Motion and Heat Transfer in Turbulent Vortex Pairs
A two-dimensional problem of turbulent vortex pairs originated by an instantaneous dynamical impulse (cylindrical puffs) or an instantaneous heat release (cylindrical thermals) is considered. The equations of vorticity and heat transfer for a turbulent motion of incompressible fluid are transformed into a non-dimensional form which includes the requirements to reach the similarity regime. The system of equations is solved numerically for various values of spatially constant eddy viscosity and heat diffusion coefficients. The obtained similarity distributions of vorticity, velocity and temperature for cylindrical puffs and thermals are discussed and compared with available experimental data. The results of computations for line puffs point at the existence of a critical value of the non-dimensional eddy viscosity coefficient. Below this value there exists a loss of momentum and heat to a wake at the rear of the vortex pair.
R. S. SCORER, Natural aerodynamics, Pergamon Press, 1958.
J. M. RICHARDS, Experiments on the motions of isolated cylindrical thermals through unstratified surroundings, Int. J. Air. Wat. Poll., 7, 1, 13-34, 1963.
J. M. RICHARDS, Puff motions in unstratified surroundings, J. Fluid Mech., 21, 1, 97-106, 1965.
GEE TSANG, Laboratory study of line thermals, Atm. Env., 5, 6, 445-471, 1971.
GEE TSANG, Entrainment of ambient fluid by two-dimensional starting plumes and thermals, Atm. Env., 6, 2, 123-132, 1972.
D. K. LILLY, Numerical solutions for the shape-preserving two-dimensional thermal convection element, J. Atm. Sci., 21, 1, 83-98, 1964.
N.A. PHILIPS, An example of non-linear computational instability, in: The atmosphere and the sea in motion, New-York, 1959.
A. ARAKAWA, Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow, J. Comput, Phys., 1, 2, 119-143, 1966.
T. MAXWORTHY, Turbulent vortex rings, J. Fluid Mech., 64, 2, 227-239, 1974.
A. EPSTEIN, V. HENDRIKSON, Some peculiarities of jet flows in a deflecting stream, Rozpr. Inżyn., 22, 3, 421-426, 1974.
Y. KAMOTANI, J. GREBER, Experiments on a turbulent jet in a cross flow, AJAA J., 10, 11, 1425-1429, 1972.
LOH-NIEN FAN, Turbulent buoyant jets into stratified or flowing ambient fluids, W. M. Keck Lab. Hydr. Wat. Res., Div. Eng. Appl. Sci., Calif., Inst. Tech., Passadena, Calif., Rep.