Energy and Momentum Transfer in Air Shocks

[+] Author and Article Information
John W. Hutchinson

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138

J. Appl. Mech 76(5), 051307 (Jun 15, 2009) (7 pages) doi:10.1115/1.3129773 History: Received July 28, 2008; Revised January 27, 2009; Published June 15, 2009

A series of one-dimensional studies is presented to reveal basic aspects of momentum and energy transfer to plates in air blasts. Intense air waves are initiated as either an isolated propagating wave or by the sudden release of a highly compressed air layer. Wave momentum is determined in terms of the energy characterizing the compressed layer. The interaction of intense waves with freestanding plates is computed with emphasis on the momentum and/or energy transferred to the plate. A simple conjecture, backed by numerical simulations, is put forward related to the momentum transmitted to massive plates. The role of the standoff distance between the compressed air layer and the plate is elucidated. Throughout, dimensionless parameters are selected to highlight the most important groups of parameters and to reduce parametric dependencies to the extent possible.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Momentum , Waves
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Figure 1

Normalized wave energy/area and momentum/area for a isolated right-ward moving planar wave with an initial peak pressure p0 in air and a prescribed velocity distribution

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Figure 2

Ratio of kinetic energy/area at t=0 to total wave energy/area as a function of initial peak pressure for a wave with a prescribed initial velocity distribution

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Figure 3

Normalized momentum/area of rightward traveling wave produced by an initially compressed air layer with excess energy/area ΔE0, mass/area m0, and pressure p0. (a) Momentum/area versus time for two initial pressures. (b) Momentum/area of the emerged wave.

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Figure 4

Ratio of momentum/area transmitted to a plate to the momentum/area of the incident wave in terms of the generalized Taylor FSI parameter β in Eq. 16 and the two dimensionless parameters characterizing the wave. The values ΔE0/I0catm=1 and 1.1 correspond to a wave 7 released with w=0.05 m with p0/patm=16 and 127, respectively, at three distances from the plate (d=0.4 m, 0.7 m and 1.2 m.

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Figure 5

Configuration and notation for simulations releasing compressed air layer at t=0 with no standoff distance to plate. (a) No backing to compressed layer. (b) Rigid backing to compressed layer.

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Figure 6

An example for the case of the compressed layer with rigid backing and a plate with zero standoff distance. The evolution of the several components of the energy of the system with time is plotted until the time when the plate acquires its maximum velocity. The energy/area ΔE in the air to the left and right of the plate is the sum of the kinetic energy and the excess internal energy as defined in Eq. 12. As noted from the top curve, the numerical method conserves energy to a high degree of accuracy. In this example, value for mp is equivalent to a 1 cm thick steel plate; the maximum velocity attained by the plate is 120 m/s.

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Figure 7

Ratio of the maximum kinetic energy/area transmitted to plate to the initial excess energy/area in the compressed layer for the case with no standoff between the plate and the layer. (a) No backing to the compressed layer. (b) Rigid backing to the compressed layer.

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Figure 8

Configuration for simulations of energy transferred to plate with standoff d. The compressed air layer has rigid backing.

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Figure 9

The maximum kinetic energy/area transmitted to plate as a function of the standoff distance between the plate and the compressed air layer plotted for a specific set of dimensionless parameters. For reference, a set of dimensional parameters that corresponds to these results is: hatm=0.33 m, h=0.012 m, ΔE0=0.24 MJ/m2, mp=40 kg/m2, m0=0.4 kg/m2 and p0=10.5 MPa. The limit for large standoff is discussed in the text.



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