ALBERT

Description: An analysis is made for the variable fluid property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary layer equations appropriate to the variable property situation were carried out for gases and liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free convection heat transfer under variable property conditions. This calculation method is well established in the heat transfer field. It involves the use of results which have been derived for constant property fluids, and of a set of rules (called reference temperatures) for extending these constant property results to variable property situations. For gases, the constant property heat transfer results are generalized to the variable property situation by replacing beta (expansion coefficient) by one over T sub infinity and evaluating the other properties at T sub r equals T sub w minus zero point thirty-eight (T sub w minus T sub infinity). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including beta) at this same T sub r. It is worthwhile noting that for these fluids, the film temperature (with beta equals one over T sub infinity for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary layer thickness and velocity parameters.

Description: The year 1954 marked the 50th anniversary of the Prandtl boundary-layer theory from which we may date the beginning of man's understanding of the dynamics of real fluids. A backward look at this aspect of the history of the last 50 years may be instructive. This paper (1) attempts to compress the events of those 50 years into a few thousand words, to tell in this brief space the interesting story of the development of a new concept, its slow acceptance and growth, its spread from group to group within its country of origin, and its diffusion to other countries of the world. The original brief paper of Prandtl (2) was presented at the Third International Mathematical Congress at Heidelberg in 1904 and published in the following year. It was an attempt to explain the d'Alembert paradox, namely, that the neglect of the small friction of air in the theory resulted in the prediction of zero resistance to motion. Prandtl set himself the task of computing the motion of a fluid of small friction, so small that its effect could be neglected everywhere except where large velocity differences were present or a cumulative effect of friction occurred This led to the concept of boundary layer, or transition layer, near the wall of a body immersed in a fluid stream in which the velocity rises from zero to the free-stream value. It is interesting that Prandtl used the term Grenzsehicht (boundary layer) only once and the term Ubergangsschicht (transition layer) seven times in the brief article. Later writers also used Reibungsschicht (friction layer), but most writers today use Grenzschicht (boundary layer).

Description: The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

Description: An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.

Description: Charts have been prepared relating the thermodynamic properties of air in chemical equilibrium for temperatures to 15,000 degrees k and for pressures 10(-5) to 10 (plus 4) atmospheres. Also included are charts showing the composition of air, the isentropic exponent, and the speed of sound. These charts are based on thermodynamic data calculated by the National Bureau of Standards.

Description: The presence of radomes and instruments that are sensitive to water films or ice formations in the nose section of all-weather aircraft and missiles necessitates a knowledge of the droplet impingement characteristics of bodies of revolution. Because it is possible to approximate many of these bodies with an ellipsoid of revolution, droplet trajectories about an ellipsoid of revolution with a fineness ratio of 10 were computed for incompressible axisymmetric air flow. From the computed droplet trajectories, the following impingement characteristics of the ellipsoid surface were obtained and are presented in terms of dimensionless parameters: (1) total rate of water impingement, (2) extent of droplet impingement zone, and (3) local rate of water impingement. These impingement characteristics are compared briefly with those previously reported for an ellipsoid of revolution with a fineness ratio of 5.

Description: Some results of recent experimental investigations at supersonic and transonic speeds are presented to show the present status in the estimation of load distributions on controls and adjacent wing surfaces resulting from the deflection of flap controls and spoiler controls. The results indicate that the development of methods for predicting loads associated with controls has not kept pace with the acquisition of experimental data. At low supersonic speeds sweeping the hinge line induces strong three-dimensional-flow characteristics which cannot be treated by the simplified methods previously developed for controls without sweep. At transonic speeds the estimation of loads associated with controls must usually be dependent upon experimental information inasmuch as the latest attempts to predict chordwise and spanwise loadings have met with only limited success.

Description: An investigation at a free-stream Mach number of 2.02 was made to determine the effects of a propulsive jet on a wing surface located in the vicinity of a choked convergent nozzle. Static-pressure surveys were made on a flat surface that was located in the vicinity of the propulsive jet. The nozzle was operated over a range of exit pressure ratios at different fixed vertical distances from the flat surface. Within the scope of this investigation, it was found that shock waves, formed in the external flow because of the presence of the propulsive jet, impinged on the flat surface and greatly altered the pressure distribution. An integration of this pressure distribution, with the location of the propulsive jet exit varied from 1.450 propulsive-jet exit diameters to 3.392 propulsive-jet exit diameters below the wing, resulted in an incremental lift for all jet locations that was equal to the gross thrust at an exit pressure ratio of 2.86. This incremental lift increased with increase in exit pressure ratio, but not so rapidly as the thrust increased, and was approximately constant at any given exit pressure ratio.

Description: Heating requirements for satisfactory cyclic de-icing over a wide range of icing and operating conditions have been determined for a gas-heated, 36deg swept airfoil of 6.9-foot chord with a partial-span leading-edge slat. Comparisons of heating requirements and effectiveness were made between the slatted and unslatted portions of the airfoil. Studies were also made comparing cyclic de-icing with continuous anti-icing, and cycll.cde-icing systems with and without leading-edge ice-free parting strips. De-icing heat requirements were approximately the same with either heated or unheated parting strips because of the aerodynamic effects of the 36deg sweep angle and the spanwise saw-tooth profile of leading-edge glaze-ice deposits. Cyclic de-icing heat-source requirements were found to be one-fourth or less of the heat requirements for complete anti-icing. The primary factors that affected the performance of the cyclic de-icing heating system were ambient air temperature, heat distribution, and thermal lag.

Description: Numerical solutions of the differential equation obtained from the momentum theorem for the development of a turbulent boundary layer along a thermally insulated surface in two-dimensional and in radial shock-free flow are presented in tabular form for a range of Mach numbers from 0.100 to 10. The solution can be used in a step-wise procedure with any given distribution of favorable pressure gradients and for zero pressure gradients. Solutions are also given for use with moderate adverse pressure gradients. The mean velocity in the boundary layer is approximated by a power-law profile. In view of the stepwise integration methods to be used, the exponent designated the profile shape can be varied along the surface between the integral fraction limits 1/5 and 1/11 through interpolation. Agreement obtained between theoretical and experimental boundary-layer development in a supersonic nozzle at a nominal Mach number of 2 indicates the general validity of the approximations used in the analysis - in particular, the method of extrapolating low-speed skin-friction relations to high Mach number flows. The extrapolation method used assumes that the skin-friction coefficient depend primarily on Reynolds number, provided that the density and the kinematic viscosity are evaluated at surface conditions.