ALBERT

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: No abstract available

Description: Previous work on turbulent heat transfer and flow in tubes was generalized and applied to flow in non-circular passages of equilateral triangular and square cross section. Expressions for eddy diffusivity that had been verified for flow and heat transfer in tubes were assumed to apply in general along lines normal to a wall. Velocity distributions, wall shear-stress distributions, and friction factors, as well as wall heat-transfer distributions, wall temperature distributions, and average heat-transfer coefficients were calculated. In addition, results from a previous analysis for axial flow between rods were compared with new experimental data. For calculating wall temperature distributions, uniform heat generation in the passage wall and uniform heat transfer at the outer surface were assumed. The application of the results is restricted to moderately small peripheral wall temperature variations. Calculations were made for Reynolds numbers from 20,000 to 900,000 and Prandtl numbers from 0.73 to 300. Results show that velocities, shear stresses, and heat transfer in the region near the corner were lower than average values and were zero at the corner. Friction factors and average Nusselt numbers were lower than in a tube.

Description: An investigation of the thrust characteristics and internal pressure distributions of two convergent-divergent 15 deg. half-angle exhaust nozzles having area ratios of 6 and 9 was made in the NASA Lewis 10- by 10-foot supersonic wind tunnel. The tests were conducted at free-stream Mach numbers of 0, 2.0, 2.5, 3.0, and 3.5 over a range of nozzle pressure ratios from 3 to 105. Attempts were made to induce separation of the overexpanded nozzle flow using secondary airflow and a wedge. Nozzle flow expansion under all free-stream conditions followed one-dimensional theory until separation from the nozzle wall occurred. In quiescent air the nozzle flow expanded to a pressure approximately one-half the base pressure before separation. When the nozzles were tested with supersonic external flow at the same effective pressure ratios, the nozzle flow separated with negligible expansion below the base pressure. The effect of a supersonic stream on internal nozzle flow separation characteristics was well defined only at a free-stream Mach number of 2.0. Thrust data at supersonic free-stream conditions indicate that only a small percentage of the ideal nozzle thrust will be available at nozzle pressure ratios below design. However, the overexpanded primary nozzle thrust loss was decreased by injecting large quantities of secondary air near the nozzle exit. In most cases no net gain in thrust resulted from secondary-air injection when the nozzle thrust was compared with the ideal thrust of both the primary and secondary airflows.

Description: Wind tunnel tests recorded the effect of decelerators on flow at various supersonic speeds. Rigid parachute models were tested for the effects of porosity, shroud length, and number of shrouds. Flexible model parachutes were tested for effects of porosity and conical-shaped canopy. Ribbon dive brakes on a missile-shaped body were tested for effect of tension cable type and ribbon flare type. The final test involved a plastic sphere on riser lines.

Description: No abstract available

Description: Measurements of average heat transfer and friction coefficients and local heat transfer coefficients were made with helium flowing through electrically heated smooth tubes with length-diameter ratios of 60 and 92 for the following range of conditions: Average surface temperature from 1457 to 4533 R, Reynolds numbe r from 3230 to 60,000, heat flux up to 583,200 Btu per hr per ft2 of heat transfer area, and exit Mach numbe r up to 1.0. The results indicate that, in the turbulent range of Reynolds number, good correlation of the local heat transfer coefficients is obtained when the physical properties and density of helium are evaluated at the surface temperature. The average heat transfer coefficients are best correlated on the basis that the coefficient varies with [1 + (L/D))(sup -0,7)] and that the physical properties and density are evaluated at the surface temperature. The average friction coefficients for the tests with no heat addition are in complete agreement with the Karman-Nikuradse line. The average friction coefficients for heat addition are in poor agreement with the accepted line.

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: No abstract available

Description: Convection is called free is the stresses (including the normal pressure) to which the fluid is subjected at its boundaries do not perform mechanical work, that is, if all the boundaries of the fluid are stationary. The case where this is not true is termed forced convection. It corresponds to the action on the fluid of some mechanical suction pumping the fluid.

Description: The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics.

Description: Upon impact of a solid body on the plane surface of a fluid, there occurs on the vetted surface of the body an abrupt pressure rise which propagates into both media with the speed of sound. Below, we assume the case where the speed of propagation of sound in the body which falls on the surface of the fluid may be regarded as infinitely large in comparison with the speed of propagation of sound in the fluid; that is, we shall assume that the falling body is absolutely rigid. IN this case, the entire relative speed of the motion which takes place at the beginning of the impact is absorbed by the fluid. The hydrodynamic pressures arising thereby are propagated from the contact surface within the fluid with the speed of sound in the form of compression and expansion waves and are gradually damped. After this, they are dispersed like impact pressures, reach ever larger regions of the fluid remote fran the body and became equal to zero; in the fluid there remain hydrodynamic pressures corresponding to the motion of the body after the impact. Neglecting the forces of viscosity and taking into account, furthermore, that the motion of the fluid begins from a state of rest, according to Thomson's theorem, we may consider the motion of an ideal compressible fluid in the process of impact to be potential. We examine the case of impact upon the surface of a ccmpressible fluid of a flat plate of infinite extent or of a body, the immersed part of the surface of which may be called approximately flat. In this report we discuss the first phase of the impact pressure on the surface of a fluid, prior to the appearance of a cavity, since at this stage the hydrodynamic pressures reach their maximum values. Observations, after the fall of the bodies on the surface of the fluid, show that the free surface of the fluid at this stage is almost completely at rest if one does not take into account the small rise in the neighborhood of the boundaries of the impact surface.

Description: Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.

Description: The increasing importance of high-speed flow leads to similar problems in various fields of research which are summarized in what follows. Typical of all cases is the conversion of high kinetic energy into extreme thermodynamic states with temperatures of several thousand degrees, frequently connected with dissociation and ionization of the gas involved. There is also a characteristic small sensitivity to the processes discussed in the case of gases of low molecular weight (light gases). The penetration of meteors into the atmosphere of the earth at astronomical speeds results in temperatures higher than those of the surface of the sun. Such temperatures may be produced in shock tubes, with light gases used as the driving gas. For supersonic fighters the problem of propulsion is less difficult to solve than the problem of large heating, on the surface and in the combustion chamber. Finally, for the space-travel rocket, astronomical speeds have to be reached which require the lightest possible gases as propellants. Here again, dissociation processes in the combustion chamber are of considerable importance.

