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The Measurement of Fuel-Air Ratio by Analysis for the Oxidized Exhaust Gas
"An investigation was made to determine a method of measuring fuel-air ratio that could be used for test purposes in flight and for checking conventional equipment in the laboratory. Two single-cylinder test engines equipped with typical commercial engine cylinders were used. The fuel-air ratio of the mixture delivered to the engines was determined by direct measurement of the quantity of air and of fuel supplied and also by analysis of the oxidized exhaust gas and of the normal exhaust gas. Five fuels were used: gasoline that complied with Army-Navy fuel Specification No. AN-VV-F-781 and four mixtures of this gasoline with toluene, benzene, and xylene" (p. 1).
Performance of B. M. W. 185-Horsepower Airplane Engine
"This report deals with the results of a test made upon a B. M. W. Engine in the altitude chamber of the Bureau of Standards, where controlled conditions of temperature and pressure can be made to simulate those of the desired altitude. A remarkably low value of fuel consumption - 041 per B. H. P. hour - is obtained at 1,200 revolutions per minute at an air density of 0.064 pound per cubic foot and a brake thermal efficiency of 33 per cent and an indicated efficiency of 37 per cent at the above speed and density. In spite of the fact that the carburetor adjustment does not permit the air-fuel ratio of maximum economy to be obtained at air densities lower than 0.064, the economy is superior to most engines tested thus far, even at a density lower than 0.064, the economies superior to most engines tested thus far, even at a density (0.03) corresponding to an altitude of 25,000 feet" (p. 1).
Stability of the Parachute and Helicopter
This report deals with an extension of the theory of stability in oscillation to the case of aircraft following a vertical trajectory, and particularly to the oscillations of parachutes.
Supplies and Production of Aircraft Woods
The purpose of this report is to present in brief form such information as is available regarding the supplies of the kinds of wood that have been used or seem likely to become important in the construction of airplanes, and the amount of lumber of each species normally put on the market each year. A general statement is given of the uses to which each kind of wood is or may be put.
The Lagrangian Multiplier Method of Finding Upper and Lower Limits to Critical Stresses of Clamped Plates
"The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the truss, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Raleigh-Rite method of finding upper limits" (p. 1).
The Kiln Drying of Wood for Airplanes
This report is descriptive of various methods used in the kiln drying of woods for airplanes and gives the results of physical tests on different types of woods after being dried by the various kiln-drying methods.
A Low-Speed Experimental Investigation of the Effect of a Sandpaper Type of Roughness on Boundary-Layer Transition
Report describing the effects of an area of roughness on the velocity and turbulence measurements of an airfoil. It details the effects of the size, location, and height of the roughness on the Reynolds number. From Summary: "An investigation was made in the Langley low-turbulence pressure tunnel to determine the effect of size and location of a sandpaper type of roughness on the Reynolds number for transition."
The effect of cowling on cylinder temperatures and performance of a Wright J-5 engine
This report presents the results of tests conducted to determine the effect of different amounts and kinds of cowling on the performance and cylinder temperatures of a standard Wright J-5 engine. These tests were conducted in conjunction with drag and propeller tests in which the same cowlings were used. Four different cowlings were investigated varying from the one extreme of no cowling on the engine to the other extreme of the engine completely cowled and the cooling air flowing inside the cowling through an opening in the nose and out through an annular opening at the rear of the engine. Each cowling was tested at air speeds of approximately 60, 80, and 100 miles per hour.
Preliminary Report on the Problem of the Atmosphere in Relation to Aeronautics
A report to the Weather Bureau, Washington DC, from the chairman of the Subcommittee on the Atmosphere in Relation to Aeronautics describing the activities accomplished and the proposal of work to be undertaken by the subcommittee.
A Method of Estimating the Knock Rating of Hydrocarbon Fuel Blend
"The usefulness of the knock ratings of pure hydrocarbon compounds would be increased if some reliable method of calculating the knock ratings of fuel blends was known. The purpose of this study was to investigate the possibility of developing a method of predicting the knock ratings of fuel blends" (p. 1).
