1 RELATED RESEARCHES

6 The computational fluid dynamics (CFD) is currently considered as a vital device for the study of fluid dynamics and developing a new aircraft, Neal M. C 1. Advances had been made in understanding helicopter fluid aerodynamics using CFD, Gordon J.L 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.

7 Perera GAPR et al 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.

8 However, in “CFD analysis of complete helicopter configuration-lessons learnt from the go-ahead project” performed by René S. and George N. B. 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.

9 Christian R. 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.

10 Nik A. et Al 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.

11 Nik A. et al 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.

12 Nik A. R. N. M. and Barakos G. 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.

13 Ulrich K. et al 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.

14 Gupta R. and Agnimitra 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.

15 Khier w. et al 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.

16 Fraunhofer IWES et al 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.

17 Tung, C and Ramachandran K. 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 AERODYNAMICS

18 The 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 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.

19 During 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 15.

20 In hovering flight, Collective pitch angle, tip Mach number and blade wake affect overall performance requirement for hover flight.

21 Collective 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 16.

22 A 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 16.

23 The 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 16.

24 For 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. 15.

25 During 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 14.

26 When 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 horizontal 14

2.3 SOFTWARE REVIEW

2.3.1 SOLIDWORKS

27 Solid 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 WORK

28 From 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.

29 Through 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.

30 We 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.

31 We 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.

32 We can use different kind of constraints while drawing the sketch such as horizontal, perpendicular, vertical, coincident and etc.

2.3.2 ANALYSIS OF OPEN FOAM

33 OpenFOAM 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.

34 There 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.

2.4 APPLYING COMPUTATIONAL FLUID DYNAMIC

35 Computational 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.

36 CFD 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:

(1)

Momentum Equations;

For X direction;

(2)

For Y direction;

(3)

For z direction;

(4)

Energy Equation;

(5)

Where,

x, y and z – three different directions component

? – Density of air

u, v and w – Velocity component in different direction.

37 From 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.

38 When 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.

39 In 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 MODELS

40 To 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. 17

41 Turbulence 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)

42 This 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.

Spalart-Allmaras

K-Epsilon(?) Model

K-Omega(?) Model

43 Here 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-ALLMARAS

44 This 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. 18

2.6.2 K-EPSILON(?) MODEL

45 This 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;

(6)

Equation for turbulent viscosity;

(7)

Turbulent kinetic energy;

(8)

Dissipation ?;

(9)

Where,

C1? = 1.44, C2? = 1.92, C3? = 0.09, ?k = 1.0, ?? = 1.3

2.6.3 K-OMEGA (?) MODEL

46 It 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;

(10)

Turbulence kinetic energy;

(11)

Specific dissipation rate;

(12)

CHAPTER 03

METHODOLOGY

3.1 RESEARCH PROCEDURE

1 Our 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.

3.1.1 SOLID MODELING

2 The 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 GENERATION

3 A 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.

4 Finally, 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 SIMULATION

5 Our 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 MODELS

6 Turbulence 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.

7 We 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.