Oscillatory Channel Flow Research Articles

A time-varying diffusivity model for shear dispersion in oscillatory channel flow

An analysis is presented of the shear dispersion in turbulent channel flow forced by a purely oscillatory pressure gradient. The flow is described by an algebraic eddy viscosity model in which the instantaneous flow and viscosity are inter-dependent. Both eddy viscosity and eddy diffusivity contain a second-harmonic time-varying component. The effective transport equation is derived using a two-time-scale perturbation analysis, which also yields a closed-form expression for the dispersion coefficient. Numerical results demonstrate that, in this problem, the time-varying component of the eddy diffusivity can have a finite effect on the dispersion coefficient, which can be as much as a 30% difference from that obtained from a time-invariant eddy viscosity model.

A hybrid spectral/boundary‐integral approach for transient viscoelastic flow exiting a channel

A hybrid spectral/boundary element approach is proposed to examine the influence of Couette channel flow on transient coating of highly elastic fluids. The viscoelastic instability of one‐dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson‐Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free‐surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate‐of‐strain tensor components in the free‐surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a non‐linear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non‐linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating.

Evolution of turbulence in an oscillatory flow in a smooth-walled channel: a viscous secondary instability mechanism.

In this paper, a comparison is made of the evolution of turbulence in oscillatory channel flows with a zero-mean velocity in two and three dimensions, using the numerical technique of the lattice Boltzmann method. The results confirm a primary two-dimensional instability. Evidence is shown of a secondary, viscous three-dimensional instability mechanism acting in the oscillatory boundary layer, which is consistent with experimental observations.

A pseudo‐viscoelastic approach for transient polymeric flow exiting a channel

AbstractThe influence of elasticity of a fluid exiting a channel is examined on transient coating downstream. A hybrid spectral/boundary element approach is proposed to solve the problem. The flow inside the channel is assumed to be fully developed. A viscoelastic instability of one‐dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson–Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free‐surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate‐of‐strain tensor components in the free‐surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a nonlinear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non‐linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating. Copyright © 2003 John Wiley & Sons, Ltd.

Application of the lattice Boltzmann method to transition in oscillatory channel flow

In this study the applicability of the lattice Boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated. The model has been compared to exact analytical solutions in the laminar case (Reδ < 100, where Reδ is the Reynolds number based on the Stokes layer) for the Womersley parameter 1 < α < 31. In this regime, there was good agreement between numerical and exact analytical solutions. The model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity. For these transitionary flows the parameters were varied in the range 400 < Reδ < 1000 and 4 < α < 16. Disturbances superimposed on the numerical solution triggered the two-dimensional primary instability. This phenomenon has not been numerically evaluated over the range of α or Reδ currently investigated. The results are consistent with quasi-steady linear stability theories and previous numerical investigations.

Direct numerical simulation of transition to turbulence in an oscillatory channel flow

In this Note, we present results of the numerical simulation of transition to turbulence for a purely oscillatory channel flow. These simulations were performed for various values of the Reynolds number, the so-called Stokes parameter being equal to 4. The methodology used for the flow simulation relies on a combination of finite element space approximations with time-discretization by operator splitting; it has shown to be very effective, even when it is applied to relatively complex domains with strong expansions at the inlet and outlet of the channel. The numerical results obtained agree qualitatively well with previous experiments by other investigators. To cite this article: L.H. Juárez, E. Ramos, C. R. Mecanique 331 (2003).

The oscillatory channel flow with arbitrary wall injection

In this article, we consider the laminar oscillatory flow in a low aspect ratio channel with porous walls. For small-amplitude pressure oscillations, we derive asymptotic formulations for the flow parameters using three different perturbation approaches. The undisturbed state is represented by an arbitrary mean-flow solution satisfying the Berman equation. For uniform wall injection, symmetric solutions are obtained for the temporal field from both the linearized vorticity and momentum transport equations. Asymptotic solutions that have dissimilar expressions are compared and shown to agree favourably with one another and with numerical experiments. In fact, numerical simulations of both linearly perturbed and nonlinear Navier-Stokes equations are used for validation purposes. As we insist on verifications, the absolute error associated with the total time-dependent velocities is analysed. The order of the cumulative error is established and the formulation based on the two-variable multiple-scale approach is found to be the most general and accurate. The explicit formulations help unveil interesting technical features and vortical structures associated with the oscillatory wave character. A similarity parameter is shown to exist in all formulations regardless of the mean-flow selection.

