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Numerical and experimental study to evaluate aerodynamic characteristics in supersonic ow over a double wedge airfoil is carried out using Fluent software and a supersonic wind tunnel, respectively. The Schlieren visualization method was also used to develop the experimental step of this study. The supersonic wind tunnel reached a proximately a Mach number of 1.8. The result got showed oblique shock waves visualization on double-wedge airfoil and the numerical simulation, the flow behavior as function of Mach number, pressure, temperature and density in the flow field on the computational model. The simulation allowed to observe the shock wave and the expansion fan in the leading and tailing edge of double-wedge airfoil. From the numerical and experimental comparison, an agreement at the shock wave angle and Mach number was observed, with a difference about 1.17% from the experimental results.

It is very relevant to understand the compressible fluid ow and some phenomenon presented in compressible ow turbomachines, blades cascades, aeronautics, aerodynamics and in any fluid motion where exist high ow velocities. Traditionally, supersonic airfoils are classified into two types, namely double wedge and bi-convex airfoils. In internal and external flows at high velocities, normal and oblique shock waves formation are presented. The shock waves generate irreversibilities and discontinuities in the flow, vibration and aeroacoustics noise [

Experimentation was carried out in a supersonic wind tunnel. The test section has a rectangular shape, the top wall has the convergent-divergent profile and the bottom wall plate has 25 pressure taps, see

The double-wedge airfoil dimensions are 38.10 by 25.40 mm with the angle of 6.60. The double-wedge airfoil is showed in

In

On the other hand, with the aim to know the flow behavior in the double-wedge airfoil, an experiment was realized at 1.6 Mach number and the static pressure data were registered at this condition. The static pressure used to compute the Mach number, temperature and density in the wind tunnel test section. These results are showed in

The Schlieren method consists in emitting a ray of light from the light source of 12 volts, this ray passes through a convex mirror and then by a slit, that strikes the concave mirror No. 1. After that this light ray passes through the Schlieren window of the supersonic wind tunnel, where is located the double wedge profile and it is reflected into the concave mirror No. 2. Therefore the light ray is projected on a plane mirror, which is located in front of the screen where resulting image is projected,

Calculations have been performed with a commercial software FLUENT. This code uses the finite volume method and Navier-Stokes equations are solved on a structured grid. The code solves the fully compressible Navier-Stokes equations with implicit formulation. Turbulence is simulated with the standard-Є (two equations) model, type

Pressure tap | P (Pa) | P_{o} (Pa) | T_{o} (K) | ρ_{0} (kg/m^{3}) | P/P_{o} | M | T (K) | ρ (kg/m^{3}) |
---|---|---|---|---|---|---|---|---|

