بسم الرحمن الرحيم University of Khartoum Faculty of engineering Mechanical engineering department
Msc Renewable Energy Numerical Techniques
Prepared by: 1. Ahmed Abd Almahmoud Ahmed Yassin 2. Abubaker Mohammed Ahmed Elbashir
Rabi alawal 1432 February 2011
Abstract
The complex commercial computational fluid dynamics software fluent offers a convenient way to model fluid dynamics problems. This study involved two dimensional aerofoil NACA 4412. The purpose was to reproduce published or experimental data for NACA 4412 in the subsonic flow regimes in order to become familiar with fluent, and to establish a verified solution method. We use k-ɛ turbulence models were computed and compared with published or experimental data. For all of the cases considered, the comparisons showed excellent agreement among the results, with the predicted section lift coefficients being within 10% of the measured values.
1. Introduction Advances in computing technology and software have revolutionized the design process of engineering vehicles such as aircraft and automobiles. In the area of fluid dynamics, there are many commercial computational fluid dynamics (CFD) packages available for modeling flow in or around objects. The first step in modeling a problem involves the creation of geometry and meshes with a preprocessor. gambit is a program that can be employed to produce models in two and three dimensions, using structured or unstructured Meshes, which can consist of a variety of elements, such as quadrilateral, triangular or tetrahedral elements. Once a grid has been developed, a solver, such as, multi-physics FEMLAB and FLUENT, is employed to solve the governing equations of the problem. In this investigation fluent was employed, which uses a finite volume scheme to solve the continuity, momentum and energy equations with the associated boundary conditions. The purpose of this investigation was to become familiar with gambit and fluent, develop a solution method and verify it with published data for various two dimensional aerofoil, in subsonic flow simulation involved the NACA 4412. The computed solutions were presented, and were shown to compare very well with published data, with the difference between the predicted and experimental section lift coefficients. 2. Computational Case Studies: Flow regime Subsonic
Aerofoil NACA 4412
Mach number 0.169
Attack angle α 0 2 4 6 8 10 12 14 16 18 20
Flow model k-ɛ turbulence models
We take Renolds number from experimental data Re = 30000. Re = U D/ν. (ν = 15.68*10-6 D = 4*2/1000.
U = (30000*15.68*10-6 )/0.008 = 58.8 m/s.
M = U/c. c = √(T*R*γ) = √(300*287*1.4) = 347 m/s. → M = 58.8/347 = 0.169 Mach Number = 0.169.
3. FLUENT Simulations: First we select aerofoil NACA 4412 by NACA program and insert the data file to gambit by vertex data then we draw the geometry and flow domain and specified the faces in flow domain. A C-grid mesh, presented in Figure1, was used in this simulation. Three meshes with increasing cell density were used to confirm that the predicted results were grid independent for the flow solutions.
Figure 1: C-grid used in the fluent simulation.
The simulation was performed on Toshiba p-c which consisted of 2.0GHz dual-core processor with 3.0GB memory (RAM), was loaded with the Windows vista and 32-bit operating system. The two dimensional precision version of fluent (version 6.3.26) was used, executing the steady implicit coupled solver, which simultaneously solved a system of governing equations (continuity, momentum and energy). Pressure far-field boundary conditions were applied at sea-level conditions (gauge pressure of 101,325 Pa and temperature of 300 K). Air density was treated as an ideal gas. When a turbulence model was used, default values were adopted, with the exception that the turbulence specification method was set to a turbulent viscosity ratio 1 and turbulent intensity 10%. For the solver, the modified turbulent viscosity was set to a first-order upwind discretization scheme. 4. Turbulence Model: The k-ɛ model devised in 1972 is one such model, using two transport equations to represent the turbulent viscosity. It is often used in engineering problems since it performs well for a broad range of turbulent flows. Two variants with better performance are offered in fluent, notably the renormalization group (RNG) and realizable k-ɛ models. The RNG k-ɛ model was adopted due to its improved performance in flow areas where vortices and rotation are present.
5. Simulation results: 1. Pressure distribution(pascal): 1.1.static pressure:
1.2.dynamic pressure:
1.3. Total pressure:
2.Velocity magnitude:
3. Static Temperature Distribution:
4. Total Temperature Distribution:
5. Solution screen for NACA 4412 Aerofoil Properties:
6. Lift Coefficient convergence for angle 14:
7. Drag Coefficient convergence for Angle 14:
8. Stream function (kg/s):
9. Plot of static pressure:
10.Plot of properties (molecular viscosity):
6. NACA4412 Aerofoil Simulation Data for Lift & Drag Coefficient Vs Attack angle (α):
1.6
Drag and Lift Coefficient
1.4 1.2 1 Drag Coefficient 0.8
Lift Coefficient
0.6 0.4 0.2 0 0
2
4
6
8
10
12
14
16
18
attack angle in degree
α
Cd
Cl
0 2 4
0.0276 0.0318 0.0397
0.444 0.6733 0.8857
6 8
0.05124 0.06701
1.07998 1.2488
10 12
0.0873 0.11339
1.383 1.4697
14 16
0.14724 0.19484
1.5015 1.4747
18 20
0.258996 0.3319
1.4002 1.3244
7. Experimental Data for Naca 4412:
20
22
Discussion: The comparisons showed excellent agreement among the results, with the predicted section lift coefficients. Lift coefficient curve has stall angle 14 in simulation and 13 in experimental data and that very well results because the difference is very small. If a drag coefficient gives a negative values that due to the drop of pressure at the end of aerofoil and it is lower than in front part of it. The lift force go to decrease after stall angle . In aircraft application if increases attack angle over stall angle that represent danger. The maximum value of velocity of air at a face of airfoil and decreasing till zero at end of it. Stall angle is a function of Reynolds number and drag coefficient highly dependent on Reynolds number. Stall angle in experimental data 13 degree and in simulation 14 degree and that we obtained in same mach number for both and we obtain a lift coefficient nearly same that in experimental data. We avoid a negative values of drag coefficient by insert X = cos α and Y= sin α ,in report window of fluent.
References: 1. Abbott, I.H., and Von Doenhoff, A.E., Theory of Wing Sections: Including a Summary of Airfoil Data, Dover Publications, Inc., New York, USA, 1959. 2. Daniel Norrison and Eddie ly , fluent simulation of airflow around aerofoil , RMIT university , Australia, 2006. 3.David Heffley , Aerodynamic Characteristics of a NACA 4412 Airfoil, Baylor university,2007.
