Numerical Simulation Of Flow Around Hovering Rotor Using CFD
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03-03-2010, 06:10 PM

The overall goal of the work presented in this thesis is to extend the physical understanding of the external aerodynamics associated with the rotating case of Hovering Rotor using Computational Fluid Dynamics (CFD) technique.
Rotating blades encounter tip vortices coming from preceding blades, which results in Blade Vortex Interaction(BVI) responsible for producing dynamic effects. Understanding the complex flow field due to this dynamic effects produced by wakes is therefore very important for the prediction of effects such as blade loading, acoustic and vibration. The purpose of the present work is to understand complex flow field in general and wakes behind the blades in particular.
The problem can be solved by using Moving Wall Method and Multiple Reference Frames (MRF) formulation. MRF divides the domain in to two regions. In this work, the problem is set up using Moving Wall Method in which tangential velocity is imposed on the blade walls in the form of angular velocity. The results obtained are based on steady state Reynolds-Averaged Navier-Stokes solver with moving walls have been used for the prediction of vortical flow over the hovering rotor. The scheme is based on multi-block structured grid, finite volume method.

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Presented By
11-Anthony Tony-

The aerodynamics of the helicopter rotor is one of the most interesting and challenging problems facing aerodynamicists. The wake which is produced due to high dynamic pressure at the tip of rotor blades consists of strong vortices form and trail from each blade tip. Accurate prediction of the rotor wake is one of the biggest challenges facing the rotor craft industry today. Understanding the detailed prediction of rotor loads, performance, vibration and acoustics which also interacts with the fuselage, empennage and the tail rotor of the helicopter. The position and the strength of the wake are influenced by many factors including blade geometry, number of blades, rotor thrust, angle of attack of the tip path plane and operating state of the helicopter.
There are three possible approaches for the accurate prediction of the wake in the helicopter: Experimentation(sometimes including real flight testing), Theoretical analysis and Computational or Stimulation methods. Experimentation currently difficult and expensive since it is very hard to measure or visualize flow on spinning blade of a rotor. Theoretical analysis has its limitations because the set of equations that govern fluid flow are so complex that they can only be solved for very simple cases. The only viable alternative is computer simulation. With rapidly increasing computer power and memory now available, it has become feasible to perform full simulations of the air flow around the rotor blade that allow engineer to accurately predict the position and strength of the rotor wake, in turn, accurately predict the performance and aero acoustics of the entire helicopter. A relative new tool in the exploration of this regime is Computational Fluid Dynamics (CFD).
CFD is a technique of producing numerical solutions to a system of particles differential equations which describes the fluid flow. CFD simulations are done by discrete methods and purpose is to better understand a quantitatively and qualitatively physical flow phenomenon which is then often used to improve engineering design.

The rotator of a helicopter provides three basic functions: 1. The generations of a vertical lifting force (trust) in opposition to the aircraft weight ; 2.The generation of a horizontal propulsive force for forward flight ; and 3. A means of generating forces and moments to control the altitude and position of the helicopter. The rotor designer considerable knowledge of aerodynamics environment in which the rotor operates and how the aerodynamics loads affect the blade dynamics response and overall rotor behavior . designers are more concerned with performance loads ,vibration levels , external and internal noise , stability and control , and handling qualities. Proper design of the rotor is critical to meeting the performance specification for the helicopter as a whole. Any small improvement in rotor efficiencies can potentially result in significant increase in aircraft payload capability, maneuver margins or forward flight speed.
The high dynamic pressure found at the tips of a helicopter blade produces a concentration of aerodynamic forces there. as a consequence ,strong vortices form and trail from each blade tip. The vortices are convicted downward below the rotor and form a series of interlocking ,almost helical trajectories. For the most part ,the net flow velocity at the plane of rotor and in the rotor wake itself is comprised of the velocities induced by these tip vortices. For this reason, predicting the strengths and locations of the tip of the vortices play an important role in determining rotor performance and in designing the rotor

The development of the auto gyro and , later ,the helicopter owes much to the introduction of hinges about which the blades are free to move . The most important of these hinges is a flapping hinge which allows the blade to flap, i.e. to move in a plane containing the blade and the shaft. Now blade which is fee to flap experience large Coriolis moments in the plane of rotation and rotation and a further hinge “ called the drag or lag hinge “is provided to relieve these moments . Lastly the blade can be feathered about a third axis , usually parallel to the blade span ,to enable the blade pitch angle to be changed.


