MAY 2018
ACKNOWLEDGEMENT1. In conducting this research we have received magnificent help from many quarters, which we like to put on record with great gratitude and great pleasure.
2. This research was supported by Department of Aeronautical Engineering, General Sir John Kotelawala Defence University. First and foremost we would gratefully remind Senior lecturer Mr. SLMD Rangajeewa who gave us the guidance throughout this project with insight and expertise that greatly assisted the research as the project supervisor to share his knowledge without any hesitation. Also the lessons he gave us on Computational Fluid Dynamics was a major benefit in completing the project successfully.

3. We offer our sincere gratitude to Wg Cdr CJ Hettiarachchi and Mrs JI Abeygoonawardhan of Department of Aeronautical Engineering for directing us in every possible ways to make this project a success and for their advices and assistance in keeping our progress on schedule.
5. Finally this research made possible through the help and support from parents who provide the financial support and their encouragement throughout our study.

DECLARATION OF AUTHORSHIPWe, EH Karunarathne, Rabin Shahi and M. Emmanuel declare that this titled, ‘Bell 412 Helicopter Main Rotor Aerodynamic Simulation with CFD’ and the work presented in it are our own. We confirm that:
??This work was done wholly or mainly while in candidature for a degree at this university.
??Where we have consulted the published work of others that has been always clearly attributed.
??Where we have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely our own work.
??We have acknowledged all main sources of help.
4573 O/C EH KARUNARATHNE ……………………..
4736 O/C RABIN SHAHI ……………………..
ENG/F/0031 D/SM. EMMANUEL ……………………..

DECLARATION BY SUPERVISORI certify that the above statement made by the authors is true and that this thesis is suitable for submission to the university for the purpose of evaluation.
Research Supervisor
Senior Lecturer
Department of Aeronautical Engineering
Faculty of Engineering
Kotelawala Defence University
Sri Lanka
Date: …………………………

LIST OF FIGURE TOC h z c “Figure” Figure 1 : Boeing VR-7 Airfoil in Air Foil Tool Web Site PAGEREF _Toc514583256 h 16Figure 2 : Bell 412 Helicopter Dimensions PAGEREF _Toc514583257 h 17Figure 3 : Solid Work Modeling 2 PAGEREF _Toc514583258 h 18Figure 4 : Solid Work Modeling 1 PAGEREF _Toc514583259 h 18Figure 5 : Solid Work Modeling 2 PAGEREF _Toc514583260 h 19Figure 6 : Mesh Generation PAGEREF _Toc514583261 h 19Figure 7 : Center Cylinder in Solid Work Model PAGEREF _Toc514583262 h 20Figure 8 : Solid Work Model for With Ground Effect PAGEREF _Toc514583263 h 20Figure 9 : Blockmesh PAGEREF _Toc514583264 h 21Figure 10 : snappyHexMesh PAGEREF _Toc514583265 h 22Figure 11 : Post processing of the rotor PAGEREF _Toc514583266 h 29Figure 12 : Post processing of the simulation PAGEREF _Toc514583267 h 30Figure 13 : Momentum Theory PAGEREF _Toc514583268 h 32Figure 14 : Blade Element Theory PAGEREF _Toc514583269 h 34
LIST OF TABLE TOC h z c “Table” Table 1 : Bell 412 Helicopter Rotor Specifications PAGEREF _Toc514583270 h 17Table 2 : Rotational Center PAGEREF _Toc514583271 h 22Table 3 : Boundary Conditions PAGEREF _Toc514583272 h 27Table 4 : Boundary Conditions PAGEREF _Toc514583273 h 27Table 5 : Simulated Results PAGEREF _Toc514583274 h 28Table 6 : Bell 412 Helicopter Specifications PAGEREF _Toc514583275 h 36Table 7 : Theoretical results & CFD results analysis PAGEREF _Toc514583276 h 41

ACRONYMSNACA: National Advisory Committee for Aeronautics
CFD: Computational Fluid Aerodynamics
FVM: Finite Volume Method
SST: Shear Stress Transport
CCM+: Computational Continuum Mechanics
NASA: National Aeronautics and Space Administration
HMB2: Helicopter Multi-Block solver version 2.0
BET: Blade element theory
SLAF: Sri Lanka Air force
RANS: Reynolds-Averaged Naiver-Stokes
AOA : Angle of Attack
HIGE: Hover in Ground Effect
HOGE: Hover out of Ground Effect
Open FOAM : Open Field Operation and Manipulation
NOMENCLATURE??: Coefficient of drag
??: Coefficient of lift
??: Coefficient of moment
??: Coefficient of Thrust
I : Turbulent intensity
?? : Reynold’s number
P : Power Required
Vi : Induced Velocity
Vc : Flow Velocity
?: Angular Velocity
? : Mechanical Efficiency
K: Turbulence kinetic energy

CHAPTER 01INTRODUCTION1.1 INTRODUCTION1The CFD analysis is very dynamic that we can simulate and investigate the flow around all kinds of vehicles. In the past the computers were not that capable which they are now. Those computers in olden days were not able to calculate large number of equations in the specific time required. The engineers were fully depended upon the numerical and experimental techniques. The numerical techniques were only able to perform for very basic flow with few equations. Similarly, for the experiments, test itself is very expensive, time consuming and not easy. The wind tunnel was used mostly for aerospace and automobile industry but was not effective as per the expectations.

2The latest technique that is able to compute the flow field to large extent is the Computational fluid dynamics (CFD) analysis. It is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena by solving the mathematical equations which govern these processes using a numerical process. CFD analysis complements testing and experimentation therefore reducing the total effort required in the laboratory. The result of CFD analysis is relevant in engineering data used in conceptual studies of new designs, detailed product development, troubleshooting and redesign.

3These days we can find its wide applicability and use in aerospace industries than in past. Moreover for the last decades the aerodynamics of the helicopter rotor has been the interesting as well as the challenging issue for the engineers. The accurate prediction of the rotor wake is one of the biggest challenges facing by the rotorcraft industry today. Hence to understand the overall prediction of rotor loads, performance and vibration of rotor of the helicopter is critically important to design a rotorcraft. Although there are number of research been carried out for few helicopters but neither of them can define the exact flow.
4Therefore we are proceeding to carry out the similar type of research on CFD analysis of the main rotor of Bell 412 helicopter to predict the aerodynamic behavior of the rotor in Forward flight compare with theoretical values but with the motive of precision and reduction of the errors using some convincing software.

1.2 AIM
5The aerodynamics of the helicopter rotor has been the interesting as well as the challenging issue for the engineers. Thus understanding of the overall prediction of rotor loads, performance and vibration of rotor of the helicopter is critically important to design a rotorcraft. The accurate prediction of the rotor wake is one of the biggest challenges facing by the rotorcraft industry today. Hence to understand the overall prediction of rotor loads, performance and vibration of rotor of the helicopter is crucial. Therefore the CFD analysis of the main rotor of helicopter with the latest software can led to more accurate results than before. It will reduce cost, time and effort with benefit of achieving more accuracy.

1.3 OBJECTIVESThe main objective of our research project is:
To model solid model of Bell 412 main rotor.

To perform CFD simulation of that solid model in Forward flight.

To calculate the tip velocity, thrust required, power required, coefficient of lift, coefficient of drag and coefficient of moment from CFD simulation.

To compare the results of CFD simulation with the theoretical results based on momentum theory and blade element theory.

CHAPTER 02LITERATURE REVIEW2.1 RELATED RESEARCHES6The computational fluid dynamics (CFD) is currently considered as a vital device for the study of fluid dynamics and developing a new aircraft, Neal M. CCITATION Nea2 l 1033 1. Advances had been made in understanding helicopter fluid aerodynamics using CFD, Gordon J.L CITATION Gor07 l 1033 2. Deferent helicopter CFD analysis had been done comparing CFD analysis results and experimental data or blade element theory results. The majority of helicopter CFD analysis reviewed in this literature showed that CFD analysis results were in reasonable agreement with experimental data and few showed a bit discrepancy between CFD analysis results and experimental data. The following paragraphs mentions different helicopter CFD analysis reviewed.

