scholarly journals The turbulent Prandtl number in a pure plume is 3/5

2017 ◽  
Vol 822 ◽  
pp. 774-790 ◽  
Author(s):  
John Craske ◽  
Pietro Salizzoni ◽  
Maarten van Reeuwijk

We derive a new expression for the entrainment coefficient in a turbulent plume using an equation for the squared mean buoyancy. Consistency of the resulting expression with previous relations for the entrainment coefficient implies that the turbulent Prandtl number in a pure plume is equal to 3/5 when the mean profiles of velocity and buoyancy have a Gaussian form of equal width. Entrainment can be understood in terms of the volume flux, the production of turbulence kinetic energy or the production of scalar variance for either active or passive variables. The equivalence of these points of view indicates how the entrainment coefficient and the turbulent Prandtl and Schmidt numbers depend on the Richardson number of the flow, the ambient stratification and the relative widths of the velocity and scalar profiles. The general framework is valid for self-similar plumes, which are characterised by a power-law scaling. For jets and pure plumes it is shown that the derived relations are in reasonably good agreement with results from direct numerical simulations and experiments.

1981 ◽  
Vol 16 (1) ◽  
pp. 57-61
Author(s):  
M. A. Gol'dshtik ◽  
S. S. Kutateladze ◽  
A. M. Lifshits

1946 ◽  
Vol 19 (1) ◽  
pp. 176-186
Author(s):  
J. H. E. Hessels

Abstract The rubber particles in the latex of Hevea brasiliensis are present in the form of a polydispersion, and their diameters lie within the range of 0.1 to 3 microns. The rubber hydrocarbon itself is composed of a mixture of macromolecules of different degrees of polymerization. Rubber latex is, therefore, a system which is at the same time both polydispersed and polymolecular. It is well known that the degree of dispersion of a substance governs to a great extent certain properties of the substance. Moreover, astonishing as it may seem, in the great number of investigations which have been made of the composition and properties of latex and crude rubber, almost no attention has been paid to the part which may be played by the dimensions of the latex particles. However, in an investigation concerned with the centrifugation of latex, Loomis and Stump have called attention to this possibility, and in a study of latex obtained by fractionation, and in which the majority of the latex particles were of large dimensions, McGavack came to the conclusion that the protein content is proportional to the surface area of the globules. This limited knowledge of the subject seemed to warrant a more thorough study of the problem, which is of fundamental importance both from the theoretical and practical points of view. The investigation as a whole divided itself into three essential parts: (1) separation of latex into fractions containing particles of different sizes, and measurement of the state of dispersion in these fractions, (2) a study of the relation of these fractions to the composition of the rubber, i.e., the relation between the content of nonrubber components and the size of the latex particles, and (3) a study of the changes in the properties of the rubber hydrocarbon with change in the size of the latex particles. The latex used in this investigation was ordinary latex, containing 38–40 per cent dry-rubber content and preserved with ammonia. For the most important points, a concentrated latex (creamed latex containing 60 per cent dry-rubber content) was also tested. These two latices were about two years old when the investigation was started, and they gave results which were in good agreement with each other. In the present paper, only the data obtained with the first of the two latices are presented.


Author(s):  
Firat Kiyici ◽  
Ahmet Topal ◽  
Ender Hepkaya ◽  
Sinan Inanli

A numerical study, based on experimental work of Inanli et al. [1] is conducted to understand the heat transfer characteristics of film cooled test plates that represent the gas turbine combustor liner cooling system. Film cooling tests are conducted by six different slot geometries and they are scaled-up model of real combustor liner. Three different blowing ratios are applied to six different geometries and surface cooling effectiveness is determined for each test condition by measuring the surface temperature distribution. Effects of geometrical and flow parameters on cooling effectiveness are investigated. In this study, Conjugate Heat Transfer (CHT) simulations are performed with different turbulence models. Effect of the turbulent Prandtl Number is also investigated in terms of heat transfer distribution along the measurement surface. For this purpose, turbulent Prandtl number is calculated with a correlation as a function of local surface temperature gradient and its effect also compared with the constant turbulent Prandtl numbers. Good agreement is obtained with two-layered k–ϵ with modified Turbulent Prandtl number.


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