Some experimental investigations of the fine scale structure of turbulence

Abstract

In this thesis some properties of the fine scale structure have been investigated experimentally. The terminology “fine scale structure” means, in the author's opinion, small eddies which are different from energy?containing eddies. Recent experiments of Rao et al. as well as the results of the present investigation have shown that beyond a certain frequency the rate of occurrence of the high?frequency pulses is independent of filter frequency f_c. The above result, according to the author, is of great significance as it permits f_c to be considered as a demarcation frequency between large eddies and the small eddies, and shows markedly different characteristics from white noise. A closer examination of energy and dissipation spectra indicates that this frequency f_c is slightly higher than the frequency corresponding to maximum dissipation but nearly one?third of Kolmogoroff frequency. All the experiments on high?frequency pulses reported in this thesis were conducted with f_c as the mid?band filter frequency. The above paragraph is included here mainly to make the definition of the fine scale structure of turbulence clear as used in this thesis, since it was felt by the author that this terminology is used with slightly different meanings by different investigators in the past few years. The experiments were conducted in grid turbulence and in boundary layers with zero as well as favourable pressure gradients leading to relaminarization and the conclusions arrived at in this investigation are given below: (1) For all the three flows, the rate of occurrence of the high frequency pulses was found to scale with the zero?crossing length scale ? (= U/f_c where C is the rate of zero crossings of the u? signal and U is the free?stream velocity) and the value of U/f_c was found to be almost constant and nearly equal to 6.0 at all Reynolds numbers irrespective of the type of flow. (2) The values of the pulse rate (f_p) determined by using the technique described in Appendix were found to be nearly equal to half the rate of zero crossings of the unprocessed u? signal, in all the three flows. (3) The average width of the high?frequency pulses normalised with the Kolmogoroff length scale (?) exhibited a linear increase with Reynolds number in grid turbulence as well as in zero?pressure?gradient boundary layers. (4) In grid turbulence the mesh length scale (m) and the integral length scale L did not scale with f_p. Taylor’s microscale was found to be nearly equal to the zero?crossing length scale. (5) In both the boundary?layer flows f_p was found to be 3 to 5 times f_c. (6) In the flat?plate boundary layer, the high?frequency pulses in the wall region were in synchronisation with the negative part of the u? signal whereas towards the outer edge of the boundary layer this synchronisation was found with the positive part of the u? signal as well as with the negative part of the v? signal. In the middle region of the boundary layer no correlation was found between the pulses and the positive and negative parts of the signals. (7) In the case of favourable pressure gradient, the synchronisation between the u? signal and the pulses noticed in the case of the flat plate decreased and almost disappeared in the highly accelerated zone. (8) The value of f_p was found to be constant all across the boundary layer in the zero as well as in the pressure?gradient cases at each station except very near the wall where a reduction of f_p by nearly 20% was noticed. (9) During acceleration of the boundary layer the fluctuating quantities u?, v? and u?v? remained nearly constant along each streamline except very near the wall region, a result similar to the results already reported by Blackwelder & Kovasznay. (10) The turbulent energy balance in the accelerated boundary layer was found to change markedly from that in the zero?pressure?gradient case. The advection term which is generally negative in zero pressure gradient became positive during acceleration. The diffusion became negative as the flow moved in the accelerated zone. These gradients were such that the diffusion was always towards the wall. (11) The width of the high?frequency pulses as well as the length of the runs (distance between the adjacent zero crossings) exhibited a near log?normal distribution. The standard deviation to the mean for the pulses was 0.25 and for the runs 0.35 in both the flows. All the above results lead to the basic conclusion that the fine scale structures (vortex filaments) are convected by the fluid at the mean free?stream velocity with an average spacing of 6 times the zero?crossing length scale. The width of these vortex filaments is k? where ? is the Kolmogoroff length scale and k is a number linearly varying with Reynolds number. The zero?crossing length scale (?) seems to play a fundamental role in turbulence and does not seem to be directly connected with the Taylor microscale except in the case of isotropic turbulence (within the range of the Reynolds numbers so far covered).