Large eddy simulations of the flow field and temperature separation in the Ranque–Hilsch vortex tube Tanvir Farouk, Bakhtier Farouk * Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, PA 19104, United States Received 22 October 2006; received in revised form 5 March 2007 Available online 27 June 2007 Abstract A computational fluid dynamic model is used to predict the flow fields and the associated temperature separation within a Ranque– Hilsch vortex tube. The large eddy simulation (LES) technique was employed for predicting the flow and temperature fields in the vortex tube. A vortex tube with a circumferential inlet stream and an axial (cold) outlet stream and a circumferential (hot) outlet stream was considered. The temporal evolutions of the axial, radial and azimuthal components of the velocity along with the temperature, pressure and density fields within the vortex tube are simulated. Performance curves (temperature separation versus cold outlet mass fraction) were obtained for a specific vortex tube with a given inlet mass flow rate. Simulations were carried out for varying amounts of cold outlet mass flow rates. Predictions from the present large eddy simulations compare favorably with available experimental measurements. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Ranque–Hilsch vortex tube; Modeling; Large eddy simulations; Temperature separation 1. Introduction The vortex tube is a simple device with no moving parts that is capable of dividing a high pressure flow into two rel- atively lower pressure flows with temperatures higher and lower than that of the incoming flow. The device consists of a simple circular tube, with one or more azimuthal noz- zles for flow inlet and two outlets for flow exits. High pres- sure air enters the tube azimuthally at one end and produces a strong vortex flow in the tube. The gas is sepa- rated into two streams having different temperatures, one flowing along the outer wall and the other along the axis of the tube. The gas streams leaving through the exits located along the outer wall and along the axis are at higher and lower temperatures, respectively, than the inlet gas temperature. This effect is referred to as the ‘‘tempera- ture separation” and was first observed by Ranque in 1931 when he was studying processes in a dust separation cyclone [1]. Intense experimental and numerical studies of the Ranque–Hilsch vortex tubes began since then and con- tinue even today [2–9]. Despite the simplicity of its geome- try, the energy separation phenomenon is quite intriguing. Various theories have been proposed in the literature to explain the ‘‘temperature separation” effect since the initial observations by Ranque [1]. In his pioneering work on the vortex tube, Hilsch [10] suggested that angular velocity gra- dients in the radial direction give rise to frictional coupling between different layers of the rotating flow resulting in the migration of energy via shear work from the inner layers to the outer layers. Other investigators have attributed the energy separation to work transfer via compression and expansion. Several variations of this theory are described in the literature, differing according to the mechanism that drives the fluid motion. Harnett and Eckert [11] invoked turbulent eddies, Ahlborn and Gordon [12] described an embedded secondary circulation and Stephan et al. [13] proposed the formation of Go ¨rtler vortices on the inside wall of the vortex tube that drive the fluid motion. All these theories treat individual particles as small refrigeration systems, each undergoing thermodynamic cycles that are 0017-9310/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2007.03.048 * Corresponding author. E-mail address: bfarouk@coe.drexel.edu (B. Farouk). www.elsevier.com/locate/ijhmt International Journal of Heat and Mass Transfer 50 (2007) 4724–4735