Showing papers on "Open-channel flow published in 1992"
TL;DR: In this paper, a complete set of perturbations, ordered by energy growth, is found using variational methods. But the optimal perturbation is not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbance to grow by as much as three orders of magnitude.
Abstract: Transition to turbulence in plane channel flow occurs even for conditions under which modes of the linearized dynamical system associated with the flow are stable. In this paper an attempt is made to understand this phenomena by finding the linear three‐dimensional perturbations that gain the most energy in a given time period. A complete set of perturbations, ordered by energy growth, is found using variational methods. The optimal perturbations are not of modal form, and those which grow the most resemble streamwise vortices, which divert the mean flow energy into streaks of streamwise velocity and enable the energy of the perturbation to grow by as much as three orders of magnitude. It is suggested that excitation of these perturbations facilitates transition from laminar to turbulent flow. The variational method used to find the optimal perturbations in a shear flow also allows construction of tight bounds on growth rate and determination of regions of absolute stability in which no perturbation growth is possible.
1,083 citations
TL;DR: In this paper, the response of wall-flow turbulence to high-frequency spanwise oscillations was investigated by direct numerical simulations of a planar channel flow subjected either to an oscillatory spanwise crossflow or to the span-wise oscillatory motion of a channel wall.
Abstract: The response of wall‐flow turbulence to high‐frequency spanwise oscillations was investigated by direct numerical simulations of a planar channel flow subjected either to an oscillatory spanwise cross‐flow or to the spanwise oscillatory motion of a channel wall. Periods of oscillation, Tosc+=Toscuτ2/ν, ranging from 25 to 500 were studied. For 25≤Tosc+≤200 the turbulent bursting process was suppressed, leading to sustained reductions of 10% to 40% in the turbulent drag and comparable attenuations in all three components of turbulence intensities as well as the turbulent Reynolds shear stress. Oscillations at Tosc+=100 produced the most effective suppression of turbulence. The results were independent of whether the oscillations were generated by a cross‐flow or by the motion of a channel wall. In the latter case, suppression of turbulence was restricted to the oscillating wall while the flow at the other wall remained fully turbulent. Spanwise oscillations may provide a simple and effective method for control of turbulence in wall‐bounded flows.
453 citations
TL;DR: In this article, low-Reynolds-number effects are observed in the inner region of a fully developed turbulent channel flow, using data obtained either from experiments or by direct numerical simulations.
Abstract: Low-Reynolds-number effects are observed in the inner region of a fully developed turbulent channel flow, using data obtained either from experiments or by direct numerical simulations. The Reynolds-number influence is observed on the turbulence intensities and to a lesser degree on the average production and dissipation of the turbulent energy. In the near-wall region, the data confirm Wei and Willmarth's (1989) conclusion that the Reynolds stresses do not scale on wall variables. One of the reasons proposed to account for this behavior, namely, the 'geometry' effect or direct interaction between inner regions on opposite walls, was investigated in some detail by introducing temperature at one of the walls, both in experiment and simulation. Although the extent of penetration of thermal excursions into the opposite side of the channel can be significant at low Reynolds numbers, the contribution these excursions make to the Reynolds shear stress and the spanwise vorticity in the opposite wall region is negligible. In the inner region, spectra and cospectra of the velocity fluctuations u and v change rapidly with the Reynolds number, the variations being mainly confined to low wavenumbers in the u spectrum.
228 citations
TL;DR: In this article, the authors developed a model that predicts all the essential features of the curves of pressure and flow rate versus time in the oscillatory flow regime, but fluid elasticity was found not to be an essential element.
Abstract: Certain polymers exhibit two distinct branches in their capillary flow curves (wall shear stress versus apparent wall shear rate). This gives rise to oscillatory flow in constant‐piston‐speed rheometers and to flow curve hysteresis in controlled‐pressure rheometers. These curious phenomena have attracted considerable interest over a period of many years, but their basic mechanisms are still the subject of debate. Building on previous work we have developed a model that predicts all the essential features of the curves of pressure and flow rate versus time in the oscillatory flow regime. Fluid compressibility and the second branch of the flow curve are necessary features of the model, but fluid elasticity is found not to be an essential element. While our macroscopic measurements do not prove it conclusively, our data lead us to believe that on the high‐flow‐rate branch of the flow curve there is slip along a cylindrical fracture surface near the wall. The jump to the high‐flow branch occurs when this fracture occurs, at an upper critical value of the shear stress, while the jump back to the low‐flow branch occurs when adhesion is established at the fracture surface at a lower critical shear stress.
