On surface pressure fluctuations beneath turbulent flow round bluff bodies

Abstract

Rapid distortion theory is used to calculate surface pressure fluctuations beneath a turbulent flow incident on a two-dimensional bluff body. These pressures depend on the ratio, L_∞/a, of integral scale to body dimension: we give results in the two asymptotic limits L_∞/a [Gt ] 1 and L_∞/a [Lt ] 1. The large-scale limit is described by ‘quasi-steady’ theory – which we review here; and for the small-scale limit we introduce a ‘quasi-homogeneous’, or ‘slowly-varying’, approximation. The theory is compared with field and laboratory measurements and it is found that most measurements lie between the theoretical asymptotes, following the predicted trends.

A number of general conclusions have been obtained for which there are new physical explanations – and which laboratory and field experiments appear to confirm.

1. The r.m.s. pressure fluctuations, p′, caused by upwind turbulence, decrease in strength with distance from the stagnation point when L_∞/a [Lt ] 1; but p′ increases with distance from the stagnation point when L_∞/a [Gt ] 1.

2. For a given dimension of an obstacle, a, transverse to the flow field, p′ increases as the dimension, b, parallel to the flow field increases. At the stagnation point of an elliptical cylinder, when L_∞/a [Lt ] 1, \[ p^{\prime} = {\textstyle\frac{1}{2}}\rho u^{\prime}_{\infty} U_{\infty}(1+b/a)(L_{\infty}/a)^{\frac{1}{2}} \] where u′_∞, U_∞ are the upwind r.m.s. turbulent and mean velocities and ρ is the density.

3. The fluctuating pressure has a cross-correlation length in the flow direction a factor of a/L_∞ higher when L_∞/a [Lt ] 1 than when L_∞/a [Gt ] 1. In the axial direction the correlation length is again greater (though this time of the same order in L_∞/a) when the incident turbulence is of small scale than when it is of large scale.