# A note on the pressure field within an outward moving free annulus

Abstract: The outward radial expansion of a free liquid annulus is a common problem of both earlier and current ICF blanket design. Whether the annulus fractures or not depends on the internal pressure and surface stability. In this paper a model based on incompressible cylindrically symmetric flow is used to get a theoretical solution similar to that of the Rayleigh's solution for bubble dynamics. The pressure inside the annulus is found positive all time but the peak is lowering during the expansion. Besides, both surfaces are Taylor stable during such motion. Thus, it is concluded that an annulus in outward radial motion will not cavitate or breakup.

## Summary (1 min read)

### THE BACKGROUND

- In an Inertia Confinement Fusion (ICF) reactor, the chamber wall may be protected from the neutron radiation bya neutron absorbtntg,falling liquidblanket, which surrounds the fusion site.
- I,e, heating at conslm_tvolun,c, The neutron absorbing liquid thus finds itself suddenly possessing much higher internal pressure tiron its surroundings (due to its increasedinternal energy), and will fragment due to the propagation of a rarefaction wave into the liquid, Interestingly, for the case of the dLscretejet array, the fragmentation of the liquid results not in the ft}rmatlonof small liquid chunks.
- On the contrary, because of geoiaetj-y and neutr_ energy density _radient, fcagmentataonresults ftrSi in the break-off of mdtvld_aal annullhorn each jet, which thencollide with Figure 1.

### O=?(R')-e(R)

- The integradon (over timO of Equation la gives a global continuity equation, During the outward motion, the velocity profllo is known from thecontinuity equation.
- The pressure is close to zero, That is, ZO.litl.h_l:Itrdgu_ EQUATION.
- The,total momentum can becalculated also by an integration of over the whole annulus P(R)--O . (3b).

### ,, CONCLUSIONS

- Wher_ the p-bi-is the rate of the momentum ctmnge Aaad flus is _hievable in the simple tmmodeal caleutetton along with the other calcutadons.
- The total rate of find outisthe total momentumof the annuluscalculated ¢tmnge can be obtained by integration over the v,,hole from this equation (l-V)exactly overlaps on tyre, curve body.

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