## Evaluating rotor profile design with Turbulent models

*-Bhagavan Hindustani*

Computational Fluid Dynamics (CFD) is one of the most intriguing branches of Engineering. CFD tools enable us to simulate real life fluid flow situations digitally. Right from simulating water flowing through a pipe to simulating the air flow of air around a rocket travelling through space, one can sue CFD. To simulate the designs of different types of wings and rotary systems used in designing a helicopter, CFD analysis forms an integral part. In this article, we will be discussing about the different turbulent models used in the design analysis of an air foil.

Here we evaluate NACA 23012 with a NACA external air foil and their efficiencies using Star-CCM+, one of the most widely used CFD software. We will compare those results to the experimental data acquired by wind tunnel testing. This article is based on the technical paper * ‘Validation of Turbulence Models in STAR-CCM+ by N.A.C.A. 23012 Airfoil*‘. It was presented at the 2009 ASEE Northeast Section Conference held at Bridgeport, Connecticut, USA.

Characteristics

### Various Turbulent Models

Turbulent flows fill the entire universe. They are they reason why clouds form. Star dust is turbulent in nature. Most fluid flows in everyday life are turbulent in nature. Basically turbulent flow is unsteady, consists of swirls or eddies and is diffusive in nature. As the universe is full of turbulent flows, it is natural that all our flying machines fly in a turbulent environment. So turbulence models are used to evaluate different designs for a helicopter rotor.

### What are turbulent models

Turbulent models are mathematical models based on various theories. These theories have strong intuitive backing from Physics. These mathematical models which are in differential / integral forms are simplified using numerical methods. Numerical methods however require tremendous computational requirement. Although modern computing is good enough for simple flows, complex flow computations take time typically a couple of days to 1 week, with high end research computations taking weeks.

#### Choice of turbulent models

Hence the researcher must choose the turbulent models based on the problem being studied and to what extent they intend to study. There is no general turbulent model that can solve all problems as it is well known that the governing differential equation, “Navier-Stokes Equation” still doesn’t have an exact solution. But there are a few models, each of which solves a particular class of problem with a certain acceptable level of accuracy.

That being said, all turbulent models are just closer approximations to real life results.

### Turbulent models in discussion

In this paper, we will compare the results of three turbulence models with the wind tunnel results. For the ease of understanding and simplicity, we will not include many equations. The equations of the turbulent models are too technical and complex for layman, hence not included. Basic equations and a basic description of these models are as below:

- K-Epsilon model
- K-Omega model
- RST model (Reynolds Stress transport)

**K-Epsilon model**

This model is a two-equation model where there are two transport equations. One each for Kinetic energy K and its dissipation rate Epsilon (ε). This model was used quite extensively in the industry for several decades. Nowadays researchers use it for simple flows. Realizable K-Epsilon uses a two layer approach

**K-Omega model**

This model is basically an improvement over the K-Epsilon model. Omega is the term that indicates rate of dissipation, but for rotational flows. The main advantage of this model is the improved performance for boundary layers under adverse pressure gradients.This case uses a SST (Shear Stress Transport) K-Omega model This model basically blends K-Epsilon model for far-field and K-Omega model near the walls. This model is widely accepted in the aerospace industry because of its proximity to the experimental results.

**Reynolds Stress Transport models**

Reynolds stress model is also known as the second-moment closure model. It is called so because, 6 independent stress equations are additionally solved, thus bringing the CFD result much closer and accurate to the actual flow behaviour. This is one of the most complex models of turbulent models. This study uses a Quadratic Pressure Strain RST model in Star-CCM+.

Before proceeding to computations for various configurations, the choice of turbulent model has to be made. By performing computations using different models for different configurations, one can arrive at the right model through comparison. This procedure is discussed below.

**Experimental Setup**

The above figures represent the air foil and the flap at different angles of attack. The air foil experiences different forces while in flight and those forces are as below:

L = Lift force

D = Drag force

N = Normal force to the surface

R = Aerodynamic force

A = Axial force

V∞ = Free stream velocity

α = Angle of attack

The chord length of the NACA 23012 is 20 inches and the chord length of the flap is 4 inches. The air stream velocity is 35.71 m/s and the flap deflections are at 0, 20 and 40 degrees respectively for all the three models.

### Use of finite element modelling

Any simulation requires the splitting the fluid domain into small domains of computation. This activity is meshing. In Star-CCM+, inorder to begin computation for each small domain, one must split them into smaller ones. Below, you can see the meshing.

The choice of mesh comes from standard guidelines and from experience. But hexhedral mesh and quad mesh better than triangular ones for complex flows. This case makes use of hexahedral mesh.

**Results of the comparison**

The following graphs represent the accuracy of each turbulence model in comparison to the wind tunnel testing results at different scenarios.

The above graph show the accuracy of different turbulence models in comparison with the experimental values. It is clear that the RST model is close in terms of accuracy to the experimental values followed by K-Omega SST model.

Even in this case it is quite clear that the RST model once again gives the most accurate results of all the models followed by K-Omega SST model.

Again RST model trumps the other model in terms of accuracy in comparison with the experimental values. But in this case with high angle of deflection, even the RST values varied higher than the values at lower deflection angles. This gives a clear idea that RST model is better than k-Omega SST model for this problem.

### Velocity Contour discussion

It is clear from the above velocity contour that the velocity at the bottom of the air foil is lower than that on the top side. One can observe that at high deflection angles of air flap, creation of a lot of drag force behind the flap takes place. Here the velocity of the air is almost 0. This is why while braking an aircraft, the air flaps are flipped down to generate enough drag and to halt faster.

The whole purpose of this article is to bring the maths and science behind designing the rotors and other lift surfaces of the flying machines. One can observe that a lot of engineering and effort goes into designing and simulating any flying machines before it takes to the skies.

*The original research paper link* : **https://www.researchgate.net/publication/259864767_Validation_of_Turbulence_Models_in_STAR-CCM_by_NACA_23012_Airfoil_Characteristics**