Assuming that CFD solutions will be more and more used to characterize losses in terms of drag for external flows and head loss for internal flows, we suggest to replace single-valued data, like the drag force or a pressure drop, by field information about the losses. These information are gained when the entropy generation in the flow field is analyzed, an approach that often is called second law analysis (SLA), referring to the second law of thermodynamics. We show that this SLA approach is straight-forward, systematic and helpful when it comes to the physical interpretation of the losses in a flow field. Various examples are given, including external and internal flows, two phase flow, compressible flow and unsteady flow. Finally, we show that an energy transfer within a certain process can be put into a broader perspective by introducing the entropic potential of an energy.

Losses in a flow field due to single conduit components often are characterized by experimentally determined head loss coefficients K. These coefficients are defined and determined with the pressure as the critical quantity. A thermodynamic definition, given here as an alternative, is closer to the physics of flow losses, however. This definition is based upon the dissipation of mechanical energy as main quantity. With the second law of thermodynamics this dissipation can be linked to the local entropy generation in the flow field. For various conduit components K values are determined and physically interpreted by determining the entropy generation in the component as well as upstream and downstream of it. It turns out that most of the losses occur downstream of the components what carefully has to be taken into account when several components are combined in a flow network.

Diffusers and nozzles within a flow system are optimized with respect to their wall shapes for a given change in cross sections. The optimization target is a low value of the head loss coefficient K, which can be linked to the overall entropy generation due to the conduit component. First, a polynomial shape of the wall with two degrees of freedom is assumed. As a second approach six equally spaced diameters in a diffuser are determined by a genetic algorithm such that the entropy generation and thus the head loss is minimized. It turns out that a visualization of cross section averaged entropy generation rates along the flow path should be used to identify sources of high entropy generation before and during the optimization. Thus it will be possible to decide whether a given parametric representation of a component’s shape only leads to a redistribution of losses or (in the most-favored case) to minimal values for K.

In the present study, we introduce a method which we call the glass box optimization (GBO) method as a strategy how to reduce flow losses whenever numerical data based on computational fluid dynamics (CFD)-results are available. Based on local values of the velocity and entropy generation fields, a systematic analysis of the loss mechanisms involved is used in order to develop control mechanisms for the reduction of losses due to a conduit component. Furthermore, it is shown how the losses are distributed between a component itself and the adjacent flow field. Since often a large amount of the losses occurs outside of the actual component, it is discussed under which circumstances an optimized component leads to improved efficiency of an entire fluid flow network. The method is exemplified for turbulent flow through a 90 deg bend.

Losses in a flow through conduit components of a pipe system can be accounted for by head loss coefficients K. They can either be determined experimentally or from numerical solutions of the flow field. The physical interpretation is straight forward when these losses are related to the entropy generation in the flow field. This can be done based on the numerical solutions by the second law analysis (SLA) successfully applied for steady flows in the past. This analysis here is extended to unsteady laminar flow, exemplified by a periodic pulsating mass flow rate with the pulsation amplitude and the frequency as crucial parameters. First the numerical model is validated by comparing it to results for unsteady laminar pipe flow with analytical solutions for this case. Then K-values are determined for the benchmark case of a 90 deg bend with a square cross section which is well-documented for the steady case already. It turns out that time averaged values of K may significantly deviate from the corresponding steady values. The K-values determined for steady flow are a good approximation for the time-averaged values in the unsteady case only for small frequencies and small amplitudes.