Spot Spreading Research Articles

Short-scale effects on model boundary-layer spots

This theoretical work, on the spot in an otherwise laminar boundary layer, concerns the initial-value problem for three-dimensional inviscid disturbances covering a wide range of scales. The study asks whether or not comparatively short scales can have a substantial impact on the spot spreading rate, as well as on other important features including the spot structure. It is found that such scales act to reduce the spread angle to approximately 11°, close to the experimental observations for transitional/turbulent spots, as opposed to the angle of 19.47° for waves near or behind the spot trailing edge. The scales emerge from coupling uniform shear flow directly with the local uniform stream and then analysing large-time features. The leading edge and trailing edge of the spot are also examined in detail, along with other structural properties. It is concluded that nonlinearity and short-scale effects probably combine to restrict the global spread angle as above, while viscous sublayer bursting among other things completes the spot structure. Related work on nonlinear, trailing-edge and leading-edge behaviours and comparisons with experiments are also discussed.

The Use of Transition Region Characteristics to Improve the Numerical Simulation of Heat Transfer in Bypass Transitional Flows

A method is presented for improving the numerical prediction of bypass transition heat transfer on a flat plate in a high‐disturbance environment with zero or favorable pressure gradient. The method utilizes low Reynolds number k‐ε turbulence models in combination with the characteristic parameters of the transition region. The parameters representing the characteristics of the transition region used are the intermittency, transition length and turbulent spot properties. An analysis is made of the transition length in terms of turbulent spot variables. The nondimensional spot formation rate, required for the prediction of the transition length, is shown by the analysis to be a function of the spot spreading angle, the dimensionless spot velocity ratio and the dimensionless spot area ratio. The intermittency form of the k‐ε equations was derived from conditionally averaged equations which have been shown to be an improvement over global‐time‐averaged equations for the numerical calculation of the transition region. The numerical predictions are in general good agreement with the experimental data and indicate the potential use of the method in accelerating flows. Turbulence models of the k‐ε type are known to underpredict the transition length. The present work demonstrates how incorporating transition region characteristics improves the ability of two‐equation turbulence models to simulate bypass transition for flat plates with potential application to turbine vanes and blades.

Studies on the lattice distortion and substructures of shocked lamellae in naturally shocked quartz

One unshocked and 9 naturally shocked single quartz crystal grains with 1–6 sets of shock lamellae from the Ries, West Germany, and the Lake Lappajarvi, Finland, covering a range from unshocked quartz withNo = 1.544 to nearly completely glassy quartz withNo = 1.461 have been used for X-ray precession and Laue investigations. Four of the shocked grains have preliminarily been studied under a transmission electron microscope. It is found that quartz havingNo less than 1.539 shows intensive anisotropic cell expansion and lattice disordering which gradually increase asNo decreases. Shock-induced lattice distortion of quartz is clearly shown on both precession and Laue photographs. For the weakly shocked quartz (p < 200 kb) slight to pronounced spreading of spots is observed. When the pressure reaches 200 kb, both concentric spreading of spots having long ‘tails’ and concentric rings (powder pattern) are revealed on the same photograph, which means that besides a part of single crystal there also exist randomly oriented tiny ‘fragments’ of quartz in this shocked quartz grain. As pressure increases from 230 to 315 kb, more and more crystalline puases in the quartz grains have transformed from solid state into silica glass, and the concentric rings and the long ‘tails’ disappear and the spot spreading becomes slight again, but reflection intensities become much lower in comparison with those of weakly shocked quartz.

Turbulent spots in plane Poiseuille flow–flow visualization

The structure and spreading of turbulent spots in plane Poiseuille flow were studied through flow visualization, in the Reynolds number range 1100 to 2200 (based on centerline velocity and channel half-height). The spot spreading half-angle varied from 6° for the lowest Re to 12° for the highest Re. The propagation velocity of the rear laminar–turbulent interface was slightly above 50% of the centerline velocity. Spotsplitting, as reported in earlier studies, seems to occur only at low Re.

Programmed multiple development : Brief review and study of extended programs

Introduced in 1951, multiple development by repeated solvent advances improves the resolution available from a given chromatographic system. Repeated solvent advances compress the top-to-bottom “width” of a thin-layer chromatograhic spot by the factor (1 — R F.N ), where R F.N express the final location of the spot between the origin and the solvent front. Spots near the front become almost lines drawn parallel to the solvent front, but near the origiin spot shape change little. In contrast, all spot developed by programmed multiple development (PMD) are line-like. PMD, introduced in 1973, adds solvent removals to solvent advances while, throughout, solvent flows constantly towards the front. Both advances and removals are carried out automatically and relatively rapidly. Used in thin-layer chromatography, PMD spots tend to be uniformly tight and do not reflect the characteristics of the origin. Therefore, PMD is currently used mainly to improve the separability and molecular density of spots. The form of PMD that is called centered PMD compresses spots laterally as well as longitudinally, so that the molecules of a given spot are brought and held together during successive developements. this further improves trace detectability. It also allows separations to continue without spot spreading as long as necessary or desired. Thoma predicted that continued multiple development will change the proportion of the chromatographic bed devoted to components ultimately found slightly morel than halfway (0.6) toward the solvent front. Tests support the prediction but show that the effect is minor if only some dozens of multiple developments are involved. The principal result of extended programs is a steady improvement of resolution throughout the chromatogram.