Evaluation of the drag force by integrating the energy dissipation rate in Stokes flow for 2D domains using the FEM
Abstract
The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are postprocessing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles  a circle, an ellipse and a crosssection of a prolate spheroid  with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the farfield boundary enclosing the domain, the drag force on the boundary of the body can be obtained.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 September 1991
 DOI:
 10.1002/fld.1650130503
 Bibcode:
 1991IJNMF..13..557G
 Keywords:

 Aerodynamic Drag;
 Finite Element Method;
 Flow Resistance;
 NavierStokes Equation;
 Skin Friction;
 Two Dimensional Flow;
 Boundary Conditions;
 Computational Fluid Dynamics;
 Energy Dissipation;
 Incompressible Flow;
 Prolate Spheroids;
 Fluid Mechanics and Heat Transfer