Investigation of Large Scale Flow Structures in an Offset Attaching Jet Using Spectral Linear Stochastic Estimation

Abstract

The large scale ∞ow structures in an ofiset attaching jet with an ofiset height equal to the jet height and Re = 44 000 were studied using simultaneous measurements of the ∞uctuating wall pressure along the streamwise direction and the ∞uctuating velocity fleld estimated using a spectral linear stochastic estimation (LSE) technique. Box fllters were used to examine the ∞ow structures with difierent characteristic frequencies. The results showed evidence of difierent dominant ∞ow structures in the ∞ow. The instantaneous distributions of the estimated velocities and vorticity were examined for periods when difierent modes were prominent and showed difierences in the behavior of the ∞ow structures in the ∞ow. Ofiset jets with modest ofiset distances are used in a range of difierent cooling applications. The ofiset jets produce a local maximum in the heat transfer where they attached to the wall. The magnitude of the heat transfer at this point decreases as the ofiset distance of the jet (Hs) increases even for jets with Hs=Hj • 1 despite an increase in the turbulence level in the ∞ow near this point. This suggest there may be a change in the way the ∞ow structures interact with the wall as Hs changes even for Hs=Hj • 1. Recently, Gao and Ewing 4 studied the ∞ow structures in ofiset attaching jet with Hs=Hj • 1 using the correlation between the ∞uctuating wall pressure and the ∞uctuating velocities, and found features near the reattachment point similar to other reattaching shear layer ∞ows such as ∞ow over a backward facing step or ∞ow separated from a blufi body. 2,9,10 In particular, there were shedding mode motions with a frequency of fXr=Uj … 0:5 to 1 and a low frequency ∞apping instability with fXr=Uj < 0:2. Here, Xr is the mean reattachment length. The structures formed in the inner shear layer then developed downstream and appeared to merge with the structures in the outer shear layer of the jet. The outer shear layer structures grew in size while the jet was attaching to the wall and eventually became similar to the structures in a planar wall jet with a frequency fHj=Uj < 0:1. Gao and Ewing 5 studied the coherence of the ∞uctuating pressure and velocity in an ofiset jet with Hs=Hj = 1 and the propagation velocity of the structures in this ∞ow by considering the change in the phase of the cross-spectra of the ∞uctuating pressure along the wall and the cross-spectra of the ∞uctuating wall pressure and ∞uctuating velocity throughout the ∞ow. They found that the propagation speed of these motions varied with frequency. In particular, they found evidence of two modes in the inner shear layer, 0:6 . fXr=Uj . 0:9 and 0:9 . fXr=Uj . 1:4, that had difierent propagation velocities. They also found evidence that motions with 0:3 . fXr=Uj . 0:6 propagated downstream slower than the higher frequency motions. These slower motions appear to be associated with the structures that eventually form the wall jet structures travelled slower than the inner shear layer structures. The propagation velocity for the motions with fXr=Uj < 0:3 varied linearly with frequency and was consistent with a ∞apping motion. The objective of this investigation was to examine if the dynamics and interactions of difierent structures can be captured in the instantaneous ∞uctuating velocities estimated using a spectral linear stochastic estimation technique. 3 In this approach, the instantaneous velocity fleld is estimated from simultaneous time resolved measurements of the ∞uctuating wall pressure using coe‐cients that depend on the pressure velocity cross-spectra. Tinney et al. 12 and Hall and Ewing 6 found that the spectral LSE produced better estimations