Channel Of Rectangular Cross-section Research Articles

Heat Transfer Around Sharp 180-deg Turns in Smooth Rectangular Channels

Measured Nusselt numbers are presented for forced convection within and around sharp 180-deg turns in smooth channels of rectangular cross section. Separately determined top wall, bottom wall, and side wall values are presented individually along with azimuthal averages. The geometry of the channels and connecting turn is characterized by the parameters W*, the ratio of upstream and downstream channel widths; D*, the nondimensional channel depth; and H*, the nondimensional clearance at the tip of the turn. Results from nine combinations of these parameters are presented at several values of channel Reynolds number to illustrate the effect of turn geometry on the heat transfer distributions.

Linearly stratified, rotating flow over long ridges in a channel

The flow of a rotating, linearly stratified fluid over a long symmetric ridge in a channel is investigated experimentally. The laboratory apparatus consists of a long channel of rectangular cross section. The upper bounding surface is a transparent, horizontal plane; the lower boundary is a horizontal flexible belt. The belt serves as a false bottom of the channel and is translated parallel to its long axis. Topographic features are mounted on the belt and are towed through a salt-stratified fluid which is otherwise at rest relative to a rotating observer; the channel rests on a rotating table whose rotation axis is vertical. The most important dimensionless parameters governing the motion are the Rossby and Ekman numbers, a stratification parameter defined as the ratio of the Brunt-Vaisala frequency to the Coriolis parameter, and the geometrical parameters defining the aspect ratio of the ridge, the ridge height to channel depth ratio and the ridge to channel width ratios. An analysis is presented that demonstrates the conditions under which centrifugal effects can be neglected in such laboratory experiments. The analysis also shows the conditions under which the laboratory flows should be a good approximation to the quasigeostrophic potential vorticity equations and attendant boundary conditions for the oceans and atmosphere. This analysis is made for a general three-dimensional topographic feature; i.e. it is not restricted to a long ridge. The laboratory system seems to be an excellent vehicle for modelling oceanic flows but does not properly reproduce a non-Boussinesq term in the atmospheric equation. An analysis for an infinitely long ridge is presented. The predictions so obtained are in good qualitative agreement with the experiments. The quantitative agreement, for the range of parameters considered however, is shown to be poor and this is attributed to neglecting the effects of the lateral bounding surfaces. The experiments demonstrate that for fixed rotation, stratification and free stream speed, the streakline deflection caused by the topography decays with height. For such experiments the flow in the lower levels for positive upward rotation deflects to the left before reaching the ridge, then continues to deflect to the left on the upwind side of the ridge before beginning a rightward drift slightly upstream of the mountain crest. 1 his rightward drift continues on the downwind side of the ridge and well downstream ot the ridge itself before reaching a maximum shift, from which a leftward drift again begins. Increased rotation, other parameters being held fixed, provides stronger horizontal streakhne deflections. Stronger stratification, other parameters being fixed leads to stronger downslope winds and possibly flow separation in the lee. Various charactenstics of the flow field, such as the distance upstream to which substantial streakline curvature is observed, are measured as functions of the various system parameters; comparisons with the infinite ridge theory are also made The downstream motion is accompanied by lee waves for the major portion of the parameter space examined. The amplitude of these waves is shown to decrease with increased rotation other parameters being held fixed. Some non-rotating experiments and these are shown to be in good agreement with the model of Long (1955) and the measured wavelengths are found to be in good agreement with linear theory and laboratory measurements made by other investigators. Measurements of Queney (1947) are presented which show that the horizontal wavelenghts of the waves decrease for increased rotation, other parameters being fixed. A flow regime map based on the observed structure of the vertical wave motion is developed and it is shown that for the range of parameters considered, rotation plays only a minor role, if any.

