On the evaluation of time-dependent fluid-dynamic forces on bluff bodies

• Main Author: Noca, Flavio
• Format: Dissertation
• Language: English
• Subjects: engineering, aerospace; engineering, marine and ocean; engineering, mechanical
• ISBN: 0591433834; 9780591433838

We present some exact expressions for the evaluation of time-dependent forces on a body in an incompressible and viscous cross-flow which only require the knowledge of the velocity field (and its derivatives) in a finite and arbitrarily chosen region enclosing the body.
Given a control volume V with external surface S which encloses an arbitrary body, the fluid-dynamic force F on the body can be evaluated from one of the following three expressions (in abbreviated form):$$\eqalign{{\bf F}&=-{1\over {\cal N}-1}{d\over {dt}}\int\sb{V}{\rm x}\wedge\omega dV+\oint\sb{S}\ {\bf n}\cdot\Upsilon\sb1dS + {\rm body\ motion\ terms},\cr{\bf F}&=-{d\over{dt}}\int\sb{V} {\bf u}dV+\oint\sb{S}\ {\bf n}\cdot\Upsilon\sb2dS + {\rm body\ motion\ terms},\cr{\bf F}&=\ {\rm no\ volume\ integral\ terms} + \oint\sb{S}\ {\bf n}\cdot\Upsilon\sb3dS +{\rm body\ motion\ terms},\cr}$$where $\cal N$ is the space dimension, u is the flow velocity, $\omega$ is the vorticity, x is the position vector, and the tensors $\Upsilon\sb1,\ \Upsilon\sb2,\ \Upsilon\sb3$ depend only on the velocity field u and its (spatial and temporal) derivatives.
The first equation is already known for either simply connected domains or inviscid flows. We re-derive it here for viscous flows in doubly connected domains (i.e. domains which include a body). We then obtain the second and third equation through a simple algebraic manipulation of the first equation.
These expressions are particularly useful for experimental techniques like Digital Particle Image Velocimetry (DPIV) which provide time sequences of 2D velocity fields but not pressure fields.
They are tested experimentally with DPIV on two-dimensional, low Reynolds number circular cylinder flows. Both steady and unsteady motions are studied.