flow depends on a non-dimensional parameter is the mean velocity along the pipe, v is the coefficient of kinematic viscosity and a is the radius of the pipe, which is bent into a coil of radius R. Dean's analysis was limited to small values of D. Later, Barua developed an asymptotic boundary-layer theory for large values of D and showed for these values of D that the resistance coefficient γc is much larger than that for the corresponding straight pipe. The present work deals with the flow in a curved pipe as it develops from a uniformly distributed velocity at the entrance to a fully developed profile. Barua's results for the fully developed flow are adopted as downstream conditions in the present work. The ratio of the entry lengths of the curved ipe and the corresponding straight one is shown to be proportional to D−1/2 when D is large. Thus, the entry length for a curved pipe is much shorter than that for the corresponding straight pipe.

Resistance to flow in alluvial channels

Abstract: A direct method of predicting flow resistance and uniform velocity in alluvial channels is developed. The method covers all known bed-form regimes and not only eliminates trial-and-error computations and use of rigid-boundary channel flow formulas but also avoids the difficulties associated with the use of the various existing alluvial channel flow computation techniques. The study shows that the Darcy-Weisbach friction factor can be expressed as a unique function of the ratio of the bed form and grain shear stress components for any anticipated discharge and flow geometry, the bed-form shear component being uniquely determinable from the flow and channel material characteristics. The results confirm that the friction factor is nonconstant but varies with the bed-form regime. The applicability of the method to laboratory flumes, field canals, and natural rivers is illustrated.

Viscous incompressible flow between concentric rotating spheres. Part 3. Linear stability and experiments

Abstract: The stability of flow of a viscous incompressible fluid contained between a stationary outer sphere and rotating inner sphere is studied theoretically and experimentally. Previous theoretical results concerning the basic laminar flow (part 1) are compared with experimental results. Small and large Reynolds number results are compared with Stokes-flow and boundary-layer solutions. The effect of the radius ratio of the two spheres is demonstrated. A linearized theory of stability for the laminar flow is formulated in terms of toroidal and poloidal potentials; the differential equations governing these potentials are integrated numerically. It is found that the flow is subcritically unstable and that the observed instability occurs at a Reynolds number close to the critical value of the energy stability theory. Observations of other flow transitions, at higher values of the Reynolds number, are also described. The character of the stability of the spherical annulus flow is found to be strongly dependent on the radius ratio.

Hydromagnetic flow past a porous flat plate with hall effects

Abstract: An investigation is made of the flow of a conducting liquid past an infinite porous flat plate taking Hall effects into account, the liquid being permeated by a transverse magnetic field. It is shown that asymptotic solution for the velocity and magnetic field exists both for suction or blowing at the plate. Further when the magnetic Reynolds number is very small, the flow pattern is remarkably similar to that for a non-conducting flow past a flat plate in a rotating frame.

Effect of flow on the acoustic resonances of an open‐ended duct

Abstract: The effect of flow on the acoustic resonances of an open‐ended, hard‐walled duct is analyzed. The flow produces acoustic losses both in the interior of the duct and at the ends. Unless the duct is very long, typically 100 times the diameter, the losses at the ends dominate. At flow Mach numbers in excess of 0.4 the losses are so large that axial duct resonances are almost completely suppressed. The plane‐wave Green’s function for the duct with flow is expressed in terms of the (experimentally determined) pressure reflection coefficients at the ends of the duct, and the flow dependence of the complex eigenfrequencies of the duct is obtained. Some observations concerning the noise produced by the flow in the duct are also reported.Subject Classification: 28.60.

Disturbances in a Boundary Layer Introduced by a Low Intensity Array of Vortices

Abstract: To acquire insight into the role of free-stream turbulence on laminar-turbulent transition, the interaction between a boundary layer and an array of single-wavenumber vortices convected at the mean free-stream velocity is studied analytically and numerically. For small amplitudes, the effect of a spectrum can be obtained by superposition. The flow field is taken to be the sum of the steady laminar field (Blasius) plus a flow field ascribable to the effects of the vortex array. This latter flow field is further subdivided into the portion that exists in the absence of the plate (the vortex array itself) plus a flow field representing the alteration to that array due to the shearing mean flow and no-slip and impermeability conditions at the plate surface. This last portion of the flow field is described by a nonhomogeneous Orr–Sommerfeld equation with phase speed unity and real wavenumber. The forcing function depends on the mean flow and on the free-stream disturbance array. The problem is not an eigenvalu...

