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Regular versus Mach reflection for converging polygonal shocks
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
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.

Place, publisher, year, edition, pages
2007. Vol. 17, no 1-2, 43-50 p.
Keyword [en]
shock focusing; annular shock tube; imploding shock; shock reflection
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-7430DOI: 10.1007/s00193-007-0091-0ISI: 000248819100004Scopus ID: 2-s2.0-34547854293OAI: oai:DiVA.org:kth-7430DiVA: diva2:12455
Note
QC 20100707Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2012-05-21Bibliographically approved
In thesis
1. On focusing of shock waves
Open this publication in new window or tab >>On focusing of shock waves
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
converging shock, Euler equations, imploding shock, Mach reflection, regular reflection, shock focusing, shock tube
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-4479 (URN)978-91-7178-741-5 (ISBN)
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
2. On dynamics and thermal radiation of imploding shock waves
Open this publication in new window or tab >>On dynamics and thermal radiation of imploding shock waves
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Converging cylindrical shock waves have been studied experimentally. Numericalcalculations based on the Euler equations and analytical comparisons basedon the approximate theory of geometrical shock dynamics have been made tocomplement the study.Shock waves with circular or polygonal shock front shapes have been createdand focused in a shock tube. With initial Mach numbers ranging from 2 to4, the shock fronts accelerate as they converge. The shocked gas at the centreof convergence attains temperatures high enough to emit radiation which isvisible to the human eye. The strength and duration of the light pulse due toshock implosion depends on the medium. In this study, shock waves convergingin air and argon have been studied. In the latter case, the implosion lightpulse has a duration of roughly 10 μs. This enables non-intrusive spectrometricmeasurements on the gas conditions.Circular shock waves are very sensitive to disturbances which deform theshock front, decreasing repeatability. Shocks consisting of plane sides makingup a symmetrical polygon have a more stable behaviour during focusing,which provides less run-to-run variance in light strength. The radiation fromthe gas at the implosion centre has been studied photometrically and spectrometrically.Polygonal shocks were used to provide better repeatability. Thefull visible spectrum of the light pulse created by a shock wave in argon hasbeen recorded, showing the gas behaving as a blackbody radiator with apparenttemperatures up to 6000 K. This value is interpreted as a modest estimation ofthe temperatures actually achieved at the centre as the light has been collectedfrom an area larger than the bright gas core.As apparent from experimental data real gas effects must be taken intoconsideration for calculations at the implosion focal point. Ideal gas numericaland analytical solutions show temperatures and pressures approaching infinity,which is clearly not physical. Real gas effects due to ionisation of theargon atoms have been considered in the numerical work and its effect on thetemperature has been calculated.The propagation of circular and polygonal have also been experimentallystudied and compared to the self-similar theory and geometrical shock dynamics,showing good agreement.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2010. vii, 73 p.
Series
Trita-MEK, ISSN 0348-467X ; 2010:03
Keyword
converging shock waves, polygonal shock waves, temperature measurments, argon, plasma creation, ionisation, spectrometry
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-12365 (URN)978-91-7415-610-2 (ISBN)
Presentation
2010-04-16, S40, KTH, Teknikringen 8D, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
QC 20110502Available from: 2010-04-12 Created: 2010-04-12 Last updated: 2011-05-02Bibliographically approved
3. Energy concentration by converging shock waves in gases
Open this publication in new window or tab >>Energy concentration by converging shock waves in gases
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Converging shock waves have been studied experimentally in a shock tube, and numerically using inviscid calculations and the theory of geometrical shock dynamics. The converging shock waves were created in a shocktube with two modular test sections designed to create cylindrical respectively spherical waves. In the spherical case the shock waves take the shape of spherical cap before propagating into a cone, while the cylindrical shocks converge in a fully circular cylindrical chamber.

The dynamics and symmetry of circular and polygonal cylindrical shock waves with initial Mach numbers ranging from 2 to 4 were studied. The shocked gas at the centre of convergence attains temperatures high enough to emit radiation which is visible to the human eye. The strength and duration of the light pulse due to shock implosion depends on the medium. In this study, shock waves converging in air, argon, nitrogen and propane have been studied. Circular shock waves are very sensitive to disturbances which deform the shock front, decreasing repeatability. Shocks consisting of plane sides making up a symmetrical polygon have a more stable behaviour during focusing, which provides less run-to-run variance in light strength. The radiation from the gas at the implosion centre has been studied photometrically and spectrometrically. The full visible spectrum of the light pulse created by a shock wave in argon has been recorded, showing the gas behaving as a blackbody radiator with apparent temperatures up to 6,000 K. This value is interpreted as a modest estimation of the temperatures actually achieved at the centre as the light has been collected from an area larger than the bright gas core. Circular shock waves attained higher temperatures but the run-to-run variation was significant. The propagation of circular and polygonal shocks was also studied using schlieren photography and compared to the self-similar theory and geometrical shock dynamics, showing good agreement.

Real gas effects must be taken into consideration for calculations at the implosion focal point. Ideal gas numerical and analytical solutions show temperatures and pressures approaching infinity, which is clearly not physical. Real gas effects due to ionisation of the argon atoms have been considered in the numerical work and its effect on the temperature has been calculated.

A second convergent test section was manufactured, designed to smoothly transform a plane shock wave into the shape of a spherical cap. After the convergent transformation the spherical shock propagates through a conical section, where it is aimed to retain the spherical shape and converge in the tip of the truncated cone, which has an end radius of 0.3 mm. Spherical implosion is more efficient than cylindrical and the target volume is much smaller than that in the cylindrical chamber. The new set-up does not suffer from large losses through reflections. Spectrometric and photometrical measurements of the implosion show significantly stronger radiation of longer duration. Preliminary results show measured apparent blackbody temperatures up to 27,000 K during implosion of shock waves of initial Mach number MS = 3.9.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. vii, 80 p.
Series
Trita-MEK, ISSN 0348-467X ; 2012:09
National Category
Natural Sciences
Identifiers
urn:nbn:se:kth:diva-95186 (URN)978-91-7501-368-8 (ISBN)
Public defence
2012-05-25, D2, Lindstedtsvägen 5, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Note
QC 20120521Available from: 2012-05-21 Created: 2012-05-15 Last updated: 2012-05-21Bibliographically approved

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