Description: Ideally, the reflection of a shock from the closed end of a shock tube provides, for laboratory study, a quantity of stationary gas at extremely high temperature. Because of the action of viscosity, however, the flow in the real case is not one-dimensional, and a boundary layer grows in the fluid following the initial shock wave. In this paper simplifying assumptions are made to allow an analysis of the interaction of the shock reflected from the closed end with the boundary layer of the initial shock afterflow. The analysis predicts that interactions of several different types will exist in different ranges of initial shock Mach number. It is shown that the cooling effect of the wall on the afterflow boundary layer accounts for the change in interaction type. An experiment is carried out which verifies the existence of the several interaction regions and shows that they are satisfactorily predicted by the theory. Along with these results, sufficient information is obtained from the experiments to make possible a model for the interaction in the most complicated case. This model is further verified by measurements made during the experiment. The case of interaction with a turbulent boundary layer is also considered. Identifying the type of interaction with the state of turbulence of the interacting boundary layer allows for an estimate of the state of turbulence of the boundary layer based on an experimental investigation of the type of interaction. A method is proposed whereby the effect of the boundary-layer interaction on the strength of the reflected shock may be calculated. The calculation indicates that the reflected shock is rapidly attenuated for a short distance after reflection, and this result compares favorably with available experimental results.

Description: In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

Description: A number of semiempirical approximate methods exist for determining the characteristics of the turbulent boundary layer on a curvilinear surface. At present, among these methods, the one proposed by L. G. Loitsianskii is given frequent practical application. This method is sufficiently effective and permits, in the case of wing profiles with technically smooth surfaces, calculating the basic characteristics of the boundary layer and the values of the overall drag with an accuracy which suffices for practical purposes. The idea of making use of the basic integral momentum equation ((d delta(sup xx))/dx) + ((V' delta(sup xx))/V) (2 + H) = (tau(sub 0))/(rho V(exp 2)) proves to be fruitful also for the solution of the problems in the determination of the characteristics of the turbulent boundary layer on a rough surface.

Description: The effect of the location of transition on the heat transfer to the turbulent incompressible boundary layer is analyzed. The analysis indicates that considerably higher heat-transfer rates may occur for some distance downstream if the transition is very late. The results of a limited experimental investigation are in substantial agreement with the results of the analysis. If the extent of the transition region is known, the analysis also allows adequate prediction of heat-transfer coefficients within the transition region. The nature of this analysis is such that it should predict local shear coefficients in the transition region equally well.

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: Boundary-layer-transition and heat-transfer measurements were obtained from flight tests of blunt and sharp cones having apex angles of 50 deg. The test Mach number range was from 1.7 to 4.7, corresponding to free-stream Reynolds numbers, based on cone base diameter, of 18. 3 x 10(exp 6) and 32.1 x 10(exp 6), respectively. Transition on both models occurred at a local Reynolds number of 1 x 10(exp 6) to 2 X 10(exp 6) based on distance from the stagnation point. Transition Reynolds numbers based on momentum thickness were between 320 and 380 for the blunt cone. The model surface roughness was 25 rms microinches or greater. Turbulent heat transfer to the conical surface of the blunt cone at a Mach number of 4 was 30 percent less than that to the surface of the sharp cone. Available theories predicted heat-transfer coefficients reasonably well for the fully laminar or turbulent flow conditions.

Description: Skin temperatures and surface pressures have been measured on a slightly blunted cone-cylinder-flare configuration to a maximum Mach number of 9.89 with a rocket-propelled model. The cone had a t o t a l angle of 25 deg and the flare had a 10 deg half-angle. Temperature data were obtained at eight cone locations, four cylinder locations, and seven flare locations; pressures were measured at one cone location, one cylinder location, and three flare locations. Four stages of propulsion were utilized and a reentry type of trajectory was employed in which the high-speed portion of flight was obtained by firing the last two stages during the descent of the model from a peak altitude of 99,400 feet. The Reynolds number at peak Mach number was 1.2 x 10(exp 6) per foot of model length. The model length was 6.68 feet. During the higher speed portions of flight, temperature measurements along one element of the nose cone indicated that the boundary layer was probably laminar, whereas on the opposite side of the nose the measurements indicated transitional or turbulent flow. Temperature distributions along one meridian of the model showed the flare to have the highest temperatures and the cylinder generally to have the lowest. A maximum temperature of 970 F was measured on the cone element showing the transitional or turbulent flow; along the opposite side of the model, the maximum temperatures of the cone, cylinder, and flare were 545 F, 340 F, and 680 F, respectively, at the corresponding time.

Description: The heat transfer and pressures on the surfaces of several flat-plate models with various external crosswise stiffener arrangements are presented. The tests were made in a free jet at Mach numbers of 0.77, 1.39, and 1.98 for Reynolds numbers of 3 x 10(exp 6), 7 x 10(exp 6), and 14 x 10(exp 6), respectively, based on a length of 1 foot. The addition of external crosswise stiffeners to the flat-plate models caused large pressure and heat-transfer variations on the surfaces of the models.

Description: In the investigation of stability of a two-dimensional laminar flow with respect to small disturbances, a disturbance of the stream function moving downstream (in the direction of the x-axis) by the "partial wave formula" is described.

Description: The literature on turbulent heat transfer has in the course of years attained a considerable volume. Since this very complicated problem has not as yet found a complete solution, further studies in this field may be expected. The heat engineer must therefore accomodate himself to a constantly increasing number of theories and formulas. Since the theories generally start from hypothetical assumptions, and since they contain true and false assertions, verified knowledge and pure suppositions often being intermingled in a manner difficult to tell them apart, the specialist had difficulty in forming a correct evaluation of the individual studies. The need therefore arises for a presentation of the problem of turbulent heat transfer which is not initially bound by hypothetical assumptions and in which uninvestigated can be clearly distinguished form each other. Such a presentation will be given in the present treatment. Brief remarks with regard to the development of the theory of local heat transfer are included.

