THRUST PULSATION OF COAXIAL MAIN ROTOR, CAUSED BY THE BLADES RELATIVE POSITION

The influence of reciprocal position of the upper rotor blades in respect to the lower rotor blades is characteristic for coaxial main rotor. It is established that the initial azimuth of the blade, for example, of the upper rotor’s which does not coincide with the initial azimuth of the lower rotor blades, affects the level of vibrations caused by the rotors thrust pulsations, the level of noise, generated mainly by coaxial rotor. This paper presents numerical studies which assess the effect of the initial azimuth of the upper rotor blades ("phasing") on the helicopter coaxial rotor thrust force pulsation. The research was carried out applying the calculation method based on the nonlinear vortex theory in a non-stationary formulation. The results of the helicopter coaxial rotor with different initial azimuths of the upper rotor blade relatively to the azimuth of the lower rotor blade flow around numerical simulation are presented. The influence of the blades "phasing" on the rotor thrust coefficient change and thrust force pulsation magnitude is shown. The flow of a six-bladed coaxial main rotor (two rotors with 3 blades) was simulated in the oblique flow mode at speeds of 51.25 m/s and 71.75 m/s at the rotor angles of attack– 5 0 and – 12 0 , respectively. The change in the coefficient of the main rotor thrust per revolution at different values of "phasing" was studied. The coaxial rotor thrust coefficient is determined by summing the lower and upper rotors thrust coefficients respectively. Thus, at some "phasing" the thrust coefficient of the lower and upper rotors increase intensifies the thrust pulsations, and at others, the peaks of the upper and lower rotors pulsations are displaced and the total coaxial rotor thrust coefficient changes per one revolution with smaller amplitude. It is established what "phasing" produce the maximum values of thrust pulsation, and at which-a minimum of thrust pulsation.


INTRODUCTION
The area where coaxial helicopters are applied is determined by their characteristic featuressmall overall dimension, high thrust-to-weight ratio and maneuverability, as well as aerodynamic symmetry ( fig. 1). These features have provided them with a convenient base on small-sized take-off and landing sites of ships which are designed for various purposes. Features of coaxial helicopters are associated with the main rotors reactive moment compensating new method implementation compared to single-rotor helicopters. The coaxial helicopter propellers reactive moments are mutually balanced right on their axis of rotation. Due to the coaxial helicopter aerodynamic symmetry, there are almost no connections between longitudinal and lateral movement, independence of control channels and simplicity of piloting are provided [1]. 05 At the same time, the helicopter with a coaxial design is made a demand to eliminate the upper and lower rotor blades collision during flight operation, reduce vibrations caused by the propeller thrust pulsations, and reduce noise generated mainly by the coaxial main rotor. It was determined that the blade initial azimuth of the upper propeller, for example, which does not coincide with the initial azimuth of the lower propeller blade, affects the above-mentioned features of the coaxial helicopter.

АВИАЦИОННАЯ И РАКЕТНО-КОСМИЧЕСКАЯ ТЕХНИКА
The upper rotor blades initial azimuth on the helicopter coaxial rotor thrust pulsation effect evaluation by means of computational methods seems to be rational. Currently, there are many methods for numerical study of helicopter main rotor aerodynamic characteristics. Calculation methods based on the non-stationary setting of nonlinear vortex theory both on the basis of a thin carrier surface [2 -4] and on the basis of a carrier line (thread) [5] are distinguished among them. The first method allows you to determine the nonstationary aerodynamic characteristics of the main rotor with arbitrary shaped blades as planned, and the secondwith the use of stationary results of helicopter profiles blowouts adjusted for non-stationarity. A more detailed description of the main rotor blowout process is given by grid methods, both with and without taking into account viscosity. However, their application to main rotor aerodynamic characteristics determination is associated with a number of difficulties. Firstly, methods of this type require large computational resources, secondly, the calculation flapping movement of the blades and cyclic control for the forward flight mode (oblique flow mode) is associated with the solution of a number of special problems on calculated grids deformation. The main rotor operation on axial flow modes (hovering modes) [6 -8] was mainly modeled applying grid methods.
The oblique flow mode of the helicopter main rotor is characterized by the flapping movement of the blades, swinging in the rotation plane, the blades elastic deformation and cyclic change in the angle of installation for one revolution of the propeller. The record of these features is demonstrated in [9]. However, this approach, which requires very large computational resources, is not appropriate for parametric exploratory research. Paper [10] demonstrating the example of hard main rotor modeling shows the application areas of different methods in various software packages. It is shown that the method based on the vortex theory demonstrates good results of the main rotor traction characteristics, especially, for calculating the main rotor vibration loads caused by thrust pulsation [11].
Therefore, this paper produces numerical studies on assessing the effect of the upper propeller blades initial azimuth on the helicopter coaxial main rotor thrust pulsation. The research was carried out using the calculation method based on the nonlinear vortex theory in a non-stationary setting.

ABOUT THE METHOD OF CALCULATION
This paper produces a numerical study on the basis of a nonlinear blade propeller theory in a non-stationary setting based on a thin bearing surface [2,3]. According to this theory propeller blades are replaced by extremely thin base surfaces in the form of Si as planned coinciding with the shape of the blades themselves and curved according to the law of curvature of their median surfaces. An ideal incompressible medium is considered. The flow outside the propeller blades and their traces is considered to be vortex-free ΔΦ=0. The ; Том 23, № 04, 2020 Научный Вестник МГТУ ГА Vol 23, № 04, 2020 Civil Aviation High Technologies determined by summing the aerodynamic load on the panels. The wake form is drawn up as a result of calculation ( fig. 3). The numerical method for the helicopter main rotor aerodynamic characteristics determination, which is under consideration, has been carefully approbated and the approbation justified the reliability of the results obtained [2 -5]. Fig. 3. The wake behind a coaxial rotor vortex structure

COMPUTATIONAL RESEARCH RESULTS
We studied the flow of a six-blade coaxial main rotor (two propellers with 3 blades) in the oblique flow mode at speeds of V1=51.25 m/s (the angle of attack of the propeller αн = -5 0 ) and V2 =71.75 m/s (αн = -12 0 ). Propeller geometric and kinematic parameters are shown in Table 1. Modeling of the main rotor non-stationary airflow starts with the moment when the lower propeller blade takes the initial position with the azimuth of ψ = 0. The second upper propeller blade can take the position with the azimuth other than zero, for example, with a shift by a certain angle Δψ, which is conditionally called "phase" or "phasing" (fig. 4). The first lower propeller rotates counterclockwise when viewed from above, and the second upper propellerclockwise. Depending on the phase of Δψ while rotating the upper and lower propellers blades intersect at different time moments. The analysis of the results obtained makes it possible to assess the effect of the upper propeller blades initial azimuth Δψ on the helicopter coaxial main rotor thrust pulsation. In particular, when the values of the upper rotor initial azimuth are about zero, we can see the occurrence of the thrust pulsation maximum values, which, for example, when the flow velocity equals to V2=71.75 m/s exceeds the average value of СТ, by 35% but minimum thrust pulsationat Δψ ≈ 60 0 .