ALBERT

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: 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: 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: 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 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: 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 rate of heat transfer between a fluid stream in turbulent flow and a smooth, solid wall is largely controlled by the relatively high resistance of the laminar sublayer next to the wall. Although this laminar layer ii extremely thin, heat can be transferred through it only by molecular diffusion. Hence the resistance of this layer is very much greater than for a layer the same thickness farther out in the stream where turbulent exchange is the controlling factor. The thickness of the laminar layer is difficult to define precisely, since there is a gradual transition to the turbulent flow outside, but for the usual scale of many engineering applications almost half the temperature difference between the fluid and the wall occurs in a layer of a few thousands of an inch in thickness. When the wall is made of porous material and a coolant gas is forced through the wall into the stream, it has been found that a very small flow rate of the coolant is remarkably effective in keeping the wall at a low temperature. The coolant flow rate required is such as to give an average velocity normal cooling wall of the order of 1 per cent of the main stream velocity. This flow rate is so low that clearly the injected gas must act as an insulator rather than as a normal coolant. Because of its relatively low velocity, the injected gas can have very little influence on heat convection or momentum transfer in the turbulent stream, and its effect must be confined to the laminar sublayer. The possible influence of the coolant flow on the thickness of the laminar layer will be discussed in Section V.

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: 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: No abstract available

Description: No abstract available

Description: A large number of papers have been devoted to the problem of integration of equations of two-dimensional steady nonvertical adiabatic motion of a gas. Most of these papers are based on the application of the hodograph method of S. A. Chaplygin in which the plane of the hodograph of the velocity is taken as the region of variation of the independent variables in the equations of motion; the equations become linear in this plane. The exact integration of these equations is, however, obtained in the form of infinite series containing hypergeometric functions. The obtaining of such solutions and their investigation involves extensive computations. As a result, methods have been developed for the approximate integration of the equations of motion first transformed to a linear form. S. A. Chaplygin first pointed out such an approximate method applicable to flows in which the Mach number does not exceed 0.4.

Description: A study is made herein of the irrotational adiabatic motion of a gas in the transition from subsonic to supersonic velocities. A shape of the de Laval nozzle is given, which transforms a homogeneous plane-parallel flow at large subsonic velocity into a supersonic flow without any shockwaves beyond the transition line from the subsonic to the supersonic regions of flow. The method of solution is based on integration near the transition line of the gas equations of motion in the form investigated by S. A. Christianovich.

Description: By means of characteristics theory, formulas for the numerical treatment of stationary compressible supersonic flows for the two-dimensional and rotationally symmetrical cases have been obtained from their differential equations.

Description: The turbulent flow in a conical diffuser represents the type of turbulent boundary layer with positive longitudinal pressure gradient. In contrast to the boundary layer problem, however, it is not necessary that the pressure distribution along the limits of the boundary layer(along the axis of the diffuser) be given, since this distribution can be obtained from the computation. This circumstance, together with the greater simplicity of the problem as a whole, provides a useful basis for the study of the extension of the results of semiempirical theories to the case of motion with a positive pressure gradient. In the first part of the paper,formulas are derived for the computation of the velocity and.pressure distributions in the turbulent flow along, and at right angles to, the axis of a diffuser of small cone angle. The problem is solved.

Description: Strain gages were used to measure blade vibrations possibly causing failure in the 10-stage compressor of the 19XB jet-propulsion engine. The seventh and tenth stages were of great concern as a result of failures experienced by the manufacturer. Strain-gage records were obtained from all stages during acceleration, deceleration, and constant speed runs. Curves are presented herein showing the maximum allowable vibratory stress for a given speed, the change of the damping coefficient with the mounting of a strain gage at the base of the blade, the effect of rotor speed, on blade natural frequency, and the effect of the order of first bending-mode vibration on stress. It was found that for all stages the lower the order of vibration the higher the stress but no destructive vibrations were detected.

