The often used Nusselt number is critically questioned with respect to its physical meaning. Based on a rigorous dimensional analysis, alternative assessment numbers are found that in a systematic ...way separately account for the quantitative and qualitative aspect of a heat transfer process. The qualitative aspect is related to the entropy generated in the temperature field of a real, irreversible heat transfer. The irreversibility can be quantified by referring it to the so-called entropic potential of the energy involved in the transfer process.
In order to teach heat transfer systematically and with a clear physical background, it is recommended that entropy should not be ignored as a fundamental quantity. Heat transfer processes are ...characterized by introducing the so-called “entropic potential” of the transferred energy, and an assessment number is based on this new quantity.
Energy transfer operations or processes are systematically analyzed with respect to the way they can be assessed. It turns out that the energy transfer should not only be characterized by the ...operation or process itself but that it should be seen in a wider context. This context is introduced as the entropic potential of the energy that is transferred. It takes into account the overall transfer from the energy in its initial and finite states, i.e., starting as pure exergy when it is a primary energy, for example, and ending as pure anergy when it has become part of the internal energy of the ambient. With this concept an energy devaluation number can be defined which has several properties with a reasonable physical background. Two examples of different complexity of the process assessed are given and discussed with respect to the physical meaning of the new energy devaluation number.
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.
The subject of this study concerns a method of manufacture of porous media for which the solid matrix is capable of experiencing deformation under the influence of the flow field. Conventionally, the ...matrix design parameters, elasticity and pore geometry, cannot be precisely controlled and the choice of parameters is limited to existing available media. Here a solution is provided that uses an indirect solid-free form fabrication process that combines 3D Printing with an infused Polydimethylsiloxane elastomer to provide a highly deformable matrix with controlled pore architecture. The manufacturing method is presented in detail. Local microscopy analysis of the manufactured matrix shows that the method has a high capability to accurately create pore structures at length scales as low as 0.75 mm. Experimental flow measurements further validate that the intended pore geometry is able to be reproduced in highly deformable matrices. The experimentally determined permeability of the deformable matrix is determined to agree with the intended within 95 %.
A comprehensive review of film-sensors shows that they are primarily operated in a passive mode, i.e. without being actively heated to an extent, whereby they create a heat transfer situation on ...their own. Only when these sensors are used for wall shear stress measurements, the detection of laminar/turbulent transition, or the measurement of certain flow velocities, they are operated in an active mode, i.e. heated by an electrical current (after an appropriate calibration). In our study we demonstrate how these R(T)-based sensors (temperature dependence of the electrical resistance R) can also be applied in an active mode for heat transfer measurements. These measurements can be made on cold, unheated bodies, provided certain requirements with respect to the flow field are fulfilled. Our new sensors are laminated nickel- and polyimide-foils manufactured with a special technology, which is also described in detail.
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.
•The reason for negative “loss” coefficients is revealed on a sound physical background.•The exchange of energy due to diffusion between adjacent branches of a junction is computed.•A method for the ...computation and visualization of dissipative and diffusive energy change is shown.•Examples in terms of detailed CFD-solutions of the flow through a junction are presented.
In this study, the phenomenon of negative “loss”-coefficients reported in various studies about turbulent branched flows through combining junctions is investigated systematically. It turns out, that the “loss” for one branch of a junction and its adjacent ducts only in parts is due to devaluation of mechanical energy, which would be a real loss, so that the term energy change is more appropriate. The other part of the energy change which is not due to a loss is due to a mutual energy transfer between the two partial flows. As a consequence, non-dimensional coefficients should be called energy change coefficients rather than head loss coefficients whenever branching of flows occurs. Furthermore, a method is introduced by which losses and the energy transfer are determined directly in the flow field. The field values allow a quantification and visualization of the local loss and work transfer, while their integral values can be used to quantify the individual contributions of losses and energy transfer within the energy change of a flow through a junction.
Entropy production in incompressible turbulent shear flows of Newtonian fluids is analysed systematically and incorporated into a CFD code. There are four different mechanisms of entropy production: ...dissipation in a mean and fluctuating velocity field and heat flux in a mean and fluctuating temperature field. Based on asymptotic considerations wall functions for the four production terms are developed. These wall functions are mandatory when high-Reynolds number turbulent models are used since peak values of entropy production occur in the immediate vicinity of a wall. As an example pipe flow with heat transfer is analysed and compared to results from a direct numerical simulation with special emphasis on the entropy production in the near wall region.
Entropy production in turbulent shear flows with heat transfer is calculated locally and afterwards integrated over the whole flow domain. This quantity can serve as a parameter to determine the ...efficiency of turbulent heat transfer processes. Based on the time averaged entropy balance equation, four different mechanisms of entropy production can be identified and cast into mathematical equations. They are: dissipation in the mean and the fluctuating velocity fields and heat flux due to the mean and the fluctuating temperature fields.
It turns out that no additional balance equation has to be solved, provided the turbulent dissipation rate is known in the flow field together with the mean velocity and temperature distribution. Since all four entropy production rates show very steep gradients close to the wall numerical solutions are far more effective with wall functions for the production terms. These wall functions are mandatory when high Reynolds number turbulent models are used, as for example the high Reynolds number
k–
ε model, like in our case. As an example, flow through a heated pipe with a twisted tape inserted is calculated in detail including the local entropy production rate. For this configuration experimental results show an increase in heat transfer as well as in pressure drop when the spiral slope of the twisted tape is increased. Therefore, no optimum of the spiral slope can be found in the experiments. An analysis based on entropy production, however, reveals that there is a distinct optimum for a certain slope of the twisted tape. Thus, entropy production can be used as an efficiency parameter with respect to minimizing the loss of available work in a process.
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