&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Many mechanical engineering systems are exploring designs and analysis of advanced 3D printable heat exchangers with complex internal features. However, inclusion of any feature that is required to promote heat transfer, also increases head loss significantly. We have developed a mathematical model that would allow a user to optimize the variables of a piping system in a heat exchanger. The design is based on a solar thermal heater that uses a heat exchanger with one inlet pipe to bring cool fluid in and then distributes it among multiple out-going pipes. Inlet and outlet pipes possess conical features to create diode type flow characteristics that promote high flow rate in one direction but less flow rate in the opposite direction. To simplify our model, we will consider all flow to be of a non-compressible liquid flowing in the horizontal direction (no Δ Z). We used Python and Visual Basic to create programs that allow a user to optimize a flow through the described heat exchanger system. The word optimize, in terms of heat exchangers, can have several meanings. In the realm of heat exchangers, there are clear trade-offs. More turbulence in our system provides a more effective heat transfer, however, the trade-off is the mechanism that increases the turbulence causes a decrease in head pressure. &nbsp;Our model gives the user control over the geometric features and dimensions to encompass a wide range of possibilities. For example, one can change the base and top diameters of the conic features, spacing between two features, number of features, length of the pipe, impact of joints, and type of internal surface of the heat exchanger pipes.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; We have employed analytical minor head loss models from the prior literature for the internal conical features. The head loss between two conical features are calculated as major head losses. However, spacing between two conical features may produce an additional minor head loss which is referred to as shock losses. Shock losses are a minor loss associated with a flow through a sudden expansion. If the distance between two conical features is &gt; 10 times the hydraulic diameter of the expansion (base of conical features), the shock losses are zero. Within that range, powerful eddies that form along the outer edge of the expansion flow do not have time to lose their energy before they interfere with the developed flow. This interference is what creates the shock losses. There is a well -developed relationship for the shock losses in the laminar regime. Additionally, prior experimental values for shock losses were developed assuming a fully developed flow in a pipe of uniform size flush with a sudden expansion also of uniform size. Our heat exchanger piping system with internal conical features differ from prior models. First, our entrance is not of uniform size, it is a gradually contracting conical section. Second, our sudden expansion is not flush with the wall of the expansion diameter, there will be some distance d from the expansion wall that is equal to the height of the conical section. Finally, there is no mathematical model for the turbulent regime.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; We will present two solutions to identify challenges in our experimental model. The first solution allows for the conic features to be placed at a sufficient distance where the shock losses are insignificant (&gt;10X Dh). The second model, theoretically, will account for the shock losses by adding a “Fudge Factor”. This “Fudge Factor” will be added as an additional minor loss per conic section. The fudge factor is added as a ratio (0-1) between the actual distance that separates the conical features and the distance10X Dh. We will also perform the L9 Taguchi Design of experiment to optimize the impact of various variables so that we can minimize the head losses from two directions. Finally, we will 3D print pipes with conical features to investigate the accuracy of our model and to develop empirical equations.

Mathematical Modelling of a Two-Way Head Loss Analysis by Designing a 3d Printable Piping System With Internal Features for Solar Thermal Heaters

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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