A spectacular instability has been observed in low density round jets when the density ratio of jet fluid to ambient fluid falls below a threshold of approximately 0.6. This phenomenon has been observed in non-buoyant jets of helium in air, heated air jets and heated buoyant jets. The oscillation of the flow near the nozzle is extremely regular and periodic and consists of ring vortices. Even the smaller scale structures that appear downstream exhibit similar regularity. A theory for predicting the onset of this oscillation is based on finding regions of absolute instability from linear stability analysis of parallel flow. However, experiments suggest that the theory is at least incomplete and fortuitous as the oscillation is not a linear process. The present work is to observe and understand the process of regeneration of these oscillations by conducting numerical simulations. Here, two-dimensional, plane jets were simulated because they undergo a qualitatively similar process. A spatial and temporal picture of a heated jet has been obtained numerically. A perturbation expansion was used to obtain a system of conservation laws for compressible flows which is valid for low Mach numbers. The low Mach number approximation removes the high frequency acoustic waves from the flow field. This enables a larger time step to be taken without making the calculation unstable. To ensure that all the scales of motion are properly resolved, calculations were done at a low Reynolds number. The governing equations were discretized in space using second-order finite difference formulas on a staggered grid. Velocity fields were advanced using a second-order Adams-Bashforth explicit scheme and then corrected by solving for pressure such that continuity is satisfied at every time step. The Poisson problem for pressure requires the time derivative of the density which was approximated by a third-order backward difference formula. Gauss-Siedel iteration was used to find the pressure. Several numerical tests were conducted prior to simulations of variable density jets to check the stability and accuracy of the code. Two dimensional driven cavity flow calculations were done as a first test. Then a calculation of a forced, spatially developing, incompressible, plane mixing layer was done to check the time accuracy of the code. After obtaining satisfactory performance of the code for the different test cases, two-dimensional, variable density jets were simulated. Since the plane jet extends ad infinitum in the streamwise direction, a sufficiently large domain was used to capture all the relevant physics in the downstream regions of the jet. An advective boundary condition was imposed at the exit plane. Rigid, slipwall conditions were employed to prescribe lateral boundary conditions. A 2-D, incompressible plane jet was simulated first. The jet profile was approximated by two hyperbolic tangent shear layers. The most unstable mode of the inviscid shear layer for this profile, along with its first and second harmonics, was imposed on the velocity profile at the inlet plane. The amplitude of oscillation of the harmonics was chosen so as to provide sufficient energy in the perturbation to accelerate the growth of the layer. No explicit phase lag was introduced in the perturbation. The flow was allowed to develop long enough to wash out the effect of the initial condition. The results obtained for this case indicate that experimentally realized phenomena such as vortex pairing were captured in this simulation. Furthermore, to check the convective nature of instability of the incompressible jet, the forcing at the inlet plane was turned off. The disturbances were gradually convected downstream, out of the computational domain. Next, two-dimensional heated, non-buoyant jets were studied numerically. The effects of the ratio of jet density to ambient density S, the velocity ratio R, and jet width W, on the near field behavior of an initial laminar jet and the regeneration mechanism of the self-sustaining vortices were explored. The theory based on domain of absolute/convective instability identifies these three parameters. No initial perturbation was necessary to start roll-up of the shear layer. For certain choices, e.g., S= 0.75, R = 20, W =10.5, self-sustaining oscillations appeared spontaneously, and these cycles repeated for very long simulation intervals. Waviness on the jet shear layers grow and roll-up into vortices as in constant density shear layers. But unlike the incompressible plane jet, these vortices grow much larger and mixes more with the surrounding fluid. As these vortices evolve, packets of fluid break away as trailing legs similar to side jet expulsions observed in round jets and plumes. The growing vortices disturb the upstream shear layer. Consistently with linear theory, which predicts absolute instability for these parameters, these disturbances are able to grow and roll up. If these disturbances travelled faster than the downstream vortices, it would not be possible for the cycle to repeat. With sufficient shear between the co-flowing streams (R not too small), the entire regeneration process was found to begin from roughly the same streamwise location. Furthermore, it is the symmetric, varicose mode which occurs. At a slightly larger density ratio (S = 0.8, R = 10), self-sustaining oscillations appeared, but each new cycle began slightly farther downstream. It seems likely that these values are close to the boundary in parameter space between self-sustained oscillatory and convectively unstable behaviors. Jet width also influences the selection of these two behaviors. When jet width was reduced, W = 6, even for S = 0.75,R = 20, each new cycle began to shift downstream. For larger jet width (W = 12.3), self-sustaining oscillations occur but the response is now as an asymmetric sinuous mode after a short initial varicose mode. The detailed processes that have now been revealed in plane jets should serve as guidelines for the study of such processes in the technologically more important round jets.

Supercritical fluid jets provide a complex flow pattern and are present in many engineering applications. To date, studies have focused on wall jets, free jets, and two-dimensional offset jets. As a result, our understanding of three-dimensional offset jets is lacking. A deeper understanding of three-dimensional offset jets is important as they are seen in many engineering applications. Understanding the flow patterns of three-dimensional offset jets will aid hydraulic engineers to reduce anthropogenic effects when designing new and rehabilitating older hydraulic structures. The purpose of this study was to evaluate the effects of tailwater level and asymmetry ratio on three-dimensional offset jets. A physical model was constructed and three sets of experiments were conducted. Each set of experiments evaluated the effects of the Reynolds number, tailwater level, or asymmetry ratio. Velocity measurements were taken with an acoustic Doppler velocimeter. The acoustic Doppler velocimeter measured all three components of velocity which allowed the calculation of all six components of Reynolds shear stresses and ten components of triple velocity correlation. The effects of Reynolds number, tailwater level, and asymmetry ratio on streamwise flow development, distributions of mean velocities, and distribution of turbulence statistics were evaluated. Reynolds number effects were found to be insignificant at Reynolds number greater than 53,000. Two different trends were observed in the behavior of three-dimensional offset jets at different tailwater levels. At low tailwater levels the jet will not reattach to the channel bottom as it does at higher tailwater levels. Increasing the asymmetry ratio of an offset jet will make the jet curve towards the channel wall and bottom faster. Once reattached to the wall the velocity decay rate is greatly reduced. The results found in this study will be useful to a hydraulic engineer designing new or rehabilitating older hydraulic structures which have flow characteristics similar to that of three-dimensional offset jets. The data acquired during this study adds to the available data usable for calibration and validation of turbulence models. All three components of velocity were measured simultaneously which allowed to calculation of the six Reynolds shear stresses and ten triple velocity correlation terms. All velocities and turbulence statistics in this study were measured simultaneously which provides a data set that has rarely been seen before.

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Digitized by Kansas Correctional Industries

Call number: LD2668 .T4 1956 L54 / Master of Science

Call number: LD2668 .T4 1959 B86

Call number: LD2668 .T4 1965 C45 / Master of Science

A first measurement of Electroweak W + 2 jets production at high dijet mass is performed using sqrt(s) = 7 TeV pp collision data from the Atlas experiment corresponding to 4.6 fb−1 of integrated luminosity. The background only hypothesis is excluded with a significance of 4.89-σ. A cross section of σ = 325 ± 6 (lumi) ±32 (stat) +63−70(syst) ±86 (theo) fb is extracted in the fiducial region.

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