Second-Law Analysis: A Powerful Tool for Analyzing Computational Fluid Dynamics (CFD) Results

Second-law analysis (SLA) is an important concept in thermodynamics, which basically assesses energy by its value in terms of its convertibility from one form to another. Highly-valued forms of energy in this context are called exergy, defined as those energies from which the maximum theoretical work is obtainable when the energy is interacting with the environment to equilibrium (see Moran et al. [1], for example). The counterpart of exergy, also called available work, is anergy, so that with this concept energy can generally be regarded as the sum of exergy and anergy. As a consequence of the second law of thermodynamics, exergy can be lost but cannot be created. Therefore, in a reversible process, exergy is preserved, whereas irreversibility (like losses in a flow field) leads to a loss of exergy (in favor of the corresponding increasing anergy). Losses in flow and heat transfer fields can, thus, be determined by their impact on the exergy, i.e., by determining the exergy losses. These losses of exergy are thermodynamically linked to the generation of entropy by the so-called Gouy Stodola theorem. It states that the lost exergy corresponds to the product of entropy generation and the environmental temperature (see, again, Moran et al. [1]). From a thermodynamic point of view, the quality of a flow or heat transfer process can be assessed by the entropy generation rate in this process (see Herwig [2]). However, entropy almost never appears in the textbooks of fluid dynamics and heat transfer (see, e.g., Batchelor, et al. [3] and Incropera, et al. [4]). This concept is widely ignored perhaps because the irreversibility effect is often fundamentally important in these two disciplines. After Bejan [5,6] laid the foundation with respect to analyzing and optimizing thermal systems with the SLA approach, the SLA of flow and heat transfer problems received more and more attention. Applying the SLA in computational fluid dynamics (CFD), Kock and Herwig [7] extended this concept to an in-depth analysis of turbulent flows and identified four different mechanisms of entropy generation: dissipation in a mean and fluctuating velocity field and heat flux in a mean and fluctuating temperature field. They also suggested how to calculate the entropy generation rates with the Reynolds Averaged Navier–Stokes (RANS) results. Herwig [2] stated that, with the help of the SLA, one may answer four important questions regarding a momentum and/or heat transfer process: