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WT computer program developed to calculate rotor power required by, and output thrust produced by, fan in closed-loop wind tunnel. Uses blade-element theory to calculate aerodynamic forces along each blade of fan. Written in APL2.
Stage B, composed of tandem-airfoil rotor B and stator B, was tested with uniform inlet flow and with hub radial, tip radial and 90 degree one-per-revolution circumferential distortion of the inlet flow as part of an overall program to evaluate the effectiveness of tandem airfoils for increasing the design point loading capability and stable operating range of rotor and stator blading. The results of this series of tests provide overall performance and blade element data for evaluating: (1) the potential of tandem blading for extending the loading limit and stable operating range of a stage representative of a middle stage of an advanced high pressure compressor, (2) the effect of loading split between the two airfoils in tandem on the performance of tandem blading, and (3) the effects of inlet flow distortion on the stage performance. The rotor had an inlet hub/tip ratio of 0.8 and a design tip velocity of 757 ft/sec. With uniform inlet flow, rotor B achieved a maximum adiabatic efficiency of 88.4% at design equivalent rotor speed and a pressure ratio of 1.31. The stage maximum adiabatic efficiency at design equivalent rotor speed with uniform inlet flow was 82.5% at a pressure ratio of 1.28. Tip radial and circumferential distortion of the inlet flow caused substantial reductions in surge margin.
The empirical relation between the induced velocity, thrust, and rate of vertical descent of a helicopter rotor was calculated from wind tunnel force tests on four model rotors by the application of blade-element theory to the measured values of the thrust, torque, blade angle, and equivalent free-stream rate of descent. The model tests covered the useful range of C(sub t)/sigma(sub e) (where C(sub t) is the thrust coefficient and sigma(sub e) is the effective solidity) and the range of vertical descent from hovering to descent velocities slightly greater than those for autorotation. The three bladed models, each of which had an effective solidity of 0.05 and NACA 0015 blade airfoil sections, were as follows: (1) constant-chord, untwisted blades of 3-ft radius; (2) untwisted blades of 3-ft radius having a 3/1 taper; (3) constant-chord blades of 3-ft radius having a linear twist of 12 degrees (washout) from axis of rotation to tip; and (4) constant-chord, untwisted blades of 2-ft radius. Because of the incorporation of a correction for blade dynamic twist and the use of a method of measuring the approximate equivalent free-stream velocity, it is believed that the data obtained from this program are more applicable to free-flight calculations than the data from previous model tests.
The empirical relation between the induced velocity, thrust, and rate of vertical descent of a helicopter rotor was calculated from wind tunnel force tests on four model rotors by the application of blade-element theory to the measured values of the thrust, torque, blade angle, and equivalent free-stream rate of descent. The model tests covered the useful range of C(sub t)/sigma(sub e) (where C(sub t) is the thrust coefficient and sigma(sub e) is the effective solidity) and the range of vertical descent from hovering to descent velocities slightly greater than those for autorotation. The three bladed models, each of which had an effective solidity of 0.05 and NACA 0015 blade airfoil sections, were as follows: (1) constant-chord, untwisted blades of 3-ft radius; (2) untwisted blades of 3-ft radius having a 3/1 taper; (3) constant-chord blades of 3-ft radius having a linear twist of 12 degrees (washout) from axis of rotation to tip; and (4) constant-chord, untwisted blades of 2-ft radius. Because of the incorporation of a correction for blade dynamic twist and the use of a method of measuring the approximate equivalent free-stream velocity, it is believed that the data obtained from this program are more applicable to free-flight calculations than the data from previous model tests.
The effects of low aspect ratio blading on aerodynamic performance were examined. Four individual transonic compressor stages, representative of the inlet stage of an advanced high pressure ratio core compressor, are discussed. The flow phenomena for the four stages are investigated. Comparisons of blade element parameters are presented for the two different aspect ratio configurations. Blade loading levels are compared for the near stall conditions and comparisons are made of loss and diffusion factors over the operating range of incidence angles.
Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes.
Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes.
Static vibration and flutter analysis of a straight elastic axis blade was performed based on a finite element method solution. The total potential energy functional was formulated according to linear beam theory. The inertia and aerodynamic loads were formulated according to the blade absolute acceleration and absolute velocity vectors. In vibration analysis, the direction of motion of the blade during the first out-of-lane and first in-plane modes was examined; numerical results involve NASA/DOE Mod-0, McCauley propeller, north wind turbine and flat plate behavior. In flutter analysis, comparison cases were examined involving several references. Vibration analysis of a nonstraight elastic axis blade based on a finite element method solution was performed in a similar manner with the straight elastic axis blade, since it was recognized that a curved blade can be approximated by an assembly of a sufficient number of straight blade elements at different inclinations with respect to common system of axes. Numerical results involve comparison between the behavior of a straight and a curved cantilever beam during the lowest two in-plane and out-of-plane modes.
The methodology used by the General Rotorcraft Aeromechanical Stability Program (GRASP) to model the characteristics of the flow through a helicopter rotor in hovering or axial flight is described. Since the induced flow plays a significant role in determining the aeroelastic properties of rotorcraft, the computation of the induced flow is an important aspect of the program. Because of the combined finite-element/multibody methodology used as the basis for GRASP, the implementation of induced velocity calculations presented an unusual challenge to the developers. To preserve the modelling flexibility and generality of the code, it was necessary to depart from the traditional methods of computing the induced velocity. This is accomplished by calculating the actuator disc contributions to the rotor loads in a separate element called the air mass element, and then performing the calculations of the aerodynamic forces on individual blade elements within the aeroelastic beam element.
The methodology used by the General Rotorcraft Aeromechanical Stability Program (GRASP) to model the characteristics of the flow through a helicopter rotor in hovering or axial flight is described. Since the induced flow plays a significant role in determining the aeroelastic properties of rotorcraft, the computation of the induced flow is an important aspect of the program. Because of the combined finite-element/multibody methodology used as the basis for GRASP, the implementation of induced velocity calculations presented an unusual challenge to the developers. To preserve the modelling flexibility and generality of the code, it was necessary to depart from the traditional methods of computing the induced velocity. This is accomplished by calculating the actuator disk contributions to the rotor loads in a separate element called the air mass element, and then performing the calculations of the aerodynamic forces on individual blade elements within the aeroelastic beam element.
A method for a strongly idealized case of vertical excitation and for rolling and pitching moment excitation of a four bladed hingeless rotor on an up-focussing flexible mount is developed. The aeroelastic rotor impedances are computed directly with a finite blade element method that includes aerodynamics. The rotor impedance matrix for three or more blades is determined from the root moment impedance for a single blade by a simple multiblade transformation rule. Force and moment amplitudes transferred from the rotor to support are found to be critically dependent on the support dynamics.
In an improved method which retains the advantage of separate treatment of rotor and airframe, the rotor impedance is used to correct the input to the airframe. This improved method is illustrated for a strongly idealized case of vertical excitation and then for rolling and pitching moment excitation of a four bladed hingeless rotor on an up-focussing flexible mount. Contrary to the usual approach that represents aeroelastic blade motions by a series of normal blade modes in vacuum, the aeroelastic rotor impedances are computed directly with a finite blade element method that includes aerodynamics. The rotor impedance matrix for three or more blades is determined from the root moment impedance for a single blade by a simple multiblade transformation rule. Force and moment amplitudes transferred from the rotor to the support are found to be critically dependent on the support dynamics.
This paper will present an approach in design optimization of a proprotor in a forward flight condition with several acoustic objective functions that simulate community response. An adjoint-capable blade element momentum theory (BEMT), implemented in CCBlade.jl, will be used to compute the blade forces and inflow properties required to compute tonal and broadband noise using the second-generation Aircraft NOise Prediction Program (ANOPP2). The influence of broadband noise, observer location, and choice of perception constraint on optimized values of rotation rate, chord distribution, and twist angle will be shown. It is determined that broadband self-noise is an influential source noise mechanism in the design optimization when frequency weighting is used to predict the noise at an out-of-plane observer position.
