ALBERT

Description: An analysis is made for the variable fluid property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary layer equations appropriate to the variable property situation were carried out for gases and liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free convection heat transfer under variable property conditions. This calculation method is well established in the heat transfer field. It involves the use of results which have been derived for constant property fluids, and of a set of rules (called reference temperatures) for extending these constant property results to variable property situations. For gases, the constant property heat transfer results are generalized to the variable property situation by replacing beta (expansion coefficient) by one over T sub infinity and evaluating the other properties at T sub r equals T sub w minus zero point thirty-eight (T sub w minus T sub infinity). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including beta) at this same T sub r. It is worthwhile noting that for these fluids, the film temperature (with beta equals one over T sub infinity for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary layer thickness and velocity parameters.

Description: The necessity of reducing heat transfer to reentry vehicles has led I to the consideration of both radiative and ablation shields. The paper reviews briefly the heating problems for manned vehicles and the means whereby ablation and radiation afford thermal protection. The principal energy disposal and weight parameters are then presented and their relation to the vehicle and trajectory parameters is discussed. A comparative analysis of three types of ablation shield is made and broad conclusions are drawn as to the type of shield most appropriate to manned reentry vehicles.

Description: The year 1954 marked the 50th anniversary of the Prandtl boundary-layer theory from which we may date the beginning of man's understanding of the dynamics of real fluids. A backward look at this aspect of the history of the last 50 years may be instructive. This paper (1) attempts to compress the events of those 50 years into a few thousand words, to tell in this brief space the interesting story of the development of a new concept, its slow acceptance and growth, its spread from group to group within its country of origin, and its diffusion to other countries of the world. The original brief paper of Prandtl (2) was presented at the Third International Mathematical Congress at Heidelberg in 1904 and published in the following year. It was an attempt to explain the d'Alembert paradox, namely, that the neglect of the small friction of air in the theory resulted in the prediction of zero resistance to motion. Prandtl set himself the task of computing the motion of a fluid of small friction, so small that its effect could be neglected everywhere except where large velocity differences were present or a cumulative effect of friction occurred This led to the concept of boundary layer, or transition layer, near the wall of a body immersed in a fluid stream in which the velocity rises from zero to the free-stream value. It is interesting that Prandtl used the term Grenzsehicht (boundary layer) only once and the term Ubergangsschicht (transition layer) seven times in the brief article. Later writers also used Reibungsschicht (friction layer), but most writers today use Grenzschicht (boundary layer).

Description: A variational method is presented for solving eigenvalue problems which arise in connection with the analysis of convective heat transfer in the thermal entrance region of ducts. Consideration is given, to both situations where the temperature profile depends upon one cross-sectional coordinate (e.g. circular tube) or upon two cross-sectional coordinates (e.g. rectangular duct). The variational method is illustrated and verified by application to laminar heat transfer in a circular tube and a parallel-plate channel, and good agreement with existing numerical solutions is attained. Then, application is made to laminar heat transfer in a square duct as a check, an alternate computation for the square duct is made using a method indicated by Misaps and Pohihausen. The variational method can, in principle, also be applied to problems in turbulent heat transfer.

Description: No abstract available

Description: Most analytical studies of ablating layers which melt before they vaporize have been restricted to the stagnation region of bodies (e.g., see Sutton). To determine conditions all along the body, it is important to include the deceleration force that opposes the downstream flow of liquid. Some treatment has already been given to this problem, but it is rather limited because of the idealization of the considered configuration or the omission of some important features of the problem. This note gives a more general discussion of the phenomena that occur when a body force acts on a melting boundary layer. The basis for these remarks is an analysis of the flow of a material like Pyrex over a two-dimensional body. The liquid density, specific heat, and conductivity are assumed constant. To determine the conditions under which deceleration effects are important and to simplify the basic equations, all variables except velocity and time are made dimensionless in the usual way.

Description: Large quantities of high-temperature air are needed for work with hypersonic flight problems. At temperatures above 2500 degrees Reamur, where conventional heat exchangers have exceeded their material limits, regenerative pebble-bed exchangers may be used with high-temperature refractories. The design of such a heat exchanger requires the use of reliable heat-transfer coefficients for a packed bed. Considerable data are available on the subject, but they spread over two orders of magnitude at any one Reynolds number value. The facility from which the present data were obtained is used at the Lewis Research Center (NASA) for testing air-breathing engine components. The purpose of this work was to obtain heat-transfer data during the initial operation of the bed as a guide to the design of similar equipment. The facility was designed with a conservative estimate of the heat-transfer coefficient, and is shown schematically. Temperatures throughout the packing were measured continuously so that point values of the coefficient might be obtained.

