Undular Jump in Open‐Channel Flow Over a Sill

The paper reports experimental data on a steady flow with a free surface over a rectangular sill at the bottom of a rectangular channel. The paper focuses on the parameter range in which a qualitative change in flow pattern accompanied by formation of an undular jump is observed. It is shown that transition from the bottom state the surface state of head and tail conjugation to occurs when the second critical depth is reached over the downstream edge of the sill. Conditions of transition from a free state to a submerged state of flow over the sill are considered; conditions of validity of the assumption that the first critical depth is reached over the sill are discussed.     

Cavities behind a spillway with a wide sill

The paper reports experimental results on flow regimes with and without cavities behind a rectangular sill in an open channel. Photographs illustrating the shapes of the free ends of the cavities are given. It is shown that the domains of existence of various flow regimes overlap in the phase space of problem parameters, which leads to nonuniqueness of various functions of the parameters. Quantitative information is obtained for free surface profiles, the discharge coefficient, and the pressure on the flow bottom.     

Analysis of Thermal Flow in a Rotating Porous U-Turn Duct Using Lattice Boltzmann Method

The lattice Boltzmann method is carried out to investigate the heat transfer enhancement in a U-turn duct which is partially filled with a porous media. The porous layer is inserted at the core of the duct and is modeled using the Brinkman–Forchheimer assumptions. In order to validate the results, first a channel flow problem without any porous layer is compared with available data. Second, the porous Couette flow and partially porous channel flow are successfully compared with the studies of other researchers. Then, fluid flow in a clear U-turn duct is studied looking carefully at the velocity, curvature and rotation effects. Finally, the effects of porous layer thickness on the rate of heat transfer and pressure drop are investigated. Parametric studies are conducted to evaluate the effects of various parameters (i.e., Reynolds number, Darcy number, rotation number), highlighting their influences on the thermo-hydrodynamics behavior of the flow. The optimum values of porous layer thickness are presented for specific flow parameters.     

Flow and mixing characteristics of pulsed confined opposed jets in turbulent flow regime

A numerical study is performed on a two-dimensional confined opposed-jet configuration to gain basic understanding of the flow and mixing characteristics of pulsed turbulent opposed-jet streams. The sinusoidal pulsating flows with different temperature are imposed at opposed-jet inlets, which are mixed with each other in a confined flow channel. The current mathematical model taking the effect of temperature-dependent thermo-physical properties of fluid into account can present a good prediction for opposed-jet streams compared with experimental data. The numerical results indicate that introduction of temperature difference between opposed jet flows can lead to an asymmetric flow field immediately after jet impact, and the sinusoidal flow pulsations can effectively enhance mixing rate of opposed jets. Parameter studies are conducted for optimization of pulsed opposed jets. The effect of Reynolds number and flow pulsation as well as the configuration geometry on the mixing performance are discussed in detail. Examination of the flow and thermal field shows that the mixing rate is highly dependent on the vortex-induced mixing and residence time of jet fluid in the exit channel.     

Bathymetry reconstruction based on the zero-inertia shallow water approximation

The knowledge of the channel bed topography is paramount in modeling the hydrodynamics of open channel flows. Indeed, flow models based on the Shallow Water Approximation require prior information on the channel bed topography to accurately capture the flow features in natural rivers, estuaries, and flood plains. We present here a numerical technique for reconstructing the channel bed topography from given free surface elevation data for steep open channel flows for which the zero-inertia shallow water approximation holds. In this context, the shallow water equations are modified by neglecting inertia terms while retaining the effects of the bed slope and friction terms. We show in this work that by algebraic manipulation, we can recast the governing equations into a single first-order partial differential equation which describes the inverse problem which consists in finding the bed topography from known free surface elevation data. Interestingly, the analysis shows that the inverse problem does not require the knowledge of the bed roughness. The forward problem is solved using MacCormack’s explicit numerical scheme by considering unsteady modified shallow water equations. However, the inverse problem is solved using the method of characteristics. The results of the inverse and the forward problem are successfully tested against each other on two different test cases.     