Regimes of axisymmetric flow in an internally heated rotating fluid

A boundary-layer scale analysis is presented for steady, zonally symmetric flow in a Cartesian channel of rectangular cross-section, subject to uniform internal heating, and cooling at the lateral boundaries, using an approach based on that of Hignett, Ibbetson & Killworth for a related system. Six main flow regimes are identified, depending chiefly upon the magnitude of the parameter ℙ defined as the square of the ratio of the (non-rotating) thermal-boundary-layer thickness scale to that of the Ekman layers adjacent to the horizontal boundaries. For , where [Aopf ] is the Rayleigh number and ε the channel aspect ratio), the flow consists of an advectively dominated interior, characterized by a balance between vertical advection and internal heat generation, diffusively dominated thermal boundary layers adjacent to the sidewalls, and horizontal, viscously dominated Ekman layers (for non-zero rotation rate). If ℙ [Lt ] 1, the flow is only weakly modified by rotation, but as ℙ increases through unity, rotation tends to inhibit heat transfer and thickens the thermal boundary layers. Provided ℙ [Gt ] ε2σ −2, (where σ is the Prandtl number), the zonal flow is predominantly geostrophic, though not given by the conventional thermal-wind scale (based on the total thermal contrast ΔT) unless ℙ [Gt ] 1.The results of the scale analysis are compared with laboratory measurements and numerical simulations of steady flow in a rotating, cylindrical annulus subject to (radially non-uniform) internal heating and sidewall cooling. Over the range of parameters accessible in the laboratory, the azimuthal velocity scale and thermal contrast were found to vary with rotation and heating rates in the way predicted from the scale analysis for the Cartesian system. Above a certain critical value of ℙ (for the geometry used here ℙt ≈ 1), the baroclinic wave regime was found to occur, corresponding to where rotational constraints first begin to influence significantly the heat transfer of the axisymmetric flow. The numerical simulations are compared with the laboratory measurements, and used to extend the ranges of rotation rate and aspect ratio over which the scale analysis could be verified. Good agreement was found for the dependence of globally averaged flow parameters on ℙ, and the dynamical characteristics of each regime were further verified using explicit calculations of the balance of terms in the basic equations from the numerical model.Further applications of the scaling technique to other, related systems are also discussed, together with a consideration of its generalization to systems of geophysical interest.

Turbulent flow of gas in a curvilinear channel in the presence of suction from a separation region

Integral parameters that characterize reversible and irreversible changes in the flux of the total pressure in channels with perforated walls are introduced. An experimental investigation was made of subsonic gas flow in curvilinear channels of rectangular cross section in the presence of suction of gas from a separation region of the flow formed on an internal (convex) strongly curved wall of the channel. The optimal position of the suction slit was determined and it was shown to be possible to reduce appreciably the loss in the channel and improve its gas-dynamic characteristics. Two-dimensional turbulent flow of an incompressible fluid in curvilinear channels in the presence of suction was simulated numerically. The mathematical model is based on the complete system of Navier-Stokes equations, additional differential equations for the energy of the turbulence and the rate of its dissipation, special correction equations to take into account the curvature of the streamlines, and model boundary conditions for the sections of the walls through which the suction of the fluid takes place.

Cylindrical Flow in and Over Channels of Irregular Shape

AbstractEarlier work by Nye (1965), who obtained numerical solutions for axial independent flow of a non-linear Glen material in channels of rectangular, elliptic, and parabolic cross-sections with a null-slip basal condition, is extended by using an inverse technique. Exact analytical solutions are obtained for flow in irregular-shaped channels (subject to symmetry restrictions) for both a Newtonian and an n = 3 Glen material. The cross-sections are regulated by multi-parameters. Solutions are obtained for two types of channel: (a) those whose side walls meet the free ice surface vertically, and (b) periodic channel arrays whose basal profiles do not intersect the free ice surface, i.e. overfilled channels. Solutions for the second type have not been presented previously. The solutions for then= 3 Glen material employ a small parameter which limits the geometry variation to perturbations on semicircular or uniform-depth channels. Basal slip conditions can be incorporated although results are not presented here.

Cylindrical Flow in and Over Channels of Irregular Shape

AbstractEarlier work by Nye (1965), who obtained numerical solutions for axial independent flow of a non-linear Glen material in channels of rectangular, elliptic, and parabolic cross-sections with a null-slip basal condition, is extended by using an inverse technique. Exact analytical solutions are obtained for flow in irregular-shaped channels (subject to symmetry restrictions) for both a Newtonian and an n = 3 Glen material. The cross-sections are regulated by multi-parameters. Solutions are obtained for two types of channel: (a) those whose side walls meet the free ice surface vertically, and (b) periodic channel arrays whose basal profiles do not intersect the free ice surface, i.e. overfilled channels. Solutions for the second type have not been presented previously. The solutions for the n = 3 Glen material employ a small parameter which limits the geometry variation to perturbations on semicircular or uniform-depth channels. Basal slip conditions can be incorporated although results are not presented here.

Some observations of the subcritical transition in plane Poiseuille flow

The subcritical transition in plane Poiseuille flow (generated in a long wind channel of rectangular cross-section) was studied experimentally. Cylinder-generated vortical disturbances were introduced into the parabolic flow (in the test section) or the inlet flow. The parabolic flow was also disturbed by a controlled periodic jet from a wall orifice. On the basis of the three kinds of observations, we come to the conclusion that the minimum transition Reynolds number is about 1000 and the related threshold intensity (of the external disturbance triggering the transition) is comparable to the maximum intensity of u-fluctuations in fully turbulent channel flows.

