Wavy-walled Channel Research Articles

Flow in a wavy-walled channel lined with a poroelastic layer

Motivated by physiological flows in capillaries, venules and the pleural space, the pressure-driven flow of a Newtonian fluid in a two-dimensional wavy-walled channel is investigated theoretically. The sinusoidal wavy shape is due to the configuration of underlying cells, their nuclei and intercellular junctions or clefts. The walls are lined with a thin poroelastic layer that models the glycocalyx coating of the cell surface. The upper and lower wavy walls are offset axially by the phase angle Φ ,w here Φ =0 (π )y ields an antisymmetric (symmetric) channel. Biphasic theory is employed fo rt he poroelastic layer and the flow is solved by a lubrication approximation using a small parameter, δ � 1, where δ is the channel width/wavelength ratio. The velocity fields in the core and layer are determined as perturbation expansions in δ 2 and finite-Reynolds-number effects occur at O(δ 2 )a ssuming δ 2 Re � 1. When the hydraulic resistivity, α ,t he ratio of the channel width to the Darcy permeability, is sufficiently large and Φ is near enough to π ,t he flow develops a trapped recirculation eddy within the glycocalyx layer near the widest part of the channel. This can be of significance to transport through the cellular boundary, since that location corresponds to intercellular clefts through which important fluid and solute exchange occurs. Increasing |Φ − π| diminishes the recirculation region. Increasing the Reynolds number moves the recirculation slightly upstream. Both layer velocity and wall shear stresses decrease as α increases and support the appearance of flow recirculation. Further, the wavy geometry allows a portion of the flow to enter and exit the layer, which provides a mechanism for convective transport between these two regions that otherwise have only diffusive interactions. The relevant P´ eclet number is Pe = V ∗ n b/D where D is molecular diffusivity and V ∗

Fluid flow and mass transfer in a sinusoidal wavy‐walled tube at moderate Reynolds numbers

AbstractFluid flow and mass transfer characteristics in an axisymmetric sinusoidal wavy‐walled tube are experimentally investigated in the Reynolds number range of 50 to 1000. Attention is paid to the transitional flow, which is observed in the Reynolds number range of 160 to 200. In the laminar flow regime, wall shear stress and mass transfer rate increase with the slopes of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slopes of 3/2 and 3/5, respectively. In the transitional flow regime they increase dramatically, with a sharp slope. It is found that in this flow regime, laminar‐like motion and turbulent‐like motion alternatively take place at different time intervals. This is quite different from the flow instability for the wavy‐walled channel, where Tollmien‐Schlichting waves are observed. The flow instability in the wavy‐walled tube in the transitional flow regime is considered to be responsible for a significant increase in the wall shear stress and mass transfer rate. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 650–661, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10121

Fluid flow and mass transfer characteristics in a sinusoidal wavy-walled tube at moderate Reynolds numbers for steady flow

Flow and mass transfer characteristics in an axisymmetric sinusoidal wavy-walled tube are investigated experimentally in the Reynolds number range from 50 to 1000. The flow patterns are visualized by the aluminum dust method. The measurements of the wall shear stress and the mass transfer rate for high Schmidt number are performed by the electrochemical method. The attention is focused on their characteristics, including the transitional flow. It was observed that steady flow changes into unsteady flow when the Reynolds number exceeds about 160. The wall shear stress in the minimum circular cross section of the tube and the mass transfer rate for one wavelength are shown to depend upon the Reynolds number. In the laminar flow regime they increase with the slope of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slope of 3/2 and 3/5, respectively. In the transitional flow regime both of them increase significantly with further larger slope. It is found that the laminar-like motion and turbulent-like motion occur alternatively, with different time intervals, indicating intermittent flow behavior. This is quite different from the flow instability of the wavy-walled channel in which Tollmien-Schlichting waves keeping a time-periodic flow appear.

The prediction of spatially periodic flows using a finite‐volume model

AbstractA periodic boundary condition has been developed that can be used in conjunction with a specified flow rate to produce accurate results in spatially periodic geometries. This condition is useful in situations where the flow rate is known, or more importantly, in cases where the pressure gradient is not known a priori, such as in countercurrent flows. Using the present condition, the flow rate is imposed at the inlet in terms of a bulk velocity, but the velocity field evolves as part of the solution. The condition is formulated to be suitable for both fixed and moving periodic domains. For the case of a moving domain, a correction is introduced to account for changes in the instantaneous velocity through the periodic edges. Under periodic conditions, these corrections integrate to zero over a complete (temporal) period. The new periodic condition is shown to produce accurate results for flat and wavy‐walled channels under both induced flow and countercurrent conditions. Copyright © 2003 John Wiley & Sons, Ltd.

