Showing papers in "Journal of the Aeronautical Sciences in 1955"

On the Wake and Drag of Bluff Bodies

Abstract: A modification to Kirchhoff's free streamline introduces the parameter k = √(1- C_ps), which allows arbitrary base pressure and which must depend on the dynamics of the wake. For a cylinder of given cross-sectional shape, the drag, C_D, and the wake width, d', are functions of k only. These functions are used to relate C_D and the dimensionless shedding frequency , S = nd/U_ ∞ to another number, S* = nd' / U_s, which is based on wake parameters. It is found that S* = 0.16 for all cylinders. In another approach, k is evaluated by using Karman's solution for the vortex street.

The Unsteady Forces Due to Viscous Wakes in Turbomachines

Abstract: The configuration of viscous wakes of cascade blades is approximated from single airfoil experiments. The unsteady force and moment on a downstream blade passing through such wakes is then calculated on the basis of the theory of isolated thin airfoils in nonuniform motion. The results indicate that the force is nearly proportional to the profile-drag coefficient of the upstream blades. For typical values of this coefficient and conventional cascade geometry the unsteady forces arising from passage through viscous wakes are of about the same size as those due to aerodynamic interference between the moving blade rows, previously estimated.

Supersonic diffuser instability

Abstract: Steady operation of supersonic diffusers near critical mass flow is interrupted by a transient process known as buzz. This phenomenon consists of a random sequence of individual relaxation cycles. Mass flow entering the diffuser during steady operation is suddenly cut off by a strong interaction between the subcritical shock and boundary layer on the surface of the external compression generator, which blocks the inlet. Air in the plenum chamber, stored at high pressure, then ?blows down? until the inlet can restart. The subsequent supercritical flow entering the diffuser exceeds the flow rate at the exit and the plenum chamber is re-charged to the original condition. A distinction is drawn between this phenomenon and a high frequency wave-type resonance noticed at low mass flows and during an individual buzz cycle after the diffuser shock system has been expelled. For the large diffuser tested here, this high frequency oscillation compares well to the 8th closed-end organ pipe mode of the diffuser at low mass flows and to the 9th mode during the shock-expelled phase of the buzz cycle. It is shown that burning almost always ceases in the presence of buzz. When burning was maintained during buzz, it was found to have no qualitative effect on the buzz cycle.

Separation of a supersonic turbulent boundary layer

Abstract: The separation of a supersonic turbulent boundary layer under the effect of a strong adverse gradient has been studied at M ~ 3 by examining in detail the phenomena of flow over a step and shock-wave boundary-layer interaction. Wall static pressures, total head surveys, and optical techniques, including the use of color Schlieren, were used to provide a model of the separation phenomenon. I t was found tha t : (1) When the separated region is small, the phenomenon appears to be different from when the separated region is large. For small regions the gradients are stronger, and large changes can occur for small changes in the disturbance. (2) Separation at M ~ 3 occurred at a pressure ratio of about 2, about two to three boundary-laj^er thicknesses from the start of the interaction and was unaffected by the flow downstream. (3) A considerable pressure rise occurs after the separation point. The peak pressure ratio of about 2.6 occurs approximately six to eight boundary-layer thicknesses downstream of the start of the interaction. (4) These results, combined with other investigations, indicate an extremely small change of separation pressure ratio with Mach Number. (5) The effect of Reynolds Number on the phenomenon appears to be negligible. (6) The detailed model, showing considerable pressure rise after separation, appears to be susceptible to the type of theoretical treatment proposed by Crocco and Lees. However, more results on mixing rates are needed for its direct application.

