Identification of thermodynamic patterns in variable-diameter pipelines using an improved quasi-one-dimensional model

This research looks at fluid flow with changing temperatures and related flow and heat effects in closed pipelines of different shapes, clearly including the impact of terrain and outside heat. A main problem in studying large pipeline systems is the heavy use of computing power by 3D CFD models. This research solves that by developing an accurate and efficient model that can predict these processes without needing a lot of computing resources. An improved nearly one-dimensional model was created along with a reliable calculation method. To solve the temperature-related cubic equation, a mix of a clear step-by-step calculation method and a bisection approach was used. The results show that in narrowing sections, reducing the radius from 0.03 m to 0.02 m increases fluid speed by 2.25 times, with only a 1.2 K drop in temperature. In widening sections, increasing the radius to 0.04 m lowers the speed by 44%, along with a further temperature drop of 0.8 K because of more heat loss. An important feature of the developed model and its results is that it strictly follows the rules of mass, momentum, and energy conservation. It also uniquely includes the direct change of kinetic energy into heat through hydraulic friction. The model provides accuracy similar to 3D simulations but with much less computing power needed. This was confirmed by comparing it with 3D simulations using the Shear Stress Transport (SST) turbulence model in COMSOL Multiphysics and Darcy-Weisbach calculations, showing an average difference of 1.8% and a maximum local error of 3.1%

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