7Perera GAPR et al CITATION Per16 l 1033 3 conducted a research on “helicopter main rotor aerodynamic simulation with CFD”. The main objective of their research was to analyze the selected bell 212 main rotor under two main helicopter aerodynamic theories named Blade Element Theorem and Momentum Theorem. The CFD simulation for hover, Forward flight, HIE and HOE flying maneuvers were performed. The rotor blade of NACA 0012 aero-foil was used. To simulate these rotor blades they used rotating mesh, ANSYS Fluent, a surface and volume mesh continuum containing approximately seven million polyhedral cells and Finite Volume Method (FVM) as discretization technic. In hover, 800rpm and angle of attach of 2° was used. Implicit unsteady flow solver with ideal as and SST (Mentar), K-Epsilon turbulent model, estimated drag, lift, and momentum coefficients were also taken. The simulation results and actual results were compared and further analyzed. Several deviations were observed between CFD results and real data calculation for bell 212 main rotor. The forecasted values of aerodynamic parameters for Bell 212 main rotors were little bit different than expected. In their conclusion, this particular fact was directly related to computational limitations associated with CFD.

8However, in “CFD analysis of complete helicopter configuration-lessons learnt from the go-ahead project” performed by René S. and George N. B. CITATION Ren12 l 1033 4, the finding showed that pre-test computations for economic cruise condition had been in reasonable agreement with the experimental results. The comparison considered surface pressure at various places on the fuselage taking into account the relative coarseness of the used grids. CFD results of various patterns also agreed reasonable well. But, the discrepancies in the separated flow regions at the back of the helicopter were noticed. By improving meshes, a better spatial resolution of the flow was found. The mesh quality was the key for accurate predictions as well as educated estimation of the flow regions where intensive interactions of the flow structures take place for a complex CFD computation.

9Christian R. CITATION Chr12 l 1033 5 Worked on “CFD Analysis of the Main-Rotor Blade of a Scale Helicopter Model using Overset Meshing”. The flow field was resolved utilizing star CCM+. Mesh continuum for volume and surface contained approximately seven million polyhedral cells and finite volume method discretization technic were used. An implicit unsteady flow solver, ideal gas and SST K-Omega model were applied. Hover flight and forward flight had been evaluated. Forward flight was performed by varying angle of attach of rotor shaft and collective pitch angle and freestream Mach number of 0.128 (M=0.128) was used without including cyclic pitching motion. The flight case applying cyclic pitch motion had been evaluated at zero rotor shaft angle of attach and zero collective pitch angle. The experimental data for comparison had been taken from NASA report. The results from the CFD for hover ?ight were in excellent agreement with the experimental data from wind tunnel. The CFD results for lift in cases of forward ?ight without applying cyclic motion coincided with the experimental data for lift. But there had been di?culties to produce a thrust for forward flight. It had been concluded that application of overset mesh to evaluate main rotor blades with application of computational fluid dynamic (CFD) does work.

10Nik A. et Al CITATION Nik12 l 1033 6 analyzed “computational aerodynamics for hovering helicopter rotors”. Simulation of helicopter rotors in axial flight using the helicopter multi-block (HMB2) solver of Liverpool University for range of rotor tip speeds and collective pitch setting was conducted. The Parallel Helicopter Multi-block CFD solver was used and validated for the Caradonna and Tung model rotor in hover. Prediction of rotor hover performance, wake geometry and its strength using CFD methods were discussed. The blade loads, wake geometry and wake strength were analyzed and the impact of the number of mesh points on the blade loads and wake geometry were also investigated. Mesh of more than 3.6 and 9 Million points per blade were used. Excellent agreement of the blade loads data and wake trajectories between CFD and experiment have been observed, and suggests that CFD can adequately resolve the loads and wake structure.

11Nik A. et al CITATION Wah06 l 1033 7 worked on “numerical analysis of an isolated main helicopter rotor in hovering and forward flight”. In this work aerodynamic characteristics of a 5-seater helicopter with various rotor geometry operating in forward flight mode were simulated with FLUENT software. The main objective was to calculate the aerodynamic load generated by rotor during hovering and various forward flight velocity range. Consequences of using shaft rotational velocity and various rotor configuration had been also simulated. The method used to model the rotating rotor were multiple references rotating frame and standard viscous k-? turbulent flow model. Rotor rotated in hover flight and forward flight. Calculation of coning angle and flapping angle was based on blade element theory. The comparison had been made between CFD results and blade element results. The CFD simulation results and blade element theorem analysis were found to be in good agreement.

12Nik A. R. N. M. and Barakos G. CITATION Nik17 l 1033 8 worked on “Performance and Wake Analysis of Rotors in Axial Flight Using Computational Fluid Dynamics Flow”. The aim of the work was to validate the HMB solver and to improve the existing basic knowledge about the studied subject in this research. The analysis was carried out using HMB on rotors in hover and vertical ascend flight, the surface pressure over the blades, the performance of integrated rotor, and the trajectory of vortex wake. The results were evaluated with the experimental data of the UH-1H rotor. The investigation of detailed rotor velocity field of the tip vortex in hover flight was performed. HMB solver predicted well the rotor blade aerodynamic performance in comparison to experimental data and HELIX-I data. Small discrepancies could be observed for low ascending rate. A strong similarity of the swirl velocity profile had been found. The reasonable agreement between predicted results and experimental data were found for hover flight and descent rate. Unsteady solution was suggested for rotor in vortex ring state. This work validated HMB solver on rotor in axial flights utilizing several rotor test data.

13Ulrich K. et al CITATION Kow14 l 1033 9 worked on “CFD-simulation of the rotor head influence to the rotor-fuselage interaction” they investigated interaction phenomenon of fluid-structure of a rotorcraft in fast forward flight. Detailed model, involving the swashplate and the control rods was considered because of the great influence of the main rotor head on the wake structure. The rotor head configuration had been simulated in many variants to find the solution of the influence of the components. The Compact reconstruction fifth order Weighted Essentially Non-Oscillatory fluid state reconstruction scheme for an improved rotor wake conservation was applied. An up wind HLLC Riemann was used to solve the flux computation. The fundamental variation of unsteady flow behaviors was noticed by analyzing the flow field and force. The substantial impact of incoming flow from the rotor wake was observed. The strong difference was found particularly in the region of low intensity of the wake after comparing different configuration.

14Gupta R. and Agnimitra CITATION RGu10 l 1033 10 performed on” Computational fluid dynamics analysis of a twisted three-bladed H-Darrieus rotor” to evaluate the performance of a twisted three-bladed H-Darrieus rotor steady-state two-dimensional computational fluid dynamics analysis was studied utilizing FLUENT 6.2 software. Unstructured-mesh finite volume method coupled with moving mesh technique to solve mass and momentum conservation equations were applied for simulation of the flow over the rotor blade. The standard k-? turbulence model was chosen for pressure-velocity coupling Second-order upwind discretization scheme. drag coefficient , lift coefficient, and drag-to-lift coefficient were analyzed with respect to angle of attack (AoA) for two chord Reynolds numbers(Re). The power coefficient (Cp) of the rotor and the effect of twist angle at the chord ends on effective performance of rotor were analyzed. Validation was made by using experimental data for twisted three-blade Darrius rotor. The comparison of the two approaches showed good agreement.
15Khier w. et al CITATION WKh07 l 1033 11 conducted the research on “Trimmed CFD Simulation of a Complete Helicopter Configuration”. The aim of research was to evaluate the aerodynamic interference between the rotating elements and no rotating elements of the rotorcraft. It was performed utilizing the flight mechanics tool HOST weakly coupled to the RANS solver FLOWer. The flow over rotorcraft configuration under various flight conditions was simulated. The analysis showed a noticeable variation in the load distribution between isolated main rotor and full rotorcraft case. Slight disagreement in the computed pressure was found on rotor blades between the isolated rotor and the complete helicopter. The power consumption was found to be negligible. Major variations in surface pressure and the fuselage loads were observed.16Fraunhofer IWES et al CITATION IHe12 l 1033 12 worked on “Aerodynamic Simulation of the MEXICO Rotor “to validate open source CFD toolbox OpenFoam against the MEXICO data-set. The steady state and time-accurate simulations were conducted using the Spalart-Allmaras turbulence model for many operating cases. Axisymmetric inflow for three different wind speeds were used. The numerical data were evaluated with pressure distributions from many blade sections and PIV-flow data from the region located near the wake. A good agreement between numerical results and experimental data was found.