Aerodynamic Flutter Derivatives for a Flexible Wing with Supersonic and Subsonic Edges

Abstract: A box method is developed for obtaining the generalized air forces on an oscillating flexible wing in supersonic flow with both supersonic and subsonic edges. Essentially, the method consists of representing the wing by a grid of square boxes and determining the influence of one box on another. These aerodynamic pressure influence coefficients when tabulated, permit the flutter analysis of an arbitrary wing with arbitrary normal modes to be carried out in a routine way. The coefficients satisfy the linearized unsteady supersonic flow equations and the downwash boundary conditions, and, in addition, are formulated in a manner independent of the modal shapes of the structure. The box method is applied to some simplified examples involving rigid body modes, and agreement with other methods is seen to be reasonably good. The box procedure appears to offer a simple routine manner of analyzing flexible wings for supersonic flutter analyses which is well adapted to programming on computing machinery. However, the square box method as developed here for subsonic edges is inapplicable to Mach Numbers below M = 1.414 without further modification. Some suggested modifications for extending below the M = 1.414 range are discussed in the body of the paper.

Propagation of stall in a compressor blade row

Abstract: Recent experimental observations on compressors, in particular those of Rannie and Iura, have clarified some features of the phenomenon of stall propagation. Using these observations as a guide, the process of stall in an airfoil cascade has been characterized by a static pressure loss across the cascade which increases discontinuously at the stall angle, the turning angle being affected in only a minor way. Deductions from this simple model yield the essential features of stall propagation such as dependence of the extent of stalled region upon operating conditions, the pressure loss associated with stall, and the angular velocity of stall propagation. Using two-dimensional approximation for a stationary or rotating blade row, free from interference of adjacent blade rows, extent of the stalled region, the total pressure loss and stall propagation speed are discussed in detail for a general cascade characteristic. Employing these results, the effect of stall propagation upon the performance of a single-stage axial compressor is illustrated and the mechanism of entering the regime of stall propagation is discussed. The essential points of the results seem to agree with experimental evidence.

A Provisional Analysis of Turbulent Boundary Layers with Injection

Abstract: SUMMARY Prandtl's analysis of the incompressible turbulent boundary layer over a flat plate is extended in this report to include the effect of uniform, transverse fluid injection. The nondimensional parameters characterizing such a flow are deduced by dimensional reasoning. A velocity profile is generated by considering the flow over a plane wall; this distribution reduces to the universal log law when the mass transfer is zero. The expression also serves to relate the local skin friction to the boundary-layer thickness. When these relationships are used in conjunction with the von Karman integral, the problem becomes mathematically specified. Since only a limited amount of experimental data is available, it is necessary to assign to certain parameters that arise in the velocity profile the constant values they have for no mass transfer. When more measurements are completed, it may be possible to adjust these parameters as or if required. The results give the variation of average skin-friction coefficient with the injection ratio and the Reynolds Number based on the streamwise coordinate. The agreement between these results and the experimental data available is found to be satisfactory. The significant reductions in skin friction, and therefore in heat trans­ fer, to be realized with small rates of injection are indicated.

The Dynamic Motion of a Missile Descending Through the Atmosphere

Abstract: A method is presented for computing rapidly, yet accurate^, the dynamic motion of a ballistic-type missile descending through the atmosphere. The equations of motion are separated into a set of "static" trajectory equations (zero angle of attack) and a set of "rotational" equations describing the oscillatory motion of the missile about its center of gravity. A transformation allows the rotational equations to be written in a manner analogous to the equation for an undamped oscillating spring mass system with the mass equal to unity and a time variable spring constant. For given initial conditions this equation can be solved to obtain the envelope of maximum angle of attack. An additional transformation allows the calculation of the complete oscillatory motion at any time during the trajectory as a function of the maximum angle of attack at that time. This solution shows that the maximum angle of attack of a missile descending through the atmosphere at relatively constant speed is reduced even when the aerodynamic damping is neglected.

A Simple Laminar Boundary Layer with Secondary Flow

Abstract: The incompressible laminar boundary layer over a flat plate is studied for the simple case where the stream lines in the free flow have a parabolic shape. An exact solution of the boundary layer equations is derived. No separation occurs, even when there is a strong adverse pressure gradient along the stream lines, so that in this instance the secondary flow has a favorable influence. Because of the variation of total pressure from one stream line to another in the free stream, the total pressure within the boundary layer at a given point can exceed that of the corresponding free stream.

