An experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh numbers ($1.18\leq {\rm Ra}\leq 242$). Both the experiments and the SPH calculations were performed for positive ($0.1\leqΔT\leq 10$ K) and negative ($-10\leqΔT\leq -0.1$ K) temperature differences between the source and the surrounding fluid. In all cases a pair of steady, counter-rotating vortices is formed, accompanied by a plume of vertically ascending flow just above the source for $ΔT>0$ and a vertically descending flow just below the source for $ΔT<0$. The maximum flow velocities always occur within the ascending/descending plumes. The SPH predictions are found to match the experimental observations acceptably well with root-mean-square errors in the velocity profiles of the order of $\sim 10^{-5}$ m s$^{-1}$. The fact that the SPH method is able to reveal the detailed features of the flow phenomenon demonstrates the correctness of the approach.
The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction, in which cases heat transfer occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. We obtain a simple linear criterion t…
The paper presents the comparative study of the vortex-induced cooling of a heated channel for the four different cross-sections of the rigid cylinder, i.e., circular, square, semi-circular, and triangular, with or without the rigid/flexible splitter plate at the Reynolds number (based on the hydraulic diameter) of 200. The study presents a comprehensive analysis of the flow and thermal performance for all the cases. For flexible plate cases, a partitioned approach is invoked to solve the coupled fluid-structure-convection problem. The simulations show the reduction in the thermal boundary lay…
The main objective of this paper is to study the flow characteristics of a rotating, isothermally heated circular cylinder with a vertical arc-shaped control plate placed downstream. Stream function-Vorticity ($ψ-ω$) formulation of two dimensional (2-D) Navier-Stokes (N-S) equations is considered as the governing equation and the simulations are performed for different distances of the control plate ($0.5$, $1$, $2$, $3$), rotational rates ($0.5$, $1$, $2.07$, $3.25$) at Prandtl number $0.7$ and Reynolds number $150$. The governing equations are discretized using the Higher Order Compact (HOC)…
The impact of liquid drops on a heated solid surface is of great importance in many engineering applications. This paper describes the simulation of the drop-wall interaction using the smoothed particle hydrodynamics (SPH) method. The SPH method is a Lagrangian mesh-free method that can be used to solve the fluid equations. A vaporization model based on the SPH formulation was also developed and implemented. A parametric study was conducted to characterize the effects of impact velocity and wall temperature on the impact outcome. The present numerical method was able to predict different outco…
The main objective of this paper is to study the effect of a cold, vertical, arc-shaped control plate on the flow characteristics and forced convective heat transfer mechanism across a rotary oscillating, isothermally heated circular cylinder. Two-dimensional, unsteady, incompressible, laminar, and viscous flow of a Newtonian, constant property fluid is considered across the cylinder. The simulations are performed with an in-house code for various gap ratios between the control plate and the cylinder ($0\leq d/R_0 \leq 3$), maximum angular velocity ($0.5\leq α_m \leq 4$) and frequency ratio of…
From Sheared Annular Centrifugal Rayleigh-Bénard Convection to Radially Heated Taylor-Couette Flow: Exploring the Impact of Buoyancy and Shear on Heat Transfer and Flow Structure
This paper experimentally investigates the convection in a fast rotating Tangent Cylinder (TC), for Ekman numbers down to $E=3.36\times10^{-6}$, in a configuration relevant to the liquid core of the Earth. In the apparatus, the TC results from the Proudman-Taylor constraint incurred by rotating a hemispherical fluid vessel heated in its centre by a protruding heating element of cylindrical shape. The resulting convection that develops above the heater, i.e within the TC, is shown to set in for critical Rayleigh numbers and wavenumbers respectively scaling as $Ra_c\sim E^{4/3}$ and $a_c\sim E^{…
The interaction of liquid drops and heated surfaces is of great importance in many applications. This paper describes a numerical method, based on smoothed particle hydrodynamics (SPH), for simulating n-heptane drop impact on a heated surface. The SPH method uses numerical Lagrangian particles, which obey the laws of fluid dynamics, to describe the fluid flows. By incorporating the Peng-Robinson equation of state, the present SPH method can directly simulate both the liquid and vapor phases and the phase change process between them. The numerical method was validated by two experiments on drop…
