A scaling analysis for point–particle approaches to turbulent multiphase flows

Simple dimensional arguments are used in establishing three different regimes of particle time scale, where explicit expression for particle Reynolds number and Stokes number are obtained as a function of nondimensional particle size (d/η)$(d/\eta )$ and density ratio. From a comparative analysis of the different computational approaches available for turbulent multiphase flows it is argued that the point–particle approach is uniquely suited to address turbulent multiphase flows where the Stokes number, defined as the ratio of particle time scale to Kolmogorov time scale (_τp/_τk)$({\tau }_p/{\tau }_k)$, is greater than 1. The Stokes number estimate has been used to establish parameter range where point–particle approach is ideally suited. The point–particle approach can be extended to handle “finite-sized” particles whose diameter approach that of the smallest resolved eddies. However, new challenges arise in the implementation of Lagrangian–Eulerian coupling between the particles and the carrier phase. An approach where the inter-phase momentum and energy coupling can be separated into a deterministic and a stochastic contribution has been suggested.     

Wake response of a stationary finite-sized particle in a turbulent channel flow

Here we consider the effect of a finite-sized stationary particle in a channel flow of modest turbulence at _Reτ=178.12${\mathit{Re}}_{\tau }=178.12$. The size of particle is varied such that the particle Reynolds number ranges from about 40 to 450. The location of the particle is chosen to be either in the buffer layer (_yp+=17.81)$(y_{p+}=17.81)$ or at the channel center. Fully resolved direct numerical simulations of the turbulent channel flow around the particles is performed. Here the ambient turbulence intensity relative to the mean velocity seen by the particle is large (I=23.16%)$(I=23.16\%)$ in the buffer region, while it is substantially lower (I=4.09%)$(I=4.09\%)$ at the channel center. We present results on turbulence modulation due to the particle in terms of wake dynamics and vortex shedding.     

Chaining of weakly interacting particles suspended in viscoelastic fluids

An asymptotic theory based on multipole expansions is presented for multiparticle interactions in unbounded, weakly viscoelastic, creeping flows. The theory accounts for non-Newtonian sphere–sphere interactions that are of order O(De(a/R)²)$\text{O}(De{(a/R)}^2)$, where De is the Deborah number, a the sphere radius and R is the sphere–sphere separation. Analytic expressions are derived for the non-Newtonian correction to the multisphere mobility matrix for non-neutrally buoyant sedimenting spheres, and for neutrally buoyant spheres suspended in a shear flow. It is shown that these expressions give rise to particle chaining in simulations of interacting spherical particles.     

The stress concentration factor for slightly roughened random surfaces: Analytical solution

We derive an analytical solution to the stress concentration factor (_kt)$(k_t)$ for slightly roughened random surfaces. Topology is assumed to possess Gaussian distribution of heights and auto correlation length, ACL  . For our development, we combine Gao’s first-order perturbation method, the Hilbert transform, and an energy conservation principal related to the Parseval theorem.The root-mean-square (RMS) value of _kt$k_t$ results in a function of the ratio RMS-roughness to ACL. The derived formula agrees with experimental results previously reported. The results provide insight for more efficient design.     

The effect of different inlet conditions of air in a rectangular channel on convection heat transfer: Turbulence flow

Theoretical and empirical correlations for duct flow are given for hydrodynamically and thermally developed flow in most of previous studies. However, this is commonly not a realistic inlet configuration for heat exchanger, in which coolant flow generally turns through a serpentine shaped passage before entering heat sinks. Accordingly, an experimental investigation was carried out to determine average heat transfer coefficients in uniformly heated rectangular channel with 45° and 90° turned flow, and with wall mounted a baffle. The channel was heated through bottom side with the baffle. In present work, a detailed study was conducted for three different height of entry channel (named as the ratio of the height of entry channel to the height of test section (${\overline{H}}_{\text{c}}=h_{\text{c}}/H$)) by varying Reynolds number (${\mathit{Re}}_{\text{Dh}}$). Another variable parameter was the ratio of the baffle height to the channel height (${\overline{H}}_{\text{b}}=h_{\text{b}}/H$). Only one baffle was attached on the bottom (heating) surface. The experimental procedure was validated by comparing the data for the straight channel with no baffle. Reynolds number $({\mathit{Re}}_{\text{Dh}})$ was varied from 2800 to 30,000, so the flow was considered as only turbulent regime. All experiments were conduced with air accordingly; Prandtl number (Pr) was approximately fixed at 0.71. The results showed that average Nusselt number for θ = 45° and θ = 90° were 9% and 30% higher, respectively, than that of the straight channel without baffle. Likewise, the pressure drop increased up to 4.4 to 5.3 times compare to the straight channel.     

