Counting lifts of Brauer characters

In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if \phi \in IBrp(G) is a Brauer character of a solvable group such that \phi has an abelian vertex subgroup Q, then the number of lifts of \phi in Irr(G) is at most |Q|. In order to accomplish this, we develop several results about lifts of Brauer characters in p-solvable groups that were previously only known to be true in the case of groups of odd order.Comment: A different proof of Theorem 1 is in the paper "The number of lifts of Brauer characters with a normal vertex" by J.P. Cossey, M.L.Lewis, and G. Navarro. Hence, we do not expect to try to publish this note. We feel that the proof in this paper is of independent interes

Lifts and vertex pairs in solvable groups

Suppose $G$ is a $p$-solvable group, where $p$ is odd. We explore the connection between lifts of Brauer characters of $G$ and certain local objects in $G$, called vertex pairs. We show that if $\chi$ is a lift, then the vertex pairs of $\chi$ form a single conjugacy class. We use this to prove a sufficient condition for a given pair to be a vertex pair of a lift and to study the behavior of lifts with respect to normal subgroups

Investigation of Heat Transfer From

The convective heat transfer from the surface of an ellipsoidal forebody of fineness ratio 3 and 20-inch maximum diameter was investigated in clear air for both stationary and rotating operation over a range of conditions including air speeds up to 240 knots, rotational speeds up to 1200 rpm, and angles of attack of 0 deg, 3 deg, and 6 deg. The results are presented in the form of heat-transfer coefficients and the correlation of Nusselt and Reynolds numbers. Both a uniform surface temperature and a uniform input heater density distribution were used. The experimental results agree well with theoretical predictions for uniform surface temperature distribution. Complete agreement was not obtained with uniform input heat density in the laminar-flow region because of conduction effects. No significant effects of rotation were obtained over the range of airstream and rotational speeds investigated. Operation at angle of attack had only minor effects on the local heat transfer. Transition from laminar to turbulent heat transfer occurred over a wide range of Reynolds numbers. The location of transition depended primarily on surface roughness and pressure and temperature gradients. Limited transient heating data indicate that the variation of surface temperature with time followed closely an exponential relation

Comparison of Heat Transfer from Airfoil in Natural and Simulated Icing Conditions

An investigation of the heat transfer from an airfoil in clear air and in simulated icing conditions was conducted in the NACA Lewis 6- by 9-foot icing-research tunnel in order to determine the validity of heat-transfer data as obtained in the tunnel. This investiation was made on the same model NACA 65,2-016 airfoil section used in a previous flight study, under similar heating, icing, and operating conditions. The effect of tunnel turbulence, in clear air and in icingwas indicated by the forward movement of transition from laminar to turbulent heat transfer. An analysis of the flight results showed the convective heat transfer in icing to be considerably different from that measured in clear air and. only slightly different from that obtained in the icing-research tunnel during simulated icing

Preliminary Investigation of Cyclic De-Icing of an Airfoil Using an External Electric Heater

An investigation was conducted in the NACA Lewis icing research tunnel to determine the characteristics and requirements of cyclic deicing of a 65,2-216 airfoil by use of an external electric heater. The present investigation was limited to an airspeed of 175 miles per hour. Data are presented to show the effects of variations in heat-on and heat-off periods, ambient air temperature, liquid-water content, angle of attack, and. heating distribution on the requirements for cyclic deicing. The external heat flow at various icing and heating conditions is also presented. A continuously heated parting strip at the airfoil leading edge was found necessary for quick, complete, and consistent ice removal. The cyclic power requirements were found to be primarily a function of the datum temperature and heat-on time, with the other operating and meteorological variables having a second-order effect. Short heat-on periods and high power densities resulted in the most efficient ice removal, the minimum energy input, and the minimum runback ice formations. The optimum chordwise heating distribution pattern was found to consist of a uniform distribution of cycled power density in the impingement region. Downstream of the impingement region the power density decreased to the limits of heating which, for the conditions investigated, extended from 5.7 percent chord on the upper surface of the airfoil to 8.9 percent chord on the lower surface. Ice removal did not take place at a heater surface temperature of 32 F; surface temperatures of approximately 50 to 100 F were required to effect removal. Better de-icing performance and greater energy savings would be possible with a heater having a higher thermal efficiency

