Automotive Computational Fluid Dynamics (CFD) Analysis

     This post is about the numerical analysis of an Ahmed body. It was a new experience because of the area between the car's floor and the road which is different from most of the numerical analysis performed in open channel aeronautics and turbo-machinery.

     The numerical analysis was performed using the commercial software, SolidWorks Flow Simulation. The software employs κ − ε turbulence model with damping functions, SIMPLE-R (modified), as the numerical algorithm and second-order upwind and central approximations as the spatial discretization schemes for the convective fluxes and diffusive terms. The time derivatives are approximated with an implicit first-order Euler scheme. Flow simulation solves the Navier–Stokes equations, which are formulations of mass, momentum, and energy conservation laws for fluid flows. To predict turbulent flows, the Favre-averaged Navier–Stokes equations are used.

     The software generates Cartesian mesh using immersed boundary method. The mesh had a cell size of 0.035 m in the far field regions within the computational domain. A fine mesh was need between the road the the car's floor to make sure the interaction of the car's floor with the road was captured accurately. Therefore the mesh between the car's floor and the road was refined to have a cell size of 0.00875 m. Another mesh control was applied around the body to refine the mesh with a cells size of 0.0175 m to capture the trailing vortices. The resulting mesh had 209,580 total cells, among those cells, 31,783 cells were at the solid fluid boundary. The computational domain size was ~1L x 1.12L x 3L where L being the vehicle's length. The computational domain along with the computational mesh is shown in Fig. 1.

Fig. 1 Mesh, computational domain and the boundary conditions.

     The red arrows within the Fig. 1 represents the inlet boundary condition of ambient (free-stream) velocity and the blue arrows represent the outlet boundary condition of the ambient pressure. The green arrows represents the co-ordinates axes direction.

     The results from the numerical analysis were compared with [1-3]. The results are within 10% of the experimental results. The velocity (superimposed by the velocity streamlines) and pressure profiles around the car body at various free-stream velocities is shown in Fig. 2.

Fig. 3 Velocity and pressure plots. From the top, Row 1, L-R; ambient velocity of 30 and 40 m/s. Row 2, L-R; ambient velocity of 60 and 80 m/s. Row 3, ambient velocity of 105 m/s.

     It was a good experience learning about automotive CFD after spending a long time in aeronautic/turbo-machinery CFD. Thank you for reading. Please share my work. If you would like to collaborate on a project please reach out.

[1] F.J.Bello-Millán, T.Mäkelä, L.Parras, C.delPino, C.Ferrera, "Experimental study on Ahmed's body drag coefficient for different yaw angles", Journal of Wind Engineering and Industrial Aerodynamics, Volume 157, October 2016, Pages 140-144.

[2] Guilmineau E., Deng G.B., Queutey P., Visonneau M. (2018) Assessment of Hybrid LES Formulations for Flow Simulation Around the Ahmed Body. In: Deville M. et al. (eds) Turbulence and Interactions. TI 2015. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 135. Springer, Cham.

[3] A. Thacker, S.Aubrun, A.Leroy, P.Devinant, "Effects of suppressing the 3D separation on the rear slant on the flow structures around an Ahmed body", Journal of Wind Engineering and Industrial Aerodynamics, Volumes 107–108, August–September 2012, Pages 237-243.

Vertical Axis Wind Turbine Computational Fluid Dynamics Analysis

     This post is be about the validation and verification of the computational fluid dynamics analysis of a three blade vertical axis wind turbine. The turbine had a diameter of 2 m with each blade being 1 m tall. The blades had an NACA-0018 airfoil cross section.

     The computational fluid dynamics analysis employed the κ-ε turbulence model with damping functions as the turbulence model, SIMPLE-R as the numerical algorithm. The spatial discretization schemes for the convective fluxes and diffusive terms used are the second order upwind and central approximations, respectively. An implicit first-order Euler scheme is employed to approximate the time derivatives.

     The Cartesian computational mesh with immersed boundary method had a total of 769,357 cells. Among those 769,357 cells, 166,188 cells were around the turbine blades. Mesh controls were employed to refine the mesh near the turbine blades. A time step of 3e^-3 was employed. The computational domain inlet was 1.5 D away from the turbine and the outlet was 3D away. The computational domain walls on the sides were 1D x 1.5D, where D represents the turbine diameter. The mesh and the computational domain are shown in Fig. 1. The vertical teal arrow represents the force of gravity, the curved teal arrow represents the direction of turbine rotation. The dark blue arrow represents the direction of free stream velocity.