The oscillatory channel flow with large wall injection

In the presence of smallamplitude pressure oscillations, the linearized NavierStokes equations are solved to obtain an accurate description of the timedependent field in a channel having a rectangu...

The linear instability of an oscillatory two-phase channel flow in the limit of small Stokes numbers

The linear instability of an oscillatory two-phase channel flow in the limit of small Stokes numbers

An analysis of conjugate heat transfer from a heated wall in a channel with zero-mean oscillatory flow for small oscillatory flow Reynolds numbers

An exact solution for small oscillatory flow Reynolds numbers is presented for the fully-developed zero-mean oscillatory flow and heat transfer in a two-dimensional channel with a wall uniformly heated to simulate the forced-convection cooling of electronic components on printed circuit boards. The other channel wall is insulated and all thermal properties are taken to be constant. Also, results are given in terms of time-averaged Nusselt number as functions of oscillatory flow Reynolds number and Wormersely number, based on both channel height and tidal displacement as the characteristic lengths, and for two specific cases with air and water as the cooling fluid media.

An investigation of transition to turbulence in bounded oscillatory Stokes flows Part 2. Numerical simulations

The stability of oscillatory channel flow to different classes of infinitesimal and finite-amplitude two- and three-dimensional disturbances has been investigated by direct numerical simulations of the Navier–Stokes equations using spectral techniques. All infinitesimal disturbances were found to decay monotonically to a periodic steady state, in agreement with earlier Floquet theory calculations. However, before reaching this periodic steady state an infinitesimal disturbance introduced in the boundary layer was seen to experience transient growth in accordance with the predictions of quasi-steady theories for the least stable eigenmodes of the Orr–Sommerfeld equation for instantaneous ‘frozen’ profiles. The reason why this growth is not sustained in the periodic steady state is explained. Two-dimensional infinitesimal disturbances reaching finite amplitudes were found to saturate in an ordered state of two-dimensional quasi-equilibrium waves that decayed on viscous timescales. No finite-amplitude equilibrium waves were found in our cursory study. The secondary instability of these two-dimensional finite-amplitude quasi-equilibrium states to infinitesimal three-dimensional perturbations predicts transitional Reynolds numbers and turbulent flow structures in agreement with experiments.

Two‐equation (k, ϵ) turbulence computations by the use of a finite element model

AbstractA finite element technique is presented and applied to some one‐ and two‐dimensional turbulent flow problems. The basic equations are the Reynolds averaged momentum equations in conjunction with a two‐equation (k, ϵ) turbulence model. The equations are written in time‐dependent form and stationary problems are solved by a time iteration procedure. The advection parts of the equations are treated by the use of a method of characteristics, while the continuity requirement is satisfied by a penalty function approach. The general numerical formulation is based on Galerkin's method. Computational results are presented for one‐dimensional steady‐state and oscillatory channel flow problems and for steady‐state flow over a two‐dimensional backward‐facing step.

Observation of waves during oscillatory channel flow

We have observed steady and oscillatory flow through a two-dimensional channel expansion. The experimental results are supported by numerical solutions of the unsteady Navier–Stokes equations. This work was prompted by the recent discovery of vortex waves during steady flow past a moving indentation in a channel wall. Our work deals with both asymmetric channels, in which we show that vortex waves are observed during oscillatory flow with rigid walls, and with symmetric channels, in which a vortex street is observed. We believe that the vortex street is not a vortex wave, but the result of a shear-layer instability.

Closure to “Transverse Dispersion in Oscillatory Channel Flow”

Closure to “Transverse Dispersion in Oscillatory Channel Flow”

Discussion of “Transverse Dispersion in Oscillatory Channel Flow”

Discussion of “Transverse Dispersion in Oscillatory Channel Flow”

Discussion of “Transverse Dispersion in Oscillatory Channel Flow”

Discussion of “Transverse Dispersion in Oscillatory Channel Flow”

Transverse Dispersion in Oscillatory Channel Flow

An analysis of published data on dye dispersion in homogeneous estuaries shows that the dimensionless transverse dispersion coefficient is large compared with results in steady flow in straight channels. The hypothesis is made that transverse currents of three kinds are responsible for the large coefficients. The results of laboratory tests with oscillatory flow in meandering channels are described. Point injections of dye and subsequent measurements of the dye cloud are made. These results support the hypothesis that the transverse currents cause the large transverse dispersion coefficients. The results suggest that the spiral secondary currents associated with the channel meanders are the principal reason for the large coefficients.