Pressure-driven startup flows of liquid crystalline polymers through slit cells

A wavy texture occurs in the flows of liquid crystalline polymers through a slit cell. In the present paper the development of the wavy texture is examined in pressure-driven startup flows for four types of slit cells, using a liquid crystalline solution of 50 wt% hydroxypropylcellulose (HPC). There exists a comparatively long induction period until the wavy texture appears after the startup of the flow, and the induction time decreases with increasing apparent shear rate. However, it is found that the apparent shear strain at which the wavy texture emerges is independent of the apparent shear rate though the value of the apparent shear strain slightly varies with the type of flow cell. Furthermore, the light scattering experiments are carried out to examine the structure of wavy texture. After the startup of the flow, a homogeneous pattern of the light scattering quickly shrink in size and a spike pattern perpendicular to the flow direction is emphasized. While the wavy texture is seen, the ellipsoidal pattern of light scattering oscillates with the same frequency as the passage of the wavy texture. A structure of scattering objects in the wavy texture is proposed, based on the observation of change in the light scattering pattern with time.     

Velocity field of convergent flow into a rectangular slit for a polymeric fluid

Three-dimensional velocity distributions in the entry region of a rectangular slit contraction were investigated using a dual-beam laser Doppler velocimeter. The flow of a silicone oil (a Newtonian fluid) and a solution of silicone rubber in the same silicone oil (a viscoelastic fluid) was studied at low Reynolds numbers (Re < 0.5). In contrast to the usual velocity distribution of a Newtonian fluid, the viscoelastic fluid showed the following characteristic features: (1) a pronounced axial velocity overshoot immediately after the slit entrance and a maximum before the slit exit; (2) appearance of an axial flow deceleration region just before the sharp acceleration near the slit entrance. Even more remarkably, a saddle form of velocity profile was found in the entrance region. This flow pattern is completely different from that found for Newtonian fluids and has not yet been explained using existing rheological analysis.Parts of this paper were presented at the IX. Intern. Congress on Rheology at Acapulco (Mexico), October 8–13, 1984     

Hydrodynamics of viscous fluid through porous slit with linear absorption

The exact solutions for the viscous fluid through a porous slit with linear ab-sorption are obtained. The Stokes equation with non-homogeneous boundary conditions is solved to get the expressions for the velocity components, pressure distribution, wall shear stress, fractional absorption, and leakage flux. The volume flow rate and mean flow rate are found to be useful in obtaining a convenient form of the longitudinal velocity component and pressure difference. The points of the maximum velocity components for a fixed axial distance are identified. The value of the linear absorption parameter is ran-domly chosen, and the rest available data of the rat kidney to the tabulate pressure drop and fractional absorption are incorporated. The effects of the linear absorption, uniform absorption, and flow rate parameters on the flow properties are discussed by graphs. It is found that forward flow occurs only if the volume flux per unit width is greater than the absorption velocity throughout the length of the slit, otherwise back flow may occur. The leakage flux increases with the increase in the linear absorption parameter. Streamlines are drawn to help the analysis of the flow behaviors during the absorption of the fluid flow through the renal tubule and purification of blood through an artificial kidney.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Direct Numerical Simulation of a Fully Developed Turbulent Flow over a Wavy Wall

Turbulent flow over a sinusoidal solid wavy surface was investigated by a direct numerical simulation using a spectral element technique. The train of waves has an amplitude to wavelength ratio of 0.05. For the flow conditions (Re=hU _b/2ν= 3460) considered, adverse pressure gradients were large enough to cause flow separation. Numerical results compare favorably with those of Hudson's (1993) measurements. Instantaneous flow fields show a large variation of the flow pattern in the spanwise direction in the separated bubble at a given time. A surprising result is the discovery of occasional velocity bursts which originate in the separated region and extend over large distances away from the wavy wall. Turbulence in this region is very different from that near a flat wall in that it is associated with a shear layer which is formed by flow separation. Received 17 April 1996 and accepted 19 November 1997     

Generation of the mean flow in the fluid layer with a nonuniformly heated wavy boundary

The problem of convection in the horizontal fluid layer with a wavy lower boundary is considered. It is shown that for the periodic temperature distribution with a certain phase shift given on the wavy boundary, in the fluid layer a unidirectional horizontal flow arises. The flow velocity linearly decreases with increase in attitude and depends on the relief distribution wavelength. There is an optimum wavelength (of the order of the layer thickness) at which the velocity reaches its maximum value.     

Study of steady viscous flow through a wavy channel: non-orthogonal coordinates

In this paper we consider the steady flow of a viscous fluid through a channel bounded by two sinusoidally varying plates differing in phase by π and separated by a mean distance 2h. For the non-varying channel, the classical parabolic velocity profile for the fully developed flow is well known. An attempt here is made to analyze the flow in a generalized non-orthogonal coordinate system that renders the wavy channels as plane walls. Continuity equation and Navier-Stokes equations are presented in the generalized coordinate system and simplified through use of small perturbation under small Reynolds number approximation. Flow characteristics such as centerline velocity and drag force have been evaluated and discussed.     

