Secondary Flows in Asymmetrical Contractions

Abstract

Due to the global energy crisis, there is a growing need to make industrial processes more efficient and clean. One such method is to use effective and renewable working fluids in power and refrigeration cycles. Research in this field during the past decade has placed supercritical CO2 (SCO2) in the forefront due to its non-ideal properties and abundance in nature but, to fully understand their heat transfer properties, insight into boundary layer flow and hydrodynamic instabilities are crucial. Experimental setups such as closed loop wind tunnel contraction facilities are needed which provide a laminar steady flow to take boundary layer measurements. However, using a contraction causes various problems such as formation of secondary flows like boundary layer separation, Gortler vortices, cross-flows and non-uniformity’s. In this study a novel 1D contraction shape with curvature on only one side is pro- posed. This will completely eliminate the risk of Gortler vortices on the bottom plate and make it a suitable candidate for boundary layer experiments. Nevertheless, the risk of the other secondary flows and Gortler vortices on the top wall disturbing this laminar flow remains. Hence, the present research aims to optimise this 1D contraction to reduce the risk of such secondary flows and analyse the growth of Gortler vortices on the top wall using numerical simulations.

Steady state laminar simulations were performed to optimise the design of the 1D wind tunnel contraction. Optimum contraction and settling chamber lengths were found by identifying the risk of flow separation and boundary condition effects respectively. For the optimisation of the contraction wall shape, a family of transformed fifth order polynomial curves with varying inflection point distances were selected. To identify the curve with least risk of boundary layer separation and lowest flow non-uniformity, a multi- objective optimisation procedure was implemented. The procedure found that a curve with inflection point of 101mm downstream of contraction inlet gives the best performance.

To analyse the effect of Gortler vortices on outlet uniformity, unsteady laminar simulations were performed on the contraction by forcing sinusoidal perturbations of different wavenumbers. This study found that perturbations form symmetrical steady steam-wise Gortler vortices in the contraction. The most unstable wavenumber was found to be 𝜆=83.33 𝑚-1 which formed secondary vortices of high vorticity. However it was also seen that for all wavenumbers, the vortices lose energy as they exit the contraction and do not affect the bottom boundary layer. Further, the effects of a side wall on the formation of Gortler vortices were also investigated. The results showed that the Gortler vortex closest to the wall is absorbed into high vorticity corner vortices, while those close to the centreline develop into steady Gortler vortices. No effect on the centreline velocity profile was seen due to the vortices making the 1D contraction suitable for boundary layer experiments. Finally, it was also seen that the 1D contraction shape produces asymmetrical Gortler vortices due to alternative perturbation methods such as random inlet perturbations.