190 citations
TL;DR: Turbulent Taylor vortex flow is studied in experiments for Reynolds numbers 10 3
Abstract: Turbulent Taylor vortex flow is studied in experiments for Reynolds numbers ${10}^{3}$R${10}^{6}$. Simple scaling of the torque with Reynolds number is m/Inot observed for any range of R, although the characteristic time scales and the transport of passive scalars are found to scale with the global torque measurements. Above a nonhysteretic transition observed at R=1.3\ifmmode\times\else\texttimes\fi{}${10}^{4}$, the torque has a Reynolds number dependence similar to the drag observed in wall-bounded shear flows such as pipe flow and flow over a flat plate.
187 citations
TL;DR: In this article, the authors provided an analysis of the flow in the neighbourhood of the cusp, via an idealized problem which is solved completely: the cylinders are represented by a vortex dipole and the solution is obtained by complex variable techniques.
Abstract: When two cylinders are counter-rotated at low Reynolds number about parallel horizontal axes below the free surface of a viscous fluid, the rotation being such as to induce convergence of the flow on the free surface, then above a certain critical angular velocity Ωc, the free surface dips downwards and a cusp forms. This paper provides an analysis of the flow in the neighbourhood of the cusp, via an idealized problem which is solved completely: the cylinders are represented by a vortex dipole and the solution is obtained by complex variable techniques. Surface tension effects are included, but gravity is neglected. The solution is analytic for finite capillary number [Cscr ], but the radius of curvature on the line of symmetry on the free surface is proportional to exp (−32π[Cscr ]) and is extremely small for [Cscr ] [gsim ] 0.25, implying (in a real fluid) the formation of a cusp. The equation of the free surface is cubic in (x, y) with coefficients depending on [Cscr ], and with a cusp singularity when [Cscr ] = ∞.The influence of gravity is considered through a stability analysis of the free surface subjected to converging uniform strain, and a necessary condition for the development of a finite-amplitude disturbance of the free surface is obtained.An experiment was carried out using the counter-rotating cylinders as described above, over a range of capillary numbers from zero to 60; the resulting photographs of a cross-section of the free surface are shown in figure 13. For Ω Ωc, the downward-pointing cusp forms, and its structure shows good agreement with the foregoing theory.
182 citations
TL;DR: The addition of a dissipation step to the widely used McCormack numerical scheme is proposed for solving one-dimensional open-channel flow equations according to the theory of total variation diminishing (TVD) schemes that are capable of capturing sharp discontinuities without generating the spurious oscillations that more classical methods do.
Abstract: The addition of a dissipation step to the widely used McCormack numerical scheme is proposed for solving one-dimensional open-channel flow equations. The extra step is devised according to the theory of total variation diminishing (TVD) schemes that are capable of capturing sharp discontinuities without generating the spurious oscillations that more classical methods do. At the same time, the extra step does not introduce any additional difficulty for the treatment of the source terms of the equations. Results from several computations are presented and comparison with the analytical solution for some test problems is shown. The overall performance of the method can be considered very good, and it allows for accurate open-channel flow computations involving hydraulic jumps and bores.
159 citations
TL;DR: In this paper, the late stages of transition from the?-vortex stage up to turbulence are investigated by postprocessing data from a direct numerical simulation of the complete K-type transition process in plane channel flow at a Reynolds number of 5000 (based on channel halfwidth and laminar centreline velocity).