Fluid Flow and Mass Transfer in a Sinusoidal Wavy-Walled Tube at Moderate Reynolds Numbers.

Fluid flow and mass transfer characteristics in an axisymmetric sinusoidal wavy-walled tube are investigated experimentally in the Reynolds number range from 50 to 1 000. The attention is paid to the transitional flow, which is observed in the Reynolds number range of 160 to 200. In the laminar flow regime wall shear stress and mass transfer rate increase with the slope of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slope of 3/2 and 3/5, respectively. In the transitional flow regime they increase dramatically with a sharp slope. It is found that lamiar-like motion and turbulent-like motion alternatively take place with different time intervals in this flow regime. This is quite different from the flow instability for the wavy-walled channel, in which the Tollmien-Schlichting waves are observed. The flow instability in the wavy-walled tube is considered to be responsible for a significant increment of the wall shear stress and mass transfer rate in the transitional flow regime.

Forced convection in a wavy-wall channel

The rates of heat transfer for flow through a sinusoidally curved converging–diverging channel has been analyzed using a simple coordinate transformation method and the spline alternating-direction implicit method. The effects of the wavy geometry, Reynolds number and Prandtl number on the skin-friction and Nusselt number have been studied. Results show that the amplitudes of the Nusselt number and the skin-friction coefficient increase with an increase in the Reynolds number and the amplitude–wavelength ratio. The heat transfer enhancement is not significant at smaller amplitude wavelength ratio, however, at a sufficiently larger value of amplitude wavelength ratio the corrugated channel will be seen to be an effective heat transfer device, especially at higher Reynolds numbers.

Supersonic moist air flow with condensation in a wavy wall channel

The characteristics of Prandtl-Meyer expansion of supersonic flow with condensation along a wavy wall in a channel are investigated by means of experiments and numerical analyses. Experiments are carried out for the case of moist air flow in an intermittent indraft supersonic wind tunnel. The flow fields are visualized by a Schlieren system and the distributions of static pressure along the upper wavy wall are measured by a scanning valve system with pressure transducers. In numerical analyses, the distributions of streamlines, Mach lines, iso-pressure lines, and iso-mass fractions of liquid are obtained by the two-dimensional direct marching method of characteristics. The effects of stagnation temperature, absolute humidity, and attack angle of the upper wavy wall on the generation and the locations of generation and reflection of an oblique shock wave are clarified. Futhermore, it is confirmed that the wavy wall plays an important role in the generation of an oblique shock wave and that the effect of condensation on the flow fields is apparent.

Effect of Surface Roughness of Pipe on Residual Liquid after Passage of Gas Liquid Interface.

A thin liquid film is left on wall after passage of a gas liquid interface front in a horizontal circular pipe filled up with water. The effect of the surface roughness of the inner surface of the pipe on the residual liquid film thickness is studied analytically and experimentally. Taking account of the increase of the pressure drop owing to the surface roughness of a wavy wall, the residual liquid film thickness on a wavy wall is analyzed by the same method as the thickness of film remaining on a surface of a solid withdrawn from a quiescent liquid. The numerical analysis of the pressure drop in a wavy wall channel is performed by an integral momentum method. The present study suggests that the surface roughness (2e) of the pipe effects on the residual liquid film thickness δ if δ<2e.

Linear stability of two-dimensional steady flow in wavy-walled channels

Linear stability of fully developed two-dimensional periodic steady flows in sinusoidal wavy-walled channels is investigated numerically. Two types of channels are considered: the geometry of wavy walls is identical and the location of the crest of the lower and upper walls coincides (symmetric channel) or the crest of the lower wall corresponds to the furrow of the upper wall (sinuous channel). It is found that the critical Reynolds number is substantially lower than that for plane channel flow and that when the non-dimensionalized wall variation amplitude ε is smaller than a critical value (about 0.26 for symmetric channel, 0.28 for sinuous channel), critical modes are three-dimensional stationary and for larger ε, two-dimensional oscillatory instabilities set in. Critical Reynolds numbers of sinuous channel flows are smaller for three-dimensional disturbances and larger for two-dimensional disturbances than those of symmetric channel flows. The disturbance velocity distribution obtained by the linear stability analysis suggests that the three-dimensional stationary instability is mainly caused by local concavity of basic flows near the reattachment point, while the critical two-dimensional mode resembles closely the Tollmien–Schlichting wave for plane Poiseuille flow.

