E. Leonardi

The Development of a Bubble Rising in a Viscous Liquid

The rise and deformation of a gas bubble in an otherwise stationary liquid contained in a closed, right vertical cylinder is investigated using a modified volume-of-fluid (VOF) method incorporating surface tension stresses. Starting from a perfectly spherical bubble which is initially at rest, the upward motion of the bubble in a gravitational field is studied by tracking the liquid–gas interface. The gas in the bubble can be treated as incompressible. The problem is simulated using primitive variables in a control-volume formulation in conjunction with a pressure–velocity coupling based on the SIMPLE algorithm. The modified VOF method used in this study is able to identify and physically treat features such as bubble deformation, cusp formation, breakup and joining. Results in a two-dimensional as well as a three-dimensional coordinate framework are presented. The bubble deformation and its motion are characterized by the Reynolds number, the Bond number, the density ratio, and the viscosity ratio. The effects of these parameters on the bubble rise are demonstrated. Physical mechanisms are discussed for the computational results obtained, especially the formation of a toroidal bubble. The results agree with experiments reported in the literature.

AIR FLOW AND HEAT TRANSFER IN VENTILATED DISC BRAKE ROTORS WITH DIAMOND AND TEAR-DROP PILLARS

This study is part of an ongoing research project investigating the airflow and heat transfer of different disc brake rotors. This article reports on three geometries: straight radial vane (SRV) rotor; SRV rotor with rounded vanes (SRV-R); and a rotor with diamond and teardrop pillars (DTDP) instead of vanes. The total heat transfer from the SRV-R and DTDP passages is up to 20% greater than that for the SRV rotor. As much as 35% more heat is lost from the free side friction surface than the hub side friction surface. Flow development through the DTDP rotor passages is also noted.

A computational study of transient plane front solidification of alloys in a Bridgman apparatus under microgravity conditions

A mathematical model of heat, momentum and solute transfer during directional solidification of binary alloys in a Bridgman furnace has been developed. A fixed grid single domain approach (enthalpy method) is used. The effects of coupling with the phase diagram (a concentration-dependent melting temperature) and of thermal and solutal convection on segregation of solute, shape and position of the solid/liquid interface are investigated. A vorticity–stream function formulation is used for calculation of the velocity fields. The results presented include calculations at 1 and 10 μg, both neglecting and including the dependence of melting temperature on concentration.

Mixed convection in vertical, cylindrical annuli

Abstract The laminar flow patterns and heat transfer for air contained in the enclosure formed between two vertical, concentric cylinders and two horizontal planes have been studied numerically. The inner cylinder and one of the horizontal planes are heated and rotated about the vertical axis; the other horizontal plane and outer cylinder are cooled and kept stationary. This geometry simulates the gaps at the ends of the rotor of a small, air-cooled, vertically mounted electric motor. The results facilitate the thermal design of such a motor. The influences of geometry (described by the radius ratio R and aspect ratio A), Ra and Re on temperature and velocity distributions have been investigated. Solutions have been obtained for 0.25 ⩽ A ⩽ 4.0, 1.2 ⩽ R ⩽ 8.0, 10 ⩽ Re ⩽ 300 and 103 ⩽ Ra ⩽ 105. It has been found that for low values of R and high values of Re the flow is dominated by centrifugal forces, whereas for high A and Ra buoyancy effects determine the flow patterns and, therefore, the heat transfer. Monocellular flow patterns have been found for the cases where one of these forces is dominant; otherwise two- or three-cell structures have been obtained.

An evaluation of synthetic jets for heat transfer enhancement in air cooled micro‐channels

Purpose – The development of novel cooling techniques is needed in order to be able to substantially increase the performance of integrated electronic circuits whose operations are limited by the maximum allowable temperature. Air cooled micro‐channels etched in the silicon substrate have the potential to remove heat directly from the chip. For reasonable pressure drops, the flow in micro‐channels is inherently laminar, so that the heat transfer is not very large. A synthetic jet may be used to improve mixing, thereby considerably increasing heat transfer. This paper seeks to address this issue.Design/methodology/approach – CFD has been used to study the flow and thermal fields in forced convection in a two‐dimensional micro‐channel with an inbuilt synthetic jet actuator. The unsteady Navier‐Stokes and energy equations are solved. The effects of variation of the frequency of the jet at a fixed pressure difference between the ends of the channel and with a fixed jet Reynolds number, have been studied with ...

