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NASA NTRS1988

Euler equation computations for the flow over a hovering helicopter rotor

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

Roberts, Thomas Wesley↗

NASA NTRS1978

A theoretical investigation of the aerodynamics of low-aspect-ratio wings with partial leading-edge separation

A numerical method is developed to predict distributed and total aerodynamic characteristics for low aspect-ratio wings with partial leading-edge separation. The flow is assumed to be steady and inviscid. The wing boundary condition is formulated by the quasi-vortex-lattice method. The leading-edge separated vortices are represented by discrete free vortex elements which are aligned with the local velocity vector at mid-points to satisfy the force free condition. The wake behind the trailing-edge is also force free. The flow tangency boundary condition is satisfied on the wing, including the leading- and trailing-edges. Comparison of the predicted results with complete leading-edge separation has shown reasonably good agreement. For cases with partial leading-edge separation, the lift is found to be highly nonlinear with angle of attack.

Mehrotra, S. C.↗

NASA NTRS1987

Spanwise pressure distribution on delta wing with leading-edge vortex flap

The aerodynamic characteristics of a highly swept planar delta wing employing conical leading edge flaps are numerically investigated, using a free vortex sheet method that is based on an advanced, three-dimensional inviscid flow panel method employing quadratic doublet distributions to represent the wing surface and the rolled-up vortex sheet and wake. Upward flap deflection shifts the negative pressure peak inboard of the basic wing and develops a significant suction pressure on the flap that then produces thrust component in the direction of flight; overall drag is thereby reduced.

Reddy, C. S.↗

NASA NTRS1971

Development and application of a method for predicting rotor free wake positions and resulting rotor blade air loads. Volume 1: Model and results

Rotor wake geometries are predicted by a process similar to the startup of a rotor in a free stream. An array of discrete trailing and shed vortices is generated with vortex strengths corresponding to stepwise radial and azimuthal blade circulations. The array of shed and trailing vortices is limited to an arbitrary number of azimuthal steps behind each blade. The remainder of the wake model of each blade is an arbitrary number of trailing vortices. Vortex element end points were allowed to be transported by the resultant velocity of the free stream and vortex-induced velocities. Wake geometry, wake flow, and wake-induced velocity influence coefficients are generated by this program for use in the blade loads portion of the calculations. Blade loads computations include the effects of nonuniform inflow due to a free wake, nonlinear airfoil characteristics, and response of flexible blades to the applied loads. Computed wake flows and blade loads are compared with experimentally measured data. Predicted blade loads, response and shears and moments are obtained for a model rotor system having two independent rotors. The effects of advance ratio, vertical separation of rotors, different blade radius ratios, and different azimuthal spacing of the blades of one rotor with respect to the other are investigated.

Sadler, S. G.↗

NASA NTRS1981

Effect of leading-edge vortex flaps on aerodynamic performance of delta wings

The effect of leading-edge vortex flaps on the aerodynamic characteristics of highly swept-back wings is analytically investigated, using the free vortex sheet method. The method, based on a three-dimensional inviscid flow model, is an advanced panel type employing quadratic doublet distributions to represent the wing surface, rolled-up vortex sheet and wake and is capable of computing forces, moments and surface pressures.

Reddy, C. S.↗

NASA NTRS1987

Analyzing Wakes From Hovering-Helicopter Rotor Blades

New method for analyzing free wake of hovering-helicopter rotor produces more reliable results and requires less computer time. Copes with wake instabilities, both physical and numerical, that afflict usual time-stepping analysis methods. Tip-vortex position, in coordinates moving with rotor blade, updated in relaxation procedure. Wake-airflow solution reached when updates converge to steady wake shape.

Bliss, D. B.↗

NASA NTRS1976

Calculation of the longitudinal aerodynamic characteristics of wing-flap configurations with externally blown flaps

An analytical method for predicting the longitudinal aerodynamic characteristics of externally blown flap configurations is described. Two potential flow models make up the prediction method: a wing and flap lifting-surface model and a turbofan engine wake model. A vortex-lattice lifting-surface method is used to represent the wing and multiple-slotted trailing-edge flaps. The jet wake is represented by a series of closely spaced vortex rings normal to a centerline which is free to move to conform to the local flow field. The two potential models are combined in an iterative fashion to predict the jet wake interference effects on a typical EBF configuration. Comparisons of measured and predicted span-load distributions, individual surface forces, forces and moments on the complete configuration, and flow fields are included.

