Eddy viscosity in decaying swirl flow in a pipe

Prediction of heat transfer coefficient for swirling flows can be made provided the values of the eddy viscosity are available. In the present work the axial and tangential velocity fields are surveyed in a pipe for the determination of eddy viscosity. The data thus obtained were utilised to determine the influence of the axial Reynolds number and swirl number on the eddy viscosity. An empirical relationship is suggested to determine the eddy viscosity as a function of Reynolds number and swirl number.Nomenclature A_T angular momentum, equation (10) - a coefficient, equation (1) - b coefficient, equation (1) - D pipe diameter - f friction factor - F(y) initial condition function, equation (8) - J₀ Bessel's function of the first kind of order zero - J₁ Bessel's function of the first kind of order one - R pipe radius - Re Reynolds number, u_avD/ - r radial coordinate - S_n swirl number, equation (6) - (S_n)_in swirl number at the inlet of the test pipe - u axial velocity - u_av mean axial velocity in pipe - W non-dimensional local tangential velocity, w/u_av - w tangential velocity - X non-dimensional axial coordinate, x/D - x axial coordinate - y non-dimensional radial coordinate, r/R - z non-dimensional parameter, 4(1+/)/Re(x/D) - kinematic eddy viscosity - _n eigenvalues, equation (7) - kinematic viscosity - density