The calculation of pressure on slender airplanes in subsonic and supersonic flow
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WINGS, COMPLETE - THEORY↗
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The dynamics and control of large flexible space structures. Part B: Development of continuum model and computer simulation
The equations of motion of an arbitrary flexible body in orbit were derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit was modelled. The example considers both the inplane and three dimensional motion of the beam in orbit. In the case of planar motion with only flexible vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion was decoupled from the pitch motion. However, for small values of the ratio and small amplitude pitch motion, the elastic motion was governed by a Hill's 3 term equation. Numerical simulation of the equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate. Also numerical simulations of the first order nonlinear equations of motion for a long flexible beam in orbit were performed. The effect of varying the initial conditions and the number of modes was demonstrated.
Bainum, P. M.↗
Dynamics of a flexible body in orbit
The equations of motion of an arbitrary flexible body in orbit are derived. The model includes the effects of gravity with all its higher harmonics. As a specific example, the motion of a long, slender, uniform beam in circular orbit is modeled. The example considers the inplane motion of the beam in orbit. In the case of planar motion with only flexural vibrations, the pitch motion is not influenced by the elastic motion of the beam. For large values of the square of the ratio of the structural modal frequency to the orbital angular rate the elastic motion is decoupled from the pitch motion. However, for small values of this ratio and small amplitude pitch motion, the elastic motion is governed by a Hill's 3-term equation. Numerical simulation of this equation indicates the possibilities of instability for very low values of the square of the ratio of the modal frequency to the orbit angular rate.
Kumar, V. K.↗
On the structure, interaction, and breakdown characteristics of slender wing vortices at subsonic, transonic, and supersonic speeds
Slender wing vortex flows at subsonic, transonic, and supersonic speeds were investigated in a 6 x 6 ft wind tunnel. Test data obtained include off-body and surface flow visualizations, wing upper surface static pressure distributions, and six-component forces and moments. The results reveal the transition from the low-speed classical vortex regime to the transonic regime, beginning at a freestream Mach number of 0.60, where vortices coexist with shock waves. It is shown that the onset of core breakdown and the progression of core breakdown with the angle of attack were sensitive to the Mach number, and that the shock effects at transonic speeds were reduced by the interaction of the wing and the lead-edge extension (LEX) vortices. The vortex strengths and direct interaction of the wing and LEX cores (cores wrapping around each other) were found to diminish at transonic and supersonic speeds.
Erickson, Gary E.↗
ASPIRE Aerodynamic Models and Flight Performance
The Advanced Supersonic Parachute Inflation Research Experiments (ASPIRE) project waslaunched to develop the capability for testing supersonic parachutes at Mars-relevant conditions.Three initial parachute tests, targeted as a risk-reduction activity for NASA's upcoming Mars2020 mission, successfully tested two candidate parachute designs and provided valuable data onparachute inflation, forces, and aerodynamic behavior. Design of the flight tests depended onflight mechanics simulations which in turn required aerodynamic models for the payload, andthe parachute. Computational Fluid Dynamics (CFD) was used to generate these models preflightand they are compared against the flight data after the tests. For the payload, thereconstructed aerodynamic behavior is close to the pre-flight predictions, but the uncertaintiesin the reconstructed data are high due to the low dynamic pressures and accelerations duringthe flight period of comparison. For the parachute, the predicted time to inflation agrees wellwith the pre-flight model; the peak aerodynamic force and the steady state drag on the parachuteare within the bounds of the pre-flight models, even as the models over-predict the parachutedrag at supersonic Mach numbers. Notably, the flight data do not show the transonic dragdecrease predicted by the pre-flight model. The ASPIRE flight tests provide previouslyunavailable valuable data on the performance of a large full-scale parachute behind a slenderleading body at Mars-relevant Mach number, dynamic pressure and parachute loads. TheASPIRE results are used to propose a new model for the parachute drag behind slender bodiesto aid future experiments.