Diaphragms for Aeronautic Instruments
This investigation was carried out at the request of the National Advisory Committee for Aeronautics and comprises an outline of historical developments and theoretical principles, together with a discussion of expedients for making the most effective use of existing diaphragms actuated by the hydrostatic pressure form an essential element of a great variety instruments for aeronautic and other technical purposes. The various physical data needed as a foundation for rational methods of diaphragm design have not, however, been available hitherto except in the most fragmentary form.
A Comparison of Theory and Experiment for High-Speed Free-Molecule Flow
Comparison of free-molecule-flow theory with the results of wind-tunnel tests performed to determine the drag and temperature-rise characteristics of a transverse circular cylinder.
Nomenclature for Aeronautics
The nomenclature for aeronautics presented in this Report No. 474 is a revision of the last previous report on this subject (i.e., Report no. 240.) This report is published for the purpose of encouraging greater uniformity and precision in the use of terms relating to aeronautics, both in official documents of the Government and in commercial publications. Terms in general use in other branches of engineering have been included only where they have some special significance in aeronautics, or form an integral part of its terminology.
A Theoretical Investigation of Longitudinal Stability of Airplanes with Free Controls Including Effect of Friction in Control System
"The relation between the elevator hinge moment parameters and the control forces for changes in forward speed and in maneuvers is shown for several values of static stability and elevator mass balance. The stability of the short period oscillations is shown as a series of boundaries giving the limits of the stable regions in terms of the elevator hinge moment parameters. The effects of static stability, elevator moment of inertia, elevator mass unbalance, and airplane density are also considered" (p. 1).
Icing-Protection Requirements for Reciprocating-Engine Induction Systems
Report presenting an investigation of the icing of aircraft-engine induction systems. Criterions for safe operation and for the design of new induction system are established through the investigation. The results were obtained from laboratory investigations of carburetor-supercharger combinations, wind-tunnel investigations of air scoops, multicylinder-engine studies, and flight investigations.
Lifting-Surface-Theory Aspect-Ratio Corrections to the Lift and Hinge-Moment Parameters for Full-Span Elevators on Horizontal Tail Surfaces
"A limited number of lifting-surface-theory solutions for wings with chordwise loadings resulting from angle of attack, parabolic-arc camber, and flap deflection are now available. These solutions were studied with the purpose of determining methods of extrapolating the results in such a way that they could be used to determine lifting-surface-theory values of the aspect-ratio corrections to the lift and hinge-moment parameters for both angle-of-attack and flap-deflection-type loading that could be used to predict the characteristics of horizontal tail surfaces from section data with sufficient accuracy for engineering purposes. Such a method was devised for horizontal tail surfaces with full-span elevators" (p. 1).
Determination of the Profile Drag of an Airplane Wing in Flight at High Reynolds Numbers
Report presenting flight tests to determine the profile-drag coefficients of a portion of the original wing surface of an all-metal airplane and a portion of the wing made aerodynamically smooth and more nearly fair than the original section. Tests were also carried out to determine the point of transition from laminar to turbulent boundary layer and to determine the velocity distribution along the upper surface of the wing.
Ice Prevention on Aircraft by Means of Engine Exhaust Heat and a Technical Study of Heat Transmission From a Clark Y Airfoil
"This investigation was conducted to study the practicability of employing heat as a means of preventing the formation of ice on airplane wings. The report relates essentially to technical problems regarding the extraction of heat from the exhaust gases and its proper distribution over the exposed surfaces. In this connection a separate study has been made to determine the variation of the coefficient of heat transmission along the chord of a Clark Y airfoil. Experiments on ice prevention both in the laboratory and in flight show conclusively that it is necessary to heat only the front portion of the wing surface to effect complete prevention" (p. 3).
