Zhao, Ma Chuanyan, Zhang

(1. Jiangsu Nanjing Institute of Aeronautics and Astronautics 210016,2. Institute of Equipment Technology of Artillery Air Defense Forces, General Armament Department,

Beijing100012,3. Institute of UAV, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 2 100 16)

In this paper, four key steps of numerical simulation of airfoil using Fluent software, namely numerical modeling, mesh generation, calculation and result analysis, are introduced, and the important role of this software in the calculation of an unmanned airfoil and the relationship between this technology and wind tunnel test technology are illustrated with examples.

Fluent keywords; ; Numerical simulation; Grid division; Calculate and solve; Results In the analysis, the classification number of China Library is V22 1, the document identification number is A, and the document number is1008-1(2008)11-0069-02.

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(1) Introduction

The overall design of aircraft is divided into three processes: conceptual design, preliminary design and detailed design. The process of preliminary design is to refine and optimize the geometric shape, use some computational fluid dynamics (CFD) software for numerical simulation, and conduct wind tunnel experiments to obtain full-scale models and full-scale prototypes. This process occupies a large proportion in aircraft design, but due to the limitation of our existing hardware conditions and the extensive use of calculation software, the model we designed still needs continuous wind tunnel experiments to get more conclusive data, which greatly increases manpower, material resources and financial resources. How can we solve this problem? To solve this problem, we should start from two aspects. On the one hand, we should find a reasonable physical model of the problem we are most concerned about, on the other hand, we should find an accurate calculation model, that is, a reasonable calculation grid to describe the physical model. In this way, how to choose a reasonable software for numerical simulation is the key. Fluent is a popular CFD software package in the world, which is widely used in aircraft design. It can not only predict the changing trend of flight parameters, but also diagnose and analyze the problems in aircraft design, thus shortening the design cycle of aircraft and effectively reducing the design cost. This paper will use Fluent software to simulate and analyze the airfoil of a certain UAV.

(3) the solution process

1. Establish the control equation

The establishment of control equations must be carried out before solving any problems. The unknowns in computational fluid dynamics are (x, y, z), velocity components are (u, v, w), atmospheric pressure is p, density is ρ, and temperature is t in coordinate system. For incompressible fluid, density is a known quantity, which can be solved only by momentum equation, continuity equation and state equation. Momentum equation and continuous equation can be expressed as the general form of governing equation:

? ψφ+div(ρ？ t

→

vφ)= div(γgradφ)+S( 1)

Its expansion form is:

? (ρΦ)? (ρu φ)？ (ρυφ)? (ρw φ)？ φφφ?

? =? Γ+++? +S？ +? Γ? +? Γ? x x y z？ y？ x？ t y z z？

Where φ is a general variable, which can represent the variables to be solved for U, V, W and T; γ is the generalized diffusion coefficient; S is a generalized source term. The terms in equation (1) are transient terms, convection terms, diffusion terms and source terms in turn. For a specific equation, φ, γ and s have a specific form:

(2) The basic principle of computational fluid dynamics and the overall calculation flow of Fluent.

1. Basic principles

The fluid mechanics problem is transformed into algebraic equations that can be solved by computer by discrete method, so as to seek approximate numerical solutions of physical quantities (flow parameters) at discrete points of flow field.

2. Overall calculation process

The overall calculation flow of Fluent is shown in the following figure:

All the governing equations can be handled by appropriate mathematics, and the factors in the equations can be simplified.

The variable, time-varying term, convection term and diffusion term are written in standard form, and then the other terms at the right end of the equation are collectively called source terms, thus becoming a general differential equation. We only need to consider the numerical solution of the general differential equation (1) and write the source program to solve the equation (1), which is enough to solve different types of fluid flow and heat transfer problems. For different φ, as long as the program is called repeatedly, and the appropriate expressions of γ and S, as well as the appropriate initial conditions and boundary conditions, can be solved.

2. Solution method

Date of receipt: July 29, 2008

Author's brief introduction Zhao (1980-), male (man), from Zunhua, Hebei, master's degree, majoring in aircraft design; Ma Chuanyan (1972-), male, from Anqing, Anhui Province, is an engineer in the Equipment Technology Research Institute of Artillery Air Defense Forces of the General Armament Department, and his research direction is aircraft design. Zhang (1966-), male, from Nanjing, Jiangsu Province, vice president of UAV Research Institute of Nanjing University of Aeronautics and Astronautics, whose research direction is aircraft overall design.

