Shock-wave shapes around spherical-and cylindrical-nosed bodies.

Billig, F. S.

doi:10.2514/3.28969

Cited by 286 publications

(106 citation statements)

References 3 publications

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“…This variation can be at least partially explained by the growing lateral displacement of the primary bow shock with decreasing Mach number: for a larger shock radius, the secondary sphere will effectively lie further inside the shock at the same initial position, hence a larger radius ratio will be required to achieve the same degree of repulsion. Therefore, in an attempt to scale out the effect of the primary bow-shock location, in figure 16(b) we present the same velocity data, but with the abscissa now the scaled distance (r 1 + 2r 2 )/R s , where R s is the radial location of the primary bow shock (at the initial axial location of the sphere centres) as given by the correlation of Billig (1967). This modified abscissa is thus the initial lateral location of the outer secondary-sphere edge, normalized by the bow-shock displacement.…”

Section: Effect Of Mach Number It Is Clear From Comparing the Results Inmentioning

confidence: 99%

Dynamical separation of spherical bodies in supersonic flow

2012

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An experimental and computational investigation of the unsteady separation behaviour of two spheres in Mach-4 flow is carried out. The spherical bodies, initially contiguous, are released with negligible relative velocity and thereafter fly freely according to the aerodynamic forces experienced. In experiments performed in a supersonic Ludwieg tube, nylon spheres are initially suspended in the test section by weak threads which are detached by the arrival of the flow. The subsequent sphere motions and unsteady flow structures are recorded using high-speed (13 kHz) focused shadowgraphy. The qualitative separation behaviour and the final lateral velocity of the smaller sphere are found to vary strongly with both the radius ratio and the initial alignment angle of the two spheres. More disparate radii and initial configurations in which the smaller sphere centre lies downstream of the larger sphere centre each increases the tendency for the smaller sphere to be entrained within the flow region bounded by the bow shock of the larger body, rather than expelled from this region. At a critical angle for a given radius ratio (or a critical radius ratio for a given angle), transition from entrainment to expulsion occurs; at this critical value, the final lateral velocity is close to maximum due to the same 'surfing' effect noted by Laurence & Deiterding (J. Fluid Mech., vol. 676, 2011, pp. 396-431) at hypersonic Mach numbers. A visualization-based tracking algorithm is used to provide quantitative comparisons between the experiments and high-resolution inviscid numerical simulations, with generally favourable agreement.

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Section: Effect Of Mach Number It Is Clear From Comparing the Results Inmentioning

confidence: 99%

Dynamical separation of spherical bodies in supersonic flow

2012

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“…Numerical solutions obtained for M 1 = 2 are represented on figure 9. From theoretical and experimental results, Billig proposed in [4] to model the geometrical form of the shock wave by a hyperbola. Then, the distance ∆ of the shock from the obstacle, measured on the stagnation line (y = 1), is approximated in [4] by:…”

Section: Steady-state Supersonic Flow Around a Cylindermentioning

confidence: 99%

A high-resolution penalization method for large Mach number flows in the presence of obstacles

2009

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A penalization method is applied to model the interaction of large Mach number compressible flows with obstacles. A supplementary term is added to the compressible Navier-Stokes system, seeking to simulate the effect of the Brinkmanpenalization technique used in incompressible flow simulations including obstacles. We present a computational study comparing numerical results obtained with this method to theoretical results and to simulations with Fluent software. Our work indicates that this technique can be very promising in applications to complex flows.

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“…In space applications, it has been found to be largely consistent with the fast magnetosonic Mach number, M f , when fitted with observations of distant shock crossings of Venus, Earth and Mars [Slavin et al, shown to become better in agreement with gas dynamic theory. This is attributed to the decrease in the IMF strength since wave takes a size and shape similar to the obstacle [Billig, 1967]. Saturn's magnetosphere is a blunt body (as opposed to a pointed wedge) and a detached bow shock is thus formed in the dayside region [Slavin et al, 1985].…”

Section: Size and Shapementioning

confidence: 99%

The Near-Saturn Magnetic Field Environment

Sulaiman

2017

Springer Theses

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Shock waves exist throughout the universe and are fundamental to understanding the nature of collisionless plasmas. The complex coupling between charged particles and electromagnetic fields in plasmas give rise to a whole host of mechanisms for dissipation and heating across shock waves, particularly at high Mach numbers. While ongoing studies have investigated these process extensively both theoretically and via simulations, their observations remain few and far between. This thesis presents a study of very high Mach number shocks in a parameter space that has been poorly explored and identifies reformation using in situ magnetic field observations from the This non-axisymmetry is revealed to have an impact in the rotation of the magnetic field and is significant enough to influence the magnetic shear at the magnetopause.

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Shock-wave shapes around spherical-and cylindrical-nosed bodies.

Cited by 286 publications

References 3 publications

Dynamical separation of spherical bodies in supersonic flow

Dynamical separation of spherical bodies in supersonic flow

A high-resolution penalization method for large Mach number flows in the presence of obstacles

The Near-Saturn Magnetic Field Environment

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