Computation of stage‐discharge relationships affected by unsteady flow

Abstract: The dynamic relationship between stage and discharge which is unique to a particular flood for a selected station along the river can be determined via a mathematical model based on the complete one-dimensional equations of unsteady flow, i.e., the equations for the conservation of mass and momentum of the flood wave, and the Manning equation which accounts for energy losses. By assuming the bulk of the flood wave moves as a kinematic wave, the need for spatial resolution of the flood can be eliminated, and only the time variation of either the discharge or stage at the selected station is necessary for the computation of the other. The mathematical model can be used in river forecasting to convert the forecast discharge hydrograph into a stage hydrograph which properly reflects the unique dynamic stage-discharge relationship produced by the variable energy slope of the flood discharge. The model can be used also in stream gaging to convert a recorded stage hydrograph into a discharge hydrograph which properly accounts for the effects of unsteady flow. The model is applied to several observed floods at selected stations along the Lower Mississippi, Red, and Atchafalaya Rivers. The root mean square errors between observed and computed discharges are in the range of 3 to 7 percent, values well within the accuracy of the observations. A simple, easily-applied graphical procedure is also provided for estimating the magnitude of the effect of the unsteady flow on stage-discharge ratings. As a general rule, the dynamic effect may be significant if the channel bottom slope is less than 0.001 ft/ft (about 5 ft/mi) when the rate of change of stage is greater than about 0.10 ft/hr.

Implicit Numerical Modeling of Unsteady Flows

Abstract: A numerical model based on the equations of unsteady flow in open channels is used to compute unsteady flows in rivers and reservoirs. The cross sections of the waterways range from uniform to highly irregular, the type of flow ranges from slowly varied to abrupt changes in discharge, and nearly all combinations of boundary conditions are encountered. The model uses an implicit finite difference method. The versatility, accuracy, stability, and efficiency of the method is demonstrated by field measurements.

The behavior of a power‐law fluid flowing through a sudden expansion: Part I. A numerical solution

Abstract: A numerical solution for the axisymmetric flow of an inelastic power-law fluid through an abrupt circular expansion is presented. The equations of motion were solved using an Alternating Direction Implicit method. Both a stream tube-real tube and a real tube-real tube model were investigated and the conditions for significant upstream diffusion of momentum were specified. Secondary flow characteristics and the bulk flow field development are predicted as a function of the flow behavior index (n) and of the Reynolds number. Some results are presented to show the influence of the expansion ratio.

Laminar flow of non-newtonian fluids in an eccentric annulus

Abstract: Esso Production Research Co. developed a technique for predicting the volumetric flow rate and velocity distribution for laminar flow of power-law and Bingham-plastic fluids in an eccentric annulus. This flow situation occurs during drilling of cementing of oil or gas wells. The volumetric flow rate is presented as a series of dimensionless plots of fluid properties, pipe diameters, eccentricity, and pressure drop, which are obtained by numerically integrating the velocity profile from a finite difference solution of the equations of continuity and motion after transformation into bipolar coordinates. The numerical procedure was verified by comparing the calculations with previously published results for the special cases of Newtonian flow in an eccentric annulus and non-Newtonian flow in a concentric annulus and with limited experimental data for Bingham-plastic flow in an eccentric annulus. The results indicate that the technique is accurate in predicting the volumetric flow rate and velocity distribution within the range of variables specified and on the degree of conformity of the fluid to the rheological model used.

