Large-scale Structures in Rayleigh-Benard Convection and Flow Over Waves

Günther A.

An experimental investigation is carried out on large-scale structures of the fluid velocity and temperature in the turbulent flow over a heated, wavy surface. The study is motivated in part by the findings of Gong et al. (1996), who report a spanwisevariation of the mean streamwise velocity in a boundary layer flow over a train of waves; where the width of the wind tunnel was only four times the wavelength. The flow conditions considered herein are similar to the ones of recent pointwise measurements (Hudson et al., 1996) or direct numerical simulations (e.g. Cherukat et al., 1998).Spatio-temporal information on the fluid temperature is obtained from liquid crystal thermometry (LCT). Using liquid-dispersed liquid crystal particles, the technique is developed and calibrated in a thermally stratified fluid layer. Influences of the fluid properties and the optical configuration are thorougly assessed and provide the basis for a wide range of potential measurement applications. Digital particle image velocimetry (PIV) is used to examine the spatial variation of the velocity in different planes of the flow. As a reference situation for a transient flow with heat transfer, LCT and PIV measurements are ♀rst applied to turbulent Rayleigh-B‼ernard convection in water. Quantitative structural information is obtained from the two-point correlation function and a proper orthogonal decomposition (POD) of the wall-normal velocity component at a Rayleigh number of 7.8´☻, and a Prandtl number of 4:8. Both methods reveal dominant contributions with a characteristic scale of two layer depths in the direction parallel to the wall, where POD analysis proves to be a more e♂ective tool in order to distinguish between the different persistent modes.At isothermal conditions, streamwise-oriented structures in the developed flow through a channel with a flat top and a wavy bottom wall are obtained from PIV measurements. For the presented results, the wave amplitude is ten times smaller than the wavelength Λ and Reynolds numbers between 500 and 7300, defined with the bulk velocity and the half-height of the channel, are considered. The spanwise variation of the velocity fluctuations is assessed in a plane parallel to the top wall, and in one that intersects with the wavy surface at an uphill location. In contrast to the findings of Gong et al. (1996), no significant spanwise variations of the streamwise mean velocity were observed, indicating that the aspect ratio of 12:1 is large enough to assume homogeneity in this direction. A POD analysis of the streamwise velocity fluctuations reveals dominant eigenfunctions with a characteristic spanwise scale of 1.5Λ, in agreement with the scale of the spanwise perturbation of the streamwise velocity at laminar conditions.POD analysis of the turbulent velocity field close to the uphill section of thewavy surface enables us to connect the eigenfunctions of the dominant modes (scale1.5Λ) to smaller scales that are represented by higher POD modes. Extrema of thecorresponding eigenfunctions are located in the vicinity of the maximum Reynoldsshear stress region. When comparing the results obtained at the Reynolds numbers3800 and 7300, we find indications that the relative fractional contribution of theeigenfunctions characterized by scale 1.5Λ increases with increasing Reynolds number.We further relate the dominant modes to an instability that is catalized by thewavyness of the bottom wall.To the knowledge of the author for the ♀rst time, structural information is obtainedfor the flow over heated waves. A constant heat flux condition is imposed at the wavy surface through a resistively heated foil. LCT is used to obtain spatiotemporal temperature fields above an uphill location of the wavy surface. Two conditions at different Reynolds numbers with (mixed convection) and without (forcedconvection) a buoyancy in uence are considered. For a Reynolds number of 3300, this effect is negligible. POD analysis reveals, for the two dominant modes, eigenfunctions with a characteristic spanwise scale of 1.5Λ, in agreement with the findings for the velocity field. The 1.5♥Λ scale is therefore obtained from both, temperatureand velocity fields. Together with the extrema of the eigenfunctions for higher PODmodes that were observed above the uphill side of the wavy surface, they play animportant role with respect to the uctuation energy of the velocity and temperature(to which the two dominant modes contribute more than 30%). They also provide a mechanism for the convective transport of heat between the wavy surface and the bulk fluid.