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Results for “strip theory”

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NASA NTRS1976

Effect of modified aerodynamic strip theories on rotor blade aeroelastic stability

Various existing unsteady aerodynamic strip theories which have been developed in the past for both fixed and rotary wing aeroelastic analyses are modified in the paper so as to make them applicable to the coupled flap-lag-torsional aeroelastic problem of a rotor blade in hover. These corrections are primarily due to constant angle of attack, constant inflow and variable free stream velocity due to lead-lag motion. Next, the modified strip theories are incorporated in a coupled flap-lag-torsional aeroelastic analysis of the rotor blade in hover and the sensitivity of the aeroelastic stability boundaries to the aerodynamic assumptions is examined.

Friedmann, P.↗

NASA NTRS1960

Some Divergence Characteristics of Low-Aspect-Ratio Wings at Transonic and Supersonic Speeds

The problem of chordwise, or camber, divergence at transonic and supersonic speeds is treated with primary emphasis on slender delta wings having a cantilever support at the trailing edge. Experimental and analytical results are presented for four wing models having apex half-angles of 5 deg, 10 deg, 15 deg, and 20 deg. A Mach number range from 0.8 to 7.3 is covered. The analytical results include calculations based on small-aspect-ratio theory, lifting-surface theory, and strip theory. A closed-form solution of the equilibrium equation is given, which is based on low-aspect-ratio theory but which applies only to certain stiffness distributions. Also presented is an iterative procedure for use with other aerodynamic theories and with arbitrary stiffness distribution.

Woolston, Donald S.↗

NASA NTRS1998

Design and Performance Calculations of a Propeller for Very High Altitude Flight

Reported here is a design study of a propeller for a vehicle capable of subsonic flight in Earth's stratosphere. All propellers presented were required to absorb 63.4 kW (85 hp) at 25.9 km (85,000 ft) while aircraft cruise velocity was maintained at Mach 0.40. To produce the final design, classic momentum and blade-element theories were combined with two and three-dimensional results from the Advanced Ducted Propfan Analysis Code (ADPAC), a numerical Navier-Stokes analysis code. The Eppler 387 airfoil was used for each of the constant section propeller designs compared. Experimental data from the Langley Low-Turbulence Pressure Tunnel was used in the strip theory design and analysis programs written. The experimental data was also used to validate ADPAC at a Reynolds numbers of 60,000 and a Mach number of 0.20. Experimental and calculated surface pressure coefficients are compared for a range of angles of attack. Since low Reynolds number transonic experimental data was unavailable, ADPAC was used to generate two-dimensional section performance predictions for Reynolds numbers of 60,000 and 100,000 and Mach numbers ranging from 0.45 to 0.75. Surface pressure coefficients are presented for selected angles of attack. in addition to the variation of lift and drag coefficients at each flow condition. A three-dimensional model of the final design was made which ADPAC used to calculated propeller performance. ADPAC performance predictions were compared with strip-theory calculations at design point. Propeller efficiency predicted by ADPAC was within 1.5% of that calculated by strip theory methods, although ADPAC predictions of thrust, power, and torque coefficients were approximately 5% lower than the strip theory results. Simplifying assumptions made in the strip theory account for the differences seen.

Koch, L. Danielle↗

NASA NTRS1944

On the general theory of thin airfoils for nonuniform motion

General thin-airfoil theory for a compressible fluid is formulated as boundary problem for the velocity potential, without recourse to the theory of vortex motion. On the basis of this formulation the integral equation of lifting-surface theory for an incompressible fluid is derived with the chordwise component of the fluid velocity at the airfoil as the function to be determined. It is shown how by integration by parts this integral equation can be transformed into the Biot-Savart theorem. A clarification is gained regarding the use of principal value definitions for the integral which occur. The integral equation of lifting-surface theory is used a s the starting point for the establishment of a theory for the nonstationary airfoil which is a generalization of lifting-line theory for the stationary airfoil and which might be called "lifting-strip" theory. Explicit expressions are given for section lift and section moment in terms of the circulation function, which for any given wing deflection is to be determined from an integral equation which is of the type of the equation of lifting-line theory. The results obtained are for airfoils of uniform chord. They can be extended to tapered airfoils. One of the main uses of the results should be that they furnish a practical means for the analysis of the aerodynamic span effect in the problem of wing flutter. The range of applicability of "lifting-strip" theory is the same as that of lifting-line theory so that its results may be applied to airfoils with aspect ratios as low as three.

BIBLIOGRAPHY-WINGS↗

NASA NTRS1972

Unsteady rotor aerodynamics at low inflow and its effect on flutter.

A comprehensive flutter analysis has been developed utilizing compressible unsteady aerodynamics for a helicopter rotor at a low inflow condition. The rotor is treated as a nonuniform rotating beam with finite bending and torsional stiffness. The unsteady aerodynamic representation incorporates the effects of spanwise variations in Mach number and reduced frequency by applying available two-dimensional theories in a strip theory fashion. The results are characterized by an oscillation of the apparent aerodynamic damping with decreasing frequency ratio (oscillation frequency/rotational frequency) which suggests a new flutter criteria for rotors. These results are correlated with available experimental data.