The rotor wake consist of a shed vortex sheet and a concentrated vortex at the tip as shown in There is a bound circulation on the rotor blade associated with lift, and conversation of vorticity requires that the circulation be trailed into the wake at blade tip and root. The strong tip vortices are dominant feature in the rotor wake . Vorticity is also shed and trailed into the wake ,creating the vortex sheet, as a result of changes in the circulation on the blade. The trailed vorticity is oriented parallel to the local free stream when it leaves the blade , similar to the tip vortex. Because of the rotation of the blade, lift and circulation are highest near the tip. Both reach a maximum before decreasing rapidly to zero at the tip ,which creates a trailing vorticity of high strength at the edge of a wake to roll-up quickly into a concentrated tip vortex.
Rotating blades encounter tip vortices shed from proceeding blades, which result in a phenomenon known as Blade Vortex Interaction (BVI). As the blades on the helicopter rotate , they disturb the air the pass through , causing a wake that spirals off
the trailing edge of each blade. This is the wake (particularly the vortex from the blade tip ) being hit by the following blade that produces the loud vibrating sound. In order to minimize the sound caused by these collision , an accurate understanding of the blade-vortex interaction is essential. These unsteady loads are also an important factor in the vibration ,noise and performanse of the helicopter.
The helicopter operates in a variety of flight regimes. These include hover, climb, descent, or forward flight. In addition it undergoes maneuvers, which may comprise a combination of these basic flight regimes. In hover or axial flight, the flow is ax symmetric, and the flow through the rotor is either upward or downward. This is the easiest flow regimto analyses
and, at last in principle, the easiest to predict by means of mathematical models . Here ,the rotor has zero forward speed and zero vertical speed (no climb or descent). The rotor flow field is therefore azimuthally ax symmetric. The fluid velocity in increased smoothly as if it is entrained into and through the rotor disk plane. There is no jump in the velocity across the disc, although because a trust is produced, there must be jump of pressure over the disk. All helicopters spend considerable time in hover, which is a flight condition where the they are specifically designed to be operationally efficient. In hover, the main purpose of the rotor is to provide a vertical lifting force in opposition to the aircraft weight. However in the forward flight the rotor must also provide a propulsive force to overcome the aircraft drag.
The preliminary design of the main rotor must encompass the following key aerodynamics considerations :
1) General sizing : this will include a determination of disk loading and rotor tip speed to decide for rotor diameter.
2) Blade platform : this will include chord , solidity , number of blades , and blade twist .
3) Airfoil section of the blade.
The following play an important role in meeting overall performance requirement in hovering.
1) COLLECTIVE PITCH ANGLE : Collective pitch angle changes angle of attack of all blades by an equal amount on unison .The collective pitch controls the average blade pitch. This in turn ,changes the blade lift and the average rotor trust , turning the craft on its vertical axis . As drag on the blade increases with the pitch angle , which requires extra power to the compensate the change in drag . the collective pitch angle is , therefore , the preliminary manifold pressure control.
2) TIP MACH NUMBER : A high rotor tip speed gives the rotor a high level of stored rotational kinetic energy for a given radius and reduces design weight. However , there are two important factors that work against the use of high tip speed : compressibility effects and noise. Compressibility effects manifest as increased rotor power requirements . rotor noise also increases rapidly with increasing tip match number. Experimental work confirm that operation at lower tip mach number is desirable to maximize hovering performance . At higher tip mach numbers performance degrades because to the increasing compressibility losses.
3) BLADE WAKE : The wake from the rotating blade comprises ,in part ,a vortical shear layer or vortex sheet, with a concentrated vortex formed at the blade tip . The vortex sheet comprised of vorticity with vectors aligned mainly normal to and parallel to the trailing edge of the blade. Fig.3 showing wake behind a rotor blade , strength of which depends on the span wise gradient of the lift on the blade(trailed vorticity) , time rate of change of vorticity (shed vorticity). Experiments have shown that blade tip vortices are almost fully rolled up within only a few degrees of blade rotation .

