Scaling, Complexity, and Design Aspects in Computational Fluid Dynamics

Fluids

Sheldon Wang¹ 

[1] McCoy School of Engineering, Midwestern State University, Texas Tech University System, 3410 Taft Blvd., Wichita Falls, TX 76310, USA;

关键词: sucker rod pump;    scaling;    complexity;    relaxation time;    perturbation;   

DOI  :  10.3390/fluids6100362

来源: DOAJ

【 摘 要 】

With the availability of more and more efficient and sophisticated Computational Fluid Dynamics (CFD) tools, engineering designs are also becoming more and more software driven. Yet, the insights in temporal and spatial scaling issues are still with us and very often imbedded in complexity and many design aspects. In this paper, with a revisit to a so-called leakage issue in sucker rod pumps prevalent in petroleum industries, the author would like to demonstrate the need to use perturbation approaches to circumvent the multi-scale challenges in CFD with extreme spatial aspect ratios and temporal scales. In this study, the gap size between the outer surface of the plunger and the inner surface of the barrel is measured with a mill (one thousandth of an inch) whereas the plunger axial length is measured with inches or even feet. The temporal scales, namely relaxation times, are estimated with both expansions in Bessel functions for the annulus flow region and expansions in Fourier series when such a narrow circular flow region is approximated with a rectangular one. These engineering insights derived from the perturbation approaches have been confirmed with the use of full-fledged CFD analyses with sophisticated computational tools as well as experimental measurements. With these confirmations, new perturbation studies on the sucker rod leakage issue with eccentricities have been presented. The volume flow rate or rather leakage due to the pressure difference is calculated as a quadratic function with respect to the eccentricity, which matches with the early prediction and publication with comprehensive CFD studies. In short, a healthy combination of ever more powerful modeling tools along with the physics, mathematics, and engineering insights with dimensionless numbers and classical perturbation approaches may provide a balanced and more flexible and efficient strategy in complex engineering designs with the consideration of parametric and phase spaces.

【 授权许可】

Unknown