Exact and limiting solutions of fluid flow for axially oscillating cylindrical pipe and annulus

The Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatory flows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillating cylindrical annulus. In both the cases, in addition to the exact expressions for the velocity profiles, particular emphasis has been given for the determination of approximate velocity distributions for the high frequency and low frequency or quasi-static limits. It is shown that, for sufficiently large value of an appropriate frequency parameter, the velocity distribution inside the axially or longitudinally oscillating cylindrical annulus can be approximated as a superposition of the velocity distribution inside an axially oscillating cylindrical pipe of radius $${\bar R_o}$$ R ¯ o and the velocity distribution outside an axially oscillating cylindrical pipe of radius $${\bar R_i}$$ R ¯ i , where $${\bar R_i}$$ R ¯ i and $${\bar R_o}$$ R ¯ o are the inner and outer radii of the axially oscillating annulus, respectively.

Numerical Analysis of the Improving Thermal Energy Efficiency of Taylor-couette Flow

This paper deals with adimensionnal analysis of natural convection in a horizontal cylindrical annulus. The inner cylinder is isothermally heated and rotates with an angular velocity Ω, however the outer one is kept cold and motionless. The gap between cylinders is defined by an adimensional radius ratio f. The numerical study was carried out using COMSOL Multiphysics. The effects of Rayleigh number ranging from 102 to 106, radius ratio and rotation velocity on the flow pattern and the thermal behavior in the annulus are then elaborated. Particular attention is paid to the effect of different parameters on the local Nusselt numbers on the inner and outer cylinders, the mean Nusselt number and the energy efficiency of the process. Results show that the mean Nusselt number increases with the increase of Rayleigh number. However, it decreases with the increase of the radius ratio f because of the narrowing of the annulus. The results prove also that the heat transfer rate drops with the rise of rotation velocity. Finally, it was found that the energy efficiency achieved its maximum for lower Rayleigh numbers Ra=103, and lower rotation velocities.

Investigation of Heat Transfer Characteristics in a Rotating Convection System With Bi-Directional Thermal Gradients

A series of rotating convection experiments have been conducted in a novel configuration, which comprises a cylindrical annulus with spot heating on the bottom outer edge and uniform cooling on the inner surface. Such a system provides bi-directional thermal gradients in both radial and vertical directions, thereby reenacting the thermal gradient patterns encountered in the atmosphere. Bulk heat transfer characteristics are studied by quantifying the overall Nusselt number, Nu, for a range of Taylor number, Ta, heating rate, Q, and Rayleigh number, Ra. Temperature measurements are carried out at different locations with the help of thermocouples. The Nusselt number is found to be quite sensitive to the buoyancy and relatively insensitive to the rotation rate. The correlation for Nu as a function of Ra revealed different power law exponents for low and high Ta values. The varying exponent is attributed to the presence of baroclinic eddies at high Ta, which in turn is verified with the help of flow visualization. The heat transfer characteristics in this new configuration are significantly different compared to other conventional rotational convection systems, where thermal gradients are present in only one direction.

Supergravitational turbulent thermal convection

High–Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth’s gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Rayleigh number is large enough. The convective rolls revolve in prograde direction, signifying the emergence of zonal flow. The present findings open a new avenue on the exploration of high–Rayleigh number turbulent thermal convection and will improve the understanding of the flow dynamics and heat transfer processes in geophysical and astrophysical flows and other strongly rotating systems.