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On focusing of shock waves
KTH, School of Engineering Sciences (SCI), Mechanics.
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Both experimental and numerical investigations of converging shock waves have been performed. In the experiments, a shock tube was used to create and study converging shock waves of various geometrical shapes. Two methods were used to create polygonally shaped shocks. In the first method, the geometry of the outer boundary of the test section of the shock tube was varied. Four different exchangeable shapes of the outer boundary were considered: a circle, a smooth pentagon, a heptagon, and an octagon. In the second method, an initially cylindrical shock wave was perturbed by metal cylinders placed in various patterns and positions inside the test section. For three or more regularly spaced cylinders, the resulting diffracted shock fronts formed polygonal shaped patterns near the point of focus. Regular reflection was observed for the case with three cylinders and Mach refection was observed for cases with four or more cylinders. When the shock wave is close to the center of convergence, light emission is observed. An experimental investigation of the light emission was conducted and results show that the shape of the shock wave close to the center of convergence has a large influence on the amount of emitted light. It was found that a symmetrical polygonal shock front produced more light than an asymmetrical shape.

The shock wave focusing was also studied numerically using the Euler equations for a gas obeying the ideal gas law with constant specific heats. Two problems were analyzed; an axisymmetric model of the shock tube used in the experiments and a cylindrical shock wave diffracted by cylinders in a two dimensional test section. The results showed good agreement with the experiments. The temperature field from the numerical simulations was investigated and shows that the triple points behind the shock front are hot spots that increase the temperature at the center as they arrive there.

As a practical example of shock wave focusing, converging shocks in an electrohydraulic lithotripter were simulated. The maximum radius of a gas bubble subjected to the pressure field obtained from the lithotripter was calculated and compared for various geometrical shapes and materials of the reflector. Results showed that the shape had a large impact while the material did not influence the maximum radius of the gas bubble.

Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , vii, 73 p.
Series
Trita-MEK, ISSN 0348-467X ; 2007:06
Keyword [en]
converging shock, Euler equations, imploding shock, Mach reflection, regular reflection, shock focusing, shock tube
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-4479ISBN: 978-91-7178-741-5 (print)OAI: oai:DiVA.org:kth-4479DiVA: diva2:12458
Public defence
2007-09-21, F3, Valhallavägen 79, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20100706Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2010-07-06Bibliographically approved
List of papers
1. Focusing of strong shocks in an annular shock tube
Open this publication in new window or tab >>Focusing of strong shocks in an annular shock tube
2007 (English)In: Shock Waves, ISSN 0938-1287, E-ISSN 1432-2153, Vol. 15, no 3-4, 205-217 p.Article in journal (Refereed) Published
Abstract [en]

Focusing of strong shock waves in a gas-filled thin convergence chamber with various forms of the reflector boundary is investigated experimentally and numerically. The convergence chamber is mounted at the end of the horizontal co-axial shock tube. The construction of the convergence chamber allows the assembly of the outer chamber boundaries of various shapes. Boundaries with three different shapes have been used in the present investigation-a circle, an octagon and a smooth pentagon. The shock tube in the current study was able to produce annular shocks with the initial Mach number in the range M-s = 2.3-3.6. The influence of the shape of the boundary on the shape and properties of the converging and reflected shock waves in the chamber has then been investigated both experimentally and numerically. It was found that the form of the converging shock is initially governed by the shape of the reflector and the nonlinear interaction between the shape of the shock and velocity of shock propagation. Very close to the center of convergence the shock obtains a square-like form in case of a circular and octagonal reflector boundary. This is believed to stem from the instability of the converging shock front triggered by the disturbances in the flow field. The outgoing, reflected shocks were also observed to be influenced by the shape of the boundary through the flow ahead as created by the converging shocks.

Keyword
shock focusing, annular shock tube, converging shock, reflected shock, AUFS vector splitting scheme
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-7427 (URN)10.1007/s00193-006-0035-0 (DOI)000239249200005 ()2-s2.0-33746453712 (Scopus ID)
Note

QC 20141128

Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2017-12-14Bibliographically approved
2. Controlling the form of strong converging shocks by means of disturbances.
Open this publication in new window or tab >>Controlling the form of strong converging shocks by means of disturbances.
2007 (English)In: Shock Waves, ISSN 0938-1287, E-ISSN 1432-2153, Vol. 17, no 1-2, 29-42 p.Article in journal (Refereed) Published
Abstract [en]

The influence of artificial disturbances on the behavior of strong converging cylindrical shocks is investigated experimentally and numerically. Ring-shaped shocks, generated in an annular cross sectional shock tube are transformed to converging cylindrical shocks in a thin cylindrical test section, mounted at the rear end of the shock tube. The converging cylindrical shocks are perturbed by small cylinders placed at different locations and in various patterns in the test section. Their influence on the shock convergence and reflection process is investigated. It is found that disturbances arranged in a symmetrical pattern will produce a symmetrical deformation of the converging shockfront. For example, a square formation produces a square-like shock and an octagon formation a shock with an octagonal front. This introduces an alternative way of tailoring the form of a converging shock, instead of using a specific form of a reflector boundary. The influence of disturbances arranged in non-symmetric patterns on the shape of the shockfront is also investigated.