17Tung, C and Ramachandran K. CITATION Tun92 l 1033 13 performed on” Hover performance analysis of advanced rotor blades” with aim of validating available hover flight prediction methods. This work used wake, an extensive set of loads and performance data as experimental basis. These data were captured from a pressure instrumented model UH-60 rotor. The model was had replaceable tips, comprising a tapered and a BERP-type tip which allowed evaluation of the effects of rotor blade configuration. The central prediction method analyzed was a vortex embedded, free-wake and full-potential CFD method named HELIX-I. It was noticed that HELIX-I code provides great comparisons with the data comprising surface pressure, wake and performance. It was observed that the HELIX-I code provides a good compromise between comprehensive nature of Navier-Stokes methods and the speed of boundary integral methods.

2.2 ROTOR AERODYNAMICS18The helicopter main rotor generates vertical lifting force in against the aircraft weight and horizontal propulsive force (thrust) for forward flight. It provides a means of producing forces and moments to control the altitude and position of the helicopter CITATION Cha00 l 1033 14. The knowledge of aerodynamics loads effects on the rotor blade dynamic response and environment in which the rotor operates is important. Helicopter has ability to hover and to perform forward flight.

19During hover, the helicopter main rotor blades move considerable volumes of air in a downward direction. This process accelerates the air to relatively high velocities and requires lots of horsepower. To perform hovering flight, the helicopter main rotor must generate lift (L) equal to the total weight (W) of the helicopter. with an increase of blade pitch and high rotor blades speed, the necessary lift for a hover is induced and reach a state of stable stationary hover. The rotor tip vortex affects negatively the effectiveness of the outer blade portions in hover flight. The lift(L) of following blade is severely affected by vortex of preceding blade. For hovering the helicopter requires high power. This high-power requirement is effect of continuous creation of new vortexes and ingestion of existing vortexes. Unlike out of ground effect (OGE) operation, in ground effect (IGE) operation, the downward airflow patterns and outward airflow patterns tend to restrict vortex generation. Restriction of vortex generation results in increasing of efficiency of outboard part of the rotor blade and reduces overall turbulence of system produced by ingestion and recirculation of the vortex swirls CITATION Adm13 l 1033 15.
20In hovering flight, Collective pitch angle, tip Mach number and blade wake affect overall performance requirement for hover flight.
21Collective pitch angle changes angle of attack of all rotor blades by an equal amount. The collective pitch is operated to control the average rotor blade pitch. Change in pitch angle changes the blade lift (L) and the average rotor trust (T) and increase the drag on blades. Increase in drag requires extra power CITATION Sha09 l 1033 16.
22A high rotor tip speed provides the rotor a high level rotational kinetic energy for a given radius. The high rotor tip speed reduces the rotor design weight. However, compressibility effects and noise are two factors that oppose the use of high rotor tip speed. The compressibility effects increase rotor power requirements. With increase in Mack number the rotor noise increases rapidly. For maximum hover flight performance lower tip Mach number is required CITATION Sha09 l 1033 16.

23The wake due to the rotating blade comprises, in part, a vertical vortex sheet, with formation of concentrated vortex at the blade tip. The vortex sheet has a vorticity with vectors aligned mainly normal to and parallel to the trailing edge of the blade. Experiments have shown that blade tip vortices are almost fully rolled up within only a few degrees of blade CITATION Sha09 l 1033 16.

24For forward flight the rotor is tilted forward, and total lift and thrust forces are also tilted forward and generate resultant lift-thrust force. The generated resultant force that can be resolved into two components: lift (L) acting vertically upward and thrust (T) acting horizontally in the direction of flight. In addition to lift and thrust forces, there is weight and drag. For steady forward flight, lift, thrust, drag, and weight must be in balance. When lift force exceeds weight, the helicopter accelerates vertically until both forces are balanced; if thrust is less than drag, the helicopter slows down until the forces are in balance. CITATION Adm13 l 1033 15.

25During forward flight, airflow moves opposite to the flightpath of rotorcraft. The velocity of air-flow equals the velocity of rotorcraft in forward flight. The velocity of air flow across the blade is determined by: the point location of the rotor blade in plane of rotation at a given time, blade rotational velocity, and airspeed of the helicopter determine the velocity of the airflow across the blades. The airflow on rotating blade varies continuously with rotation of blade. The highest airflow velocity occurs over the one side of plane of rotation for advancing blade in a rotor system and decreases to rotational velocity over the nose. It continues to decrease until the lowest velocity of airflow occurs over other side for retreating blade CITATION Adm13 l 1033 14.

26When the helicopter begins to accelerate from a hover, the rotor system becomes more efficient. Transitional lift results from improved rotor efficient due to acceleration of helicopter from hover flight to forward flight. As in-coming wind produced by helicopter movement enters the rotor system, vortices and turbulent stay behind and the airflow becomes more horizontalCITATION Adm13 l 1033 142.3 SOFTWARE REVIEW2.3.1 SOLIDWORKS27Solid Work is a software which is used for solid modeling computer aided design (CAD) and computer aided engineering (CAE). Through this software we can easily sketch 2D structure and by extruding feature we can get it 3D model very easily. From this software we can design separate parts according to our own dimensions and assemble those parts together easily. And also from this software we can designed mechanical system as well as we can simulate through this software. But in this research we have used different kind of software to simulate the solid work design.
2.3.2 BASIC CONCEPT OF SOLID WORK28From sketch option we can create different kind of shapes like rectangle, circle, lines, curves and etc. And also from this we can insert smart dimensions, so that we could able to make a design according to our own dimensions. Mirror option also could be used through this sketch option.
29Through the feature option we can convert 2D model to 3D model easily by using extrude option. And if we want to make a hole or cut in that 3D object we could use extrude cut option in this feature panel. If we want some smooth edges, some other features like fillet, shell and draft could be used. To create airfoil, curve feature has used in the designing stage.
30We can flow simulate through the solid work Flow Simulation option but it is not much accurate as Open Foam and other simulation software. So throughout this experiment we didn’t use that option in solid work.

31We can assembly parts through this software. We can sketch different parts of model in different pages and after completing the parts, it can be assembled together and complete with one solid 3D model.

32We can use different kind of constraints while drawing the sketch such as horizontal, perpendicular, vertical, coincident and etc.
2.3.2 ANALYSIS OF OPEN FOAM33OpenFOAM is a structure for creating application executables that utilization bundled usefulness contained inside an accumulation of roughly 100 C+ libraries. OpenFOAM is dispatched with around 250 pre-incorporated applications that fall with two classifications: solvers, that are each intended to take care of a speci?c issue in ?uid (or continuum) mechanics; and utilities, that are intended to perform assignments that include information control. The solvers in OpenFOAM cover an extensive variety of issues in fluid dynamics. Some of them are compressible, multiphase, incompressible, heat transfer etc. The users in OpenFOAM can expand the accumulation of solvers, utilities and libraries in OpenFOAM, utilizing some pre-essential learning of the hidden strategy, physics and programming procedures included. The pre-processing and post-processing conditions are made associated with OpenFOAM. The interface to the pre-and post-preparing are themselves OpenFOAM utilities, subsequently guaranteeing steady information dealing with over all conditions. The post handling is went with ParaView programming.

34There are some limited numbers of CFD simulations done so far using dynamic mesh in openFOAM. These simulation projects are done with pimpleDyMFoam solver. For example: the simulation of the wind turbines and propellers. Therefore we have proceeded with our CFD project on Bell 412 main rotor with the very close studies of the simulations of wind turbine and propeller. Most of the techniques and ideas are drawn from these existing simulations and modified appropriately for our CFD project.