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: 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 has been conducted on a one-sixth segment of an annular turbojet combustor to determine the effects of modification in air-flow distribution and total-pressure loss on the performance of the segment. The performance features investigated during this series of determinations were the altitude operational limits and the temperature-rise efficiency. Altitude operational limits of the combustor segment, for the 19XB engine using the original combustor-basket design were approximately 38,000 feet at 17,000 rpm and 26,000 feet at 10,000 rpm. The altitude operational limits were approximately 50,000 feet at 17,000 rpm and 38,000 feet at 10,000 rpm for a combustor-basket design in which the air-passage area in the basket was redistributed so as to admit gradually no more than 20 percent of the air along the first half of the basket. In this case the total pressure loss through the combustor segment was not appreciably changed from the total-pressure loss for the original combustor basket design. Altitude operational limits of the combustor segment for the 19XB engine were above 52,000 feet at 17,000 rpm and were approximately 23,000 feet at 10,000 rpm for a combustor-basket design in which the distribution of the air-passage area in the basket was that of the original design but where the total-pressure loss was increased to 19 times the inlet reference kinetic pressure at an inlet-to-outlet density ratio of 2.4. The total-pressure loss for the original design was 14 times the inlet kinetic reference pressure at an inlet-to-outlet density ratio of 2.4.

Description: A heat-transfer investigation was conducted with air flowing through an electrically heated silicon carbide tube with a rounded entrance, an inside diameter of 3/4 inch, and effective heat-transfer length of 12 inches over a range of Reynolds numbers up to 300,000 and a range of average inside-tube-wall temperatures up to 2500 R. The highest corresponding local outside-tube-wall temperature was 3010 R.

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: The calculation of the phenomena within the boundary layer of bodies immersed in a flow underwent a decisive development on the basis of L. Prandtl's trains of thought, stated more than forth years ago, and by numerous later treatises again and again touching upon them. The requirements of the steadily improving aerodynamics of airplanes have greatly increased with the passing of time and recently research became particularly interested in such phenomena in the boundary layer as are caused by small external disturbances. Experimental results suggest that, for instance, slight fluctuations in the free stream velocities as they occur in wind tunnels or slight wavelike deviations of outer wing contours from the prescribed smooth course as they originate due to construction inaccuracies may exert strong effects on the extent of the laminar boundary layer on the body and thus on the drag. The development of turbulence in the last part of the laminar portion of the boundary layer is, therefore, the main problem, the solution of which explains the behavior of the transition point of the boundary layer. A number of reports in literature deal with this problem,for instance, those of Tollmien, Schlichting, Dryden, and Pretsch. The following discussion of the behavior of the laminar boundary layer for periodically oscillating pressure variation also purports to make a contribution to that subject.

Description: Some aerodynamic relations are derived which exist between two infinitely long airfoils if one is in a straight flow and the other in oblique flow, and both present the same profile in the direction of flow.

Description: At the request of the Junkers Aircraft and Engine Construction Company, Engine Division, Dessau Main Plant, an investigation was made using the interferometer method on the two turbine-blade profiles submitted. The interferometer method enables making visible the differences in density and consequently the boundary layers that develop when a flow is directed on the profile. Recognition of the points on the profile at which separation of flow occurs is thus possible. By means of the interference photographs the extent of the dead-water region may be ascertained. The size of the dead-water region provides evidence as to the quality of the flow and allows a qualitative estimate of the amount of the flow losses. Interference photographs thus provide means of judging the utility of profiles under specific operating conditions and provide suggestions for possible changes of profile contours that might help to improve flow relations. Conclusions may be drawn concerning the influence of the blade-spacing ratio, the inlet-air angle, and the connection between the curvature of the profile contour and the point of separation of the flow from the profile surface.

Description: The cavitation in nozzles on airfoils of various shape and on a sphere are experimentally investigated. The limits of cavitation and the extension of the zone of the bubbles in different stages of cavitation are photographically established. The pressure in the bubble area is constant and very low, jumping to high values at the end of the area. The analogy with the gas compression shock is adduced and discussed. The collapse of the bubbles under compression shock produces very high pressures internally, which must be contributory factors to corrosion. The pressure required for purely mechanical corrosion is also discussed.

Description: This paper includes the following topics: 1) Characteristic differential equations; 2) Treatment of practical examples; 3) First example: Diffuser; and 4) Second Example: Nozzle.

Description: This paper contains a tabulation of functions of the Mach number which are frequently used in high-speed aerodynamics. The tables extend from M = 0 to M = 10.0 in increments of 0.01 and are based on the assumption that air is a perfect gas having a specific heat ratio of 1.400.

Description: The conference on Turbojet-Engine Thrust-Augmentation Research was organized by the NACA to present in summarized form the results of the latest experimental and analytical investigations conducted at the Lewis Flight Propulsion Laboratory on methods of augmenting the thrust of turbojet engines. The technical discussions are reproduced herewith in the same form in which they were presented. The original presentation in this record are considered as complementary to, rather than substitutes for, the committee's system of complete and formal reports.