The starting point of any numerical method is the mathematical model , i.e. the set of partial differential or integro-differential equation and boundary conditions . A solution method is usually designed for a particular set of equations. Trying to produce a general purpose solution method, i.e. one which is applicable to all flows, is impractical, if not impossible and , as with most general purpose tools , they are usually not optimum for any one application.
After selecting the mathematical model, one has to choose a suitable discretization method, i.e. a method of approximating the differential equations by a system of algebraic equations for the variables at some set of discrete locations in space and time. There are many approaches, but the most important of which
are: finite difference (FD) , finite volume (FV) , and finite element (FE) methods.
The conservation equation can be written in many different forms, depending on the coordination system and the basis vectors used. For example one can select Cartition , cylindrical, spherical, curvilinear orthogonal coordinate system , which may be fixed or moving . The choice depends on the target flow, and man influence the discretizationn method and grid type to be used.
The discrete location at which the variables are to be calculated are defined by numerical grid which is essentially a discrete representation of the geometrical domain on which the problem is to be solved .It divides the solution domain into a finite number of sub domains ( elements , control volumes etc). Some of the options available are following: A.STRUCTURED (REGULAR) GRID: ---
Regular or structured grid consist of families of grid lines with the property that members of a single family do not cross each other and cross each member of the other family only once . This allows the lines of a given set to be numbered consecutively . The position of any grid point (or control volume) within the domain is uniquely identified by a set of two(in 2D) or three(in 3D) indices e.g.(i,j,k). Structured grids may be of H-,O-,or C-type; the names are derived from the shapes of the grid lines.
In a block structured grid , there is two (or more) level subdivision of solution domain . On the coarse level , there are blocks which are relatively large segments of the domain ; their structure may be irregular and they may or may not overlap. On the fine level (within each block) a structured grid is defined . Special treatment is necessary at block interfaces. Block structured grid with overlapping blocks are something called composite or chimera grids
For very complex geometries , the most flexible type of grids is one which can fit an arbitrary solution domain boundary. In principle , such grids could be used with any discretization scheme, but they are best adapted to the finite volume and finite element approaches. The elements or volume controls may have any shape ; nor is there a restriction on the number of neighbor element or nodes . In practice , grids made of triangles or quadrilaterals in 2D. and tetrahedral or hexahedra in 3D are most often used . Such grids can be generated automatically by existing algorithms . If desired , the grid can be generated automatically by existing algorithms . If desired , the grid can be made orthogonal , the aspect ratio is easily controlled , and the grid may be easily locally refined. The advantage of flexibility is offset by the disadvantage of the irregularity of the data structure . Node location and neighbor connections need be specified explicitly . The matrix of the algebric equation system no longer has regular , diagonal structure; the band width needs to be reduced by reordering of the points . The solvers for algebraic equation system are usually slower than those for regular grids .Unstructured grids are usually used with finite element methods and , increasingly , with finite volume methods . Computer codes for unstructured grids are more flexible. They need not change when the grids is locally refined, or when elements or control volumes of different shapes are used. However, grid generation and pre-processing are usually much more difficult .
Following the choice of grid type , one has to select the approximations to be used in the discretization process. In a finite difference method , approximatations to be used in the discretiazation process. In a finite difference method , approximations for the derivatives at the grid points have to be selected . In a finite volume method , one has to select the method of approximating surface and volume integrals . In a finite element method . one has to choose the shape functions (elements) and weighing functions.
Discretization yields a large system of non-linear algebraic equation . The method of solution depend on the problem . For unsteady flows, methods based on those used for intial value problems for ordinary differential equations( marching in time )are used . At each time step an elliptic problem has to be solved . Steady flow problems are usually solved by pseudo-time marching or an equivalent iteration scheme is used to solve them . These methods use successive linearization of the equations and the resulting linear systems are almost always solved by iterative techniques. The choice of solver depends on the grid type and the number of the nodes involved in each algebraic equation .
Finally, one needs to set the convergence criteria for the iterative methods . Usually, there are two levels of iteration; inner iterations, within which the linear equation are solved , and outer iterations , that deal with the non-linearity and coupling of the equations. Deciding when to stop the iterative process on each level is important , from both the accuracy and efficiency points of view
The solution method should have certain properties. In most cases, it is not possible to analyze the complete solution method. One analyzes the components of the method; if the components do not possess the desired properties, neither will the complete method but the reverse is not necessarily true .The most important properties are summarized below.
1. CONSISTENCY: The discretization should become exact as the grid spacing tends to zero.
2. STABILITY: A numerical solution method is to be stable if it does not magnify the errors that appear in the course of numerical solution process..
3. CONVERGENCE: A numerical method is said to be convergent if the solution of the discretized equation tends to the exact solution of the differential equation as the grid spacing tends to zero.
4. BOUNDEDNESS: Numerical solution should lie within proper bounds.
5. REALIZABILITY: Models of phenomena which are too complex to treat directly ( for example , turbulence , combustion , or multiphase flow ) should be designed to guarantee physically realistic solution .
6. ACCURACY: Numerical solution of fluid flow and heat transfer problems are only approximate solutions.
A. modeling errors, which are defined as the difference between the actual flow and the exact solution of the mathematical model
B.discretization errors , defined as the difference between the exact solution of the conservation equation and the exact solution of the conservation equation and the exact solution of the algebraic system of equation obtained by discretizing these equation, and
C.iteration errors , defined as the difference between the iterative and exact solution of the algebraic equation system.

