An experimental study of reflected liquefaction shock waves with near-critical downstream states in a test fluid of large molar heat capacity

Abstract

Near-critical states have been achieved downstream of a liquefaction shock wave, which is a shock reflected from the endwall of a shock tube. Photographs of the shocked test fluid (iso-octane) reveal a rich variety of phase-change phenomena. In addition to the existence of two-phase toroidal rings which have been previously reported, two-phase structures with a striking resemblance to dandelions and orange slices have been frequently observed. A model coupling the flow and nucleation dynamics is introduced to study the two-wave system of shock-induced condensation and the liquefaction shock wave in fluids of large molar heat capacity. In analogy to the one-dimensional Zeldovich–von Neumann–Döring (ZND) model of detonation waves, the leading part of the liquefaction shock wave is a gasdynamic pressure discontinuity (Δ ≈ 0.1 μm, τ ≈ 1 ns) which supersaturates the test fluid, and the phase transition takes place in the condensation relaxation zone (Δ ≈ 1–103 μm, τ ≈ 0.1–100 μs) via dropwise condensation. At weak to moderate shock strengths, the average lifetime of the metastable state, τ ∞ 1/J, is long such that the reaction zone is spatially decoupled from the forerunner shock wave, and J is the homogeneous nucleation rate. With increasing shock strength, a transition in the phase-change mechanism from nucleation and growth to spinodal decomposition is anticipated based on statistical mechanical arguments. In particular, within a complete liquefaction shock the metastable region is entirely bypassed, and the vapour decomposes inside the unstable region. This mechanism of unmixing in which nucleation and growth become one continuous process provides a consistent framework within which the observed irregularities can be explained.

Symmetry breaking, ring formation and other phase boundary structures in shock tube experiments on retrograde fluids

“…Collapsing waves are supersonic relative to the front of the waves. This is confirmed in § 4 by analysing some rings in photographs published in Gulen et al (1994). The Mach numbers of the rings analysed in § 4 range from 2 to 4.…”

“…It is interesting to see whether the outer fronts of rings of cloud propagate supersonically as predicted by case 3 of § 3. An example of such photographs is figure 18 of Gulen et al (1994), which is copied here as figure 18. The diameter of the window is 57.4 mm.…”

“…Many authors have contributed to the study of flows with phase transitions in shock tubes, such as Bauschdorff (1975), Glass, Kalra & Sisilian (1977), Homer & Hurle (1972), Kotake & Glass (1977), Kawada & Mori (1973), Lee (1978), Sisilian (1975), Sisilian & Glass (1976), and Wu (1977). Dettleff et al (1979), Gulen, Thompson & Cho (1994), Thompson, Carofano & Kim (1986), and Thompson et al (1987) carried out experimental and computational studies on phase transitions in shock tubes using Figure 2. A compression shock is sent into stable vapour at rest.…”

“…This suggests that the ring formation has nothing to do with fluid vortices, nor shock strength. Some photographs published in Gulen et al (1994) showed that some rings expanded in the direction vertical to the incident shock at a Mach number 4 when the incident shock was of Mach number 2.87. One ring grew to 4.1 mm in radius in less than 6 µs.…”

“…Despite these analytical results for the model, whether this model exhibits the ring formation phenomenon (a) still remains to be investigated. Furthermore, there is another issue that was overlooked in the early attempts to explain the wave patterns in shock tube experiments: the experimental apparatus in Dettleff et al (1979) and Gulen et al (1994) was rotationally symmetric cylinders. The initial state of the fluid was also cylindrically symmetric.…”