Modelling turbulence around and inside porous media based on the second moment closure

To predict turbulence in porous media, a new approach is discussed. By double (both volume and Reynolds) averaging Navier–Stokes equations, there appear three unknown covariant terms in the momentum equation. They are namely the dispersive covariance, the macro-scale and the micro-scale Reynolds stresses, in the present study. For the macro-scale Reynolds stress, the TCL (two-component-limit) second moment closure is applied whereas the eddy viscosity models are applied to the other covariant terms: the Smagorinsky model and the one-equation eddy viscosity model, respectively for the dispersive covariance and the micro-scale Reynolds stress. The presently proposed model is evaluated in square rib array flows and porous wall channel flows with reasonable accuracy though further development is required.     

On the instantaneous formation of cavitation in hydrodynamic lubricationSur la formation instantanée de la cavitation en lubrification hydrodynamique

We consider the Elrod–Adams model extending the classical lubrication Reynolds equation to the case of the possible presence of a cavitation region. We show that the behaviour of the pressure and saturation depends crucially on the behaviour of the separation $h(t,x,y)$ among the two surfaces. In particular, we exhibit some simple formulations for which we prove (rigorously) that a cavitation region is formed instantaneously (even for initially saturated flows). Some numerical experiences are also given. To cite this article: J.I. Díaz, S. Martin, C. R. Mecanique 334 (2006).     

A priori study for the modelling of velocity–interface correlations in the stratified air–water flows

This work concerns the modelling of stratified two-phase turbulent flows with interfaces. We consider an equation for an intermittency function $\alpha (\mathbf{x}\text{,}t)$ which denotes the probability of finding an interface at a given time t and a given point $\mathbf{x}$. In Wacławczyk and Oberlack (2011) a model for the unclosed terms in this equation was proposed. Here, we investigate the performance of this model by a priori tests, and finally, based on the a priori data discuss its possible modification and improvements.     

Experimental investigation on wake characteristics behind a yawed square cylinder

The wake vortical structures of a square cylinder at different yaw angles to the incoming flow ($\alpha =$0°, 15°, 30° and 45°) are studied using a one-dimensional (1D) hot-wire vorticity probe at a Reynolds number (Re) of about 3600. The results are compared with those obtained in a yawed circular cylinder wake. The Strouhal number (St_N) as well as the mean drag coefficient ($C_{D_N}$), normalized by the velocity component normal to the cylinder axis, follow the independent principle (IP) satisfactorily up to $\alpha =$40°. Using the phase-averaging analysis, both the coherent and the remaining contributions of velocity and vorticity are quantified. The flow patterns of the coherent spanwise vorticity (${\omega }_z$) display obvious Kármán vortex streets and their maximum concentrations decrease as $\alpha$ increases. Similar phenomena are also shown in the coherent contours of the streamwise ($u$) and transverse ($v$) velocities as well as the Reynolds shear stress ($uv$). The contours of the spanwise velocity ($w$) and Reynolds shear stress ($uw$), however, experience an increasing trend for the maximum concentrations with increasing yaw angle. These results indicate an enhancement of the three-dimensionality of the wake and the reduction of vortex shedding strength as $\alpha$ increases. While general similarities to the wake behind a yawed circular cylinder are found in terms of flow features, some differences between the two wakes at different yaw angles are highlighted.     

Instability of Navier slip flow of liquidsInstabilité des écoulements glissant de liquides.

We investigate the stability problem related to the basic slip flows of liquids in plane microchannels by using the Navier slip concept. We found that if the Navier slip parameter ($N_s$) equals 0.06, the critical Reynolds number (${\mathit{Re}}_{\mathrm{cr}}$) becomes 213.6. There are short-wave instabilities, however, when we further increase $N_s$ to 0.07 or 0.08. ${\mathit{Re}}_{\mathrm{cr}}$ becomes 132.9 for $N_s=0.08$ if we neglect the short-wave instability. To cite this article: A.K.-H. Chu, C. R. Mecanique 332 (2004).     

Numerical verification of the weak turbulent model for swell evolution

The purpose of this article is to numerically verify the theory of weak turbulence. We have performed numerical simulations of an ensemble of nonlinearly interacting free gravity waves (a swell) by two different methods: by solving the primordial dynamical equations describing the potential flow of an ideal fluid with a free surface, and by solving the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. In both cases we have observed effects predicted by this theory: frequency downshift, angular spreading and formation of a Zakharov–Filonenko spectrum $I_{\omega }\sim {\omega }^{\mathrm{-4}}$. To achieve quantitative coincidence of the results obtained by different methods, we have to augment the Hasselmann kinetic equation by an empirical dissipation term $S_{\mathrm{diss}}$ modeling the coherent effects of white-capping. Using the standard dissipation terms from the operational wave predicting model (WAM) leads to a significant improvement on short times, but does not resolve the discrepancy completely, leaving the question about the optimal choice of $S_{\mathrm{diss}}$ open. In the long run, WAM dissipative terms essentially overestimate dissipation.     

Scaling of the near-wall layer beneath turbulent separated flow

This paper is a continuation of an earlier paper [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438] in which it is proposed that each Reynolds stress has its own velocity scale. Two of these, $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$, are directly related by definition to the r.m.s. of the wall-shear-stress fluctuations (${\tau }_x$ and ${\tau }_z$) in the streamwise and transverse directions. They are also velocity scales for the true dissipation of the turbulent kinetic energy and the Kolmogorov velocity and length scales at the surface. From asymptotic considerations it is shown that the other two scales are related to averages involving instantaneous gradients of wall-shear-stress fluctuations. The measurements, made using pulsed-wire anemometry into the viscous sublayer, show that $u_{\tau }^{\prime }$ and $w_{\tau }^{\prime }$ are also the velocity scales for the respective streamwise and transverse fourth-order velocity moments, together with the viscous velocity scale ($\nu /y$). Normalised, the fourth-order moments show an inner-layer-like behaviour independent of both position and direction, like that seen in the second-order moments [P.E. Hancock, Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows, Eur. J. Mech. B Fluids 24 (2005) 425–438]. However, not surprisingly, the third order moments exhibit an effect of mean shear, seen in the skewing of the probability distributions. Though not measured directly, the measurements imply the behaviour of the averaged products of fluctuations in wall-shear-stress and wall-pressure-gradient ($\overline{{\tau }_x\partial p/\partial x}$ and $\overline{{\tau }_z\partial p/\partial z}$). Normalised, they also are independent of position and direction. Some of the results presented apply more generally to the near-wall region beneath turbulent flow.