Showing papers in "Journal of the Aeronautical Sciences in 1957"

An Investigation of Effects of Certain Types of Structural NonHnearities on Wing and Control Surface Flutter

Abstract: This paper presents some effects of nonlinear structural terms on the flutter of a wing capable of bending and twisting and, also, of a system including a control surface. Several type , of nonlinearities in the stiffness are investigated, including free play, a hysteresis loop, and cubic variations. These are introduced in the torsional degree of freedom of the wing and in the aileron stiffness in the three degree of freedom system. Calculations have been made on an analog computer. A wind-tunnel investigation of one case having free play in the torsional degree of freedom has been made, and good correlation between theory and experiment is shown. The results indicate that the stability of a nonlinear system is highly dependent on the magnitude of initial displacements of the system from equilibrium. I t is shown that in many cases the flutter speed is decreased by increasing the initial disturbance. The results also indicate that when a nonlinear system becomes unstable its flutter may become self-limited.

Inviscid Hypersonic Flow Over Blunt-Nosed Slender Bodies

Abstract: At hypersonic speeds the drag/area of a blunt nose is much larger than the drag/area of a slender afterbody, and the energy contained in the flow field in a plane at right angles to the flight direction is nearly constant over a downstream distance many times greater than the characteristic nose dimension. The transverse flow field exhibits certain similarity properties directly analogous to the flow similarity behind an intense blast wave found by G. I. Taylor and S. C. Lin. Conditions for constant energy show that the shape of the bow shock wave R(x) not too close to the nose is given by R/d = K_1 (γ)(d/c)^(1/2) for a body of revolution, and by R/d = K_0(γ) (x/d)^(2/3) for a planar body, where d is nose diameter, or leading-edge thickness. A comparison with the experiments of Hammitt, Vas, and Bogdonoff on a flat plate with a blunt leading-edge at M_∞ = 13 in helium shows that the shock wave shape is predicted very accurately by this analysis. The predicted surface pressure distribution is somewhat less satisfactory. Energy considerations combined with a detailed study of the equations of motion show that flow similarity is also possible for a class of bodies of the form r_b ~ x^m, provided that m' ≤ m ≤ 1, where m' = 3/4 for a planar body and m' = (3/2(γ+1))/(3γ + 2) for a body of revolution. When m < m' the shock shape is not similar to the body shape, and except for the constant energy flows the entire flow field some distance from the nose must depend to some extent on the details of the nose geometry. Be again again utilizing energy and drag considerations one finds that at hypersonic speeds the inviscid surface pressures generated by a blunt nose are larger than the pressures produced by boundary layer growth on a flat surface over a distance from the nose of order l, where l/d ≃ 1/15 ((Re_d)/M_∞^2))^3 (Here Re_d is free-stream Reynolds number based on leading-edge thickness.) Thus at M_∞ = 15 the viscous interaction effects should be important for Re_d 3000 the inviscid pressure field is dominant and determines the boundary layer development, skin friction and heat transfer over the forward portion of the body. These rough estimates are in qualitative agreement with the experimental results of References 7 and 9.

New Methods in Heat Flow Analysis With Application to Flight Structures

Abstract: New methods are presented for the analysis of transient heat flow in complex structures, leading to drastic simplifications in the calculation and the possibility of including nonlinear and surface effects. These methods are in part a direct application of some general variational principles developed earlier for linear thermodynamics.1-3 They are further developed in the particular case of purely thermal problems to include surface and boundary-layer heat transfer, nonlinear systems with temperature-dependent parameters, and radiation. The concepts of thermal potential, dissipation function, and generalized thermal force are introduced, leading to ordinary differential equations of the Lagrangian type for the thermal flow field. Because of the particular nature of heat flow phenomena, compared with dynamics, suitable procedures must be developed in order to formulate each problem in the simplest way. This is done by treating a number of examples. The concepts of penetration depth and transit time are introduced and discussed in connection with onedimensional flow. Application of the general method to the heating of a slab, with temperature-dependent heat capacity, shows a substantial difference between the heating and cooling processes. An example of heat flow analysis of a supersonic wing structure by the present method is also given and requires only extremely simple calculations. The results are found to be in good agreement with those obtained by the classical and much more elaborate procedures.