Abstract: The late stages of transition, from the ?-vortex stage up to turbulence, are investigated by postprocessing data from a direct numerical simulation of the complete K-type transition process in plane channel flow at a Reynolds number of 5000 (based on channel half-width and laminar centreline velocity). The deterministic roll-up of the high-shear layer that forms around the ?-vortices is examined in detail. The new vortices arising from this process are visualized by plotting three-dimensional surfaces of constant pressure. Five vortices are observed, with one of these developing into a strong hairpin-shaped vortex. Interactions between the different vortices, and between the two channel halves, are found to be important. In the very last stage of transition second-generation shear layers are observed to form and roll up into new vortices. It is postulated that at this stage a sustainable mechanism of wall-bounded turbulence exists in an elementary form. The features which are locally present include high wall shear, sublayer streaks, ejections and sweeps. Large-scale energetic vortices are found to be an important part of the mechanism by which the turbulence spreads to other spanwise positions. The generality of the findings are discussed with reference to data from simulations of H-type and mixed-type transition
121 citations
109 citations
TL;DR: In this article, the relative roughness resistance equation was used to reproduce the n−VR retardance curves in a grassed channel, and the authors described some problems associated with stability design.
Abstract: The resistance to flow in a grassed channel is linked directly to the relative roughness of the flow through long‐accepted boundary‐layer principles. The difference between flow over grass linings and linings composed of rigid materials such as riprap or concrete lies in the tendency of the grass to deform under an imposed fluid shear. This deformation results in a smoothing of the channel roughness with increasing flow. Mathematically, this can be accommodated with coefficients that define the Darcy‐Weisbach friction factor and are dependent on relative values of boundary shear and vegetative stiffness. The emphasis of the paper is on showing that the relative roughness resistance equation can successfully reproduce the n‐VR retardance curves. Aspects of channel stability are discussed and the paper describes some problems associated with stability design.
103 citations
TL;DR: In this article, the linear stability of the Kolmogorov flow ψ0=sin(y) (Kolmogov flow) is considered, taking into account viscosity, linear friction, and confinement (lateral walls).
Abstract: The linear stability of the parallel flow ψ0=sin(y) (Kolmogorov flow) is considered, taking into account viscosity, linear friction, and confinement (lateral walls). The computations provide neutral stability curves in the parameter space, wave numbers, and wave speeds, as well as the spatial structure of first unstable modes. Evidence is presented that stability parameters depend nonuniformly on the confinement. It is shown that already weak transverse confinement significantly decreases the longitudinal wavelength of perturbations at instability onset. Strong confinement changes the character of the instability into an oscillatory one instead of a purely exponential growing mode, which is obtained for weakly confined systems. Theoretical predictions of critical parameters are in reasonable agreement with experimental results in electromagnetically driven flows of conducting fluids.
TL;DR: In this paper, the use of the McCormack explicit finite difference scheme and the treatment of the boundary problem in the development of a one-dimensional simulation model that solves the St. Venant equations of the unsteady open channel flow is described.
Abstract: This paper describes the use of the McCormack explicit finite difference scheme and the treatment of the boundary problem in the development of a one-dimensional simulation model that solves the St. Venant equations of the unsteady open channel flow. External and internal boundaries are considered. Various illustrative cases are presented to show the efficiency of this technique.
TL;DR: In this article, an upwind finite difference scheme based on flux difference splitting is presented for the solution of the equations governing unsteady open channel hydraulics, and an approximate Jacobian needed for splitting the flux differences is defined that satisfies the conditions required to construct a first-order upwind conservative discretization of the equation.
Abstract: SUMMARY An upwind finite difference scheme based on flux difference splitting is presented for the solution of the equations governing unsteady open channel hydraulics. An approximate Jacobian needed for splitting the flux differences is defined that satisfies the conditions required to construct a first-order upwind conservative discretization of the equations. Added limited second-order corrections make the resulting scheme robust and accurate for the computation of all regimes of open channel flow. Some numerical results and comparisons with other classical schemes under exacting conditions are presented.
TL;DR: In this article, a three-dimensional hydrodynamic model is applied to flows in open channels and the model incorporates a second-moment turbulence-closure model that has demonstrated considerable skill in simulating turbulent flows.
Abstract: A three-dimensional, hydrodynamic model is applied to flows in open channels The model incorporates a second-moment turbulence-closure model that has demonstrated considerable skill in simulating turbulent flows in laboratory experiments and in various geophysical and engineering boundary layers The closure model consists of differential equations for turbulence energy and turbulence length scale The remaining second-moment equations are reduced to a set of algebraic equations in which tendency, advection, and diffusion terms are omitted To account for the effect of the free surface on the bulk of the channel flow, a modification of the macroscale equation is introduced; the rest of the model equations and their attendant nondimensional constants remain unchanged The model performance is assessed using laser-Doppler anemometer measurements on the centerline of a large number of laboratory, smooth and rough, homogeneous and stratified, open-channel flows with different values of the aspect ratio Good agreement is found between the model and data in every case Because the model is based upon a self-consistent framework and is able to reproduce the many experiments provided here, the model can be used with confidence in environmental applications
TL;DR: In this paper, a reconsideration of the fundamental role of the characteristics in the determination of the up-wind weighting and the use of the conservation form of the governing equations, leads to a new Petrov-Galerkin scheme entitled the characteristic dissipative Galerkin method.
