Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session EQ: Reacting Flows II: Detonations & Modeling |
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Chair: David Kassoy, University of Colorado Room: 202B |
Sunday, November 23, 2008 4:10PM - 4:23PM |
EQ.00001: Effects of Stochasticity on Deflagration-to-Detonation Transition in Obstructed Channels V.N. Gamezo, E.S. Oran, T. Ogawa Deflagration-to-Detonation Transition (DDT) in obstructed channels involves multiple stochastic phenomena, including flow instabilities, turbulence, many interactions between shocks, flames, and vortices, and the resulting hot-spot formation. Since the detonation usually arises from one of many hot spots that stochastically appear in the system, there is some uncertainty in time and location for the detonation initiation. Small fluctuations of density, temperature, and composition play an important role in the development of stochasticity in experimental systems, which are also affected by uncertainties in initial conditions. The real cause of stochasticity, however, is embedded in the complexity of underlying physical phenomena, and can cause a stochastic behavior of numerical solutions that model these phenomena. Here we use a deterministic numerical model based on reactive Navier-Stokes equations that are solved using a deterministic method. Stochastic properties of the model system are evaluated using multiple numerical experiments for the same configuration. To trigger the stochastic response, we vary the initial background temperature within an interval of 0.01~K, which is too small to have systematic effects on the solution. Resulting run-up distances to DDT show a stochastic dispersion similar to that observed in physical experiments. [Preview Abstract] |
Sunday, November 23, 2008 4:23PM - 4:36PM |
EQ.00002: Initial-value problem for small perturbations in an idealized CJ detonation Carlos Chiquete, Anatoli Tumin The initial-value problem for perturbations in idealized overdriven detonations was considered by Erpenbeck (Phys. Fluids, Vol. 5, No. 1962, pp. 604-614) and Tumin (Phys. Fluids, Vol. 19, No. 10, 2007). The solution requires an analysis of fundamental solutions for homogeneous systems of ODEs of the direct and adjoint problems. Because the fundamental solutions can be singular at the end of the reaction zone, the initial-value problem requires a more detailed asymptotic analysis in the vicinity of the sonic point. Sharpe (PRSL A, Vol. 453, 1997, pp. 2603-2625) and Short et al. (JFM, Vol. 595, 2008, pp. 45-82) provided a rigorous asymptotic analysis of the direct problem in the case of idealized gaseous and condensed-phase models of detonations. In the present work, the asymptotic analysis of the adjoint problem in the vicinity of the sonic point is completed. Analysis of the fundamental solutions leads to a conclusion that the structure of the initial-value problem remains the same as for the overdriven detonation. [Preview Abstract] |
Sunday, November 23, 2008 4:36PM - 4:49PM |
EQ.00003: Detonation attenuation by a porous medium and its subsequent re-initiation Brian Maxwell, Matei Radulescu The detonation attenuation by a series of cross-flow cylinders, and its subsequent re-initiation mechanisms are studied experimentally and numerically, for a one-step chemically reacting fluid. A decrease in the scale of the blocking cylinders, or an increase in the number of the cylinders, is seen to delay the re-establishment of a self-sustained detonation. A detailed reconstruction of the detonation reflection and diffraction around the obstacles will be given, along with the complex flow fields involving wave reflections at the exit of the porous medium. The re-initiation mechanism is observed to be a function of not only the strength of wave reflections, but also the strength of the expansion wave following the reactive front, which affects the chemical kinetic rates behind the shock. A global model is proposed, which takes into account the momentum losses in terms of the flow blockage by the porous medium. [Preview Abstract] |
Sunday, November 23, 2008 4:49PM - 5:02PM |
EQ.00004: Simulations of Pulse Detonation Engines with MHD Thrust Augmentation Christopher Zeineh, Timothy Roth, Lord Cole, Ann Karagozian, Jean-Luc Cambier Pulse detonation rocket engines (PDREs) have received significant attention in recent years due to their potentially superior performance over constant-pressure engines. Yet unsteady chamber pressures cause the PDRE flow to be either over-expanded or under-expanded for the majority of the cycle, with substantial performance loss in atmospheric flight applications. The present computational studies examine the potential benefits of using magneto-hydrodynamic (MHD) thrust augmentation by extracting energy via a generator in the PDRE nozzle and applying it to a separate, secondary stream. In the present studies, which involve both transient quasi-1D and 2D numerical simulations, the energy extracted from the nozzle flow is directly applied to a by-pass air stream through an MHD accelerator. The air stream is first shocked by the under-expanded nozzle flow and raised to high temperature, allowing thermal ionization. The specific conditions for thrust augmentation are examined. Alternative configurations utilizing a magnetic piston in the PDRE chamber are also explored. Results show potential performance gains but with significant challenges, depending on the operating and flight conditions. [Preview Abstract] |
