ALBERT

Description: Direct numerical simulations of Rayleigh-Taylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible Navier-Stokes formulation in a non-equilibrium thermodynamic framework. The two-dimensional flow is studied in an isolated box with non-periodic walls in both vertical and horizontal directions. The non-conducting interface separating the two air masses is impulsively removed at t = 0 (depicting a heaviside function). No external perturbation has been used at the interface to instigate the instability at the onset. Computations have been carried out for rectangular and square cross sections. The formulation is free of Boussinesq approximation commonly used in many Navier-Stokes formulations for RTI. Effect of Stokes’ hypothesis is quantified, by using models from acoustic attenuation measurement for the second coefficient of viscosity from two experiments. Effects of Stokes’ hypothesis on growth of mixing layer and evolution of total entropy for the Rayleigh-Taylor system are reported. The initial rate of growth is observed to be independent of Stokes’ hypothesis and the geometry of the box. Following this stage, growth rate is dependent on the geometry of the box and is sensitive to the model used. As a consequence of compressible formulation, we capture pressure wave-packets with associated reflection and rarefaction from the non-periodic walls. The pattern and frequency of reflections of pressure waves noted specifically at the initial stages are reflected in entropy variation of the system.

Description: A rigorous and systematic computational and theoretical study, the first of its kind, for the laminar natural convective flow above rectangular horizontal surfaces of various aspect ratios ϕ (from 1 to ∞) is presented. Two-dimensional computational fluid dynamic (CFD) simulations (for ϕ → ∞) and three-dimensional CFD simulations (for 1 ≤ ϕ 〈 ∞) are performed to establish and elucidate the role of finiteness of the horizontal planform on the thermo-fluid-dynamics of natural convection. Great care is taken here to ensure grid independence and domain independence of the presented solutions. The results of the CFD simulations are compared with experimental data and similarity theory to understand how the existing simplified results fit, in the appropriate limiting cases, with the complex three-dimensional solutions revealed here. The present computational study establishes the region of a high-aspect-ratio planform over which the results of the similarity theory are approximately valid, the extent of this region depending on the Grashof number. There is, however, a region near the edge of the plate and another region near the centre of the plate (where a plume forms) in which the similarity theory results do not apply. The sizes of these non-compliance zones decrease as the Grashof number is increased. The present study also shows that the similarity velocity profile is not strictly obtained at any location over the plate because of the entrainment effect of the central plume. The 3-D CFD simulations of the present paper are coordinated to clearly reveal the separate and combined effects of three important aspects of finiteness: the presence of leading edges, the presence of planform centre, and the presence of physical corners in the planform. It is realised that the finiteness due to the presence of physical corners in the planform arises only for a finite value of ϕ in the case of 3-D CFD simulations (and not in 2-D CFD simulations or similarity theory). The presence of physical corners is related here to several significant aspects of the solution—the conversion of in-plane velocity to out-of-plane velocity near the diagonals, the star-like non-uniform distribution of surface heat flux on heated planforms, the three-dimensionality of the temperature field, and the complex spatial structure of the velocity iso-surfaces. A generic theoretical correlation for the Nusselt number is deduced for the averaged surface heat flux for various rectangular surfaces (1 ≤ ϕ 〈 ∞) over a wide range of Grashof number. Innovative use of numerical visualization images is made to generate a comprehensive, quantitative understanding of the physical processes involved.

Description: Spinning cylinder rotating about its axis experiences a transverse force/lift, an account of this basic aerodynamic phenomenon is known as the Robins-Magnus effect in text books. Prandtl studied this flow by an inviscid irrotational model and postulated an upper limit of the lift experienced by the cylinder for a critical rotation rate. This non-dimensional rate is the ratio of oncoming free stream speed and the surface speed due to rotation. Prandtl predicted a maximum lift coefficient as C L max = 4 π for the critical rotation rate of two. In recent times, evidences show the violation of this upper limit, as in the experiments of Tokumaru and Dimotakis [“The lift of a cylinder executing rotary motions in a uniform flow,” J. Fluid Mech. 255 , 1–10 (1993)] and in the computed solution in Sengupta et al. [“Temporal flow instability for Magnus–robins effect at high rotation rates,” J. Fluids Struct. 17 , 941–953 (2003)]. In the latter reference, this was explained as the temporal instability affecting the flow at higher Reynolds number and rotation rates (〉2). Here, we analyze the flow past a rotating cylinder at a super-critical rotation rate (=2.5) by the enstrophy-based proper orthogonal decomposition (POD) of direct simulation results. POD identifies the most energetic modes and helps flow field reconstruction by reduced number of modes. One of the motivations for the present study is to explain the shedding of puffs of vortices at low Reynolds number ( Re = 60), for the high rotation rate, due to an instability originating in the vicinity of the cylinder, using the computed Navier-Stokes equation (NSE) from t = 0 to t = 300 following an impulsive start. This instability is also explained through the disturbance mechanical energy equation, which has been established earlier in Sengupta et al. [“Temporal flow instability for Magnus–robins effect at high rotation rates,” J. Fluids Struct. 17 , 941–953 (2003)].