On the Vibration of Thin Cylindrical Shells Under Internal Pressure

Abstract: : It is shown that for thin cylinders the internal pressure has a very significant effect on the natural vibration characteristics. For these cylinders, particularly those having smaller length-to-diameter ratios, the mode associated with the lowest frequency is in general not the simplest mode. In fact, the frequency spectrum may be so arranged that the frequency decreases with an increase in the number of circumferential nodes. The exact number of circumferential nodes which occur in the mode associated with the lowest frequency depends on the ratios h/a, L/a, and the internal pressure, where h is the wall thickness, a is the cylinder radius, and L is the axial half-wave length. When the internal pressure is small, the number of circumferential nodes at the lowest frequency decreases rapidly with increasing internal pressure; and the 'fundamental' frequency - the lowest frequency at each internal pressure - increases rapidly with increasing internal pressure. At higher values of internal pressure the frequency spectrum tends to be arranged in the regular manner: the frequency increases with the increasing number of circumferential nodes; and the lowest frequency rises with the internal pressure, but at a slower rate.

Newtonian Flow Theory for Slender Bodies

Abstract: As an aid to the aerodynamicist in the design of air frames for hypersonic speeds (speeds faster than about Mach 5), Newtonian flow theory is examined from the point of view of gas dynamics and hypersonic small-disturbance theory. The usual theory is shown to result as the first approximation of an expansion valid for small X = (7 — 1 ) / ( Y + 1). A basic similarity parameter N = (7 + l ) / ( 7 — l)ikfo0 5 is introduced. A general solution of the first approximation for the flow past slender bodies (bodies which cause only a small disturbance to the stream) a t zero angle of attack is given. An important condition which limits the application of the theory is noted—namely, that the pressure coefficient on the surface not fall to zero. The theory is then applied to cones and to bodies whose shape is r = x.

Stagnation Point of a Blunt Body in Hypersonic Flow

Abstract: The purpose of this paper is to present a method of calculation devised to yield all the important information on the symmetric inviscid hypersonic flow in the stagnation point region of a blunt body. The problem is the same as that considered by Hayes3 who used a slightly different approach. I t is demonstrated that Hayes' results are valid in the stagnation point region and can hence be considered a basis for constructing less restricted solutions. Equations are presented giving velocity, pressure, detachment distance, and vorticity. The values of shock detachment distance and body pressure coefficient are compared with experimental data for spheres. The pressure comparison shows that the results of Hayes and the theory presented herein represent a better approximation than the Newtonian impact theory for hypersonic Mach Numbers. In conclusion, the possibility of refinements to this analysis is discussed.

Interaction of a Plane Shock and Oblique Plane Disturbances With Special Reference to Entropy Waves

Abstract: The problem of the interaction between a plane entropy wave of arbitrary orientation and a plane oblique shock of infinite extent is investigated. As a result of the interaction, it is found that, in the perturbed flow field downstream of the shock, three kinds of disturbances are present—namety, an entropy mode, a vorticity mode, and a sound mode. The nature of the sound wave generated depends on the orientation of the upstream disturbance. Within certain orientations of the upstream disturbance, the sound waves generated downstream attenuate. Beyond these orientations, the sound waves generated have constant amplitudes. When the downstream sound waves are not attenuated, there is no phase shift in the entropy disturbance across the shock; when the downstream sound waves are attenuated, a phase shift occurs in the entropy disturbance across the shock. An illustrative example is given for the interaction between a plane normal shock and a sinusoidal entropy wave. At a given shock strength the amplitudes of the shock displacement and the downstream disturbances generated are plotted as functions of the orientation of the upstream disturbance.

A Theoretical and Experimental Study of Airplane Dynamics in Large-Disturbance Maneuvers

Abstract: This paper reviews an effort to solve some problems of largedisturbance maneuvering flight. The period covered is from 1949 to the present, and results of both theoretical and flight test investigations are presented. The rolling pull-out, a critical maneuver for vertical tail loads, was chosen for study. Equations of motion were developed, and solutions were compared with responses obtained from flight tests. The equations, validated by this comparison, were then applied to critical present-day airplane configurations, and a general study of large-disturbance motion was made including variation of pertinent parameters. This paper represents a first step in the study of nonlinear aspects of airplane dynamics and control in large-disturbance maneuvers. Results show that inertial and aerodynamic nonlinearities introduce destabilizing tendencies not predicted by linear theory. Although complex equations are required to predict motions accurately, the characteristics of the motion may be described using simple mathematical techniques.