Description: The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

Description: Viscosities and thermal conductivities, suitable for heat-transfer calculations, were estimated for about 200 gases in the ground state from 100 to 5000 K and 1-atmosphere pressure. Free radicals were included, but excited states and ions were not. Calculations for the transport coefficients were based upon the Lennard-Jones (12-6) potential for all gases. This potential was selected because: (1) It is one of the most realistic models available and (2) intermolecular force constants can be estimated from physical properties or by other techniques when experimental data are not available; such methods for estimating force constants are not as readily available for other potentials. When experimental viscosity data were available, they were used to obtain the force constants; otherwise the constants were estimated. These constants were then used to calculate both the viscosities and thermal conductivities tabulated in this report. For thermal conductivities of polyatomic gases an Eucken-type correction was made to correct for exchange between internal and translational energies. Though this correction may be rather poor at low temperatures, it becomes more satisfactory with increasing temperature. It was not possible to obtain force constants from experimental thermal conductivity data except for the inert atoms, because most conductivity data are available at low temperatures only (200 to 400 K), the temperature range where the Eucken correction is probably most in error. However, if the same set of force constants is used for both viscosity and thermal conductivity, there is a large degree of cancellation of error when these properties are used in heat-transfer equations such as the Dittus-Boelter equation. It is therefore concluded that the properties tabulated in this report are suitable for heat-transfer calculations of gaseous systems.

Description: Charts have been prepared relating the thermodynamic properties of air in chemical equilibrium for temperatures to 15,000 degrees k and for pressures 10(-5) to 10 (plus 4) atmospheres. Also included are charts showing the composition of air, the isentropic exponent, and the speed of sound. These charts are based on thermodynamic data calculated by the National Bureau of Standards.

Description: Some results of recent experimental investigations at supersonic and transonic speeds are presented to show the present status in the estimation of load distributions on controls and adjacent wing surfaces resulting from the deflection of flap controls and spoiler controls. The results indicate that the development of methods for predicting loads associated with controls has not kept pace with the acquisition of experimental data. At low supersonic speeds sweeping the hinge line induces strong three-dimensional-flow characteristics which cannot be treated by the simplified methods previously developed for controls without sweep. At transonic speeds the estimation of loads associated with controls must usually be dependent upon experimental information inasmuch as the latest attempts to predict chordwise and spanwise loadings have met with only limited success.

Description: Heating requirements for satisfactory cyclic de-icing over a wide range of icing and operating conditions have been determined for a gas-heated, 36deg swept airfoil of 6.9-foot chord with a partial-span leading-edge slat. Comparisons of heating requirements and effectiveness were made between the slatted and unslatted portions of the airfoil. Studies were also made comparing cyclic de-icing with continuous anti-icing, and cycll.cde-icing systems with and without leading-edge ice-free parting strips. De-icing heat requirements were approximately the same with either heated or unheated parting strips because of the aerodynamic effects of the 36deg sweep angle and the spanwise saw-tooth profile of leading-edge glaze-ice deposits. Cyclic de-icing heat-source requirements were found to be one-fourth or less of the heat requirements for complete anti-icing. The primary factors that affected the performance of the cyclic de-icing heating system were ambient air temperature, heat distribution, and thermal lag.

Description: No abstract available

Description: No abstract available

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

Description: Large-deflection theory is used to compute buckling loads of simply supported initially perfect cylinders under axial compression, external pressure, and combinations of axial compression and internal or external pressure. Important results are obtained by taking into account prebuckling deformations and stresses induced by edge support. For example, the presence of these deformations and stresses can reduce the axial-compression buckling load of an unpressurized perfect cylinder to 50 percent of the classical value.

Description: A pool boiling apparatus was mounted on a counterweighted platform which could be dropped a distance of nine feet. By varying the size of the counterweight, the effective gravity field on the equipment was adjusted between zero and unity. A study of boiling burnout in water indicated that a variation in the critical heat flux according to the one quarter power of gravity was reasonable. A consideration of the transient burnout process was necessary in order to properly interpret the data. A photographic study of nucleate boiling showed how the velocity of freely rising vapor bubbles decreased as gravity was reduced. The bubble diameters at the time of breakoff from the heated surface were found to vary inversely as gravity to the 1/3.5 power. Motion pictures were taken to illustrate both nucleate and film boiling in the low gravity range.