Description: Measurements of aerodynamic heat transfer have been made along the hemisphere and cylinder of a hemisphere-cylinder rocket-propelled model in free flight up to a Mach number of 3.88. The test Reynolds number based on free-stream condition and diameter of model covered a range from 2.69 x l0(exp 6) to 11.70 x 10(exp 6). Laminar, transitional, and turbulent heat-transfer coefficients were obtained. The laminar data along the body agreed with laminar theory for blunt bodies whereas the turbulent data along the cylinder were consistently lower than that predicted by the turbulent theory for a flat plate. Measurements of heat transfer at the stagnation point were, in general, lower than the theory for stagnation-point heat transfer. When the Reynolds number to the junction of the hemisphere-cylinder was greater than 6 x l0(exp 6), the transitional Reynolds number varied from 0.8 x l0(exp 6) to 3.0 x 10(exp 6); however, than 6 x l(exp 6) when the Reynolds number to the junction was less, than the transitional Reynolds number varied from 7.0 x l0(exp 6) to 24.7 x 10(exp 6).

Description: The unsteady aerodynamic forces, [based on two-dimensional incompressible flow considerations], are determined for an unstaggered cascade, the blades of which are vibrating in phase in an approach flow parallel to the blades.

Description: The net heat of combustion of the product formed by the reaction of diborane with a mixture of acetylene and ethylene was found to be 20,440 +/- 150 Btu per pound for the reaction of liquid fuel to gaseous carbon dioxide, gaseous water, and solid boric oxide. The measurements were made in a Parr oxygen-bomb calorimeter, and the combustion was believed to be 98 percent complete. The estimated net-heat of combustion for complete combustion would therefore be 20,850 +/- 150 Btu per pound.

Description: The heat of combustion of the product formed by the reaction acetylene and diborane was found to be 20,100 +/- 100 Btu per pound for the reaction of liquid fuel to gaseous carbon dioxide, gaseous water, and solid boric oxide. The measurements were made in a Parr oxygen-bomb calorimeter, and chemical analyses both of the sample and of the combustion products indicated combustion in the bomb calorimeter to have been 97 percent complete. The estimated net heat of combustion for complete combustion would therefore be 20,700 +/- 100 Btu per pound.

Description: In dusty air flows occurring in industrial practice in transport by air pressure of friable materials, in the drying, annealing, and so forth, of a pulverized solid mass in suspension, and in other processes, the concentration of solid particles usually has a magnitude of the order of 1 kg per 1 kg of air. At such a concentration, the ratio of the volume of the particles to the volume of the air is small (less than one-thousandth part). However, regardless of this, the presence of a solid admixture manifests itself in the rules for the velocity distribution of the air in a dusty air flow. As a result, the rules of velocity change are different for clean and for dusty air flows. The estimation of the influence of the admixture on the velocity of the motion of the flow presents a definitive interest. One of the attempts to estimate that influence on the axial velocity of a free axially symmetrical jet with admixtures was made by Abramovich. Abramovich assumed beforehand that the fine particles of the admixture in the jet are subject to the motion of the air (that is, that the velocity of the admixture is approximately equal to the local velocity of the air); he then took as the basis of his considerations, in solving the problem, the condition that the amount of motion of the two-phase jet must be constant.

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: 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: This report is concerned with fluid mechanics of two-dimensional cascades, particularly turbine cascades. Methods of solving the incompressible ideal flow in cascades are presented. The causes and the order of magnitude of the two-dimensional losses at subsonic velocities are discussed. Methods are presented for estimating the flow and losses at high subsonic velocities. Transonic and supersonic flows in lattices are then analyzed. Some three-dimensional features of the flow in turbines are noted.

Description: The fundamental, practically the most important branch of the modern mechanics of a viscous fluid or a gas, is that branch which concerns itself with the study of the boundary layer. The presence of a boundary layer accounts for the origin of the resistance and lift force, the breakdown of the smooth flow about bodies, and other phenomena that are associated with the motion of a body in a real fluid. The concept of boundary layer was clearly formulated by the founder of aerodynamics, N. E. Joukowsky, in his well-known work "On the Form of Ships" published as early as 1890. In his book "Theoretical Foundations of Air Navigation," Joukowsky gave an account of the most important properties of the boundary layer and pointed out the part played by it in the production of the resistance of bodies to motion. The fundamental differential equations of the motion of a fluid in a laminar boundary layer were given by Prandtl in 1904; the first solutions of these equations date from 1907 to 1910. As regards the turbulent boundary layer, there does not exist even to this day any rigorous formulation of this problem because there is no closed system of equations for the turbulent motion of a fluid. Soviet scientists have done much toward developing a general theory of the boundary layer, and in that branch of the theory which is of greatest practical importance at the present time, namely the study of the boundary layer at large velocities of the body in a compressed gas, the efforts of the scientists of our country have borne fruit in the creation of a new theory which leaves far behind all that has been done previously in this direction. We shall herein enumerate the most important results by Soviet scientists in the development of the theory of the boundary layer.

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 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: 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: Transfer functions descriptive of the response of most engine variables were determined from transient data that were obtained from approximate step inputs in fuel flow and in exhaust-nozzle area. The speed responses of both spools to fuel flow and to turbine-inlet temperature appeared as identical first-order lags. Response to exhaust-nozzle area was characterized by a first-order lag response of the outer-spool speed, accompanied by virtually no change in inner-spool speed.

Description: The static lateral- and directional-stability characteristics of a high-speed fighter-type airplane, obtained from wind-tunnel tests of a model, are presented. The model consisted of a thin, unswept wing of aspect ratio 2.3 and taper ratio 0.385, a body, and a horizontal tail mounted in a high position on a vertical tail. Rolling-moment, yawing moment, and cross-wind-force coefficients are presented for a range of sideslip angles of -5 deg. to +5 deg, for Mach numbers of 0.90, 1.45, and 1.90. Data are presented which show the effects on the lateral and directional stability of: (1) component parts of the complete model, (2) modification of the empennage so as to provide different heights of the horizontal tail above the wing plane, (3) angle of attack, and (4) dihedral of the wing.