Description: The condensation of water vapor in an air consequences: acquisition of heat (liberated heat vaporization; loss of mass on the part of the flowing gas (water vapor is converted to liquid); change in the specific gas constants and of the ratio k of the specific heats (caused by change of gas composition). A discontinuous change of state is therefore connected with the condensation; schlieren photographs of supersonic flows in two-dimensional Laval nozzles show two intersecting oblique shock fronts that in the case of high humidities may merge near the point of intersection into one normal shock front.

Description: The recent experiments by Jakob and Erk, on the resistance of flowing water in smooth pipes, which are in good agreement with earlier measurements by Stenton and Pannell, have caused me to change my opinion that the empirical Blasius law (resistance proportional to the 7/4 power of the mean velocity) was applicable up to arbitrarily high Reynolds numbers. According to the new tests the exponent approaches 2 with increasing Reynolds number, where it remains an open question whether or not a specific finite limiting value of the resistance factor lambda is obtained at R = infinity. With the collapse of Blasius' law the requirements which produced the relation that the velocity in the proximity of the wall varied in proportion to the 7th root of the wall distance must also become void. However, it is found that the fundamental assumption that led to this relationship can be generalized so as to furnish a velocity distribution for any empirical resistance law. These fundamental assumptions can be so expressed that for the law of velocity distribution in proximity of the wall as well as for that of friction at the wall, a form can be found in which the pipe diameter no longer occurs, or in other words, that the processes in proximity of a wall are not dependent upon the distance of the opposite wall.

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: The flow about a conical body of an ideal compressible fluid is considered. Assume that the velocity of the oncoming flow at infinity W is directed along the z-axis. The system of Cartesian coordinates x, y, z with origin at the vertex of the cone O is shown. From the considerations,of the dimensional theory, it may be found that along any ray issuing from O the components of the velocity u, v, W+w along the coordinate axes will maintain a constant value. It is further assumed that the conical body has such shape and disposition relative to the flow that u, v, and w are small in comparison with W.

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: For a certain Mach number of the oncoming flow, the local velocity first reaches the value of the local velocity of sound (M = 1) at some point on the surface of the body located within the flow. This Mach number is designated the critical Mach number M(sub cr). By increasing the flow velocity, a supersonic local region is formed bounded by the body contour and the line of transition from subsonic to supersonic velocity. As is shown by observations with the Toepler apparatus, at a certain flow Mach number M 〉 M(sub cr) a shock wave is formed near the body that closes the local supersonic region from behind. The formation of the shock wave is associated with the appearance of an additional resistance defined as the wave drag. In this paper, certain features are described of the flow in the local supersonic region, which is bounded by the contour of the body and the transition line, and conditions are sought for which the potential flow with the local supersonic region becomes impossible and a shock wave occurs. In the first part of the paper, the general properties of the potential flow in the local supersonic region, bounded by the contour of the profile and the transition line, are established. It is found that at the transition line, if it is not a line of discontinuity, the law of monotonic variation of the angle of inclination of the velocity vector holds (monotonic law). An approximation is given for the change in velocity at the contour of the body. The flow about a contour having a straight part is studied. In the second part of the paper, an approximation is given of the magnitudes of the accelerations at the interior points of the supersonic region. With the aid of these approximations, it is shown that for profiles convex to the flow the breakdown of the potential flow,associated with an increase of the Mach number of the oncoming flow, cannot be due to the formation of an envelope of the characteristics within the supersonic region. On the basis of the monotonic law, the transitional Mach number M is found, beyond which the potential flow with local supersonic region becomes impossible.

Description: In the present paper, the motion of a gas in a plane-parallel Laval nozzle in the neighborhood of the transition from subsonic to supersonic velocities is studied. In a recently published paper, F. I. Frankl, applying the holograph method of Chaplygin, undertook a detailed investigation of the character of the flow near the line of transition from subsonic to supersonic velocities. From the results of Tricomi's investigation on the theory of differential equations of the mixed elliptic-hyperbolic type, Frankl introduced as one of the independent variables in place of the modulus of the velocity, a certain specially chosen function of this modulus. He thereby succeeded in explaining the character of the flow at the point of intersection of the transition line and the axis of symmetry (center of the nozzle) and in studying the behavior of the stream function in the neighborhood of this point by separating out the principal term having, together with its derivatives, the maximum value as compared with the corresponding corrections. This principal term is represented in Frankl's paper in the form of a linear combination of two hypergeometric functions. In order to find this linear combination, it is necessary to solve a number of boundary problems, which results in a complex analysis. In the investigation of the flow with which this paper is concerned, a second method is applied. This method is based on the transformation of the equations of motion to a form that may be called canonical for the system of differential equations of the mixed elliptic-hyperbolic type to which the system of equations of the motion of an ideal compressible fluid refers. By studying the behavior of the integrals of this system in the neighborhood of the parabolic line, the principal term of the solution is easily separated out in the form of a polynomial of the third degree. As a result, the computation of the transitional part of the nozzle is considerably simplified.