35Computational Fluid Dynamic (CFD) is one of the main tool to perform in Researches and the industrial applications. From this CFD analysis we can predict, how the system component are working, how the fluid flow behavior and it provides a qualitative and quantitative prediction of fluid flows by means of following methods,
Numerical Method
Software tools
Mathematical Modeling
So that we can implement our design and make necessary development in design. And it has been using in industry for many years. Some of basic applications are given bellow;
Flow and heat transfer in industrial processes
Aerodynamics of ground vehicles, aircraft, missiles.
Film coating, thermoforming in material processing applications.
Flow and heat transfer in propulsion and power generation systems.

Ventilation, heating, and cooling flows in buildings.
Heat transfer for electronics packaging applications.

36CFD is the latest branch of engineering In CFD it used numerical method and the algorithm method to solve and analyze the problem in fluid flows. This analysis have done through the basic governing equation in CFD which are in partial differential form. This equation will convert in to computer programs by using high level computer languages. Existing commercial CFD codes are capable of simulating a very wide variety of physical processes besides fluid flow. This CFD describe the pressure, temperature, density and the velocity of the moving fluid, which given in the Naiver-stoke equations. In Naiver-Stock equation it contain energy equation, momentum equation and the continuity equation which are given bellow.
Continuity Equation:
???t+ ? ?u?x+ ?v?y+ ?w?z =0(1)
Momentum Equations;
For X direction;
??u?t+ ?(?uu)?x+ ?(?uv)?y+ ?(?uw)?z= -?p?x+ ?(?2u?x2+ ?2u?y2+ ?2u?z2)(2)

For Y direction;
??u?t+ ?(?uu)?x+ ?(?uv)?y+ ?(?uw)?z= -?p?y+ ?(?2v?x2+ ?2v?y2+ ?2v?z2)(3)
For z direction;
??u?t+ ?(?uu)?x+ ?(?uv)?y+ ?(?uw)?z= -?p?z+ ?(?2w?x2+ ?2w?y2+ ?2w?z2)(4)

Energy Equation;
??E?t+ ?(?uE)?x+ ?(?vE)?y+ ?(?wE)?z= -?pu?x-?pv?y- ?pw?z+S (5)
x, y and z – three different directions component
? – Density of air
u, v and w – Velocity component in different direction.

37From this CFD analysis, it can have great control over the physical process and provides the ability to isolate specific phenomena for study. And from experiment we could only have data in limited number of locations in the system but through the CFD simulation it can analysis data in large number of locations and give comprehensive set of flow parameters for examination. Experimental process may get much expensive compare to the CFD process and the cost of CFD process may get reduce when the computers get more powerful. The simulation could be executed in short period of time as well as we could simulate in real conditions. This are the main advantage of computational fluid dynamic.

38When we discuss about the limitation of CFD, the CFD solutions relay in physical model of real world processes such as compressibility, chemistry, turbulence and many more. Through the CFD it can get much accurate data as the physical model on which they are based on. When the computer solve the equation it invariably introduce numerical errors which include round-off errors and due to the approximation in numerical mode it will give truncation errors. The accuracy of the solution mainly depend on the initial boundary conditions given in to the numerical mode.
39In CFD it divided in to three main processing which are pre-processing, solving and post-processing. In pre-processing, it need to be created Mesh for the solid work model. For that software like Open Foam and Gambit could be used according to our own boundary conditions.

2.5 GENERAL TURBULANCE MODELS40To solve CFD problems it consist of three main components which are geometry and grid generation, setting up a physical model and post processing the compute data. In the turbulence it results in increasing energy dissipation, mixing, heat transfer and the drag. The way geometry and the grid are generated and the set problem is computed are very well known. Precise theories are available. But it is not true for setting up a physical model for turbulence flow. There for it need to create the ideal model with the minimum amount of complexity. The complexity of the model will increase with the amount of information required about the flow field. The key elements of turbulence are time dependent and the three dimensional. CITATION POD07 l 1033 1741Turbulence models can be categorized in to several different approaches which are by solving the Reynolds-averaged Navier-Stokes equations with suitable models for turbulent quantities or by computing them directly.
Reynolds-Averaged Navier-Stokes (RANS) Models
Eddy Viscosity Model (EVM)
Non-linear Eddy Viscosity Model (NLEVM)
Differential Stress Model (DSM)
Detached eddy simulation (DES)
Large-eddy simulation (LES)
Direct numerical simulation (DNS)
Reynolds stress transport models
Direct numerical simulations
2.6 REYNOLDS-AVERAGED NAVIER-STOKES MODELS (RANS)42This method is the mainly use method in Engineering industry. This can be categorized according to the wall function, number of variables and their types. So we mainly focus on following models in RANS.
K-Epsilon(?) Model
K-Omega(?) Model
43Here this k-Epsilon model further divided in to two types of models, which are standard K-Epsilon model (SK-?) and the Realizable K-Epsilon model (RNGK-?). And also this K-omega model also divided in to two models which are standard K-omega model (SK-?) and the shear stress transport K-Omega model (SSTK-?).

2.6.1 SPALART-ALLMARAS44This equation solves a modelled transport equation for kinematic eddy turbulent viscosity. It easy to resolve near the wall. From this model it shows good results for boundary layer subjected to adverse pressure gradient in especially wall bounded flows involve in aerospace applications. This could be used for the supersonic and transonic applications. This model is not calibrated for the general industrial flows. This model is very effective in low Reynolds numbers. Minimum boundary layer resolution of 10-15 cells should be there to resolve the equation. The formulation provide wall shear stress and heat transfer coefficient. This model cannot rely on the turbulence isotropic calculations. CITATION Jim17 l 1033 182.6.2 K-EPSILON(?) MODEL
45This model mainly focus on the affect the turbulent kinetic energy. In this model it take the kinetic viscosity is isotropic as an assumption, or the ratio between rater of deformation and the Reynolds’ number is same in all directions. This model used commonly in industrial applications rather than the other two models. This model gives reasonably accurate results. Under different pressure gradients it gives the equilibrium boundary layers and free shear flows. This usually use for free shear layer flow with small pressure gradient. This model poorly perform in strong separations, large pressure gradients, unconfined flows, curved boundary layers, rotating flows and flows in non-circular ducts. Among the two type of this model (RNG) K-? model perform better than the SK-? model.
For k and ? it use two transport equations for turbulent length and the viscosity.

Equation for turbulent length;
Equation for turbulent viscosity;
Turbulent kinetic energy;
??t?k+ ?y?xi?kui= ?y?xi?+?t?k?k?xi+Pk+Pd+??+YM+Sk(8)
Dissipation ?;
?y?x??+ ?y?xi??ui= ??xj?+?t?????xj+C1??kPk+C3?Pb-C2???2k+Sk(9)
C1? = 1.44, C2? = 1.92, C3? = 0.09, ?k = 1.0, ?? = 1.3
2.6.3 K-OMEGA (?) MODEL46It is two equation model which means it use two transport equations to represent the turbulent properties of the flow. This also a common equation model. This can be integrated to the wall without using the wall functions. From this equations, it accounts history effects such as diffusion and convection of turbulence energy. Here kinetic energy (k) is one of variable. It determines the energy in turbulence. The other variable is dissipation (?), it determine the scale of turbulence.
For kinematic eddy viscosity;
Turbulence kinetic energy;
Specific dissipation rate;
???t+Uj???xj=?S2-??2+??xjv+?kvT???xj+2(1-F1)??21??k?xj???xj (12)

1Our research methodology will begin from modeling the SOLIDWORKS solid model of the main rotor of the Bell 412 helicopter. A surface and volume mesh continuum will be generated that will contain approximately millions polyhedral cells, where the Finite Volume Method (FVM) will be chosen as a discretization technique. The software to generate the rotating mesh will be Gambit software. The subsequent CFD simulations will be conducted with open Foam 17.06 software in subsonic flow regimes. Also an implicit unsteady flow solver, with an ideal gas and a SST K-Omega turbulence model will be used. Forward flight case will be examined. At last we will compare the theoretical and simulated results. In step wise it will go like this;
Solid modeling
Mesh generation
CFD Simulation
Turbulence model
Solutions and Calculations.

2The solid model of the main rotor of Bell 412 helicopter will be created using Solid Works 2015 drawing software. The airfoil data and other required data about dimensions and profile configurations of Bell 412 helicopter will be taken from the Sri Lanka Airforce (SLAF).