Abstract: Many open‐channel flow problems may be modeled as depth‐averaged flows. Petrov‐Galerkin finite element methods, in which up‐wind weighted test functions are used to introduce selective numerical dissipation, have been used successfully for modeling open‐channel flow problems. The underlying consistency and generality of the finite element method is attractive because separate computational algorithms for subcritical and supercritical flow are not required and algorithm extension to the two‐dimensional depth‐averaged flow equations is straightforward. Here, a reconsideration of the fundamental role of the characteristics in the determination of the up‐wind weighting and the use of the conservation form of the governing equations, leads to a new Petrov‐Galerkin scheme entitled the characteristic dissipative Galerkin method. A linear stability analysis illustrates the selective damping of short wavelengths and excellent phase accuracy achieved by this scheme, as well as its insensitivity to parameter variati...
TL;DR: In this paper, the authors consider the two-dimensional quasi-steady Stokes flow of an incompressible Newtonian fluid occupying a time-dependent simply-connected region bounded by a free surface.
Abstract: We consider the two-dimensional quasi-steady Stokes flow of an incompressible Newtonian fluid occupying a time-dependent simply-connected region bounded by a free surface. The motion is driven by a constant surface tension acting at the free boundary so that, with the effects of gravity ignored, one expects the boundary to approach a circular form as time evolves. It is shown that, if at some initial instant the region occupied by the fluid is given by a rational conformal map of the unit disc, then it must retain this property as long as the region remains simply-connected. Moreover, its evolution may be described analytically; in simple cases this description is explicit, but in more complicated problems the numerical integration of a system of first order differential equations may be required.
TL;DR: In this article, a finite body in an incompressible viscous flow is shown to be contributed by a potential flow and fluid elements of non-zero vorticity in a revealing formulation.
Abstract: Forces on a finite body in an incompressible viscous flow are shown to be contributed by a potential flow and fluid elements of non-zero vorticity in a revealing formulation. The present study indicates that the potential flow play also a geometric role in determining the contribution of the fluid elements. Consideration is given to a solid body moving through a fluid, fluid accelerating past a solid body and a solid body which oscillates in a uniform stream. The effects of induced-mass and inertial forces appear naturally in the formulation and are separated from the contribution due to the surface vorticity and that due to the vorticity within the flow. Physical significance of the present analysis for vortical flows about a finite body is illustrated by examples, e.g. flow past a circular cylinder or an ellipsoid of revolution.
TL;DR: In this article, the authors used the critical point theory to analyze the surface flow patterns that constitute the imprints of the outer flow and to give a rational and coherent description of the vortical system generated by separation.