Description: An investigation to determine the steady-state and surge characteristics of the J57-P-1 two-spool turbojet engine with various inlet air-flow distortions was conducted in the altitude wind tunnel at the NACA Lewis laboratory. Along with a uniform inlet total-pressure distribution, one circumferential and three radial pressure distortions were investigated. Data were obtained over a complete range of compressor speeds both with and without intercompressor air bleed at a flight Mach number of 0.8 and at altitudes of 35,000 and 50,000 feet. Total-pressure distortions of the magnitudes investigated had very little effect on the steady-state operating line for either the outer or inner compressor. The small radial distortions investigated also had engine over that obtained with the uniform inlet pressure distribution. The circumferential distortion, however, raised the minimum speed at which the engine could operate without encountering surge when the intercompressor bleeds were closed. This increase in minimum speed resulted in a substantial reduction in the operable speed range accompanied by a reduction in the altitude operating limit.

Description: The performance and operational characteristics of the J71-A2 turbojet-engine afterburner were investigated for a range of altitudes from 23,000 to 60,000 feet at a flight Mach number of 0,9 and at flight Mach numbers of 0.6, 0.9, and 1.0 at an altitude of 45,000 feet. The combustion performance and altitude operational limits, as well as the altitude starting characteristics have been determined.

Description: The first four stages were found to cause a major part of the poor low-speed efficiency of this compressor. The low design-speed over-all pressure ratio at surge was caused by the first and the twelfth to fifteenth stages. The multiple over-all performance curves in the intermediate-speed range were at least partly the result of double-branched characteristic curves for the third and seventh stages.

Description: The condensation pressure of air was determined over the range of temperature from 60 to 85 K. The experimental results were slightly higher than the calculated values based on the ideal solution law. Heat of vaporization of oxygen was determined at four temperatures ranging from about 68 to 91 K and of nitrogen similarly at four temperatures ranging from 62 to 78 K.

Description: The heat requirements for the icing protection of two radome configurations have been studied over a range of design icing conditions. Both the protection limits of a typical thermal protection system and the relative effects of the various icing variables have been determined. For full evaporation of all impinging water, an effective heat density of 14 watts per square inch was required. When a combination of the evaporation and running wet surface systems was employed, a heat requirement of 5 watts per square inch provided protection at severe icing and operating conditions.

Description: The trajectories of droplets in the air flowing past NACA 65(1)-208 airfoil and an NACA 65(1)-212 airfoil, both at an angle of attack of 4 degrees, were determined. The amount of water in droplet form impinging on the airfoils, the area of droplet impingement, and the rate of droplet impingement per unit area on the airfoil surface affected were calculated from the trajectories and are presented. The amount, extent, and rate of impingement of the NACA 65(1)-208 airfoil are compared with the results for the NACA 65(1)1-212 airfoil. Under similar conditions of operation, the NACA 65(1)-208 airfoil collects less water than the NACA 65(1)-212 airfoil. The extent of impingement on the upper surface of the NACA 65(1)-208 airfoil is much less than on the upper surface of the NACA 65(1)-212 airfoil, but on the lower surface the extents of impingement are about the same.

Description: The present status of available information relative to the prediction of shock-induced boundary-layer separation is discussed. Experimental results showing the effects of Reynolds number and Mach number on the separation of both laminar and turbulent boundary layer are given and compared with available methods for predicting separation. The flow phenomena associated with separation caused by forward-facing steps, wedges, and incident shock waves are discussed. Applications of the flat-plate data to problems of separation on spoilers, diffusers, and scoop inlets are indicated for turbulent boundary layers.

Description: The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

Description: An investigation of forced-convection heat transfer and associated pressure drops was conducted with air flowing through electrically heated Inconel tubes having various degrees of square-thread-type roughness, an inside diameter of 1/2 inch, and a length of 24 inches. were obtained for tubes having conventional roughness ratios (height of thread/radius of tube) of 0 (smooth tube), 0.016, 0.025, and 0.037 over ranges of bulk Reynolds numbers up to 350,000, average inside-tube-wall temperatures up to 1950deg R, and heat-flux densities up to 115,000 Btu per hour per square foot. Data The experimental data showed that both heat transfer and friction increased with increase in surface roughness, becoming more pronounced with increase in Reynolds number; for a given roughness, both heat transfer and friction were also influenced by the tube wall-to-bulk temperature ratio. Good correlation of the heat-transfer data for all the tubes investigated was obtained by use of a modification of the conventional Nusselt correlation parameters wherein the mass velocity in the Reynolds number was replaced by the product of air density evaluated at the average film temperature and the so-called friction velocity; in addition, the physical properties of air were evaluated at the average film temperature. The isothermal friction data for the rough tubes, when plotted in the conventional manner, resulted in curves similar to those obtained by other investigators; that is, the curve for a given roughness breaks away from the Blasius line (representing turbulent flow in smooth tubes) at some value of Reynolds number, which decreases with increase in surface roughness, and then becomes a horizontal line (friction coefficient independent of Reynolds number). A comparison of the friction data for the rough tubes used herein indicated that the conventional roughness ratio is not an adequate measure of relative roughness for tubes having a square-thread-type element. The present data, as well as those of other investigators, were used to isolate the influence of ratios of thread height to width, thread spacing to width, and the conventional roughness ratio on the friction coefficient. A fair correlation of the friction data was obtained for each tube with heat addition when the friction coefficient and Reynolds number were defined on the basis of film properties; however, the data for each tube retained the curve characteristic of that particular roughness. The friction data for all the rough tubes could be represented by a single line for the complete turbulence region by incorporating a roughness parameter in the film correlation. No correlation was obtained for the region of incomplete turbulence.

Description: The performance of a 16-stage axial-flow compressor, in which the mean-radius solidity was reduced from 1.28 to 1.02 in the fourteenth through sixteenth stage rotors was determined. The performance of this modification was compared with that of the compressor with original rotors. The reduced solidity resulted in slightly improved performance.