3.1.2 MESH GENERATION3A mesh is a discretization of the geometric domain. The accuracy of the CFD simulation strongly depends on the quality of the grid. A good quality grid considering the flow physics leads to faster convergence and better solution. Thus design and construction of a quality grid is crucial to the success of the CFD analysis. For the mesh generation we will implement the Gambit Software because it is suitable for generating polyhedral cells and also it’s relatively easy accessible. In our research we will create the structured mesh because of requirement of less computational memory and cost, data locality, available solution algorithms, high degree of control and alignment leading to better convergence. Also polyhedral cells will be taken into consideration because polyhedral meshes showed better accuracy, lower memory demand, shorter computational speed and faster convergence behavior than other shaped cells.
4Finally, surface mesh and subsequently volume mesh which is generated will be made as rotating mesh using Gambit software. We will select Finite Volume Method (FVM) for the discretization method. More cells can give higher accuracy. The downside is increased memory and CPU time. Millions of cells are huge and should be avoided if possible. However, they are common in aerospace and automotive applications. Thus we also will be also generating nearly 3-5 million polyhedral cells in the volume mesh continuum.

Then our next step will be to set boundary conditions. After generating the mesh by using the gambit software we will allocate the boundary types and continuum types for the box domain which was used for all three simulations.

3.1.3 CFD SIMULATION5Our next step will be CFD simulation. The simulation will be carried out in openFoam17.06 solver software. The CFD simulation will be done for Forward flight. For that we will take the meshed volume continuum from Gambit. For simulation purpose we will consider the working fluid as air and will assume that the main rotor operating in the standard atmospheric conditions. During our simulation we will be requiring reference values for quantities like air density, temperature, pressure, viscosity, enthalpy etc. Therefore in such cases we will consider respective values at standard atmospheric sea level conditions.
We will use turbulent model in CFD simulation.

3.1.4 TURBULANCE MODELS6Turbulence flows are three dimensional, fluctuating and chaotic (full of eddies and wakes).Governing equations cannot be solved for 3D turbulent flows of engineering interest. Turbulence model describes turbulent motion, allow calculation of mean flow variables and do not require calculations of the entire time history at spatial locations. Therefore a turbulence model is a computational procedure to close the system of mean flow equations. Turbulence models allow the calculation of the mean flow without first calculating the full time-dependent flow field. We only need to know how turbulence affected the mean flow.

7We are considering Reynolds-Averaged Naiver-Stokes (RANS) model for computing the turbulent flow. These models simplify the problem to the solution of two additional transport equations and introduce an Eddy-Viscosity (turbulent viscosity) to compute the Reynolds Stresses. There are several turbulent models under it. For a turbulence model to be useful, it must have wide applicability, be accurate, simple and economical to run. Therefore we will choose k-? SST model because this model has proved to be a very good turbulence model for many engineering applications that provides a good trade-off between computational cost and accuracy. However, it requires a good resolution of the near-wall region which is a memory intensive case. But still its accuracy is not compromised. We will employ the k-? or the k-? model to compute the flow field and use it as initial conditions for the k-? SST as it exhibits sensitivity to the initial conditions.

3.1.5 SOLUTION AND CALCULATIONS8Finally, from the CFD simulation we will determine the tip velocity of rotor, thrust required, power required, coefficient of lift and coefficient of drag and coefficient of moment. And for theoretical calculations, on the basis of blade element theory and momentum theory, we will again calculate tip velocity of rotor, thrust required, power required, coefficient of lift, coefficient of drag and coefficient of moment by using the maintenance manual and other necessary data documents from SLAF about Bell 412 helicopter.
CHAPTER 04PRE PROCESSING1Here we have selected Boeing VR-7 airfoil and we start to design the solid work 1:1 model. First we have designed the model in MMGS (millimeter, grams, and seconds) unit system. But when this model run in the Open Foam it will take unlimited time to analyze the details, because it take 1 mm as a one part so there will be many number of parts. So we redesigned the model with MKS unit system and analyze it in Open Foam. So after that we have crated Mesh using Open Foam software and finally simulate it by using the same software.

4.1 SOLID MODELLINGright18846802The solid model of the main rotor was 1:1 and it was created using the solid work 2015 software. We found the co-ordinates of Boeing VR-7 (Vertol 7) airfoil which used as the airfoil in Bell 412 helicopter. For that we used website. CITATION Air171 l 1033 19 From there the DAT file which had the co-ordinate of Boeing vr-7 has been downloaded. Then the co-ordinates of x and y inserted in to MS Excel 2013 software and changed it with adding Z co-ordinates as “0”. In DAT file it contained X and Y co-ordinates only. It helped to draw the airfoil in XY plane in solid work. Throughout the modeling part we have used the Meter, Kilogram, and Second (MKS) as the Unit System.

Figure SEQ Figure * ARABIC 1 : Boeing VR-7 Airfoil in Air Foil Tool Web Site
Figure SEQ Figure * ARABIC 2: Bell 412 Helicopter Dimensions-95251905
3The designing of the airfoils has begun with the front plane of the Solid Work software. After selecting the airfoil which we created using downloaded co-ordinates, the chord length was corrected to the actual value of the bell 412 helicopter chord length. Then, the 2D sketch was converted to 3D sketch by using extrude feature in Solid Work. In this conversion the actual values of the helicopter. The actual values are given in the following table (1). These dimensions are taken from the internet and Sri Lanka Airforce (SLAF). CITATION Bel18 l 1033 20 So this is a 1:1 model. To develop proper mesh in Open Foam we have to make the solid model in Close Entities. To do that we make sure every step of solid model designing should indicate as Close Entities.
Table SEQ Table * ARABIC 1:Bell 412 Helicopter Rotor SpecificationsBell 412 Rotor Dimensions
Root Chord Length 0.40386 m
Tip Chord Length 0.2159 m
Rotor Diameter 14.0208 m
Hub Diameter 1.02 m
Wing length 6.4504m
No of Blades 4
Figure SEQ Figure * ARABIC 3 : Solid Work Modeling 2-1143004019550Figure SEQ Figure * ARABIC 4 : Solid Work Modeling 1center0
Figure SEQ Figure * ARABIC 5 : Solid Work Modeling 2
Figure SEQ Figure * ARABIC 6 : Mesh Generationright11074404After designing the complete Bell 412 rotor. We used this model in Open Foam software. The origin was not in the middle after designing the rotor. A new co-ordinate system has been used and named as Co-ordinate System 1. But we couldn’t create the proper Mesh for that model, because the Open Foam software could not find the origin. It always take the rotating axis to the nearest wall of the rotor hub. The error has been shown in the figure number (6).

5To correct that error, very thin cylinder was drew through the rotor center axis and the diameter of that cylinder is negligible compare to the rotor dimensions. After the adjustment the Open Foam software could able to identify the origin of the rotor. The Solid Work adjustment is shown in the following figure (7).

center0Figure SEQ Figure * ARABIC 7 : Center Cylinder in Solid Work Model
6After that the model created for the hover case without ground effect, it required to make another model for simulate the hover case with the ground effect. So it required to draw a solid surface in the bottom of the top plane. So a solid flat cylinder was drew under the top plane which was having the diameter much bigger than the helicopter rotor diameter. And it was 10m bellow to the top plane. The sketch of that model shown in the bellow figure (8).

Figure SEQ Figure * ARABIC 8 : Solid Work Model for With Ground Effect4.2 MESH GENERATION7Meshing is probably the trickiest part of the whole study. As has been stated previously, since the geometry is quite complex, snappyHexMesh is required. Meshing with snappyHexMesh requires several actions to be performed. The first one is to create a background mesh using blockMesh. The three dimensional background meshes was generated in order to perform a three-dimensional simulation, with all boundaries as patches except in case of HIGE. In HIGE the bottom patch is taken as wall. The total of around 1.8 million cells were been created for all three cases of the flight. The background mesh was created in a way so that it can approximate size of the STL geometry of the Bell 412 main rotor. The dimensions of the block as well as the STL geometry of the Bell 412 main rotor were scaled in units of meters.

