Planar shock cylindrical focusing by a perfect-gas lens

P. E. Dimotakis; R. Samtaney

doi:10.1063/1.2186553

Planar shock cylindrical focusing by a perfect-gas lens

P. E. Dimotakis^*, R. Samtaney

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

Abstract

We document a gas lensing technique that generates a converging shock wave in a two-dimensional wedge geometry. A successful design must satisfy three criteria at the contact point between the gas lens and the wedge leading edge to minimize nonlinear reflected and other wave effects. The result is a single-point solution in a multidimensional parameter space. The gas lens shape is computed using shock-polar analysis for regular refraction of the incident shock at the gas lens interface. For the range of parameters investigated, the required gas-lens interface is closely matched by an ellipse or hyperbola. Nonlinear Euler simulations confirm the analysis and that the transmitted shock is circular. As the converging transmitted shock propagates down the wedge, its shape remains nearly uniform with less than 0.1% peak departures from a perfect circular cylinder segment. Departure from the design criteria leads to converging shocks that depart from the required shape. The sensitivity to incident shock Mach number, as well as the qualitative effects of the presence of boundary layers are also discussed.

Original language	English (US)
Article number	031705
Journal	Physics of Fluids
Volume	18
Issue number	3
DOIs	https://doi.org/10.1063/1.2186553
State	Published - Mar 2006
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to acknowledge discussions with Paul Miller, Omar Hurricane, and Karnig Mikaelian of the Lawrence Livermore National Laboratory (LLNL), as well as discussions and exchanges with Hans Hornung, Dale Pullin, Dan Meiron, Amy Lam, and David Hill of Caltech. This work was performed under the auspices of the U.S. Department of Energy by the U.C. LLNL, under Contract No. W-7405-Eng-48, DOE/Caltech ASC/ASAP Subcontract No. B341492.

Keywords

Aerodynamics
Boundary layers
Flow simulation
Mach number
Shock waves

ASJC Scopus subject areas

Computational Mechanics
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes

Access to Document

10.1063/1.2186553

Cite this

@article{a49aab432cf84906a9b489f716603092,

title = "Planar shock cylindrical focusing by a perfect-gas lens",

abstract = "We document a gas lensing technique that generates a converging shock wave in a two-dimensional wedge geometry. A successful design must satisfy three criteria at the contact point between the gas lens and the wedge leading edge to minimize nonlinear reflected and other wave effects. The result is a single-point solution in a multidimensional parameter space. The gas lens shape is computed using shock-polar analysis for regular refraction of the incident shock at the gas lens interface. For the range of parameters investigated, the required gas-lens interface is closely matched by an ellipse or hyperbola. Nonlinear Euler simulations confirm the analysis and that the transmitted shock is circular. As the converging transmitted shock propagates down the wedge, its shape remains nearly uniform with less than 0.1% peak departures from a perfect circular cylinder segment. Departure from the design criteria leads to converging shocks that depart from the required shape. The sensitivity to incident shock Mach number, as well as the qualitative effects of the presence of boundary layers are also discussed.",

keywords = "Aerodynamics, Boundary layers, Flow simulation, Mach number, Shock waves",

author = "Dimotakis, {P. E.} and R. Samtaney",

note = "Funding Information: The authors would like to acknowledge discussions with Paul Miller, Omar Hurricane, and Karnig Mikaelian of the Lawrence Livermore National Laboratory (LLNL), as well as discussions and exchanges with Hans Hornung, Dale Pullin, Dan Meiron, Amy Lam, and David Hill of Caltech. This work was performed under the auspices of the U.S. Department of Energy by the U.C. LLNL, under Contract No. W-7405-Eng-48, DOE/Caltech ASC/ASAP Subcontract No. B341492.",

year = "2006",

month = mar,

doi = "10.1063/1.2186553",

language = "English (US)",

volume = "18",

journal = "Physics of Fluids",

issn = "1070-6631",

publisher = "AIP Publishing",

number = "3",

}

TY - JOUR

T1 - Planar shock cylindrical focusing by a perfect-gas lens

AU - Dimotakis, P. E.

AU - Samtaney, R.

N1 - Funding Information: The authors would like to acknowledge discussions with Paul Miller, Omar Hurricane, and Karnig Mikaelian of the Lawrence Livermore National Laboratory (LLNL), as well as discussions and exchanges with Hans Hornung, Dale Pullin, Dan Meiron, Amy Lam, and David Hill of Caltech. This work was performed under the auspices of the U.S. Department of Energy by the U.C. LLNL, under Contract No. W-7405-Eng-48, DOE/Caltech ASC/ASAP Subcontract No. B341492.

PY - 2006/3

Y1 - 2006/3

N2 - We document a gas lensing technique that generates a converging shock wave in a two-dimensional wedge geometry. A successful design must satisfy three criteria at the contact point between the gas lens and the wedge leading edge to minimize nonlinear reflected and other wave effects. The result is a single-point solution in a multidimensional parameter space. The gas lens shape is computed using shock-polar analysis for regular refraction of the incident shock at the gas lens interface. For the range of parameters investigated, the required gas-lens interface is closely matched by an ellipse or hyperbola. Nonlinear Euler simulations confirm the analysis and that the transmitted shock is circular. As the converging transmitted shock propagates down the wedge, its shape remains nearly uniform with less than 0.1% peak departures from a perfect circular cylinder segment. Departure from the design criteria leads to converging shocks that depart from the required shape. The sensitivity to incident shock Mach number, as well as the qualitative effects of the presence of boundary layers are also discussed.

AB - We document a gas lensing technique that generates a converging shock wave in a two-dimensional wedge geometry. A successful design must satisfy three criteria at the contact point between the gas lens and the wedge leading edge to minimize nonlinear reflected and other wave effects. The result is a single-point solution in a multidimensional parameter space. The gas lens shape is computed using shock-polar analysis for regular refraction of the incident shock at the gas lens interface. For the range of parameters investigated, the required gas-lens interface is closely matched by an ellipse or hyperbola. Nonlinear Euler simulations confirm the analysis and that the transmitted shock is circular. As the converging transmitted shock propagates down the wedge, its shape remains nearly uniform with less than 0.1% peak departures from a perfect circular cylinder segment. Departure from the design criteria leads to converging shocks that depart from the required shape. The sensitivity to incident shock Mach number, as well as the qualitative effects of the presence of boundary layers are also discussed.

KW - Aerodynamics

KW - Boundary layers

KW - Flow simulation

KW - Mach number

KW - Shock waves

UR - http://www.scopus.com/inward/record.url?scp=33645471930&partnerID=8YFLogxK

U2 - 10.1063/1.2186553

DO - 10.1063/1.2186553

M3 - Article

AN - SCOPUS:33645471930

SN - 1070-6631

VL - 18

JO - Physics of Fluids

JF - Physics of Fluids

IS - 3

M1 - 031705

ER -

Planar shock cylindrical focusing by a perfect-gas lens

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this