**2.2.6 Conclusion remarks**

Analysis of results achieved by unsteady lift modeling and viscous effects simulation method shows that they can be used with sufficient accuracy in rotor analysis and construction.

The aim of this particular simulation is to use advantages of vortex methods. For example, vortex methods use the description of flow field of the smallest range; aerodynamic forces can be obtained with small number of vortices. On the other hand, singular vortex distribution can be accurately determined by using data obtained in small time range. Vortex methods, also, permit boundary layer simulation at large Reynolds's number by local concentration of computational points.

Achieved results imply the direction for the further development of this program


On the basis of analysis of presented model and program package for viscous effects and unsteady lift simulation it can be concluded that this subchapter presents an original scientific contribution, applicable in aerodynamic analyses of practical problems in helicopter rotor projecting.

frame *H*, connected with the rotor and rotates together with it; it is obtained by rotating

frame *P*, connected to the flapping hinge, so that the *y*-axis is oriented along the blade;

; keeping the common *z*-axis;

  , while it is rotated for the

from the origin of *P*, and


fixed frame *F*, with *x*-axis in the direction of flight, and *z*-axis oriented upwards;

(pitch angle) with respect to the *P*.

<sup>2</sup> *B B me xR M*

where *B* is moment of inertia about *Px* , *mb* mass of the blade, *<sup>g</sup> x* position of blade center of

The flow field is assumed to be potential (inviscid and irrotational) and incompressible. In

The equation is the same, both for steady and unsteady flows. Owing to that, methods for steady cases can be applied for the solution of unsteady flow problems, as well.

0 5.


In case of inviscid problems, it is necessary to satisfy Kutta condition at the trailing edge. Based on unsteady Bernoulli equation, the difference between upper and lower surface


2 2

*U L*

*V V CC C dl*

2 2 2

*V V t*

*p p V V* 

 

*t*

*M*

 (10)

*LE*

*<sup>g</sup>* sin *<sup>A</sup>*

cos *<sup>b</sup>*

its origin is displaced from the rotating axis for the value *e*

In derivation of the equations of motion, the following was assumed: the rotor does not vibrate, and its rotation velocity is constant,

With assumptions above mentioned, equation of blade flapping motion is:

that case, velocity potential satisfies the Laplace equation 0 .

unsteady form of the Bernoulli equation: 2 2 2

*U L*

*PP P*

pressure coefficients, in case of the thin lifting surface, is:

frame *B*, connected to the blade, displaced for the value *e*

the F frame for a certain azimuth angle

with respect to the frame *H*;

gravity in *P* frame, and *MA* is aerodynamic moment.

unsteady boundary condition: <sup>0</sup> *VV n <sup>T</sup>*

*Dt* 

the blade is considered absolutely rigid.

angle 

tilted for the value

**2.3.3 Aerodynamics** 

Unsteadiness is introduced by:

Kelvin theorem: <sup>0</sup> *<sup>D</sup>*

where: - is velocity potential,*V*

*n*

### **2.3 Improved solution approach for aerodynamics loads of helicopter rotor blade in forward flight**

This subchapter presents the numerical model developed for rotor blade aerodynamics loads calculation. The model is unsteady and fully three-dimensional. Helicopter blade is assumed to be rigid, and its motion during rotation is modeled in the manner that rotor presents a model of rotor of helicopter Aerospatiale SA 341 "Gazelle".
