The present study investigates the response of turbulence in a non-equilibrium flows such as transient periodic channel flows and spatially developing boundary layers subjected to pressure gradients. Such a fundamental study is important to understand noise generation in complex wall-bounded turbulent flows. First, to understand the flow dynamics in transient accelerating flows, direct numerical simulations (DNS) of periodic channel flows responding to an impulse acceleration are carried out. The turbulent flow undergoes reverse transition toward a quasi-laminar state, followed by a retransition phase to the new equilibrium state. To reduced simulation cost, the minimal-span methodology is applied and evaluated for simulations of transient flows.Next, to study non-equilibrium boundary layer flows in the presence of convex wall curvature, DNS simulations over an airfoil (suction side) and a flat plate are compared. Both cases are characterized by matching adverse pressure gradient (APG) along the streamwise direction. For the airfoil boundary layer, existing DNS data obtained by Wu et al. (2019) of flow around a controlled-diffusion (CD) airfoil is used. For the flat-plate boundary layer, a DNS simulation is carried out, with prescribed pressure gradient distribution that matches that of the airfoil case. Comparison between the two cases shows how wall curvature affects turbulence in an APG boundary layer. Overall, similar boundary layer development in both cases indicates that a flat-plate boundary layer can serve as a low-cost surrogate of an airfoil boundary layer.Lastly, various existing analytical models are evaluated on their predictions of wall pressure fluctuations, which are essential for fan noise prediction. Limitations of the existing models are evaluated; new parameters that do not involve the ill-defined wall friction in a boundary layer under strong APG are proposed. The primary role of the mean velocity logarithmic layer in affecting the overlap range of the wall pressure spectrum is also demonstrated. A new wall pressure spectrum model is proposed and tested in a wide range of boundary layer flow scenarios. The new wall pressure spectrum model is the first generalized model designed for boundary layer flows with a wide range of pressure gradients and Reynolds numbers.
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