Description: There are investigated the problems of the flow of a supersonic jet out of a vessel with plane side walls and the problem of the supersonic flow about a wedge when there is a zone of local subsonic velocities ahead of the wedge.

Description: This paper makes the following assumptions: 1) The flowing gases are assumed to have uniform energy distribution. ("Isoenergetic gas flows," that is valid with the same constants for the the energy equation entire flow.) This is correct, for example, for gas flows issuing from a region of constant pressure, density, temperature, end velocity. This property is not destroyed by compression shocks because of the universal validity of the energy law. 2) The gas behaves adiabatically, not during the compression shock itself but both before and after the shock. However, the adiabatic equation (p/rho(sup kappa) = C) is not valid for the entire gas flow with the same constant C but rather with an appropriate individual constant for each portion of the gas. For steady flows, this means that the constant C of the adiabatic equation is a function of the stream function. Consequently, a gas that has been flowing "isentropically",that is, with the same constant C of the adiabatic equation throughout (for example, in origination from a region of constant density, temperature, and velocity) no longer remains isentropic after a compression shock if the compression shock is not extremely simple (wedge shaped in a two-dimensional flow or cone shaped in a rotationally symmetrical flow). The solution of nonisentropic flows is therefore an urgent necessity.

Description: The authors regret that due to the lack of time the investigations could not be carried out to a more finished form. Especially in the first part it was intended to include a few further applications and to use them in the general considerations of this part. In spite of the fact that the intentions of the authors could not be realized, the authors felt that it would serve the aims of the competition to present part I in its present fragmentary form. The topics include: 1) A Few General Remarks Covering the Prandtl-Busemann Method; and 2) Effect of Compressibility in Axially Symmetrical Flow around an Ellipsoid.

Description: In the present paper which deals with the heat transfer between the gas and the wall for large temperature drops and large velocities use is made of the method of Dorodnitsyn of the introduction of a new independent variable, with this difference, however, that the relation between the temperature field (that is, density) and the velocity field in the general case considered is not assumed given but is determined from the solution of the problem. The effect of the compressibility arising from the heat transfer is thus taken into account (at the same time as the effect of the compressibility at the large velocities). A method is given for determining the coefficients of heat transfer and the friction coefficients required in many technical problems for a curved wall in a gas flow at large Mach numbers and temperature drops. The method proposed is applicable both for Prandtl number P = 1 and for P not equal to 1.

Description: The present report consists of two parts. The first part deals with the two-dimensional stationary flow in the presence of local supersonic zones. A numerical method of integration of the equation of gas dynamics is developed. Proceeding from solutions at great distance from the body the flow pattern is calculated step by step. Accordingly the related body form is obtained at the end of the calculation. The second part treats the relationship between the displacement thickness of laminar and turbulent boundary layers and the pressure distribution at high speeds. The stability of the boundary layer is investigated, resulting in basic differences in the behavior of subsonic and supersonic flows. Lastly, the decisive importance of the boundary layer for the pressure distribution, particularly for thin profiles, is demonstrated.

Description: There has been under development for the high-speed wind tunnel of the LFA an optical measuring arrangement for the qualitative and quantitative investigation of flow. By the use of interference measurements, the determination of density at the surface of the bodies being tested in the air stream and in the vicinity of these bodies can be undertaken. The results obtained so far in the simple preliminary investigations show that it is possible, even at a low Reynolds number, to obtain the density field in the neighborhood of a test body by optical means. Simple analytical expressions give the relation between density, pressure, velocity, and temperature. In addition to this, the interference measurement furnishes valuable data on the state of the boundary layer, that is, the sort of boundary layer (whether laminar or turbulent), as well as the temperature and velocity distribution.

Description: It is known that compression shocks which lead from supersonic to subsonic velocity cause the flow to separate on impact on a rigid wall. Such shocks appear at bodies with circular symmetry or wing profiles on locally exceeding sonic velocity, and in Laval nozzles with too high a back pressure. The form of the compression shocks observed therein is investigated.

