Channel Half-width Research Articles

Analysis of the overall accuracy in LDV measurement of film flow in an inclined channel

In this paper the measurement accuracy of laser-Doppler-velocimeter (LDV) measurements in film flows is discussed. Error bounds for the measured velocity can be established by direct comparison of the experimental results with an exact analytical solution for film flows in channels with rectangular cross section. The validity check of the solution is performed by comparing the film height measurements with the corresponding theoretical values. A lower limit for the error bounds of the LDV measurements is predicted for given and fixed uncertainties of the fluid and flow parameters. The dimensionless velocity distribution and the dimensionless film height in an unidirectional open channel flow depend only on the parameter k = H/B, the ratio of the classical two-dimensional film height H to the channel half width B. For increasing k the deviation between the two-dimensional theory and the analytical solution also increases. The solution is independent of the Reynolds number, provided that the flow remains laminar. Experimental results for vertical Reynolds numbers below 0.1 are presented. The experimental results are in excellent agreement with the analytical solutions.

Entrance length and pulsatile flows of a model concentrated suspension

The flow behaviour of Phillips et al.’s suspension model [Phys. Fluids A 4, 30 (1991)] in channel and pulsatile flows is investigated by a combination of analytical and numerical methods (using an unstructured finite volume method). In the channel flow, we found that the kinematics develop faster than the concentration, with an entrance length of 0.2H3/a2, where H is the channel half width, and a is the particles’ radius. The corresponding entrance length for the concentration is 0.5H3/a2. In time‐periodic flows, the steady‐state kinematics and the stresses are periodic in time, and yet the steady‐state concentration (and thus the viscosity) is time‐independent. This feature is perhaps a critical test of the model, and indeed of any model in which the flux is quasi‐linear in the generalized strain rate.

Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence

A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds-number-dependency of its peak value. The following canonical flow geometries are considered: an incompressible turbulent boundary layer under zero pressure gradient, a fully developed two-dimensional channel and a cylindrical pipe flow. Data were collected from 47 independent experimental and numerical studies, which cover a Reynolds number range of Rθ=U∞θ/v=300−20,920 for the boundary layer with θ the momentum thickness and R+=u*R/v=100-4,300 for the internal flows with R the pipe radius or the channel half-width. It is found that the peak value of the rms-value normalised by the friction velocity, u*, is within statistical errors independent of the Reynolds number. The most probable value for this parameter was found to be 2.71±0.14 and 2.70±0.09 for the case of a boundary layer and an internal flow, respectively. The present survey also includes some data of the streamwise velocity fluctuations measured over a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and this property of the normalised peak value may for instance be exploited to estimate the wall shear stress from the streamwise velocity fluctuations. We also consider the skewness of the streamwise velocity fluctuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the equations of the third-order moment of velocity fluctuations. These results for the peak value of the rms of the streamwise velocity fluctuations and also the coincidence of this peak with the zero value of the third moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furthermore, these results can be also used as a requirement which turbulence models for the second and triple velocity correlations should satisfy.

Low Reynolds number fully developed two-dimensional turbulent channel flow with system rotation

Theoretical and experimental studies have been performed on fully developed twodimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u* for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. A Coriolis region where the Coriolis force effect predominates is shown to exist in addition to conventional regions such as viscous and buffer regions. A flow regime diagram that indicates ranges of these regions as a function of Re* and |Ω|v/u2* is given from which the overall flow structure in a rotating channel can be obtained.Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u2* ≤ 0.0030 (these values correspond to Re = 2UmD/v from 1700 to 10000 and rotation number R0 = 2|Ω|D/Um up to 0.055; Um is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.

