Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session EQ: Reacting Flows I |
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Chair: David Kassoy, University of Colorado Room: Salt Palace Convention Center 251 E |
Sunday, November 18, 2007 4:10PM - 4:23PM |
EQ.00001: Route to instability in cellular detonations Matei I. Radulescu, Gary J. Sharpe, James J. Quirk Through highly resolved direct numerical simulations of detonation cellular structures performed on large domains, we show that with increasing sensitivity of the reaction rates, the cellular front transits from a regular pattern to a highly irregular one, characterized by transverse wave merging and formation of new triple points on the front. We formulate a new method to study the distribution of the spacings between triple points of the same family and correlate their distribution with the sensitivity of the reaction rates. It is found that past a critical value of activation energy, a period doubling bifurcation occurs, with the preferred cell size having twice its original value. Simultaneously, higher frequency oscillations appear through a period halving bifurcation, hence significantly broadening the range of characteristic cell sizes of the front. The non-linear mechanisms responsible for the generation of these higher modes is discussed. [Preview Abstract] |
Sunday, November 18, 2007 4:23PM - 4:36PM |
EQ.00002: Non-Equilibrium Thermodynamics of Reactive Systems Joseph Powers, Samuel Paolucci Construction of the Slow Invariant Manifold (SIM) for a reactive system is coming to be realized as the linchpin in a rational method of reduced kinetics. Here a method of constructing a finite dimensional SIM based on identifying critical points and connecting them with trajectories is shown for a spatially homogeneous reactive system. The relation between this analysis and classical as well as irreversible thermodynamics is examined. Extensions to reactive flow systems are considered. [Preview Abstract] |
Sunday, November 18, 2007 4:36PM - 4:49PM |
EQ.00003: ABSTRACT WITHDRAWN |
Sunday, November 18, 2007 4:49PM - 5:02PM |
EQ.00004: Initial-value problem for stability of detonations in a circular pipe Anatoli Tumin, Ivan Shalaev Erpenbeck (1962) formulated the hydrodynamic stability of detonations as an initial-value problem for three-dimensional perturbations in an unbounded domain. In the present work, we address the initial-value problem for perturbations of idealized one-reaction detonations in a circular pipe. Using the Laplace transform with respect to time, Fourier series with respect to the azimuthal angle, and an expansion into Bessel's functions of the radial variable, the problem is reduced to an inhomogeneous system of ODEs with the axial coordinate as the independent variable. For each radial and azimuthal mode, the inverse Laplace transform can be presented as an expansion of the solution into the normal modes. The dispersion relation for the discrete spectrum requires solving the homogeneous ODEs for the adjoint system (instead of inhomogeneous equations in the normal mode formulation), and evaluating an integral through the reaction zone. The solution of the initial-value problem gives a convenient tool for getting the receptivity problem solution. Numerical examples illustrate that it is necessary to explore the receptivity coefficients together with the conventional eigenvalue analysis in order to understand the possible scenarios of the flow dynamics. It is shown that the radiation condition for perturbations at the end of the reaction zone is a trivial consequence of the adjoint solution's properties. [Preview Abstract] |
Sunday, November 18, 2007 5:02PM - 5:15PM |
