Rotor Blade In Hover Research Articles

Hover Performance Prediction Using Full-Potential Method and Comparison with Experiments

A computational and experimental effort to investigate the e ow around rotor blades in hover is presented. The experimental analysis of the e owe eld in the immediate vicinity of the blade is supported by laser velocimetry (LV) performed on the three-dimensional velocity e eld around the bladesection and in its nearwake. A specie c LV data processingmethod based onthemomentumequationapplied around a bladesectionhasbeen developed to identify the contribution of the induced-drag component to the total sectional drag coefe cient. From the computational approach, some improvements to a vortex embedding full-potential method are checked by direct comparisons withtestdata. Comparisonsareperformed foroverallrotorairloads (thrustand torquecoefe cients ),localsectional coefe cients (liftanddragcontributions ),ande owe eldcharacteristics,includingthetipvortexpathandthespanwise circulation distribution.

Adaptive CFD analysis for rotorcraft aerodynamics

An adaptive, parallel computational fluid dynamics (CFD) technique is developed to compute rotor-blade aerodynamics. For this purpose an error indicator is formulated and coded into an adaptive finite element framework. It is shown that the error indicator is effective in resolving the global features of the flow-field. Furthermore, for efficiency and problem size considerations, once the interpolation errors are reduced to acceptable levels, the adaptive refinement is done only in regions affected by the vortical flows. To accomplish this, a novel vortex core detection technique is used to capture vortex tubes. The combination of interpolation error estimate and vortex core detection technique proved to be very effective in computing vortical flow-field of rotor blades. Example adaptive, parallel calculations of hovering rotor blades, requiring 1–3 million tetrahedral elements, are presented.

A multigrid Navier-Stokes CFD code for rotor computations

This paper presents the development of a multigrid Navier-Stokes code TLNS3DR for rotary wing calculations. The TLNS3DR is developed from the fixed-wing TLNS3D code by including a rotation term and making necessary modifications on boundary conditions. The TLNS3D code solves the thin-layer Navier-Stokes equations using an explicit multistage Runge-Kutta type of time stepping with multigrid method. The TLNS3DR code reformulates the TLNS3D code in the rotor blade-fixed moving frame of reference and solves relative motion of fluids. In this paper, the formulation of the Navier-Stokes equations in the moving frame of reference in terms of relative velocity is given. Several numerical examples are then presented. The results of rotor blade in hover calculated by the new TLNS3DR code seem quantitative correct. The computation also shows that this multigrid code is efficient.

Aeroelastic analysis of composite rotor blades in hover

The aeroelastic phenomena of a composite rotor blade in hover is investigated using a finite element method. A large deflection type beam theory is used for the one-dimensional global deformation analysis of the hingeless, isolated rotor undergoing arbitrary large displacements and rotations, but small strains. The sectional elastic constants of a composite box beam, including warping deformations, are determined from the refined cross-sectional finite element method. A two-dimensional, quasi-steady strip theory is applied for the aerodynamic calculation. Complete nonlinear equations are solved by the Newton—Raphson method to obtain an equilibrium position and the stability equations are linearized about this position. The modal approach method based on coupled rotating natural modes is used for the flutter analysis. The effects of fiber orientation and stacking sequences on the aeroelastic stability have been investigated.

New type of embedded laser Doppler velocimeter for measurement of rotary wings boundary layer

An experimental method has been developed to determine the velocity profiles across the boundary layer of rotary wings. The measurement, based on laser Doppler velocimetry, has been tested on a helicopter rotor blade in hover. The main components of the prototype are embedded in an untwisted blade. The beams converging at the measurement volume, which can be moved along perpendicular to the surface, and the signals backscattered by flow particles, are collected through rotating fiber optic cables to a transmitter insuring the connection with fixed components (laser source, photomultipliers, burst spectrum analyzer, computer, etc.). Measurements, performed in a frame linked to the rotating blade for one radial distance from the rotation axis and at a chord abscissa x/c=0.25, have involved the tangential velocity component (chordwise) and the crossflow component (spanwise). The boundary layer has been explored at different rotating speeds of the blade. The accuracy of velocity components measurements has been evaluated in the region very close to the wall and far from the wall. The velocity profiles obtained in different hovering test conditions have shown the efficiency of the present embedded laser Doppler velocimeter method, which can also be applied to rotors in forward flight, wind turbines, etc. Undoubtly, the new database obtained on the rotating boundary layer will constitute an essential support for the physical models and computational works.

Refined Aeroelastic Analysis of Hingeless Rotor Blades in Hover

The aeroelastic response and stability of hingeless rotor blades in hover are investigated using both refined structural and aerodynamic models. Finite elements based on a large deflection-type beam theory are used for structural analysis. Although the strain components in the beam element are assumed to be small compared to unity, no kinematical limitations are imposed on the magnitude of displacements and rotations. A three-dimensional aerodynamic model including compressibility effect, which is a thin lifting-surface theory based on the unsteady vortex lattice method, is applied to evaluate the aerodynamic loads. A thin lifting-surface and its wake are represented by a number of the quadrilateral vortex-ring elements. The wake geometry is prescribed from the known generalized equations. Numerical results of the steady-state deflections and the stability for the stiff in-plane rotor blade are presented. It is found that the three-dimensional aerodynamic tip-relief, unsteady wake dynamics, and compressibility effects, not predicted in the two-dimensional strip theory, play an important role in the hingeless rotor aeroelastic analysis in hover.