Abstract: Separation in three-dimensional flows leads to the formation of vortical structures resulting from rolling up of the viscous flow "sheet," initially contained in a thin boundary layer, which springs up from the surface into the outer perfect fluid flow. A clear physical understanding of this phenomenon must be based on a rational analysis of the flowfield structure using the critical-point theory. With the help of this theory, it is possible to interpret correctly the surface flow patterns that constitute the imprints of the outer flow and to give a rational and coherent description of the vortical system generated by separation. This kind of analysis is applied to separated flows forming on typical obstacles, the field of which has been thoroughly studied by means of visualizations and probings using multihole pressure probes and laser velocimetry. Thus, the skin friction line patterns of a transonic channel flow and of a multibody launcher are interpreted. Then, the vortical systems of a delta wing and an afterbody at an incidence are considered. The last two configurations are a missile fuselage-type body and an oblate ellipsoid. I. Introduction F LIGHT at high-incidenc e of combat aircraft or hypersonic vehicles during re-entry, as well as that of tactical missiles, raises practical interest on the study of three-dimensional separated flows. Applications also concern internal flows, in particular air intakes and turbomachines in which the often complex geometry of the channel and the existence of shock waves almost inevitably lead to boundary-laye r separation. In three-dimensional flows, separation entails the formation of vortical structures—frequently, but improperly, called vortices to simplify—form ed by rolling up of the viscous flow "sheet," previously confined in a thin layer attached to the wall, which suddenly springs into the outer nondissipative flow. Although it has been known for a long time, this phenomenon is still incompletely understood from a physical point of view and it is delicate to model due to the flowfield complexity, all the components of which are difficult to capture properly. Many predictive methods are based on perfect fluid models, the first of which use the vortex sheet concept. Such a sheet is defined as a surface of tangential discontinuity for the velocity field. The computational method can use different schemes: doublets, vortex filaments, vortex particles, and so forth. Publications in this domain are too numerous to be cited here. A greater accuracy in flow prediction can be obtained in the solution of the complete Euler equations, which allows, in theory, automatic capture of sheet-like disconti
TL;DR: In this article, mechanistic models have been developed for each of the existing two-phase flow patterns in an annulus, namely bubble flow, dispersed burst flow, slug flow, and annular flow.
Abstract: This paper reports that mechanistic models have been developed for each of the existing two-phase flow patterns in an annulus, namely bubble flow, dispersed bubble flow, slug flow, and annular flow. These models are based on two-phase flow physical phenomena and incorporate annulus characteristics such as casing and tubing diameters and degree of eccentricity. The models also apply to the new predictive means for friction factor and Taylor bubble rise velocity. Given a set of flow conditions, the existing flow pattern in the system can be predicted. The developed models are applied next for predicting the flow behavior, including the average volumetric liquid holdup and the average total pressure gradient for the existing flow pattern. In general, good aggrement was observed between the experimental data and model predictions.
TL;DR: In this paper, a near-wall two-equation model for turbulent heat fluxes is derived from the temperature variance and its dissipation-rate equations and the assumption of gradient transport.
TL;DR: In this paper, two-dimensional, depth-averaged, unsteady flow equations in a transformed coordinate system are solved numerically by using the MacCormack s...
Abstract: To analyze flows in channel expansions and contractions, two-dimensional, depth-averaged, unsteady flow equations in a transformed coordinate system are solved numerically by using the MacCormack s...
TL;DR: In this paper, an analytical model was developed to predict the heat transfer coefficient and friction factor of the louver fin geometry used in automotive radiators, based on boundary layer and channel flow equations, and accounts for the flow efficiency in the array.
Abstract: This paper is concerned with prediction of the air-side heat transfer coefficient of the louver fin geometry used in automotive radiators. An analytical model was developed to predict the heat transfer coefficient and friction factor of the louver fin geometry. The model is based on boundary layer and channel flow equations, and accounts for the[open quote] flow efficiency[close quotes] in the array, as previously reported by Webb and Trauger. The model has no empirical constants. The model allows independent specifications of all of the geometric parameters of the touver fin. This includes the number of louvers over the flow depth, the louver width and length, and the louver angle. The model was validated by predicting the heat transfer coefficient antifriction factor of 32 louver arrays tested by Davenport, which spanned hydraulic diameter based Reynolds numbers of 300-2800. At the highest Reynolds number, all of the heat transfer coefficients were predicted within a maximum error of [minus]14 /+ 25 percent, and a mean error of +/- percent. The high Reynolds number friction factors were predicted with a maximum error [minus]22 / + 26 percent, with a mean error of +/- 8 percent. The error ratios were slightly higher at the lowestmore » Reynolds numbers. 11 refs., 14 figs., 2 tabs.« less
TL;DR: In this paper, the shape and dimensions of a straight threshold channel are obtained by numerically solving the momentum balance equation for the fluid and the force balance equations for a sediment particle at the condition of impending motion.
Abstract: The shape and dimensions of the cross section of a straight threshold channel are obtained by numerically solving the momentum balance equation for the fluid and the force balance equation for a sediment particle at the condition of impending motion. The first equation accounts for lateral momentum diffusion from the center of the channel toward its banks, that is caused by Reynolds stresses. The resulting bank profile is accurately described by a fifth‐degree polynomial that is quite different from the cosine, parabolic, or exponential profiles that have been traditionally assumed to represent the shape of a threshold bank. In fact, it is demonstrated here that the cosine and parabolic bank shapes are unstable, while the exponential is overly stable. Equations for the design of threshold channel cross sections are presented. Channel dimensions predicted by these equations are in good agreement with values obtained from laboratory experiments.
