Helicopter main rotor FSI analysis using parametric blade model as an application for multidisciplinary optimization

This work is part of a research program aimed at finding new approaches and design solutions for helicopter main rotor modelling using multidisciplinary optimization. It is the fourth stage of an individual research program that includes preliminary tasks such as parametric modelling of a single blade, CFD modelling of a full main rotor for different flight conditions, and preliminary structural modelling of a blade. The main goal of this work is to present the parametric modelling of the rotor blade body and structure as an application for complex simulation. The paper demonstrates the method of advanced analysis of the entire rotor and provides exemplary results obtained from complicated analyses. The analytical foundation for combined fluid-structure analysis is presented. The parametric design method is shown to be applicable for different blade planform shapes and various section airfoils. The blade CFD fluid domain is also prepared using the parametric method, as well as the blade’s inner structure. The simulation parameters from the previous stages of research, which serve as inputs to the FSI analysis, are outlined. These previously obtained parameters are combined and introduced into an FSI simulation to assess their compatibility and applicability. The configuration procedure of the analysis and the boundary conditions are presented. The obtained numerical results are then compared with analytical assumptions. The simulation products, which serve as inputs for further analysis, are presented with graphical representations. The time and memory consumption of the simulation are outlined. The application of the described work in an optimization loop is proposed. As a result of this research, new options for main rotor optimization are developed. The paper demonstrates some crucial possibilities of FSI analysis in the described simulation cases. The use of combined parametric modeling with fluid-structure interaction analysis for different flight conditions is presented as a new perspective for multidisciplinary design optimization of a helicopter rotor system.


Introduction
Modern military helicopters are designed to operate in various flight conditions and environments, with manufacturers and governments working together to enhance their effectiveness in military operations.There are currently two main streams of rotorcraft design.The first focuses on finding new aerodynamic configurations, such as combining the construction of the main rotor with a pusher propeller.[1], [2].The second stream aims to enhance existing helicopter designs by improving aerodynamic and structural solutions.[3]- [5].
The Polish Military University of Technology is also involved in developing new rotorcraft design possibilities.This work is part of a comprehensive research program aimed at optimizing the aerodynamics and structure of the main rotor.This article represents the fourth phase of the research program, following previous analyses of rotorcraft construction and main rotor computational fluid dynamics (CFD) using parametric modeling.The program were preceded with an rotorcraft construction analysis which results were published in [6].The latter parts included the main rotor CFD analysis using parametric modeling and preparing the blade structure using parametrization, this work were published in [7].In each phase the parametrization of the model is used because of planned optimization loop.
Parametrization of the rotor blade allows designers to explore different blade shapes and structures using geometric parameters or dimensionless coefficients.This method offers advantages in terms of time efficiency and the ability to evaluate various design variants The benefits of parametrization for rotor blades have been described in [8], [9].In this study, parametric models are used to generate the CFD fluid domain and the blade's inner structure.Examples of using parametric models for airfoil shape and structure and aerodynamic performance are also provided in [10], [11] for an airfoil shape and [12]- [14] for structure and aerodynamic performance.
The parametric models for blade shape, fluid domains, and inner structure were created using a graphic programming language called GRIP, which is provided with Siemens NX software.GRIP allows users to generate the desired shape of any airframe part by combining commands and inputting parameters.The language also includes inertia analysis functions, enabling initial strength calculations within the code.By combining logical functions, the designed shape can be initially optimized.Examples of using the GRIP language are shown in [15]- [17].
To achieve the research objectives and find new solutions for main rotor blade optimization, a combination of CFD analysis and structural finite element analysis (FEA) is required.To accurately describe the phenomenon, these tools can be combined in a fluid-structure interaction (FSI) simulation.FSI simulations allow for the examination of the influence of aerodynamic loads on the structure and the subsequent impact of deformation on the generated loads.While FSI is commonly used in wind turbine simulations [18]- [20], its application in rotorcraft simulations is less frequently described in published studies.
In this phase of the study, previously evaluated and prepared solutions for CFD main rotor analysis and blade structure preparation using parametric modeling were utilized.The blade's parametric model was generated using geometric and shape parameters, with the geometry based on an existing helicopter rotor.The codes developed generate the geometry of the rotor blades for the CFD part of the FSI analysis and the blade with the inner structure for the MES part of the simulation.The GRIP program code allows end users to input blade parameters and vary the geometries for simulation testing.
The simulation was prepared using a CFD environment, with the movement of the blades analytically calculated.MATLAB was used to determine the values of collective pitch control and cyclic control, which were then inputted into the CFD simulation to simulate rotor movement under different flight conditions.Meshes were generated for the CFD domain and MES analysis, with mesh sizes chosen to obtain acceptable results within a reasonable time frame.The FSI simulation was conducted, starting with a one-way analysis where aerodynamic loads were transferred to the model, followed by a twoway FSI simulation using solver coupling.The construction was evaluated to ensure it met the strength requirements for desired performance possibilities.To the best of the co-authors' knowledge, similar research combining the proposed methods for helicopter main rotor design and optimization has not been conducted before.

