REDUCED DYNAMICAL MODELS OF NONISOTHERMAL TRANSITIONAL GROOVED-CHANNEL FLOW

Reduced dynamical models are derived for transitional flow and heat tr ansfer in a periodically grooved channel. The full governing partial d ifferential equations are solved by a spectral element method. Spontan eously oscillatory solutions are computed for Reynolds number Re great er than or equal to 300 and proper orthogonal decomposition is used to extract the empirical eigenfunctions at Re=430, 750, 1050, and Pr=0.7 1. In each case, the organized spatio-temporal structures of the therm ofluid system are identified, and their dependence on Reynolds number is discussed. Low-dimensional models are obtained for Re=430, 750, and 1050 using the computed empirical eigenfunctions as basis functions a nd applying Galerkin's method. At least four eigenmodes for each field variable are required to predict stable, self-sustained oscillations of correct amplitude at ''design'' conditions. Retaining more than six eigenmodes may reduce the accuracy of the low-order models due to noi se introduced by the low-energy high order eigenmodes. The low-order m odels successfully describe the dynamical characteristics of the flow for Re close to the design conditions. Far from the design conditions, the reduced models predict quasi-periodic or period-doubling routes t o chaos as Re is increased. The case Pr=7.1 is briefly discussed. (C) 1997 American Institute of Physics.