Low-Reynolds-number modelling of flows over a backward-facing step

The complex turbulent flow behind a backward-facing step is modelled using a full Reynolds stress closure. In order to develop a closure model that can resolve the complex near-wall flow in the recirculation region and in the recovery region downstream of the reattachment point, the performance of a low and a high Reynolds number version of the full Reynolds stress closure is examined and compared. Furthermore, the effects of redistribution modelling on the calculated flow is studied by comparing the performance of three redistribution models: one return-to-isotropy model and two with mean-strain effects. The results are grid independent and show that the flow downstream of the step is best described by a low-Reynolds-number model that does not depend on the conventional wall function assumption. However, the skin friction behavior is correctly predicted by the stipulation of a wall function. Of the three redistribution models examined, the return-to-isotropy model gives results that are in excellent agreement with measurements. Finally, the calculated results are adversely affected by refining the redistribution models to include meanstrain effects.     

Numerical investigation of vortical evolution in a backward-facing step expansion flow

A numerical investigation of laminar flow over a backward-facing step is presented for the Reynolds number in the range of 50Re2500. The objective of this numerical investigation is to add to the existing knowledge of the backward-facing step flow to deepen our understanding of the expansion flow structure. We proceed with the analysis by verifying the computer code through the Pearson vortex problem. We then perform a parametric study by varying the Reynolds number, with the aim of determining whether or not there exists a critical Reynolds number, above which reattachment length on the channel floor decreases. We also concentrate on subjects that have been little explored in the flow, examples of which are the onset of a single vortex in the primary eddy and how the recirculating bubble containing flow reversals is torn into smaller eddies. Eddy distortion, leading to mobile saddle points, and the merging of eddies are also discussed in this study.     

Axisymmetric instability of pressure-driven flow in an annular channel at high Reynolds numbers

For the pressure-driven flow in an annular channel, its linear instability with respect to axisymmetric perturbations at high Reynolds numbers is investigated within the framework of the triple-deck theory. It is shown that the problem is reduced to that of the two-dimensional linear instability of the Poiseuille flow in a plane channel. The ratio of the inner to outer radii of the channel is found at which the instability is minimal.     

Secondary flow of a conducting fluid in a rotating straight annular pipe

A theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight annular pipe of circular cross-section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it and also there is imposed a uniform magnetic field transverse to the motion. The secondary flow pattern has been studied in detail for small values of angular velocity and Hartman number.     

Phase resolved measurements of the statistical flow behavior of a backward-facing step flow controlled by a sinusoidal Lorentz-force

In order to gain deeper inside into the behavior of a Lorentz-force controlled flow behind a backward-facing step, measurements with a laser Doppler velocity profile sensor were undertaken. By varying the frequency of the sinusoidal Lorentz-force the influence on the turbulence statistics was studied. Moreover, phase resolved measurement data is presented. The results confirm the characteristic frequency determined on basis of the momentum thickness beforehand. The aim of this study is to understand the influence of the different incitation signals and to reduce the reattachment length. The statistical results show a dependency of the turbulence degree on the excitation frequency as well as a deformation of the flow profile behind the step. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Axial dispersion in pressure perturbed flow through an annular pipe oscillating around its axis

A method of moment is employed to study the axial dispersion of passive tracer molecules released in an unsteady pressure-driven flow through an annular pipe which is oscillating around its longitudinal axis. The flow unsteadiness is caused by the oscillation of the tube around its axis as well as by a periodic pressure gradient. A finite difference implicit scheme is adopted to solve the Aris integral moment equations arising from the unsteady convective-diffusion equation for all time periods. The main objective is to study the nature of the dispersion coeffcient and mean concentration distribution under the sole as well as combined oscillation of the two driving forces. The behaviour of the dispersion coeffcient due to the variation of the aspect ratio, the absorption parameter for purely periodic flow has been examined and the sound response from dispersion coeffcient is found with the variation of these parameters in the sole presence of pressure pulsation. There is a remarkable difference in the behavior of the dispersion coeffcient depending on whether the ratio of two frequencies arising from the oscillations of the tube and the pressure gradient possesses a proper fraction or not. Oscillation of the tube produces much more dispersion than the pulsation of the pressure gradient and their combined effect leads to a further increase in dispersion. Tube oscillation shows a stronger effect on the dispersion coeffcient than the pressure pulsation though the effect of physical parameters are pronounced in the presence of pressure pulsation. The effect of the frequency parameter on the axial distribution of mean concentration is insensible when the oscillation of the annular tube is the only forcing. However this effect is much noticeable under the combined action of both forcing and much more effective under the sole influence of pressure pulsation.     

Axial dispersion in pressure perturbed flow through an annular pipe oscillating around its axis

A method of moment is employed to study the axial dispersion of passive tracer molecules released in an unsteady pressure-driven flow through an annular pipe which is oscillating around its longitudinal axis. The flow unsteadiness is caused by the oscillation of the tube around its axis as well as by a periodic pressure gradient. A finite difference implicit scheme is adopted to solve the Aris integral moment equations arising from the unsteady convective-diffusion equation for all time periods. The main objective is to study the nature of the dispersion coeffcient and mean concentration distribution under the sole as well as combined oscillation of the two driving forces. The behaviour of the dispersion coeffcient due to the variation of the aspect ratio, the absorption parameter for purely periodic flow has been examined and the sound response from dispersion coeffcient is found with the variation of these parameters in the sole presence of pressure pulsation. There is a remarkable difference in the behavior of the dispersion coeffcient depending on whether the ratio of two frequencies arising from the oscillations of the tube and the pressure gradient possesses a proper fraction or not. Oscillation of the tube produces much more dispersion than the pulsation of the pressure gradient and their combined effect leads to a further increase in dispersion. Tube oscillation shows a stronger effect on the dispersion coeffcient than the pressure pulsation though the effect of physical parameters are pronounced in the presence of pressure pulsation. The effect of the frequency parameter on the axial distribution of mean concentration is insensible when the oscillation of the annular tube is the only forcing. However this effect is much noticeable under the combined action of both forcing and much more effective under the sole influence of pressure pulsation.     