Large eddy simulation of particle-laden turbulent channel flow

Particle transport in fully-developed turbulent channel flow has been investigated using large eddy simulation (LES) of the incompressible Navier–Stokes equations. Calculations were performed at channel flow Reynolds numbers, Reτ, of 180 and 644 (based on friction velocity and channel half width); subgrid-scale stresses were parametrized using the Lagrangian dynamic eddy viscosity model. Particle motion was governed by both drag and gravitational forces and the volume fraction of the dispersed phase was small enough such that particle collisions were negligible and properties of the carrier flow were not modified. Material properties of the particles used in the simulations were identical to those in the DNS calculations of Rouson and Eaton [Proceedings of the 7th Workshop on Two-Phase Flow Predictions (1994)] and experimental measurements of Kulick et al. [J. Fluid Mech. 277, 109 (1994)]. Statistical properties of the dispersed phase in the channel flow at Reτ=180 are in good agreement with the DNS; reasonable agreement is obtained between the LES at Reτ=644 and experimental measurements. It is shown that the LES correctly predicts the greater streamwise particle fluctuation level relative to the fluid and increasing anisotropy of velocity fluctuations in the dispersed phase with increasing values of the particle time constant. Analysis of particle fluctuation levels demonstrates the importance of production by mean gradients in the particle velocity as well as the fluid-particle velocity correlation. Preferential concentration of particles by turbulence is also investigated. Visualizations of the particle number density field near the wall and along the channel centerline are similar to those observed in DNS and the experiments of Fessler et al. [Phys. Fluids 6, 3742 (1994)]. Quantitative measures of preferential concentration are also in good agreement with Fessler et al. [Phys. Fluids 6, 3742 (1994)].

Topology of fine-scale motions in turbulent channel flow

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

An Investigation of Improved Dynamic Sub-Grid Scale Models by Simulating a Turbulent Channel Flow.

Two types of recently developed improved dynamic sub-grid scale (SGS) models were investigated by simulating turbulent channel flow at Re=180 normalized by channel half-width and friction velocity. The results of those models were compared with DNS data obtained by Kim et al. in 1987. One model developed by Meneveau et al. in 1994, called, the Lagrangean dynamic SGS model, appeared to show some superiority in eliminating the numerical instability that is often observed in the original dynamic SGS model proposed by Germano et al. In 1991, because the results of the model showed good agreement with those of the original dynamic SGS model without statistically homogeneous direction of turbulent flow that is required in the original one. The results of the other model developed by Vreman et al. in 1994, which is called the dynamic mixed SGS model showed better agreement with DNS data than that of the original dynamic SGS model but some numerical instability was still observed.

An Investigation of the Localized Dynamic Mixed SGS Model and its Application to Turbulent Channel Flow.

The drawbacks of the dynamic sub-grid scale eddy viscosity model proposed by Germano et al. in 1991 are that homogeneous direction of turbulence is required to eliminate numerical instability due to negative eddy viscosity and that the model is unable to predict sub-grid scale turbulent energy backscattering from sub-grid scale to grid scale. In the present study, the localized dynamic sub-grid scale model proposed by Meneveau et al. in 1994 was utilized with the mixed sub-grid scale model proposed by Vreman et al. in 1994 to eliminate these shortcomings. A newly developed eddy viscosity type sub-grid scale model was used instead of Smagorinsky's model which does not require the local equilibrium state of SGS energy. The proposed model was tested by simulating turbulent channel flow at Re=180 normalized by channel-half width and friction velocity. The results showed good agreement with direct numerical simulation data obtained by Kim et al. Relationships between the turbulent coherent structures and the Grid scale turbulent energy dissipation by the SGS model were also investigated. Some advantages of using the scale similarity model to simulate turbulent coherent structures were pointed out.

A numerical study of turbulent supersonic isothermal-wall channel flow

A study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation. Mach numbers, based on the bulk velocity and sound speed at the walls, of 1.5 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel half-width, are of the order of 3000. Because of the relatively low Reynolds number, all of the relevant scales of motion can be captured, and no subgrid-scale or turbulence model is needed. The isothermal boundary conditions give rise to a flow that is strongly influenced by wall-normal gradients of mean density and temperature. These gradients are found to cause an enhanced streamwise coherence of the near-wall streaks, but not to seriously invalidate Morkovin's hypothesis : the magnitude of fluctuations of total temperature and especially pressure are much less than their mean values, and consequently the dominant compressibility effect is that due to mean property variations. The Van Driest transformation is found to be very successful at both Mach numbers, and when properly scaled, statistics are found to agree well with data from incompressible channel flow results.

