Journal of Physics E: Scientific Instruments, 1971
... 505 Page 5. RJ Adrian and R J Goldstein perform the ensuing analysis for the simple case in w... more ... 505 Page 5. RJ Adrian and R J Goldstein perform the ensuing analysis for the simple case in which r= (ut, yo, ZO). ... where the Doppler frequency WD = ~ KU Sin 8 (=2?TVD) (16) is identical to equation (l), and A is the photocathode area illuminated by the scattered light waves. ...
ABSTRACT High-Speed Multi-Frame Laser Schlieren is used for visualization of a range of explosive... more ABSTRACT High-Speed Multi-Frame Laser Schlieren is used for visualization of a range of explosive and non-explosive events. Schlieren is a well-known technique for visualizing shock phenomena in transparent media. Laser backlighting and a framing camera allow for Schlieren images with very short (down to 5 ns) exposure times, band pass filtering to block out explosive self-light, and 14 frames of a single explosive event. This diagnostic has been applied to several explosive initiation events, such as exploding bridgewires (EBW), Exploding Foil Initiators (EFI) (or slappers), Direct Optical Initiation (DOI), and ElectroStatic Discharge (ESD). Additionally, a series of tests have been performed on "cut-back" detonators with varying initial pressing (IP) heights. We have also used this Diagnostic to visualize a range of EBW, EFI, and DOI full-up detonators. The setup has also been used to visualize a range of other explosive events, such as explosively driven metal shock experiments and explosively driven microjets. Future applications to other explosive events such as boosters and IHE booster evaluation will be discussed. Finite element codes (EPIC, CTH) have been used to analyze the schlieren images to determine likely boundary or initial conditions to determine the temporal-spatial pressure profile across the output face of the detonator. These experiments are part of a phased plan to understand the evolution of detonation in a detonator from initiation shock through run to detonation to full detonation to transition to booster and booster detonation.
Characteristics of the Karhunen–Loéve expansion of a strongly inhomogeneous random process posses... more Characteristics of the Karhunen–Loéve expansion of a strongly inhomogeneous random process possessing small viscous length scales and a large outer scale have been investigated in relation to the application of the expansion to turbulent flow fields. Monte Carlo simulations of a randomly forced Burgers’ equation with zero velocity boundary conditions generate the random process numerically and the Karhunen–Loéve (KL) eigenfunctions and the eigenvalue spectra are computed for different Reynolds numbers. The eigenfunctions possess thin viscous boundary layers at the walls and are independent of Reynolds number in the core, where the random process is quasihomogeneous. The eigenfunctions and eigenvalues of the outer, large scale motions obey a principle of Reynolds number similarity. Eigenvalue spectra contain much of the energy in the first few modes, but they are as broad as ordinary trigonometric power spectra. The rate at which the expansion converges to within 90% of the total ene...
Conditional averages of turbulent flow quantities can be approximated in terms of unconditional c... more Conditional averages of turbulent flow quantities can be approximated in terms of unconditional correlation data by means of stochastic estimation. The validity and accuracy of this procedure are investigated by comparing stochastic estimates to conditional averages measured in four turbulent flows: grid turbulence, the axisymmetric shear layer of a round jet, a plane shear layer, and pipe flow. Comparisons are made for quantities that are separated from the conditional data in time or space, and for turbulent pressures, as well as turbulent velocities. In each case, the linear estimate accurately represents large scale structure. Nonlinear quadratic estimation shows little improvement over linear estimation, because the second-order terms are small for probable values of the turbulent fluctuations.
Given their small size, microchannels are susceptible to being blocked by small amounts of solid ... more Given their small size, microchannels are susceptible to being blocked by small amounts of solid matter. The lifetime of certain microfluidic devices depends on their ability to maintain flow without interruption, and certain microfluidic applications require devices that include the transport of either liquids that may contain impurities or liquids that intentionally contain particles. Under the conditions studied in the
... schlieren photography, by particle image velocimetry (PIV) in air, and by PIV in transparent,... more ... schlieren photography, by particle image velocimetry (PIV) in air, and by PIV in transparent, polymeric witness plates. ... The visible light emitted from the aluminum chamber following each laser pulse results from laser-induced argon gas breakdown through multi-photon ...
The analysis of Reeks (1977) for particle dispersion in isotropic turbulence is extended so as to... more The analysis of Reeks (1977) for particle dispersion in isotropic turbulence is extended so as to include a nonlinear drag law. The principal issue is the evaluation of the inertial time constants, βα−1, and the mean slip. Unlike what is found for the Stokesian drag, the time constants are functions of the slip velocity and are anisotropic. For settling velocity, VT, much larger than root-mean-square of the fluid velocity fluctuations, u0, the mean slip is given by VT. For VT→0, the mean slip is related to turbulent velocity fluctuation by assuming that fluctuations in βα are small compared to the mean value. An interpolation formula is used to evaluate βα and VT in regions intermediate between conditions of VT→0 and VT≫ u0. The limitations of the analysis are explored by carrying out a Monte-Carlo simulation for particle motion in a pseudo turbulence described by a Gaussian distribution and Kraichnan’s (1970) energy spectrum.