Pierce, G. A.↗

NASA NTRS1974

Application to rotary wings of a simplified aerodynamic lifting surface theory for unsteady compressible flow

A general method of predicting airloads is applied to helicopter rotor blades on a full three-dimensional basis using the general theory developed for a rotor blade at the psi = pi/2 position where flutter is most likely to occur. Calculations of aerodynamic coefficients for use in flutter analysis are made for forward and hovering flight with low inflow. The results are compared with values given by two-dimensional strip theory for a rigid rotor hinged at its root. The comparisons indicate the inadequacies of strip theory for airload prediction. One important conclusion drawn from this study is that the curved wake has a substantial effect on the chordwise load distribution.

Rao, B. M.↗

NASA NTRS1982

An estimation of aerodynamic forces and moments on an airplane model under steady state spin conditions

The problem of estimating the aerodynamic characteristics of a wing body configuration of a spinning airplane at extreme angles of attack and spin rates is approached by the application of strip theory. Semiempirical methods are used to estimate the aerodynamic force distributions over each component using static, nonrotational wind-tunnel test data. To these predictions, corrections are applied to account for the primary rotational flow effects which are significant at large spin rates. The results of this modified strip theory are shown to be in good agreement with spin tunnel rotary balance test data.

Pamadi, B. N.↗

NASA NTRS2000

Model Validation of Wake-Vortex/Aircraft Encounters

Wake-vortex effects on an 10% scale model of the B737-100 aircraft are calculated using both strip theory and vortex-lattice methods. The results are then compared to data taken in the 30ft x 60ft wind tunnel at NASA Langley Research Center (LaRC). The accuracy of the models for a reduced geometry, such with the horizontal stabilizer and the vertical tail removed, is also investigated. Using a 10% error in the circulation strength and comparing the model's results with the experiment illustrates the sensitivity of the models to the vortex circulation strength. It was determined that both strip theory and the vortex lattice method give accurate results when all the geometrical information is used. When the horizontal stabilizer and vertical tail were removed there were difficulties modeling the sideforce coefficient and pitching moment. With the removal of only the vertical tail unacceptable errors occurred when modeling the sideforce coefficient and yawing moment. Lift could not be accurately modeled with either the full geometry or the reduced geometry.

Pete, Kimberly R.↗

NASA NTRS1982

NASTRAN flutter analysis of advanced turbopropellers

An existing capability developed to conduct modal flutter analysis of tuned bladed-shrouded discs in NASTRAN was modified and applied to investigate the subsonic unstalled flutter characteristics of advanced turbopropellers. The modifications pertain to the inclusion of oscillatory modal aerodynamic loads of blades with large (backward and forward) variable sweep. The two dimensional subsonic cascade unsteady aerodynamic theory was applied in a strip theory manner with appropriate modifications for the sweep effects. Each strip is associated with a chord selected normal to any spanwise reference curve such as the blade leading edge. The stability of three operating conditions of a 10-bladed propeller is analyzed. Each of these operating conditions is iterated once to determine the flutter boundary. A 5-bladed propeller is also analyzed at one operating condition to investigate stability. Analytical results obtained are in very good agreement with those from wind tunnel tests.

Elchuri, V.↗

NASA NTRS1993

Finite element calculations of transonic flutter in cascades

Aeroelastic stability and response of turbomachinery cascades operating in the transonic regime are explored using a new computational approach. The two-dimensional unsteady Euler equations are used to model the transonic cascade flows, and the cascade blades are modeled as thin plates. To minimize the discretization incompatibility, both the fluid and the solid domains are discretized using finite element procedures. The fluid and the structural models are coupled at the element level by introducing a channel theory, which is analogous to a strip theory in the classical sense. The system of space-discretized equations is marched forward in time using an explicit four-stage Runge-Kutta scheme. Results of free vibration analyses of typical blades are presented and compared to published finite element and Rayleigh-Ritz results. Aeroelastic stability and response characteristics of several transonic cascades are investigated using the new quasi-3D model. These results demonstrate the present 3D finite element blade model is capable of capturing aeroelastic instabilities involving higher modes, including (plate-type) camber bending modes.

Hsiao, Chingteng↗

NASA NTRS1983

Estimation of parameters involved in high angle-of-attack aerodynamic theory using spin flight test data

The difficulty in applying parameter estimation techniques to spinning airplanes is due in part to the unwieldy number of possible combinations of terms in the equations of motion, when the model structure is unknown. The combination of high angle of attack and high rotation rate results in aerodynamic functions which are quite complex. For wing dominated configurations it is advantageous to use aerodynamic theory to generate the model structure. In this way, the number of unknown parameters is reduced and the model accuracy may be increased. Under conditions for which the theory is inadequate, however, model accuracy may be reduced. Strip theory, for example, is incapable of predicting autorotative rolling moments indicated by wind tunnel tests at angles of attack exceeding 40 degrees. An improved aerodynamic theory would be necessary to successfully apply the technique advanced for such regions.