Description: In this article, the flow above a rotating disc, which was first studied by von Kármán for a Newtonian fluid, has been investigated for a Bingham fluid in three complementary but separate ways: by computational fluid dynamics (CFD), by a semi-analytical approach based on a new transformation law, and by another semi-analytical approach based on von Kármán’s transformation. The full equations, which consist of a set of partial differential equations, are solved by CFD simulations. The semi-analytical approach, in which a set of ordinary differential equations is solved, is developed here by simplifying the full equations invoking several assumptions. It is shown that the new transformation law performs better and reduces to von Kármán’s transformation as a limiting case. The present paper provides a closed-form expression for predicting the non-dimensional moment coefficient which works well in comparison with values obtained by the full CFD simulations. Detailed variations of tangential, axial, and radial components of the velocity field as a function of Reynolds number ( Re ) and Bingham number ( Bn ) have been determined. Many subtle flow physics and fluid dynamic issues are explored and critically explained for the first time in this paper. It is shown how two opposing forces, viz., the viscous and the inertial forces, determine certain important characteristics of the axial-profiles of non-dimensional radial velocity (e.g., the decrease of maxima, the shift of maxima, and the crossing over). It has been found that, at any Re , the maximum value of the magnitude of non-dimensional axial velocity decreases with an increase in Bn , thereby decreasing the net radial outflow. A comparison between the streamline patterns in Newtonian and Bingham fluids shows that, for a Bingham fluid, a streamline close to the disc-surface makes a higher number of complete turns around the axis of rotation. The differences between the self-similarity in a Newtonian fluid flow and the non-similarity in a Bingham fluid flow are expounded with the help of a few compelling visual representations. Some major differences and similarities between the flow of a Newtonian fluid above a rotating disc and that of a Bingham fluid, deduced in the present investigation, are brought together in a single table for ready reference. Two limiting cases, viz. Bn → 0 and Re → ∞, are considered. The present results show that the Bingham fluid solution progressively approaches the von Kármán’s solution for a Newtonian fluid as the Bingham number is progressively reduced to zero ( Bn → 0). It is also established here that, for finite values of Bn , the Bingham fluid solution progressively approaches the von Kármán’s solution for a Newtonian fluid as the non-dimensional radius and Reynolds number increase. The higher the value of Bn , the higher is the required value of Re at which convergence with the solution for Newtonian fluid occurs.

Description: We formulate a comprehensive analysis for the radial pressure variation in flow through microchannels within corotating (or static) discs, which is important for its fundamental value and application potential in macrofluidic and microfluidic devices. The uniqueness and utility of the present approach emanate from our ability to describe the physics completely in terms of non-dimensional numbers and to determine quantitatively the separate roles of inertia, centrifugal force, Coriolis force, and viscous effects in the overall radial pressure difference (Δ p io ). It is established here that the aspect ratio (ratio of inter-disc spacing and disc radius) plays only a secondary role as an independent parameter, its major role being contained within a newly identified dynamic similarity number ( Ds ). For radial inflow, it is shown that the magnitude of Δ p io decreases monotonically as the tangential speed ratio ( γ ) increases but exhibits a minima when Ds is varied. For radial outflow, it is shown that Δ p io increases monotonically as the flow coefficient ( ϕ ) decreases but evinces a maxima when Ds is varied. It is further shown that for the radial inflow case, the minima in the magnitude of Δ p io exist even when the rotational speed of the discs is reduced to zero (static discs). The demonstrated existence of these extrema (i.e., minima for radial inflow and maxima for radial outflow) creates the scope for device optimization.