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A mathematical model and computer program were implemented to study the main rotor free wake geometry effects on helicopter rotor blade air loads and response in steady maneuvers. The theoretical formulation and analysis of results are presented.
The structure of two-dimensional turbulent jets and wakes is studied using two eddy viscosity models. The turbulent energy equation is used together with the mean momentum equations, and the system is closed by introducing eddy coefficients. The fine structure turbulence is obtained by applying proper boundary conditions at the mean turbulent interface position. The results, after a second averaging process, are compared with available experimental data.
Equations are presented which provide approximate parameters describing surface heating and tektite deceleration during atmosphere passage. Numerical estimates of these parameters using typical initial and ambient conditions support the conclusion that the commonly assumed trajectories would not have produced some of the observed surface markings. It is suggested that tektites did not enter the atmosphere singly but rather in a swarm dense enough to afford wake shielding according to a shock envelope model which is proposed. A further aerodynamic mechanism is described which is compatible with hemispherical pits occurring on tektite surfaces.
A subsonic-flow panel code has been modified to handle the effects of a propeller wake. The effects of the propeller were modelled by a system of ring vortices of constant strength. Principles based on the blade element theory and the momentum theory were used to evaluate the swirl velocity and the pressure increase, across the propeller. Theoretical calculations are compared to experimental results at a Mach number of 0.50. The discrepancies between the theory and the experimental results are analysed. Suggestions for improvements to enhance the accuracy of the theoretical prediction are indicated.
A modified slender body theory was used in modelling the flowfield around an axisymmetric body at zero angle of attack. The model was defined in an attempt to characterize body-induced effects on helicopter rotor performance and loading using efficient computation methods. The streamfunction for an axial source distribution was applied in the body model, which was then adapted to the helicopter analysis code (CAMRAD). The body-induced velocities were calculated for separate locations on the rotor disk. Three different rotor models in nonuniform inflow with a free wake geometry were considered. Comparison of predictions with data on ellipsoidal and axisymmetric bodies showed good agreement for moderately thick ellipsoidal bodies. Oscillatory blade bending moments were increased by the presence of the body, but overall performance impact was negligible. Computational efficiency was 10-20 percent better than with a potential flow panel code.
A subsonic flow panel code has been modified to handle the effects of a propeller wake. The effects of the propeller were modelled by a system of ring vortices of constant strength. Principles based on the blade element theory, the vortex theory and the momentum theory were used to evaluate the axial velocity increase, the swirl velocity and the pressure increase across the propeller. Theoretical calculations are compared to experimental results at Mach numbers up to 0.70 over a range of angles of attack. The discrepancies between the theory and the experimental results are analyzed. Suggestions for improvements to enhance the accuracy of the theoretical prediction are indicated.
The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.
This report provides an updated version of analytical documentation for the V072 Rotor Wake/Stator Interaction Code. It presents the theoretical derivation of the equations used in the code and, where necessary, it documents the enhancements and changes made to the original code since its first release. V072 is a package of FORTRAN computer programs which calculate the in-duct acoustic modes excited by a fan/stator stage operating in a subsonic mean flow. Sound is generated by the stator vanes interacting with the mean wakes of the rotor blades. In this updated version, only the tonal noise produced at the blade passing frequency and its harmonics, is described. The broadband noise component analysis, which was part of the original report, is not included here. The code provides outputs of modal pressure and power amplitudes generated by the rotor-wake/stator interaction. The rotor/stator stage is modeled as an ensemble of blades and vanes of zero camber and thickness enclosed within an infinite hard-walled annular duct. The amplitude of each propagating mode is computed and summed to obtain the harmonics of sound power flux within the duct for both upstream and downstream propagating modes.
Flow computations around two-element and three-element configurations are presented and compared to detailed experimental measurements. The k-epsilon-v(exp 2)(bar) model has been applied and the ability of the model to capture streamline curvature effects, wake-boundary layer confluence, and laminar/turbulent transition is discussed. The numerical results are compared to experimental datasets that include mean quantities (velocity and pressure coefficient) and turbulent quantities (Reynolds normal and shear stresses).