明渠气二相流的双流体模型

从解决平均二相流基本方程的封闭问题出发,分析了水利工程中气水二相流的特点,介绍了据此提出的可用于水利工程稀疏气泡流计算的双流体模型,并对明渠气水二相流进行了算例验证。     

A Direct theory of viscous fluid flow in channels

This paper deals with an Eulerian formulation of the theory of directed fluid sheets appropriate for incompressible, linear viscous fluid flow in channels with arbitrary shapes for their major boundaries which may be moving or fixed. Special cases of the theory are applied to a number of two-dimensional fluid flow problems and these solutions are in general discussed for unsteady flow. Specific applications include fluid flow in a channel whose boundaries are symmetric with respect to a middle plane in the channel, subjected to time-dependent pressure gradient at one end; and to lubrication problems in a general shaped channel when one of the channel walls is a fixed plane while the other is moving with a constant velocity. Flow of a viscous fluid with a free surface over a fixed boundary is also discussed.Dedicated to J. L. Ericksen on the occasion of his Sixtieth Birthday     

Analytic Approximate Solution for a Flow of a Second-Grade Viscoelastic Fluid in a Converging Porous Channel

The problem of a two-dimensional steady flow of a second-grade fluid in a converging porous channel is considered. It is assumed that the fluid is injected into the channel through one wall and sucked from the channel through the other wall at the same velocity, which is inversely proportional to the distance along the wall from the channel origin. The equations governing the flow are reduced to ordinary differential equations. The boundary-value problem described by the latter equations is solved by the homotopy perturbation method. The effects of the Reynolds and crossflow Reynolds number on the flow characteristics are examined.     

Calculation of three-dimensional weakly expanding flow in jets and channels

The results are given of a calculation of laminar flow in a channel of square section and the motion of a turbulent jet from a cruciform nozzle in an ambient flow. To calculate the secondary flows, the field of the transverse velocity is decomposed into irrotational and solenoidal components. The results of the calculation of the flow in the channel are compared with the calculations of other authors and experimental data. To calculate the flow in the turbulent jet, a one-parameter turbulence model is used, and the influence of the inhomogeneity of the distribution of the longitudinal component of the velocity on the components of the Reynolds stress tensor is taken into account. The results of calculation of the flow in the jet behind a cruciform nozzle are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 36–44, July–August, 1984.     

An investigation of thermally stratified turbulent channel flow with temperature oscillation on the bottom wall by large eddy simulation

Thermally stratified shear turbulent channel flow with temperature oscillation on the bottom wall of the channel is calculated to investigate the behavior of turbulent flow and heat transfer by use of large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objective of this study is to deal with the effect of the temperature oscillation on turbulent behavior of thermally stratified turbulent channel flow and to examine the effectiveness of the LES technique for predicting statistically unsteady turbulent flow driven by time-varying buoyancy force. To validate the present calculation, thermally stratified shear turbulent channel flow is computed and compared with available data obtained by direct numerical simulation (DNS), which confirm that the present approach can be used to predict thermally stratified turbulent channel flow satisfactorily. Further, to illustrate the effect of the temperature oscillation with different Richardson numbers and periods of the oscillation on turbulence characteristics, the phase-averaged mean value and fluctuation of the resolved velocities and temperature, and instantaneous velocity fluctuation structures are analyzed.     

A conditional sampling method based on fuzzy clustering for the analysis of large-scale dynamics in turbulent flows

A conditional sampling technique, based on fuzzy clustering, is used to educe the organization of the secondary flow motions observed in the large-eddy simulation of a turbulent square channel flow. The data analysed are the multi-valued time series obtained from sampling the secondary velocity components at a fixed cross-section of the channel, over consecutive time steps. The mean values of the secondary flow motion velocities are one order of magnitude lower than their r.m.s values. The purpose of the conditional sampling scheme used is to replace the picture of the secondary flow motions provided by the unconditional time mean with several ensemble averages. In this way the whole variability of the instantaneous data can be split in two parts: one for the difference between the observed ensemble averages, and the other for the variability within each ensemble. Unlike other conditional sampling schemes which sort only part of the data into one or more families depending on an externally fixed condition, the fuzzy clustering approach used here first determines the optimum number of families or clusters and then classifies all the recorded time steps. The results show that the local turbulence intensities of the ensemble averages obtained from fuzzy clustering can be reduced by one order of magnitude. In addition, the classification of all the time steps into several clusters or families enables the large scale dynamics of the educed structures to be analysed.     