CFD model for FSI analysis
The working environment of a rotor is very complex due to the axial rotation and simultaneous change of the rotor blade angles as a function of azimuth.To prepare a model for FSI analysis, both a CFD and FEM model must be prepared.The CFD model is prepared with the shape of the air domain, which depends on the simulation conditions.The blade shape is generated using user-inserted dimensions and the proposed airfoil shape.An example of blade shape parametrization is presented in Figure 1.Additionally, the domain for analysis is prepared in accordance with the blade shape.A different domain is prepared for n-bladed rotor simulation, and a different domain is prepared for 1blade simulation.The preparation and analysis of the CFD model for the optimization procedure were presented in [21].

FEM model for FSI analysis
The FEM model for FSI analysis is also parametrized.To adjust the structure, initial stress calculations need to be conducted.Analytical calculations are performed using MATLAB, and the final internal shape fitting is implemented in the GRIP programming language.The generated shape is based on a real blade structure, consisting of a composite spar and skin in the front, and honeycomb in the back.The spar is filled with foam to maintain its shape.The shape of the parametrized blade is presented in Figures 2A and 2B.The Figure 2A shows the inner structure of the geometry.The parts are highlighted using different colours: green -skin, brown -spar, grey -honeycomb and beige -foam.The image 2B describes the full shape of the generated blade with the chord change across the span.

FSI analysis in optimisation procedure
The proposed research aims to combine aero-structural optimization in a loop to achieve improved performance and strength of the main rotor.The final stage of the research involves using FSI analysis to evaluate the model and make changes to the geometrical model of the CFD and FEM models.The procedure is illustrated in Figure 3.
The procedure begins with determining the mission requirements, which serve as the basis for the performance requirements that need to be met.These requirements are essential for designing a rotorcraft capable of fulfilling its intended missions, such as payload, forward speed, and climb.To determine reasonable parameters, existing constructions designed for similar missions are analyzed.The trends identified from this analysis serve as a reference for proposing initial geometric and aerodynamic parameters for the main rotor blade.
The next step in the procedure involves analytical calculations.During this phase, the blade trimming is determined based on the required rotorcraft mass and airspeed.This allows for the establishment of the aerodynamic loads on the blade.Combined with the mass moments of inertia from centrifugal force, flap, and lag moments, these calculations provide the moments acting on the rotor blade's strength elements.The results of the mathematical analysis serve as inputs for parametric modeling.
Parametric modeling is used to generate the blade shape using the dimensions obtained from the trim and performance calculations.The pitch angle of the rotor blade and the blade position angles for the CFD analysis are also provided.This enables the generation of the air domain for single rotor blade or n-bladed main rotor CFD simulations.The second part of parametric modeling involves creating the blade with its inner strength structure.The dimensions of the spar are calculated within the GRIP code and applied to a chosen number of blade cutouts.This allows for mass reduction, as the spar thickness is determined by the strength requirements.The shape of the foam inside the spar and the geometry of the honeycomb section from the trailing edge to the spar are also generated.The CAD models for CFD and FEM applications serve as inputs for FSI simulations, as shown in Figure 3. Firstly, the single blade simulation is conducted, where the model of a blade in the air domain is combined with the structural model.The airflow is modeled in a steady simulation using the inflow angles that were determined during the analytical calculation of thrust and trim.This method is less computationally demanding and takes much less time to obtain numerical results.
The initial step is to check the deformations of a blade in a one-way FSI simulation, where the loads are transferred from the CFD into the FEM model.This allows for a quick assessment of the reasonableness of the results.
The second step is a two-way FSI simulation, where the loads are transferred to the FEM model and then the deformation of the rotor blade is transferred to the CFD model to assess the influence of the deformation on the produced aerodynamic forces.The results of this part of the research are described in this work.
The construction is evaluated to determine if it fulfills the requirements of the strength elements and performance conditions.If any requirements are not met, the parameters of the model are adjusted and the construction is re-evaluated.
The next stage is to analyze the main rotor blade in its working environment under different flight conditions.The CFD simulation is prepared for an n-bladed rotor, with the simulated blade motion dependent on its azimuthal position.The resulting aerodynamic forces will be combined with the structural FEM model to apply the deformation to the rotor model.The results of this simulation will also be evaluated to determine if the construction meets the requirements.