Scale-by-scale energy budget in a turbulent boundary layer over a rough wall

Hot-wire velocity measurements are carried out in a turbulent boundary layer over a rough wall consisting of transverse circular rods, with a ratio of 8 between the spacing (w) of two consecutive rods and the rod height (k). The pressure distribution around the roughness element is used to accurately measure the mean friction velocity ($U_{\tau }$) and the error in the origin. It is found that $U_{\tau }$ remained practically constant in the streamwise direction suggesting that the boundary layer over this surface is evolving in a self-similar manner. This is further corroborated by the similarity observed at all scales of motion, in the region $0.2⩽y/\delta ⩽0.6$, as reflected in the constancy of Reynolds number ($R_{\lambda }$) based on Taylor’s microscale and the collapse of Kolmogorov normalized velocity spectra at all wavenumbers.A scale-by-scale budget for the second-order structure function $〈{(\delta u)}^2〉$ ($\delta u=u(x+r)-u(x)$, where u is the fluctuating streamwise velocity component and r is the longitudinal separation) is carried out to investigate the energy distribution amongst different scales in the boundary layer. It is found that while the small scales are controlled by the viscosity, intermediate scales over which the transfer of energy (or $〈{(\delta u)}^3〉$) is important are affected by mechanisms induced by the large-scale inhomogeneities in the flow, such as production, advection and turbulent diffusion. For example, there are non-negligible contributions from the large-scale inhomogeneity to the budget at scales of the order of $\lambda$, the Taylor microscale, in the region of the boundary layer extending from $y/\delta =0.2$ to 0.6 ($\delta$ is the boundary layer thickness).     

Study of the rotational diffusivity coefficient of fibres in planar contracting flows with varying turbulence levels

The Fokker–Planck equation is solved by describing the evolution of a 3D fibre orientation state along a planar contraction. A constant value of the effective rotational diffusion coefficient was determined for four different turbulent flow cases in planar contractions, reported experimentally in the literature. Two hypotheses for the non-dimensional rotational diffusivity are presented, each based on two different turbulent time scales, i.e. the Kolmogorov time scales and the time scale associated with large energy bearing eddies. These hypotheses are dependent on either the Reynolds number, based on the Taylor micro-scale, and/or a non-dimensional fibre length. The hypothesis, based on the assumption of long fibres, _Lf/η?25$L_{\text{f}}/\eta ?25$, compared to the Kolmogorov scale and in the limit of large _Reλ${\mathit{Re}}_{\lambda }$ seems to capture the basic trends presented in the literature. This hypothesis has also the feature of predicting effects of varying fibre length within certain limits. Accordingly, by modeling the variation of turbulent quantities along the contraction in a CFD analysis, local values of rotational diffusivity can be evaluated with the mentioned hypothesis, based on either Kolmogorov time scale or Eulerian integral time scale.     

Shear-layer acoustic radiation in an excited subsonic jet: experimental study

The subharmonic acoustic radiation of a tone excited subsonic jet shear-layer has been investigated experimentally. Two jet velocities $U_j=20\text{m}?{\text{s}}^{\mathrm{?1}}$ and $U_j=40\text{m}?{\text{s}}^{\mathrm{?1}}$ were studied. For $U_j=20\text{m}?{\text{s}}^{\mathrm{?1}}$, the natural boundary-layer at the nozzle exit is laminar. When the perturbation is applied, the fluctuations of the first and the second subharmonics of the excitation frequency are detected in the shear-layer. In addition, the first subharmonic near pressure field along the spreading jet is constituted of two strong maxima of sinusoidal shape. The far-field directivity pattern displays two lobes separated by an extinction angle ${\theta }^{?}$ at around 85° from the jet axis. These observations follow the results of Bridges about the vortex pairing noise. On the other hand, for $U_j=40\text{m}?{\text{s}}^{\mathrm{?1}}$, the initial boundary-layer is transitional and only the first subharmonic is observed in the presence of the excitation. The near pressure field is of Gaussian shape in the jet periphery and the acoustic far-field is superdirective as observed by Laufer and Yen. The state of the initial shear-layer seems to be the key feature to distinguish these two different radiation patterns. To cite this article: V. Fleury et al., C. R. Mecanique 333 (2005).     

A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates

Free edge delamination in composite structures results from very localised stress fields which induce a stress concentration promoting the nucleation of an interfacial crack. To predict such a delamination onset at the free edge of a $(\pm \theta {)}_s$ laminate in traction, use is made of a strength and toughness criterion which combines a stress condition with an energy analysis. A generalised plane strain model allows to determine the stress distribution near the free edge and the energy released by the nucleation of an interfacial crack. The results show that this approach can predict the delamination onset for $((\pm 10{)}_s\text{,}(\pm 20{)}_s)$ laminates provided the interfacial fracture energy and interlaminar shear strength are known. These characteristic values can be identified with the help of traction tests performed on samples with different thicknesses.