The objective of the investigation reported in this thesis is to study the characteristics of a turbomachinery rotor wake, both analytically and experimentally. The constitutive equations for the rotor wake are developed using generalized tensors and a non-inertial frame of reference. Analytical and experimental investigation is carried out in two phases; the first phase involved the study of a cascade wake in the absence of rotation and three dimensionality. In the second phase the wake of a rotor is studied. Simplified two- and three-dimensional models are developed for the prediction of the mean velocity profile of the cascade and the rotor wake, respectively, using the principle of self-similarity. The effect of various major parameters of the rotor and the flow geometry is studied on the development of a rotor wake. Laws governing the decay of the wake velocity defect in a cascade and rotor wake as a function of downstream distance from the trailing edge, pressure gradient and other parameters are derived.
In-situ measurements of ambient electron densities with satellite-borne cylindrical probes exhibit periodic variations synchronous with the satellite's spin cycle. Representing these fluctuations as a superposition of effects attributable to both the presence of the satellite wake and the geomagnetic field leads to a model of the modulations of accelerated electron current to cylindrical probes in which one modulation component displays current variations dependent upon the probe-velocity angle (psi) and the other displays variations dependent upon the angle between the probe axis and the geomagnetic field lines (beta). The modulations produce an electron current decrease whenever the probe axis rotates into the satellite wake or whenever the probe axis rotates toward alignment with the geomagnetic field lines. With increasing altitude, the modulation dependent upon psi decreases whereas the modulation dependent upon beta increases. The analysis results imply that the most accurate of atmospheric electron densities by satellite-borne cylindrical probes come from measurements taken out of the satellite's wake and when the probe axis is within 20 degrees of being perpendicular to the geomagnetic field lines.
Observation that in situ measurements of ambient electron densities with satellite-borne cylindrical probes exhibit periodic variations synchronous with the satellite spin cycle. Representing these fluctuations as a superposition of effects attributable to both the presence of the satellite wake and the geomagnetic field leads to a model of the modulations of accelerated electron current to cylindrical probes in which one modulation component displays current variations dependent on the probe velocity angle (psi), and the other displays variations dependent on the angle between the probe axis and the geomagnetic-field lines (beta). The modulations produce an electron current decrease whenever the probe axis rotates into the satellite wake or whenever the probe axis rotates toward alignment with the geomagnetic-field lines. As altitude increases, the modulation dependent on psi decreases, whereas the modulation dependent on beta increases. The psi-dependent modulation component can be associated with the presence of a wake structure, and the beta-dependent component can be associated with the magnetic influence on the transport properties of thermal electrons, assuming that the electron fluxes are predominant along the field lines. The analysis results imply that the most accurate determinations of atmospheric electron densities by satellite-borne cylindrical probes come from measurements taken out of the wake of the satellite when the probe axis is within 20 deg of being perpendicular to the geomagnetic-field lines.
The problem of determining the vertical axis control requirements for landing a VTOL aircraft on a moving ship deck in various sea states is examined. Both a fixed-base piloted simulation and a nonpiloted simulation were used to determine the landing performance as influenced by thrust-to-weight ratio, vertical damping, and engine lags. The piloted simulation was run using a fixed-based simulator at Ames Research center. Simplified versions of an existing AV-8A Harrier model and an existing head-up display format were used. The ship model used was that of a DD963 class destroyer. Simplified linear models of the pilot, aircraft, ship motion, and ship air-wake turbulence were developed for the nonpiloted simulation. A unique aspect of the nonpiloted simulation was the development of a model of the piloting strategy used for shipboard landing. This model was refined during the piloted simulation until it provided a reasonably good representation of observed pilot behavior.
Theoretical methods are being developed to predict the mutual interference between rotor wakes and the hull for semibuoyant vehicles. The objective of the investigation is to predict the pressure distribution and overall loads on the hull in the presence of rotors whose locations, tilt angles, and disk loading are arbitrarily specified. The methods involve development of potential flow models for the hull alone in a nonuniform onset flow, a rotor wake which has the proper features to predict induced flow outside the wake, and a wake centerline specification technique which accounts for the reactions of the wake to a nonuniform crossflow. The flow models are used in sequence to solve for the mutual influence of the hull and rotor(s) on each other and the resulting loads. A flow separation model is included to estimate the influence of separation on hull loads at high sideslip angles. Only limited results have been obtained to date. These were obtained on a configuration which was tested in the Ames Research Center 7- by 10-Foot Low Speed Tunnel under Goodyear Aircraft Corporation sponsorship and indicate the nature of the interference pressure distribution on a configuration in hover.