Pressure Loss Through Sharp 180 Deg Turns in Smooth Rectangular Channels

Measured pressure distributions, pressure loss coefficients, and surface streamline visualizations are presented for 180 deg turns in smooth, rectangular cross-section channels. The flow geometry models situations that exist in multipass internal cooling of gas turbine engine airfoils. The turn geometry is characterized by parameters W*, the ratio of upstream and downstream channel widths; D*, the nondimensional channel depth; H*, the nondimensional clearance height at the tip of the turn; and R*, the nondimensional corner fillet radius. The present results cover a range of combinations of geometry parameters and Reynolds numbers to aid in prediction of coolant flow rates in present and future cooled airfoil designs.

Boundary Shear in Smooth Rectangular Channels

The results of some experiments are reported concerning the boundary shear stress and boundary shear force distributions in a smooth channel of rectangular cross section. An empirically derived equation is presented which gives the percentage of the total shear force carried by the walls as a function of the breadth/depth ratio. Ancillary equations are presented giving the mean wall, bed, and bed center line shear stresses as functions of aspect ratio. A comparison is made between boundary shear stress distributions in open channel and closed conduit flows at comparable aspect ratios. Certain differences are noted in both the distributions and the mean resistance coefficients on account of different secondary flow structure. The results will be useful to those engaged in resistance, sediment, or dispersion studies.

Laminar Forced Convection Heat Transfer in Curved Channels of Rectangular Cross Section

縦横比0.8から5まで計8種の形状の,長方形断面曲り管内の発達した層流強制対流熱伝達を,熱流束一定で断面の周囲壁温が一定の仮定のもとで,ディーン数11～320(Re数100～3600)について数値解を求めた.その結果,いくつかの縦横比において,ディーン数の増加につれて付随渦の発生・消滅・再発生がある.付随渦の発生に伴い.平均管摩擦係数,平均ヌセルト数は著しく増加する。

Characteristics of Turbulent Flow and Mass Transfer in Divergent Channels of Rectangular Section

The characteristics of turbulent flow and mass transfer in divergent channels of rectangular cross-section were experinlentally investigated and the typical effects of main flow and the secondary flow on mass transfer were discussed. Sherwood number Shx, could be suitably expressed by Reynolds number Rex, and acceleration parameter K. Sherwood numbers Shx, in the entrance region of mass concentration were proportional to Rex, 0.83 for every diver-gent angle in the present experiment. The velocity profiles in the upper region were recognized as a composite structure consisting of those for the inner and outer layers. but it was difficult to predict the velocity profiles in the lower region with the plane jet profile.

Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel

Results of laboratory experiments are presented in which a finite volume of homogeneous fluid was released instantaneously into another fluid of slightly lower density. The experiments were performed in a channel of rectangular cross-section, and the two fluids used were salt water and fresh water. As previously reported, the resulting gravity current, if viscous effects are negligible, passes through two distinct phases: an initial adjustment phase, during which the initial conditions are important, and an eventual self-similar phase, in which the front speed decreases as t−1/3 (where t is the time measured from release). The experiments reported herein were designed to emphasize the inviscid motion. From our observations we argue that the current front moves steadily in the first phase, and that the transition to the inviscid self-similar phase occurs when a disturbance generated at the endwall (or plane of symmetry) overtakes the front. If the initial depth of the heavy fluid is equal to or slightly less than the total depth of the fluid in the channel, the disturbance has the appearance of an internal hydraulic drop. Otherwise, the disturbance is a long wave of depression. Measurements of the duration of the initial phase and of the speed and depth of the front during this phase are presented as functions of the ratio of the initial heavy fluid depth to the total fluid depth. These measurements are compared with numerical solutions of the shallow-water equations for a two-layer fluid.

Vortex shedding in rotating flows

Abstract A rotating tow facility whose principle element is a long acrylic channel of rectangular cross-section has been developed. A smooth flexible belt, which can be translated along the channel axis, serves as a false horizontal floor. The system is mounted on a turntable which rotates at a constant angular speed about a vertical axis. The working fluid is bounded above by a sheet of acrylic plastic which can be tilted to simulate the beta effect. Topographic features are mounted on the belt and the flow past these obstacles is made visible by utilizing the electrolytic precipitation technique and recorded by a video tape camera system which translates with the belt. A series of fplane experiments on the flow past a right circular cylinder extending from the belt to the upper bounding surface is investigated in the Reynolds number range 65 < Re < 2,300. It is shown that rotation and the cylinder aspect ratio have a strong influence on the resulting flow characteristics including the Strouhal number. F...

Investigation of the distribution of the static pressure and the tangential stresses on the walls of a curvilinear channel

The results are given of experimental investigations into the deformation of the field of the static pressure and the tangential stresses on the walls of a channel of rectangular cross section under the influence of longitudinal curvature.

