Multi-Dimensional Adaptive Simulation of Shock-Induced Detonation in a Shock Tube (original) (raw)
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Computers & Structures, 2009
An adaptive finite volume approach is presented to accurately simulate shockinduced combustion phenomena in gases, particularly detonation waves. The method uses a Cartesian mesh that is dynamically adapted to embedded geometries and flow features by using regular refinement patches. The discretisation is a reliable linearised Riemann solver for thermally perfect gas mixtures; detailed kinetics are considered in an operator splitting approach. Besides easily reproducible ignition problems, the capabilities of the method and its parallel implementation are quantified and demonstrated for fully resolved triple point structure investigations of Chapman-Jouguet detonations in low-pressure hydrogen-oxygen-argon mixtures in two and three space dimensions.
Efficient simulation of multi-dimensional detonation phenomena
2002
The paper presents a solution strategy for Euler equations for multiple thermally perfect gaseous species with detailed chemical reaction. Via operator-splitting a high-resolution finite-volume scheme and a stiff ODE solver are coupled. A parallel blockstructured adaptive mesh refinement algorithm is utilized to achieve the required local resolution. A highly resolved computation of regular detonation-cell patterns of the hydrogen-oxygen-argon system demonstrates the efficiency of the entire approach.
High-resolution simulation of detonations with detailed chemistry
Analysis and Numerics For Conservation Laws, 2005
Numerical simulations can be the key to the thorough understanding of the multi-dimensional nature of transient detonation waves. But the accurate approximation of realistic detonations is extremely demanding, because a wide range of different scales need to be resolved. This paper describes an entire solution strategy for the Euler equations of thermally perfect gas-mixtures with detailed chemical kinetics that is based on a highly adaptive finite volume method for blockstructured Cartesian meshes. Large-scale simulations of unstable detonation structures of hydrogen-oxygen detonations demonstrate the efficiency of the approach in practice.
Parallel adaptive simulation of multi-dimensional detonation structures
2003
The approximation of transient detonation waves requires numerical methods that are able to resolve a wide range of different scales. Especially the accurate consideration of detailed chemical kinetics is extremely demanding. This thesis describes an efficient solution strategy for the Euler equations of gas dynamics for mixtures of thermally perfect species with detailed, non-equilibrium reaction that tackles the problem of source term stiffness by temporal and spatial dynamic mesh adaptation. All gas dynamically relevant scales are sufficiently resolved. The blockstructured adaptive mesh refinement technique of Berger and Colella is utilized to supply the required resolution locally on the basis of hydrodynamic refinement criteria. This adaptive method is tailored especially for time-explicit finite volume schemes and uses a hierarchy of spatially refined subgrids which are integrated recursively with reduced time steps. A parallelization strategy for distributed memory machines is developed and implemented. It follows a rigorous domain decomposition approach and partitions the entire grid hierarchy. A time-operator splitting technique is employed to decouple hydrodynamic transport and chemical reaction. It allows the separate numerical integration of the homogeneous Euler equations with time-explicit finite volume methods and the usage of an time-implicit discretization only for the stiff reaction terms. High-resolution shock capturing schemes are constructed for the homogeneous Euler equations with complex equation of state. In particular, a reliable hybrid Roe-solver-based method is derived. The scheme avoids unphysical values due to the Roe linearization and utilizes additional numerical viscosity to stabilize the approximation of strong shocks that inherently appear at the head of detonation waves. In different test configurations it is shown that this hybrid Roe-type method is superior for detonation simulation to any other method considered. Large-scale simulations of unstable detonation structures of hydrogen-oxygen detonations run on recent Beowulf clusters demonstrate the efficiency of the entire approach. In particular, computations of regular cellular structures in two and three space dimensions and their development under transient conditions, e.g. Mach reflection and diffraction, are presented. The achieved resolutions go far beyond previously published results and provide new reference solutions. I want to thank my thesis advisor Prof. Dr. Georg Bader for his continuing interest and support of my work. His generosity to share his ideas with me was the starting point for the work of this thesis. After pushing things forward he gave me the opportunity to develop an independent research. He provided me with the necessary computational resources and never rested in assuring a modern parallel working environment even under difficult circumstances. I would like to express my special thanks to Prof. Dr. Rolf Rannacher for supporting my usage of the HEidelberg LInux Cluster System, one of the world-fastest Linux Beowulf-clusters. The large-scale simulations in this thesis would not have been possible without the access to this competitive system. I am grateful to Dr. Klaus Schenk who prepared the project 'Analysis and Simulation of Flows for Multicomponent Gas-Mixtures' within the DFG-priority research program 'Analysis and Numerics of Conservation Laws' that supported me during my entire work. This thesis is based mainly on results of this long-term project and applies them to the important problem class of detonation waves. Only the support of the ANumE program gave me the opportunity to present parts of my work on international meetings. Finally, I thank Dr. Guntram Berti for reading a draft version of the whole manuscript and his helpful comments.