Simulation properties
The FSI simulation was prepared using Siemens Star CCM+.The geometry for the CFD and FEM analysis was imported into the software, ensuring no collisions between the CAD geometry and the simulation environment.The mesh was generated using the automated mesh function, which can be applied to new geometries in an automated process.The minimum size of the surface elements was set at 1% of the base element, which was established at 0.5 m.The boundary layer was also applied.The skin of the blade and the spar were meshed using the thin mesher option, with polyhedral elements used for the fluid and tetrahedral elements used for the solids.
The boundary conditions for the CFD parts were set as a velocity inlet, pressure outlet, and wall for the blade surface.In Star CCM+, the solver parameters were set simultaneously in the continua options.The fluid part of the simulation was set as an unsteady simulation using the K-Omega SST turbulence model.
For the FEM simulation, an unsteady simulation was also applied.To simulate the different materials of the blade components, the multi-part and multi-component solid solver was used, with the solid stress option.The blade was fixed at the root, and the load was applied to simulate the centrifugal force.The time step for the simulation was set at 0.001s, with 30 inner iterations and the continuity stopping criterion for each time step.

Exemplary simulation results
To verify the capabilities of the simulation, hover conditions for the MTOW of 4900 were simulated.The inflow conditions were prepared using data obtained from earlier stages of the research.The forces created on the blade were similar to those required for hover.Figure 3 shows the blade displacement, with some areas that should be further examined under more complex flight conditions.Figure 4 shows the resultant stress in the blade spar, with areas that also need to be checked for endurance during flight.It can be observed that the construction has the potential to be thinner, but this should be evaluated under different flight conditions.

Conclusion
As described in the introduction, this paper presents the next stage of our research program, which aims to explore new methods for main rotor design using modern techniques within an optimization loop.In this step, one-blade two-way FSI simulations were conducted as an initial step before preparing the FSI analysis of a blade with its motion due to rotational movement and pitch change in an azimuth function.
The results confirm that the blade parametric model is a quick and efficient solution for preparing FSI simulations.The CFD and FEM models were generated in just a few minutes using the prepared code.The compatibility between the CFD domain and the FEM model was ensured by subtracting the exact blade shape from the domain.There were no issues with mesh generation, and the models were compatible with the software.
The results of the CFD analysis align with the analytical expectations and previous standalone CFD simulations.The mathematical model of the inflow for the one-blade simulation provides accurate results.
The FEM analysis, as part of the FSI simulation, demonstrated the influence of the pressure load on the blade.The stress on the strength elements and the displacement of the blade were analyzed to identify weak points in the structure and make necessary design corrections.These design corrections will be implemented using dedicated software or code to facilitate the optimization loop.
This study presents a new approach to aerostructural analysis of main rotor blades using a parametric approach.The application of parametric geometry significantly reduces design time.The results serve as a foundation for preparing a structural model for full n-bladed main rotor FSI analysis, which includes the motion of the main rotor blades.
Another benefit of this procedure is the flexibility it offers in changing the external blade shape or inner strength structure shape.This is crucial for developing an optimization loop that can identify the best aerodynamic properties and strength elements to meet performance requirements.

Funding:
The methods and results presented in this paper have been obtained during research works conducted within the university research project entitled "Methods of optimal design of aircraft to improve their structural and aerodynamic properties".This work was financed by the Military University of Technology (Warsaw, PL), in 2023, under the university research project UGB-819/ 2023.

Figure 4 Figure
Figure 2A Blade structure parametrization

Figure 4 7 Figure 5
Figure 4 Blade displacement for the hover with MTOW 4900 kg