This is the oldest method for numerical solution of PDEâ„¢s, believed to have been introduced by Euler in the 18th century. It is also the easiest method to use for simple geometries. The starting point is the conservation equation in differential form. The solution domain is covered by a grid. The solution domain is covered by a grid. At each grid point, the differential equation is approximated by replacing the partial derivatives by approximations in terms of the nodal values of the functions. The result is one algebraic equation per grid node, in which the variable value at that and a certain number of neighbor nodes appear as unknowns. In principle, the FD method can be applied to any grid type. However, in all application of the FD method knows to the authors, it has been applied to structured grids. The grid lines serve as local coordinate lines.
Taylor series expansion or polynomial fitting is used to obtained approximation to the first and second derivatives of the variables with respect to the coordinates. When necessary, these methods are also used to obtain variable values at location other than grid nodes (interpolation). The most widely used methods of approximating derivatives by finite differences. On structured grids, the FD method is very simple and effective. It is especially easy to obtain higher-order schemes on regular grids. The disadvantage of FD methods is that the conservation is not enforced unless special care is taken. Also, the restriction to simple geometries is a significant disadvantage in complex flows.
The FV method uses the integral form of the conservation equation as its starting point. The solution domain is subdivided into a finite number of contiguous control volumes (CVs), and the conservation equation are applied to each CV . At the centroid of each
CV lays a computational node at which the variable values are to be calculated. Interpolation is used to express variable values at the CV surface in terms of the nodal (CV-center) values. Surface and volumes integrals are approximated using suitable quadrative formulae. As a result, one obtains an algebraic equation for each CV, in which a number of neighbor nodal values appear. The FV method can accommodate any type of grid , so it is suitable for complex geometries . The grid defines only the control volume boundaries and not be related to a coordinate system. The method is conservative by construction, so long as integrals (which represent convective and diffusive fluxes) are the same for the CVs sharing the boundaries
The FV approach is perhaps the simplest to understand and to program.
The disadvantage of FV method compared to FD schemes is that methods of order higher than second are more difficult to develop in 3D. This is due to the fact that FV approaches require three levels of approximation: interpolation , differentiation , and integration .
The FE method is similar to the FV method in many ways. The domain is broken into a set discrete volumes or finite elements that are generally unstructured; in 2D, they are usually triangles or quadrilaterals , while in 3D tetrahedral or hexahedra are most often used . The distinguishing feature of FE method is that the equations are multiplied by a weight function before they are integrated over the entire domain. In the simplest FE methods, the solution is approximated by a linear shape function within each element in a way that guarantees continuity of the solution across element boundaries . Such a function can be constructed from its values at the corners of the elements. The weight function is usually of the same form .This approximation is then substituted into the weighted integral of the conservation law and the equations to be solved are derived by requiring the derivative of the integral with respect to each nodal value to be zero ; this corresponds to selecting the best solution within the set of allowed functions ( the one with minimum residual ) . The result is a set of non-linear algebraic equation.
An important advantage of finite element method is ability to deal with arbitrary geometries; there is an extensive literature devoted to the construction of grids for finite element methods . The grid are easily refined; each element is simply subdivided. Finite element methods are relatively easy to analyze mathematically and can be shown to have optimality properties for certain type of equations, The principal drawback, which is shared by any methods that uses unstructured grids , is that the matrices of the liberalized equation are not as well structured as for regular grids makings it more difficult to find efficient solution methods .
