Heaving Airfoil Simulation

This post is about a 2D NACA 0012 heaving aerofoil. Heaving motion is achieved by changing the angle of attack on the aerofoil based on the Eqn. 1.

α_e = arctan[2*π*St_a*cos(2*π*f_h*t)]+ α_i               Eqn. 1

w.r.t. Eqn. 1, α_e is the effective angle of attack, St_a is Strouhal number, f_h is the heaving frequency.

The case S1 and H6 from [1] are compared in the animations below.

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References

[1] https://doi.org/10.1121/10.0001419

Formation Flight Computational Fluid Dynamics

     This is a post about computational fluid dynamics analysis of formation flight.

     The results from an analysis of three unmanned combat aerial vehicles (UCAVs) flying in a V-type formation are presented. The chosen UCAV configuration, shown in Figs. 1-2 and available for download here, is named SACCON (Stability And Control Configuration) UCAV. This configuration is used because of the availability of the geometric and aerodynamic data, used in the validation and verification of the numerical analysis. The SACCON UCAV is designed by NATO's (North Atlantic Treaty Organization) RTO (Research and Technology Group) under Applied Vehicle Task Group (AVT-161) to assess the performance of military aircrafts.

Fig. 1, SACCON UCAV

Fig. 2, Technical drawing for the SACCON UCAV

     The simulation is performed using commercially available computational fluid dynamics code.  The details about the solver and the discretization schemes are presented next. The simulation is performed using SIMPLE-R solver for pressure-velocity coupling. The diffusive terms of the Navier-Stokes equations are discretized using central differentiating scheme while the convective terms are discretized using the upwind scheme of second order. The κ-ε turbulence model with damping functions is implemented to model turbulence. The simulation predicts three-dimensional steady–state flow over UCAVs.

     The Reynolds and Mach number of flow are set at 1e6 and 0.15, respectively. The two trailing UCAVs are placed 3 wingspans behind the leading UCAV. The trailing UCAVs are a wingspan apart. The V-type configuration is chosen because it is the most common observation in birds (author's observation). The V-type formation is shown in Fig. 3. All three UCAVs are at 5° angle-of-attack.

Fig. 3, The V-type formation (top view)

     The boundaries of the computational domain are located at a distance equivalent to 10 times the distance between the nose of the leading UCAV and the tail of the trailing UCAV. The mesh is made of 821,315 cells. Mesh controls are used to refine the mesh in the areas of interest i.e. on the surfaces of the UCAVs and in the wake of all three UCAVs. A cartesian mesh with immersed boundary method is used for the present study. The computational domain with mesh is shown in Fig. 4 while a closeup of the mesh is shown in Fig. 5.

Fig. 4, The computational domain and mesh

Fig. 5, Closeup of mesh, notice the refined wakes of the UCAVs

     For validation and verification, the lift and drag forces from the present study are compared with studies [1-2]. The results are in close agreement with [1,2] As a result of flying in a formation, an improvement in the lift-to-drag ratio of 10.05% is noted. The lift-to-drag ratio of the trailing UCAVs is at 11.825 in comparison with a lift-to-drag ratio of a single UCAV, i.e. 10.745. The lift coefficient is increased by 7.43% while the drag coefficient decreased by 2.174%. The reason(s) to why the efficiency increases will be looked upon later, if ever the author has the time and will power ☺.

     The results from post processing of the simulations are presented in Figs. 6-7. The pressure iso-surfaces colored by velocity magnitude are shown in Fig. 6. While the velocity iso-surfaces colored by pressure magnitude are shown in Fig. 7.

Fig. 6, Flight direction towards the reader

Fig. 7, Flight direction away from the reader

     Thank you very much for reading. If you would like to collaborate on research projects, please reach out.

[1] https://doi.org/10.2514/1.C031386

[2] https://doi.org/10.1155/2017/4217217

Hypersonic Flow over a Two Dimensional Heated Cylinder

     This post is about the simulation of hypersonic flow over a heated circular cylinder, in two dimensions.

     Equation 1 is used as a relationship between Mach and the Reynold number.