Description: The absence of experimental data in the literature concerning a viscosity difference for normal and equilibrium liquid hydrogen may be attributed to the limited reproducibility of "oscillating disk" measurements in a liquid-hydrogen environment. Indeed, there is disagreement over the viscosity values for equilibrium liquid hydrogen even without proton spin considerations. Measurements presented here represent the first application of the piezoelectric alpha quartz torsional oscillator technique to liquid-hydrogen viscosity measurements.

Description: No abstract available

Description: An investigation was undertaken to determine the feasibility of depositing integrally bonded plasma-sprayed tungsten coatings onto 80-volume-percent tungsten - 20-volume-percent uranium dioxide composites. These composites were face clad with thin tungsten foil to inhibit uranium dioxide loss at elevated temperatures, but loss at the unclad edges was still significant. By preheating the composite substrates to approximately 3700 degrees F in a nitrogen environment, metallurgically bonded tungsten coatings could be obtained directly by plasma spraying. Furthermore, even though these coatings were thin and somewhat porous, they greatly inhibited the loss of uranium dioxide. For example, a specimen that was face clad but had no edge cladding lost 5.8 percent uranium dioxide after 2 hours at 4750 dgrees F in flowing hydrogen. A similar specimen with plasma-spray-coated edges, however, lost only 0.75 percent uranium dioxide under the same testing conditions.

Description: Local values of heat transfer coefficients have been measured experimentally for helium and hydrogen gas flowing through an electrically heated inconel tube. The experiment was conducted primarily to determine the effect on the heat transfer coefficient of a large density change, radially, in the heat transfer fluid. This large density change was accomplished with relatively high surface temperatures as compared to fluid bulk temperatures or more commonly referred to as high surface to fluid bulk temperature ratio. The large temperature ratio was achieved by precooling the gas with liquid nitrogen. Data were measured for local values of surface to fluid bulk temperature ratios up to 4.5, Reynolds numbers in the turbulent flow region, surface temperatures up to 2300 R, heat flux up to 1,600,000 Btu/(hr)(sq ft) and length to diameter ratio of 250. A comparison of this data with the conventional heat transfer correlation equation (Dittus-Boelter eq.) is shown on a curve of Nusselt number divided by Prandtl number versus the Reynolds number. The gas properties were evaluated at the film temperature and the Reynolds number was modified by evaluating the velocity term at the fluid bulk temperature and the density at the film temperature.

Description: No abstract available

Description: No abstract available

Description: Analytical techniques are presented that permit the calculation of heat-transfer rates with various thermal-protection systems for liquid-cryogenic-propellant tanks subjected to on-board, solar, and planetary heat fluxes . The effectiveness of these protection systems in reducing propellant heating is shown both for ideal heat-transfer models and for a simplified hydrogen-oxygen terminal stage used for typical Mars missions.

Description: The device considered utilizes an unsteady expansion process for the purpose of total-enthalpy multiplication. Analyses were conducted for both perfect and real air in equilibrium, assuming idealized diaphragm bursts, centered expansion waves, and continuum flow. Results of the study showed the expansion tube capable of outperforming the conventional shock tunnel by a factor of approximately 2 in velocity for the same test-section ambient density and pressure. The degree of dissociation is low at all phases of the thermodynamic cycle in the expansion tube; thus the test-section air has a good possibility of being in equilibrium. Maximum pressures involved in the cycle for duplicating a typical reentry from a lunar mission are low enough for existing pressure-vessel techniques. Both the known and anticipated advantages and disadvantages of this new concept are also discussed.

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: Consideration is given to the fully developed heat transfer characteristics for longitudinal laminar flow between cylinders arranged in an equilateral triangular array. The analysis is carried out for the condition of uniform heat transfer per unit length. Solutions are obtained for the temperature distribution, and from these, Nusselt numbers are derived for a wide range of spacing-to-diameter ratios. It is found that as the spacing ratio increases, so also does the wall-to-bulk temperature difference for a fixed heat transfer per unit length. Corresponding to a uniform surface temperature around the circumference of a cylinder, the circumferential variation of the local heat flux is computed. For spacing ratios of 1.5 - 2.0 and greater, uniform peripheral wall temperature and uniform peripheral heat flux are simultaneously achieved. A simplified analysis which neglects circumferential variations is also carried out, and the results are compared with those from the more exact formulation.

