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Equations for Adiabatic but Rotational Steady Gas Flows without Friction

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.
Date: August 1, 1947
Creator: Schäefer, Manfred
Partner: UNT Libraries Government Documents Department

Two-Dimensional Potential Flows

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.
Date: November 1949
Creator: Schäefer, Manfred & Tollmien, W.
Partner: UNT Libraries Government Documents Department

Flow of Gas Through Turbine Lattices

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.
Date: May 1, 1956
Creator: Deich, M E
Partner: UNT Libraries Government Documents Department

A Method for Rapid Determination of the Icing Limit of a Body in Terms of the Stream Conditions

Description: The effects of existing frictional heating were analyzed to determine the conditions under which ice formations on aircraft surfaces can be prevented. A method is presented for rapidly determining by means of charts the combination of-Mach number, altitude, and stream temperature which will maintain an ice-free surface in an icing cloud. The method can be applied to both subsonic and supersonic flow. The charts presented are for Mach numbers up to 1.8 and pressure altitudes from sea level to 45,000 feet.
Date: March 1953
Creator: Callaghan, Edmund E. & Serafini, John S.
Partner: UNT Libraries Government Documents Department

General Correlation of Temperature Profiles Downstream of a Heated Air Jet Directed at Various Angles to Air Stream

Description: An experimental investigation was conducted to determine the temperature profiles downstream of heated air jets directed at angles of 90 deg, 60 deg, 45 deg, and 30 deg to an air stream. The profiles were determined at two positions downstream of the jet as a function of jet diameter, jet density, jet velocity, free-stream density, free-stream velocity, jet total temperature, orifice flow coefficient, and jet angle. A method is presented which yields a good approximation of the temperature profile in terms of the flow and geometric conditions.
Date: December 1952
Creator: Ruggeri, Robert S.
Partner: UNT Libraries Government Documents Department

Impingement of Cloud Droplets on 36.5-Percent-Thick Joukowski Airfoil at Zero Angle of Attack and Discussion of Use as Cloud Measuring Instrument in Dye-Tracer Technique

Description: The trajectories of droplets i n the air flowing past a 36.5-percent-thick Joukowski airfoil at zero angle of attack were determined. The amount of water i n droplet form impinging on the airfoil, the area of droplet impingement, and the rate of droplet impingement per unit area on the airfoil surface were calculated from the trajectories and cover a large range of flight and atmospheric conditions. With the detailed impingement information available, the 36.5-percent-thick Joukowski airfoil can serve the dual purpose of use as the principal element in instruments for making measurements in clouds and of a basic shape for estimating impingement on a thick streamlined body. Methods and examples are presented for illustrating some limitations when the airfoil is used as the principal element in the dye-tracer technique.
Date: September 1, 1957
Creator: Brun, R. J. & Vogt, Dorothea E.
Partner: UNT Libraries Government Documents Department

Impingement of water droplets on NACA 65(1)-208 and 65(1)-212 airfoils at 4 degrees angle of attack

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.
Date: May 1, 1953
Creator: Brun, R. J.; Gallagher, H. M. & Vogt, D. E.
Partner: UNT Libraries Government Documents Department

Droplet Impingement and Ingestion by Supersonic Nose Inlet in Subsonic Tunnel Conditions

Description: The amount of water in cloud droplet form ingested by a full-scale supersonic nose inlet with conical centerbody was measured in the NACA Lewis icing tunnel. Local and total water impingement rates on the cowl and centerbody surfaces were also obtained. All measurements were made with a dye-tracer technique. The range of operating and meteorological conditions studied was: angles of attack of 0 deg and 4.2 deg, volume-median droplet diameters from about 11 to 20 microns, and ratios of inlet to free-stream velocity from about 0.4 to 1.8. Although the inlet was designed for supersonic (Mach 2.0) operation of the aircraft, the tunnel measurements were confined to a free-stream velocity of 156 knots (Mach 0.237). The data are extendable to other subsonic speeds and droplet sizes by dimensionless impingement parameters. Impingement and ingestion efficiencies are functions of the ratio of inlet to free-stream velocity as well as droplet size. For the model and range of conditions studied, progressively increasing the inlet velocity ratio from less than to greater than 1.0 increased the centerbody impingement efficiency and shifted the cowl impingement region from the inner- to outer-cowl surfaces, respectively. The ratio of water ingested by the inlet plane to that contained in a free-stream tube of cross section equal to that at the inlet plane also increased with increasing inlet velocity ratio. Theoretically calculated values of inlet water (or droplet) ingestion are in good agreement with experiment for annular inlet configurations.
Date: May 1958
Creator: Gelder, Thomas F.
Partner: UNT Libraries Government Documents Department

