Shock Fitting For Converging Cylidrical Shocks In Hydrodynamics And Ideal Magnetohydrodynamics
KAUST DepartmentPhysical Science and Engineering (PSE) Division
Embargo End Date2022-07-12
Permanent link to this recordhttp://hdl.handle.net/10754/670162
MetadataShow full item record
Access RestrictionsAt the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis will become available to the public after the expiration of the embargo on 2022-07-12.
AbstractConverging shocks have long been a topic of interest in theoretical fluid mechanics, and are of prime importance in inertial confinement fusion. However, tracking converging shocks in numerical schemes poses several challenges. Numerical schemes based on shock capturing inherently diffuse out shocks to multiple grid cells, making it hard to track the shock. Converging shocks are significantly harder to track, as this numerical smearing is much more significant when converging shocks approach the axis of convergence. To mitigate this problem, we transform the conservation laws to a non-inertial frame of reference in which the accelerating shock is stationary. A system of equations is derived based on the transformed conservation laws coupled to the shock speed obtained from jump conditions and a characteristic-based derivation of a relation governing shock acceleration. We solve these equations using a finite volume method. Our numerical results compare favorably with the analytical value of Guderley exponent for self-similarly converging cylindrical hydrodynamic shocks. Results for fast magnetosonic shock in MHD are also presented and compared with results from geometrical shock dynamics (GSD). Results from our shock fitting method, developed without any approximation to the original ideal magnetohydrodynamics equations, provide further credibility to GSD applied to converging fast magnetosonic shocks. This sort of shock fitting is a precursor to future multidimensional stability analysis of imploding shocks.
CitationArshad, T. (2021). Shock Fitting For Converging Cylidrical Shocks In Hydrodynamics And Ideal Magnetohydrodynamics. KAUST Research Repository. https://doi.org/10.25781/KAUST-96M90
Showing items related by title, author, creator and subject.
Geometrical shock dynamics for magnetohydrodynamic fast shocksMostert, W.; Pullin, D. I.; Samtaney, Ravi; Wheatley, V. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016-12-12) [Article]We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Investigation on Shock Induced Stripping Breakup Process of A Liquid DropletLiu, Yao; Wen, Chihyung; Shen, Hua; Guan, Ben (21st AIAA International Space Planes and Hypersonics Technologies Conference, American Institute of Aeronautics and Astronautics (AIAA), 2017-03-02) [Conference Paper]Stripping breakup process of a single liquid droplet under the impact of a planar shock wave is investigated both experimentally and numerically. The droplet breakup experiment is conducted in a horizontal shock tube and the evolution of the droplet is recorded by direct high-speed photography. The experimental images clearly illustrate the droplet interface evolution features from its early to relatively late stage. Compressible Euler equations are solved using an in-house inviscid upwind characteristic space-time conservation element and solution element (CE/SE) method coupled with the HLLC approximate Riemann solver. A reduced five-equation model is employed to demonstrate the air/liquid interface. Numerical results accurately reproduce the water column and axi-symmetric water droplet breakup processes in experiments. The present study confirms the validity of the present numerical method in solving the shock wave induced droplet breakup problem and elaborates the stripping breakup process numerically in a long period. Droplet inner flow pattern is depicted, based on which the drives of protrusions emerged on the droplet surface are clearly seen. The droplet deformation is proved to be determined by not only the outer air flow, but also the inner liquid flow.
Numerical Study on Liquid Droplet Internal Flow Under Shock ImpactGuan, Ben; Liu, Yao; Wen, Chih-Yung; Shen, Hua (AIAA Journal, American Institute of Aeronautics and Astronautics (AIAA), 2018-08-01) [Article]The establishment of an internal flowfield inside a single water droplet subjected to shock-wave impact is numerically and theoretically investigated. The main focus is on the description of the droplet internal flow pattern, which is believed to be one of the dominant factors in initial droplet deformation. The droplet internal flow pattern holds steady for quite a long time after the incident shock passage, and a saddle point is observed for the first time. Accordingly, the saddle point inside the droplet flow is used as a characteristic point to describe the internal flow. Cases of different incident shock strengths are tested, and a theoretical prediction is proposed to delineate the correlation between the saddle point steady position and the strength of the incident shock wave. The numerical cases are found to be in good agreement with the prediction. The present study helps to complete the understanding of the overall droplet aerobreakup phenomenon.