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Detonation of Gaseous Mixtures
Published in Kenneth M. Bryden, Kenneth W. Ragland, Song-Charng Kong, Combustion Engineering, 2022
Kenneth M. Bryden, Kenneth W. Ragland, Song-Charng Kong
Consider a combustible mixture of gaseous fuel and air in a long tube. The mixture is ignited at the closed end of the tube. A flame forms and begins to propagate along the tube at laminar flame speed. The propagating flame gradually loses its smooth shape and becomes wrinkled. As a result of the increase in effective flame surface, the flame accelerates with respect to the unburned gas. The wrinkled, fluctuating flame front generates turbulence and weak pressure pulses that run ahead of the flame front and gradually preheat the gas ahead of the flame, causing the flame to speed up. High-speed Schlieren photography (a light-scattering technique sensitive to density gradients) of the transition from a flame (subsonic combustion–deflagration) to a detonation (supersonic combustion) shows that as the flame accelerates, the pressure pulses become stronger, coalesce, and further preheat the gas ahead of the flame. Eventually, a pocket of gas ahead of the flame reaches its autoignition temperature and produces a local explosion. The rapidly expanding gases produce a shock wave that interacts with the walls, sending a forward propagating shock that rapidly ignites the fuel ahead and a backward moving shock that dies out. The forward moving shock–combustion complex is a detonation, and the rearward moving shock is called a retonation (Figure 8.1). This process is called the deflagration-to-detonation transition (DDT). Note that the velocity can be obtained from the slope of the various lines indicated in Figure 8.1.
Governing Equations of Fluid Mechanics and Heat Transfer
Published in Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 2020
Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar
where Vn and Vt are the normal and tangential components of the velocity vector, respectively. These equations also apply to moving shock waves if the velocity components are measured with respect to the moving shock wave. In this case, the normal component of the flow velocity ahead of the shock (measured with respect to the shock) can be related to the pressure behind the shock by manipulating the previous equations to form Vn12=γ+12p1ρ1(p2ρ1+γ−1γ+1)
Compressible flow of gases
Published in Bernard S. Massey, John Ward-Smith, Mechanics of Fluids, 2018
Bernard S. Massey, John Ward-Smith
Since u1 is the upstream velocity relative to the shock wave this result expresses the velocity with which a moving shock advances into stationary fluid. For an infinitesimal pressure change p2/p1 = 1 and the expression reduces to the velocity of sound (p1γ/ρ1). For values of p2/p1 greater than unity, the velocity of propagation is always greater than the velocity of sound. Thus the shock waves produced by explosions, for example, are propagated with velocities in excess of sonic velocity.
A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation laws
Published in International Journal of Computational Fluid Dynamics, 2020
Huaibao Zhang, Guangxue Wang, Fan Zhang
The shock/density-wave interaction problem of Shu and Osher (1989) is characterised by a right-moving shock wave of Mach number 3 interacting with high-frequency sine waves in the density field. This problem is initialised by A multi-scale wave structure evolves after the shock wave interacts with the oscillating density wave, and both shock-capturing and wave-resolution capabilities are evaluated for the methods considered herein via this problem. This case is run on a grid of N = 201 points which are uniformly distributed, and the final computing time is t = 1.8. Since there is no theoretical solution for this problem, a fine-grid numerical solution via the WENO-MR on a grid of N = 2001 points is used as a reference.
Problem-independent nonlinear switch for newly designed WENO-BO-Z scheme
Published in International Journal of Computational Fluid Dynamics, 2019
Ghulam M. Arshed, Ovais U. Khan
The initial conditions for the Shu-Osher problem (Shu and Osher 1989) are given by with zero-order extrapolation boundary conditions. A moving shock wave at is interacting with an entropy wave of amplitude and wavenumber . The initial entropy wave in a still fluid is moving ahead of the shock wave. Its interaction with the shock wave results in an amplified refracted entropy wave with a higher wavenumber and a generated acoustic wave comprising shocklets and travelling faster with almost the same wavenumber as the incident entropy wave. The numerical solution computed over 201 grid points and the reference solution computed over 4001 grid points are presented at , when the shock location is at (Figure 3). Both the problem-dependent switch (2.19) and problem-independent switch (2.21) are almost equally capable of capturing the resolution of each wave. However, the former switch is more capable, especially at the problematic interface () between the generated acoustic and the refracted entropy waves and in the portion of the refracted entropy wave immediately next to this interface.
Development of a Modified Seventh-Order WENO Scheme with New Nonlinear Weights
Published in International Journal of Computational Fluid Dynamics, 2021
Kaveh Fardipour, Kamyar Mansour
Interaction between a moving shock wave and an interface between two fluids leads to the development of a spike. Over time, roll-up and mixing of two fluid regions evolve around this spike. Figure 16 shows density profiles of these results with 20 uniformly spaced levels ranging from 1 to 8 at . We enlarged these contours around the spike for better comparison. One can observe in this figure, roll-up and mixing evolve more for the modified scheme, which shows this scheme has lower numerical dissipation.