Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width s of the spanwise varying roughness on the total drag and on the flow structures. We apply sandgrain roughness, in the form of alternating rough and smooth bands to the inner cylinder. Numerically, the Taylor number is O(10 9 ) and the roughness width is varied between 0.47 s = s/d 1.23, where d is the gap width. Experimentally, we explore Ta = O(10 12 ) and 0.61 s 3.74. For both approaches the radius ratio is fixed at η = r i /r o = 0.716, with r i and r o the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacings. Both numerically and experimentally, we find a maximum in the angular momentum transport as function ofs. This can be atributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.

Abstract

Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor-Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, 3-D roughness has not been previously considered in depth.Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been improved to simulate a random rough surface of monodisperse sand grains, which is characterized by the equivalent sand grain height k s . Taylor numbers range from T a = 1.0 × 10 7 (corresponding to Re τ = 82) to T a = 1.0 × 10 9 (Re τ = 635). We focus on the influence of the roughness height k + s in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from k + s = 5 up to k + s = 92, where the superscript '+' indicates non-dimensionalization in viscous units.We analyse the global response of the system, expressed both by the dimensionless angular velocity transport N u ω and by the friction factor C f . An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness k + s is calculated to be 1.33k, where k is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behavior to that of the Nikuradse (VDI-Forschungsheft 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer.

No abstract

Abstract

We present a pseudopotential lattice Boltzmann method to simulate liquid–liquid emulsions with a slightly soluble surfactant. The model is investigated in 2‐D, over a wide parameter space for a single, stationary, immiscible droplet, and surface tension reduction by up to 15% is described in terms of a surfactant strength Λ (which roughly follows a Langmuir isotherm). The basic surfactant model is shown to be insufficient for arresting phase segregation—which is then achieved by changing the liquid–liquid interaction strength locally as a function of the surfactant density. 3‐D spinodal decomposition (phase separation) is simulated, where the surfactant is seen to adapt rapidly to the evolving interfaces. Finally, for pendent droplet formation in an immiscible liquid, the addition of surfactant is shown to alter the droplet‐size distribution and dynamics of newly formed droplets. © 2018 The Authors. AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers. AIChE J, 65: 811–828, 2019

No abstract

Abstract