On the use of a low-Reynolds extension to the Chen±Kim k ±e model to predict thermal exchanges in the case of an impinging plasma jet Rodolphe Bolot * , Michel Imbert 1 , Christian Coddet 2 LERMPS ± UTBM, 90010 Belfort Cedex, France Received 26 September 1998; received in revised form 15 May 2000 Abstract The present paper is devoted to the modeling of an impinging argon/hydrogen plasma jet under atmospheric plasma spraying conditions. A two-layer extension to the Chen±Kim k±e turbulence model was implemented in the Phoenics code, allowing the prediction of temperature and velocity ®elds in the turbulent jet and the description of the viscous sublayer at the surface of the front body. The predictions of thermal exchanges are compared to results obtained with a heuristic formula deduced from experiments and taken from the literature. A comparison is also made with results obtained with some other models and the results indicate that the present proposed model is by far the most accu- rate. Ó 2001 Elsevier Science Ltd. All rights reserved. 1. Introduction Although the standard k±e model was originally intended to the study of ¯ows over ¯at plates, it is often used as a ®rst approximation or for simplicity in many ¯ow situations and particularly for the study of plasma jets [1±11]. Nevertheless, it is known to give poor pre- dictions in a certain number of cases and especially in the case of round jets for which a quite large overesti- mation of the jet expansion is predicted. For this reason, modi®cations based on the work of Rodi are sometimes used in order to obtain a better description of round jets [1±3,10]. Nevertheless, the use of those modi®cations is only possible for free jet studies and not impinging ones, so that the standard k±e model is often used without any modi®cation in the case of impinging jets [11±14]. Since it is not valid in laminar boundary layers, this model also uses wall functions in order to describe friction and thermal exchanges with solid bodies. Wall functions are extensively used mainly for the purpose of computational economy. Nevertheless, there are many ¯ow situations in which this approach should not be used, particularly when the boundary layer includes signi®cant variations of thermodynamic properties and transport coecients, which is especially true in the case of plasma jets. The most used wall function is certainly the logarithmic one [1,11]. Meanwhile, one has to keep in the range of validity of the law and not apply it within the viscous sublayer. Consequently, grid re®nement should sometimes be avoided. An alternative approach is the use of low-Reynolds extensions to turbulence models with an adequate grid re®nement in the wall region. Numerous extensions to the standard k±e model have been proposed in the literature. They dier from the standard model in that local modi®cations of the constants of the turbulence model are used and that extra source terms are sometimes added to the transport equations of turbulence quantities. Several of those models were described and tested in the case of a simple ¯ow over a ¯at plate by Patel [15]. Even if those models give good predictions in a range of cases, there are still ¯ow situations in which their use is not recommended. For example, the use of low-Reynolds extensions to International Journal of Heat and Mass Transfer 44 (2001) 1095±1106 www.elsevier.com/locate/ijhmt * Corresponding author. Tel.: +33-3-84-58-31-60; fax: +33-3- 84-58-32-86. E-mail addresses: rodolphe.bolot@utbm.fr (R. Bolot), mi- chel.imbert@utbm.fr (M. Imbert), christian.coddet@utbm.fr (C. Coddet). 1 Tel. +33-3-84-58-31-86; fax: +33-3-84-58-32-86. 2 Tel.: +33-3-84-58-30-23; fax: +33-3-84-58-32-86. 0017-9310/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 7 - 9 3 1 0 ( 0 0 ) 0 0 1 8 5 - X