Structure of the temperature field in a flow over heated waves

Liquid crystal thermometry (LCT) was used to quantify temperature fields in a flow over resistively heated waves and assess the effect of the large-scale longitudinal structures that were previously obtained in the velocity field for an isothermal flow (A. Günther and P. Rudolf von Rohr, submitted article, 2002). The wavelength 6 was 10 times larger than the amplitude, and the considered Reynolds numbers were 725 and 3300, defined with the bulk velocity and the half-channel height. A constant heat flux was imposed at the wavy bottom wall. For the first time, LCT was used to determine the fluid temperature in a wall-bounded flow with heat transfer. The dominant spanwise scale obtained from a proper orthogonal decomposition (POD) of the fluid temperature field above an uphill location of the wavy wall was 1.56. It agrees well with the one previously obtained for a decomposition of the streamwise velocity.     

Free-convection boundary-layer flow of a non-Newtonian fluid along a vertical wavy surface

A theoretical analysis of laminar free-convection flow over a vertical isothermal wavy surface in a non-Nevvtonian power-law fluid is considered. The governing equations are first cast into a nondimensional form by using suitable boundary-layer variables that substract out the effect of the wavy surface from the boundary conditions. The boundary-layer equations are then solved numerically by a very efficient implicit finite-difference method known as the Keller-Box method. A sinusoidal surface is used to elucidate the effects of the power-law index, amplitude wavelength, and Prandtl number on the velocity and temperature fields, as well as on the local Nusselt number. It is shown that the local Nusselt number varies periodically along the wavy surface. The wave-length of the local Nusselt number variation is half that of the wavy surface, irrespective of whether the fluid is a Newtonian fluid or a non-Newtonian fluid. Comparisons with earlier works are also made, and the agreement is found to be very good.     

Drag reduction of a nonnewtonian fluid by fluid injection on a moving wall

Summary A boundary layer problem of a nonnewtonian fluid flow with fluid injection on a semi-infinite flat plate whose surface moves with a constant velocity in the opposite direction to that of the uniform mainstream is analyzed. Concluding similarity equations are solved numerically to show the dependence of the problem to the velocity ratio λ of the plate to uniform flow and to the injection velocity parameter C. The critical values of λ and C for each nonnewtonian power-law index n are obtained, and their significance in drag reduction is discussed. Received 26 August 1997; accepted for publication 21 October 1998     

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

A mathematical study is developed for the electro-osmotic flow of a nonNewtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer(EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelen...     

Velocity profile measurement by ultrasonic doppler method

The ultrasonic velocity profile measuring method has been developed at PSI for application in fluid mechanics and fluid flow measurement. It uses pulsed ultrasonic echography together with the detection of the instantaneous Doppler shift frequency. This method has the following advantages over the conventional techniques: (1) an efficient flow mapping process, (2) applicability to opaque liquids, and (3) a record of the spatiotemporal velocity field. After a brief introduction of its principle, the characteristics and specifications of the present system are given. Then examples in fluid engineering for oscillating pipe flow, T-branching flow of mercury, and recirculating flow in a square cavity are described that confirm the method's advantages. Several other works under way by other investigators are introduced. A potential for in-depth study of fluid dynamics is demonstrated by several examples from an investigation of modulated wavy flows in a rotating Couette system. The position-averaged power spectrum and the time-averaged energy spectral density were used to study the dynamic characteristics of the flow, and subsequently the velocity field was decomposed into its intrinsic wave structure based on two-dimensional Fourier analysis.     

Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder

PIV technique is applied for measurements of instant velocity distributions in a liquid film flowing down an inclined tube in the form of a wavy rivulet. An application of special optical calibration is applied to correct distortion effects caused by the curvature of the interface. A vortex flow of liquid is observed inside a wave hump in the reference system moving with wave phase velocity. Conditionally averaged profiles of longitudinal and transverse components of liquid velocity are obtained for different cross-sections of developed non-linear waves. It is shown that the increase in wave amplitude slightly changes the location of the vortex center. The analysis of modification of vortex motion character due to wavy flow conditions, such as tube inclination angle, film Reynolds number, wave excitation frequency, is fulfilled.     