A set of realizable second order models for boundary-free turbulent flows is presented. The constraints on second order models based on the realizability principle are re-examined. The rapid terms in the pressure correlations for both the Reynolds stress and the passive scalar flux equations are constructed to exactly satisfy the joint realizability. All other model terms (return-to-isotropy, third moments, and terms in the dissipation equations) already satisfy realizability. To correct the spreading rate of the axisymmetric jet, an extra term is added to the dissipation equation which accounts for the effect of mean vortex stretching on dissipation. The test flows used in this study are the mixing shear layer, plane jet, axisymmetric jet, and plane wake. The numerical solutions show that the unified model equations predict all these flows reasonably. It is expected that these models would be suitable for more complex and critical flows.
A set of realizable second order models for boundary-free turbulent flows is presented. The constraints on second order models based on the realizability principle are re-examined. The rapid terms in the pressure correlations for both the Reynolds stress and the passive scalar flux equations are constructed to exactly satisfy the joint realizability. All other model terms (return-to-isotropy, third moments, and terms in the dissipation equations) already satisfy realizability. To correct the spreading rate of the axisymmetric jet, an extra term is added to the dissipation equation which accounts for the effect of mean vortex stretching on dissipation. The test flows used in this study are the mixing shear layer, plane jet, axisymmetric jet, and plane wake. The numerical solutions show that the unified model equations predict all these flows reasonably. It is expected that these models would be suitable for more complex and critical flows.
The effects of ambient turbulence on decay and descent of aircraft wake vortices are studied using a validated, three-dimensional: large-eddy simulation model. Numerical simulations are performed in order to isolate the effect of ambient turbulence on the wake vortex decay rate within a neutrally-stratified atmosphere. Simulations are conducted for a range of turbulence intensities, by injecting wake vortex pairs into an approximately homogeneous and isotropic turbulence field. The decay rate of the vortex circulation increases clearly with increasing ambient turbulence level, which is consistent with field observations. Based on the results from the numerical simulations, simple decay models are proposed as functions of dimensionless ambient turbulence intensity (eta) and dimensionless time (T) for the circulation averaged over a range of radial distances. With good agreement with the numerical results, a Gaussian type of vortex decay model is proposed for weak turbulence: while an exponential type of Tortex decay model can be applied for strong turbulence. A relationship for the vortex descent based on above vortex decay model is also proposed. Although the proposed models are based on simulations assuming neutral stratification, the model predictions are compared to Lidar vortex measurements observed during stable, neutral, and unstable atmospheric conditions. In the neutral and unstable atmosphere, the model predictions appear to be in reasonable agreement with the observational data, while in the stably-stratified atmosphere, they largely underestimate the observed circulation decay with consistent overestimation of the observed vortex descent. The underestimation of vortex decay during stably-stratified conditions suggests that stratification has an important influence on vortex decay when ambient levels of turbulence are weak.
The present paper is concerned with the application of an analytical crack-closure model to study crack growth under various load histories. The model was based on a concept like the Dugdale model, but modified to leave plastically deformed material in the wake of the advancing crack tip. The thickness effect was accounted for by using a 'constraint' factor on tensile yielding at the crack tip. The model was used to correlate crack-growth rates under constant-amplitude loading, and to predict crack growth under variable-amplitude loading on a high-strength aluminum alloy (7475-T7351) sheet material. The experimental data was obtained from Zhang et al. Predicted crack-growth lives agreed well with experimental data. For ten crack-growth tests subjected to various variable-amplitude load histories, the ratio of predicted-to-experimental lives ranged from 0.54 to 1.19. The mean value of predicted-to-experimental lives was 0.95 with a standard error of 0.2 for a constraint factor of 1.9.