Description: The characteristics of the position and form of the transition surface through the critical velocity are computed for flow through flat and round nozzles from subsonic to supersonic velocity. Corresponding considerations were carried out for the flow about profiles in the vicinity of sonic velocity.

Description: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

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: Contents include the following: Characteristic differential equations - initial and boundary conditions. Integration of the second characteristic differential equations. Direct application of Meyer's characteristic hodograph table for construction of two-dimensional potential flows. Prandtl-Busemann method. Development of the pressure variation for small deflection angles. Numerical table: relation between deflection, pressure, velocity, mach number and mach angle for isentropic changes of state according to Prandtl-Meyer for air (k = 1.405). References.

Description: Six, 3-inch-chord symmetrical airfoil sections having systematic variations in thickness and thickness location were tested at Mach numbers near flight values for propeller-shank sections. The tests, the results of which are presented in the form of schlieren photographs of the flow past each model and pressure-distribution charts for two of the model, were performed to illustrate the effects of compressibility on the flow past thick symmetrical airfoil sections. Representative flow photographs indicated that at Mach numbers approximately 0.05 above the critical Mach number a speed region was reached in which the flow oscillated rapidly and the separation point and the location of the shock wave were unstable. Fixing the transition on both surfaces of the airfoil was effective in reducing these rapid oscillations. The pressure distributions showed that the section normal-force coefficients for thick airfoils were very erratic at subcritical speeds; at supercritical speeds the section normal-force coefficients for the thick airfoils became more regular. Drag coefficients showed that considerable drag decreases can be expected by decreasing the model thickness ratio.

Description: A heat-transfer investigation was conducted with air flowing through an electrically heated silicon carbide tube with a rounded entrance, an inside diameter of 3/4 inch, and an effective heat-transfer length of 12 inches over a range of Reynolds numbers up to 300,000 and a range of average inside-tube-wall temperature up to 2500 R. The highest corresponding local outside-tube-wall temperature was 3010 R. Correlation of the heat-transfer data using the conventional Nueselt relation wherein physical properties of the fluid were evaluated at average bulk temperature resulted in a separation of data with tube-wall-temperature level. A satisfactory correlation of the heat-transfer data was obtained, however, by the use of modified correlation parameters wherein the mass velocity G (or product of average air density and velocity evaluated at bulk temperature P(sub b)V(sub b)) in the Reynolds number was replaced by the product of average air velocity evaluated at the bulk temperature and density evaluated at either the average inside-tube-wall temperature or the average film temperature; in addition, all the physical properties of air were correspondingly evaluated at either the average inside-tube-wall temperature or the average film temperature.

Description: In the lecture series starting today author want to give a survey of a field of aerodynamics which has for a number of years been attracting an ever growing interest. The subject is the theory of flows with friction, and, within that field, particularly the theory of friction layers, or boundary layers. A great many considerations of aerodynamics are based on the ideal fluid, that is the frictionless incompressibility and fluid. By neglect of compressibility and friction the extensive mathematical theory of the ideal fluid, (potential theory) has been made possible. Actual liquids and gases satisfy the condition of incomressibility rather well if the velocities are not extremely high or, more accurately, if they are small in comparison with sonic velocity. For air, for instance, the change in volume due to compressibility amounts to about 1 percent for a velocity of 60 meters per second. The hypothesis of absence of friction is not satisfied by any actual fluid; however, it is true that most technically important fluids, for instance air and water, have a very small friction coefficient and therefore behave in many cases almost like the ideal frictionless fluid. Many flow phenomena, in particular most cases of lift, can be treated satisfactorily, - that is, the calculations are in good agreement with the test results, -under the assumption of frictionless fluid. However, the calculations with frictionless flow show a very serious deficiency; namely, the fact, known as d'Alembert's paradox, that in frictionless flow each body has zero drag whereas in actual flow each body experiences a drag of greater or smaller magnitude. For a long time the theory has been unable to bridge this gap between the theory of frictionless flow and the experimental findings about actual flow. The cause of this fundamental discrepancy is the viscosity which is neglected in the theory of ideal fluid; however, in spite of its extraordinary smallness it is decisive for the course of the flow phenomena.

Description: Wind-tunnel tests of a full-scale model of the Republic XF-91 airplane having swept-back wings and a vee tail were conducted to determine both the stability and control characteristics of the model longitudinally, laterally, and directionally. Configurations of the model were investigated involving such variables as external fuel tanks, a landing gear, trailing-edge flaps, leading-edge slats, and a range of wing incidences and tail incidences.