Description: No abstract available

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

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

Description: A new technique for measuring heat-transfer rates on free-flight models in a ballistic range is described in this report. The accuracy of the heat-transfer rates measured in this way is shown to be comparable with the accuracy obtained in shock-tube measurements. The specific results of the present experiments consist of measurements of the stagnation-point heat-transfer rates experienced by a spherical-nosed model during flight through air and through carbon dioxide at velocities up to 18,000 feet per second. For flight through air these measured heat-transfer rates agree well with both the theoretically predicted rates and the rates measured in shock tubes. the heat-transfer rates agree well with the rates measured in a shock tube. Two methods of estimating the stagnation-point heat-transfer rates in carbon dioxide are compared with the experimental measurements. At each velocity the measured stagnation-point heat-transfer rate in carbon dioxide is about the same as the measured heat-transfer rate in air.

Description: A recently developed radiant-heating test technique for simulation of aerodynamic heating in wind tunnel is describes. The heating device, which utilized quartz-tube lamps, was operated successfully while exposed directly to a supersonic airstream. Tests were made on a calibration panel, and experimental temperature and pressure data are presented. Results indicate that initial heating rates of about 26 Btu/(sq ft) (sec) are obtainable at a distance of 12 inches from the heater. Further applications of the basic design are discussed briefly.

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

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

Description: 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: An analysis is presented for obtaining two-dimensional temperature profiles and heat transfer in a radiation-absorbing gray gas of uniform absorptivity under the combined influence of thermal radiation, conduction, and gas flow. The gas is enclosed in a channel of infinite width and finite length formed by two semi-infinite parallel flat plates. These plates are black emitting surfaces, and the ends of the channel are formed by porous black surfaces through which the gas can flow into or out of the channel. These porous black end surfaces are used to simulate the radiation environment external to the channel. First, results are obtained for heat transfer between the plates in the absence of both conduction and flow. These results are found to be in good agreement with those obtained for the same conditions by previous workers. Results are then presented for heat transfer between the plates for the case of a radiating and conducting, but stagnant, gas separating the plates. The effects of the interactions between radiation and conduction are discussed. It was found that the heat transfer for combined radiation and conduction in an absorbing gas is slightly greater than the sum for each process taken separately. Finally, results are given for heat transfer from the plates to a flowing, radiating gas in the absence of conduction. The two plates are at the same temperature, and the gas enters the channel with uniform velocity and temperature. The results obtained for this case indicate that the heat transferred to the flowing gas from the constant temperature surfaces goes through a maximum as the absorptivity of the gas increases. This is in qualitative agreement with earlier results obtained by other investigators. All the results are presented in terms of dimensionless parameters, for the sake of generality, and the derivation of the dimensionless parameters, which are indicative of the effects of conduction and flow is presented.

Description: The overall objectives of the Symposium were to afford (1) an opportunity for workers in the field to describe the equipment and procedures currently in use for measuring thermal radiation properties of solids, (2) an opportunity for constructive criticism of the material presented, and (3) an open forum for discussion of mutual problems. It was also the hope of the sponsors that the published proceedings of the Symposium would serve as a valuable reference on measurement techniques for evaluating thermal radiation properties of solids, partic.ularly for those with limited experience in the field. Because of the strong dependence of emitted flux upon temperature, the program committee thought it advisable to devote the first session to a discussion of the problems of temperature measurement. All of the papers in Session I were presented at the request of and upon topics suggested by the Committee. Because of time and space limitations, it, was impossible to consider all temperature measurement problems that might arise--the objective was rather to call to the attention of the reader some of the problems that might be encountered, and to provide references that might provide solutions.

Description: A preliminary theoretical study was conducted of a new technique for producing high-enthalpy gas flows. The device considered utilizes an unsteady expansion process for the purpose of total-enthalpy multiplication. Analyses were conducted for both perfect and real air in equilibrium, assuming idealized diaphragm bursts, centered expansion waves, and continuum flow. Results of the study showed the expansion tube capable of outperforming the conventional shock tunnel by a factor of approximately 2 in velocity for the same test-section ambient density and pressure. The degree of dissociation is low at all phases of the thermodynamic cycle in the expansion tube; thus the test-section air has a good possibility of being in equilibrium. Maximum pressures involved in the cycle for duplicating a typical reentry from, a lunar mission are low enough for existing pressure-vessel techniques. Both the known and anticipated advantages and disadvantages of this new concept are also discussed.

