K. Velusamy

Transient natural convection over a heat generating vertical cylinder

Abstract A numerical solution for the transient natural convection over heat generating vertical cylinders of various thermal capacities and radii is presented. A fully implicit finite difference technique is used to solve the non-linear set of equations. The rate of propagation of the leading edge effect is given special consideration. It is found that this rate, predicted by the one-dimensional conduction solution, is slower than that resulting from the boundary layer solution. Also, it increases as the radius and thermal capacity of the cylinder decrease, and as the surface heat flux increases. The transient boundary layer thickness is found to exceed its steady-state value while the transient average heat transfer coefficient is found to reach a minimum, as low as 53% of its steady-state value for the highest value of the modified Grashof number studied. Excellent agreement with previous experimental steady-state data as well as with one-dimensional theoretical results is obtained.

Fully developed flow and heat transfer in semi-elliptical ducts

A control volume-based numerical solution is described for the fully developed laminar flow and heat transfer in ducts of semi-elliptical cross section. Both an isothermal and a uniform axial heat flux condition on the duct walls have been considered. Numerical results for velocity and temperature profiles, friction factor, pressure defect, and Nusselt number are presented for a wide range of duct aspect ratios from 0.1 to 0.999. Comparison with earlier numerical results for the limiting case of semicircular duct and with analytical solution for fully elliptical ducts is excellent. For ducts in which the baseplate is on the major axis, friction factor and Nusselt number for the uniform heat flux condition increase as the aspect ratio decreases, with values for the lowest aspect ratio of 0.1 being about 25 percent larger than those for a semicircular duct. For ducts with the baseplate on the minor axis, all characteristics exhibit a nonmonotonic behavior with respect to the aspect ratio. While the maximum velocity and pressure defect exhibit a mild maximum for aspect ratio of 0.6, the friction factor and Nusselt number exhibit a minimum at the same aspect ratio. The ratio of Nusselt number to friction factor is higher for semi-elliptical ducts in comparison to that for other ducts, such as sinusoidal, circular segmental, and isosceles triangular ducts.

Laminar mixed convection in vertical elliptic ducts

Abstract A control volume based numerical solution is described for the fully developed mixed convection in vertical ducts of elliptic cross-section. The duct wall is supplied with a uniform axial heat rate while the thickness and thermal conductivity of the duct wall are such that the wall temperature is circumferentially uniform. Results for velocity and temperature distributions, friction factor, Nusselt number and critical Rayleigh number are presented for a wide range of duct aspect ratios and Rayleigh numbers. It is found that during mixed convection, fluid with a higher axial velocity exists around the foci of the elliptical cross-section, leading to substantial heat transfer enhancement in this region of the duct. The ratio of friction factor during mixed convection to that during forced convection is low in elliptical ducts compared to that in a circular duct. Also, the ratio of Nusselt number to friction factor is higher for elliptic ducts compared to that for a circular duct, irrespective of the value of the Rayleigh number. The critical Rayleigh number, at which flow reversal is initiated in the core region, is higher for elliptic ducts compared to that for a circular duct.

Numerical Investigation of Vortex Shedding Past a Finite Circular Cylinder Mounted on a Flat Plate

Flow past a circular cylinder mounted on a flat plate normal to the flow direction is numerically simulated. Three-dimensional mass and momentum conservation equations are solved to obtain the detailed spatio-temporal dynamics of wake vortices revealed through the velocity and pressure data. Particular attention is focused on the junction between the flat plate and the cylindrical cross-section, which is well known to be a rich source of three-dimensional vortical structures. The wake–boundary layer interaction region generates necklace vortices, which are popularly known as horseshoe vortices. The effect of spanwise height (H/D) of the cylinder on these vortices and their unsteady wake characteristics are investigated. The forces acting on the cylinder and the Strouhal periodicities are validated for Re = 200, apart from presenting qualitative features, such as streamlines and vorticity contours. The aspect ratio of the cylinder is found to have predominant influence on the primary and secondary vortex structures. Streakline visualization is developed to study the spatio-temporal dynamics of interaction between the wake and the boundary-layer. An assessment of the two types of boundary conditions, viz., free-slip and no-slip (the latter due to bed friction) are investigated. Vortex shedding is found to be completely suppressed for smaller aspect ratios (H/D) ≤ 1.0, with a stabilized flow pattern in the aft of the cylinder, while it persists for H/D > 1.0.

A computational study of flow mal-distribution on the thermal hydraulic performance of an intermediate heat exchanger in LMFBR

The flow and thermal non-uniformities occurring in the intermediate heat exchanger (IHX) of a liquid metal-cooled fast breeder reactor have been characterized through numerical simulations. For modeling the primary and secondary sodium flow through the IHX, an equivalent anisotropic porous medium approach has been used. The pressure drop in the equivalent porous medium is accounted through the inclusion of additional pressure drop terms in the Navier–Stokes equations, with the help of standard correlations for cross flow or parallel flow over tubes. For secondary sodium flow, the effects of a flow distributor device with orifices and baffles at the inlet have also been included, in addition to axial flow through the tubes. The heat exchange between primary and secondary streams is incorporated in the form of a volumetric heat source or sink term, which is corrected iteratively. The resulting flow distributions are in reasonable agreement with available experimental results. The study shows that the temperature of the secondary sodium flow at the exit can be made more uniform by exchanging less heat near the inner wall of IHX, as compared to the region close to the outer wall, using suitable flow distribution devices.

Leading edge effect during transient buoyancy induced flow adjacent to a vertical cylinder

Abstract The rate of propagation of the leading edge effect (LEE) during transient natural convection adjacent to a vertical solid cylinder is estimated from five different criteria. The cylinder has an appreciable thermal capacity and is subjected to a sudden heat generation. Numerical results are presented for a wide range of cylinder radii and heat flux values for two fluids, air and water. It is found that unlike the case of a flat plate, there is no unique criterion which would always estimate the fastest rate of propagation of LEE in water. However in air, the criterion due to Brown and Riley (J. Fluid Mech59, 225–237 (1973)) always predicts the fastest rate of propagation. Also, the effect of cylinder radius on the rate at which the LEE propagates through different fluids is different. For identical conditions, the LEE propagates faster in air than in water, as expected. Present results obtained by dropping the curvature terms in the governing equations match very well with previous analytical results for a flat plate.