Correlation of unsteady pressure and inflow velocity fields of a pitching rotor blade

Predictions from four different analytical methods are compared with measurements of unsteady inflow velocity and surface pressure distributions on a pitching rotor blade in hover. The test case is a stiff two-bladed teetering rotor constructed from full-scale tail rotor blades, subjected to w/rev simple harmonic pitch oscillations under incompressible flow conditions. The chordwise distributions of unsteady pressure at three radial locations on the blade are compared with Theodorsen's and Loewy's two-dimensional incompressible unsteady aerodynamic theories and with Kaladi's pulsating doublet distribution method. Inflow velocity is predicted successfully using Peters' modal theory for steady as well as dynamic pitch conditions. The effect of dynamic inflow on rotor unsteady surface pressure is studied. At inboard radial locations, Loewy's two-dimensional theory for even harmonics of forcing frequency and Theodorsen's two-dimensional theory for odd harmonics provide efficient and reliable predictions of unsteady blade surface pressure. At outboard radial locations, panel or modal methods have to be used to predict amplitude and phase of unsteady pressure. Tip effects, mean pitch angle effects, and effects of rotation have been demonstrated. Nomenclature b = number of blades C(k) — Theodorsen's lift deficiency function, F + IG C'(k) = modified lift deficiency function for the rotor, F' + iG' Cp = pressure coefficient, 2(p - p y)/pfl2r2

Aeroelastic stability of hingeless rotor blade in hover using large deflection theory

The coupled flap-lag-torsion aeroelastic stability of a hingeless rotor blade in hover is investigated using finite elements based on large deflection beam theory. The finite element equations of motion for beams undergoing arbitrary large displacements and rotations, but small strains, are obtained from Hamilton's principle. The stability boundary is calculated assuming blade motions to be small perturbations about the nonlinear steady equilibrium deflections, which are obtained through an iterative Newton-Raphson method. The p-k- mudal flutter analysis based on coupled rotating natural modes is used. Various unsteady two dimensional strip theories are used to evaluate the aerodynamic loads

Aeroelastic response of composite rotor blades considering transverse shear and structural damping

The effects of transverse shear deformations and structural damping on the flutter phenomena of a composite rotor blade in hover have been investigated using the finite element method. First-order shear deformation theory with rotary inertia effects and a damped element model of composite laminates are employed for the structural formulation. A quasisteady aerodynamic theory with a dynamic inflow model is used. Torsion-related out-of-plane warping and noncirculatory aerodynamic components are also incorporated in the formulation. Using these structural and aerodynamic tools, several numerical studies are carried out, first to validate the current approach and second to show the effects of transverse shear deformations and structural damping on the aeroelastic stability of a composite rotor as a function of fiber orientation. The predictions derived by the frequency analysis of this model are found to be more accurate than those given by an alternative approach compared with experimental data. It is shown that the transverse shear flexibility tends to lower the frequency of the rotor, and generally has a destabilizing effect on the lag mode and a stabilizing effect on the flap mode. It is also presented that the magnitude of structural damping can be controlled by changing ply orientation angle. CT cd c, EA

A new sensitivity analysis for structural optimization of composite rotor blades

This paper presents the mathematical details of the formulation for the sensitivity derivatives for the structural dynamic, aeroelastic stability, and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semi-analytical approach, because certain derivatives are evaluated by a finite difference scheme. Using this formulation, sensitivity derivatives for structural dynamic and aeroelastic stability characteristics were evaluated for a composite rotor blade. Useful conclusions regarding the relative merits of the semi-analytical approach, when compared to a pure finite difference approach, are obtained. In addition, influence of ply orientation angles on the vibratory hub loads in forward flight is also considered.

Aeroelastic stability of composite hingeless rotor blades in hover—Part II: Results

In Part I of this two-part paper, an aeroelastic stability analysis was presented for isolated hingeless, composite rotor blades in the hovering flight condition, which was based on a mixed finite element method. Herein, the focus is to present numerical results obtained from this analysis. First, certain of these results are compared with those of existing aeroelastic stability analyses for validation. Next, the numerical accuracy and convergence characteristics of the current approach are quantified. Finally, parametric studies are performed to investigate the effects of composite elastic coupling and thrust condition on the blade's aeroelastic stability, especially that of the lightly damped lead-lag mode. The stability of some of the elastically coupled cases studied was sensitive to the nonclassical couplings; indeed, in one case a significant error appeared, accentuated at high thrust levels, when bending-shear coupling was neglected. Another significant effect stems from changes in the equilibrium solution for elastic twist due to extension-twist coupling. The necessity of including such effects in the blade model for general-purpose analysis is noted.

