On the flow past ellipses in a Hele-Shaw cell

In this work we investigate the effect of vertical confinement and inertia on flow past thin ellipses in a Hele-Shaw cell (with centre line velocity $U_c$ height 2 $h$ ) with different aspect ratios for symmetrical flows at an angle attack, using asymptotic methods numerical simulations. A Stokes region is identified ellipse vertices which results to bluff bodies. Comparison analysis indicates close agreement over ‘flat’ portion ellipse, $\delta =(b/a)=0.05$ , where $a$ $b$ are semi-major -minor axes, respectively. Two conditions investigated attack 10 $^\circ$ fixed =0.05$ . Firstly, $\varLambda =(U_ca/\nu )(h/a)^2 \ll 1$ increasing rear stagnation point (RSP) moving from potential-flow prediction when $\epsilon =h/a$ very small two-dimensional Stokes-flow $\epsilon$ large. Secondly, increased ={O}(\epsilon )$ RSP moves towards trailing edge located there ={O}(1)$ Under these attached exponentially decaying shear layer or ‘viscous tail’ formed. modified Bernoulli equation depth-averaged flow, together Kutta–Joukowski theorem used predict drag lift coefficients include linear nonlinear contribution, corresponding circulation component, Close found up