A numerical study of flow through wavy-walled channels

SUMMARY A numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented. © 1998 John Wiley & Sons, Ltd.

Convective heat transfer in periodic wavy passages

The rates of heat transfer for flow through a periodic array of wavy passages are studied with an accurate numerical scheme. The flow was observed to be steady until Re around 180 after which self-sustained oscillatory flow was observed. The self-sustained oscillations lead to the destabilization of laminar thermal boundary layers, replenish the near-wall fluid with the fluid in the core region, and thus provide a natural mechanism of heat and mass transfer enhancement. In the steady-flow regime, the average Nusselt numbers for the wavy wall channel were only slightly larger than those for a parallel-plate channel. On the other hand, in the transitional-flow regime, the enhancement of heat transfer was about a factor of 2.5. Friction factors for the wavy channel were about twice those for the parallel-plate channel in the steady-flow region, and remained almost constant in the transitional regime.

Mass transfer enhancement in a symmetric sinusoidal wavy-walled channel for pulsatile flow

Mass transfer characteristics in a sinusoidal wavy-walled channel are investigated experimentally for pulsatile flow with varying flow parameters, i.e. net flow, amplitude and frequency of fluid oscillation. We show that combination of flow separation and fluid oscillation leads to a significant enhancement in the mass transfer rate under laminar flow conditions. This enhancement is due to rapid fluid mixing induced by the dynamic behavior of the vortex in this channel. The Sherwood number for pulsatile flow can be expressed by the following relation: Sh p m = Sh s m + Sh o m where m is the exponent, and subscripts mean s—steady flow, o—oscillatory flow and p—pulsatile flow. Although the value of m depends on the amplitude of fluid oscillation, it becomes constant at large amplitude, i.e. m = 4.

Three-dimensionality of oscillatory flow in a two-dimensional symmetric sinusoidal wavy-walled channel

Oscillatory flow in a two-dimensional symmetric sinusoidal wavy-walled channel is investigated experimentally in a wide range of flow parameters. Attention is focused on the transition from a two-dimensional to a threedimensional flow. The critical Reynolds number for the transition to three-dimensional flow varies with the Strouhal number for the forced oscillation, and this value is lowest in the 0.02-0.03 range of Strouhal numbers. Two distinct three-dimensional flows are formed; time-symmetric flow and time-asymmetric flow, distinguished from each other by whether or not the Strouhal number exceeds about 0.02.

Heat Transfer Characteristics in a Wavy-Walled Channel

Technical Briefs Heat Transfer Characteristics in a Wavy-Walled Channel N. Saniei, N. Saniei Department of Mechanical Engineering, Southern Illinois University, Edwardsville, IL 62026-1805 Search for other works by this author on: This Site PubMed Google Scholar S. Dini S. Dini Western New England College, Springfield, MA 01095 Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information N. Saniei Department of Mechanical Engineering, Southern Illinois University, Edwardsville, IL 62026-1805 S. Dini Western New England College, Springfield, MA 01095 J. Heat Transfer. Aug 1993, 115(3): 788-792 (5 pages) https://doi.org/10.1115/1.2910756 Published Online: August 1, 1993 Article history Received: August 1, 1992 Revised: March 1, 1993 Online: May 23, 2008

Transition of oscillatory flow in a symmetric sinusoidal wavy-walled channel

Oscillatory flow in a two-dimensional sinusoidal wavy-walled channel is investigated experimentally. Attention is focused on the transition of two-dimensional to three-dimensional flow. The critical value of Reynolds number at the onset of three-dimensional flow strongly depends on Strouhal number. The flow is most unstable in the range of Strouhal numbers between 0.02 and 0.03. Two distinct three-dimensional flows are formed and their distinction can be made only by whether or not the Strouhal number exceeds about 0.02. Steady flow is free from the transition, which is due to a three-dimensional centrifugal instability of the flow.

Two-Dimensional Numerical Analysis of Oscillatory Flow in a Symmetric Sinusoidal Wavy-Walled Channel. Flow Patterns and Wall Shear Stresses.

