Empirical Wall-Pressure Spectral Modeling for Zero and Adverse Pressure Gradient Flows

Wall-pressure spectra models for supersonic and hypersonic turbulent boundary layers

“…The Reynolds number effect on the overlap region of the spectrum is introduced through the ratio C 1 over C 3 R −0.57 T , which determines the size of the predicted overlap region. Goody's model gives good predictions when compared to both numerical and experimental data over a range of Reynolds and Mach numbers [40,8,9]. Figure 11 shows that Goody's model reproduces correctly the pressure spectrum from low up to high frequencies, including the overlap region across a range of Mach numbers.…”

“…Lee's [9] model was validated against experimental data from the literature for zero and adverse pressure gradient flows. Lee also assessed five recent models proposed by other authors and concluded that the models proposed by Goody [3] and Hu & Herr [8] are the most accurate ones for zero pressure gradient flows.…”

“…The shape of the predicted spectrum is reproduced correctly but the amplitude is under-estimated with the deviations being larger Goody's model was also investigated in conjunction with the compressibility corrections. Goody's model performs well in the low and medium frequency regions of the spectrum (Section 3.11), as well as overall in subsonic and supersonic zero-pressure gradient flows [3,40,8,9]. The modified Goody's model (COMPRA-G) takes the following form:…”

“…Past studies have focused on low speed flows with the compressibility effects neglected [1,2,3], or weak compressibility effects were taken into account [4,5,6,7]. More recent papers have introduced the effects of favourable and adverse pressure gradient [8,9] without considering high-speed compressible flows. Existing models may provide an accurate description of the pressure fluctuations for incompressible flows, however, fail to predict the spectra in supersonic and hypersonic TBL, as the results of this study also show.…”

Numerical study of 3-D finlets using Reynolds-averaged Navier–Stokes computational fluid dynamics for trailing edge noise reduction

“…A recently developed empirical WPS model by Lee 17 was used to predict the WPS at a point near the trailing edge, which is given as where βc=(θ/τ)(dp/dx), a=2.82△2[false(6.13△−0.75+dfalse)e][4.2(Π/△)+1], △=δ/δ*, Π=0.8false(βc+0.5false)3/4, RT=(δ/Ue)/(υ/uτ2), d=4.76false(1.4/△false)0.75[0.375e−1], and e=3.7+1.5βc. In addition, ω is the angular frequency, δ is the boundary layer thickness, δ* is the boundary layer displacement thickness, θ is the boundary layer momentum thickness, dp / dx i...…”