Mendenhall, M. R.↗

NASA NTRS1990

Free wake analysis of hover performance using a new influence coefficient method

A new approach to the prediction of helicopter rotor performance using a free wake analysis was developed. This new method uses a relaxation process that does not suffer from the convergence problems associated with previous time marching simulations. This wake relaxation procedure was coupled to a vortex-lattice, lifting surface loads analysis to produce a novel, self contained performance prediction code: EHPIC (Evaluation of Helicopter Performance using Influence Coefficients). The major technical features of the EHPIC code are described and a substantial amount of background information on the capabilities and proper operation of the code is supplied. Sample problems were undertaken to demonstrate the robustness and flexibility of the basic approach. Also, a performance correlation study was carried out to establish the breadth of applicability of the code, with very favorable results.

Quackenbush, Todd R.↗

NASA NTRS1986

Euler solutions for the flow around a hovering helicopter rotor

A method for computing the flow around a hovering helicopter rotor is presented. The solution procedure is divided into two parts. The first part is a finite volume solution of the Euler equations for the near field flow around a rotor blade. The second part is a free wake approach for determining the wake geometry and induced velocities. These two parts are solved in a coupled fashion. The rolled-up vortex wake of the rotor is included in the Euler computational domain through a nonlinear perturbation technique. This eliminates the numerical diffusion of the wake vorticity due to truncation error and artificial viscosity without the need for excessive grid resolution near the vortex core. The method is used to compute both hovering rotor and wing/vortex interaction flows, and the results are compared to experiment.

Roberts, T. W.↗

NASA NTRS1976

A computer program to calculate the longitudinal aerodynamic characteristics of wing-flap configurations with externally blown flaps

A vortex lattice lifting-surface method is used to model the wing and multiple flaps. Each lifting surface may be of arbitrary planform having camber and twist, and the multiple-slotted trailing-edge flap system may consist of up to ten flaps with different spans and deflection angles. The engine wakes model consists of a series of closely spaced vortex rings with circular or elliptic cross sections. The rings are normal to a wake centerline which is free to move vertically and laterally to accommodate the local flow field beneath the wing and flaps. The two potential flow models are used in an iterative fashion to calculate the wing-flap loading distribution including the influence of the waves from up to two turbofan engines on the semispan. The method is limited to the condition where the flow and geometry of the configurations are symmetric about the vertical plane containing the wing root chord. The calculation procedure starts with arbitrarily positioned wake centerlines and the iterative calculation continues until the total configuration loading converges within a prescribed tolerance. Program results include total configuration forces and moments, individual lifting-surface load distributions, including pressure distributions, individual flap hinge moments, and flow field calculation at arbitrary field points.

Mendenhall, M. R.↗

NASA NTRS1993

Free-wake computation of helicopter rotor flowfields in forward flight

A new method has been developed for computing advancing rotor flows. This method uses the Vorticity Embedding technique, which has been developed and validated over the last several years for hovering rotor problems. In this work, the unsteady full potential equation is solved on an Eulerian grid with an embedded vortical velocity field. This vortical velocity accounts for the influence of the wake. Dynamic grid changes that are required to accommodate prescribed blade motion and deformation are included using a novel grid blending method. Free wake computations have been performed on a two-bladed AH-1G rotor at low advance ratios including blade motion. Computed results are compared with experimental data. The sudden variations in airloads due to blade-vortex interactions on the advancing and retreating sides are well captured. The sensitivity of the computed solution to various factors like core size, time step and grids has been investigated. Computed wake geometries and their influence on the aerodynamic loads at these advance ratios are also discussed.

Ramachandran, K.↗

NASA NTRS1972

Investigation of the stability of the tip vortex generated by hovering propellers and rotors.

The objective of this experimental and theoretical investigation was to determine what factors and mechanisms are involved in vortex interaction and instability and how these phenomena manifest themselves. To answer these questions, the schlieren method of flow visualization was used to observe the wakes generated by two- and four-bladed model propellers and rotors. A concurrent free-wake analysis was conducted for comparative purposes. Schlieren pictures showing wake asymmetry, interaction, and instability are presented. Various factors and mechanisms believed to be responsible for these are discussed along with the effects produced by the number of blades, collective pitch, and tip speed. Free-wake calculations that qualitatively confirm those factors responsible for wake asymmetry and interaction are also presented.