Fluid dynamics deals with the motion of liquids and gases, which when studied macroscopically, appear to be continuous in structure. All the variables are considered to be continuous functions of the spatial coordinates and time. The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the flow of fluids. They model weather, the movement of air in the atmosphere, ocean currents, water flow in a pipe, as well as many other fluid flow phenomena. The Navier-Stokes equations for irrotational flow, i.e.,
for x u = =0,
Where u = velocity vector field,
= thermodynamic internal energy,
p = pressure,
T = temperature,
= viscosity,
KH = heat conduction coefficient,
F = external force per unit mass,
= density
,and .
The Navier-Stokes equations are time-dependent and consist of a continuity equation for conservation of mass, three conservation of momentum equations and conservation of energy equation. There are four independent variables in the equation - the x, y, and z spatial coordinates, and the time t; six dependent variables - the pressure p, density , temperature T, and three components of the velocity vector u. Together with the equation of state such as the ideal gas law - p V = n R T, the six equations are just enough to determine the six dependent variables. In general, all of the dependent variables are functions of all four independent variables. Usually, the Navier-Stokes equations are too complicated to be solved in a closed form. However, in some special cases the equations can be simplified and may admit analytical solutions (see "Differential Equation" for a very brief introduction).
¢ Incompressible fluid - In fluid dynamics, an incompressible fluid is a fluid whose density is constant. It is the same throughout space and it does not change through time. According to the continuity equation, it also implies u = 0. It is an idealization used to simplify analysis. In reality, all fluids are compressible to some extent.
¢ In viscid or Stokes flow - Viscous problems are those in which fluid friction have significant effects on the solution. Problems for which friction can safely be neglected are called in viscid. The Reynolds number (R=( usL)/ , where us is the mean fluid velocity, and L is the characteristic length, e.g., the cross-section of the pipe) can be used to evaluate whether viscous or in viscid equations are appropriate to the problem. High Reynolds numbers indicate that the inertial forces are more significant than the viscous forces. However, even in high Reynolds number regimes certain problems require that viscosity be included. In particular, problems calculating net forces on bodies (such as the wings on aircraft) should use viscous equations. Stokes flow occurs at very low Reynolds™s numbers, such that inertial forces can be neglected compared to viscous forces.
¢ Steady flow - Another simplification of the equations is to set all changes of fluid properties with time to zero. This is called steady flow, and is applicable to a large class of problems, such as lift and drag on a wing or flow through a pipe.
¢ Boussinesq approximation - In fluid dynamics, the Boussinesq approximation is used in the field of buoyancy-driven flow. It states that density differences are sufficiently small to be neglected, except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids. Boussinesq flows are common in nature (such as atmospheric fronts, oceanic circulation, downhill winds), industry (dense gas dispersion, fume cupboard ventilation), and the built environment (natural ventilation, central heating). The approximation is extremely accurate for many such flows, and makes the mathematics and physics simpler.
¢ Laminar vs. turbulent flow - Turbulence is flow dominated by recirculation, eddies, and apparent randomness .Flow in which turbulence is not exhibited is called laminar It is believed that turbulent flows obey the Navier-Stokes equations. However, the flow is so complex that it is not possible to solve turbulent problems from first principles with the computational tools available today or likely to be available in the near future.
The lift for helicopter can be derived from Eq.(2) of the Navier-Stoker Equations The resulting formula can be reduced to a very simple form if we assume that the air flow velocity in the X-direction ux is much smaller than that in the Z-direction uz (uy = 0). Thus for uz >>ux ,
uz [d(uz)/dz] = -(1/ ) dp/dz ------- (4)
Integrating Eq.(4) yields:
{ [(-uz2)2 - (-uz1)2]} / 2 = (p2 - p1) -------- (5)
where uz is negative as it is pointing toward the negative z direction Computation for the lifting force follows exactly the same line as developed previously. In stationary position, the helicopter's engine provides only the lifting force. According to the principle of angular momentum conservation, the body would turn in the opposite direction of the rotating blades. Fig 06 LIFT FOR HELICOPTER
