Droplet motion induced by weak shock waves

Abstract

An experimental study of the motion of small water droplets in a shock tube is reported. Droplet displacement data were obtained by means of reflected-light stroboscopic illumination for droplet diameters in the range 87–575 μm, and for shock strengths, Δ P / P 1 , in the range 0·0018–0·3. The displacement data are fitted by means of best-fit polynomials in time, which are used to compute droplet velocities, accelerations, and drag coefficients. All of our drag coefficient data have values which are larger than the steady drag at the same Reynolds numbers. The differences are attributed to time changes of the relative fluid velocity U r . This may affect the size of the recirculating region and, therefore, the drag. In particular, it is argued that the drag is larger or smaller than the steady drag, depending on whether the d U r / dt is negative or positive, respectively. Our experiments, which were performed for dU r / dt < 0, confirm this expectation. Furthermore, it is shown that the difference between steady and transient drag coefficients, at the same Reynolds number, depends only on the value of a parameter A = (ρ p /ρ 0 −1)( D / U 2 r )( dU r / dt ). Here ρ p and ρ 0 are the densities of the droplets and of the surrounding gas, respectively, and D is the droplet diameter. In fact, in the Reynolds number range 3·2 < Re < 77, where multiple data are available having the same value of Re but having different values of A , the drag data can be expressed as C D = C DS ( Re ) – KA , where C DS ( Re ) is the steady drag at the instantaneous Reynolds number Re , and K is a constant of order 1.