片持ち回転はりの構造最適化

A basic study concerning the structural optimization of a rotor blade subject to steady combined loadings is conducted. The combined loadings are assumed to be composed of distributed axial and lateral loadings which are simulating the centrifugal force and airloadings for a rotor blade in hover. To simplify the problem, the blade is modeled as a cantilevered rotating beam with the plane tapered cross section. The minimum deflection problem of the cantilevered rotating beam is formulated as an optimization problem involving inequality constraints and solved using optimal control methodology. Optimum area distributions are determined numerically for typical combinations of combined loadings and effects of the centrifugal force on the optimum solutions are discussed. Numerical results reveal clearly the important role of the axial loading on the optimum solution and inclusion of the centrifugal force to the structural optimization of the rotor blade should be essential.

Visualization and measurement of the tip vortex core of a rotor blade in hover

Detailed measurements with a laser Doppler velocimeter (LDV) have been performed in the tip region and in the tip vortex core of a single-bladed model rotor in hover. The testing was conducted at a rotor tip speed of 32 m/s, a Reynolds number of 269,000, and at two values of the rotor thrust coefficient, 0.0022 and 0.0057. Strobed laser sheet flow visualization was used to verify the steadiness of the tip vortex trajectory in the near wake and quantify the vortex trajectory to guide LDV surveys of the vortex core. A remotely aligned off-axis receiving optics system enabled measurement of vortex core velocity profiles at large focal lengths. The core self-induced velocity components extracted from these data are presented. The data exhibit evidence of secondary structure even inside the rotational core of the vortex, the axial velocity profile along the core has been extracted and presented in the wake of a spinning rotor. It is seen that the tip vortex of a rotating blade differs considerably in structure from a fixed-wing vortex.

Velocity field of a lifting rotor blade in hover

The authors gratefully acknowledge the support of this work by the U.S. Army Research Office as part of the Center for Rotary Wing Aircraft Technology, Contract DAAG29-82-K- 0094, monitored by Dr. Robert E. Singleton.

Reconstruction of a Three-Dimensional, Transonic Rotor Flowfield from Holographic Interferograms

Holographic interferometry and computer-assisted tomography (CAT) are used to determine the transonic velocity field of a model rotor blade in hover. A pulsed ruby laser recorded 40 interferograms with a 2-ft-diam field of view near the model rotor-blade tip operating at a tip Mach number of 0.90. After digitizing the interferograms and extracting fringe-order functions, the data are transferred to a CAT code. The CAT code, based on the filtered back-projection technique, then calculates the perturbation velocity in several planes above the blade surface. The values from the holography-CAT method compare favorably with previously obtained numerical computations near the blade tip. The results demonstrate the technique's potential for threedimensional transonic rotor flow studies.

Full-potential circular wake solution of a twisted rotor blade in hover

A solution for transonic flow past a twisted rotor blade in hover is obtained using a modified version of the full-potential code ROT22 and a circular wake. The flow is also evaluated for a fixed-wing-type straight wake. The solutions for the straight wake and circular wake, and the circular wake and a two-dimensional wake are compared. The data reveal that the circular wake and the general two-dimensional wake solutions have similar characteristics.

Helicopter Linear Noise

F OLLOWING Ffowcs-Williams and Hawkings' theory,' the three-dimensional quasi-steady fullpotential rotor flow analysis code ROT22, adapted from Jamesons' FLO22 code, is run in conjunction with the Farassat Noise code and the linear noise made by rotor blade in hover investigated. For the case considered, the study, while it confirms the earlier finding that the blade volume displacement is a dominant source of helicopter noise, contradicts a previously drawn conclusion namely that the blade tip loading makes a significant contribution to the overall noise. The thickness noise is further compared with the one calculated from the Schmitz-Yu code. It is shown that the inclusion of blade profile curvature in the calculations improves the negative peak amplitudes overpredicted by a Schmitz-Yu study.

Dynamic Stability of a Bearingless Circulation Control Rotor Blade in Hover

The aeroelastic stability of flap bending, lead-lag bending and torsion of a bearingless circulation control rotor blade in hover is investigated using a finite element formulation based on Hamilton's principle. The flexbeam, the torque tube and the outboard blade are discretized into beam elements, each with fifteen nodal degrees of freedom. Quasisteady strip theory is used to evaluate the aerodynamic forces and the airfoil characteristics are represented either in the form of simple analytical expressions or in the form of data tables. A correlation study of analytical results with the experimental data is attempted for selected bearingless blade configurations with conventional airfoil characteristics.

Dynamic Stability of a Rotor Blade Using Finite Element Analysis

The aeroelastic stability of flap bending, lead-lag bending, and torsion of a helicopter rotor blade in hover is examined using a finite element formulation based on the principle of virtual work. Quasi-steady two-dimensional airfoil theory is used to obtain the aerodynamic loads. The rotor blade is discretized into beam elements, each with ten modal degrees of freedom. The resulting nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The flutter solution is calculated assuming blade motion to be a small perturbation about the steady solution. The normal mode method based on the coupled rotating natural modes about the steady deflections is used to reduce the number of equations in the flutter eigenanalysis. Results are presented for hingeless and articulated rotor blade configurations.

Application of the Finite Element Method to Rotary‐Wing Aeroelasticity

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.