Entropy generation in a plane turbulent oscillating jet J. Cervantes * , F. Solorio Department of Thermal Engineering, School of Engineering, National University of Mexico, Mexico, DF 04510, Mexico Received 5 July 2001; received in revised form 8 January 2002 Abstract The entropy generation in a plane turbulent jet is revisited. This flow is characterized by quasi-periodic lateral oscillations, documented in the literature, due to the instability of the flow. Based on the laws of Thermodynamics, an analysis of the entropy generation has been presented by Bejan [Entropy Generation Minimization. The Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes, Wiley, New York, 1996, p. 61]. In this paper, a term has been added that takes into account the experimentally observed oscillations. The results are compared for the cases with oscillations and without oscillations. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Plane turbulent jets; Entropy generation; Flow oscillations 1. Introduction Turbulent flows are characterized by fluctuations that are generally considered as random and are there- fore described by means of their statistical properties. This random nature of turbulent flows is apparent for the small scales of the flow, but it may be not for the large scales, as it has been suggested in the literature during the last two or three decades. This fact is espe- cially remarkable in the case of free turbulent shear flows – jets, wakes and mixing layers – where it has been detected a coherent, and to a certain extent, determin- istic behavior [1,2]. In many cases, oscillations with clearly distinctive frequencies have been detected and measured [3,4]. No matter what the origin of the oscillations could be, the evolution of the flow is always accompanied by thermodynamic entropy generation. This generation intuitively increases with the entrainment at the flow boundaries, as a result of the mixing and lateral exten- sion of the flow with the surrounding, quiescent fluid. Bejan [5] has recently developed the theoretical basis to quantify the entropy generation in a variety of physical situations of interest in engineering, as it is the case of a plane turbulent jet. In this paper, a modified version of the model de- veloped by Bejan for a plane turbulent jet is presented. It is included now the energy associated to the observed lateral oscillations of the flow. 2. Lateral oscillations of plane turbulent jets There are many instances in Fluid Mechanics, where repetitive phenomena, almost periodic, are present with clearly distinctive frequencies [6]. This is the case of the lateral oscillations in a plane turbulent jet, whose char- acteristic frequencies, when scaled with the appropriate local variables, compose a unique dimensionless pa- rameter. The origin of these oscillations is the instability of the flow, either at the first stages of the viscous regime, or rather, once the turbulent regime has been established, when the flow penetrates and drags the surrounding fluid, experiencing a kind of buckling or lateral oscilla- tion. In the first case – the laminar flow, where the oscil- lations are easily detectable and quantifiable by means of various experimental techniques – the conventional analysis of the problem is the one derived from the theory of the linear stability of the flow. The existence of a defined disturbance is postulated, superimposed to a known laminar flow, and the behavior of the distur- bance, in time and space, is analyzed. If it grows the flow International Journal of Heat and Mass Transfer 45 (2002) 3125–3129 www.elsevier.com/locate/ijhmt * Corresponding author. Fax: +52-5622-8106. E-mail address: jgonzalo@servidor.unam.mx (J. Cervantes). 0017-9310/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0017-9310(02)00039-X