TL;DR: In this paper, the effect of uneven wall temperature on the local heat transfer coefficient in a rotating square channel with smooth walls and radial outward flow is investigated for Reynolds numbers from 2500 to 25,000 and rotation numbers from 0 to 0.352.
Abstract: The effect of uneven wall temperature on the local heat transfer coefficient in a rotating square channel with smooth walls and radial outward flow is investigated for Reynolds numbers from 2500 to 25,000 and rotation numbers from 0 to 0.352. Three cases of thermal boundary conditions are studied: (1) four walls uniform temperature, (2) four walls uniform heat flux, and (3) leading and trailing walls hot and two side walls cold. It is shown that the heat transfer coefficients on the leading surface are much lower than that of the trailing surface due to rotation. For case 1, the leading surface heat transfer coefficient decreases and then increases with increasing rotation numbers, and the trailing surface heat transfer coefficient increases monotonically with rotation numbers. The trailing surface heat transfer coefficients, as well as those for the side walls, for case 2 are higher than for case 1, and the leading surface heat transfer coefficients for cases 2 and 3 are significantly higher than for case 1.
TL;DR: In this paper, a theoretical analysis to determine the effects of mass addition on the inviscid but rotational and compressible flowfield in a porous duct with the injection rate dependent on the local pressure is performed for large ratios of length-to-duc t diameter.
Abstract: A theoretical analysis to determine the effects of mass addition on the inviscid but rotational and compressible flowfield in a porous duct with the injection rate dependent on the local pressure is performed for large ratios of length-to-duc t diameter. The problem of describing the flow is reduced to the solution of a single integral equation. The ratio of specific heat 7, and a constant pressure exponent u, measuring the dependence of the rate of mass injection on the local pressure, are the parameters of the solutions. The integral equation is solved numerically, and parametric results are presented for 7, varying from 1 to f and for n varying from 0 to 1. A choking phenomenon is exhibited at a critical length of the duct in the vicinity of which the Mach number approaches unity. The choking condition, which is relevant to the operation of nozzleless solid-propellant rocket motors, is obtained parametrically in the present study and compared with corresponding results for irrotational, quasi-one-dimensional flow. The rotationality reduces the choking pressure. Nomenclature A = cross-sectional area of the duct a = radius of the duct C = average speed-of-sound in the fluid cp = the specific heat of the fluid at constant pressure h = half-height of channel 7sp = specific impulse of the motor K = constant prefactor in the burning-rate law for the propellant / = length of the duct M = Mach number m = mass burning rate of the propellant n = pressure exponent in the burning-rate law for the propellant P = nondimensional pressure p/pQ p = dimensional pressure R - ratio of the specific impulse obtained by assuming quasi-one-dimensional flow to the specific impulse obtained by assuming rotational flow r = dimensional radial coordinate 5 = perimeter of the duct T - temperature t = time u = axial component of the velocity Vw = injection velocity v = radial component of the velocity X — nondimensional axial strained coordinate defined in Eq. (23) x = dimensional axial coordinate y = distance normal to.the propellant surface y = ratio of specific heat A =. boundary-layer thickness 8 = gas-phase flame standoff distance 17 = dimensional transverse coordinate in channel flow p pp = gas density = propellant density = function related to entropy
TL;DR: A review of the current knowledge on the fluid mechanics and heat transfer behavior of viscoelastic aqueous polymer solutions in channel flow is presented in this paper, where both turbulent and laminar flow conditions are considered.