To stabilize the helicopter, a tail rotate is installed to counteract this trend. By applying more or less pitch angle to the tail rotor blades, it can
also be used to make the helicopter turn left or right. Forward motion is achieved by tilting the spinning rotor in the direction of the flight (see Figure 05). There are many factors related to the rotor blades to limit the maximum speed of a helicopter at about 400 km/h.
The main rotor blade was modeled by using sliding mesh method and tail rotor however was simulated by using the Multiple references Rotating Frame (MRF) method. Using the standard k-‚¬ turbulent flow model , the rotor will be simulated using MRF method and the capability of FLUENT software on simulating helicopter rotor blade in hovering and forward flight will be evaluated . The aerodynamic load (ie ; lift and drag ) of complete helicopter with different rotor configuration was analyzed . By concerning the effect of rotor downwash, the total fuselage drag of the helicopter was calculated based on the equivalent flat plate area and the isolated rotor drag was simulated using MRF method offered by FLUENT. Furthermore, the isolated helicopter rotor blade was simulated from hovering mode to the maximum allowable cruising flight speed as calculated using BET .
During forward flight, the helicopter main rotor blades is dynamically flapping , and pitching about the rotational axis . The lack of expertise to modeling this dynamic motion , the blade is assumed stationary while the fluid is assumed rotating in the reference rotational axis .To ensure the flow encountered by every blade is in actual condition , all the main rotor blade at every azimuth angle was set to the correct pitch and coning angle as calculated using BET this technique will seems equivalent to the dynamically flapping rotor blade rotating at its rotational axis . In this simulation the rotational axis is different correspond to the forward flight speed and the rotor tip path plane (TTP).
The helicopter main rotor blade flapping coefficient (ie ; longitudinal flapping , and a lateral flapping , ),rotor coning angle , and the cyclic pitch coefficient (ie ; longitudinal cycling , and lateral cyclic , ) as a function of blade azimuth angle can respectively be modeled using Eq 1 and Eq 2 [7,8] . By allowing the blade to freely flapping about its rotational axis , this phenomenon permit both the blade at advancing and retreating side to produce equal amount of lift force to encounter the asymmetric of flow field generated in both rotor blade sides.
ß() = - cos n - sin n) Eq1
(r,) = + - cos- sin Eq2
The sectional blade angle of attack can be measured using Eq 3
8( ) =
Eq 3
Where = = , collective pitch , and angle of tip path plane ,
In CFD analysis, the computational domain (or control volume )used is based on the closed-test section wind tunnel. The bigger ratio between computational domain and rotor size was used to minimize the blockage effect or wall boundary effect particularly below the rotating rotor where the airflow induced downstream by the rotor .The appropriate height between rotor and bottom wall boundary is important because it may increase the effect of ground to the rotor performance . For that reason , the helicopter rotor of radius R=5.345m and R=4.80m was simulated in the computational domain with the clearance size of A=5R ,B=10R,C=20R,D=15R,E=10R between rotor and upper wall(A),bottom wall(B),pressure outlet boundary ©.velocity inlet boundary (D) and port and starboard wall boundary(E).The rotor rotational speed , for rotor of 5.345 m and 4.80m radius set to 394rpm and 413.74 rpm respectively .Speed at inlet boundary condition was set zero for static flight condition to the maximum continuous attainable flight speed for every rotor configuration .
In pre-processing stage , both the blade and the computational domain were meshed using tetrahedral grid type . Table 2 depict the size of the grid used for 3-bladed rotor simulation .
Grid Size
Level Cells Faces Nodes Partitions
0 764623 1583651 164266 1
2 cell zones , 7 face zones
The solver setting must be done correctly .In this simulation , the large ratio of computational domain to the rotor diameter was applied . The absolute velocity formulation was chosen where the most of the flow inside the computational domain is irrotational . For residual convergence stabilization purposes, the under relaxation factors for pressure was reduced by 33% and for momentum , turbulent kinetic energy ,and turbulent dissipation were reduced by 44%.

