The wake generated by the rotor of a helicopter can exert a strong interference effect on the fuselage and the horizontal/vertical tail. The occurrence of icing on the rotor can obviously make this interplay more complex. In the present study, numerical simulation is used to analyze the rotor wake in icing conditions. In order to validate the overall mathematical/numerical method, the results are compared with similar data relating to other tests; then, different simulations are conducted considering helicopter forward flight velocities of 0, 10, 20, 50, and 80 knots and various conditions in terms of air temperature (atmospheric temperature degrading from −12°C to −20°C or from −20°C to −26°C). The results indicate that the rotor aerodynamic performance (i.e., the lift-to-drag ratio distribution of the rotor disc) drops significantly once the rotor undergoes ice accretion. More importantly, the icing exerts a different influence of the wake dynamics depending on the atmospheric conditions. Interestingly, the rime-ice firstly occurs on the inner portion of rotor blades and then diffuses outward along the blade radial direction with the decrease in atmospheric temperature.
Rotor blade ice accretion is a great hazardous factor that requires attention in helicopter design. This mainly affects the rotor aerodynamic performance and rotor wake feature, increases the complexity of aerodynamic interference between the rotor and fuselage, as well as the horizontal/vertical tail, and degrades the flight performance and flying qualities, threating helicopter flight safety. Understanding the sensitivity of ice accretion and aerodynamic performance, as well as rotor wake feature and flight dynamic characteristics degradation, are essential in helicopter certification programs to ensure safety during flight in icing conditions. Early in 1974, a series of simulated and natural icing tests have been conducted to determine the capability of helicopters to operate in icing conditions [
Without considering rotor icing, the free-vortex wake method is capable of directly modeling the helicopter rotor wake feature. This can be performed in various ways, such as by means of constant vorticity straight-line filaments [
In icing conditions, the free-vortex wake method should at least be combined with the rotor icing model, in order to simulate the helicopter rotor wake feature. Further considering the inflight helicopter trim problem embedded with the free-vortex wake method, more considerations might be developed, such as the rotor discrete aerodynamic model and complete helicopter flight dynamics model.
The present study presents a numerical simulation approach to simulate the helicopter rotor wake in icing conditions. First, the rotor free-vortex wake model was adopted to simulate the rotor wake geometry. Then, a numerical rotor discrete aerodynamic model was developed to solve the rotor force and moment acting on the helicopter. In addition, a rotor icing model was integrated into the discrete rotor aerodynamic model, which allows the model to predict the increments of iced rotor force, and torque and rotor flapping coefficients. In order to solve the iteration of the non-uniform distribution of rotor induced velocity and rotor flapping coefficients, a Crossed Coupling Iteration (CCI) algorithm was proposed. Furthermore, a helicopter flight dynamics model was also developed to conduct the inflight helicopter trim calculation. The rotor wake geometry of a helicopter at different flight velocity was numerically simulated and demonstrated, and the results and analysis were developed. Finally, a summary was presented.
The rotor free-vortex wake model was developed to predict the rotor wake in icing conditions in the present study, based on the lifting surface theory and vortex method. The circulation of the blade-attached vortex was calculated using the lifting surface theory, and the lifting surface was arranged in the blade mid-arc surface. Along the blade-span wise direction, the lifting surface was divided into
According to the rotor vortex wake method, the rotor wake can be classified as near wake and far wake. Near wake is fixed in the tangent plane, which is located at the trailing edge of the blade mid-arc surface. In this region (
In Formula (1), the
Considering the rotor icing, an engineering rotor icing model needs to be developed. This mainly involves the introduction of the icing-related increments of rotor thrust, horizontal force, side force, torque coefficients, and icing-related increment of flapping coefficients into the uniced flight dynamics model.
The basic lift and drag coefficients of the rotor-blade airfoil due to icing are, as follows:
The coefficients for rotor thrust, side force, horizontal force, and torque due to icing are, as follows:
The iced-rotor flapping model in the Fourier series form can be presented, as follows:
In Formulas (2), (3), and (4), the rotor thrust, horizontal force, side force and torque coefficients, as well as the rotor flapping coefficients, were calculated using the following Rotor Discrete Aerodynamic Model. Furthermore, the corresponding increments caused by icing can be calculated by the established engineering icing model in [
The rotor discrete aerodynamic model was developed to embed the rotor free-vortex wake model and rotor icing model into the following helicopter flight dynamics model. In the process of modeling and numerical simulation, based on the principle of equal annular area, the rotor disc was divided into
The discrete expressions of the rotor thrust, horizontal force, side-force, and torque coefficients can be deduced, as follows:
where,
The
The equations for the rotor coning and first-order longitudinal and lateral flapping coefficients in the rotor flapping model are, as follows:
The expressions of
When Formula (5) was solved, the rotor coning and first-order longitudinal and lateral flapping coefficients can be obtained by solving the nonlinear equations, that is, Formula (9).
In the present study, a nonlinear flight dynamic model of a single rotor helicopter with a tail rotor was developed, as follows:
In Formula (13), the resultant force vector (
In the above formula, the rotor force (
In Formula (14), the tail rotor force (
In the present study, the rotor free-vortex wake model and rotor icing model were incorporated into the rotor discrete aerodynamics model to output the
As shown in
Bagai and Leishman’s PIPC algorithm [
Using the five-point central difference method, the first order differential terms of the governing equation in Formula (1) can be presented, as follows:
The
Then, the governing equation in Formula (1) can be presented, as follows:
Since both the five-point central difference and mean velocity approximation have second-order accuracy, the above Formula (18) also has second-order accuracy for the governing equation in Formula (1). Based on the Formula (18), the governing equation can be solved through the calculation of the prediction and correction in each iteration using Bagai and Leishman’s PIPC algorithm.