Remarks on the Equilibrium Turbulent Boundary Layer

Abstract: Two similarity laws are known for the mean-velocity profile in a turbulent boundary layer with constant pressure. These are Prandtl's law of the wall and Karman's momentum-defect law. The first law has recently been generalized empirically to flows with arbitrary pressure gradient by Ludwieg and Tillmann, and the second law to a certain class of equilibrium flows by F. Clauser. In the present paper it is shown that the pressure distribution corresponding to a given equilibrium flow cam be computed by assuming that a certain parameter D = (τ_w/q)dq/dτ_w is constant, where q and τ_w are the dynamic pressure in the free stream and the shearing stress at the wall, respectively. The hypothesis D = constant is suggested by a study of the integrated continuity equation and is supported by a rigorous analogy between the class of equilibrium flows defined by Clauser and the class of laminar flows studied by Falkner and Skan. The hypothesis D = constant is also verified using experimental data for several equilibrium turbulent flows and is interpreted physically from a kinematic point of view. Two hypothetical limiting cases of equilibrium flow are described. At one extreme is the boundary Layer in a sink flow, with a completely logarithmic mean-velocity profile outside the sublayer. At the other extreme is a continuously separating boundary layer in a dimensionless pressure gradient (x/q)dq/dx approximately twice that for the corresponding laminar flow. Typical shearing-stress profiles are computed for several equilibrium turbulent flows, including the two limiting cases.

Plastic Stability Theory of Thin Shells

Abstract: Ai = plasticity coefficients B = axial rigidity, B = Est/(1 v ) D = bending rigidity, D = Est /12(1 v), also diameter ei = strain intensity E = modulus of elasticity E„ = secant modulus Et = tangent modulus k = buckling coefficient, k =

Supersonic Flutter of a Cylindrical Shell

Abstract: (1) SUMMARY The aerodynamic instability of traveling waves on a cylindrical shell exposed to an external supersonic air stream and containing an internal fluid is examined on the hypothesis of short wave length (compared with the radius and length of the shell). The stability criterion for an empty isotropic shell and the negative damping ratio when this criteria is not met are determined. It is shown that the negative damping ratio calculated in the absence of structural damping decreases monotonically with an increase in structural damping, but structural damping cannot prevent in­ stability and may render an otherwise stable motion weakh^ unstable. HE FOLLOWING ANALYSIS of the dynamic instability (panel flutter) of thin-walled cylindrical shells under the action of an exterior supersonic flow is pre­ sented as a sequel to an earlier formulation of the twodimensional problem.1 In that paper panel flutter was studied as a traveling wave phenomenon, following Kelvin's classical analysis of the surface waves pro­ duced by wind blowing over water. We remark at the outset that all of the essential features of this approach to panel flutter are elucidated by the two-dimensional analysis without recourse to any approximations beyond those implicit in the assumptions of small disturbances, a perfect fluid, and an infinite surface; however, further analysis and additional approximations are necessary in order to render the results applicable to practical con­ figurations.!

Circumferential Inlet Distortions in Axial Flow Turbomachinery

Abstract: An actuator disc type of analysis is carried out to determine the effect of a nonuniformity in the circumferential velocity profile entering an axial flow stage of turbomachinery. The analysis is restricted to study of incompressible, inviscid flow with the assumption of hub/ t ip ratios close to unity reducing the problem to two dimensions. Expressions are derived giving the attenuation of the velocity distortion through the stage, the circumferential shift in the profile, and the fluctuation in load felt by the rotor blades passing through the nonuniform velocity field, all as a function of stage geometry. Results are given for compressor, turbine, and free wheeling stages as a function of wheel speed, stage loading, and mean stagger angle. General conclusions and design recommendations are made with respect to minimizing blade load fluctuation and optimizing distortion attenuation.