Comparison of High-Speed Operating Characteristics of Size 215 Cylindrical-Roller Bearings as Determined in Turbojet Engine and in Laboratory Test Rig
A comparison of the operating characteristics of 75-millimeter-bore (size 215) cylindrical-roller one-piece inner-race-riding cage-type bearings was made by means of a laboratory test rig and a turbojet engine. Cooling correlation parameters were determined by means of dimensional analysis, and the generalized results for both the inner- and the outer-race bearing operating temperatures are computed for the laboratory test rig and the turbojet engine. A method is given that enables the designer to predict the inner- and outer-race turbine roller-bearing temperatures from single curves, regardless of variations in speed, load, oil flow, oil inlet temperature, oil inlet viscosity, oil-jet diameter, or any combination of these parameters.
An Introduction to the Laws of Air Resistance of Aerofoils
Report presents methods of calculating air resistance of airfoils under certain conditions of flow phenomena around the airfoil.
On the plane potential flow past a lattice of arbitrary airfoils
The two-dimensional, incompressible potential flow past a lattice of airfoils of arbitrary shape is investigated theoretically. The problem is treated by usual methods of conformal mapping in several stages, one stage corresponding to the mapping of the framework of the arbitrary line lattice and another significant stage corresponding to the Theodorsen method for the mapping of the arbitrary single wing profile into a circle. A particular feature in the theoretical treatment is the special handling of the regions at an infinite distance in front of and behind the lattice. Expressions are given for evaluation of the velocity and pressure distribution at the airfoil boundary. An illustrative numerical example is included.
Icing-protection requirements for reciprocating-engine induction system
From Summary: "Despite the development of relatively ice-free fuel-metering systems, the widespread use of alternate and heated-air intakes, and the use of alcohol for emergency de-icing, icing of aircraft-engine induction systems is a serious problem. Investigations have been made to study and to combat all phases of this icing problem. From these investigations, criterions for safe operation and for design of new induction systems have been established. The results were obtained from laboratory investigations of carburetor-supercharger combinations, wind-tunnel investigations of air scoops, multicylinder-engine studies, and flight investigations. Characteristics of three forms of ice, impact, throttling, and fuel evaporation were studied."
Line-Vortex Theory for Calculation of Supersonic Downwash
"The perturbation field induced by a line vortex in a supersonic stream and the downwash behind a supersonic lifting surface are examined to establish approximate methods for determining the downwash behind supersonic wings. Lifting-lines methods are presented for calculating supersonic downwash. A bent lifting-line method is proposed for computing the downwash field behind swept wings. When applied to triangular wings with subsonic leading edges, this method gives results that, in general, are in good agreement with the exact linearized solution" (p. 635).
A radar method of calibrating airspeed installations on airplanes in maneuvers at high altitudes and at transonic and supersonic speeds
A method of calibrating the static-pressure source of a pitot static airspeed installation on an airplane in level flight, dives, and other maneuvers at high altitude and at transonic and supersonic speeds is described. The method principally involves the use of radar-phototheodolite tracking equipment. The various sources of error in the method are discussed and sample calibrations are included.
The reversibility theorem for thin airfoils in subsonic and supersonic flow
A method introduced by Munk is extended to prove that the light-curve slope of thin wings in either subsonic flow or supersonic flow is the same when the direction of flight of the wing is reversed. It is also shown that the wing reversal does not change the thickness drag, damping-in-roll parameter or the damping-in-pitch parameter.
Equilibrium Operating Performance of Axial-Flow Turbojet Engines by Means of Idealized Analysis
"A method of predicting equilibrium operating performance of turbojet engines has been developed, with the assumption of simple model processes for the components. Results of the analysis are plotted in terms of dimensionless parameters comprising critical engine dimensions and over-all operating variables. This investigation was made of an engine in which the ratio of axial inlet-air velocity to compressor-tip velocity is constant, which approximates turbojet engines with axial-flow compressors" (p. 673).
