Finner Missile CFD Simulation

     This post is about the CFD analysis of a missile in flight at an ambient mach number of 0.5 - 4.5. The missile geometry is shown in Fig. 1. The CAD files for the missile are available to download here.

Fig. 1, Finner missile CAD

     The projectile had dimensions as given in [1]. The simulations are validated with published literature [1, 2]. SolidWorks Flow Simulation Premium software is employed for the simulations. Fig. 2 shows results of C_nα, C_mα and C_d at various Mach numbers compared with the published results [1, 2]. It can be seen that the results are in close agreement with the experimental data.

Fig. 2, Δα = 1°

The mesh has 7,486,591 cells in total. With 417,064 cells on the missile surface. Special mesh refinements are added in the regions of interest i.e. regions with high gradients, the wake and on the surface of the missile. The mesh is shown in Fig. 3.

Fig. 3, The computational mesh

The results from the CFD post processing are presented next. iso-surfaces showing pressure distribution around the missile, coloured by Mach number are shown in Fig. 4. the scale for Fig. 4 ranges from 0 - 6.0.

Fig. 4, CFD post processing

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

[1] Vishal A. Bhagwandin and Jubaraj Sahu, "Numerical Prediction of Pitch Damping Stability Derivatives for Finned Projectiles Numerical Prediction of Pitch Damping Stability Derivatives for Finned Projectiles", Journal of Spacecraft and Rockets, volume 51, number 5, 2014

[2] Jacob Allen and Mehdi Ghoreyshi, "Forced motions design for aerodynamic identification and modeling of a generic missile configuration", Aerospace Science and Technology, volume 77, pp 742-754, 2018

Flapping Aerofoil For Propulsion

     This post is about a 2D NACA 0012 aerofoil undergoing forced flapping motion for propulsion purposes. Heaving motion is achieved by applying a vertical velocity on the aerofoil based on the Eqn. 1. Similarly the pitching motion is achieved by applying a rotational velocity, governed by Eqn. 2.

v_y = 2*π*f_h*H_o*sin(2*π*f_h*t)                                              Eqn. 1

ω = -2*π*f_h*ϑ*sin[(2*π*f_h*t) + 1.5708]                               Eqn. 2

     w.r.t. Eqn. 1-2 reduced frequency is defined as (2*π*f_h*H_o/U∞)), f_h is the frequency of oscillations, while ω, t and ϑ_o represent rotational velocity, instantaneous time and maximum pitching angle. H_o is the heaving amplitude and U∞ is the free stream velocity.

     The flapping motion is achieved by a combination of the heaving and pitching. In this particular simulation, the aerofoil is in the propulsion mode, meaning the feathering parameter χ is less in magnitude than 1.0. Feathering parameter is defined by Eqn. 3.

χ = ϑ/arctan(h0*2*π*f_h/U∞)                                  Eqn. 3

     The boundary conditions employed for the simulation are at Re 1,000, K = 1.41, H_o = aerofoil chord length, χ = 0.5489 and f_h = 0.003391 Hz. The animation of the pressure, vorticity and velocity contours is shown in Fig. 1.

Fig. 1, Flow animation, fluid flow direction is from left to right.

     The results of present simulation are compared with [1]. In terms of maximum lift, a maximum deviation of 5% is observed as compared to [1], as shown in Fig. 2. The maximum lift coefficient for available data is ~4.224 while the maximum lift coefficient from the present simulation is ~4.057. The average thrust produced is within 2% of [1]. Average thrust coefficient per cycle from [1] is 0.9957 while the result from present simulation reveals the thrust coefficient to be 1.0098.

Fig. 2, A comparison of coefficient of lift.

If you want to collaborate on the research projects related to turbo-machinery, aerodynamics, renewable energy, please reach out. Thank you very much for reading.

References

[1] https://doi.org/10.1017/jfm.2017.508

The Fan Car

     The idea to reduce Drag and/or improve Downforce on a vehicle using fans at the rear has been around for decades. Specially in the world of motorsports. Examples include Gordon Murray's BT46 and the T50. Here an explanation is made as to why placing a fan behind a car or a container-carrier truck can be used to improve fuel economy.

     The sample car model is of the renowned Ahmed Body. For validation of the numerical simulation, please refer to this post.

     Fig. 1 shows pressure isosurfaces around the car body both with and without fans installed at the rear. It is clear that the pressure difference between rear and front of the car is more when the fans are not available. More pressure difference results in more Drag and a relatively bad fuel economy.

Fig. 1, T-B; Fan disabled, fan enabled

     Fig. 2 shows cross section view of the car. It can be seen that the the boundary layer is re-energized and as a result the flow separation is significantly reduced by adding a fan at the rear. By adding a fan, the vortices are not only moved away from the rear-end of the car but also have smaller size and less intensity, as shown in Fig. 3.