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: Research was conducted to determine the effect of the electrode parameters of spacing, configuration, and material' on the energy required for ignition of a flowing propane-air mixture. In addition, the data were used to indicate the energy distribution along the spark length and to confirm previous observations concerning the effect of spark duration on ignition energy requirements. The data were obtained with a mixture at a fuel-air ratio of 0.0835 (by weight), a pressure of 3 inches of mercury absolute, a temperature of 80 F, and a mixture velocity of 5 feet per second. Results showed that the energy required for ignition decreased as the electrode spacing was increased; a minimum energy occurred at. a spacing of 0.65 inch for large electrodes. For small electrodes, the spacing for minimum energy was not sharply defined. Small-diameter electrodes required less energy than large-diameter electrodes if the spacing was less than the optimum distance of 0.65 inch; at a spacing equal to the optimum distance, no difference was noted. Significant effects of electrode material on ignition energy were ascribed to differences in the type of spark discharges produced; glow discharges required higher energy than the arc-glow discharges. With pure glow discharges, the ignition energy was substantially constant for lead, cadmium, brass, aluminum, and tungsten electrodes. A method is described for determining the energy distribution along a glow discharge. It was found that one-third to one-half of the energy in the spark was concentrated in a small region near the cathode electrode, and the remainder was uniformly distributed across the spark gap. It was impossible to ascertain the dependence of ignition on. this distribution. It was also observed that long-duration (600 microsec) sparks required much less energy for ignition than did short-duration (1 microsec) sparks.

Description: Surge characteristics of the XJ34-WE-32 turbojet engine were determined over a range of altitudes. Several typical oscillograph traces during which surge occurred are presented. The effect of altitude on the surge line and it's relation to the steady-state operating region are shown.

Description: The theory of Taylor and Maccoll (Ref,1) gives the surface pressure on an infinite cone in supersonic flow as a function of the cone vertex angle and the free stream Mach number and static pressure for a gas of vanishing viscosity. When a slender conical probe is used together with an impact pressure probe to determine the static pressure and Mach number in a low density gas stream, it is desirable to have some theoretical estimate of the effect of viscous boundary layer on the probe readings. Theoretical and experimental results with respect to impact probes have been presented in Refs. 5 and 6. A simple approximation for a conical probe based on linearized supersonic flow and compressible boundary layer theory is presented here.

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.

Description: No abstract available

Description: No abstract available

Description: Tests of a 1/5 scale model of a proposed 153-foot high-speed submarine have been conducted in the Langley full-scale tunnel at the request of the Bureau of Ships, Department of the Navy. The test program included: (1) force tests to determine the drag, control effectiveness, and static stability characteristics for a number of model configurations, both in pitch and in yaw, (2) pressure measurements to determine the boundary-layer conditions and flow characteristics in the region of the propeller, and (3) an investigation of the effects of propeller operation on the model aerodynamic characteristics. In response to oral requests from the Bureau of Ships representatives t hat the basic data obtained in these tests be made available to them as rapidly as possible, this data report has been prepared to present some of the more pertinent results. All test results given in the present paper are for the propeller-removed condition and were obtained at a Reynolds number of approximately 22,300,000 based on model length.

Description: Investigations were conducted of a 12 degree 21-inch conical diffuser of 2:l area ratio to determine the interrelation of boundary layer growth and performance characteristics. surveys were made of inlet and exit from, longitudinal static pressures were recorded, and velocity profiles were obtained through an inlet Reynolds number range, determined From mass flows and based on inlet diameter of 1.45 x 10(exp 6) to 7.45 x 10(exp 6) and a Mach number range of 0.11 to approximately choking. These investigations were made to two thicknesses of inlet boundary layer. The mean value, over the entire range of inlet velocities, of the displacement thickness of the thinner inlet boundary layer was approximately 0.035 inch and that of the thicker inlet boundary layer was approximately six times this value. The loss coefficient in the case of the thinner inlet boundary layer had a value between 2 to 3 percent of the inlet impact pressure over most of the air-flow range. The loss coefficient with the thicker inlet boundary layer was of the order of twice that of the thinner inlet boundary layer at low speeds and approximately three times at high speeds. In both cases the values were substantially less than those given in the literature for fully developed pipe flow. The static-pressure rise for the thinner inlet boundary layer was of the order of 95 percent of that theoretically possible over the entire speed range. For the thicker inlet boundary layer the static pressure rise, as a percentage of that theoretically possible, ranged from 82 percent at low speeds to 68 percent at high speeds.

Description: Performance and boundary-layer data were taken in a 12 degree 10-inch inlet-diameter conical diffuser of 2:1 exit- to inlet-area ratio. These data were taken for two inlet-boundary-layer conditions. The first condition was that of a thinner inlet boundary later (boundary-layer displacement thickness, delta* approximately equal to 0.034) produced by an inlet section approximately 1 inlet diameter in length between the entrance bell and the diffuser. The second condition was a thicker inlet boundary layer (delta* approximately equal to 0.120) produced by an additional inlet section length of approximately 6 diameters. Longitudinal static-pressure distributions were measured fro wall static orifices. Transverse total- and static-pressure surveys were made at the inlet and exit stations. Boundary-layer velocity distributions were measured at seven stations between the inlet and exit. These data were obtained for a Reynolds number (based on inlet diameter) range of 1 x 10(exp 6) to 3.9 x 10(exp 6). The corresponding Mach number range was from M = 0.2 to choking. At the maximum-power-available condition supersonic flow was obtained as far as 4.5 inches downstream from the diffuser inlet with a maximum Mach number of M approximately equal to 1.5. The total-pressure loss through the diffuser in percentage of inlet dynamic pressure was approximately 2.5 percent for the thinner inlet boundary later and 5.5 percent for the thicker inlet boundary later over the lower subsonic range. These valued increased with increasing flow rate- the values for the thicker inlet boundary later more than those for the thinner inlet boundary layer. The diffuser effectiveness, expressed as the ratio of the actual static-pressure rise to the ideal static-pressure rise, was about 85 percent for the thinner inlet boundary layer and about 67 percent for the thicker inlet boundary later in the lower subsonic range. These values decrease with increasing flow rate. Separated flow was observed for both inlet-boundary-layer conditions in the region of adverse pressure gradient just downstream of the transition curvature from inlet section to diffuser. The flow for the thinner-inlet-boundary-layer condition did not fully re-establish itself along the diffuser walls. The thicker inlet-boundary-layer flow, while not completely re-establishing the normal flow pattern downstream of the separated region, did re-establish more successfully than the thinner inlet boundary layer.

Description: This document presents equations for the two-dimensional stationary problem of gas dynamics, and uses them to derive other equations, including equations for vorticity.