Comparative drag measurements at transonic speeds of rectangular sweptback NACA 65-009 airfoils mounted on a freely falling body
From Summary: "Directly comparable drag measurements have been made of an airfoil with a conventional rectangular plan form and an airfoil with a sweptback plan form mounted on freely falling bodies. Both airfoils had NACA 65-009 sections and were identical in span, frontal area, and chord perpendicular to the leading edge. The sweptback plan form incorporated a sweepback angle of 45 degrees. The data obtained have been used to establish the relation between the airfoil drag coefficients and the free-stream Mach number over a range of Mach numbers from 0.90 to 1.27. The results of the measurements indicate that the drag of the sweptback plan form is less than 0.3 that of the rectangular plan form at a Mach number of 1.00 and is less than 0.4 that at a Mach number of 1.20."
Theoretical comparison of several methods of thrust augmentation for turbojet engines
"A theoretical investigation of tail-pipe burning, water injection at the compressor inlet, combination tail-pipe burning plus water injection, bleedoff, and rocket-assist methods thrust augmentation for turbojet engines was made for an engine representative of those in current use. The effect of augmented liquid ratio on augmented thrust ratio and the effects of altitude and flight Mach number on the performance of various methods were determined. The additional take-off weight involved by the use of the different thrust augmentation methods, as well as the effect of the various thrust augmentation methods on the range of a representative aircraft was also investigated" (p. 727).
Theoretical Study of the Tunnel-Boundary Lift Interference Due to Slotted Walls in the Presence of the Trailing-Vortex System of a Lifting Model
"The equations presented in this report give the interference on the trailing-vortex system of a uniformly loaded finite-span wing in a circular tunnel containing partly open and partly closed walls, with special reference to symmetrical arrangements of the open and closed portions. Methods are given for extending the equations to include tunnel shapes other than circular. The rectangular tunnel is used to demonstrate these methods. The equations are also extended to nonuniformly loaded wings" (p. 361).
Theoretical and experimental investigation of heat transfer by laminar natural convection between parallel plates
Results are presented of a theoretical and experimental investigation of heat transfer involving laminar natural convection of fluids enclosed between parallel walls oriented in the direction of the body force, where one wall is heated uniformly, and the other is cooled uniformly. For the experimental work, parallel walls were simulated by using an annulus with an inner-to-outer diameter ratio near 1. The results of the theoretical investigation are presented in the form of equations for the velocity and temperature profiles and the ratio of actual temperature drop across the fluid to the temperature drop for pure conduction. No experimental measurements were made of the velocity and temperature profiles, but the experimental results are compared with theory on the basis of the ratio of the actual temperature drop to the temperature drop for pure conduction. Good agreement was obtained between theory and experiment for axial temperature gradients of 10 degrees F. per foot or larger.
Determination of lateral-stability derivatives and transfer-function coefficients from frequency-response data for lateral motions
A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.
A Method for the Design of Sweptback Wings Warped to Produce Specified Flight Characteristics at Supersonic Speeds
One of the problems connected with the sweptback wing is the difficulty of controlling the location of the center of pressure and hence the pitching moment. A method is presented for designing a wing to be self-trimming at a given set of flight conditions. Concurrently, the spanwise distribution of load on the wing is made to be approximately elliptical, in an effort to maintain low wing drag.
An Investigation of the Maximum Lift of Wings at Supersonic Speeds
This report presents the results of an exploratory investigation carried out in the Langley 9-inch supersonic tunnel to determine the maximum lift of wings operating at supersonic speeds. A variety of wing plan forms of random thickness distributions were tested at Mach numbers of 1.55, 1.90, and 2.32 and at Reynolds numbers varying between 0.74 x 10(6) and 0.27 x 10(6) at angles of attack ranging from zero up through the angle at which maximum lift occurred. Subsequent pressure-distribution tests on wings of triangular and rectangular plan forms were made at a Mach number of 2.40.
Calculated spanwise lift distributions, influence functions, and influence coefficients for unswept wings in subsonic flow
Spanwise lift distributions have been calculated for nineteen unswept wings with various aspect ratios and taper ratios and with a variety of angle-of-attack or twist distributions, including flap and aileron deflections, by means of the Weissinger method with eight control points on the semispan. Also calculated were aerodynamic influence coefficients which pertain to a certain definite set of stations along the span, and several methods are presented for calculating aerodynamic influence functions and coefficients for stations other than those stipulated. The information presented in this report can be used in the analysis of untwisted wings or wings with known twist distributions, as well as in aeroelastic calculations involving initially unknown twist distributions.
