Asymptotic expansions and energy methods applied to three dimensional aircraft maneuvers involving energy climbs and turns

Energy climbs, energy turns, and asymptotic expansions

A quasi-three-di mensional integral method is used to solve the problem of the isothermal incompressible turbulent jet. The jet is submerged and is circular at its origin. The mathematical model is based on two integral momentum equations, one written for a direction parallel to the jet centerline and the other for a direction perpendicular to the centerline. For their solution, the entrainment rate into the jet is determined as the linear combination of a modified straight jet entrainment and the entrainment into a vortex pair. The family of velocity profiles required for the integration of the momentum equations is three-dimensional. The profiles are determined along the jet centerline on the basis of the distorted jet cross sections, thus being nonsimilar. The mathematical model is numerically solved, yielding the internal jet flowfield. Results are compared to experiments with different injection velocity to crossflow velocity ratios and with different injection angles. Agreement between theory and experiment is found to be satisfactory in some cases and good in others.

Prediction of a Three-Dimensional Circular Turbulent Jet in Crossflow

A jet stream issuing normally from both sharp- and blunt-nose ogive-cylinder configurations into a hypersonic flow was investigated by a side-by-side experimental and numerical simulation. At a hypersonic Mach number of 12, strong interaction between jet-induced and bow shock wave systems, the jet plume trajectory, and the separated-flow surface shear pattern were highlighted for basic understanding. After the numerical solution was verified with the experimental data, the flowfield topology was reconstructed. Several unique features of this inviscid-viscous interaction phenomenon of shock-wave formation, vortical flow structure, and jet plume were delineated.

Interaction of jet in hypersonic cross stream

Impingement systems are common place in many turbine cooling applications Generally these systems consist of a target plate that is cooled by the impingement of multiple orthogonal jets While it is possible to achieve high target surface heat transfer with this configuration, the associated pressure drop is generally high and the cooling efficiency low Furthermore, especially in large impingement arrays, the build-up of cross flow from upstream jets can be significant and result in deflection of downstream impingement jets reducing the resultant heat transfer coefficient distribution This paper presents a computational and experimental investigation into the use of shaped elliptical or elongated circular impingement holes designed to improve the penetration of the impinging jet across the coolant passage This is of particular interest where there is significant cross flow Literature review and computational investigations are used to determine the optimum aspect ratio of the impingement jet The improved heat transfer performance of the modified design is then tested in an experimental rig with varying degrees of cross flow at engine representative conditions In all cases a 16% increase in the Nusselt number on the impingement target surface in the downstream half of the cooling passage was achieved Under the first 4 impingement holes Nusselt number enhancement of enhancement of 28–77% was achieved provided no additional cross flow was present in the passage When appropriately aligned, a significant reduction in the stress concentration factor caused by the addition of a hole can be achieved using this designCopyright © 2006 by ASME

Enhancement of Impingement Cooling in a High Cross Flow Channel Using Shaped Impingement Cooling Holes

Af — area of the jet nozzle Ap — surface area of the baffle plate C — circumference of a jet in a cross flow Cp = pressure coefficient defined by Eq. (4) dj = diameter of the jet nozzle De = effective diameter of a multiple array of jets, the diameter of a circle with an area equal to the total area of the jet nozzles D = diameter of the baffle plate (Fig. 2); diameter of a cylindrical body placed between the jets (Figs. 6, 8)

Aerodynamics of jets pertinent to VTOL aircraft

The interaction between a jet exhausting normally from a lifting surface into a uniform airstream is explored theoretically and experimentally. A theoretical model of the flow is discussed in which the entrainment of the mainstream fluid by the j et is accounted for directly, without recourse to an empirical equation for the jet centerline. Making use of the observation that the jet deforms from a circular cross section into an elliptical cross section as it progresses downstream, the continuity and momentum equations are solved to provide the jet path. The velocity field induced by the jet is then determined by replacing the jet by a sink-doublet distribution. The distribution of sinks represents the entrainment effect of the jet, and the doublet distribution represents the blockage effect of the jet. Lifting surface theory is used to predict the loading on the adjacent lifting surface. The theory does account for the three-dimensionality of the problem, and there is good agreement between theory and the results of an experiment conducted on a 10% thick straight wing at AR = 3.

G. H. Burghart

Papers

Pressure Distribution on a Rectangular Wing with a Jet Exhausting Normally into an Airstream