Oscillatory How in a two-dimensional symmetric wavy-walled channel is studied by means of a finite element method over wide ranges of How parameters of the Reynolds and Strouhal numbers. Two-dimensional numerical computations show the variations of How separation and wall shear stress with time. The fluid motion is found to be most unstable in the limited Strouhal number range of 0.02-0.03 as the Reynolds number increases. That is, time and spatial periodicities of the How are not established. Steady streaming induced by oscillatory motion is also examined, and the vortex strength for the steady streaming has a peak at this Strouhal number range, independent of the Reynolds number.

Mass transfer in a symmetric sinusoidal wavy-walled channel for oscillatory flow

Mass transfer enhancement due to oscillatory flow has been studied in a symmetric sinusoidal wavy-walled channel by using an electrochemical technique. Experiments were carried out for viscosity-and inertia-dominated flows. In the viscosity-dominated flow regime, the mass transfer rate increases with the Reynolds number and decreases with the Strouhal number. The dominant mechanism of mass transfer enhancement is steady streaming which results from the nonlinear interaction of the curved wall with oscillatory flow. In the inertia-dominated flow regime, the mass transfer rate depends on the Reynolds number, while the effect of the Strouhal number becomes insignificant. Mass transfer is primarily enhanced by chaotic advective mixing, which is produced by the vortex formation-ejection cycle observed during oscillatory flow. Inertia-dominated flows yield much better mass transfer enhancement than viscosity-dominated flows. It is suggested that there is an optimum Strouhal number that produces the best mass transfer, in terms of the compactness and energy efficiency of a pulsatile pumping system.

Multiple Stability Boundaries of Tubes in a Normal Triangular Cylinder Array

This paper reports on experiments using a normal triangular cylinder array with a pitch-to-diameter ratio of 1.25 in air-cross-flow. The array consists of 18 tubes, in which 9 freely suspended tubes are linear iso-viscoelastically mounted. This unique tube mounting enables the linear damping of 9 cylinders (4, 3 and 2 cylinders in the first, second, and third cylinder row, respectively) to be continuously varied over a wide mass-damping parameter range of 10 &lt; μδ/(ρd2) &lt; 80. The experimentally observed phenomenon are correlated with nonlinear vibration theory terminology in order to improve the characterization of the excitation mechanisms. Experimental results are presented showing three stability boundaries for one flexibly mounted tube in an otherwise fixed array, as was predicted by Lever and Weaver’s “wavy wall channel model.” Flow visualization, for that arrangement, shows that their model describes the actual fluid flow past the tube reasonably well. Furthermore, multiple stability boundaries for small groups of flexibly mounted cylinders in an otherwise fixed cylinder array have, for the first time, been measured.

Pulsatile Flow in a Symmetric Sinusoidal Wavy-Walled Channel.

Pulsatile laminar flow is examined experimentally in a two-dimensional furrowed channel with varying flow parameters. We present flow diagrams in which five flow modes are classified in terms of the Womersley number and oscillatory fraction of the flow rate for each net flow Reynolds number, on the basis of the process of vortex formation, growth and subsequent disappearance. A striking feature of pulsatile flow in the wavy-walled channel is that after the vortex ejects from the furrow, the vortex does not always disappear in the mainstream, but reattaches to the wall and eventually disappears under certain conditions, in contrast to oscillatory flow. We also show the transition to three-dimensional flow and a new flow structure in which a wave appears in the mainstream during the flow deceleration phase due to a shear layer instability.

Oscillatory flow in a symmetric sinusoidal wavy-walled channel at intermediate strouhal numbers

Oscillatory flow in a two-dimensional symmetric furrowed channel is studied numerically and experimentally over wide ranges of flow parameters. Two-dimensional numerical computations show that the vortex strength has a peak at intermediate Strouhal numbers, regardless of the Reynolds number. Flow visualization experiments support the two-dimensional computational results at low Reynolds numbers, but deviations arise at moderate Reynolds numbers. We show the transition from two-dimensional to three-dimensional flow due to instability of the flow. The critical Reynolds number for the onset of three-dimensional flow strongly depends on the Strouhal number. The fluid motion is found to be most unstable in the limited Strouhal number range of 0.02–0.03, and this is in agreement with the prediction of the two-dimensional computation. Two distinct three-dimensional flows are discovered experimentally.