Water tank and numerical model studies of flow over steep smooth two-dimensional hills

Abstract

The present work investigates the role of different treatments of the lower boundary condition on the numerical prediction of flows over two-dimensional, smooth, steep hills. Four different law of the wall formulations are tested when a large recirculating region is formed on the lee side of the hill. Numerical implementation of the near-wall functions was made through a finite elements code. The standard κ-model was used to close the averaged Navier-Stokes equations. Results are validated through original data obtained in a water tank. Measurements resorted to laser Doppler anemometry. The experiment provide detailed data for the characterization of the reverse flow in the region between the separation and the reattachment points, with emphasis on the near wall region. The experimental wall shear stress distribution is compared with the results provided by the different laws of the wall showing good agreement. The numerical predictions are shown to vary markedly between different formulations.Keywords Hill · κ-model · Laser-Doppler anemometry · Law of the wall · Separation · Wall shear stress.

Water-Tank Studies of Separating Flow Over Rough Hills

“…For flow over a smooth surface, Loureiro et al (2007a) investigated the behaviour of four different near-wall formulations for separating flows: the classical logarithmic expression, and the expressions of Mellor (1966), Nakayama and Koyama (1984) and Silva Freire (1998, 2002). The last three formulations have been specially advanced to deal with adverse pressure gradient flows: they reduce to the relevant wall laws at the appropriate limiting cases.…”

The numerical modeling of thermal turbulent wall flows with the classical κ - ε model

“…In order to extend this methodology to other geometries, two new test cases were proposed, based on studies of the asymmetric plane diffuser of Buice and Eaton (1995) and the turbulent flow over a 2D hill, studied by Loureiro et al (2007). The boundary conditions used to execute these simulations are illustrated in Figs.…”

“…(6) and (7). In the experimental works of Buice and Eaton (1995) and Loureiro et al (2007), the thermal field is not considered. They studied only the dynamical field.…”

“…These results were published in the master's dissertation of Gontijo (2009), where more details can be found. Figure (8) illustrates, respectively, the temperature profiles taken after the heated walls for the asymmetric plane diffuser of Buice and Eaton (1995) and the 2D hill of Loureiro et al (2007) test cases. The expected profile line indicates a temperature profile taken when an equivalent constant temperature is imposed, more details are given in the master's dissertation of Gontijo (2009).…”

“…In order to validate and quantify the consistence of the present research code, the numerical results are compared with an extensive experimental database, including several flows over distinct geometries, based on the works of Ng (1981), Vogel and Eaton (1985), Taylor et al (1990), Liou et al (1992), Buice and Eaton (1995) and Loureiro et al(2007 …”