Some Considerations on the Air Forces on a Wing Oscillating Between Two Walls for Subsonic Compressible Flow

Abstract: The problem of the determination of the air forces on an oscillating airfoil between plane walls has, until recently, been treated only for incompressible flow. The present paper is concerned with the important effects of compressibility, which may be of significance in such problems as the measurement of oscillating air forces or of wing flutter characteristics in wind tunnels, and in the flutter of airfoils in cascade. The possibility of the existence of an acoustic resonance phenomenon under certain critical conditions is discussed. The integral equation for the compressible case, as obtained by Runyan and Watkins in NACA T N 2552, is reviewed briefly and a method of solving the equation is given. The procedure is applied to a number of selected cases at various Mach numbers and tunnel heights. The effect of the presence of the walls is shown to be very significant near the resonant frequency and, for certain conditions, to be large even at frequencies well removed from resonance.

A Critique of Shock-Expansion Theory

Abstract: The assumptions underlying the application of shock-expansion theory to the calculation of the pressure distribution on a thin sharp-nosed two-dimensional airfoil in a supersonic stream are examined, and it is suggested that they might be expected to lead to appreciable errors when the Mach Number is large. This case is then examined by the use of the "hypersonic analogy," and it is shown that for circular-arc airfoils the pressure distribution is given to good accuracy by shock-expansion theory even when the quantities neglected are no longer small. An asymptotic form for the decay of the leading-edge shock is developed in the case of shocks that are too strong initially for the Friedrichs theory to apply.

Aerodynamics of Blasts-Diffraction of Blast Around Finite Corners

Abstract: The reflection and diffraction of strong shocks around corners of arbitrary, finite angle, and the resulting pressure and density fields have been calculated by two different methods. The second method, which is a hyperbolic procedure, appears to be useful in various types of nonlinear problems. At the end a modified procedure of the second method is outlined which promises faster convergence.

Effect of Large Deflections and Initial Imperfections on the Buckling of Cylindrical Shells Subject to Hydrostatic Pressure

Abstract: Numerous treatments of the elastic buckling of thin cylinders under various loadings and with various boundary conditions exist in the literature. In general, those analyses which involve classical small deflection shell theory predict higher buckling loads than actually found during test. In an effort to explain the discrepancy between these theoretical values and experiment, Donnell in 1934 introduced the concept of large deflections together with the consideration of initial deviations from perfect shape. This approach has been employed by Donnell and Wan to investigate the phenomena of buckling of cylinders subject to axial compression and by Loo to study torsional buckling. Both of these studies yielded results that are in substantial agreement with experiment. In this paper the buckling of a "cylinder subjected to hydrostatic pressure is analyzed from the standpoint of large deflections together with initial imperfections because of the marked discrepancy between small deformation theory and test for this type of loading. The relations derived are in line with test results.

Stability of Compressible Laminar Boundary Layer with Internal Heat Sources or Sinks

Abstract: A solution of the equations of the compressible laminar boundary layer with heat sources or heat sinks is presented. The solution is limited to the flow over a flat plate with arbitrary surface temperature and constant Prandtl Number. I t is assumed that the additional mass associated with the heat sources or sinks is negligible. Stability calculations indicate that the boundary laj^er can be stabilized by heat withdrawal near the aircraft surface (e.g., by evaporation of liquid droplets) or by heat addition near the outer edge of the boundary layer (e.g., by condensation of a vapor). In addition, heat withdrawal near the surface is shown to provide an effective means of surface cooling.

Analysis of peak-holding optimalizing control

Abstract: The peak-holding optimalizing control is analyzed under the assumption of first-order input linear group and output linear group. Design charts are constructed for determining the required input drive speed and the consequent hunting loss with specified time constants of the input and output linear groups, the hunting period, and the critical indicated difference for input drive reversal.