Gas sphere

Figure 6.4. Typical test results for a 400-ml butane fireball (Lihou and Maund, 1982), where Do = initial diameter of gas sphere D, = diameter of fireball at liftoff (at time f ) = diameter...

From the theory of polytropic gravitating gas spheres with the equation of state P = Kp1 it was known (Emden, 1907), that at 7 = 4/3 the equilibrium mass has a unique value... 

The shock wave in water results from the compression of the spherical layer of liquid in immediate contact with the high-pressure gas sphere produced by the detonation- This layer in turn compresses the next layer, and so on, so that a compression wave or shock wave is propagated radially outward thru the water. The shock wave has an extremely high pressure, but decays rapidly with distance and soon becomes an acoustic wave. Unlike a shock wave in air, the shock wave in water has no appreciable negative phase. While the compression wave is moving far outward, the original gas bubble continues... 

Fig 4 Radius of the Gas Sphere as a Function of Time, for a 0.55-Pound Tetryl Charge 300 Feet Below the Surface... 

If the compression is to be maintained in this volume, increasingly large displacements of water near the source are necessary, despite the weakening of the initial pressure at the front by spherical divergence. The pressure in the gas sphere, however, decreases as the volume determined by the spherical boundary increases, and the strength of this source must decrease. Outward accelerations of the water near the boundary will thus decrease, but as long as there is a pressure excess over hydrostatic, outward flow continues. 

The integration over all solid angles is replaced by the integration over all the surface elements dTi visible from dAi. In general, in (5.198) the integration is carried out over the entire surface area Ai of the gas space. We will show how the integration is carried out for the example of a gas sphere of diameter D = 2R, that radiates on an element dA2 of its surface. 

The spectral emissivity of the gas sphere depends on its optical thickness KG = kGD. The characteristic length Lo of the gas space introduced in (5.187), is, as could be expected, the... 

Fig. 5.79 Ratio of the spectral emissivity s G(kaD) from (5.199) for a gas sphere with diameter D to the spectral emissivity - v,g(k< (from (5.200), with. sm = (2/3)D as a function of the optical thickness kGD...

When an idealized sphere bursts, the air shock has its maximum overpressure right at the contact surface between the gas sphere and the air. Since, initially, the flow is strictly one-dimensional, a shock tube relationship between the bursting pressure ratio and shock pressure can be used to calculate the pressure in die air shock. The blast pressure, P at the surface of an exploding pressure vessel is thus estimated from the following expression (Baker et al., 1983 Prugh, 1988) ... 

Experiments on carbon dioxide accumulation were carried out in circulation systems with a gas chromatography analysis of the gas sphere. Kinematic and intrinsic viscosities of PVA water solutions were measured in a Ubbelohde viscosimeter with the hung level. 

The estimate of the explosion energy suffers from the same type of inconvenience of Brode s equation, and the analogy of the explosion of a pressurized gas vessel to a TNT one appears improper in the near field, since the vessel cannot be regarded as a point source. In this case, the correction method uses a virtual distance from the explosion center (Petes, 1971), to fictitiously move the explosion centre with respect to the surface of the expanding gas. The maximum overpressure of the shock wave, i.e. that at the contact surface between the initial expanding gas sphere and the air, is evaluated as (Baker et al., 1983 Prugh, 1988) ... 

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