Experimental velocity profiles in laminar flow around spheres at intermediate Reynolds numbers

Abstract: Seeley, Hummel & Smith (1975) reported the results of experiments to study the dynamics of flow around spheres at intermediate Reynolds numbers using a nondisturbing flow-visualization technique. The flow patterns were recorded on cine photographs and the information stored was processed in order to obtain the velocity field. The position of fluid elements shown by the photochromic indicator traces were estimated by eye on a projection screen. In this paper, a new set of results based on the same films has been reduced and computed using the ‘POLLY’ film-reading system described by Esmail, Smith & Hummel (1976). Some numerical boundary-layer solutions are included to show the reliability of the data, and comparisons with the results previously reported by Seeley et al. (1975) are presented.J. W. Smith will be pleased to send a complete set of experimental data on request.

Method for effecting heat or mass transfer

Abstract: A method and apparatus for effecting heat or mass transfer between two fluids through a membrane comprises a conduit for flow of one fluid, said conduit being at least partly defined by said membrane and the configuration of said conduit in a plane orthogonal to the general direction of flow varying periodically along the general direction of flow either inherently or in response to fluid pressure therein in such a manner that when said fluid is pulsated along the line of the general direction of flow a component of motion is induced therein which is mutually orthogonal to the surface of the membrane and general direction of flow. In preferred embodiments the conduit configuration varies periodically along the general direction of flow in order to give rise to separation and reattachment of flow at a multiplicity of zones within the conduit, whereby secondary flow is induced within said zones. The apparatus is particularly applicable to blood oxygenation and dialysis.

The development of turbulence structure in a uniform shear flow

Abstract: Measurements of the streamwise development of a variety of velocity correlations in a uniform shear flow are given and discussed. It is concluded that, in the region in which the Reynolds stresses are approximately constant, the turbulence structure is practically independent of all the initial conditions except the initial length scale. It appears that the preferential amplification of some eddy structures by the mean shear effectively destroys information about the initial conditions, apart from the initial length scale, after a total strain of about 1.5.

An experimental investigation of low Reynolds number secondary streaming effects associated with an oscillating viscous flow in a curved pipe

Abstract: This paper deals with nonlinear streaming effects in an oscillating fluid in a curved pipe. The secondary steady velocity field in the cross-sectional plane of the pipe is studied in detail. Our experimental results are compared with the theory of Lyne (1970; that part of his theory which is valid for Reynolds numbers Rs [Lt ] 1) and the theory of Zalosh & Nelson (1973). On the basis of these comparisons we conclude that the theories are in practice valid for higher Reynolds numbers Rs than was formally expected.

The laminar decay of suddenly blocked channel and pipe flows

Abstract: This paper is a theoretical investigation of the stable laminar decay of a fully established channel or pipe flow following a sudden blockage such as would be caused by the rapid closure of a valve or imposition of an end wall or gate. The development of the subsequent velocity and pressure fields is examined from the instant the initial pressure wave passes until the final decay of all motion. Three time scales of hydrodynamic interest are identified and the relevant solutions are obtained. The time scales are as follows: (i) a very short time characteristic of the passage of the pressure wave during which the velocity field adjusts inviscidly to the new boundary conditions imposed by the presence of the end wall, (ii) a short diffusion time during which the displacement interaction generated by the diffusion of the primary Rayleigh layer induces a substantial secondary motion with distinct side-wall boundary layers and an inviscid core and (iii) a long diffusion time during which the boundary layers fill the entire channel or pipe and the residual motion then dies out. The secondary flow for short diffusion times is of special interest in that it is an example of an unsteady boundary layer where the external pressure gradient and inviscid outer flow are unknown and determined by the integrated time history of the combined mass flow displacement generated by the primary- and secondary-flow boundary layers. The paper closes with some preliminary comments and experimental observations on decelerating pipe flows.

Turbomachinery vane or blade with cooled platforms

Abstract: A turbomachinery vane or blade with a cooled platform including a coolant cavity in said platform into which a plurality of cooling fluid impingement jets are projected to impinge against the platform wall and then flow along the platform wall after impingement for cooling thereof and eventual discharge from the cooling cavity along the platform surface. A plurality of dam members extend into the cooling cavity adjacent the impingement jets so as to isolate the impingement jets from cross-flow and channel flow effects from the cooling fluid passing through the cooling cavity following impingement.