Keyword
shock focusing; annular shock tube; imploding shock
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-7428 (URN)10.1007/s00193-007-0087-9 (DOI)000248819100003 ()2-s2.0-34547906425 (Scopus ID)
Note
QC 20100706 Tidigare titel: Controlling the form of strong converging shocks(20101126)Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2017-12-14Bibliographically approved
3. The Production of Converging Polygonal Shock Waves by Means of Reflectors and Cylindrical Obstacles
Open this publication in new window or tab >>The Production of Converging Polygonal Shock Waves by Means of Reflectors and Cylindrical Obstacles
2006 (English)In: Flow Dynamics / [ed] Tokuyama, M; Maruyama, S, 2006, Vol. 832, 445-449 p.Conference paper, Published paper (Refereed)
Abstract [en]

Converging and reflecting strong shock waves are investigated experimentally in a horizontal co-axial shock tube. The shock tube has a test section mounted at the end of the tube. Two different methods to produce various geometrical shapes of shock waves are tested. In the first method the reflector boundary of the test section is exchangeable and four different reflectors are used: a circle, a smooth pentagon, a heptagon and an octagon. It is shown that the form of the converging shock wave is influenced both by the shape of the reflector boundary and by the nonlinear dynamics between the shape of the shock and the velocity of the shock front. Further, the reflected outgoing shock wave is affected by the shape of the reflector through the flow ahead of the shock front. In the second method we use cylindrical obstacles, placed in the test section at various positions and patterns, to create disturbances in the flow that will shape the shock wave. It is shown that it is possible to shape the shock wave in a desired way with these obstacles. The influence of the supports of the inner body of the co-axial shock tube is also investigated. A square shaped shock wave is observed close to the center of convergence for the circular and octagonal reflectors but not in any other setups. This square-like shape is believed to be caused by the supports for the inner body.

Series
AIP CONFERENCE PROCEEDINGS, ISSN 0094-243X ; 832
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-7429 (URN)10.1063/1.2204539 (DOI)000237700400083 ()2-s2.0-33845448117 (Scopus ID)0-7354-0324-4 (ISBN)
Conference
2nd International Conference on Flow Dynamics Location: Sendai, JAPAN Date: NOV 16-18, 2005
Note
QC 20100707. Previous title: The production of strong converging shocksAvailable from: 2007-08-31 Created: 2007-08-31 Last updated: 2011-10-05Bibliographically approved
4. Regular versus Mach reflection for converging polygonal shocks
Open this publication in new window or tab >>Regular versus Mach reflection for converging polygonal shocks
2007 (English)In: Shock Waves, ISSN 0938-1287, E-ISSN 1432-2153, Vol. 17, no 1-2, 43-50 p.Article in journal (Refereed) Published
Abstract [en]

The onset of Mach reflection or regular reflection at the vertices of a converging polygonal shock wave was investigated experimentally in a horizontal annular shock tube. The converging shock waves were visualized by schlieren optics. Two different types of polygonal shock convergence patterns were observed. We compared the behavior during the focusing process for triangular and square-shaped shocks. It is shown that once a triangular shaped shock is formed, the corners in the converging shock will undergo regular reflection and consequently the shape will remain unaltered during the focusing process. A square-shaped shock suffers Mach reflections at the corners and hence a reconfiguring process takes place; the converging shock wave alternates between a square and an octagon formation during the focusing process.

Keyword
shock focusing; annular shock tube; imploding shock; shock reflection
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-7430 (URN)10.1007/s00193-007-0091-0 (DOI)000248819100004 ()2-s2.0-34547854293 (Scopus ID)
Note
QC 20100707Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2017-12-14Bibliographically approved
5. Light emission during shock wave focusing in air and argon
Open this publication in new window or tab >>Light emission during shock wave focusing in air and argon
2007 (English)In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 19, no 10, 106106-1-106106-17 p.Article in journal (Refereed) Published
Abstract [en]

The light emission from a converging shock wave was investigated experimentally. Results show that the shape of the shock wave close to the center of convergence has a large influence on the amount of emitted light. It was found that a symmetrical polygonal shock front produced more light than an asymmetrical shape. The light emission appears as the shock wave collapses. The full width at half maximum of the light pulse is about 200 ns for all geometrical shapes. It was also found that argon as a test gas produces more light than air. Numerical simulations showed good agreement with experimental results regarding the shape of the shock and the flow field behind the shock. The temperature field from the numerical simulations was investigated and shows that the triple points behind the shock front are hot spots that increase the temperature at the center as they arrive there.

Keyword
Argon; Computer simulation; Flow fields; Light emission; Temperature distribution
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-7431 (URN)10.1063/1.2796214 (DOI)000250589600059 ()2-s2.0-35748937956 (Scopus ID)
Note
QC 20100707. Uppdaterad från Submitted till Published 20100707.Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2017-12-14Bibliographically approved
6. On cylindrically converging shock waves shaped by obstacles
Open this publication in new window or tab >>On cylindrically converging shock waves shaped by obstacles
2008 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 237, no 14-17, 2203-2209 p.Article in journal (Refereed) Published
Abstract [en]

Motivated by recent experiments, numerical simulations of cylindrically converging shock waves were performed. The converging shocks impinged upon a set of 0-16 regularly space obstacles. For more than two obstacles the resulting diffracted shock fronts formed polygonal shaped patterns near the point of focus. The maximum pressure and temperature as a function of the number of obstacles were studied. The self-similar behavior of cylindrical, triangular and square-shaped shocks was also investigated.

Keyword
converging shock; Mach reflection; regular reflection; adaptive mesh refinement; overlapping structured grids
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-7432 (URN)10.1016/j.physd.2007.11.021 (DOI)000258508000053 ()2-s2.0-47049118945 (Scopus ID)
Note
QC 20100707. Uppdaterad från Submitted till Published 20100707.Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2017-12-14Bibliographically approved

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