Exact solutions of laminar-boundary-layer equations with constant property values for porous wall with variable temperature
From Summary: "Exact solution of the laminar-boundary-layer equations for wedge-type flow with constant property values are presented for transpiration-cooled surfaces with variable wall temperatures. The difference between wall and stream temperature is assumed proportional to a power of the distance from the leading edge. Solutions are given for a Prandtl number of 0.7 and ranges of pressure-gradient, cooling-air-flow, and wall-temperature-gradient parameters. Boundary-layer profiles, dimensionless boundary-layer thicknesses, and convective heat-transfer coefficients are given in both tabular and graphical form. Corresponding results for constant wall temperature and for impermeable surfaces are included for comparison purposes."
Generalized Indical Forces on Deforming Rectangular Wings in Supersonic Flight
"A method is presented for determining the time-dependent flow over a rectangular wing moving with a supersonic forward speed and undergoing small vertical distortions expressible as polynomials involving spanwise and chordwise distances. The solution for the velocity potential is presented in a form analogous to that for steady supersonic flow having the familiar "reflected area" concept discovered by Evvard. Particular attention is paid to indicial-type motions and results are expressed in terms of generalized indicial forces. Numerical results for Mach numbers equal to 1.1 and 1.2 are given for polynomials of the first and fifth degree in the chordwise and spanwise directions, respectively, on a wing having an aspect ratio of 4" (p. 595).
NACA Transonic Wind-Tunnel Test Sections
Report presents an approximate subsonic theory for the solid-blockage interference in circular wind tunnels with walls slotted in the direction of flow. This theory indicated the possibility of obtaining zero blockage interference. Tests in a circular slotted tunnel based on the theory confirmed the theoretical predictions.
A Theoretical and Experimental Investigation of the Lift and Drag Characteristics of Hydrofoils at Subcritical and Supercritical Speeds
"A theoretical and experimental investigation at subcavitation speeds was made of the effect of the free-water surface and rigid boundaries on the lift and drag of an aspect-ratio-10 hydrofoil at both subcritical and supercritical speeds and of an aspect ratio-4 hydrofoil at supercritical speeds. Approximate theoretical solutions for the effects of the free-water surface and rigid boundaries on drag at subcritical speeds are developed. An approximate theoretical solution for the effects of these boundaries on drag at subcritical speeds is also presented" (p. 661).
On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow
This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.
A flight evaluation of the longitudinal stability characteristics associated with the pitch-up of a swept-wing airplane in maneuvering flight at transonic speeds
This report presents the results of flight measurements of longitudinal stability and control characteristics made on a swept-wing jet aircraft to determine the origin of the pitch-up encountered in maneuvering flight at transonic speeds. For this purpose measurements were made of elevator angle, tail angle of attack, and wing-fuselage pitching moments (obtained from measurements of the balancing tail loads).
Analysis of Turbulent Heat Transfer, Mass Transfer, and Friction in Smooth Tubes at High Prandtl and Schmidt Numbers
From Introduction: "In the analysis given herein, which was made at the NACA Lewis laboratory, the expression for eddy diffusivity given in reference 1 is modified in order to account for the effect of kinematic viscosity in reducing the turbulence in the region close to the wall. The effects of variable viscosity and of length-to-diameter ratio are also investigated."
Experimental investigation of free-convection heat transfer in vertical tube at large Grashof numbers
Report presents the results of an investigation conducted to study free-convection heat transfer in a stationary vertical tube closed at the bottom. The walls of the tube were heated, and heated air in the tube was continuously replaced by fresh cool air at the top. The tube was designed to provide a gravitational field with Grashof numbers of a magnitude comparable with those generated by the centrifugal field in rotating-blade coolant passages (10(8) to 10(13)). Local heat-transfer coefficients in the turbulent-flow range and the temperature field within the fluid were obtained.