Fig. 2, T-B; Fan disabled, fan enabled. Red arrows represent direction of airflow

Fig. 3, L-R; Fan disabled, fan enabled

Thank you for reading. Please share my work. If you would like to collaborate on a project please reach out.

The Aerofoil

     Aerofoil, a simple geometric shape that is responsible for heavier than air flight and energy generation from of wind, hydraulic and steam turbines. However, much mystery and confusion exists about how the aerofoil works. Here an explanation is presented about the working of an aerofoil by using computational fluid dynamics and without using any equations.

     The fluid bends and tends to follow the shape of an object placed in its path when the fluid flows around the said object such as an aerofoil. This phenomenon happens due to the Coanda effect. Fig. 1 shows streamlines around an aerofoil at a Mach number of 0.22 and Reynolds number of 5e6. It can be seen from Fig.1 that the fluid starts to bend as soon as it reaches the leading edge of the aerofoil and the fluid follows the shape of the aerofoil.

Fig. 1, The white arrows represent the direction of fluid flow.

     It is well understood that, as a moving fluid bends (changes direction), a pressure difference is created across the flow path. To understand this better, consider a tornado or a typhoon (not the aircrafts). In a tornado, the fluid revolves around a central axis. Consider a point at the center of the tornado. As this point moves towards the circumference of the tornado i.e. away from the center, the pressure increases and vice-versa. This happens due to the curvature of the streamlines inside a tornado. The more the curvature difference, the more the pressure difference across the streamlines.

     In the case of symmetric aerofoils (which have top and bottom half at the same shape), there is no lift generated because the curvature of the streamlines is same on both the suction (top) and pressure (bottom) sides of the aerofoil. The resulting pressure difference between the suction and the pressure sides is zero. This can be seen in the negative coefficient of pressure (-C_p) plot shown in Fig. 2. The coefficient of pressures can be seen to overlap. This plot and subsequent figures and plots are generated using the data obtained from the computational fluid dynamics analysis of the aerofoil. Fig. 3 shows pressure distribution around the aerofoil. It is quite clear that the pressures at the top and bottom surface of the aerofoil are same, hence no lift generation. It is also evident that a pressure difference exists between leading and trailing edge of the aerofoil, hence the presence of the drag force (pressure drag) even at no angle of attack.

Fig. 2, Along the horizontal axis, 0 refers to leading edge.

Fig. 3, Air flow is from left to right.

     But, if the same aerofoil is placed at an angle to the flow, the curvature of the streamlines change, as visible in Fig. 4. Due to the different curvature on the suction and pressure side of the aerofoil, a pressure gradient in created between the suction and pressure side of the aerofoil with lower pressure at the top and higher pressure at the bottom, as shown in Figs. 5. The -C_p plots for the aerofoil at the angle of attack is shown in Fig. 5. The pressure difference is quite clear in both Figs. 5-6.

Fig. 4, The white arrows represent direction of fluid flow.

Fig. 5, Along the horizontal axis, 0 refers to leading edge.

Fig. 6, Air flow is from left to right.

     In the far field, the pressure is uniform, colored by green in Figs. 3, 6. In a case when the fluid is turning, the pressure increases as away from the center of the curvature and vice versa. Looking at the suction side, the pressure will decrease as distance to the center increases. The pressure gradient at the bottom can be explained by the same reason. This difference in pressure is what causes the lift force, as evident from Fig. 5.

     Velocity distribution around the aerofoil at an angle of attack is shown in Fig. 7. It can be seen that the fluid has more velocity at the suction side of the aerofoil as compared to the pressure side. The velocity distribution on the aerofoil without an angle of attack is same on both the pressure and suction sides of the aerofoil and is shown in Fig. 8.

Fig. 7, Air flow is from left to right.

Fig. 8, Air flow is from left to right.

     

     This again, can be explained by the pressure gradient. It can be seen from Figs. 5-6 that the pressure gradient at the suction side of the aerofoil is much more favorable as compared to the pressure side. It can be seen from Figs. 5-6 that the pressure is highest at the leading edge of the aerofoil (stagnation point). The pressure falls to its lowest magnitude past the leading edge of the aerofoil on the suction side. Meanwhile, on the pressure side, the pressure drop is less severe as compared to the suction side. As a result, the fluid faces less resistance on suction side of the aerofoil in comparison with the pressure side. This is the reason why fluid velocity is more at the top as compared to the bottom of the aerofoil, not vice versa. In all the figures, the color red means maximum magnitude and the color blue implies minimum magnitude.

If you want to collaborate on the research projects related to turbomachinery, aerodynamics, renewable energy, please reach out. Thank you very much for reading.