EQ.00005: An extension of detonation shock dynamics for Insensitive Explosives Mark Short, John Bdzil, Tariq Aslam Resolved, direct numerical simulations of the detonation of high explosives (HE) in geometries of engineering interest are largely unattainable due to the scale disparity between the shorter detonation reaction-zone length and the longer characteristic explosive charge dimension. However, multi-scale mathematical modeling, utilizing this scale disparity, has led to the development of the theory of detonation shock dynamics (or DSD). With DSD, the propagation of a detonation in a HE configuration is described by a surface evolution equation for the detonation front. For insensitive high explosives (IHE), detonations typically have two characteristic reaction stages: a fast reaction where the majority of the heat of reaction is released, followed by a second significantly slower reaction (e.g. through carbon coagulation in PBX-9502). We show that the presence of this slowly reacting, weak heat release zone can have a significant (time-dependent) influence on the evolution of a detonation in IHE. We also describe an extension to the DSD concept, specifically tailored to detonations in IHE, which treats fast-slow chemistry models. The fast chemistry is handled with a DSD front rationally coupled to a distributed, resolved (reactive burn) model for handling the slow chemistry step. [Preview Abstract] |
Sunday, November 18, 2007 5:15PM - 5:28PM |
EQ.00006: Numerical Modeling of Detonation Initiation Using Acoustic Time Scale Heat Deposition Jonathan Regele, Oleg Vasilyev, David Kassoy Localized thermal power deposition of limited duration into a reactive gas is the initiator for deflagration to detonation transition (DDT) on the microsecond time scale. Numerous spatial and temporal scales are involved in these problems making them computationally challenging. These scenarios are modeled with a newly developed shock capturing scheme that utilizes the computational efficiency of the Adaptive Wavelet-Collocation Method (AWCM). With this technique it possible to perform simulations with over 100 grid points per steady-state half-reaction length, ensuring the transient dynamics leading to detonation initiation are well resolved. Previous one-dimensional studies have demonstrated the basic sequence of events that are needed in order for a DDT process to occur. Instead of starting with a strong shock-coupled reaction zone, the initial pulse is weak enough to allow the shock and the reaction zone to decouple. Reflected compression waves generated by the inertially confined reaction zone lead to localized reaction centers, which eventually explode and further accelerate the process. Eventually a shock-coupled reaction zone forms an initially overdriven detonation, which relaxes to a steady CJ wave. New two-dimensional results using a cylindrical heat deposition in a channel demonstrate the same sequence of events, verifying the concepts of the one-dimensional work. [Preview Abstract] |
Sunday, November 18, 2007 5:28PM - 5:41PM |
EQ.00007: The Blast Wave Problem Revisited David R. Kassoy The Taylor-von Neumann-Sedov solution for a blast wave generated by \textit{instantaneous }deposition of energy at a \textit{point} is a paradigm example of rapid energy addition to a compressible gas. The traditional intuitive blast wave model (Barenblatt, \textit{Scaling, self-similarity, and intermediate asymptotics}, 47-50, Cambridge University Press, 1996) can be reformulated for \textit{time resolved} dimensional energy deposition (E$\prime )$ into a \textit{finite volume} V$\prime $ (initially containing fluid with a relatively small internal energy E$_{0}\prime $ at a modest initial temperature T$_{0}\prime )$ with systematic asymptotic methods based on a small parameter $\varepsilon $=E$_{0}\prime $/E$\prime <<$1. The energy deposition occurs on a time scale t$_{H}\prime $, short compared to the initial acoustic time t$_{a}\prime $= l$\prime $/a$_{0}\prime $ (l$\prime $ is the characteristic length of the finite volume V$\prime $, a$_{0}\prime $ is the initial acoustic speed). The large local nondimensional temperature T$\prime $/T$_{0}\prime $=O(1/$\varepsilon )$ and speed u$\prime $/a$_{0}\prime $ =O(1/$\varepsilon ^{1/2})$ imply a large local acoustic speed and a significant local Mach number M$_{l}$=O(1), respectively, such that the kinetic and internal energies are commensurate. The shock Mach number, M$_{s}$=(1/$\varepsilon ^{1/2})$, is asymptotically large for the strong blast wave. It also follows that the relatively short local acoustic time t$_{al}\prime $= l$\prime $/a$\prime =\varepsilon ^{1/2}$t$_{a}\prime $ is commensurate with the energy addition time t$_{H}\prime $. The classical similarity solution for point deposition is obtained by seeking variable combinations independent of the vanishingly small artificial length scale l$\prime $. [Preview Abstract] |
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