Illustrated in fig07 and fig08 are the contour of velocity magnitude of 3-bladed rotor at hovering flight mode that respectively captured from plan and side view. From fig 1 the expected ax symmetrical velocity distribution was generated by the blade. The ax symmetric on velocity distribution is particularly due to equivalent on the tip speed experienced by every blade at any arbitrary azimuth angle . At forward flight , the inherent asymmetric nature of flow over the rotor disc gives rise to number of aerodynamic problems that ultimately limit the rotor performance. As the flight speed is increased (Fig.09),the air now starts to trail backwards at different skew angle according to the speed of the flight . Skew angle will increase due to increase in the forward flight speed and the rotating rotor starts to produces a roll-up trailing edge vortex both at advancing and retreating side.The blade-blade vortex interaction is clearly visible at high speed of flight and possible to greatly affect the blade at advancinh side by increase the parasite drag.

Fig:07 contour of velocity magnitude of 3 Fig:08 path line of 3 Bladed rotor at forward flight mode
Bladed rotor at hovering mode coloured by velocity magnitude of v=20m/s

Fig09 and Fig10 depict the static pressure contour of rotor at element r/R=0.75 and = position. From these figures, the positive pressure is generated and acting at the lower surface while the negative pressure acting at the upper surface of the blade. The pressure increases when travel from root to the tip of the blade (Fig 11).This is because at hovering mode, the blade element at inboard operates at lower airspeed that the blade element at the outboard portion . The generation of positive pressure at lower surface of the blade element at the outboard portion .The generation of positive pressure at lower surface of the blade implies that there is a positive sign of vertical force or lift force generated by the blade for every flight speed .

Fig. 09: Contour of Velocity Magnitude of 3 bladed Fig. 10: Contour of Static Pressure of Hovering
Rotor (measured at r/R= 0.75). Rotor at Hovering Mode (Side View).
Figure 11: Contour of Static Pressure of Hovering
Rotor (blade at = 180o position).
[1] Bramwellâ„¢s Helicopter Dynamics by A.R.S Bramwell second edition(2001)
[2] Computational Methods for Fluid Dynamics by J.H
Ferziger and M.Peric third edition, Springer
[3] Computational Fluid and Solid Mechanics by Ben.Q.Li(2006),Springer
[4] Strawn, R. C. and Djomehri, M. J. (2001). Computational Modeling of
Hovering Rotor and Wake
Aerodynamics, American Helicopter Society 57th Annual Forum, Washington, DC.
[5] Sides, J., Pahlke, K. and Costes, M. (2001). Numerical Simulation of Flow Around
Helicopter at DLR and
ONERA, Editions Scientifiques et Medicales Elsevier.
[6] FLUENT News 2002
[7] Prouty, R.W., 1986. Helicopter Performance, Stability, and Control, PWS
Engineering, Boston.
[8] Leishman, G., 2002. Principles of Helicopter Aerodynamics. Cambridge
Aerospace Series, United Kingdom.
[9] Wirogo, S., and Ruith, M., 2004. Virtual Blade Model-UGM 2004. 2004 CFD
[10] Xu, M., Mamou, M. and Khalid, M. (2002). Numerical Investigation of
Turbulent Flow Past a Four- Bladed Helicopter Rotor Using k- SST Model,
The 10th Annual Conference of CFD Society of Canada, Windsor.
[11] Caradonna, F. X. and Isom, M. P. (1972). Subsonic and Transonic Potential
Flow over Helicopter Rotor Blades, AIAA Journal, No. 12, pp. 1606-1612.
[12] Chang, I. C.(1984). Transonic Flow Analysis for
Rotors, NASA TP2375.

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