Dynamics of reattachment region behind backward-facing step in a narrow channel

Dynamics of the flow reattachment behind the backward-facing step in a narrow channel is studied experimentally using the PIV technique. Reattachment region is detected by statistical characteristics of the flow velocity close to the channel bottom. Two methods of reattachment definition are applied. The reattachment region structure and extent is shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pulsating magnetohydrodynamic flow in an annular channel

Pulsating laminar flow of a viscous incompressible electrically conducting fluid in an annular channel between two infinitely long circular cylinders under a radial impressed magnetic field is considered. The solutions of magnetohydrodynamic equations have been obtained on the assumption that the space between two cylinders is small compared to their mean radius. The solutions were also obtained on the assumption of small magnetic Reynolds number with special consideration of those for low and high frequencies.     

Comparison of isotropic and anisotropic subgrid scale models in Large Eddy Simulations of a backward-facing step and square duct flow

The present paper employs the anisotropic explicit algebraic subgrid-stress model (EASM), proposed by Marstorp et al. J. Fluid. Mech. 639, 403 - 432 (2009), developed in the spirit of an earlier explicit algebraic RANS-model for statistical closures. The EASM in its elementary, computationally efficient non-dynamic version is used for Large Eddy Simulation of three-dimensional flows over a backward-facing step at a bulk Reynolds number of 4805 and a square duct at 2205. Its performance is assessed by comparison with experimental data and an own Direct Numerical Simulation. Furthermore, a set of eddy-viscosity models, including the recent σ-model, is employed for comparison. Various statistical quantities are evaluated to assess the respective performance of the different models showing, that the anisotropic EASM compares favorably to the other models. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct Numerical Simulation of turbulent heat transfer behind a backward-facing step at low Prandtl number

The paper presents Direct Numerical Simulations of the turbulent flow of a low Prandtl number fluid over a backward-facing step with heat transfer. The backward-facing step flow is investigated as a generic configuration for sudden changes in cross section. Several simulations are reported: for isothermal conditions, for heat transfer with the Prandtl number of air, and for heat transfer with the Prandtl number of liquid sodium. The simulation for air is compared to results from literature. The differences induced by reduction of the Prandtl number are then assessed by comparison of the two cases. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow over back-facing step in a narrow channel

Flow structure behind the backward facing step in a narrow channel was studied in details. The step height was 25% of the channel width. The structure of the region just behind the step forming the back-flow region is studied in details using stereo PIV technique. Time-mean 3D structures behind the step are evaluated and shown in the paper. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid flow through a helical pipe

In this paper we study the flow of incompressible Newtonian fluid through a helical pipe with prescribed pressures at its ends. Pipe’s thickness and the helix step are considered as the small parameter ɛ. By rigorous asymptotic analysis, as ɛ→ 0 , the effective behaviour of the flow is found. The error estimate for the approximation is proved.     

Fluid flow through a helical pipe

In this paper we study the flow of incompressible Newtonian fluid through a helical pipe with prescribed pressures at its ends. Pipe’s thickness and the helix step are considered as the small parameter ɛ. By rigorous asymptotic analysis, as ɛ→ 0 , the effective behaviour of the flow is found. The error estimate for the approximation is proved.     

CFD of turbulent transport of particles behind a backward-facing step using a new model—k-ε-Sp

The k-ε-S_p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models (k-ε-A_p, k-ε-k_p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.     

On the unsteady Poiseuille flow in a pipe

We show that in an unsteady Poiseuille flow of a Navier–Stokes fluid in an infinite straight pipe of constant cross-section, σ, the flow rate, F(t), and the axial pressure drop, q(t), are related, at each time t, by a linear Volterra integral equation of the second type, where the kernel depends only upon t and σ. One significant consequence of this result is that it allows us to prove that the inverse parabolic problem of finding a Poiseuille flow corresponding to a given F(t) is equivalent to the resolution of the classical initial-boundary value problem for the heat equation.     

On the unsteady Poiseuille flow in a pipe

We show that in an unsteady Poiseuille flow of a Navier–Stokes fluid in an infinite straight pipe of constant cross-section, σ, the flow rate, F(t), and the axial pressure drop, q(t), are related, at each time t, by a linear Volterra integral equation of the second type, where the kernel depends only upon t and σ. One significant consequence of this result is that it allows us to prove that the inverse parabolic problem of finding a Poiseuille flow corresponding to a given F(t) is equivalent to the resolution of the classical initial-boundary value problem for the heat equation. G. P. Galdi: Partially supported by the NSF grant DMS–0404834. K. Pileckas: Supported by EC FP6 MCToK program SPADE2, MTKD–CT–2004–014508 A. L. Silvestre: Supported by FCT-Project POCI/MAT/61792/2004