The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

The relationship between the upstream boundary layer and the low-frequency, large-scale unsteadiness of the separated flow in a Mach 2 compression ramp interaction is investigated by performing wide-field particle image velocimetry (PIV) and planar laser scattering (PLS) measurements in streamwise–spanwise planes. Planar laser scattering measurements in the upstream boundary layer indicate the presence of spanwise strips of elongated regions of uniform momentum with lengths greater than 40?. These long coherent structures have been observed in a Mach 2 supersonic boundary layer (Ganapathisubramani, Clemens & Dolling 2006) and they exhibit strong similarities to those that have been found in incompressible boundary layers (Tomkins & Adrian 2003; Ganapathisubramani, Longmire & Marusic 2003). At a wall-normal location of y/?=0.2, the inferred instantaneous separation line of the separation region is found to oscillate between x/?=?3 and ?1 (where x/?=0 is the ramp corner). The instantaneous spanwise separation line is found to respond to the elongated regions of uniform momentum. It is shown that high- and low-momentum regions are correlated with smaller and larger size of the separation region, respectively. Furthermore, the instantaneous separation line exhibits large-scale undulations that conform to the low- and high-speed regions in the upstream boundary layer. The low-frequency unsteadiness of the separation region/shock foot observed in numerous previous studies can be explained by a turbulent mechanism that includes these elongated regions of uniform momentum

Effects of upstream boundary layer on the unsteadiness of shock induced separation

A practical introduction to signal processing in scientific measurement, for scientists, engineers, researchers, instructors, and students working in academia, industry, environmental, medical, engineering, earth science, space, military, financial, and agriculture. Includes such topics as smoothing, differentiation, peak detection, integration and peak area measurements, harmonic analysis, convolution and deconvolution, Fourier filtering, least-squares curve fitting, multi-component spectroscopy, nonlinear iterative least-squares peak fitting. Provides many demonstrations and real data examples, plus download links to many free Matlab/Octave scripts and functions plus spreadsheet templates which has been widely used and have been cited in over 160 published papers, theses, and patents. Includes an appendix containing case studies, examples, and simulations, plus an alphabetical index.

A Pragmatic Introduction to Signal Processing: with applications in scientific measurement

Thank you very much for reading laser diagnostics for combustion temperature and species. As you may know, people have search numerous times for their favorite readings like this laser diagnostics for combustion temperature and species, but end up in infectious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some infectious virus inside their desktop computer.

Laser Diagnostics For Combustion Temperature And Species

Weapons and weapon systems/Conventional weapons; Weapons and weapon systems/Weapon systems; Military

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Conventional Prompt Global Strike and Long-Range Ballistic Missiles: Background and Issues [February 3, 2017]

The titular technique, KTV, is an important development in the field of laser diagnostics for supersonic and hypersonic flows, as it gives access to unexplored regimes. KTV is not plagued by the fundamental limitations of traditional tracer-particle techniques. The authors investigate the boundary-layer profiles that form over a sharp, hollow cylinder in supersonic flows of air and N${}_{2}$ via a single-laser scheme. With the use of high-repetition-rate lasers, this simple, cost-effective evaluation tool for large facilities will allow for time-resolved measurements of turbulent flows, for $e.g.$ the development of high-speed vehicles such as bullet trains.

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Single-Laser Krypton Tagging Velocimetry Investigation of Supersonic Air and N 2 Boundary-Layer Flows over a Hollow Cylinder in a Shock Tube

Seven profiles of streamwise velocity and velocity fluctuations were measured in the incoming boundary layer and immediately upstream of a 24-degree compression corner in a M∞ = 2.8, ReΘ = 1750 shock-wave/turbulent boundary-layer interaction. The measurements were made with Krypton Tagging Velocimetry (KTV) in 99% N2/1% Kr flow. Globally seeding 1% Kr into the flow (premixed N2/Kr K-bottles from distributor) alters the major non-dimensional transport properties by 0.1-0.3%. The mean-velocity and velocityfluctuation profiles in the incoming supersonic turbulent boundary layer were found to agree with datasets in the literature, thus, the baseline flow was established. The meanvelocity profiles in the region immediately upstream of the 24-degree compression corner were found to agree with Direct Numerical Simulation (DNS) results available in the literature. In addition, the presence of a shear layer was detected, and its location and orientation are compared to that in the literature.

