A Study of Drop Breakup Behind Strong Shocks with Applications to Flight

Reinecke, W. G.; Waldman, G. D.

doi:10.21236/ad0871218

Cited by 45 publications

(32 citation statements)

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“…They also provided a theoretical relation for the rate of mass reduction, which is the mass stripped away from the drop surface, by utilizing the equations from Taylor's analysis (1963). To date, the study by Reinecke and Waldman (1970) is probably the only investigation providing detailed mass reduction data based on the x-ray radiograph technology. They derived a correlation for breakup time at the catastrophic breakup regime, i.e., approximately We > 1000.…”

Section: Nomenclaturementioning

confidence: 99%

Breakup modeling of a liquid jet in cross flow

Lin

Lai

et al. 2011

Int.J Automot. Technol.

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We propose a novel breakup model to simulate the catastrophic breakup regime in a supersonic cross flow. A developed model has been extended from an existing Kelvin-Helmholtz/Rayleigh-Taylor (K-H/R-T) hybrid model. A new mass reduction rate equation, which has critical effects on overall spray structure, is successfully adopted, and the breakup length, which is an important parameter in existing model, is replaced by the breakup initiation time. Measured data from the supersonic wind tunnel with a dimension of 762×152×127 mm was employed to validate the newly developed breakup model. A nonaerated injector with an orifice diameter of 0.5 mm is used to inject water into a supersonic flow prescribed by the momentum flux ratio of the liquid jet to free stream air, q 0 . The conservation-element and solution-element (CE/SE) method, a novel numerical framework for the general conservation law, is applied to simulate the supersonic compressible flow. The spray penetration height and average droplet size along with a spray penetration axis are quantitatively compared with data. The shock train flow structures induced by the presence of a liquid jet are further discussed.

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Section: Nomenclaturementioning

confidence: 99%

Breakup modeling of a liquid jet in cross flow

Lin

Lai

et al. 2011

Int.J Automot. Technol.

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“…(4) (5) γ = 1.4 is the gas constant of air, γ l = 4.4 is the analogous constant for water and π l = 6·10 8 Pa is the stiffening constant that makes large changes in liquid pressure produce almost no changes in density. Equations (6) and (7) are closure relations for the internal energy ρe to the total energy ρE, per unit volume, for each phase.…”

Section: Two-phase Flow Modelmentioning

confidence: 99%

“…Equations (6) and (7) are closure relations for the internal energy ρe to the total energy ρE, per unit volume, for each phase. The volume fraction will propagate at a mean inter-facial velocity which is a center-of-mass estimate given in eqn (8). (8) E i and P i are volume averages of total energy and pressure respectively at the interface shown in eqn (9).…”

Section: Two-phase Flow Modelmentioning

confidence: 99%

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Optimal Control of Shock Wave Attenuation using Liquid Water Droplets with Application to Ignition Overpressure in Launch Vehicles

Moshman¹,

Sritharan²,

Hobson³

2011

International Journal of Flow Control

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This paper presents the first solution of an optimal control problem concerning unsteady blast wave attenuation where the control takes the form of the initial distribution of liquid water droplets. An appropriate two-phase flow model is adopted for compressible homogeneous two-phase flows. The dynamical system includes an empirical model for water droplet vaporization, the dominant mechanism for attenuating the jump in pressure across the shock front. At the end of the simulation interval, an appropriate target state is defined such that the jump in pressure of the target state is less than that of the simulated blast wave. Given the nature of the non-linear system, the final time must also be a free variable. A novel control algorithm is presented which can satisfy all necessary conditions of the optimal system and avoid taking a variation at the shock front. The adjoint-based method is applied to NASA's problem of Ignition Overpressure blast waves generated during ignition of solid grain rocket segments on launch vehicles. Results are shown for a range of blast waves that are plausible to see in the launch environment of the shuttle. Significant parameters of effective droplet distributions are identified. INTRODUCTIONThere exists a wide range of multi-phase and multi-fluid flow regimes. Much care must be taken in selecting an appropriate model and numeric method. Presently, the flow of interest consists of a gaseous carrier phase with many suspended water droplets. These two fluids' parameters are drastically different and the vast majority of numeric methods in the literature are ill-adapted since they introduce artificial diffusion and mixing at interfaces [1][2][3]. Other methods are poorly suited to mixtures where thermodynamic equilibrium cannot be reasonably assumed except at interfaces. Since the water droplets of interest will be smaller than 1 mm, their properties can be assumed to be homogeneous between computational cells and, therefore, many interfaces will be present in each cell. It will be impractical to use interface tracking methods or solve separate sets of equations for each fluid and to couple their properties at the interface. Instead, the following calculations implement a method proposed by [4] which has the advantage of solving the same set of differential equations throughout the domain. The method uses different equations of state for each phase and allows a difference in temperature at the gas-liquid interfaces. To close the system, a volume fraction variable α is introduced and a non-conservative PDE is appended to the conservative system. The method assumes that both phases are compressible which yields a hyperbolic system. Ignition overpressure (IOP) is a phenomenon present at the start of an ignition sequence in launch vehicles using solid-grain propellants. When the grain is ignited the pressure inside the combustion chamber quickly rises several orders of magnitude. This drives hot combustion products toward the nozzle and out to the open atmosphere at supersonic spee...

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“…The mass-time history of droplets during the stripping mode has been measured by x-ray absorption techniques ( 4 ). These data can be approximated with a cosine function of the fo rm ,…”

Section: Experimental Studiesmentioning

confidence: 99%