Description: An analysis is made of the influence that radiation exchanges between elements on the inside surface of a tube have on the wall and gas temperature distributions for forced-convection flow. The wall heat generation has a chopped sine distribution with length along the tube, which is a distribution often encountered in nuclear-reactor channels. The flowing gas is assumed transparent to thermal radiation and hence does not participate directly in the radiative exchange process. Axial heat conduction is neglected in the gas and tube wall, and the convective-heat-transfer coefficient and fluid properties are assumed constant. Several numerical examples are given to illustrate the effects of eight independent parameters such as wall emissivity, Stanton number, and length-diameter ratio. In some instances the radiation exchanges reduced the peak wall temperature or caused a reduction in the exit gas temperature because of radiation losses from the tube end openings.

Description: Cavitation damage to specimens of stainless steel, carbon steel, aluminum, and plexiglas, placed in a cavitating venturi using water and mercury as test fluids is mostly in the form of irregularly shaped pits which do not change with additional exposure to the cavitating field within the limited durations utilized. The rate of damage is very high initially, decreases for a relatively short period of time, then increases again up to the maximum test durations of 150 hours with water and 270 hours with mercury. Observation of damage effects by several independent techniques, using a variety of specimen materials, with two different fluids under various fluid dynamic conditions, leads to a suggested correlating model in terms of the cavitation bubble density and energy and specimen material strength.

Description: An experimental investigation was conducted to determine the effects of several basic variables upon the damping of the fundamental antisymmetric mode of liquids in right-circular cylindrical tanks without baffles. The variables examined include liquid depth, efflux rate, liquid amplitude, kinematic viscosity, and tank size. The data are presented in dimensionless form and compared with available theory. For the range of variables examined, variations of efflux rate and liquid amplitude were found to have no significant effects on the liquid damping. The following theoretical relationship was found to be adequate for the prediction of the variation of damping with liquid depth, kinematic viscosity, and tank size: [for equation see full text] where v is the kinematic viscosity, R is the cylinder radius, g is the acceleration due to gravity, and h is the liquid depth. However, the constant K was experimentally found in this investigation to have the value 5.23, which is 50 percent higher than the theoretically predicted value.

Description: An analysis was made to determine the energy absorbed when radiation from an external source enters a spherical cavity with diffusely reflecting walls. It was found that both the overall energy absorbed in the cavity and the local distribution of absorbed energy could be expressed in terms of simple algebraic equations that are valid for any arbitrary spatial and directional distribution of the incoming radiation. In addition, the characteristics of an isothermal spherical cavity as a possible source of near black-body radiation were investigated. This information was also expressed by simple algebraic relations.

Description: If the restriction of incompressibility in the turbulence problem is relaxed, the phenomenon of energy radiation in the form of sound from the turbulent zone arises. In order to calculate this radiated energy, it is shown that new statistical quantities, such as time-space correlation tensors, have to be known within the turbulent zone in addition to the conventional quantities. For the particular case of the turbulent boundary layer, indications are that the intensity of radiation becomes significant only in supersonic flows. Under these conditions, the recent work of Phillips is examined together with some experimental findings of the author. It is shown that the qualitative features of the radiation field (intensity, directionality) as predicted by the theory are consistent with the measurements; however, even for the highest Mach number flow, some of the assumptions of the asymptotic theory are not yet satisfied in the experiments. Finally, the question of turbulence damping due to radiation is discussed, with the result that in the Mach number range covered by the experiments, the energy lost from the boundary layer due to radiation is a small percentage of the work done by the wall shearing stresses.

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

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

Description: Several toroidal configurations applicable to missile and space-vehicle liquid storage systems were oscillated to study the natural frequencies of the antisymmetric modes of contained liquids over a range of liquid depths and tank sizes. Natural frequencies for tank oscillations parallel to the free surface of both vertical and horizontal tank orientations. Natural frequencies were obtained. The data are presented in terms of dimensionless parameters which are obtained by relating experimentally determined natural liquid frequencies to analytical expressions developed through consideration of the physics of the problem and from existing solutions for liquids in tanks having similar boundaries at the liquid surface. The experimental results obtained for the toroids indicate that these parameters are applicable to the prediction of the natural frequencies of fluids in toroids of general geometry and size.