A Gaskinetic Scheme for Nonequilibrium Planar Shock Simulations
47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, 2009
This paper reports some preliminary progress in developing a gaskinetic Computational Fluid Dynamic scheme, based on the Bhatnagar-Gross-Krook(BGK) model, to simulate a planar nitrogen shock wave with thermochemical nonequilibrium effects. The scheme is applicable for gas flows with thermal nonequilibrium effects, i.e., translational, rotational and vibrational energy relaxations, and with dissociation and recombination chemical reactions. We determine the post-shock boundary conditions with a consideration of detailed equilibrium satisfying general Rankine-Hugoniot relations. Different from those past studies which are based on the Boltzmann-like equation and split the collision term into elastic and chemical collision terms, here we consider the chemical reactions by treating them as source terms. This treatment renders us a much simpler scheme than gaskinetic schemes relying on detailed collisions. The merits of this scheme include a relatively faster computation speed than particle simulation methods and gaskinetic schemes based on the full Boltzmann equation. The gaskinetic BGK simulation results are validated with those obtained with the direct simulation Monte Carlo (DSMC) method.
Development and validation of the hybrid code for numerical simulation of detonations
Journal of Physics: Conference Series, 2018
The present paper describes a numerical code for simulation of detonation flows on hybrid computational clusters (CPU/GPU). The code can solve 1D, 2D and 3D unsteady Euler equations for multispecies chemically reacting flows using high-order shock-capturing TVD schemes and a finite-rate chemistry solver. The implementation is based on the OpenMP, MPI and CUDA technologies allowing for both flexibility and computational efficiency of the code. The program is verified on the analytical Zeldovich-von Neumann-Doering solution for the 1D detonation wave in H 2 /O 2 mixture. Some examples of 2D computations are also given.
International Journal of Hydrogen Energy, 2016
Detonation combustion initiated with a hot jet in supersonic H2-O2-Ar mixtures are investigated by large-scale three-dimensional (3D) simulations in Tianhe-2 computing system with adaptive mesh refinement method. The reactive Euler equations are utilized as the governing equations with a detailed reaction model where the molar ratio of the combustible mixture is 2:1:7 under the condition of pressure 10kPa and temperature 298K. Results show that the Mach stem surface which is formed after the shock surface reflection on the upper wall is actually a local overdriven detonation. The side walls in 3D simulations can play an important role in detonation initiation in supersonic combustible mixtures, because they can help realize triple lines collisions and reflections during the initiation process. The width of the channel has an important influence on the strength of side-wall reflections, and under certain condition there might exist a critical width between the front and back sides of the Corresponding author.
A high-resolution method for realistic detonation structure simulation
2006
Detonation simulation is one of the computationally most challenging hyperbolic problems of practical interest. The source terms from detailed non-equilibrium chemistry are usually stiff and introduce non-neglectable scales typically not present in purely hydrodynamic calculations. This paper outlines all components of an efficient solution strategy. Emphasis is put on the description of the employed shock-capturing scheme and the necessary extensions of the underlying approximative Riemann solver for thermally perfect multi-component Euler equations. Computational results confirm effectiveness and relevancy of the approach.
Novel modeling of hydrogen/oxygen detonation
2000
A standard ignition delay problem for a mixture of hydrogen, oxygen, and argon in a shock tube is extended to the viscous regime and solved using the method of Intrinsic Low Dimensional Manifolds (ILDM) coupled with a Wavelet Adaptive Multilevel Representation (WAMR) spatial discretization technique. An operator splitting method is used to describe the reactions as a system of ordinary differential equations at each spatial point. The ILDM method is used to eliminate the stiffness associated with the chemistry by decoupling processes which evolve on fast and slow time scales. The fast time scale processes are systematically equilibrated, thereby reducing the dimension of the phase space required to describe the reactive system. The WAMR captures the detailed spatial structures automatically with a small number of basis functions thereby further reducing the number of variables required to describe the system. Using a maximum of only 300 collocation points and 15 scale levels allows results with striking resolution of fine scale viscous and induction zones to be obtained. Additionally, the resolution of physical diffusion processes minimizes the effects of potentially reaction-inducing artificial entropy layers associated with numerical diffusion.