Three-dimensional spectral approximations to Stokes flow between eccentrically rotating cylinders

1991 ◽  
Vol 13 (2) ◽  
pp. 217-233 ◽  
Author(s):  
G. W. Roberts ◽  
A. R. Davies ◽  
T. N. Phillips
Keyword(s):  
Stokes Flow ◽  
Three Dimensional ◽  
Rotating Cylinders ◽  
Spectral Approximations

Transient Three-Dimensional Heat Transfer Model of a Solar Thermochemical Reactor for H2O and CO2 Splitting via Nonstoichiometric Ceria Redox Cycling

2013 ◽  
Author(s):  
Justin Lapp ◽  
Wojciech Lipiński
Keyword(s):  
Heat Transfer ◽  
Heat Recovery ◽  
Fuel Efficiency ◽  
Three Dimensional ◽  
Reactor Design ◽  
Heat Transfer Model ◽  
Heat Fluxes ◽  
Transfer Model ◽  
Rotating Cylinders ◽  
Solar Receiver

A transient heat transfer model is developed for a solar reactor prototype for H2O and CO2 splitting via two-step non-stoichiometric ceria cycling. Counter-rotating cylinders of reactive and inert materials cycling between high and low temperature zones permit continuous operation and heat recovery. To guide the reactor design a transient three-dimensional heat transfer model is developed based on transient energy conservation, accounting for conduction, convection, radiation, and chemical reactions. The model domain includes the rotating cylinders, a solar receiver cavity, and insulated reactor body. Radiative heat transfer is analyzed using a combination of the Monte Carlo method, Rosseland diffusion approximation, and the net radiation method. Quasi-steady state distributions of temperatures, heat fluxes, and the non-stoichiometric coefficient are reported. Ceria cycles between temperatures of 1708 K and 1376 K. A heat recovery effectiveness of 28% and solar-to-fuel efficiency of 5.2% are predicted for an unoptimized reactor design.

Experiments on the stability of sinusoidal flow over a circular cylinder

2002 ◽  
Vol 457 ◽  
pp. 157-180 ◽  
Author(s):  
TURGUT SARPKAYA
Keyword(s):  
Stokes Flow ◽  
Coherent Structures ◽  
High Speed ◽  
Three Dimensional ◽  
Separated Flow ◽  
Circular Cylinders ◽  
Centrifugal Forces ◽  
Complex Interactions ◽  
Sinusoidal Flow ◽  
The Stability

The instabilities in a sinusoidally oscillating non-separated flow over smooth circular cylinders in the range of Keulegan–Carpenter numbers, K, from about 0.02 to 1 and Stokes numbers, β, from about 103 to 1.4 × 106 have been observed from inception to chaos using several high-speed imagers and laser-induced fluorescence. The instabilities ranged from small quasi-coherent structures, as in Stokes flow over a flat wall (Sarpkaya 1993), to three-dimensional spanwise perturbations because of the centrifugal forces induced by the curvature of the boundary layer (Taylor–Görtler instability). These gave rise to streamwise-oriented counter-rotating vortices or mushroom-shaped coherent structures as K approached the Kh values theoretically predicted by Hall (1984). Further increases in K for a given β led first to complex interactions between the coherent structures and then to chaotic motion. The mapping of the observations led to the delineation of four states of flow in the (K, β)-plane: stable, marginal, unstable, and chaotic.

scholarly journals Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances

1992 ◽  
Vol 242 ◽  
pp. 701-720 ◽  
Author(s):  
M. Tadjfar ◽  
R. J. Bodonyi
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Stokes Flow ◽  
Free Stream ◽  
Flow Direction ◽  
Roughness Element ◽  
Three Dimensional ◽  
Unsteady Motion ◽  
Time Harmonic ◽  
Tollmien Schlichting

Receptivity of a laminar boundary layer to the interaction of time-harmonic free-stream disturbances with a three-dimensional roughness element is studied. The three-dimensional nonlinear triple–deck equations are solved numerically to provide the basic steady-state motion. At high Reynolds numbers, the governing equations for the unsteady motion are the unsteady linearized three-dimensional triple-deck equations. These equations can only be solved numerically. In the absence of any roughness element, the free-stream disturbances, to the first order, produce the classical Stokes flow, in the thin Stokes layer near the wall (on the order of our lower deck). However, with the introduction of a small three-dimensional roughness element, the interaction between the hump and the Stokes flow introduces a spectrum of all spatial disturbances inside the boundary layer. For supercritical values of the scaled Strouhal number, S0 > 2, these Tollmien–Schlichting waves are amplified in a wedge-shaped region, 15° to 18° to the basic-flow direction, extending downstream of the hump. The amplification rate approaches a value slightly higher than that of two-dimensional Tollmien–Schlichting waves, as calculated by the linearized analysis, far downstream of the roughness element.

Effect of viscous dissipation in stokes flow between rotating cylinders using BEM

2019 ◽  
Vol 30 (4) ◽  
pp. 2121-2136 ◽  
Author(s):  
Tomasz Janusz Teleszewski
Keyword(s):  
Nusselt Number ◽  
Temperature Distribution ◽  
Viscous Dissipation ◽  
Stokes Flow ◽  
Energy Equation ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Content Type ◽  
Dissipation Term ◽  
Cylinder Diameter

Purpose The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters. Design/methodology/approach The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders. Findings As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases. Originality/value The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

Sign in / Sign up

Export Citation Format

Share Document