TRPIV investigation of space-time correlation in turbulent flows over flat and wavy walls

The present experimental work is devoted to in- vestigate a new space-time correlation model for the turbulent boundary layer over a flat and a wavy walls. A turbulent boundary layer flow at Reo = 2460 is measured by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The space-time correlations of instantaneous streamwise fluctuation velocity are calculated at 3 different wall-normal locations in logarithmic layer. It is found that the scales of coherent structure increase with moving far away from the wall. The growth of scales is a manifestation of the growth of prevalent coherent structures in the turbulent boundary layer like hairpin vortex or hairpin packets when they lift up. The resulting contours of the space-time correlation exhibit elliptic-like shapes rather than straight lines. It is suggested that, instead of Taylor hypothesis, the elliptic model of the space-time correlation is valid for the wallbounded turbulent flow over either a flat wall or a wavy wall. The elliptic iso-correlation curves have a uniform preferred orientation whose slope is determined by the convection velocity. The convection velocity derived from the space-time correlation represents the velocity at which the large-scale eddies carry small-scale eddies. The sweep velocity rep- resents the distortions of the small-scale eddies and is intimately associated with the fluctuation velocity in the logarithmic layer of turbulent boundary layers. The nondimensionalized correlation curves confirm that the elliptic model is more proper for approximating the space-time correlation than Taylor hypothesis, because the latter can not embody the small-scale motions which have non-negligible distortions. A second flow over a wavy wall is also recorded using TRPIV. Due to the combined effect of shear layers and the adverse pressure gradient, the space-time correlation does not show an elliptic-like shape at some specific heights over the wavy wall, but in the outer region of the wavy wallbounded flow, the elliptic model remai     

Effects of variable fluid properties on natural convection of MHD fluid from a heated vertical wavy surface

In the present paper, the influence of temperature-dependent fluid properties, density, viscosity and thermal conductivity on MHD natural convection flow from a heated vertical wavy surface is studied. It is assumed that, the fluid density and the thermal conductivity vary as exponential and linear functions of temperature, respectively. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The model analysis used here is more relevant to liquid flow. Using the appropriate variables, the wavy surface are transformed into a flat one. The transformed boundary layer equations are solved numerically, using implicit-Chebyshev pseudospectral method, for several sets of values of the physical parameters, namely, the temperature dependent fluid properties parameters, the magnetic parameter, the amplitude-wavelength ratio parameter, and the Prandtl number. The numerical values obtained for the velocity, temperature, shearing stress, and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results were compared with numerical solutions of previous works. The present results are found to be in good agreement.     

Divergent channel flow of a liquid crystalline polymer solution

 The flow of a `model' lyotropic liquid crystal polymer, (hydroxypropyl)cellulose in water, through a rectangular channel with a divergence in the channel width, is studied by in situ light microscopy. Microscopic texture observations are related to measurements of the flow velocity field, in order to characterize the shear and elongational aspects of the flow and to examine the effects of the divergence from a narrow channel to a wide channel. A strong dependence of flow-induced texture on position in the channel is observed and is related to the interplay of shear and elongational strain. The divergence generates both a perpendicular elongational strain due to the widening of the channel, and subsequently an elongational strain along the flow direction due to the change in flow pattern from quasi-radial to unidirectional down the wide channel. Additionally side wall structure is observed to be more complex than a simple strong alignment, displaying a fine birefringent texture. Finally there is a marked dependence of the macroscopic structure on the strain history of the fluid prior to entry into the channel, indicating that very different structures of, for instance, moulded parts, can result from differences in geometry and fluid treatment prior to entry into the mould itself. Received: 12 October 1999/Accepted: 29 October 1999     

Three dimensional free convection flow and heat transfer along a porous vertical plate

The free convection flow along a vertical porous plate with transverse sinusoidal suction velocity distribution is investigated. Due to this type of suction velocity at the plate the flow becomes three dimensional one. For the asymptotic flow condition, the wall shear stress in the direction of main flow for different values of buoyancy parameter G is obtained. For G=0, the skin friction in the direction of free stream and the rate of heat transfer from the plate to the fluid are given. It is found that these results differ from those obtained by Gersten and Gross.     

Performance evaluation and optimization of semi-dimpled slit fin

In this paper, the semi-dimpled slit fin is proposed and the characteristics of heat transfer and fluid flow are analyzed based on the orthogonal experiment design method. A serial studies on the effects of fin pitch, arrangement of semi-dimple, dimple radius on heat transfer and flow characteristics of semi-dimpled slit fin are investigated. The computational results show fin pitch (Fp) has significantly effected on the performance of heat transfer and fluid flow, the influence of arrangement of semi-dimple, the dimple radius (R) and the opening direction of semi-dimples dwindle. At the same time, compared to the general semi-dimpled slit fin, the heat transfer coefficient and JF factors of the optimized fin increase by 10.7–25.1 and 2.6–7.7 %, respectively. When Re ≤ 1,521, the overall performance of slit fin is better than that of optimized fin; while Re > 1,521, the overall performance of optimized fin is better than that of slit fin. Finally, the performance evaluation plot of enhanced heat transfer of heat exchanger is applied to analyze the optimized fin, it can be seen that optimization fin have better heat transfer performance under the same power consumption.