Entropy generation happens in all real machines and processes, showing us where energy is being wasted! This important idea comes from the second law of thermodynamics, which tells us that things naturally get more messy and disordered over time. First of all, when engineers talk about entropy, they’re talking about energy that can no longer be used to do useful work. Additionally, studying entropy generation helps us find spots in pipes, engines, and other machines where energy is being lost as unwanted heat. Moreover, keeping track of thermodynamic losses through exergy analysis shows engineers exactly how efficient their designs really are. Furthermore, in any heat transfer or fluid flow situation, some energy always gets downgraded in quality – this unavoidable energy downgrade is what we measure as entropy generation rate. Most importantly, understanding where and why thermodynamic irreversibility happens in thermal systems helps engineers design better power plants, air conditioners, and engines that waste less energy and work more efficiently. In our CFD analysis, VALIDATION of a numerical paper is targeted. Regarding the validation process, the simulation completely follows the reference paper. The purpose is to study the volumetric entropy generation rate distribution throughout the fluid in the pipe.

• Reference [1]: Sahin, Ahmet Z., and Rached Ben-Mansour. “Entropy generation in laminar fluid flow through a circular pipe.” Entropy5 (2003): 404-416.

Simulation Process

Let’s consider a circular pipe with a diameter of D and a length of L through which a viscous fluid is being transported, as shown in Figure 1. We will neglect the thickness of the pipe and assume the thermal boundary condition on the surface of the pipe is a uniform heat flux q. The symmetric design of the pipe allows us to consider just a 2D section along with the axisymmetric method. The structured grid is quickly produced, which speeds the process up.

Figure 1: Schematic of heated pipe

Post-processing

Based on the given equations in the reference paper, the entropy generation rate can be calculated:

Based on the given equations in the reference paper, the entropy generation rate can be calculated:

The entropy generation rates show amazing agreement between our computer model and the research paper! We achieved error percentages below 1% at most measurement points, which proves our CFD simulation is working perfectly. The highest volumetric entropy generation happens at the end of the pipe (at location 1) where it reaches 0.305 in the paper and 0.303 in our simulation – that’s only 0.66% difference! The only spot with more error is at the very beginning (location 0) with 7.7% difference, but this is normal because entrance effects are always harder to model perfectly. Furthermore, the entropy production increases steadily as the fluid moves through the pipe, starting at 0.013 and growing to 0.305, which is more than 23 times higher! This pattern shows that irreversibility builds up as the fluid flows longer distances under heating conditions. Additionally, the table proves that our simulation correctly captures the physics of both heat transfer and fluid friction effects that cause energy quality loss in real-world systems.

The temperature contour shows us how heat spreads through the pipe flow! The fluid starts cold (around 273.1K) at the pipe entrance and then gets warmer as it flows through the heated pipe, reaching up to 424.2K at the warmest spots. We successfully captured the complete temperature profile across the entire pipe length, showing exactly how heat moves from the pipe walls to the center. The most interesting part is how the temperature changes more quickly near the walls where heat enters first, and then slowly moves toward the middle of the pipe. Also, the pattern shows that the fluid stays warmer near the walls throughout the entire pipe length, which is exactly where most entropy generation happens. This happens because the biggest temperature differences (or gradients) occur right at the wall-fluid boundary, creating perfect conditions for thermal irreversibility to develop.

Figure 2: Temperature distribution in heated pipe