A numerical and experimental study of natural convection and interface shape in crystal growth

Abstract A numerical and experimental study has been conducted on the crystal growth of succinonitrile in a horizontal Bridgman apparatus. The shape of the solid—liquid interface was significantly influenced by three-dimensional natural convection in the liquid adjacent to the interface. The interface profile observed during experiments was compared with predictions from a two-dimensional (2D) finite element analysis and a three-dimensional (3D) finite difference approach. Good agreement was achieved between the experimental and predicted results. The computed velocities in the vicinity of the interface were found also to be in good agreement with the measured experimental velocities.

Motion of Interacting Gas Bubbles in a Viscous Liquid Including Wall-Effects and Evaporation

Abstract The motion of single and multiple gas bubbles in an otherwise stationary liquid contained in a closed right vertical cylinder is investigated using a modified volume-of-fluid (VOF) method incorporating surface tension stresses. An isolated bubble was considered in a separate paper [4], where the initial bubble radius was small in comparison with that of the cylinder and watt effects were negligible. In this work the focus is on the interference effects during the motion of two initially spherical bubbles in a gravitational field, as well as the influence of the container wall on the bubble motion: the initial bubble diameter in the present study is more than half the cylinder diameter. The bubble size is also much larger than that required to satisfy the condition in which the gas can be treated as incompressible. In addition, the effect on bubble motion of the inclusion of evaporation at the gas-liquid interface as well as the bursting of a bubble through a five surface are considered. The modif...

A computational study of binary alloy solidification in the MEPHISTO experiment

Abstract A computational model is presented for the study of the solidification of a binary alloy. The enthalpy method has been modified and incorporated into both an in-house code SOLCON (Heat Transfer 98, 1998, p. 241) and the commercial CFD code CFX (CFX 4.2: Solver, 1997). The model has been used to simulate experiments on solidification of a bismuth–tin alloy which were performed during the 1997 flight of the MEPHISTO-4 experiment on the US Space Shuttle Columbia. The effects of thermal and solutal convection in the microgravity environment and of concentration-dependent melting temperature on the phase change processes are included. Comparisons of numerical solutions with actual microprobe results obtained from the MEPHISTO experiments are presented.

CFD Analysis of the Acoustic and Mean Flow Performance of Simple Expansion Chamber Mufflers

The acoustic and mean flow performance of different configurations of simple expansion chamber mufflers has been considered. The different configurations include extended inlet/outlet pipes and baffles inside the expansion section of the muffler. Both the acoustic and mean flow performance has been evaluated for each muffler. The acoustic CFD model of the muffler uses an axisymmetric grid with no mean flow and a single period sinusoid of suitable amplitude and duration imposed at the inlet boundary. The time history of the acoustic pressure and particle velocity are recorded at two points, one in the inlet pipe and the other in the outlet pipe. These time histories are Fourier transformed and the transmission loss of the muffler is calculated. The mean flow model of the muffler uses the same geometry, but has a finer mesh and has a suitable inlet velocity applied at the inlet boundary and the pressure drop across the muffler is found. The acoustic performance is compared with published experimental results.Copyright

A NUMERICAL STUDY OF SOLIDIFICATION IN THE PRESENCE OF A FREE SURFACE UNDER MICROGRAVITY CONDITIONS

A numerical study of the relative importance of Marangoni effects under microgravity conditions is presented. The mathematical formulation adopted is based on the enthalpy porosity method. One of the advantages of the fixed grid method is that a unique set of equations and boundary conditions is used for the whole domain, including both solid and liquid phases. The governing equations written in a vorticity-velocity formulation are discretized using a finite volume technique on a staggered grid. A fully implicit method has been adopted for the mass and momentum equations, while the temperature field is solved separately in order to evaluate the variation in the local liquid mass fraction. The resulting algebraic system of equations is solved using a preconditioned BI-CGStab method. Numerical results modelling the free surface, including the effects on it of Marangoni convection, are presented. The influence of the presence of argon in the gap above the free surface is investigated. During the numerical simulations presented in this paper 161 2 41 and 641 2 161 uniform meshes on the whole computational domain for values of Marangoni number ( Ma ) up to 16,120 and Rayleigh number ( Ra ) of 5 have been used.