Krypton Tagging Velocimetry (KTV) Investigation of Shock-Wave/Turbulent Boundary-Layer Interaction

This paper presents multi-path, two-photon excitation cross-section calculations for krypton, using first-order perturbation theory. For evaluation of the two-photon-transition matrix element, this paper formulates the two-photon cross-section calculation as a matrix mechanics problem. From a finite basis of states, consisting of 4p, 5s, 6s, 7s, 5p, 6p, 4d, 5d, and 6d orbitals, electric dipole matrix elements are constructed, and a Green’s function is expressed as a truncated, spectral expansion of solutions, satisfying the Schrodinger equation. Electric dipole matrix elements are evaluated via tabulated oscillator strengths, and where those are unavailable, quantum-defect theory is used. The relative magnitudes of two-photon cross-sections for eight krypton lines in the 190–220 nm range are compared to experimental excitation spectra with good agreement. This work provides fundamental physical understanding of the Kr atom, which adds to experimental observations of relative fluorescence intensity. This is valuable when comparing excitation schemes in different environments for krypton fluorescence experiments. We conclude that two-photon excitation at 212.556 nm is optimal for single-laser, krypton tagging velocimetry or krypton planar laser-induced fluorescence.

Two-photon cross-section calculations for krypton in the 190–220 nm range

Preliminary results from a two-dimensional Krypton Tagging Velocimetry (KTV-2D) investigation of a Mach 2.75 turbulent boundary and 24 degree compression corner flow are presented in this paper. KTV-2D is performed by creating a grid of tagged Kr atoms formed by intersecting laser lines and imaging the resulting fluorescence at a write step; then, after a time delay, imaging the translation of the grid by re-exciting the tagged atoms for the read step. The measurements were made in a 99% N2 and 1% Kr gas mixture. Spatial correlation was used to extract the velocity from the data. It was found that the streamwise component of the velocity in the boundary layer agrees well with the literature; however, a consistent bias was noted in the wall-normal velocity component in the boundary-layer and compression corner flows and we provide an explanation and correction for this bias which will easily be eliminated in future experimentation (the bias was a result of procedure, not inherent in the technique). The turning angle in the compression corner flow matches the result from classical inviscid theory, bringing confidence to the results.

Two-Dimensional Krypton Tagging Velocimetry (KTV-2D) Investigation of Shock-Wave/Turbulent Boundary-Layer Interaction

Krypton Tagging Velocimetry (KTV) is implemented in the flow immediately following the incident shock wave in the Stevens Shock Tube. This is motivated by the long-term goal of using KTV to measure velocity in large-scale impulse facilities. Two example cases are presented in 99% N2/1% Kr at incident shock Mach numbers of 2.86 and 2.94. The velocities as measured by KTV are, in general, higher than those calculated from the shock-speed measurements. The discrepancy is most likely due to the misalignment of splitter plate installed in the shock tube (an expansion fan likely accelerated the flow). A new excitation scheme for KTV is used that results in a higher SNR as compared to previous work. A justification of the alternate scheme is presented via a three energy level model. An overview of the shock tube is given, and a model predicting the non-equilibrium thermodynamic state of the gas immediately following the incident shock is presented.

Muhammad A. Mustafa

Papers

Single-Laser Krypton Tagging Velocimetry Investigation of Supersonic Air and N 2 Boundary-Layer Flows over a Hollow Cylinder in a Shock Tube

Krypton Tagging Velocimetry (KTV) Investigation of Shock-Wave/Turbulent Boundary-Layer Interaction

Two-photon cross-section calculations for krypton in the 190–220 nm range

Two-Dimensional Krypton Tagging Velocimetry (KTV-2D) Investigation of Shock-Wave/Turbulent Boundary-Layer Interaction

Krypton Tagging Velocimetry in the Stevens Shock Tube