Description: The vortices forming in flowing water behind solid bodies are not represented correctly by the solution of the potential theory nor by Helmholtz's jets. Potential theory is unable to satisfy the condition that the water adheres at the wetted bodies, and its solutions of the fundamental hydrodynamic equations are at variance with the observation that the flow separates from the body at a certain point and sends forth a highly turbulent boundary layer into the free flow. Helmholtz's theory attempts to imitate the latter effect in such a way that it joins two potential flows, jet and still water, nonanalytical along a stream curve. The admissibility of this method is based on the fact that, at zero pressure, which is to prevail at the cited stream curve, the connection of the fluid, and with it the effect of adjacent parts on each other, is canceled. In reality, however, the pressure at these boundaries is definitely not zero, but can even be varied arbitrarily. Besides, Helmholtz's theory with its potential flows does not satisfy the condition of adherence nor explain the origin of the vortices, for in all of these problems, the friction must be taken into account on principle, according to the vortex theorem.

Description: The use of the linearized equations of Chaplygin to calculate the subsonic flow of a gas permits solving the problem of the flow about a wing profile for absence and presence of circulation. The solution is obtained in a practical convenient form that permits finding all the required magnitudes for the gas flow (lift, lift moment velocity distribution over the profile, and critical Mach number). This solution is not expressed in simple closed form; for a certain simplifying assumption, however, the equations of Chaplygin can be reduced to equations with constant coefficients, and solutions are obtained by using only the mathematical apparatus of the theory of functions of a complex variable. The method for simplifying the equations was pointed out by Chaplygin himself. These applied similar equations to the solution of the flow problem and obtained a solution for the case of the absence of circulation.

Description: In the flow about a body with large subsonic velocity if the velocity of the approaching flow is sufficiently large, regions of local supersonic velocities are formed about the body. It is known from experiment that these regions downstream of the flow are always bounded by shock waves; a continuous transition of the supersonic velocity to the subsonic under the conditions indicated has never been observed. A similar phenomenon occurs in pipes. If at two cross sections of the pipe the velocity is subsonic and between these sections regions of local supersonic velocity are formed without completely occupying a single cross section, these regions are always bounded by shock waves.

Description: The two-dimensional motion of an incompressible fluid about a closed contour with a definite velocity in magnitude and direction at infinity is considered. If, without changing the direction of the velocity at infinity, the magnitude is increased, the configuration of the streamlines remains unchanged and only the numbering of the stream function changes. There exists only one family of curves that can serve as streamlines in the incompressible flow about a given contour (at a given angle of attack); for example, the contour of an airplane wing. The case is quite different with a compressible fluid.

Description: An investigation of the nature of the flow field behind a rectangular circular-arc wing has been conducted in the Langley 9-inch supersonic tunnel. Pitot- and static-pressure surveys covering a region of flow behind the wing have been made together with detailed pitot surveys throughout the region of the wake. In addition, the flow direction has been measured using a weathercocking vane measurements. Theoretical calculations of the variation of both downwash and sidewash with angle of attack using Lagerstrom's superposition method have been made. In addition the effect of the wing thickness on the sidewash with the wing at 0 angle of attack has been evaluated. Near an angle of attack of 0, agreement between theory and experiment is good, particularly for the downwash results, except in the plane of the wing, inboard of the tip. In this region the proximity of the shed vortex sheet and the departure of the spanwise distribution of vorticity from theory would account for the disagreement. At higher angles of attack prediction of downwash depends on a knowledge of the location of the trailing vortex sheet, in order that the downwash may be corrected for its displacement and distortion. The theoretical location of the trailing vortex sheet, based on the theoretical downwash values integrated downstream from the wing trailing edge, is shown to differ widely from the experimental case. The rolling-up of the trailing vortex sheet behind the wing tip is evidenced by both the wake surveys and the flow-angle measurements.

Description: An analysis is made to simplify pressure-drop calculations for nonadiabatic and adiabatic friction flow of air in smooth cylindrical tubes when the density changes due to heat transfer and pressure drop are appreciable. Solutions of the equation of motion are obtained by the use of Reynolds' analogy between heat transfer and skin friction. Charts of the solutions are presented for making pressure-drop calculations. A technique of using the charts to determine the position of a normal shock in a tube is described.

Description: A discussion of the interaction between normal shocks and boundary layers on the basis of experimental evidence obtained in studies of supersonic flows in passages is given. The investigation was made as a result of the inability of the existing normal-shock theory to explain phenomena involving normal shocks that occurred in the presence of boundary layers. Assumptions with regard to the character of the effects of interaction between boundary layer and normal shock are proposed; these assumptions seem to give good agreement with certain experimental results.

Description: The differential equation of Chaplygin's jet problem is utilized to give a systematic development of particular solutions of the hodograph flow equations, which extends the treatment of Chaplygin into the supersonic range and completes the set of particular solutions. The particular solutions serve to place on a reasonable basis the use of velocity correction formulas for the comparison of incompressible and compressible flows. It is shown that the geometric-mean type of velocity correction formula introduced in part I has significance as an over-all type of approximation in the subsonic range. A brief review of general conditions limiting the potential flow of an adiabatic compressible fluid is given and application is made to the particular solutions, yielding conditions for the existence of singular loci in the supersonic range. The combining of particular solutions in accordance with prescribed boundary flow conditions is not treated in the present paper.

Description: A brief summary of the contents of this paper is presented here. In part I the differential equations of the problem of a gas flow in two dimensions is derived and the particular integrals by which the problem on jets is solved are given. Use is made of the same independent variables as Molenbroek used, but it is found to be more suitable to consider other functions. The stream function and velocity potential corresponding to the problem are given in the form of series. The investigation on the convergence of these series in connection with certain properties of the functions entering them forms the subject of part II. In part III the problem of the outflow of a gas from an infinite vessel with plane walls is solved. In part IV the impact of a gas jet on a plate is considered and the limiting case where the jet expands to infinity changing into a gas flow is taken up in more detail. This also solved the equivalent problem of the resistance of a gaseous medium to the motion of a plate. Finally, in part V, an approximate method is presented that permits a simpler solution of the problem of jet flows in the case where the velocities of the gas (velocities of the particles in the gas) are not very large.

