Preliminary Numerical Investigations of Entropy Generation in Electric Machines Based on a Canonical Configuration

Abstract

Abstract:The present paper analyzes numerically the entropy generation induced by forced convection in a canonical configuration. The configuration itself includes two well known fluid dynamic problems: (1) an external flow (flow around a cylinder, Kármán flow); and (2) an internal flow (flow between two concentric rotating cylinders, Couette flow). In many daily engineering issues (e.g., cooling of electric machines), a combination of these problems occurs and has to be investigated. Using the canonical configuration, the fields of entropy generation are analyzed in this work for a constant wall heat flux but varying two key parameters (Reynolds numbers Re ∞ and Re 0 ). The entropy generation due to conduction shows an absolute minimum around Re 0 = 10, 000. The same minima can be found by a detailed analysis of the temperature profile. Thus, entropy generation seems to be a suitable indicator for optimizing heat exchange processes and delivers a large amount of information concerning fluid and heat transport.

Application of Entropy Generation to Improve Heat Transfer of Heat Sinks in Electric Machines

“…Due to a high electrical current and a low volume flow in this range, the maximum temperature as well as entropy generation due to conduction occurs at approximately 3000 rpm. This confirms the correlation between entropy generation due to conductioṅ S C and the component temperature T as already investigated in [2]. Increasing the rotational speed above 10,000 rpm causes entropy generation due to dissipation to become the dominating factor; at this point, total entropy generation is dominated by flow convection.…”

“…Compared to classical indicators such as T or h, entropy generation quantifies regions of dominating processes between near-wall regions (locally) or within the main flow (globally), as well as dominating dissipative or conductive effects within the flow field. This has already been demonstrated in [2]. It also lumps the huge data quantity contained in u = (u x , u y , u z ) T as well as temperature T into one single, scalar value.…”

“…Thus, Equation (1) includes the temperature and velocity gradients, respectively, and represents the direct entropy generation in the mean and fluctuating flow field. A more detailed explanation of each term was given by Kock [28] and can also be found in Eger et al [2]. The irreversibility ratio φ was first introduced by Bejan [29] and is defined as:…”

“…As discussed in previous publications [2,3], different transport phenomena influence heat transfer. They can, in principle, be quantified by considering classical indicators such as the local wall temperature T W or the wall heat transfer coefficient h for each component.…”

“…Regions with a high potential for optimization cannot be directly obtained in this manner. Thus, physically-based indicators must first be identified, building on top of our previous studies [4,5].…”