We experimentally study the behavior of a particle slightly denser than the surrounding liquid in solid body rotating flow. Earlier work revealed that a heavy particle has an unstable equilibrium point in unbounded rotation flows. In the confinement of the rotational flow by a cylindrical wall a heavy sphere with density 1.05 g/cm$^3$ describes an orbital motion in our experiments. This is due to the effect of the wall near the sphere, i.e. a repulsive force ($F_w$). We model $F_w$ on the sphere as a function of the distance from the wall ($L$): $F_W \propto L^{-4}$ as proposed by Takemura and…
Fully resolved simulations are used to quantify the effects of heat transfer in the presence of buoyancy on the drag of a spatially fixed heated spherical particle at low Reynolds numbers ($Re$) in the range $10^{-3} \le Re \le 10$ in a variable property fluid. The amount of heat addition from the sphere encompasses both, the heating regime where the Boussinesq approximation holds and the regime where it breaks down. The particle is assumed to have a low Biot number which means that the particle is uniformly at the same temperature and has no internal temperature gradients. Scaling buoyancy wi…
The hydrodynamic and thermal characteristics of a freely-vibrating circular cylinder in mixed convection flow are numerically investigated at low Reynolds numbers. The numerical investigations are conducted for a range of parameters, Ur = [2.0, 10], Pr = [0.7, 10] and Ri = [0.5, 2.0]. Whereas the Reynolds number, the mass ratio and the damping ratio are fixed. A secondary VIV lock-in region is found in the cases of high Richardson number Ri=2.0 for high reduced velocity values, in which the buoyancy-driven flow is non-trivial. A wide VIV lock-in region is formed with tremendous energy transfer…
The precise description of the motion of anisotropic particles in a flow rests on the understanding of the force and torque acting on them. Here, we study experimentally small, very elongated particles settling in a fluid at small Reynolds number. In our experiments, we can, to a very good approximation, relate the rate of rotation of cylindrical tungsten rods, of aspect ratios β= 8 and β= 16, settling in pure glycerol to the torque they are experiencing. This allows us to compare the measured torque with expressions obtained either in the slender-rod limit, or in the case of spheroids. Both t…
We investigate the dynamics of flows past a stationary circular cylinder embedded on spherical and cylindrical surfaces at a fixed Reynolds number of 100. For flows on surfaces, it is convenient to express the Navier-Stokes equations in exterior calculus notation. We employ the discrete exterior calculus (DEC) method (Mohamed et al. (2016)) to numerically solve the equations. We explore the role played by curvature on dynamical quantities of interest: the drag coefficient (Cd), the lift coefficient (Cl), and the Strouhal number (St). Our simulations indicate that the effect of surface curvatur…
To find the regularities of formed fingers in gravity driven coating flows on upper cylinder and sphere, the mathematical formulation to model the fingering instability on cylindrical or spherical surface which consists of a capillary wave equation and a linear perturbation equation is constructed, based on the leading order governing equation in standard cylindrical or spherical coordinate system. A disjoining pressure model is introduced to simulate the partial wetting process near moving contact line. The fingering number in high $Bo$ coating flow is focused on from a linear perspective. Us…
In this study, we use numerical simulations to investigate the flow field induced by a single magnetic microrobot rotating with a constant angular speed about an axis perpendicular to an underlying surface. A parallel solver for steady Stokes flow equations based on the boundary-element method is used for simulating these flows. A simple transformation is introduced to extend the predictive capability of the solver to cases with small unsteadiness. Flows induced by four simple robot shapes are investigated: sphere, upright cylinder, horizontally-laid cylinder, and five-pointed star-shaped pris…
The theoretical and numerical models for gravity driven coating flow on upper cylinder and sphere are formulated. Using a perturbation method, the governing equations which depend on one Bond number $Bo$ are derived for a liquid film flow down the outside of a horizontal cylinder and a sphere. They can be simplified to one-dimensional form due to the symmetries. The general structure of the two-dimensional and axisymmetric capillary waves under high $Bo$ condition is focused on. An asymptotic theory is used to solve for the free-surface profiles in the outer and inner region, respectively. Eve…
We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder…
An overset grid method was used to investigate the interaction between a particle-laden flow and a circular cylinder. The overset grid method was implemented in the Pencil Code , a high-order finite-difference code for compressible flow simulation. High-order summation-by-part operators were used at the cylinder boundary, and both bi-linear Lagrangian and bi-quadratic spline interpolation was used to communicate between the background grid and the body-conformal cylindrical grid. The performance of the overset grid method was assessed to benchmark cases of steady and unsteady flows past a cyli…