Figure SEQ Figure * ARABIC 9 : Blockmesh8Once the background mesh was created (by using the blockMesh command), now snappyHexMesh was used to refine the mesh and adapt it to the geometry (Bell 412 main rotor) that was just created in STL format. All three meshes were been activated true namely, castellated mesh, snap and layer addition. Edge and the surface refinement level were set to 6 and the layer addition was made for 50 iterations. In all three flight cases the same meshing procedure was been adapted.

Figure SEQ Figure * ARABIC 10 : snappyHexMesh4.3 DYNAMIC MESH GENERATION9The mesh generated by the snappyHexMesh utility was further processed in order to generate the dynamic mesh. The dynamic mesh was created on the base of the solid body motion taken as rotational motion with the center of rotation as the coinciding point of the solid model of the bell 412 main rotor and the background blockMesh for each case of forward, HOGE and HIGE. The rotational speed was fixed to 123 RPM or 12.88 rad/s approximately. Moreover the effect of the gravitational field in each case of flight was also included by introducing the value of ‘g’ in dynamic mesh itself. The obtained dynamic mesh was iterated for 100 iterations.

Table SEQ Table * ARABIC 2 : Rotational CenterFlight Center of Rotation
Forward (6.95968 , 0.84851, 7.00731)
HOGE (0.33662 ,-0.03299, 0.00162)
HIGE (0.33662,-0.03299, 0.00162)
10After the successful generation of the dynamic mesh, the polymesh from the latest iteration of the dynamic mesh was put into the constant folder for running the simulation.

4.5 JUSTIFICATION FOR RPM SELECTIONThe solver that we are implementing is for the incompressible flow. Therefore the tip velocity should be wisely controlled and estimated for the range of incompressible. If the tip velocity exceeds the speed of sound then the solver that we are using will crash. Therefore taking these facts into consideration we limited the tip speed of our rotor to approximately 90 m/s. thus to achieve this tip speed we had to rotate our bell 412 main rotor or otherwise dynamic mesh with the angular speed of 12.88 rad/s or 123 RPM.

CHAPTER 05CFD SIMULATION1The most important component for the successful completion of the project is the CFD simulation. Among the number of CFD simulation software like fluent, simFlow, Xflow etc. open FOAM was chosen for our simulation. The version of the openFOAM is 17.06. The three dimensional model of the Bell 412 main rotor after meshing with snappyHexMesh meshing utility, was put for running simulation.

2The solid model of Bell 412 main rotor was imported to Open FOAM from Solid works in STL format in units of meters. Moreover the blockMesh was also scaled in units of meters in Open FOAM where the solid model of the Bell 412 main rotor was adjusted.

5.2 MATERIAL AND REFERANCE VALUE3The fluid in our simulation is taken as air. It was assumed to be under the standard atmospheric condition with standard air pressure of 1.0125 Kpa, density of 1.225 kg/m3 and temperature of 300 k.
4The reference values for initial conditions and other standard parameters were same for all cases in forward flight , HOGE and HIGE except that the forward speed of 5 m/s was allocated for forward flight whereas not for others. The viscosity value was 1.4028E-4 m2/s. Other parameters values were assumed that of standard sea level conditions. The Reynolds number was fixed to 500000.

5.3 OPERATING CONDITION5The Bell 412 main rotor was assumed to be operated under standard atmospheric conditions under the action of gravity. The rotor was given the RPM of 123 and rotated about Y axis in case of HOGE and HIGE but in case of forward flight the rotational axis was taken by considering tilt angle of 7 degrees. The gravitational field was set to 9.8 m/s2 in opposite direction of Y axis.

5.4 TURBULANCE MODEL6For our research project we have made selection of k-e turbulence model.  It is a two equation model which gives a general description of turbulence by means of two transport equations (PDEs). We have made it as our choice because of its good convergence ability and low memory requirement. Furthermore it can consider the effects of free-shear layer flows with relatively small pressure gradients. It gives good compromise between computational cost and memory requirements. Moreover it also account for vortices formation also.

5.5 CALCULATION OF THE Y+ VALUE FOR k-EPSILON TURBULANT MODEL7Based on the turbulence model selected the value of the parameters were been defined. As our turbulence model selected is k-epsilon turbulence model. The determination of the y+ value was very critical. It is because the based on the value of the y+ we can define the boundary condition for the wall, which in our case is the Bell 412 main rotor. The y+ value for our problem is calculated approximately 272. Since this value was in the range between 30 and 300, our use of k-epsilon turbulence model was justified.

Skin friction coefficient (Cf) = 0.058*Re-0.2
= 0.058*500000-0.2 = 4.20E-
Wall shear stress (?w) = 0.5* Cf*?* U2
= 0.06437
Friction velocity (U?) = ?w? = 0.2292
y+ = ?*U?*y? = 1.225*0.2292*0.16671.71E-4 = 272
5.6 CALCULATION FOR INITIAL CONDITIONS FOR K-EPSILON TURBULANT MODELThe value for the k and epsilon are also calculated for our problem:
Turbulence kinetic energy (k)
k = 32(UI) 2
Where, I=5% for medium Reynolds number
= 1.5(5*0.05)2
= 0.09375
 Rate of dissipation of turbulence energy (?)
We know;
Turbulent length scale (l) = 0.07*Length of problem (L)
Where, L=14.028 m (Diameter of Bell 412 main rotor)
? = C?0.75 k1.5l where, C? = 0.09
= 0.090.75 0.093751.50.98196
= 0.004803
5.7 BOUNDARY CONDITIONFor Forward Flight and HOGE Flight
Table SEQ Table * ARABIC 3: Boundary conditionsBoundary U p nut k ?
inlet fixedValuezeroGradientcalculated fixedValuefixedValueoutlet inletOutletfixedValuecalculated inletOutletinletOutletbellRotormovingWallVelocityzeroGradientnutUSpaldingWallFunctionkqRWallFunctionepsilonWallFunctiontop slip slip slip slip slip
bottom slip slip slip slip slip
right slip slip slip slip slip
left slip slip slip slip slip
For HIGE Flight
Table SEQ Table * ARABIC 4 : Boundary conditionsBoundary U p nut k ?
inlet fixedValuezeroGradientcalculated fixedValuefixedValueoutlet inletOutletfixedValuecalculated inletOutletinletOutletbellRotormovingWallVelocityzeroGradientnutUSpaldingWall Function kqRWallFunctionepsilonWallFunctiontop slip slip slip slip slip
bottom noSlipnoSlipnoSlipnoSlipnoSlipright slip slip slip slip slip
left slip slip slip slip slip
5.8 USE OF SOLVER AND INITIAL RESULTSOur study and analysis on Bell 412 main rotor is done on the incompressible and moving body, the appropriate solver was considered as pimpleDyMFoam. Therefore the simulation was run by using pimpleDyMFoam solver. This solver is transient solver for incompressible, turbulent flow of Newtonian fluids on a moving mesh. In order to run the simulation some parameters were been set. The maximum courant number was set to 0.02 and the time step of 0.00001. The total number of iterations targeted was 10000.

From our initial iterations we conclude average values for lift coefficient, drag coefficient and moment coefficient in each case after simulation as follows:
Table SEQ Table * ARABIC 5 : Simulated ResultsFlight CL CD CM
Forward 0.0128 0.00364 0.000594
HOGE 0.0225 0.00355 -0.000113
HIGE 5.9000 0.10200 -0.91800
CHAPTER 06POST PROCESSING1The post processing of the simulation results of our CFD project was been accomplished by using ParaView software version 5.3. ParaView is an open-source application for visualizing 2D/3D data. It also supports for distributed computation models to process large data sets.

6.1 FLOW DISTRIBUTION2The post processing is still in progress because of very high requirement of iterations. Unless the sufficient numbers of iterations are run the data full data cannot be displayed. Therefore the following display is only for the initial iteration for our problem.

Figure SEQ Figure * ARABIC 11 : Post processing of the rotorright356235

Figure SEQ Figure * ARABIC 12: Post processing of the simulationCHAPTER 07THEORETICAL ANALYSIS WITH CFD RESULTS1The theoretical analysis has been done with the available data and parameters given for Bell 412 helicopter. Bell 412 flying manual was used as reference for data. Two main theories named Blade Element Theory and Momentum Theory were used for rotorcraft calculations. Many assumptions were taken for rotorcraft calculations and simulation.

