Open Access Thesis
Master of Science in Mechanical Engineering (M.S.M.E.)
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Fluid flows occurring in moving and/or deforming environments are influenced by the transient nature of their containment. In Computational Fluid Dynamics (CFD), simulating such flow fields requires effort to maintain the geometric integrity of the transient flow domain. Convective fluxes in such domains are evaluated with respect to the motion of the boundaries of the control volume. These simulations demand conservation of space in addition to the conservation of mass, momentum and energy as the solution continues in time.
The Space Conservation Law in its continuous form can be inferred by using the rules of fundamental calculus. However, implementing it in a discrete form poses substantial challenges. During mesh motion, the surfaces enclosing the control volumes sweep through three-dimensional space. As per the Space Conservation Law, the change in the control volume has to match the sum of the swept volumes of all its faces exactly. The Space Conservation Law must be satisfied accurately and consistently in order to avoid the occurrence of non-physical masses and to prevent the violation of the continuity equation.
In this work we have attempted to address the consistency issues surrounding the implementation of the Space Conservation Law in OpenFOAM. The existing method for calculation of swept volumes falls short in terms of consistency. Moreover, its capabilities are limited when it comes to complex three-dimensional mesh motions. The existing method of calculation treats swept volumes as net fluxes emanating from cell faces. We have implemented an alternate algorithm in which the swept volumes are treated as intermittent virtual cells whose volumes can be calculated in a unique and consistent manner. We will conclude by validating our approach for mesh motions of varying degrees of complexity.
Pillalamarri Narasimha Rao, Venkata Pavan, "A Consistent Algorithm for Implementing the Space Conservation Law" (2014). Masters Theses. 37.