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 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: 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: 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: 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: Characteristic methods for nonstationary flows have been published only for the special case of the isentropic flow up until the present, althought they are applicable in various places to more difficult questions too. This report derives the characteristic method for the flows which depend only on the position coordinates and time. At the same time the treatment of compression shocks is shown.

Description: The investigation of the flow in a centrifugal pump indicated that the flow patterns in frictional fluid are fundamentally different from those in frictionless fluid. In particular, the dead air space adhering to the section side undoubtedly causes a reduction of the theoretically possible delivery head. The velocity distribution over a parallel circle is also subjected to a noticeable change as a result of the incomplete filling of the passages. The relative velocity on the pressure side of the vane, which for passages completely filled with active flow would differ little from zero even at comparatively lower than normal delivery volume, is increased, so that no rapid reverse flow occurs on the pressure side of the vane even for smaller delivery volume. It was established, further, that the flow ceases to be stationary for very small quantities of water. The inflow to the impeller can be regarded as radial for the operating range an question. The velocity triangles at the exit are subjected to a significant alteration in shape ae a result of the increased peripheral velocity, which may be of particular importance in the determination of the guide vane entrance angle.

Description: On the basis of certain formulas recently established by L. Prandtl for the turbulent interchange of momentum in stationary flows, various cases of "free turbulence" - that is, of flows without boundary walls - are treated in the present report. Prandtl puts the apparent shearing stress introduced by the turbulent momentum interchange. This present report deals first with the mixing of an air stream of uniform velocity with the adjacent still air, than with the expansion or diffusion of an air jet in the surrounding air space.

Description: As a turbine rotor turns, the blades traverse the wake zones of the nozzle vanes. A periodic fluctuation of the pressure distribution around the circumference of the rotor blade is therefore caused. It was desired to investigate quantitatively this effect. At the same time, the magnitude of the force acting upon one profile of the rotor-blade lattice at various positions of this lattice relative to the nozzle lattice was to be determined.

Description: The heat losses from the envelope surface of a U.S. Navy K-type airship are evaluated to determine if the use of heat is a feasible means of preventing ice and snow accumulations on lighter-than-air craft during flight and when moored uncovered. Consideration is given to heat losses in clear air (no liquid water present in the atmosphere) and in probable conditions of icing and snow. The results of the analysis indicate that the amount of heat required in flight to raise the surface temperature of the entire envelope to the extent considered adequate for ice protection, based on experience with tests of heavier-than-air craft, is very large. Existing types of heating equipment which could be used to supply this quantity of heat would probably be too bulky and heavy to provide a practical flight installation. The heat requirements to provide protection for the nose and stern regions in assumed mild to moderate icing conditions appear to be within the range of the capacity of current types of heating equipment suitable for flight use. The amount of heat necessary to prevent snow accumulations on the upper surface of the airship envelope when moored uncovered under all conditions appear to be excessive for the heating equipment presently available for flight use, but could possibly be achieved with auxiliary ground heating equipment.

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 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: Test results are present for cascades of airfoils in retarded flow and increasing pressure as corresponds to the case of the impeller of an axial propeller pump and propeller fan.

Description: With water as driving medium and delivered medium in a device similar to a simple jet apparatus, the pressure and velocity fields of the mixing zone were explored with a pitot bar; the ratio of delivered to driving volume ranged between the values 0, 1, 2, and 4. An attempt was also made to analyze the mixing flow mathematically by integration of the equation of motion, with the aid of conventional formulas for the turbulent shearing stress, but this succeeded only approximately for the very simplified case that a driving jet is introduced in an unlimited parallel flow, while the pressure over the whole mixing field is assumed to be constant. In spite of these dissimilar assumptions for the theory and the experiment, the form of the measured and the computed velocity profiles indicates a very high degree of approximation. The pressure rise, which was approximated by Flugel's formulas, disclosed good agreement with the measured values.

Description: The characteristics introduced by the turbulence in the process of the flame propagation are considered. On the basis of geometrical and dimensional considerations an expression is obtained for the velocity of the flame propagation in a flow of large scale of turbulence.

Description: On the basis of photographic pictures the laminar flow at a pipe inlet was measured and compared with other measurements and computational results. The test setup is described in detail, and a series of the pictures obtained for turbulent flow is given.

Description: The present report deals with the effect of turbulence on the propagation of the flame. Being based upon experiments with laminar as well as turbulent Bunsen flames, both the physico-chemical and the hydro-dynamical aspects of the problem are analyzed. A number of new deductions, interesting from the point of view of engine combustion and other very rapidly changing flame reactions, are made.