Tangler, J. L.↗

NASA NTRS1987

Prediction of tip vortex self-induced motion parameters in terms of rotor blade loading

The self-induced motion of curved vortex filaments at the tip of a helicopter rotor blade is investigated analytically. The derivation of a method for inviscid roll-up (IRU) is presented in detail, with attention to the cutoff-distance reformulation of the problem, a control-volume analysis of the self-induction properties of the vortex core, the adaptation of the roll-up method of Betz (1932) to IRU in three dimensions, the treatment of linear and elliptic loading, vortices with turbulent central cores, and the effect of cutoff distance on helicopter free-wake computations. Numerical results showing the significant effect of core properties on the geometry of a rotor wake in hover are presented in graphs and briefly characterized.

Bliss, Donald B.↗

NASA NTRS1996

Wake Geometry Measurements and Analytical Calculations on a Small-Scale Rotor Model

An experimental investigation was conducted in the Langley 14- by 22-Foot Subsonic Tunnel to quantify the rotor wake behind a scale model helicopter rotor in forward level flight at one thrust level. The rotor system in this test consisted of a four-bladed fully articulated hub with blades of rectangular planform and an NACA 0012 airfoil section. A laser light sheet, seeded with propylene glycol smoke, was used to visualize the vortex geometry in the flow in planes parallel and perpendicular to the free-stream flow. Quantitative measurements of wake geometric proper- ties, such as vortex location, vertical skew angle, and vortex particle void radius, were obtained as well as convective velocities for blade tip vortices. Comparisons were made between experimental data and four computational method predictions of experimental tip vortex locations, vortex vertical skew angles, and wake geometries. The results of these comparisons highlight difficulties of accurate wake geometry predictions.

Ghee, Terence A.↗

NASA NTRS1985

Steady and unsteady incompressible free-wake analysis

The flows around highly sweptback wings and bodies of revolution at high angle of attack are described, and inviscid model approximations and mathematical formulation of the problem are given to steady and unsteady incompressible flows. A general presentation of the methods of solution is given, with emphasis on current computational techniques. Detailed descriptions of the nonlinear vortex-lattice and vortex-panel techniques are presented to show how the boundary conditions are enforced using iteration. Typical numerical results are compared with the available experimental data.

Kandil, O. A.↗

NASA NTRS1985

A new approach to the free wake problem for hovering rotors

In the present approach to the hovering rotor free wake problem, an influence coefficient solution method is used to find that rotor wake solution which is steady in a reference frame that rotates with the blades; this scheme solves directly for the conditions of free wake equilibrium by a procedure that does not involve time-stepping and the associated use of numerical damping or special convergence methods. The solution method has been implemented in a hover wake computer program having a three-part wake model for the tip vortex. All three wake regions are represented by the new Basic Curved Vortex Elements. Sample hover calculations are presented for single blade and multiblade rotors.

Bliss, D. B.↗

NASA NTRS1977

A three-dimensional viscous/potential flow interaction analysis method for multi-element wings

An analysis method and computer program were developed for the calculation of the viscosity dependent aerodynamic characteristics of multi-element, finite wings in incompressible flow. A fully-three dimensional potential flow program is used to determine the inviscid pressure distribution about the configuration. The potential flow program uses surface source and vortex singularities to represent the inviscid flow. The method is capable of analysing configurations having at most one slat, a main element, and two slotted flaps. Configurations are limited to full span slats or flaps. The configuration wake is allowed to relax as a force free wake, although roll up is not allowed at this time. Once the inviscid pressure distribution is calculated, a series of boundary layer computations are made along streamwise strips.

Dvorak, F. A.↗

NASA NTRS1985

Aerodynamic analysis of a horizontal axis wind turbine by use of helical vortex theory, volume 2: Computer program users manual

A description of a computer program entitled VORTEX that may be used to determine the aerodynamic performance of horizontal axis wind turbines is given. The computer code implements a vortex method from finite span wind theory and determines the induced velocity at the rotor disk by integrating the Biot-Savart law. It is assumed that the trailing helical vortex filaments form a wake of constant diameter (the rigid wake assumption) and travel downstream at the free stream velocity. The program can handle rotors having any number of blades which may be arbitrarily shaped and twisted. Many numerical details associated with the program are presented. A complete listing of the program is provided and all program variables are defined. An example problem illustrating input and output characteristics is solved.

Keith, T. G., Jr.↗