Theoretical and experimental investigations of the flow of a viscous fluid near the line of intersection of a cylindrical surface and a flat surface

Flow along a corner was investigated at large Reynolds numbers in, for example, [1–3]. The present author [4] considered flow in the neighborhood of a corner formed by the intersection of a plane and a concave cylindrical surface, the main attention being devoted to the formation of the three-dimensional boundary layer on the plane near the corner. It was shown that the curvature of one of the intersecting surfaces changes the flow pattern qualitatively. In the present paper, we report an investigation of the formation of the flow on a concave cylindrical surface near such a corner and consider how the flow is rearranged in the neighborhood of a corner in, for example, a channel of rectangular cross section that has an initial straight section and then a bend with a discontinuity of the curvature of the line of intersection of the concave and flat sides of the channel. The results are given of some experimental investigations of flow near the line of intersection of a flat wall and a curved (concave and convex) wall at a bend in a rectangular channel.

The effect of aspect ratio on longitudinal diffusivity in rectangular channels

In a recent paper Doshi, Daiya &amp; Gill (1978) showed that the value of Taylor's longitudinal diffusivity D for laminar flow in a channel of rectangular cross-section of breadth u and height b is about 8D0, for large values of the aspect ratio a/b, where Do is the value of the longitudinal diffusivity obtained by ignoring all variation across the channel. This superficially surprising result is confirmed by an independent method, and is shown to be caused by the boundary layers on the side walls of the channel. The primary purpose of the paper, however, is to consider the value of D in turbulent flow in a flat-bottomed channel of large aspect ratio, for which arguments based on physics are adduced in support of the formula D≈[1 + B][1 - λ(b/u)], where B and λ are positive constants independent of b. It is shown that this result is consistent with laboratory experiments by Fischer (1966). The paper concludes with a discussion of the practical effects of aspect ratio on longitudinal dispersion in channels whose cross-section is approximately rectangular.

Nonuniform Laminar Free-Surface Flow

Industrial flow processes involving molten substances or other highly viscous liquids frequently make use of conveyance by open channels. A one-dimensional analysis is undertaken of laminar flow in horizontal open channels of rectangular cross-section. A closed-form analytical solution is obtained for the non-dimensional surface profile of type H 2 and H 3 . The non-dimensional profiles are independent of the Reynolds number of flow but are a distinct function of the aspect ratio of the flow but are a distinct function of the aspect ratio of the flow cross-section. The analytically predicted profiles are found to be in good agreement with the results of experimental observations, except in the immediate vicinity of the critical depth where small discrepancies occur. In distinct contrast to turbulent flow, the location of the critical depth upstream from the brink of a vertical channel drop is found to increase with the Reynolds number of flow.

On the flow of an ionized gas in a MHD generator with segmented electrodes

In this paper a mathematical model is given, for the flow of ionised gases in a channel of MHD conversion on the hypothesis that the external magnetic field is applied only in the zone of the electrodes. The rectangular cross-section channel carriesN pairs, of segmented electrodes. The solution is expressed in terms of Fourier series distinct in the electrode zones from those in the isolators zones. The coefficients are determined by the matching conditions at the ends of the electrodes. The characteristics of the generator are determined and a computing program forN=2 is given.

Induced molecular transport due to surface acoustic waves

An investigation into the possiblity of inducing a net transport of molecules via their interaction with a propagating surface acoustic wave is reported here. A theory is presented predicting such a transport and giving a formula for the pumping rate of a device consisting of two evacuated chambers connected by a channel of rectangular cross section containing a surface on which a surface acoustic wave is propagating. This formula gives the parametric dependence of the pumping rate on the wavelength, amplitude and velocity of the surface acoustic wave, and the mean molecular velocity of the gas. The results of an experimental investigation are also given. The experiment, conducted with air at approximately 3 μ and a surface acoustic wave on a lithium niobate substrate, confirms the existence of transport and gives a pumping rate which compares favorably with the theoretical prediction. Possible applications of this effect include its use in vacuum technology and studies of surfaces and surface interactions.

Unstable Turbulent Flow in Open Channels

Controversy on the determination of the friction factor, f, for turbulent flow in open channels of rectangular cross section has existed among previous investigators. A number of them found that the Froude number affects the value of the friction factor, while others did not find such a dependence. In this study, the theoretical expression for the critical Froude number is first derived. Given a value of the Reynolds number, the flow becomes unstable above the critical Froude number. This critical Froude number, which appears to be strongly dependent upon the channel width, is then introduced in an equation by Rouse to calculate the values of the friction factor under unstable flow conditions. The influence of the Froude number on the friction factor appears to be important, but the channel width is a determinating factor as well.