A Dye-Tracer Technique for Experimentally Obtaining Impingement Characteristics of Arbitrary Bodies and a Method for Determining Droplet Size Distribution

Description: A dye-tracer technique has been developed whereby the quantity of dyed water collected on a blotter-wrapped body exposed to an air stream containing a dyed-water spray cloud can be colorimetrically determined in order to obtain local collection efficiencies, total collection efficiency, and rearward extent of impingement on the body. In addition, a method has been developed whereby the impingement characteristics obtained experimentally for a body can be related to theoretical impingement data for the same body in order to determine the droplet size distribution of the impinging cloud. Several cylinders, a ribbon, and an aspirating device to measure cloud liquid-water content were used in the studies presented herein for the purpose of evaluating the dye-tracer technique. Although the experimental techniques used in the dye-tracer technique require careful control, the methods presented herein should be applicable for any wind tunnel provided the humidity of the air stream can be maintained near saturation.
Date: March 1955
Creator: von Glahn, Uwe H.; Gelder, Thomas F. & Smyers, William H., Jr.
Partner: UNT Libraries Government Documents Department

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

Description: An investigation of the heat transfer from an airfoil in clear air and in simulated icing conditions was conducted in the NACA Lewis 6- by 9-foot icing-research tunnel in order to determine the validity of heat-transfer data as obtained in the tunnel. This investiation was made on the same model NACA 65,2-016 airfoil section used in a previous flight study, under similar heating, icing, and operating conditions. The effect of tunnel turbulence, in clear air and in icingwas indicated by the forward movement of transition from laminar to turbulent heat transfer. An analysis of the flight results showed the convective heat transfer in icing to be considerably different from that measured in clear air and. only slightly different from that obtained in the icing-research tunnel during simulated icing.
Date: September 1, 1951
Creator: Gelder, Thomas F. & Lewis, James P.
Partner: UNT Libraries Government Documents Department

Periodic Heat Transfer at Small Pressure Fluctuations

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.
Date: September 1, 1943
Creator: Pfriem, H.
Partner: UNT Libraries Government Documents Department

Heat Transfer and Hydraulic Flow Resistance for Streams of High Velocity

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.
Date: December 1, 1943
Creator: Lelchuk, V. L.
Partner: UNT Libraries Government Documents Department

Analytical Treatment of Normal Condensation Shock

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.
Date: July 1, 1947
Creator: Heybey
Partner: UNT Libraries Government Documents Department

Heat Transfer in a Turbulent Liquid or Gas Stream

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.
Date: October 1, 1944
Creator: Latzko, H.
Partner: UNT Libraries Government Documents Department

Report on Investigation of Developed Turbulence

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.
Date: January 18, 1949
Creator: Prandtl, L.
Partner: UNT Libraries Government Documents Department

Theory of Heat Transfer in Smooth and Rough Pipes

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.
Date: December 1, 1942
Creator: Mattioli, G. D.
Partner: UNT Libraries Government Documents Department

The Turbulent Flow in Diffusers of Small Divergence Angle

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.
Date: October 1, 1947
Creator: Gourzhienko, G. A.
Partner: UNT Libraries Government Documents Department

Lift Force of an Arrow-Shaped Wing

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.
Date: October 1, 1949
Creator: Gurevich, M. I.
Partner: UNT Libraries Government Documents Department

Subsonic Gas Flow Past A Wing Profile

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.
Date: July 1, 1950
Creator: Christianovich, S. A. & Yuriev, I. M.
Partner: UNT Libraries Government Documents Department

The Characteristics Method Applied to Stationary Two-Dimensional and Rotationally Symmetrical Gas Flows

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.
Date: March 1, 1949
Creator: Pfeiffer, F. & Meyer-Koenig, W.
Partner: UNT Libraries Government Documents Department

On the Theory of the Laval Nozzle

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 ...
Date: April 1, 1949
Creator: Falkovich, S. V.
Partner: UNT Libraries Government Documents Department

Gas Motion in a Local Supersonic Region and Conditions of Potential-Flow Breakdown

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 ...
Date: May 1, 1949
Creator: Nikolskii, A. A. & Taganov, G. I.
Partner: UNT Libraries Government Documents Department

Behavior of the Laminar Boundary Layer for Periodically Oscillating Pressure Variation

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.
Date: September 1, 1949
Creator: Quick, august Wilhelm & Schroeder, K.
Partner: UNT Libraries Government Documents Department