Description: One of the problems of modern cavitation research is the experimental determination of the wing loads on airfoils during cavitation. Such experiments were made on various airfoils with the support of the naval ministry at the Kaiser Wilhelm Institute for Flow Research at Goettingen.

Description: The,theory of heat.transfer from a solid body to a liquid stream could he presented previously** only with limiting assumptions about the movement of the fluid (potential flow, laminar frictional flow). (See references 1, 2, and 3). For turbulent flow, the most important practical case, the previous theoretical considerations did not go beyond dimensionless formulas and certain conclusions as to the analogy between the friction factor and the unit thermal conductance, (See references 4, 5, 6, and 7,) In order to obtain numerical results, an experimental treatment of the problem was resorted to, which gave rise to numerous investigations because of the importance of this problem in many branches of technology. However, the results of these investigations frequently deviate from one another. The experimental results are especially dependent upon the overall dimensions and the specific proportions of the equipment. In the present work, the attempt will be made to develop systematically the theory of the heat transfer and of the dependence of the unit thermal conductance upon shape and dimensions, using as a basis the velocity distribution for turbulent flow set up by Prandtl and Von Karman.

Description: In the present report the theory of free turbulence propagation and the boundary layer theory are developed for a plane-parallel free stream of a compressible fluid. In constructing the theory use was made of the turbulence hypothesis by Taylor (transport of vorticity) which gives best agreement with test results for problems involving heat transfer in free jets.

Description: Experimental results of tests made at the Langley Memorial Aeronautical Laboratory are presented to show how heat-transfer coefficients can he increased by a method utilizing the high rate of heat transfer known to exist on any heat-transfer surface in the region adjacent to the edge on which the cooling or heating fluid impinges. The results show that, for the same pressure drop, the average surface heat-transfer.coefficient can be increased 50 to 100 percent when a cooling surface having a length of four inches in the direction of fluid flow is cut to form twenty fins with a length of 0.2 inch in the direction of fluid flow and the fins are sharpened and staggered in the air stream. The percentage of increase in the surface heat-transfer coefficient obtained as a result of shortening the length of the cooling surface varies with the pressure drop of the cooling fluid in passing the surface, the increase being largest when small pressure drop is used and smallest when high pressure drop is used.

Description: A study of a flow through a straight converging-diverging nozzle of simple design has been made preliminary to studies of other supersonic flows. The diverging part of the nozzle was designed by the Prandtl-Busemann method to give a uniform pressure at its exit of 0.298 times the initial total head, that is, to give a Mach number of 1.436. Schlieren photographs of the flow and pressure-distribution measurements along the diverging part of the nozzle were made. A comparison of the theory with these measurements is presented.

Description: The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.

Description: Problems of hydraulic flow resistance and heat transfer for streams with velocities comparable with acoustic have present great importance for various fields of technical science. Especially, they have great importance for the field of heat transfer in designing and constructing boilers.of the "Velox" type. In this article a description of experiments and their results as regards definition of the laws of heat transfer in differential form for high velocity air streams inside smooth tubes are given.

Description: The effect of cyclic gas pressure variations on the periodic heat transfer at a flat wall is theoretically analyzed and the differential equation describing the process and its solution for relatively. Small pressure fluctuations developed, thus explaining the periodic heat cycle between gas and wall surface. The processes for pure harmonic pressure and temperature oscillations, respectively, in the gas space are described by means of a constant heat transfer coefficient and the equally constant phase angle between the appearance of the maximum values of the pressure and heat flow most conveniently expressed mathematically in the form of a complex heat transfer coefficient. Any cyclic pressure oscillations, can be reduced by Fourier analysis to harmonic oscillations, which result in specific, mutual relationships of heat-transfer coefficients and phase angles for the different harmonics.

Description: In an attempt to follow the time rate of change of the processes in turbulent flows by quantitative measurements the measurement of the pressure is often beset with insuperable difficulties for the reason that the speeds and hence the pressures to be measured are often very small. On the other hand, the measurement of very small pressures requires, at least, considerable time, so that the follow-up of periodically varying processes is as goad as impossible. In order to obviate these difficulties a method, suggested by Prof. Prandtl, has been developed by which the pressure distribution is simply determined from the photographic flow picture. This method is described and proved on a worked-out example. It was found that quantitatively very satisfactory results can be achieved.

Description: A method for recording the local heat-transfer coefficients on bodies in flow was developed. The cylinder surface was kept at constant temperature by the condensation of vapor except for a narrow strip which is heated separately to the same temperature by electricity. The heat-transfer coefficient at each point was determined from the electric heat output and the temperature increase. The distribution of the heat transfer along the circumference of cylinders was recorded over a range of Reynolds numbers of from 5000 to 426,000. The pressure distribution was measured at the same time. At Reynolds numbers up to around 100,000 high maximums of the heat transfer occurred in the forward stagnation point at and on the rear side at 180C, while at around 80 the heat-transfer coefficient on both sides of the cylinder behind the forward stagnation point manifested distinct minimums. Two other maximums occurred at around 115 C behind the forward stagnation point between 170,000 and 426,000. At 426,000 the heat transfer at the location of those maximums was almost twice as great as in the forward stagnation point, and the rear half of the cylinder diffused about 60 percent of the entire heat, The tests are compared with the results of other experimental and theoretical investigations.

Description: In the present report an investigation is made on a flat plate in a two-dimensional compressible flow of the effect of compressibility and heating on the turbulent frictional drag coefficient in the boundary layer of an airfoil or wing radiator. The analysis is based on the Prandtl-Karman theory of the turbulent boundary later and the Stodola-Crocco, theorem on the linear relation between the total energy of the flow and its velocity. Formulas are obtained for the velocity distribution and the frictional drag law in a turbulent boundary later with the compressibility effect and heat transfer taken into account. It is found that with increase of compressibility and temperature at full retardation of the flow (the temperature when the velocity of the flow at a given point is reduced to zero in case of an adiabatic process in the gas) at a constant R (sub x), the frictional drag coefficient C (sub f) decreased, both of these factors acting in the same sense.