In the present study, the Cross-Coupling-Iteration (CCI) algorithm was proposed to calculate the non-uniform distribution of rotor-induced velocity and the corresponding flapping coefficients (
In the CCI algorithm, two constraints were performed: the constraint on rotor-induced velocity iteration, and the constraint on rotor flapping coefficients iteration. When the non-uniform distribution of rotor-induced velocity iteration approaches to the divergence, the uniform distribution of rotor-induced velocity, based on the Rotor Momentum Model (RMM) [
The validity and accuracy of the numerical calculation method was verified through comparison with the available experimental measurements [
Blade number | 1 |
---|---|
Radius, m | 0.4064 |
Chord, m | 0.0425 |
Hinge offset, |
0.0 |
Spar length, |
0.2 |
Tip speed, m/sec | 89.37 |
Airfoil section | NACA2415 |
Collective pitch, degree | 4.0 |
Twist, degree | 0.0 |
Thrust coefficient | 0.003 |
The effects of icing on the rotor-vortex wake due to icing time and atmospheric temperature were mainly analyzed using the above mathematical model and the corresponding procedure, as well as the numerical method. Merely the wake of one blade at the azimuth of zero degree was depicted and analyzed in detail for convenience. The basic icing conditions are presented in
−26.0 | 1.0 | 20.0 | 180.0 |
Some of the reasons for the rotor free-vortex wake changes with icing time might be due to the effects of icing on the angle of attack (AOA) of the rotor blade. In comparing the uniced distribution of AOA,
Some of the reasons for this change trend might be due to the temperature effects. In general, the performance penalties caused by glaze ice is more serious than mixed ice, and subsequently by rime ice. The rotor icing tunnel test data indicated that as the temperature increased, the accreted ice shape on the outer portion of the rotor blades changed from rime to mixed, and subsequently to glaze, increasing the performance penalties [
For further comparison with the situation of the high local temperature at the blade tip region at hover in
By incorporating the rotor free-vortex wake model and rotor icing model into the rotor discrete aerodynamics model, and using the proposed Cross Coupling Iteration (CCI) algorithm, the trim calculation of the helicopter flight dynamics model in icing conditions was conducted, in order to acquire the convergent rotor free-vortex wake geometry, and investigate the effects of icing on the rotor free-vortex wake. The following conclusions that might have some significance in helicopter flight safety encounters with ice accretion can be mainly summarized, as follows: The proposed numerical simulation method appears to be an adequate tool for helicopter rotor free-vortex wake analysis in icing conditions. Both the sunk trend of the rotor free-vortex wake due to icing and the variation of the ice shape on the rotor blades might lead to rotor aerodynamic degradation: on one hand, ice accretion causes the rotor free-vortex wake to sink, and this sinking trend becomes more evident with the increase in icing time. On the other hand, a rime-ice shape initially occurs on the inner portion of rotor blades, and diffuses outward along the blade with the decrease in atmospheric temperature. In addition, the uniced area of the rotor blade tip is generated by the extremely high local temperature, preventing the occurrence of ice accretion. However, a glaze-ice shape occurs when the atmospheric temperature continues to decrease. As shown in the forward flight velocity analysis, the lift-to-drag ratio would evidently drop when helicopter rotor encounters ice accretion. When the helicopter changes from hover to forward flight in the typical condition of
Rotor coning coefficient
Rotor first-order longitudinal flapping angle
Rotor first-order lateral flapping angle
Lift coefficient of rotor-blade airfoil and drag coefficient of the rotor-blade airfoil, respectively
Rotor thrust and horizontal force coefficients
Rotor side-force and torque coefficients
Blade flapping hinge offset and rotor solidity, respectively
Function symbol
Gravitational acceleration
Blade rotational inertia and blade mass, respectively
The mass of the helicopter
The number of segments along the direction of the blade-spanwise
The number of segments along the direction of the blade-chordwise
The number of segments along the direction of the vortex age angle of the near wake sheet
The number of the vorticity straight-line segments
The number of segments along the direction of the azimuthal angle of the rotor disc
The rotor roll and pitch angular velocity
The non-dimensional local radial position along rotor blade, and rotor radius, respectively
The Euler transformation matrix
The relative wind velocity from forward flight, and upward flapping at the blade section, respectively
The non-dimensional induced velocity of the rotor disk
The rotor blade flapping angle and blade section inflow angle, respectively
The air density and rotor blade chord, respectively
The azimuthal angle of the rotor disc and azimuthal increment, respectively
The vortex age angle of the vortex filament of each blade
The rotational speed of the rotor
The increments
The pitching angle of the helicopter
The rolling angle of the helicopter
The yawing angle of the helicopter
The icing time and atmospheric temperature, respectively
The liquid water content
The median volumetric diameter
The force vector and force moment vector that acts on the helicopter
The angular momentum vector of the helicopter
The position and velocity vector of the vortex filaments
The velocity vector of the free stream
The induced velocity vector of the far wake vortex filament
The velocity vector of the far wake vortex filaments caused by the rotor blade motion
The velocity vector of the helicopter
The angular velocity vector of the helicopter
The rotor blade-attached vortex
The near wake vortex lattices and far wake vortex filaments, respectively
The ice accretion
The matrix transposition
The helicopter
The fuselage of the helicopter
The gravity of the helicopter
The horizontal tail of the helicopter
The main rotor and tail rotor of the helicopter, respectively
The vertical tail of the helicopter