Kinematic Eddy Viscosity Research Articles

The laminar and turbulent mixing of jets of compressible fluid. Part I Flow far from the orifice

For flows of jet type, the assumption of a coefficient of eddy kinematic viscosity in turbulent flow leads to the possibility of combining in one the equations for laminar and turbulent motion. An approximation to the solution of these equations is found for the flow of compressible fluid issuing from a narrow slit, far from the slit. The stream function is expanded in a power series in squares of the Mach number. Bickley's solution (1937) for the corresponding problem in incompressible flow is used to start the iterative process by which successive terms of the power series are obtained. In order to find an analytical form for the second term of the series, it has been assumed that the Prandtl number is unity, that the viscosity varies as the nth power of the absolute temperature, and that the stagnation temperature of the jet is the same as that of the surrounding gas. The solution found differs only slightly from that of Howarth (1948) and Illingworth (1949) when laminar flow is considered; only the ‘change of scale’ effect (arising from a distortion of the coordinates in Bickley's solution) is of importance. In turbulent flow the effect of the second term of the series is as important as the ‘change of scale’ effect. The effect of compressibility on the width of the mixing region is discussed for both laminar and turbulent jet flow far from the orifice.

自然の風と風洞実験.第2報

As the similarity law of the turbulent flow, the author obtains phenomenologically two conditions as follows: (1) the equal eddy REYNOLDS number, (2) the equal inteinsity of turbulence, where K denotes the eddy kinematic viscosity.

大氣中に於ける微渦の大きさ及び壽命

G. I. Taylor introduced two kinds of correlation functions to describe the nature of micro-turbulence in turbulent flow. Mean radius and mean life of micro-turbulence in the atmosphere were determined after consideration of such correlation functions and the following relations were found. where η is eddy kinematic viscosity, τ0 mean life and u' fluctuation of the velocity. where λ is mean radius of the micro-turbulence, molecular kinematic viscosity.Numerical values of mean life and mean radius of the micro-trubulence in the atmosphere were calculated from observations and it was found that they are about 6cm. and 50 sec. respectively.

渦動粘性係數の實驗式に就いて

It is a well-known fact that the coefficicnt of the molecular viscosity in air is found to increase with air temperature. For instance, an empirical formula given by Grindy and Gibson is as follows1); η=0.0001702(1+0.00329θ+0.0000070θ2) in c. g. s. units, where θ is the temperature in Centigrades. Afterware's, some analogous empirical formulae have been obtained by Rankine2), Millikan(3) and others. Correspondingly, it will be seen that the coefficient of the eddy viscosity increases with air temperature. On both theoretical and observational grounds, L. F. Richardson(1) believes that, eddy viscosity depen_??_s on the temperature difference between ground and air and on the wind velocity. In order to determine approximate'y the quanti ative relationship from the pilot-balloon observations with single theodolite; H. M. Treloar(2) has expressed it as follows: ν=70(1+0.1T)V, in which V is the wind velocity at a height of 50 meters, T the difference of temperature in Fahr. between surface soil an_??_ air at 10 feet. Here, the basis of his method rests on the assumption that the coefficient of surface friction is a universal cons ant.In this paper, we determined the eddy viscosity from an empirical formula of the ascending velocity of the pilot-balloon. When the compres-sibility of air has to be allowed, for the total resistance to the translation through an air of the balloon, in the corresponding directions, we are led by consideration of dimensions to a formula where α is the radius of balloon, ν is the kinematic coefficient of eddy viscosity, κ denotes the elasticity, viz. κ=ρ dp/dp. V is the ascending velocity of the balloon, and ρ the air density. Also, ζ is a numerical constant depending on the nature of the surface of the balloon, and n and m are the constants to be determined. Here, the force Qg is the excess of the gravity of the balloon over its total lift of the hydrogen gas, viz. where Ρ denotes the density of air, σ the hydrogen gas in the balloon, and g the acceleration of gravity. Let Lg denote the free lift of the balloon and W the weight of it, hence we have R=(Q-W)g=Lg at any height, where the balloon balanees between its resistance force and lift. It follows, substituting from (1) and (2) the coefficient of the kinematic eddy viscosity gives By using the boserved pilot-balloon's data from the double theodorite made at Haneda branch station of the C. M. O. located in the compoun 1 of the Tokyo Air-port from Sept. to Dec. in 1934, the values of n and m were found viz. n=1, m=1.591.(1) At the stational state of the atmosphere, we may put ∂p/∂z=- ρg and T=Ts-δz, hence we have dp/dρ=g/g-δR_??_RT in which R is the gas constant and δ the lapse rate of the atmospheric temperature. Wherefore, on making these substitutions, the expression (3) becomes From the data obtained by the observations made with the double theodolites from July 1932 to August 1933 at Haneda, (2) we found the value of_??_as the function of the surface air temperature (ts). This empirical relation may be written in the form in c. g. s. units and ts is in Centigrade. Let us put v0 as the value of ν when p=760mm, ts=0 and at the ground z=0, we shall have in c. g. s. units.Now we may neglect the small terms of the developed equation of (4) for obtaining a first approximation, and by the substitution of (5) in (4), we get the equation of the coefficien of the kinematic eddy viscosity in c. g. s. units