M= Re*μ*√(R*T) ÷ d*P*√γ     (1)

     w.r.t. equation 1, the parameters represent the following quantities.

     M     Freestream Mach number at 17.6
     Re    Reynolds number at 376,000
     μ     Dynamic viscosity at 1.329045e^-5 Ns.m^-2
     R     Specific gas constant at 286.9 J.(kg.K)^-1
     T     Freestream temperature 200 K
     d     Cylinder diameter at 5.6730225e^-4 m
     P     Freestream pressure at 101325 Pa
     γ     Specific heat ratio at 1.4
     Tw  Wall temperature of cylinder at 500 K
     Pr    Prandtl number at 0.736

     The boundary conditions were taken from [1]. A comparison with [1] is shown in Fig. 1. Inside Fig. 1, the red dotted line with circles represents the data from [1]. The black solid line represents the data from the present simulation. Within Fig. 1, 0° represents the stagnation point. The velocity, pressure, Mach number and temperature contours are shown in Fig. 2.

Fig. 1 A comparison with previous research [1].

Fig. 2, Top Row, L-R: Velocity and pressure contours. Bottom Row, L-R: Mach number and temperature contours.

The computational mesh and the computational domain with boundary conditions visible are shown in Fig. 3-4, respectively. The computational domain had a size of 20D x 20D. The mesh had 836,580 total cells and 944 cells were located at the solid fluid boundary. Several local mesh controls were employed to capture the shockwave properly.

Fig. 3, The computational mesh.

Fig. 4, The computational domain.

     The solution method is Finite Volume method. SIMPLE-R is the solver employed. Implicit central difference scheme for diffusion terms, second-order Upwind scheme for convective terms and first-order implicit for temporal terms are used. The mesh created uses the Cartesian mesh with Immersed Boundary method.

     Reference:

     [1] https://arc.aiaa.org/doi/10.2514/6.2004-2371 

     Thank you for reading. If you would like to collaborate on research projects, please reach out. I am looking for a PhD position, any guidance would be appreciated.

Flying Wing Design using Computational Fluid Dynamics (Verification and Validation)

     This post is about a transient simulation of the ONERA M-6 flying-wing aircraft with a cross-section of ONERA D airfoil, as shown in Fig. 1.

Fig. 1, The simulated geometry. 

     The mesh had 2,474,614 cells in total with 300,892 cells on the wing surface, as shown in Fig. 2. The computational domain is shown in Fig. 4. The computational domain walls are at a distance equal to ten times the wingspan.

Fig. 2, The computational mesh.

Fig. 3, The computational domain.

     The simulated conditions are taken from [1-4] i.e. a freestream Mach number of 0.8395 at 101,325 Pa and 293.2 K. The angle of attack is 3.06°.

     The lift force from the present numerical simulation is at 19,551.65 N as compared to the lift force of 20,438.53 N as determined by [1-4]. The numerically determined drag force from present simulation is 1,370.88 N as compared to 1,313.24 N, as determined by [1-4].

     The results of lift and drag force from the present simulation are within 4.35% and 4.2% of the results calculated by NASA [4] and [1-3]. Streamlines and pressure surface plot around the aircraft surface are shown in Fig. 4.

Fig. 4, Results.

References

[1] Le Moigne, "A Discrete Navier-Stokes Adjoint Method for Aerodynamic Optimization of Blended Wing-Body, Configurations", PhD thesis, Cranfield University, United Kingdom, 2002.

[2] J. Lee, C. S. Kim, C. Kim, O. H. Rho, and K. D. Lee, "Parallelized Design Optimization for Transonic Wings using Aerodynamic Sensitivity Analysis", AIAA Paper 2002-0264, 2002.

[3] E. J. Neilsen and W. K. Anderson, "Recent Improvements in Aerodynamic Design Optimization on Unstructured Meshes", AIAA Paper 2001-0596, 2001.

[4] 3D ONERA M6 Wing Validation, https://turbmodels.larc.nasa.gov/onerawingnumerics_val_sa.html.

     Thank you for reading. If you would like to collaborate on research projects, please reach out.