Description: An experimental investigation has been made to determine the hydro-dynamic characteristics of a 10-percent-thick hydrofoil with an aspect ratio of 3 designed to operate with acceptable efficiency at speeds in the neighborhood of 100 knots (169 fps). A cambered hydrofoil model with parabolic thickness distribution was investigated at a depth of chord over a range of angles of attack from -0.5 deg to 4.0 deg and at speeds from 120 to 210 fps. substantially wider range of operation at acceptable lift-drag ratios as well as higher maximum lift-drag-ratio values than did a hydrofoil of similar design with an aspect ratio of 1.

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

Description: A study is made of the steady laminar flow of a compressible viscous fluid in a circular pipe when the fluid is accelerated by an axial body force. The application of the theory to the magnetofluidmechanics of an electrically conducting gas accelerated by electric and magnetic fields is discussed. Constant viscosity, thermal conductivity, and electrical conductivity are assumed. Fully developed flow velocity and temperature profiles are shown, and detailed results of the accelerating flow development, including velocity and pressure as functions of distance, are given for the case where the axial body force is constant and for the case where it is a linear function of velocity. From these results are determined the pipe entry length and the pressure difference required.

Description: Measurements were made of loads induced on a flat-plate wing by an air jet exhausting perpendicularly through the wing and normal to the free-stream flow.The investigation was conducted at a free-stream Mach number of 2.0 and a Reynolds number per foot of 14.4 x 10(exp 6). An axially symmetric sonic nozzle and two supersonic nozzles were employed for the jets. The supersonic nozzles consisted of an axially symmetric nozzle with exit Mach number of 3.44 and a two-dimensional nozzle with exit Mach number of 1.76. The ratio of nozzle total pressure to free-stream static pressure was varied from 20 to 110. Negative loads were induced on the flat-plate wing by all the jets. As the nozzle pressure ratio was increased the magnitude of interference loads due to jet thrust decreased. The chordwise center-of-pressure location generally moved toward the nozzle center line as the pressure ratio was increased.

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

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

Description: Exploratory tests were made to determine the reduction of heat transfer resulting from ejection of gases at the stagnation point on a hemisphere-cone at a nominal Mach number of about 9 and at stagnation enthalpies up to 1600 BTU per pound. Helium, nitrogen, and argon gases were used as coolants. The ratio of mass flow of coolant to the mass flow of air swept out by the model projected area was less than 0.20 in all cases. The experimental heat-transfer data were normalized by the calculated stagnation-point values based on test conditions in the tunnel and are presented as a function of the surface distance from the stagnation point. The variation of shock standoff distances with mass flow and volumetric flow of the gaseous ejectants is presented along with photographs of the luminous flow field of the model during tests.

Description: Classical undamped acoustic-wave theory was used to determine analytical relations among sinusoidal perturbations of pressure and flow at the ends of a hydraulic-transmission line having a closed-end branch of arbitrary length attached at an arbitrary point. Experimental data were obtained for the equilateral case (a branch half as long as the main line connected to the main line at the midpoint) at mean flow speeds of 5 to 10 feet per second. Measured pressure-perturbation ratios agreed closely with analytical predictions. As frequencies for which the branch length was an odd multiple of 1/4 wavelength, waves in the main line were almost completely reflected at the junction point.

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

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

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

Description: An investigation at free-stream Mach numbers of 0.90 t o 1.10 was made to determine (1) the jet boundaries and the flow fields around hot and cold jets, and (2) whether a cold-gas jet could adequately simulate the boundary and flow field of hot-gas jet. Schlieren photographs and static-pressure surveys were taken in the vacinity of a sonic jet which was operated over a range of jet pressure ratios of 1 to 6, specific heat ratios at the nozzle exit of 1.29 and 1.40, and jet temperatures up to 2600 R.

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

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

Description: The thermal radiation characteristics of spherical cavities are of practical interest in connection with the absorption of radiant energy for both space-vehicle and terrestrial applications. Also, spherical cavities are of potential use as sources of black-body energy. The purpose of this brief paper is to determine both the absorption and emission characteristics of spherical cavities which are diffuse reflectors and emitters.

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: No abstract available

Description: The papers presented in this report represent the classified portion of the Second Manned Space Flight Meeting which was held in Dallas, TX, on April 22-24, 1963. The meeting was co-sponsored by the American Institute of Aeronautics and Astronautics and the National Aeronautics and Space Administration. The following subjects are discussed in the report: Manned Space Flight Programs, Launch Vehicles, Spacecraft Design, and Guidance and Control.

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

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

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

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

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