Muppidi, Suman↗
Three-dimensional simulation of slender delta wing rock and divergence
Computational simulation of three-dimensional flows around a delta wing undergoing rock and roll-divergence motions is presented. The problem is a multidisciplinary one where fluid-dynamics equations and rigid-body-dynamics equations are sequentially solved. For the fluid-dynamics part, the unsteady Euler equations, which are written relative to a moving frame of reference, are solved using an implicit, approximately-factored, central-difference, finite-volume scheme. For the rigid-body dynamics part, the Euler equation of rigid-body rolling motion is solved using a four-stage Runge-Kutta scheme. Since the applications do not include deforming wings or relative-rigid-body motions, the computational-fluid-dynamics grid, which is fixed in the moving frame of reference, does not need to be updated once it is generated.
Kandil, Osama A.↗
On the nonlinear aerodynamic and stability characteristics of a generic chine-forebody slender-wing fighter configuration
An exploratory investigation was conducted of the nonlinear aerodynamic and stability characteristics of a tailless generic fighter configuration featuring a chine-shaped forebody coupled to a slender cropped delta wing in the NASA Langley Research Center's 12-Foot Low-Speed Wind Tunnel. Forebody and wing vortex flow mechanisms were identified through off-body flow visualizations to explain the trends in the longitudinal and lateral-directional characteristics at extreme attitudes (angles of attack and sideslip). The interactions of the vortical motions with centerline and wing-mounted vertical tail surfaces were studied and the flow phenomena were correlated with the configuration forces and moments. Single degree of freedom, free-to-roll tests were used to study the wing rock susceptibility of the generic fighter model. Modifications to the nose region of the chine forebody were examined and fluid mechanisms were established to account for their ineffectiveness in modulating the highly interactive forebody and wing vortex systems.
Erickson, Gary E.↗
On the nonlinear aerodynamic and stability characteristics of a generic chine-forebody slender-wing fighter configuration
An exploratory investigation was conducted of the nonlinear aerodynamic and stability characteristics of a tailless generic fighter configuration featuring a chine-shaped forebody coupled to a slender cropped delta wing in the NASA Langley Research Center's 12-Foot Low-Speed Wind Tunnel. Forebody and wing vortex flow mechanisms were identified through off-body flow visualizations to explain the trends in the longitudinal and lateral-directional characteristics at extreme attitudes (angles of attack and sideslip). The interactins of the vortical motions with centerline and wing-mounted vertical tail surfaces were studied and the flow phenomena were correlated with the configuration forces and moments. Single degree-of-freedom, free-to-roll tests were used to study the wing rock susceptibility of the generic fighter model. Modifications to the nose region of the chine forebody were examined and fluid mechanisms were established to account for their ineffectiveness in modulating the highly interactive forebody and wing vortex systems.
Erickson, Gary E.↗
Plane and Three-Dimensional Flow at High Subsonic Speeds
For two- and three-dimensional flow in a compressible medium, a simple relation is given by which, to a first approximation, the quantitative influence of compressibility upon the velocities and pressures can be understood in a clear manner. In the application of this relation the distinct behaviors of two-dimensional and axially symmetric three-dimensional flow with increasing Mach number are brought out. For slender elliptic cylinders and ellipsoids of revolution, calculations are made of the critical Mach number; that is, the Mach number at which local sonic velocity is achieved on the body. As a further example, the lifting wing of finite span is considered, and it is shown that the increase of wing lift with Mach number at a given angle of attack is greatly dependent upon the aspect ratio b(exp 2)/F.
Gothert, B.↗
Side-force alleviation on slender, pointed forebodies at high angles of attack
A new approach of alleviating high angle-of-attack side force on slender, pointed forebodies comprising a symmetrical pair of helical separation trips to disrupt the lee-side vortices, has been demonstrated. Subsonic wind tunnel measurements on two axi-symmetric pointed bodies, a fuselage of non-circular cross-section and a wing-fuselage combination, at angles of attack up to 56 degrees are presented. Also included are water-tunnel flow visualization results portraying the action of helical trips in rapidly diffusing the leeward vortices and preventing vortex-wake asymmetry.