Description: The heat transfer in the laminar boundary layer of a heated plate in flow at high speed can be obtained by integration of the conventional differential equations of the boundary layer, so long as the material values can be regarded as constant. This premise is fairly well satisfied at speeds up to about twice the sonic speed and at not excessive temperature rise of the heated plate. The general solution of the equation includes Pohlhausen's specific cases of heat transfer to a plate at low speeds and of the plate thermometer. The solution shows that the heat transfer coefficient at high speed must be computed with the same equation as at low speed, when it is referred to the difference of the wall temperature of the heated plate in respect to its "natural temperature." Since this fact follows from the linear structure of the differential equation describing the temperature field, it is equally applicable to the heat transfer in the turbulent boundary layer.

Description: No abstract available

Description: The heat transfer accompanying turbulent flow in tubes has been treated by a new theory of wall turbulence, and a formula for smooth tubes has been derived which is asymptotic at Re approaches infinity. It agrees very well with the data available to date. The formula also holds for the flow along a flat plate if lambda is based on the velocity far away. For rough tubes, the unit conductance is shown to be a function of kv*/upsilon; the two empirical constants (delta(r), n) which appear in equation (52) cannot yet be determined because of lack of experimental data.

Description: The Reynolds law of heat transfer from a wall to a turbulent stream is extended to the case of flow of a compressible gas at high speeds. The analysis is based on the modern theory of the turbulent boundary layer with laminar sublayer. The investigation is carried out for the case of a plate situated in a parallel stream. The results are obtained independently of the velocity distribution in the turbulent boundar layer.

Description: A mathematical analysis of radiator design has been made. The volume of the radiator using least total power has been expressed in a single formula which shows that the optimum radiator volume is independent of the shape of the radiator and which makes possible the construction of design tables that give the optimum radiator volume per 100-horsepower heat dissipation as a function of the speed, of the altitude, and of one parameter involving characteristics of the airplane. Although, for a given set of conditions, the radiator volume using the least total power is fixed, the frontal area, or the length of the radiator needs to be separately specified in order to satisfy certain other requirement such as the ability to cool with the pressure drop available while the airplane is climbing. In order to simplify the specification for the shape of the radiator and in order to reduce the labor involved in calculating the detailed performance of radiators, generalized design curves have been developed for determining the pressure drop, the mass flow of air, and the power expended in overcoming the cooling drag of a radiator from the physical dimensions of the radiator. In addition, a table is derived from these curves, which directly gives the square root of the pressure drop required for ground cooling as a function of the radiator dimensions, of the heat dissipation and of the available temperature difference. Typical calculations using the tables of optimum radiator volume and the design curves are given. The jet power that can be derived from the heated air is proportional to the heat dissipation and is approximately proportional to the square of the airplane speed and to the reciprocal of the absolute temperature of the atmosphere. A table of jet power, per 100 horsepower of heat dissipation at various airplane speeds and altitudes is presented.

Description: For the tunnel corrections of compressible flows those profiles are of interest for which at least the second approximation of the Janzen-Rayleigh method can be applied in closed form. One such case is presented by certain elliptical symmetrical cylinders located in the center of a tunnel with fixed walls and whose maximum velocity, incompressible, is twice the velocity of flow. In the numerical solution the maximum velocity at the profile and the tunnel wall as well as the entry of sonic velocity is computed. The velocity distribution past the contour and in the minimum cross section at various Mach numbers is illustrated on a worked out-example.

Description: The Navier-Stokes stress principle is checked in the light of Maxwell's mechanism of friction and in connection herewith the possibility of another theorem is indicated. The Navier-Stokes stress principle is in general predicated upon the conception of the plastic body. Hence the process is a purely phenomenological one, which Newton himself followed with his special theorem for one-dimensional flows. It remained for Maxwell to discover the physical mechanism by which the shear inflow direction is developed: According to it, this shear is only 'fictitious' as it merely represents the substitute for a certain transport on macroscopic motion quantity, as conditioned by Brown's moiecular motion and the diffusion, respectively. It is clear that this mechanism is not bound to the special case of the one-dimensioilal flows, but holds for any flow as expression of the diffusion, by which a fluid differs sharply from a plastic body. If it is remembered, on the other hand, that the cause of the stresses on the plastic body lies in a certain cohesion of the molecules, it appears by no means self evident that this difference in the mechanism of friction between fluid and plastic body should not prevail in the stress principle as well, although it certainly is desirable in any case, at least subsequently, to establish the general theorem in the sense of Maxwell. Actually, a different theorem is suggested which, in contrast to that by Navier-Stokes, has the form of an unsymmetrical matrix. Without anticipating a final decision several reasons are advanced by way of a special flow which seem to affirm this new theorem. To make it clear that the problem involved here still awaits its final solution, is the real purpose behind the present article.

Description: A method is presented of comparing the performance, weight, and general dimensional characteristics of inter-coolers. The performance and dimensional characteristics covered in the comparisons are cooling effectiveness, pressure drops and weight flows of the charge and cooling air, power losses, volume, frontal area, and width. A method of presenting intercooler data is described in which two types of charts are plotted; (1) A performance chart setting forth all the important characteristics of a given intercooler and (2) a replot of these characteristics for a number of intercoolers intended to assist in making a selection to satisfy a given set of installation conditions. The characteristics of commercial intercoolers obtained from manufacturers' data and of some computed designs are presented on this basis. A standard test procedure and instrumentation are suggested whereby comparable data may be obtained by different testing organizations.

Description: This preliminary investigation was made to study the hydrodynamic properties and general behavior of simple hydrofoils. Six 5- by 30-inch plain, rectangular hydrofoils were tested in the NACA tank at various speeds, angles of attack and depths below the water surface. Two of the hydrofoils had sections representing the sections of commonly used airfoils, one had a section similar to one developed Guidoni for use with hydrofoil-equipped seaplane floats, and three had sections designed to have constant chordwise pressure distributions at given values of the lift coefficient for the purpose of delaying the speed at which cavitation begins. The experimental results are presented as curves of the lift and drag coefficients plotted against speed for the various angles of attack and depths for which the hydrofoils were tested. A number of derived curves are included for the purpose of better comparing the characteristics of the hydrofoils and to show the effects of depth. Several representative photographs show the development of cavitation on the the upper surface of the hydrofoils. The results indicate that properly designed hydrofoil sections will have excellent characteristics and that the speed at which cavitation occurs may be delayed to an appreciable extent by the use of suitable sections.