Lagrangian statistics in turbulent channel flow

Lagrangian statistics have been obtained from large eddy simulations of fully developed turbulent channel flow. Calculations were performed at Reynolds numbers of 3200 and 21,900 (based on centerline velocity and channel half-width); statistics of the Eulerian velocity field are in good agreement with both direct numerical simulation data and experimental measurements. Single-particle Lagrangian velocity autocorrelations and particle mean-square dispersion were obtained from trajectories measured for 5000 fluid elements initially in either the viscous sublayer, buffer layer, or logarithmic region. The Lagrangian velocity autocorrelation of particles initially located in the log region decreases less rapidly than for particles initially in the buffer layer, which in turn decreases more slowly than for particles initially in the viscous sublayer. The ratio of the Lagrangian to Eulerian integral timescales were found to be proportional to the inverse of the turbulence intensity, in agreement with theoretical predictions and atmospheric measurements. Growth of particle mean-square dispersion at long diffusion times is proportional to time and in agreement with theory (with the exception of the surface-normal coordinate in which the presence of the channel wall limits dispersion). However, extremely long transport times are required to achieve the asymptotic state for the dispersion.

Direct numerical simulation of turbulent transport with uniform wall injection and suction

A direct numerical simulation (DNS) of the fully developed turbulent channel flow and heat transfer with uniform wall injection and suction was carried out. The Reynolds number, which was based on the channel half-width and the friction velocity averaged on the two walls, was set to be 150, whereas the Prandtl number was 0.71. The walls were assumed to be kept at isothermal but different temperatures. With any buoyancy effect neglected, temperature was considered as a passive scalar. The computation was executed on sufficiently dense grid points by using a spectral method. The statistics obtained include the mean velocity and temperature, Reynolds stresses, and turbulent heat fluxes. Each term in the budget equations of the second-order velocity and temperature correlations and of their destruction rates was also calculated. It is found that the injection decreases the friction coefficient, but tends to stimulate the near-wall turbulence activity so that the Reynolds stresses and turbulent heat fluxes are increased, whereas the suction has an inverse influence.

Finite-difference computations of high reynolds number flows using the dynamic subgrid-scale model

The dynamic subgrid-scale model is used in finite-difference computations of turbulent flow in a plane channel, for a range of Reynolds numbers (based on friction velocity and channel half-width) between 200 and 5000. Adoption of approximate wall boundary conditions allows the use of very coarse grids in all directions. The comparison of first- and second-order moments with the reference data is satisfactory, despite the mesh coarseness. Turbulent kinetic energy budgets also compare well with DNS data. Near the wall, the dynamic formulation gives improved results over the Smagorinsky model, as observed in previous simulation. In the core of the flow where, at high Reynolds number, the turbulent eddies obey inertial-range dynamics, the Smagorinsky and dynamic models give similar results. The behavior of the model, its implementation when approximate wall boundary conditions are used, and the effect of numerical resolution are discussed.

Couple-stresses in peristaltic transport of fluids

Peristaltic pumping by a sinusoidal travelling wave in the walls of a two-dimensional channel filled with a viscous incompressible couple-stress fluid, is investigated theoretically. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio (wave amplitude:channel half width) is small. The results show that the mean axial velocity decreases with increasing couple-stress parameter eta . The phenomenon of reflux (mean flow reversal) is discussed. A reversal of velocity in the neighbourhood of the centre line occurs when the pressure gradient is greater than that of the critical reflux condition. It is found that the critical reflux pressure increases with the couple-stress parameter. Numerical results are reported for various values of the physical parameters of interest.

Finite amplitude steady states of high Reynolds number 2-D channel flow

Two-dimensional steady states of plane Poiseuille flow are found by following the evolution of a two-dimensional Navier-Stokes fluid numerically for long times. Two runs are presented, one for Reynolds number R = 4000, the other for R = 15000. The Reynolds number is based on the pressure gradient and channel half-width. The final states are characterized by an array of alternating-sign vortices. The states are accurately time independent in a frame moving with the vortices. In this frame of reference the stream function and the vorticity display an interesting correlation, showing that the flow is divided into three spatially distinct regions. Theoretical understanding of the state is sought in terms of the statistical mechanics of large numbers of discrete line vortices in the mean field limit, but without great success. Attention is devoted to characterizing the relaxed state.

