Improved scaling laws for the shock-induced dispersal of a dense particle curtain

Abstract

Experiments were performed within Sandia National Labs’ Multiphase Shock Tube to measure and quantify the shock-induced dispersal of a shock/dense particle curtain interaction. Following interaction with a planar travelling shock wave, schlieren imaging at 75 kHz was used to track the upstream and downstream edges of the curtain. Data were obtained for two particle diameter ranges ($d_{p}=106{-}125$, $300{-}355~\unicode[STIX]{x03BC}\text{m}$) across Mach numbers ranging from 1.24 to 2.02. Using these data, along with data compiled from the literature, the dispersion of a dense curtain was studied for multiple Mach numbers (1.2–2.6), particle sizes ($100{-}1000~\unicode[STIX]{x03BC}\text{m}$) and volume fractions (9–32 %). Data were non-dimensionalized according to two different scaling methods found within the literature, with time scales defined based on either particle propagation time or pressure ratio across a reflected shock. The data show that spreading of the particle curtain is a function of the volume fraction, with the effectiveness of each time scale based on the proximity of a given curtain’s volume fraction to the dilute mixture regime. It is seen that volume fraction corrections applied to a traditional particle propagation time scale result in the best collapse of the data between the two time scales tested here. In addition, a constant-thickness regime has been identified, which has not been noted within previous literature.

A volume-filtered description of compressible particle-laden flows

“…0575, is large, indicating the particle motion is negligible over the simulation duration considered (t < 3). In addition, a recent experimental study suggests that the particle phase does not begin to spread until times corresponding to our non-dimensional time of t 10 [14]. Here, t = 0 corresponds to the instant the shock interacts with the leading edge of the particle phase.…”

“…In summary, the unclosed terms can be grouped into residual stresses R u in Eqs. (14) and (33), R µ in Eq. (15), R T u , R uu , and R τ u in Eq.…”

“…In addition, a number of sub-filtered surface contributions appear in the form of interphase exchange terms, including the interphase exchange of momentum, F , in Eq. (14), as well as work due to momentum exchange, u p • F , and heat exchange, Q, in Eq. (30).…”

Shock-induced interfacial instabilities of granular media

“…The slope of the u p ( x ) profile at t B is reduced in case 6-120-50-0 since the rarefaction effect is partially offset by the more diffusive pressure field, which imposes countering pressure gradient forces throughout the column. At late time t C , the u p ( x ) profiles for both cases display a plateau, indicating a collective mobilization of particles (DeMauro et al 2019). The pressure profiles P ( x ) at t C vary little from those at t B .…”

“…Modelling granular materials as an isotropic elastic non-hardening Drucker–Prager solid, Kandan et al (2017) recognized that the instability criterion of the SDGI is equivalent to the Drucker–Prager yield criterion. However, the continuum approximation of granular materials is called into question due to the transient and non-equilibrium coupling between the interstitial gas phase and the particle skeleton in this scenario (Ben-Dor et al 1997; Britan, Shapiro & Ben-Dor 2007; DeMauro et al 2019). Previous studies revealed a complex wave spectrum inside a granular medium impinged head-on by an incident shock wave (Ben-Dor et al 1997; Britan et al 2007; Mo et al 2018, 2019; Koneru et al 2020).…”