Generalized Expression of Chorochronic Periodicity in Turbomachinery Blade-Row Interaction

The unsteady flow which is generated when 2 turbomachinery blade-rows are in relative angular motion is periodic in time with a different period in the frame of reference associated with each blade-row, and is characterized by a pitchwise traveling wave chorochronic periodicity. This periodicity is studied for arbitrary angular velocities and pitch-ratio of the 2 blade-row and simple formulae for the corresponding interblade-phase angles are given

Wall effects on pressure fluctuations in turbulent channel flow

The purpose of the present paper is to study the influence of wall-echo on pressure fluctuations $p'$, and on statistical correlations containing $p'$, {\em viz} redistribution $\phi_{ij}$, pressure diffusion $d_{ij}^{(p)}$, and velocity/pressure-gradient $\Pi_{ij}$. We extend the usual analysis of turbulent correlations containing pressure fluctuations in wall-bounded \tsc{dns} computations [Kim J.: {\em J. Fluid Mech.} {\bf 205} (1989) 421--451], separating $p'$ not only into rapid $p_{(\mathrm{r})}'$ and slow $p_{(\mathrm{s})}'$ parts [Chou P.Y.: {\em Quart. Appl. Math.} {\bf 3} (1945) 38--54], but further into volume ($p'_{(\mathrm{r};\mathfrak{V})}$ and $p'_{(\mathrm{s};\mathfrak{V})}$) and surface (wall-echo; $p'_{(\mathrm{r};w)}$ and $p'_{(\mathrm{s};w)}$) terms. An algorithm, based on a Green's function approach, is developed to compute the above splittings for various correlations containing pressure fluctuations (redistribution, pressure diffusion, velocity/pressure-gradient), in fully developed turbulent plane channel flow. This exact analysis confirms previous results based on a method-of-images approximation [Manceau R., Wang M., Laurence D.: {\em J. Fluid Mech.} {\bf 438} (2001) 307--338] showing that, at the wall, $p'_{(\mathfrak{V})}$ and $p'_{(w)}$ are usually of the same sign and approximately equal. The above results are then used to study the contribution of each mechanism on the pressure correlations in low Reynolds-number plane channel flow, and to discuss standard second-moment-closure modelling practices

Improved prediction of turbomachinery flows using near-wall Reynolds stress model,

Abstract In this paper an assessment of the improvement in the prediction of complex turbomachinery ows using a new nearwall Reynolds-stress model is attempted. The turbulence closure used is a near-wall low-turbulence-Reynolds-number Reynolds-stress model, that is independent of the distancefrom-the-wall and of the normal-to-the-wall direction. The model takes into account the Coriolis redistribution e ect on the Reynolds-stresses. The 5 mean ow equations and the 7 turbulence model equations are solved using an implicit coupled O( x 3 ) upwind-biased solver. Results are compared with experimental data for 3 turbomachinery con gurations: the ntua high subsonic annular cascade, the nasa 37 rotor, and the rwth 1 1 2 stage turbine. A detailed analysis of the ow eld is given. It is seen that the new model that takes into account the Reynolds-stress anisotropy substantially improves the agreement with experimental data, particularily for ows with large separation, while being only 30% more expensive than the k ; " model (thanks to an efcient implicit implemen tation). It is believed that further work on advanced turbulence models will substantially enhance the predictive capability of complex turbulent o ws in turbomachinery