Study of Momentum and Thermal Wakes Due to Elliptic Cylinders of Various Axes Ratios Using the Immersed Boundary Method

This chapter presents an application of the immersed boundary method (IBM) for simulating momentum and thermal wakes generated by elliptic cylinders. We consider elliptic cylinders of five different axis ratios (AR = 0.1, 0.4, 0.6, 0.8, 1.0) within a Reynolds number range where the flow was reported to be two-dimensional. We employ a direct forcing immersed boundary method to simulate wakes behind these cylinders. We first study the momentum wakes in terms of computing the critical Reynolds number for laminar separation and vortex shedding. Then, in the shedding regime, the wake is analyzed for large- and small-scale structures in its near and far field. We show that the low-frequency structures exist even in the near wake of an elliptic cylinder while such structures are observed only in the far wake of a circular cylinder. We then extend the momentum forcing method to the energy equation through thermal forcing and show that IBM predicts heat transfer characteristics accurately. We also note an unusual mean temperature behavior along the centerline of the wake and provide probable reasons for such a behavior. Our results prove that the IBM can be effectively used to simulate wakes of elliptic cylinders.