Estimation of mean turbulent kinetic energy and temperature variance dissipation rates using a spectral chart method

A method aimed at estimating epsilon (k) and epsilon (theta), respectively, the mean dissipation rates of turbulent kinetic energy k and half the temperature variance mml:mfenced close= open=theta 2 mml:mfenced 2, is developed for slightly heated turbulent flows of air. It is limited to a Prandtl number near unity and applicable to flows where temperature can be treated as a passive scalar. A significant advantage of the method is that epsilon (k) and epsilon (theta) can both be estimated from the measurement of a temperature frequency spectrum, G(theta theta)(f). The method relies on the collapse in the dissipative range of one-dimensional temperature spectra, phi (theta)(k(1)eta), when normalized with epsilon (theta), epsilon (k), and nu. This collapse ensues from a similarity analysis of scale-by-scale budgets of the second-order structure function for the temperature. A generic spectrum phi theta G(k1 eta), defined in the wavenumber range 0.07 <= k(1)eta <= 0.7, is used to construct a spectral chart. The method has been tested in several flows and found to be reliable. In particular, it is tested on the axis of a slightly heated round jet, where epsilon (k) and epsilon (theta) can be estimated accurately via the budgets of k and mml:mfenced close= open=theta 2 mml:mfenced 2, and the agreement between these estimates and the spectral chart results is almost perfect.