Rao, D. M.↗
Computation of supersonic flow fields about bodies in coning motion using a shock-capturing finite-difference technique.
A numerical method for computing the nonlinear inviscid flow field surrounding a body performing coning motion is described. The method permits accurate computation of the aerodynamic moment due to one of the four motions characterizing an arbitrary nonplanar motion. Results of computations for a slender circular cone in coning motion are presented, and show good agreement with experiment for angles of attack up to twice the cone half angle. The computational results display significant departure of the side moment from the linear theory value with increasing angle of attack, but agree well with experimental measurements. This indicates that the initial nonlinear behavior of the aerodynamic moment is determined primarily by the inviscid flow.
Schiff, L. B.↗
Nonlinear Aerodynamics of Bodies in Coning Motion
A numerical method for computing the nonlinear inviscid flowfield surrounding a body performing coning motion is described. The method permits accurate computation of the aerodynamic moment due to one of the four motions characterizing an arbitrary nonplanar motion. Results of computations for a slender circular cone in coning motion are presented, and show good agreement with experiment for angles of attack up to twice the cone half-angle. The computational results display significant departure of the side moment from the linear theory value with increasing angle of attack, but agree well with experimental measurements. This indicates that the initial nonlinear behavior of the aerodynamic moment is determined primarily by the inviscid flow.
Schiff, Lewis B.↗
Navier-Stokes Equations Based Aeroelasticity of Supersonic Transport Including Short Period Oscillations
There is renewed interest in developing new supersonic transports after the discontinuation of the Concorde supersonic jet, which was mostly limited for flights over trans-oceanic routes due to the severe noise of the sonic boom. In order to avoid the sonic boom, more slender configurations, such as the Low Boom Flight Demonstrator (LBFD) configuration, are being considered. The aeroelastic characteristics of these new supersonic transports can significantly differ from conventional aircraft. Both rigid and flexible body modes can play a significant role in aeroelastic stability. For unconventional configurations, such as aircraft with forward swept wings, the short period oscillation (SPO) has been found to significantly impact the aeroelastic response. SPO can occur due to unanticipated events such as gusts, abrupt maneuvering, etc. During the design of the Concorde, the effects of SPO was considered in detail, though its impact is not publically disclosed. Assuring stability of supersonic aircraft, particularly during descent from the supersonic Mach regime to the transonic regime, is critical. An aircraft can deviate from its normal descent trajectory due to coupling between flows and body motions. The effect of SPO needs to be considered in aeroelastic responses. Preliminary studies using quasi-steady aerodynamics show that the presence of SPO can lead to unstable response. The well-established Reynolds Averaged Navier-Stokes (RANS) equations, which are computationally feasible with current supercomputers, have been in use for aeroelastic computations for the last three decades. Recently, such efforts have begun to include trajectory motions; for instance, the effect of phugoid motion on stability is studied in Ref. 9 using the RANS equations. In this paper, the effect of SPO on aeroelastic responses of a typical supersonic transport is studied.
Guruswamy, Guru↗
Predicted Shock Envelopes about Two Types of Vehicles at Large Angles of Attack
Methods based on oblique - and normal-shock relationships and the continuity of mass flow through suitably chosen volume elements between the shock and body were developed t o predict shock envelopes about two types of vehicles being considered for atmosphere entry. One type is a high-drag capsule shape. The other type is essentially a slender tri- angular wing capable of providing high lift or high drag, depending on the angle of attack. Predicted and measured shock envelopes were compared f o Mach number range of 3 to 15 for vehicles at high angles of attack; good agreement was found. Most of the available experimental data were in a speed and temperature range in which no important real-gas effects occurred.