This paper will present an approach in design optimization of a proprotor in a forward flight condition with several acoustic objective functions that simulate community response. An adjoint-capable blade element momentum theory (BEMT), implemented in CCBlade.jl, will be used to compute the blade forces and inflow properties required to compute tonal and broadband noise using the second-generation Aircraft NOise Prediction Program (ANOPP2). The influence of broadband noise, observer location, and choice of perception constraint on optimized values of rotation rate, chord distribution, and twist angle will be shown. It is determined that broadband self-noise is an influential source noise mechanism in the design optimization when frequency weighting is used to predict the noise at an out-of-plane observer position.
Aerodynamic design parameters are presented along the overall and blade element performance, of an axial flow compressor rotor designed to study the effects of blade solidity on efficiency and stall margin. At design speed the peak efficiency was 0.844 and occurred at an equivalent weight flow of 63.5 lb/sec with a total pressure ratio of 1.801. Design efficiency, pressure ratio, and weight flow 0.814, 1.65, and 65.3(41.1 lb/sec/sq ft of annulus area), respectively. Stall margin for design speed was 6.4 percent based on the weight flow and pressure ratio values at peak efficiency and just prior to stall.
An analytical model is developed for predicting the onset of supersonic stall bending flutter in axial flow compressors. The analysis is based on a modified two dimensional, compressible, unsteady actuator disk theory. It is applied to a rotor blade row by considering a cascade of airfoils whose geometry and dynamic response coincide with those of a rotor blade element at 85 percent of the span height (measured from the hub). The rotor blades are assumed to be unshrouded (i.e., free standing) and to vibrate in their first flexural mode. The effects of shock waves and flow separation are included in the model through quasi-steady, empirical, rotor total-pressure-loss and deviation-angle correlations. The actuator disk model predicts the unsteady aerodynamic force acting on the cascade blading as a function of the steady flow field entering the cascade and the geometry and dynamic response of the cascade. Calculations show that the present model predicts the existence of a bending flutter mode at supersonic inlet Mach numbers. This flutter mode is suppressed by increasing the reduced frequency of the system or by reducing the steady state aerodynamic loading on the cascade. The validity of the model for predicting flutter is demonstrated by correlating the measured flutter boundary of a high speed fan stage with its predicted boundary. This correlation uses a level of damping for the blade row (i.e., the log decrement of the rotor system) that is estimated from the experimental flutter data. The predicted flutter boundary is shown to be in good agreement with the measured boundary.
The engine blade design optimization program STAEBL (Structural Tailoring of Engine Blades) is available at the NASA Lewis computer facility. The analysis capabilities of this program were extended to typical loading conditions for SSME turbopump blades including thermal and pressure loading. Input files for representative SSME blade designs were developed and sample optimization studies for these blades completed. The structural tailoring program combines a general optimization package and a finite element blade analysis package. The analysis package's capabilities include natural frequency, maximum stress, and forced response computation, and fatigue life and flutter analysis. Optimization is performed using the feasible directions method. The current design is modified by perturbing the design variables so that the design constraints are satisfied while the objective function, such as blade weight, is reduced at the maximum rate. The program's geometric design variables include blade thickness distribution, thickness to chord ratios, and root chord.
This presents the aerodynamic design parameters along with the overall and blade element performance of an axial-flow compressor rotor designed to study the effects of blade solidity on efficiency and stall margin. At design speed the peak efficiency was 0.892 and occurred at an equivalent weight flow of 65.0 lb/sec. The total pressure ratio was 1.83 and the total temperature ratio was 1.215. Design efficiency, weight flow, pressure ratio, and temperature ratio were 0.824, 65.3, 1.65, and 1.187, respectively. Stall margin for design speed was 10 percent based on the weight flow and pressure ratio values at peak efficiency and just prior to stall.