The 1:1 solid model was modeled for the three simulations set up according to the dimensions provided by the Bell 412 flying manual. Since main rotor was taken as isolated main rotor, analysis and considerations based only on the main rotor. We assumed that no any effect occurred due to the tail rotor motion, weight and fuselage drag effects.
For calculations empty rotor craft weight was taken. But in CFD simulations no any weight was considered. So, power calculations cannot be made for the model main rotor except the flow pattern analysis. Model main rotor was considered isolated and free from the weight effects from the airframe structure.
Standard atmospheric conditions were assumed for all three flight maneuvers. Inlet flow velocity values have taken as 35 m/s for forward flight and 0 m/s for hovering and HIGE/ HOGE.
Air was assumed to be inviscid and incompressible.
The rotor was assumed to act as a uniformly loaded disk or an actuator disk. This Implies rotor has an infinite number of blades.
The flow both upstream and downstream of the disk was assumed to be uniform and occurred at constant energy.
No rotation is imparted on the fluid by the action of the rotor.
Rotor is modeled as wings which are rotating around a central mast.

2Momentum theory was initially developed for studying propellers and then applied to helicopter propellers. The helicopter rotor can be idealized as a momentum disk. It imparts a uniform velocity (vi) to the airflow creating a change in momentum which will result in an upward thrust (T).

There are key assumptions made to apply momentum theory:
1. Air is inviscid and incompressible.
2. The rotor act as a uniformly distributed disk or as an actuator disk.
Implies rotor has an infinite number of blades thus no periodicity in the wake.
3. The flow both upstream and downstream of the disk is uniform, occurs at constant energy.
4. No rotation is imported on the fluid by the action of the rotor.
Figure SEQ Figure * ARABIC 13 : Momentum Theorycenter331470
The Ultimate Wake Velocity = Vc + 2Vi
Consider a helicopter is climbing vertically at a speed of ” Vc”,
Flow is bounded by stream tube, for above the rotor flow velocity is Vc.
Below the rotor, flow velocity and area of the stream tube will not change.
Far below the rotor the ultimate wake exists. Pressure equal to ambient value, but the velocity exceeds the previous ambient value.
The thrust generated by the main rotor was proven as,
T = (P2 – P1) = 12 ? 2 k Vi Vc + k2 V12
Where “k” has a proven value from the Momentum Theorem as,
T = m Vout – m Vin
K = 2
The power required at the Main Rotor,
P=T (Vc + Vi)
T Vc = Power required for Vertical Flight.
T Vi = Power required for induced velocity.
T = ? A (Vc + Vi) k Vi
? A Vc k Vi + ? A k Vi2 -T=0
Assume the T is known for a given operation and solving for Vi,
Vi = -VC±VC2+2T?A2During hover flight, Vc =0 and Vi =T2?AFWD flight;
Vi =V?h2VWhere; V?h2V; 2.5 (High speed approximation)
Or else,
Vi = -v2+v4+4v?h42The power required at main rotor in forward flight’
The slipstream from the rotor exerts a download force on the helicopter fuselage.
Thus, in the hover the main rotor must generate sufficient thrust to support not only the weight, but also balance this download force.

Also, in a vertical flight an additional thrust is required to overcome the download effect.

Download force will affect only Vertical and Hover flight.

In Momentum Theorem we cannot explain about the drag acted on the helicopter as we assumed the flow is inviscid. Therefore, we must use the Blade Element theory if we need to describe about the drag.
3 According to the Momentum theory, the rotor is considered as an actuator disk through a uniform flow passes. With this approach it is not possible to predict losses associated in a realistic flow around rotor blades. In Blade Element theory the rotor is modeled as wings which are rotating around a center master. Consider a main rotor consisting of a “b” number of blades having chord length of “Cr” and climbing at a velocity of “Vc” and “r” distance from “O”.

Figure SEQ Figure * ARABIC 14 : Blade Element Theoryleft329565right491490

?T=?Lcos?-?Dsin? ?R=?Dcos?+?Lsin? If ? is a small value then,
?T=?L-?D ?R=?D+?LSince the ?L is larger we can take it as it is.

Elementary power required ?P = Torque x Angular Velocity
= (?R x r) ?
The total power,
P = b ? ?P ?P = ?D r ? + T ( Vi + Vc)
?D r ?:power needed to overcome drag
T Vi + Vc:power need for lift
The Total power required;
P=b 8? C Cd R VT3 + T (Vc + Vi ) Forward flight (FWD flight)
The total power for main rotor
PTot MR = TVi+12?V3f+18?bCRCDVT31+4.3?2Where, TVi =induced power 12?V3f=fuselage parasite power
18?bCRCDVT31+4.3?2= Main rotor and parasite power
7.4 CALCULATIONSThrust generated at the main rotor (T)
(Power required at main rotor) = (Power required for vertical flight) + (Power required for induced flight)
P=TVc+TVi or,
Induced velocity; Vi=T2?A (Total power required by main rotor for hovering)=TVc+Vi+18?bcCDRVT3Vi=V?h2V Where; VV1?h>2.5Or else, vi=-v2+v4+4v?h412212(Total power required for FWD flight) = (Power required to overcome induced drag) + (power required to overcome drag) + (power required to overcome profile and parasite drag)
P = TVi+12?V3f+18?bCRCD,0VT31+4.3?2
Required data for calculation
Table SEQ Table * ARABIC 6 : Bell 412 Helicopter SpecificationsEmpty Weight of the Air Craft 3270 Kg
Rotor Radius 7.01 m
RPM of Hovering 296.18
RPM of Forward Flight 296.18
Chord Length 0.40386 m
Number of Blades 4
Download Factor 5%
Tilt Angle 7 degrees
FWD Flight Velocity 50 m/s
Density 1.225 Kg/m-3
Tip Loss Factor 0.97R
Rotor Hub 0.25R
Fuselage Drag Area 6.1347 m2
RPM for hovering = 123.05= 123.05×2? /60 rads-1 = 12.88rads-1
RPM for FWD flight= 123.05= 123.05×2? /60rads-1 =12.88rads-1
Fuselage Drag Area was estimated by calculating area of projected frontal-cross-section area of bell 412 image in using SolidWorks software.