1 | 71,594.11 | 79,593.45 | 294 | 0.943 | 0.899 | 0.392 | 285.24 | 0.874 |

2 | 68,927.66 | 79,593.45 | 294 | 0.943 | 0.866 | 0.458 | 282.16 | 0.851 |

3 | 66,261.22 | 79,593.45 | 294 | 0.943 | 0.832 | 0.519 | 279.00 | 0.827 |

4 | 63,594.77 | 79,593.45 | 294 | 0.943 | 0.799 | 0.575 | 275.74 | 0.803 |

5 | 58,261.88 | 79,593.45 | 294 | 0.943 | 0.732 | 0.683 | 268.93 | 0.755 |

6 | 52,928.98 | 79,593.45 | 294 | 0.943 | 0.665 | 0.786 | 261.65 | 0.705 |

7 | 47,596.09 | 79,593.45 | 294 | 0.943 | 0.598 | 0.889 | 253.83 | 0.653 |

8 | 42,263.19 | 79,593.45 | 294 | 0.943 | 0.531 | 0.996 | 245.36 | 0.600 |

9 | 39,596.74 | 79,593.45 | 294 | 0.943 | 0.497 | 1.051 | 240.83 | 0.573 |

10 | 34,263.85 | 79,593.45 | 294 | 0.943 | 0.430 | 1.167 | 231.08 | 0.516 |

11 | 26,264.51 | 79,593.45 | 294 | 0.943 | 0.330 | 1.365 | 214.18 | 0.427 |

12 | 22,264.84 | 79,593.45 | 294 | 0.943 | 0.280 | 1.482 | 204.31 | 0.380 |

13 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

14 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

15 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

16 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

17 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

18 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

19 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

20 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

21 | 23,598.06 | 79,593.45 | 294 | 0.943 | 0.296 | 1.441 | 207.73 | 0.396 |

22 | 18,265.16 | 79,593.45 | 294 | 0.943 | 0.229 | 1.617 | 193.07 | 0.330 |

23 | 20,931.61 | 79,593.45 | 294 | 0.943 | 0.263 | 1.524 | 200.73 | 0.363 |

24 | 23,598.06 | 79,593.45 | 294 | 0.943 | 0.296 | 1.441 | 207.73 | 0.396 |

25 | 22,264.84 | 79,593.45 | 294 | 0.943 | 0.280 | 1.482 | 204.31 | 0.380 |

^{1}^{a}Patm597 mm de Hg, Temperature 21˚C; ^{b}May 30 2016, 11:00 Time.

density based, steady, 2D space planar, velocity formulation absolute and the special discretization is, gradient: Green-Gauss, cel. Based, flow: Second Order Upwind, modified turbulent viscosity: First Order Upwind. Preliminary results of the study have reported in [

The standard k-

The turbulent kinetic energy and its rate of dissipation are obtained from the following transport equations:

In these Equations (1)-(3), G_{K} represents the generation of turbulent kinetic energy due to buoyancy, Y_{M} represents the contributions of the fluctuating dilation in compressible turbulence to the overall dissipation rate, _{k}_{ }and

The model constants, energy Prandtl is 0.85, wall Prandtl number is 0.85, _{k} and

The degree to which

where

With the aim to visualize the flow, the Schlieren method was used.

^{2}Cp = Specific heat at constant pressure, k = Thermal conductivity, v = Kinematic viscosity, m = molecular weight | ||
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Boundary conditions: | Type grid: structured | Fluid properties |

Double edged wedge: wall | Elements rectangular: 28,620 | Cp = 10050 J/Kg K |

Computational domain: pressure far field | Nodes: 29624 | K = 0.0242 W/m K |

Inlet: 1.524 Mach number, temperature: 200.73 K | V = 1.7894e-05 Kg/m-s | |

Dimensions: | M = 28.966 kg/kg mol | |

Right: 89.82 mm | Top: 317.00 mm | |

Left: 101.60 mm | Bottom: 317.80 mm |

Static temperature behavior is showed in

quently, at the middle part in the model, the flow changes direction entering in an expansion zone where temperature decreases at 183 K for 1.7 Mach number.

^{3} and in the compression zone the density is 0.402 Kg/m^{3}. After this zone the flow changes its direction in the middle part of the model entering in the expansion zone where it accelerates up to get 1.7 Mach and the density decreases to 0.298 Kg/m^{3}. Flow changes its direction again producing the second oblique shock wave in the trailing edge where the density increases to 0.331 Kg/m^{3}.

Mach numbers comparison for the experimental and numerical simulation is showed in

An experimental and numerical study was carried out to know flow behavior at the oblique shock waves in a double wedge airfoil. From flow visualization it was found that the Mach cone angles are for the shock wave at the leading edge of 46˚ and 36˚ in the trailing edge, the shock wave in the leading edge showed a better definition. Concerning the simulation results, the Mach cone angle got for the shock wave at the leading edge form the airfoil is 47˚ and for the outlet shock wave was 37˚. The simulation showed the compression and expansion zones too and the expansion fan. By comparing those results, it was found a difference about 2%.

The authors are grateful to SIP IPN for supporting part of this project through grant 20162113.

Tellez, J.L.G., Hernandez-Martinez, E., Velazquez, M.T., Herrera, J.A.O. and Quinto-Diez, P. (2016) Eva- luating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil. Engineering, 8, 862-871. http://dx.doi.org/10.4236/eng.2016.812078