Computational Study of Partially Covered Hartmann Whistle in a Sonic-Underexpanded Jet

Abstract

The present study investigates the use of Hartmann whistle as an effective passive flow control device by partially covering the entire area between the jet exit and cavity inlet using a cylindrical shield, numerically. The passive flow control is accomplished by allowing the pulsating jet to exit through two small openings in the shield: (i) near the cavity inlet, (ii) away from the cavity inlet. The studies are performed for various S/Dj values of 1.43, 2.86 and 4.28, (where S is the stand-off distance and Dj is the jet diameter). The velocity vectors indicate the jet regurgitance showing inflow/outflow phases as well as flow diversion features near the cavity mouth. The Mach contours show shock-structures as well as the flow deceleration and re-acceleration zones. It shows that the resonant oscillations are primarily driven by jet regurgitance at smaller stand-off distances but at higher stand-off distances they are mainly driven by fluid column oscillations in the shock cells, shield, as well as in the cavity regions. It also shows that the stand-off distance is a key parameter that controls the strength of shock as well as regurgitant/fluid column, oscillations. An empirical formula developed using dimensional analysis reveals that the resonance frequency of the partially covered Hartmann whistles can be obtained using the classical Helmholtz resonator analogy with the stagnation sound speed, size of the flow control openings, shield height, stand-off distance and cavity length as parameters. Thus, this paper adequately illustrates the effect of stand-off distance as well as flow control openings in modifying the shock as well as regurgitant/fluid column, oscillations in a partially covered Hartmann whistle for attaining the effective flow control .