Analog study of interacting and noninteracting multiple-loop control systems for turbojet engines
The results of an analog investigation of several turbojet-engine control configurations is presented in this report. Both proportional and proportional-plus-integral controllers were studied, and compensating terms for engine interaction were added to the control system. Data were obtained on the stability limits and the transient responses of these various configurations. Analytical expressions in terms of the component transfer functions were developed for the configurations studied, and the optimum form for the compensation terms was determined.
Minimum-drag ducted and pointed bodies of revolution based on linearized supersonic theory
The linearized drag integral for bodies of revolution at supersonic speeds is presented in a double-integral form which is not based on slender-body approximations but which reduces to the equal slender-body expression in the proper limit. With the aid of a suitably chosen auxiliary condition, the minimum-external-wave-drag problem is solved for a transition section connecting two semi-infinite cylinders. The projectile tip is a special case and is compared with the Von Karman projectile tip. Calculations are presented which indicate that the method of analysis gives good first-order results in the moderate supersonic range.
Statistical measurements of contact conditions of 478 transport-airplane landings during routine daytime operations
Statistical measurements of contact conditions have been obtained, by means of a special photographic technique, of 478 landings of present-day transport airplanes made during routine daylight operations in clear air at the Washington National Airport. From the measurements, sinking speeds, rolling velocities, bank angles, and horizontal speeds at the instant before contact have been evaluated and a limited statistical analysis of the results has been made and is reported in this report.
Charts for estimating tail-rotor contribution to helicopter directional stability and control in low-speed flight
"Theoretically derived charts and equations are presented by which tail-rotor design studies of directional trim and control response at low forward speed can be conveniently made. The charts can also be used to obtain the main-rotor stability derivatives of thrust with respect to collective pitch and angle of attack at low forward speeds. The use of the charts and equations for tail-rotor design studies is illustrated. Comparisons between theoretical and experimental results are presented. The charts indicate, and flight tests confirm, that the region of vortex roughness which is familiar for the main rotor is also encountered by the tail rotor and that prolonged operation at the corresponding flight conditions would be difficult" (p. 1).
Theoretical Prediction of Pressure Distributions on Nonlifting Airfoils at High Subsonic Speeds
"Theoretical pressure distributions on nonlifting circular-arc airfoils in two-dimensional flows with high subsonic free-stream velocity are found by determining approximate solutions, through an iteration process, of an integral equation for transonic flow proposed by Oswatitsch. The integral equation stems directly from the small-disturbance theory for transonic flow. This method of analysis possesses the advantage of remaining in the physical, rather than the hodograph, variable and can be applied in airfoils having curved surfaces" (p. 1).
Effect of ground interference on the aerodynamic and flow characteristics of a 42 degree sweptback wing at Reynolds numbers up to 6.8 x 10(6)
Report presents the results of an investigation of the effects of ground interference on the aerodynamic characteristics of a 42 degree sweptback wing at distances 0.68 and 0.92 of the mean aerodynamic chord from the simulated ground to the 0.25-chord point of the mean aerodynamic chord. Survey data behind the wing, both with and without the simulated ground, are presented in the form of contour charts of downwash, sidewash, and dynamic-pressure ratio at longitudinal stations of 2.0 and 2.8 mean aerodynamic chords behind the wing.
Measurement and Analysis of Wing and Tail Buffeting Loads on a Fighter Airplane
"The buffeting loads measured on the wing and tail of a fighter airplane during 194 maneuvers are given in tabular form, along with the associated flight conditions. Measurements were made at altitudes of 30,000 to 10,000 feet and at speeds up to a Mach number of 0.8. Least-squares methods have been used for a preliminary analysis of the data. The agreement between the results of this analysis and the loads measured in stalls is sufficiently good to suggest the examination of the buffeting of other airplanes on the same basis" (p. 1).
Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls With Application to Turbine Blade Cooling
"An approximate method for the development of flow and thermal boundary layers in the laminar region on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by the use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout the boundary layer is assumed. The velocity and temperature profiles within the boundary layer are approximated by expressions composed of trigonometric functions" (p. 339).
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