Sunday, November 23, 2008 5:02PM - 5:15PM |
EQ.00005: Solution of Reactive Compressible Flows Using an Adaptive Wavelet Method Zachary Zikoski, Samuel Paolucci, Joseph Powers This work presents numerical simulations of reactive compressible flow, including detailed multicomponent transport, using an adaptive wavelet algorithm. The algorithm allows for dynamic grid adaptation which enhances our ability to fully resolve all physically relevant scales. The thermodynamic properties, equation of state, and multicomponent transport properties are provided by CHEMKIN and TRANSPORT libraries. Results for viscous detonation in a H$_2$:O$_2$:Ar mixture, and other problems in multiple dimensions, are included. [Preview Abstract] |
Sunday, November 23, 2008 5:15PM - 5:28PM |
EQ.00006: Multidomain spectral collocation method for three-dimensional perturbations in idealized CJ detonations Anatoli Tumin, Carlos Chiquete The spectral collocation method for stability analysis of detonations allows computing the eigenvalue map for unstable modes. A multidomain version of the method provides more control over the distribution of the collocation points throughout the reaction zone. In the case of three-dimensional perturbations, the radiation condition that is usually used in the stability analysis is a nonlinear function of the eigenvalue, and it could not be incorporated explicitly into the spectral method. Recent rigorous asymptotic analysis of stability of detonations for an idealized condensed-phase model by M. Short et al. (JFM, 2008, Vol. 595, pp. 45-82) provides the radiation condition for three-dimensional perturbations that is a linear function of the eigenvalue for CJ detonations. The latter allows a direct inclusion of the radiation condition into the spectral method. In the present work, details of the multidomain spectral collocation method for CJ detonations are discussed. The results are illustrated by computations of eigenvalue maps for three-dimensional perturbations in gaseous and condensed-phase idealized one-dimensional detonations. [Preview Abstract] |
Sunday, November 23, 2008 5:28PM - 5:41PM |
EQ.00007: Multiscale Adaptive Model Reduction in Reactive Flows Samuel Paolucci, Mauro Valorani The numerical solution of mathematical models for reacting flows is a challenging task because of the simultaneous contribution of a wide range of time scales present in the system. However, the dynamics can develop very-slow and very-fast time scales separated by a range of active scales. The complexity of the problem can be reduced when fast/active and slow/active time scales gaps becomes large. We propose a numerical technique named the \textsl{G-Scheme}, to achieve multiscale adaptive model reduction. We assume that the dynamics is decomposed into active, slow, fast, and when applicable, invariant subspaces. We introduce a locally curvilinear frame of reference, defined by a set of orthonormal basis vectors, with corresponding coordinates, attached to this decomposition. The evolution of the coordinates associated with the active subspace is described by non-stiff DEs, whereas that associated with the slow and fast subspaces is accounted for by applying algebraic corrections derived from asymptotics of the original problem. Adjusting the active DEs dynamically during the time integration is the most significant feature of the \textsl{G-Scheme}, since the numerical integration is accomplished by solving a number of DEs typically much smaller than the dimension of the original problem. The effectiveness of the \textsl{G-Scheme}, is demonstrate by solving a number of relevant problems. [Preview Abstract] |
Sunday, November 23, 2008 5:41PM - 5:54PM |
EQ.00008: Effect of Initial Disturbance on The Detonation Front Structure Hua-Shu Dou, Boo Cheong Khoo Effect of initial disturbance on the detonation front structure is studied by 3D numerical simulation. The numerical method used is the high resolution computations using a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third order TVD Runge-Kutta time stepping method. Two types of disturbances are used to give perturbation for the detonation development in a narrow duct. One is the random disturbance which is imposed on the whole front, and another is the symmetrical disturbance, which is inputted within a band along the diagonal direction on the front. The results show that the developing processes of two kinds of disturbances in the detonation are different. For the random disturbance, the detonation front displays a stable spinning detonation. For the symmetrical diagonal disturbance, the detonation front displays a diagonal pattern at the earlier stage, but this pattern is unstable. Shortly, it breaks down and finally it evolves into a spinning detonation. The spinning detonations formed with the two types of disturbances are the same. This means that spinning detonation is the most stable mode for the simulated narrow duct. Therefore, for narrow ducts, implementing spinning detonation is the effect way to realize stable detonation as well as to speed the DDT (deflagration to detonation transition) process. [Preview Abstract] |
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