Motion of a circular cylinder in a viscous liquid between parallel plates

The two-dimensional motion of a cylinder in a viscous fluid between two parallel walls of a vertical channel is studied. It is found that when the cylinder moves very closely along one of the channel walls, it always rotates in the direction opposite to that of contact rolling along the nearest wall. When the cylinder is away from the walls, its rotation depends on the Reynolds number of the flow. In this study two numerical methods were used. One is for the unsteady motion of a sedimenting cylinder initially released from a position close to one of the channel walls, where the Navier-Stokes equations are solved for the fluid and Newton's equations of motion are solved for the rigid cylinder. The other method is for the steady flow in which a cylinder is fixed in a uniform flow field where the channel walls are sliding past the cylinder at the speed of the approaching flow, or equivalently a cylinder is moving with a constant velocity in a quiescent fluid. The flow field, the drag, the side force (lift), and the torque experienced by the cylinder are studied in detail. The effects of the cylinder location in the channel, the size of the channel relative to the cylinder diameter, and the Reynolds number of the flow are examined. In the limit when the cylinder is translating very closely along one of the walls, the flow in the gap between the cylinder and the wall is solved analytically using lubrication theory, and the numerical solution in the other region is used to piece together the whole flow field.This research was supported by NSF DMR91-20668 through the Laboratory for Research on the Structure of Matter at the University of Pennsylvania and from the Research Foundation of the University of Pennsylvania.     

Experimental on the liquid cooling system with thermoelectric for personal computer

In the present experimental investigation, the liquid cooling in the micro channel fin heat sink with and without thermoelectric for central processor unit (CPU) of personal computer. The micro channel heat sinks with two different channel height are fabricated from the aluminum with the length, the width and the base thickness of 28, 40, 2?mm respectively. The de-ionized water is used as coolant. Effects of channel height, coolant flow rate, and run condition of PC on the CPU temperature are considered. The liquid cooling in micro-rectangular fin heat sink with thermoelectric is compared with the other cooling techniques. The thermoelectric has a significant effect on the CPU cooling of PC. The experiments are performed at no load and full load conditions within 60?min after steady state, which the mass flow rate are 0.023, 0.017 and 0.01?kg/s. The results heat transfer rate increase with increasing coolant flow rate and higher channel. When comparing with the other cooling system, cooling system with thermoelectric gives the highest efficiency. However, thermoelectric has the high or low heat transfer rate from heat rejected and cooling capacity conditions.     

Waves behind a Step in an Open Channel

The paper presents experimental data on flow in the vicinity of a sudden elevation of channel bottom (step). The range of external flow parameters is considered for the case where the step generates waves. A distinguishing feature of these waves is that they are formed in transition from subcritical to supercritical flow. It is shown that there is a range of external parameters in which the depth at the channel exit, the depth above the step, and the distance from the step to the first wave trough depend exclusively on flow discharge.     

Averaged fluid velocities near a cylinder in turbulent flow in an open channel: Experiment

The results of experiments in which a circular cylinder located near the bottom of a rectangular channel was exposed to transverse statistically stationary turbulent subcritical flow with free surface are presented. The particle image velocimetry (PIV) was used to obtain data on the averaged velocity field near the cylinder. The gradients of the longitudinal velocity component were used to determine the shear stresses on the bottom of the channel. It is shown that the presence of the cylinder in the flow causes considerable averaged vertical velocities and a significant change in the shear stresses on the bottom of the channel.     