Simulation of Transient Natural Convection Around an Enclosed Vertical Channel

Accurate numerical calculations have been conducted for buoyancy-driven two-dimensional flow of air between two vertical parallel isothermal plates, of aspect ratio 1, placed inside a rectangular enclosure. The Grashof number based on the channel half width is 105. Insights have been obtained regarding the structure of the transient flow and thermal fields in a configuration of particular interest to electronics cooling. In the early stages of the transient the flowfield was found to be highly vortical and the net volume flow rate in the channel displayed an oscillatory behavior, periodically reversing its direction. However, the velocity profile adjacent to the heated plates maintained the same direction throughout the process, and hence the Nusselt number was relatively insensitive to the periodic flow reversal in the channel. Detailed studies of the transient flow field and the heat transfer results are presented.

High Reynolds number calculations using the dynamic subgrid-scale stress model

The dynamic subgrid-scale eddy viscosity model has been used in the large-eddy simulation of the turbulent flow in a plane channel for Reynolds numbers based on friction velocity and channel half-width ranging between 200 and 2000, a range including values significantly higher than in previous simulations. The computed wall stress, mean velocity, and Reynolds stress profiles compare very well with experimental and direct simulation data. Comparison of higher moments is also satisfactory. Although the grid in the near-wall region is fairly coarse, the results are quite accurate: the turbulent kinetic energy peaks at y+≂12, and the near-wall behavior of the resolved stresses is captured accurately. The model coefficient is o(10−3) in the buffer layer and beyond, where the cutoff wave numbers are in the decaying region of the spectra; in the near-wall region the cutoff wave numbers are nearer the energy-containing range, and the resolved turbulent stresses become a constant fraction of the resolved stresses. This feature is responsible for the correct near-wall behavior of the model coefficient. In the near-wall region the eddy viscosity is reduced to account for the energy transfer from small to large scales that may occur locally.

Mixed convection heat and Mass transfer in a vertical channel with film evaporation

AbstractNumerical results are presented for effects of latent heat transport associated with film vaporization on laminar mixed convection heat and mass transfer in a vertical channel with a half channel width b = 0.01 m. The influences of the inlet liquid mass flowrate and wall temperature on the film vaporization and the associated heat and mass transfer characteristics are examined for air‐water and air‐ethanol systems with gas Reynolds number Reg = 2000. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made in Lin et al. (1988) and Yan and Lin (1989) is only valid for systems having small liquid mass flow rates. Additionally, it is found that the interfacial heat flux is predominantly determined by latent heat transfer connected with film evaporation.

Velocity Distributions of Fully Developed Two-Dimensional Turbulent Channel Flow under Effects of Low-Reynolds Number and Coriolis Force.

Mean velocity distributions of fully developed turbulent flow have been measured in two-dimensional stationary and rotating channels under low-Reynolds number range. The turbulent structures receive Coriolis force effect as well as low-Reynolds-number effect. Three parameters Re*, Ωv/u2* and ΩD/u* (two of which are independent) where u*, D and Ω are friction velocity, channel half width and rotating angular velocity, respectively, are sufficient to describe these effects on the velocity distribution. The changes from the conventional log and defect laws are well described by these parameters. A Coriolis region where the Coriolis length scale, u*/Ω, predominates is experimentally confirmed to exist. On the suction side of a rotating channel, the turbulent structure of the wall region is similar to that on the stationary channel, while it differs on the pressure side.

The late stages of transition to turbulence in channel flow

The late stages of transition, from the Λ-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 Λ-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.

Direct numerical simulation of passive heat transfer in a turbulent channel flow

A direct numerical simulation of fully developed turbulent channel flow is used to study fully developed passive heat transfer between the channel walls. The time-dependent, three-dimensional Navier-Stokes equation and the advection-diffusion equation are solved numerically with 1064960 grid points. No subgrid point modeling is used since all the important turbulence scales are resolved. The Reynolds number, based on the channel half-width and the bulk velocity, is 2262, and the Prandtl number is 1.