Abstract: A review of the current knowledge on the fluid mechanics and heat transfer behavior of viscoelastic aqueous polymer solutions in channel flow is presented. Both turbulent and laminar flow conditions are considered. Although the major emphasis is on fully established circular pipe flow, some results are also reported for flow in a 2:1 rectangular channel. For fully established turbulent channel flow, it was found that the friction factor, f, and the dimensionless heat transfer factor, jH , were functions of the Reynolds number and a dimensionless elasticity value, the Weissenberg number. For Weissenberg values greater than approximately 10 (the critical value) the friction factor was found to be a function only of the Reynolds number; for values less than 10 the friction factor was a function of both Re and Ws. For the dimensionless heat transfer coefficient jH the corresponding critical Weissenberg value was found to be about 100. The heat transfer reduction is always greater than the friction factor reduction; consequently, the heat transfer per unit pumping power decreases with increasing elasticity. For fully established laminar pipe flow of aqueous polymer solutions, the measured values of the friction factor and dimensionless heat transfer coefficient were in excellent agreement with the values predicted for a power law fluid. For laminar flow in a 2:1 rectangular channel the fully developed friction factor measurements were also in agreement with the power law prediction. In contrast, the measured local heat transfer coefficients for aqueous polymer solutions in laminar flow through the 2:1 rectangular duct were two to three times the values predicted for a purely viscous power law fluid. It is hypothesized that these high heat transfer coefficients are due to secondary motions, which come about as a result of the unequal normal stresses occurring in viscoelastic fluids. The anomalous behavior of one particular aqueous polymer solution—namely, polyacrylic acid (Carbopol)—is described in some detail, raising some interesting questions as to how viscoelastic fluids should be classified. In closing, a number of challenging research opportunities in the study of viscoelastic fluids are presented.
TL;DR: In this paper, an oil channel has been designed and built for drag reduction research, which is also well suited for investigations on turbulent flow and in particular on the dynamics of the viscous sublayer near the wall.
Abstract: For drag reduction research an oil channel has been designed and built. It is also well suited for investigations on turbulent flow and in particular on the dynamics of the viscous sublayer near the wall. The thickness of the viscous sublayer (y+= 5) can be varied between 1 and 4 mm. Surfaces with longitudinal ribs (“riblets”), which are known to reduce drag, can have fairly large dimensions. The lateral spacing of the ribs can lie between 3 and 10 mm, as compared to about 0.5 mm spacing for conventional wind tunnels. It has been proved by appropriate tests that the oil channel data are completely equivalent to data from other facilities and with other mean flow geometries. However, the shear stress data from the new oil channel are much more accurate than previous data due to a novel differential shear force balance with an accuracy of ±0.2%. In addition to shear stress measurements, velocity fluctuation measurements can be carried out with hot wire or hot film probes. In order to calibrate these probes, a moving sled permits to emulate the flow velocities with the fluid in the channel at rest. A number of additional innovations contribute to the improvement of the measurements, such as, e.g., (i) novel adjustable turbulators to maintain equilibrium turbulence in the channel, (ii) a “bubble trap” to avoid bubbles in the channel at high flow velocities, (iii) a simple method for the precision calibration of manometers, and (iv) the elimination of (Coulomb) friction in ball bearings. This latter fairly general invention is used for the wheels of the calibration unit of the balance. The channel has a cross section of 25 × 85 cm and is 11 m long. It is filled with about 4.5 metric tons of baby oil (white paraffine oil), which is transparent and odorless like water. The kinematic viscosity of the oil is v = 1.2×10−5 m2/s, and the highest (average) velocity is 1.29 m/s. Thus, the Reynolds number range (calculated with the channel width, 0.25 m) lies between 5,000 and 26,800 for fully established turbulent flow.
TL;DR: In this article, an analysis of the effects of the passive plane porous bed of an open channel on the steady, uniform, fully developed, two-dimensional turbulent shear flow is presented.
Abstract: An analysis of the effects of the passive plane porous bed of an open channel on the steady, uniform, fully developed, two‐dimensional turbulent shear flow is presented. The effect of the pervious boundary on the free flow is taken as a perturbation of an equivalent turbulent flow over an impervious bed of the same surface texture. The turbulence field is regarded as stationary and statistically homogeneous in planes parallel to the channel bottom. Expressions for the mean velocity, the Reynolds stress, and the induced stress distributions are derived and compared with available experimental data. The new concept of induced pressure is introduced, and its functional form is obtained. The presence of a porous bed will in general cause the friction factor to be directly proportional to the Reynolds number, which agrees with experimental findings. The validity of Phillips' formula for the computation of the induced stress is discussed and clarified. The presented analysis improves our understanding of the ph...