Shock wave and detonation propagation through U-bend tubes
Introduction
Tube bends and coils are the elements, which can be used for elongating the detonation tubes of PDEs to ensure reliable deflagration-to-detonation transition (DDT) or shock-to-detonation transition (SDT). Surprisingly little work has been done on the DDT, SDT, and detonation diffraction in such elements (see [1], [2], [3] and references therein). Our recent research on a liquid-fueled air-breathing PDE [4], [5], [6] has unequivocally demonstrated that tube coils do promote DDT efficiently. It is anticipated that depending on the tube diameter, U-bend curvature, and the characteristic lengths of tube segments attached to the U-bends, different diffractions of initiating shock waves and developed detonations can result in various transient phenomena leading to SDT or failure of a developed detonation.
The objective of the research outlined in this paper is to provide experimental and computational data on gaseous fuel–air detonation waves (DW) and reactive shock waves (SW) propagating in tubes with U-bends. Such data will be used for deriving theoretical criteria to evaluate detonation initiation and stability conditions in terms of tube diameter, U-bend curvature, and characteristic lengths of tube segments between several U-bends.
Section snippets
Experimental setup
Figures 1a and b show the schematics of the experimental setups for the studies of detonation initiation and propagation in tubes with U-bends. The setups comprised the shock generator, pieces of straight tube 51 mm in inner diameter, and U-bends made of the tube of the same diameter. The far end of the tube opposite to the shock generator was closed. The internal radii of the U-bends were equal to 51 mm (Fig. 1a) and 11 mm (Fig. 1b).
The shock generator was a combustion chamber 22 cm3 in volume
Experimental results
Figures 2a and b show the shock wave velocities measured at different measuring segments of the setups of Figs. 1a and b, respectively. Shown in each figure are only five representative runs: Run 1 to Run 5. Note that all runs were well reproducible at similar initial conditions. Figures 3a–d show the pressure records registered by pressure transducers PT1–PT7 in Runs 2–5 of Fig. 2a.
In Run 1, the mean incident SW velocity at the entrance to the U-bend (segment PT1–PT2) was about 575 m/s. The
Computational approach
The mathematical model was based on the standard two-dimensional Euler equations, energy conservation equation with a chemical source term, and equation of chemical kinetics. The kinetics of propane oxidation was modeled by a single-stage overall reactionThe heat effect of the reaction entering the energy conservation equation was taken equal to 46.6 MJ/kg. The expression for a bimolecular reaction rate w = k[C3H8][O2] was used to calculate the rate of reaction, where k is the
Results of calculations
In the calculations, the same (but planar 2D) U-bend tube configurations as shown in Figs. 1a and b were studied. The tubes were initially filled with the stoichiometric propane–air mixture at p = 0.1 MPa and T0 = 298 K. A planar SW or DW was initiated by a short (10 mm long) tube section filled initially with the high-temperature (up to 2500 K) and high-pressure (up to 20 MPa) air simulating a shock generator of Fig. 1. The computational grid was uniform and contained 1600 × 400 square meshes with a size
Sensitivity analysis
To reveal the accompanying uncertainties in the computational studies, a sensitivity analysis was performed in terms of computational meshes and shock initiation techniques.
To reveal the effect of mesh “staircasing” at the curved boundaries, preliminary calculations of nonreactive and reactive SW and DW reflections from wedges were performed at different computational grids and compared with available experimental and computational data. The mesh “staircasing” affected considerably neither the
Conclusions
Thus, the experimental results obtained in tubes with U-bends demonstrated a considerable effect of the U-bend on reactive SW and DW propagation. On the one hand, the U-bend promoted the shock-induced detonation initiation. On the other hand, the DW propagating through the U-bend was subjected to complete decay or to temporary attenuation with the velocity drop of up to 15–20%.
Two-dimensional numerical simulations of reactive SW and DW transition through the U-bends revealed salient features of
Acknowledgments
This work was partly supported by the US Office of Naval Research and International Science and Technology Center. Dr. Shamshin acknowledges the support of REC 011 “Fundamental investigation of matter under extreme conditions” and CRDF within the program “Basic Research and High Education.”
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