The Effects of Inflow Uncertainties on the Characteristics of Developing Turbulent Flow in Rectangular Pipe and Asymmetric Diffuser

Abstract

In the current paper nondeterministic computational fluid dynamics (CFD) computations of three-dimensional (3D), developing, and statistically steady turbulent flow through an asymmetric diffuser with moderate adverse pressure gradient are presented. The inflow condition is assumed to be uncertain. The inlet streamwise velocity is supposed to be a stochastic process and described by the Karhunen–Loève (KL) expansion. In addition, the inlet turbulence intensity and turbulent length scale are assumed to be uncertain. The nonintrusive polynomial chaos (NIPC) expansion is used to propagate the inflow uncertainties in the flow field. The developed code is verified using a Monte Carlo (MC) simulation with 1000 Latin Hypercube samples on a planar asymmetric diffuser. A very good agreement is observed between the results of MC and polynomial chaos expansion methods. The verified uncertainty quantification method is then applied to stochastic developing turbulent flow through a 3D asymmetric diffuser. It was observed that the eigenvalues of covariance kernel rapidly decay due to the large correlation lengths and thus a few terms in the truncated KL expansion are used to describe the stochastic inlet velocity. For the KL expansion, the mean and the standard deviation are set to those measured experimentally. The uncertain inlet condition has a significant influence on the numerical results of velocity and turbulence fields specially in the developing region before the shear layers meet. It is concluded that one of the reasons for discrepancies between experimental and deterministic CFD results is the uncertainty in inflow condition. A sensitivity analysis is also performed using the Sobol’ indices and contribution of each uncertain parameter on outputs variance is presented.