ALBERT

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.