Experimental Droplet Impingement on Four Bodies of Revolution

The rate and. area of cloud droplet impingement on four bodies of revolution were obtained experimentally in the NACA Lewis icing tunnel with a dye-tracer technique. The study included spheres, ellipsoidal forebodies of fineness ratios of 2.5 and 3.0, and a conical forebody of 300 included angle and covered a range of angles of attack from 0? to 60 and rotational speeds up to 1200 rpm. The data were obtained at an airspeed of 157 knots and are correlated by dimensionless impingement parameters. In general, the experimental data show that the local and total impingement rates and impingement limits of bodies of revolution are primarily functions of the modified inertia parameters, the body shape, and fineness ratio. Both the local impingement rate and impingement limits depend upon the angle of attack. Rotation of the bodies had a negligible effect on the impingement characteristics except for an averaging effect at angle of attack. For comparable diameters the bluffer bodies had the largest total impingement efficiency, but the finer and sharper bodies had the largest values of maximum local impingement efficiency and, in most cases, the largest limits of impingement. In most cases, the impingement characteristics were less than those calculated from theoretical trajectories; in general, however, fairly good agreement was obtained between the experimental and theoretical impingement characteristics

Investigation of Heat Transfer from a Stationary and Rotating Conical Forebody

The convective heat transfer from the surface of a conical forebody having a hemispherical nose, an included angle of approximately 30 deg, and. a maximum diameter of 18.9 inches was investigated in a wind tunnel for both stationary and. rotating operation. The range of test conditions included free-stream velocities up to 400 feet per second, rotational speeds up to 1200 rpm, and. angles of attack of 0 deg and 6 deg. Both a uniform surface temperature and a uniform heater input power density were used. The Nusselt-Reynolds number relations provided good correlation of the heat-transfer data for the complete operating range at 0 deg angle of attack with and without spinner rotation, and for 6deg angle of attack with rotation. Rotational speeds up to 1200 rpm had no apparent effect on the heat-transfer characteristics of the spinner. The results obtained at 6 deg angle of attack with rotation were essentially the same as those obtained at 0 deg angle of attack without rotation. The experimental heat-transfer characteristics in the turbulent flow region were consistently in closer agreement with the results predicted for a two-dimensional body than with those predicted. for a cone. For stationary operation at 60 angle of attack, the measured heat-transfer coefficients in the turbulent flow region were from 6 to 13 percent greater on the lower surface (windward. side) than on the upper surface (sheltered side) for corresponding surface locations. The spinner-nose geometry appeared to cause early boundary-layer transition. Transition was initiated at a fairly constant Reynolds number (based on surface distance from nose) of 8.0 x 10(exp 4). Transition was completed at Reynolds numbers less than 5.0 x 10(exp 5) for all conditions investigated

Icing and De-Icing of a Propeller with Internal Electric Blade Heaters

An investigation has been made in the NACA Cleveland icing research tunnel to determine the de-icing effectiveness of an experimental configuration of an Internal electric propeller-blade heater. Two atmospheric Icing conditions and two propeller operating conditions were Investigated, In experiments with unheated blades and with heat applied to the blades both continuously and cyclically. Data are presented to show the effect of propeller speed., ambient air temperature and liquid-water concentration, and the duration of the heat-on and cycle times on the power requirements and de-Icing performance of the blade heaters. The extent of ice-covered area on the blades for various icing ax4 operating conditions has been determined. The largest iced area was obtained at the higher ambient-air temperatures and at low propeller speed. The ohord.wise extent of Icing In practically every case was greater than that covered by blade heaters. Adequate de-icing in the heated area with continuous application of heat was obtained with the power available but a maximum power, input of 1250 watts per blade was insufficient for cyclic de-Icing for the range of conditions investigated. Blade-surface temperature rates of rise of 0.2 to 0.7 F per second were obtained and the minimum cooling period for cyclic de-icing was found to be approximately 2-1/2 times the heating period