Kaattari, George E.↗
Forebody vortex control for suppressing wing rock on a highly-swept wing configuration
Free-to-roll tests were conducted in a wind tunnel with a configuration that consisted of a highly-slender forebody and a 78 deg swept delta wing. A limit cycle oscillation was observed for angles of attack between 22 and 30 deg. In general, the main flow phenomena responsible for the wing-body-tail wing rock are the interactions between the forebody and the wing vortices. Various blowing techniques were evaluated as means of wing rock suppression. Blowing tangentially aft from leeward side nozzles near the forebody tip can damp the roll motion at low blowing rates and stop it completely at higher blowing rates. At the high rates, significant vortex asymmetries are created, causing the model to stop at a non-zero roll angle. Forward blowing and alternating right/left pulsed blowing appear to be more efficient techniques for suppressing wing rock. The oscillations can be damped almost completely at lower blowing coefficients, and, apparently, no major vortex asymmetries are induced. Good agreement is observed between this study and previous water tunnel tests on the same configuration.
Suarez, Carlos J.↗
Calculations of the Supersonic Wave Drag of Nonlifting Wings with Arbitrary Sweepback and Aspect Ratio: Wings Swept Behind the Mach Lines
On the basis of a recently developed theory for finite sweptback wings at supersonic speeds, calculations of the supersonic wave drag at zero lift were made for a series of wings having thin symmetrical biconvex sections with untapered plan forms and various angles of sweepback and aspect ratios. The results are presented in a unified form so that a single chart permits the direct determination of the wave drag for this family of airfoils for an extensive range of aspect ratio and sweepback angle for stream Mach numbers up to a value corresponding to that at which the Mach line coincides with the wing leading edge. The calculations showed that in general the wave-drag coefficient decreased with increasing sweepback. At Mach numbers for which the Mach lines are appreciably ahead of the wing leading edge, the 'wave-drag coefficient decreased to an important extent with increases in aspect ratio or slenderness ratio. At Mach numbers for which the Mach lines approach the wing leading edge (Mach numbers approaching a value equal to the secant of the angle of sweepback), the wave-drag coefficient decreased with reductions in aspect ratio or slenderness ratio. In order to check the results obtained by the theory, a comparison was made with the results of tests at the Langley Memorial Aeronautical Laboratory of sweptback wing attached to a freely falling body. The variation of the drag with Mach number and aspect ratio as given by the theory appeared to be in reasonable
Harmon, Sidney M↗
Force, Surface Pressure, and Flowfield Measurements on a Slender Missile Configuration with Square Cross-Section at Supersonic Speeds
A wind-tunnel investigation of a square cross-section missile configuration has been conducted to obtain force and moment measurements, surface pressure measurements, and vapor screen flow visualization photographs for comparison with computational fluid dynamics studies conducted under the auspices of The Technical Cooperation Program (TTCP). Tests were conducted on three configurations which included: (1) body alone, (2) body plus tail fins mounted on the missile corners, and (3) body plus tail fins mounted on the missile side. This test was conducted in test section #2 of the NASA Langley Unitary Plan Wind Tunnel at Mach numbers of 2.50 and 4.50 and at a Reynolds number of 4 million per ft. The data were obtained over an angle of attack range from -4 deg. to 24 deg. and roll angles from 0 deg. to 45 deg., i.e., from a diamond shape (as viewed from the rear) at a roll angle of 0 deg. to a square shape at 45 deg.
Wilcox, Floyd J., Jr.↗
Effects of Mach number and afterbody length on aerodynamic side forces at zero sideslip on symmetric bodies at high angles of attack
Wind-tunnel measurements of side force over the Mach number range of 0.25 to 2 for pointed forebody-alone and for ogive-cylinder models of various fineness ratios up to 16, are presented. The angle of attack where side force first occurs (onset), where it returns to zero (upper limit), and its magnitude are examined. The onset angle depends only on body geometry, longer bodies having lower onset angles. The upper limit, which is about 80 deg at M = 0.25, decreases with Mach number. The maximum side forces decrease with increasing Mach number, approaching zero within the Mach number range of 0.8 to 1.2; within this range, the Mach number at which the forces approach zero varies directly with forebody slenderness.
Keener, E. R.↗