Calculations for hovering
W =9.81x 3207kg (1 +0.05) = 33033.7035N
Rotor Tip speed= 7.01×12.88=90.28m/s
Effective lift area is assumed to be between 25% and 97% of radius, therefore,
Rotor blades area = b×c×R = 4×0.40386 ×7.01x (0.97-0.25)= 8.153m2
Rotor disc Area=7.012×0.972-0.252x 3.14=135.537m2
Lift is produced from 25% to 97% of radius, therefore, lift coefficient should be calculated based on effective radius, hence,
Effective radius for lift is considered to be 0.97R
Then, velocity at 0.97R equals
R?=12.88×7.01×0.97=87.58m/sThrust generates from the main rotor;
T = W = L = 33033.7035N
Vi=T2?A=33033.70352×1.225×135.537=9.97m/scL=L0.5?VT2s =33033.70350.5×1.225×87.582×8.153=0.862; CL = 0.862
From the drag polar of NACA 0012 (CL vs CD), CD = 0.0113
From graph of CM vs Cl of NACA 0012, CM = 0.0065
Power required for hover flight
Power required to overcome induced velocity:
TVi = 9.97×33033.7035=329346.0239W
18bCdRVT3=18x4x0.40386 x0.0113×7.01×90.283=11769.88W
Total power required by main rotor to hover:
(Vi+Vc)+18bCdRVT3=11769.88+184×0.40386 x0.0113×7.01×90.283=23539.76W Calculations for FWD flight
Download factor should not be considered for forward flight, therefore,
W =9.81x 3207kg = 31460.67N
Rotor Tip speed= 7.01×12.88=90.28m/s
Effective lift area is assumed to be between 25% and 97% of radius, therefore,
Rotor blades area = b×c×R = 4×0.40386 ×7.01x (0.97-0.25) = 8.153m2
Rotor disc Area=7.012×0.972-0.252x 3.14=135.537m2
Rotor speed at 0.97R = R?=12.88×7.01×0.97=87.58m/sW= T =31460.67N
Tilt angle = 70
L= Tcos70
L=31460.67 x cos70 =31340.95N
cL=L0.5?VT2s =31226.160.5×1.225×87.582×8.153=0.815 CL=0.815
From the drag polar of NACA 0012 (CL vs CD), CD =0.01046
From graph of CM vs CL of NACA 0012, CM=0.006
Total Power required for forward flight:
P = TVi+12?V3f+18?bCRCD,0VT31+4.3?2V=5m/s
V1?h =9.97m/s
59.97=0.5<2.5 , hence,
T Vi = 31460.67×3.95=124373.67N
Power required to overcome drag acting on fuselage = 12?V3f
f= CD x S
12?V3f=0.0641×53 x1.225×0.5=4.907W
Power required to overcome profile and parasite drag =18?bCRCD,0VT31+4.3?2
Advance ratio=?=vR? =57.01×12.88=0.055 18?bCRCD,0VT31+4.3?2
= 18×1.225x4x0.40386×7.01×0.01046×12.88×7.0131+4.3x(0.055)2=13523.86W
The total power required for forward flight:
CHAPTER 08CONCLUSION8.1 CONCLUSIONThrough this Research we mainly focus on Bell 412 main rotor flow simulation and through that we found out the coefficient of drag and coefficient of lift value for the hover case of helicopter as well as the forward flight of the helicopter. In hover case also results were obtained for Hover in Ground effect and Hover without Ground Effect. Through a CFD analysis of the rotor of Bell 412 helicopter through Open Foam software, the results were obtained for coefficient of lift and coefficient of drag values. Here it used 1:1 solid work model to get the results. We also calculated the theoretical values for lift coefficient, drag coefficient and moment coefficient by using two main theories which are called as Blade Element Theory and the Momentum Theorem. Then it compared the theoretical values and computational values which obtained through calculations and the simulations respectively.

While simulating the results, openFoam gives diverging results first which cannot be happened. After changing some boundary conditions, although we managed to get improvement in results but after several iterations it got crashed.
When we compare the values, we got huge difference between theoretical and computational results. For the computational analysis, we have used K-epsilon turbulence model, and results were recorded till the iteration got crashed. For the results. It has been used nearly 25 iterations.

We got huge different between the computational results and the theoretical results. Following reasons may affect for that error between those results;
For the simulations, though we used 1:1 solid work model it is not a complete model, in the model we did not consider about the tabs and also the rotor hub, we only focus about the helicopter main wing.

The download factor did not consider in the CFD simulations.

Mass of the main rotor did not consider in the CFD simulations in HOGE and HIGE.

For the simulation we consider only the main rotor effect. Tail rotor and the fuselage effect did not consider.

Most importantly the pitch angle of the blades were considered zero which is in fact not practicable to achieve lift.

Similarly the flapping angles of the rotor were been neglected.

The results we obtained from Blade Element theorem and the Momentum Theorem were analyzed with the CFD results, and it shown in the following table (7).

Table SEQ Table * ARABIC 7 : Theoretical results & CFD results analysisParameters Theoretical Results CFD Results
Forward Flight
CL for Forward Flight 0.815 0.0128
CD for Forward Flight 0.0106 0.00364
CM for Forward 0.006 0.000594
Hover Flight
CL for hover Flight 0.862 0.0225
CD for hover Flight 0.0113 0.00355
CM for hover 0.0065 -0.000113
8.2 RECOMMENDATIONSHere we have selected Open Foam software, first our values was got converging due to some boundary conditions. But after changing some boundary condition we could able to get diverging values. But finally, from Open Foam is very difficult to simulate the rotating mesh. So we would like to invite the researchers to study about the latest software which are using nowadays and simulate their models through that software. And we recommend to use genuine software always which will give accurate results.
In the internet there are lot of online software which we have to pay and simulate our models through that software. We would like to invite researchers to get the support from that software and compare the results which you obtained from your simulations and the online simulations.

In solid work model we did not consider about the trim tab and the rotor hub. So it will not give completely the similar result to the theoretical calculations. We would like to recommend to make 1:1 Bell 412 model which is much more similar to the actual rotor, then it will give much more accurate results through the flow simulation.
To get more accurate results it need be done this simulation in much higher performance computers, so that it will give good results without any time delays. Our computers RAM capacity were not sufficient for get good results. If it used 8GB or 12GB RAM it would give good results and it will not damage or heat the computer system. While doing this simulation, we had to shut down the computers in several times.

Here we have done flow simulation only for the main rotor of the Bell 412 helicopter. We would like to invite researchers to design full scale solid work complete model with tail rotor and simulate the model and compare the results which we have got and their results. Then we could get brief idea about the effect of tail rotor and the fuselage for the lift coefficient and the drag coefficient of the Bell 412 helicopter.
We would like to invite the researchers to, make actual model of bell 412 helicopter in some scale and simulate it by using wind tunnel and compare the results. Then we could able to get idea about the computational simulation and the actual simulation results.
1 N. M. Chaderjian, “NASA,” 5 August 2013. Online. Available: Accessed 4 2 2017.

2 G. J. Leishman, Principles of Helicopter Aerodynamics with CD Extra, New York: Cambridge University Press, 2006.
3 H. J. D. S. S. R. Perera GAPR, “Helicopter Main Rotor aerodynamic simulation with CFD,” in 9th International Research Conference-KDU, Sri Lanka, Colombo, 2016.
4 R. S. a. G. N. Barakos, “CFD analysis of complete helicopter configurations – lessons learnt from the GOAHEAD project,” Aerospace Science and Technology, vol. 19, no. 1, pp. 58-71, 2012.
5 R. Christian, “CFD Analysis on the Main-Rotor Blade ofa Scale Helicopter Model using Overset Meshing,” 2012.
6 N. A. R. N. M. a. G. N. Barakos, “Computational Aerodynamics of Hovering Helcopter Rotors,” Jurnal Mekanikal, vol. 34, pp. 16-46, June 2012.
7 N. A. R. N. M. a. A. A. Wahab, “Numerical Analysis of an Isolated Main Helicopter Rotor in Hovering and Forward Flight,” 2006.
8 N. A. R. N. M. a. G. Barakos, “Performance and Wake Analysis of Rotors in Axial Flight Using Computational Fluid Dynamics,” Journal of Aerospace Technology and Management, vol. 9, no. 2, June 2017.
9 M. K. a. E. K. Ulrich Kowarsch, “CFD-simulation of the rotor head influence to the rotor-fuselage interaction,” in European Rotorcraft Forum, At Southampton, Volume: 40th, Southampton, September 2014.
10 R. G. a. A. Biswas, “Computational fluid dynamics analysis of a twisted three-bladed H-Darrieus rotor,” Journal of Renewable and Journal of Renewable and , vol. 2, no. 4, 2010.
11 M. D. T. S. a. S. W. W. Khier, “Trimmed CFD Simulation of a Complete Helicopter Configuration,” in 33rd European Rotorcraft Forum, Kazan, Russia, September 2007.
12 W. M. B. S. a. J. P. I Herraez, “Aerodynamic Simulation of the MEXICO Rotor,” Journal of Physics: Conference Series, vol. 555, no. 1, 2012.
13 T. C. a. R. K., “Hover performance analysis of advanced rotor blades,” American Helicopter Society , Alexandria, VA, United States, 1992.

14 C. Taylor, The Kingfisher Science Encyclopedia, Kingfisher, 2000.
15 F. A. Administration, Helicopter Flying Handbook, Skyhorse Publishing, 2013.
16 S. Coyle, Cyclic and Collective,, 2009.
17 p. d. R. PODGORNIK, “Turbulence models in CFD,” in Jurij SODJA, Ljubljana, 2007.
18 J. Wales, “Wikipedia,” Online. Available: Accessed 05 08 2017.

19 “Airfoil Tools,” NASA, Online. Available: Accessed 04 08 2017.

20 “Bell Helicopter Bell 412,” Flugzeug, Online. Available: Accessed 05 08 2018.