Numerical investigation of the wall pressure fluctuations in channel flows

Abstract

Numerically simulated turbulent pressure fields in a plane channel and an annulus with a 5 : 1 ratio of radii are used to evaluate the spatial structure of pressure fluctuations at the walls. Wall-pressure correlation functions in the axial and azimuthal directions, spectra, correlation functions and angular correlations of the forces acting on the cylinders of the annulus are considered. It is found that no correlation exists between the pressure values at two points which are diametrically opposed to each other in the annulus. The spectrum of the forces starts with a zero value for small wave numbers, reaches its maximum at about unity wave number and then decreases, as a -7/3rd power of the wave number.

Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli

“…Although there are still large statistical fluctuations we see that the correlation length of the axial velocity fluctuation is about five times that of the other velocity fluctuations. Corresponding results have been found for the annulus [19,21].…”

“…They showed that some of the empirical "constants" used in simple turbulence models are dependent of the cross-stream position. In [21] it has been shown that the present method can be used to calculate wall-pressure correlation functions and the resultant forces acting on the inner cylinder of the annulus.…”

“…Since then, some further integrating has been performed for cases K3, K4, and 23 using the revised method described here. Moreover, in addition to averaging over planes parallel to walls, the results found for some specific times [21] have been averaged in order to reduce the statistical fluctuations. These results are denoted by K3+, K4+, 23+.…”

“…The purpose of the method is to obtain detailed turbulent velocity and pressure fields in space and time. These may be used, for example, to investigate turbulence models [20] or wall pressure fluctuations [21]. The present method is an improved form of that described in [19].…”

Numerical study of the return of axisymmetric turbulence to isotropy

“…However, even for homogeneous turbulence, the validity of this model has been questioned (Schumann 1975) and the magnitude of the empirical constant c in it is very uncertain. Values between 0.5 (Daly 1974) and 8 (Lumley & Khajeh-Nouri 1974) have been used even in the more recent literature, mainly because of a gap in experimental data.…”