On solutions of differential and functional equations Final report

Solutions of differential and functional equation

A family of solutions of certain nonautonomous differential equations by series of exponential functions

Solution of differential equations by series of exponential function

Interaction of Aircraft Wakes From Laterally Spaced Aircraft

Large Eddy Simulations are used to examine wake interactions from aircraft on closely spaced parallel paths. Two sets of experiments are conducted, with the first set examining wake interactions out of ground effect (OGE) and the second set for in ground effect (IGE). The initial wake field for each aircraft represents a rolled-up wake vortex pair generated by a B-747. Parametric sets include wake interactions from aircraft pairs with lateral separations of 400, 500, 600, and 750 ft. The simulation of a wake from a single aircraft is used as baseline. The study shows that wake vortices from either a pair or a formation of B-747 s that fly with very close lateral spacing, last longer than those from an isolated B-747. For OGE, the inner vortices between the pair of aircraft, ascend, link and quickly dissipate, leaving the outer vortices to decay and descend slowly. For the IGE scenario, the inner vortices ascend and last longer, while the outer vortices decay from ground interaction at a rate similar to that expected from an isolated aircraft. Both OGE and IGE scenarios produce longer-lasting wakes for aircraft with separations less than 600 ft. The results are significant because concepts to increase airport capacity have been proposed that assume either aircraft formations and/or aircraft pairs landing on very closely spaced runways

Study of outgassing and decomposition of space shuttle heat protection tiles, fillers and adhesive

The purpose of this project was to determine the chemicals desorbing from the space shuttle heat protection tiles. The original protocol for this project involved direct insertion probe mass spectrometry (DIPMS) analysis of the outgassing products from the tiles. However, this method proved unsatisfactory due to the large number of compounds desorbing from the tiles. A purge and trap technique was then employed to collect and separate the chemicals desorbing from the tiles. The maximum temperature in this analysis was 180 C which is the gas chromatograph fused silica capillary column's temperature limit. The desorption was also carried out at atmospheric pressure with helium as the purge gas. A description of the modified protocol is given. All compounds are tentatively identified

Study of outgassing and decomposition of Space Shuttle heat protection tiles, fillers and adhesive

A purge and trap technique which was employed to collect and separate the chemicals desorbing from the space shuttle heat protection tiles is described. The instrumentation included a mass spectrometer and gas chromatograph

Numerical Study of a Long-Lived, Isolated Wake Vortex in Ground Effect

This paper examines a case observed during the 1990 Idaho Falls Test program, in which a wake vortex having an unusually long lifetime was observed while in ground effect. A numerical simulation is performed with a Large Eddy Simulation model to understand the response of the environment in affecting this event. In the simulation, it was found that one of the vortices decayed quickly, with the remaining vortex persisting beyond the time-bound of typical vortex lifetimes. This unusual behavior was found to be related to the first and second vertical derivatives of the ambient crosswind

Transient technique for measuring heat transfer coefficients on stator airfoils in a jet engine environment

A transient technique was used to measure heat transfer coefficients on stator airfoils in a high-temperature annular cascade at real engine conditions. The transient response of thin film thermocouples on the airfoil surface to step changes in the gas stream temperature was used to determine these coefficients. In addition, gardon gages and paired thermocouples were also utilized to measure heat flux on the airfoil pressure surface at steady state conditions. The tests were conducted at exit gas stream Reynolds numbers of one-half to 1.9 million based on true chord. The results from the transient technique show good comparison with the steady-state results in both trend and magnitude. In addition, comparison is made with the STAN5 boundary layer code and shows good comparison with the trends. However, the magnitude of the experimental data is consistently higher than the analysis

Evaluation of Fast-Time Wake Vortex Prediction Models

Current fast-time wake models are reviewed and three basic types are defined. Predictions from several of the fast-time models are compared. Previous statistical evaluations of the APA-Sarpkaya and D2P fast-time models are discussed. Root Mean Square errors between fast-time model predictions and Lidar wake measurements are examined for a 24 hr period at Denver International Airport. Shortcomings in current methodology for evaluating wake errors are also discussed

Double-diffusive instabilities of a shear-generated magnetic layer

Previous theoretical work has speculated about the existence of double-diffusive magnetic buoyancy instabilities of a dynamically evolving horizontal magnetic layer generated by the interaction of forced vertically sheared velocity and a background vertical magnetic field. Here we confirm numerically that if the ratio of the magnetic to thermal diffusivities is sufficiently low then such instabilities can indeed exist, even for high Richardson number shear flows. Magnetic buoyancy may therefore occur via this mechanism for parameters that are likely to be relevant to the solar tachocline, where regular magnetic buoyancy instabilities are unlikely.Comment: Submitted to ApJ