Considerations for the design of swirl chambers for the cyclone cooling of turbine blades and for other applications with high swirl intensity

The focus of this study lies on turbulent incompressible swirling flows with high swirl intensity. A systematic parameter study is conducted to examine the sensitivity of the mean velocity field in a swirl chamber to changes in the Reynolds number, swirl intensity and channel outlet geometry. The investigated parameter range reflects the typical kinematic flow conditions found in heat transfer applications, such as the cooling of the turbine blade known as cyclone cooling. These applications require a swirl intensity, which is typically much higher than necessary for vortex breakdown. The resulting flows are known as flow regime II and III. In comparison to flow regime I, which denotes a swirling flow without vortex breakdown, these flow regimes are characterized by a subcritical behavior. In this context, subcritical means that the flow is affected by the downstream channel section. Based on mean velocity field measurements in various swirl chamber configurations, it is shown that flow regime III is particularly sensitive to these effects. The channel outlet geometry becomes a determining parameter and, therefore, small changes at the outlet can produce entirely different flow patterns in the swirl chamber. In contrast, flow regime II, as well as flow regime I and axial channel flows, are much less sensitive to changes at the channel outlet. The knowledge about the sensitivity of the flow in different flow regimes is highly relevant for the design of a cyclone cooling system. Cooling systems employing flow regime III can result in a weakly robust flow system that may change completely over the operating range. As a remedy, the swirl intensity needs to be decreased so that flow regime III cannot be reached, which, however, reduces the maximum achievable heat transfer in the cooling system. Alternatively, the flow has to transition back from flow regime III to flow regime II or I before the flow leaves the swirl chamber. Two practical methods are presented. These findings can be directly applied in the design processes of future cyclone cooling systems, and other applications of swirling flow.     

On Disturbance Propagation in Internal-Flow Boundary Layers

The unsteady interaction of plane-channel wall boundary layers with a supersonic inviscid flow is investigated. The flow regimes in which disturbances introduced by the boundary layer developing on one wall influence the boundary layer on the other wall are considered. The regime of relatively large pressure disturbance amplitudes generated near the nozzle outlet or by deforming the channel walls is studied. In these conditions, the interaction process is described by a system of Burgers equations with retarded arguments. Numerical solutions of this system are obtained for symmetric and antisymmetric perturbations of the channel walls.     

Similarity of apparently random structures in the outer region of wall turbulence

Structural similarities between samples of individual, apparently random structures in various wall-bounded turbulent flows are examined using a template-matching technique. Two-dimensional structural patterns obtained by particle image velocimetry in a turbulent boundary layer are sampled along streamwise lines to extract one-dimensional spatial series that are used as templates. These templates are correlated with time series data obtained in turbulent pipe flow, turbulent channel flow, and atmospheric boundary layer flow in order to determine the frequency and coherency with which similar structures occur. The results indicate that a small ensemble of templates from one flow can be concatenated to represent a large fraction of the entire velocity-time history of each of the other flows by using episodes during which the various templates correlate well. Thus, within the pipe flow, channel flow, and atmospheric boundary layer, one frequently finds detailed time series segments that coincide closely, i.e., in fine detail, with a handful of templates found in a laboratory boundary layer. This type of similarity, which includes seemingly random, fine details at large and small scales, is much stronger than similarity based on statistical comparisons. The individual templates that work best, i.e., those that most frequently yield episodes of high correlation, are segments of hairpin-vortex packets. The high frequency with which these particular structures occur suggests that they are common features of all wall-bounded turbulent flows, including turbulent flows at very high Reynolds number such as the atmospheric boundary layer.     

Analytical modeling of constricted channel flow

Analytical flow models are frequently applied when describing constricted channel flow at low and moderate Reynolds numbers. A common assumption underlying such flow models is two-dimensional or axi-symmetrical flow. In this work, two analytical model approaches are formulated in order to overcome this assumption in the case of naturally occurring channel flows for which the assumption might be critiqued. Advantages and flaws of both model approaches are discussed and their outcome is compared with experimental data.