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The above equation is solved by discrete method. In this paper, convection term is adopted

The second-order upwind scheme is adopted, and the specific calculation process is as follows:

Angle of attack (degree)

9 7 5 3 1 0 -2

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Lift coefficient (cl)1.1579e+009.7433e-01

7.6 158 e-0 1 5.3755 e-0 1 3. 1093 e-0 1.9659 e-0 1-3.0399 e-02

-2.539 1e-0 1-4.7058 e-0 1-5.7540 e-0 1

Drag coefficient (Cd) 5.2242e-03

3.2343 e-03 1.6402 e-03 7.6930 e-04 3.3006 e-04 2.3602 e-04 3.2 140 e-04 9.2857 e-04 2. 1629 e-03 3.0927 e-03

Figure 1 Schematic diagram of upwind format

In the figure, φφW = 1.5φWφW? 0.5φWW，φe = 1.5φP？ 0.5 Φ w, the diffusion term still adopts the central difference, and finally:

a P φP =a W φW +a WW φWW +a E φE +a EE φEE

In the solution, because of the implicit expression of pressure, it is necessary to use a simple algorithm to correct the pressure. The specific steps are as follows:

(1) Assume initial velocity and pressure field; (2) Calculating the coefficients of the momentum equation by assuming; (3) solving the momentum equation;

(4) solving the pressure correction equation according to the speed in step 3;

(5) Correct the speed and pressure with the result 4, and return to step 2 until the iteration standard is met.

3. Grid division and grid division with boundary conditions (1)

In this paper, Gridgen in Fluent software package is used to generate airfoil mesh, and the steps are as follows:

1) airfoil geometry data reading and Gridgen related parameter setting; 2) Establishment of flow field boundary connector; 3) generating a domain; ;

4) generating a grid block; ; 5) boundary condition setting and output.

Through the above steps, the following grid division diagram is obtained on gridgen:

According to the data in the above table, the curve and polar coordinate curve of airfoil lift coefficient with angle of attack are obtained. As shown in figures 3 and 4. In addition, the pressure coefficient distribution map of pressure along the airfoil can be obtained directly by fluent software. Only the pressure distribution at 5 degrees is given here. It can be seen from the figure that the pressure distribution of the airfoil begins to diverge at 10 degrees, which proves that the stall starts from this angle.

Fig. 3 Pressure distribution on the airfoil surface at an attack angle of 5 degrees Fig. 4 Pressure distribution on the airfoil surface at an attack angle of 10 degrees.

Test data of the airfoil in wind tunnel test;

Fig. 5 Polar coordinate curve of airfoil in wind tunnel test 6 Cl-α curve of airfoil in wind tunnel test.

2. Analysis results

Analysis results: The data obtained by fluent show that when the attack angle of airfoil reaches 10 degree, the parameters of continuous equation and the coefficient of lift and drag can not continue to converge, so the calculated value is limited to some extent and stall occurs. The calculated values are quite different from the experimental parameters, which are basically consistent with the experimental data when there is no stall, and the change trend of lift with drag is also close to the polar coordinate curve obtained by the experiment.

(5) Conclusion

Fig. 2 grid-generated airfoil grid

(2) Setting boundary conditions

The boundary condition of the pressure outlet requires that the static pressure be set at the boundary of the outlet. The static pressure value is set for subsonic flow. In this paper, before the calculation, the incoming velocity of air is set to 50 m/s. The velocity inlet boundary condition is used to define the velocity of the inlet and other related scalar flow variables. The velocity inlet setting is suitable for incompressible fluids. Because the Mach number of incoming flow involved in this paper is very low, we can assume that the fluid is incompressible. The surface condition of the object is the outer surface of the airfoil.

To sum up, Fluent can calculate all airfoil data without stalling, but Fluent calculation is not accurate enough when stalling. Because Gridgen is used to mesh the calculated object, while Fluent is relatively simple and easy to realize. If we choose a more suitable model and arrange a reasonable calculation grid, we may make full use of our existing resources and get the most reliable calculation results. How to achieve the best effect and whether there is a better solution for the time being need further exploration in future practice.

refer to

Chen Zaixin, et al. Aerodynamics [M]. Beijing: Aviation Industry Press, 1993. [2] Yan Hengyuan. Aerodynamic characteristics analysis and engineering calculation of aircraft [M]. Xi 'an: Northwest Institute of Technology.

University of Technology Press, 1990.

Yan Chao, Li Junzhe. Scheme and grid effect in CFD calculation of heat flow.

Study [J]. Journal of aerodynamics, 24 (l), 2006:125-130.

[4] FLUNET Company: GAMBIT 1 TUTO RIAL.

Guide [M]. FLUNET Company, May 1998.

(4) Calculation results and analysis

1. Calculation result

The lift-drag coefficients at various angles of attack are calculated by Fluent, as shown in the following table:

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