Taylor, L. W., Jr.↗

NASA NTRS1973

Research on unsteady transonic flow theory

A two-dimensional theory is considered for the unsteady flow disturbances caused by aeroelastic deformations of a thick wing at high subsonic freestream Mach numbers, having a single, internally embedded supercritical (locally supersonic) steady flow region adjacent to the low pressure side of the wing. The theory develops a matrix of unsteady aerodynamic influence coefficients (AICs) suitable as a strip theory for aeroelastic analysis of large aspect ratio thick wings of moderate sweep, typical of a wide class of current and future aircraft. The theory derives the linearized unsteady flow solutions separately for both the subcritical and supercritical regions. These solutions are coupled together to give the requisite (wing pressure-downwash) AICs by the intermediate step of defining flow disturbances on the sonic line, and at the shock wave; these intermediate quantities are then algebraically eliminated by expressing them in terms of the wing surface downwash.

Revell, J. D.↗

NASA NTRS1985

A method for estimating the rolling moment due to spin rate for arbitrary planform wings

The application of aerodynamic theory for estimating the force and moments acting upon spinning airplanes is of interest. For example, strip theory has been used to generate estimates of the aerodynamic characteristics as a function of spin rate for wing-dominated configurations for angles of attack up to 90 degrees. This work, which had been limited to constant chord wings, is extended here to wings comprised of tapered segments. Comparison of the analytical predictions with rotary balance wind tunnel results shows that large discrepancies remain, particularly for those angles-of-attack greater than 40 degrees.

Poppen, W. A., Jr.↗

NASA NTRS1978

Three-dimensional effects on pure tone fan noise due to inflow distortion

Two dimensional, quasi three dimensional and three dimensional theories for the prediction of pure tone fan noise due to the interaction of inflow distortion with a subsonic annular blade row were studied with the aid of an unsteady three dimensional lifting surface theory. The effects of compact and noncompact source distributions on pure tone fan noise in an annular cascade were investigated. Numerical results show that the strip theory and quasi three-dimensional theory are reasonably adequate for fan noise prediction. The quasi three-dimensional method is more accurate for acoustic power and model structure prediction with an acoustic power estimation error of about plus or minus 2db.

Kobayashi, H.↗

NASA NTRS1987

Helicopter rotor induced velocities theory and experiment

An investigation has been performed to assess methods used for rotor inflow modeling. A key element of this assessment has been the recent acquisition of high quality experimental measurements of inflow velocities taken in the proximity of a lifting rotor in forward flight. Widely used rotor performance predictive methods are based on blade element strip theory coupled with an inflow model. The inflow prediction models assessed in this paper include the uniform inflow based on momentum, a skewed disk model, and two methods based on a vortex wake structure.

Berry, John D.↗

NASA NTRS1980

Illustration of airfoil shape effect on forward-swept wing divergence

A static aeroelastic analysis is presented of the divergence of untapered wings with conventional and supercritical airfoil sections at sweep angles of zero and -15 deg. One bending and one torsion mode were employed for a uniform rectangular cantilevered beam with the elastic axis at midchord, and calculations were based on a two-dimensional differential equations formulation in the structural coordinate system and in simple strip theory. A minimum divergence speed in the transonic range is obtained which is associated with the rearward shift of the aerodynamic center, and a 17% difference in minimum divergence dynamic pressure is found between a supercritical and a conventional wing. It is noted that although the strip method employed allows the assessment of the sensitivity of airfoil shapes to divergence, three-dimensional transonic aerodynamic methods should be used to predict wing divergence characteristics.

Bland, S. R.↗

NASA NTRS1953

Steady vibrations of wing of circular plan form

This paper treats the problem of determining the lift, moment, and induced drag of a thin wing of circular plan form in uniform incompressible flow on the basis of linearized theory. As contrasted to a similar paper by Kinner, in which the acceleration potential method was used, the present paper utilizes the concept of the velocity potential. Calculations of the lift and moment are presented for several deformed shapes. It is shown that considerable deviations exist between the strip theory analysis and the more exact theory. The lift, moment, and induced drag are also determined for a harmonically oscillatory circular plan form wing. As contrasted to a similar paper by Schade, in which the acceleration potential method was used, the present paper utilizes the concept of the velocity potential. Expressions for lift, moment, and induced drag are given and finally specialized to the case of a slowly oscillating circular wing.

FLUTTER - WINGS↗

NASA NTRS1984

On the prediction of auto-rotational characteristics of light airplane fuselages

A semi-empirical theory is presented for the estimation of aerodynamic forces and moments acting on a steadily rotating (spinning) airplane fuselage, with a particular emphasis on the prediction of its auto-rotational behavior. This approach is based on an extension of the available analytical methods for high angle of attack and side-slip and then coupling this procedure with strip theory for application to a rotating airplane fuselage. The analysis is applied to the fuselage of a light general aviation airplane and the results are shown to be in fair agreement with experimental data.

Pamadi, B. N.↗