Journal of Physics E: Scientific Instruments, 1971
... 505 Page 5. RJ Adrian and R J Goldstein perform the ensuing analysis for the simple case in w... more ... 505 Page 5. RJ Adrian and R J Goldstein perform the ensuing analysis for the simple case in which r= (ut, yo, ZO). ... where the Doppler frequency WD = ~ KU Sin 8 (=2?TVD) (16) is identical to equation (l), and A is the photocathode area illuminated by the scattered light waves. ...
ABSTRACT High-Speed Multi-Frame Laser Schlieren is used for visualization of a range of explosive... more ABSTRACT High-Speed Multi-Frame Laser Schlieren is used for visualization of a range of explosive and non-explosive events. Schlieren is a well-known technique for visualizing shock phenomena in transparent media. Laser backlighting and a framing camera allow for Schlieren images with very short (down to 5 ns) exposure times, band pass filtering to block out explosive self-light, and 14 frames of a single explosive event. This diagnostic has been applied to several explosive initiation events, such as exploding bridgewires (EBW), Exploding Foil Initiators (EFI) (or slappers), Direct Optical Initiation (DOI), and ElectroStatic Discharge (ESD). Additionally, a series of tests have been performed on "cut-back" detonators with varying initial pressing (IP) heights. We have also used this Diagnostic to visualize a range of EBW, EFI, and DOI full-up detonators. The setup has also been used to visualize a range of other explosive events, such as explosively driven metal shock experiments and explosively driven microjets. Future applications to other explosive events such as boosters and IHE booster evaluation will be discussed. Finite element codes (EPIC, CTH) have been used to analyze the schlieren images to determine likely boundary or initial conditions to determine the temporal-spatial pressure profile across the output face of the detonator. These experiments are part of a phased plan to understand the evolution of detonation in a detonator from initiation shock through run to detonation to full detonation to transition to booster and booster detonation.
Characteristics of the Karhunen–Loéve expansion of a strongly inhomogeneous random process posses... more Characteristics of the Karhunen–Loéve expansion of a strongly inhomogeneous random process possessing small viscous length scales and a large outer scale have been investigated in relation to the application of the expansion to turbulent flow fields. Monte Carlo simulations of a randomly forced Burgers’ equation with zero velocity boundary conditions generate the random process numerically and the Karhunen–Loéve (KL) eigenfunctions and the eigenvalue spectra are computed for different Reynolds numbers. The eigenfunctions possess thin viscous boundary layers at the walls and are independent of Reynolds number in the core, where the random process is quasihomogeneous. The eigenfunctions and eigenvalues of the outer, large scale motions obey a principle of Reynolds number similarity. Eigenvalue spectra contain much of the energy in the first few modes, but they are as broad as ordinary trigonometric power spectra. The rate at which the expansion converges to within 90% of the total ene...
Conditional averages of turbulent flow quantities can be approximated in terms of unconditional c... more Conditional averages of turbulent flow quantities can be approximated in terms of unconditional correlation data by means of stochastic estimation. The validity and accuracy of this procedure are investigated by comparing stochastic estimates to conditional averages measured in four turbulent flows: grid turbulence, the axisymmetric shear layer of a round jet, a plane shear layer, and pipe flow. Comparisons are made for quantities that are separated from the conditional data in time or space, and for turbulent pressures, as well as turbulent velocities. In each case, the linear estimate accurately represents large scale structure. Nonlinear quadratic estimation shows little improvement over linear estimation, because the second-order terms are small for probable values of the turbulent fluctuations.
Given their small size, microchannels are susceptible to being blocked by small amounts of solid ... more Given their small size, microchannels are susceptible to being blocked by small amounts of solid matter. The lifetime of certain microfluidic devices depends on their ability to maintain flow without interruption, and certain microfluidic applications require devices that include the transport of either liquids that may contain impurities or liquids that intentionally contain particles. Under the conditions studied in the
... schlieren photography, by particle image velocimetry (PIV) in air, and by PIV in transparent,... more ... schlieren photography, by particle image velocimetry (PIV) in air, and by PIV in transparent, polymeric witness plates. ... The visible light emitted from the aluminum chamber following each laser pulse results from laser-induced argon gas breakdown through multi-photon ...
The analysis of Reeks (1977) for particle dispersion in isotropic turbulence is extended so as to... more The analysis of Reeks (1977) for particle dispersion in isotropic turbulence is extended so as to include a nonlinear drag law. The principal issue is the evaluation of the inertial time constants, βα−1, and the mean slip. Unlike what is found for the Stokesian drag, the time constants are functions of the slip velocity and are anisotropic. For settling velocity, VT, much larger than root-mean-square of the fluid velocity fluctuations, u0, the mean slip is given by VT. For VT→0, the mean slip is related to turbulent velocity fluctuation by assuming that fluctuations in βα are small compared to the mean value. An interpolation formula is used to evaluate βα and VT in regions intermediate between conditions of VT→0 and VT≫ u0. The limitations of the analysis are explored by carrying out a Monte-Carlo simulation for particle motion in a pseudo turbulence described by a Gaussian distribution and Kraichnan’s (1970) energy spectrum.
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