Fig. 1, Mesh and computational domain.

     The simulations ran at a tip-speed ratio of 1.87 at a wind speed of 4.03 m.s^-1. The velocity distribution around the turbine after 4 revolutions is shown in Fig. 2. Validation of the numerical analysis was carried out using [1]. The results of power produced by the turbine were with in 4% of the experimental results [1]. An animation of the numerical analysis is also shown.

Fig. 1, Flow field around the turbine.

     Thank you for reading. If you would like to contribute to the research, both financially and scientifically, please feel free to reach out.





[1] Yi-Xin Peng, You-Lin Xu, Sheng Zhan and Kei-Man Shum, High-solidity straight-bladed vertical axis wind turbine: Aerodynamic force measurements, Journal of Wind Engineering and Industrial Aerodynamics, January 2019.

High Camber Wing CFD Simulation

     This post is about the numerical simulation of a high camber, large aspect ratio wing. The wing had an aspect ratio of 5:1. The Reynolds number of flow was 500,000. The wing was at an angle of attack of zero degree. The aero-foil employed had a cross section of NACA 9410.

     The software employed was Flow Simulation Premium. A Cartesian mesh was created using the immersed boundary method. The mesh had 581,005 cells. Among those 581,005 cells, 55,882 were at the solid-fluid boundary. A time step of ~0.00528167 s was employed*. The domain was large enough to accurately trace the flow around the wing without any numerical or reversed flow errors. The software employs κ-ε turbulence model with damping functions, SIMPLE-R (modified) as the numerical algorithm and second order upwind and central approximations as the spatial discretization schemes for the convective fluxes and diffusive terms. The time derivatives are approximated with an implicit first-order Euler scheme.

     The mesh is shown in Fig. 1. The four layers of different mesh density are also visible in Fig. 1, the mesh is refined near the wing surface using a mesh control. The velocity around the wing section is shown in Fig. 2, using a cut plot at  the center of the wing. In Fig. 2, the wing body is super imposed by pressure plot. The velocity vectors showing the direction of flow are superimposed on both the wing body and the velocity cut plot.

Fig. 1, The computational domain.

Fig. 2, The velocity and pressure plots.

     The results of the simulation was validated against the results from XFLR5 software. XFLR5 predicted slightly higher lift and slightly less drag on the wing for same boundary conditions because the XFLR5 simulations were inviscid.

     Thank you for reading. If you would like to contribute to the research, both financially and scientifically, please feel free to reach out.

     *Time step is averaged because of the fact that a smaller time step was employed at the start of the numerical simulation.

Improvement of the Volume Flow Rate Through a Blower Fan

     In this post, an improvement in the volume flow rate through the blower fan assembly made are presented. The only thing changed in the blower fan was the cross section of the fan blades. In the previous version, the blade cross section resembled a flat plate with fillets at the leading edge. The trailing edge in the previous design was blunt. In the modified design, there aero-foils were selected, namely NACA 9410, NACA 9420 and the NACA 9430. All the other parameters were kept the same to the previous case. The CAD models of the modified fan blades are shown in Fig. 1.

Fig. 1, Fan blade geometries.

     The velocity contours are shown in Fig. 2 while the pressure contours are shown in Fig. 3, super imposed with velocity vectors and the computational mesh. The volume flow rate was the most for the fan with blades having cross-section of NACA 9410 aero-foil, followed by the fan with blades having cross-section of NACA 9420 and the NACA 9430 cross sections, respectively.

Fig. 2, Pressure contours. Row 1, L-R; fan with the NACA 9430 and NACA 9420 cross sections. Row 2, fan with NACA 9410 cross sections.

Fig. 3, Velocity contours. Row 1, L-R; fan with the NACA 9430 and NACA 9420 cross sections. Row 2, fan with NACA 9410 cross sections.

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

Computational Fluid Dynamics Analysis of a Blower/Centrifugal Fan: Update 01

     In this post the results from a CFD analysis of a blower fan are presented. The fan had a diameter of 66 mm and a height of 12.57 mm. The fan's rotational velocity was at 10,000 rpm. The CAD model is shown in Fig. 1.

Fig. 1, CAD Assembly of the Blower Fan.

     The simulations were completed in SolidWorks Flow Simulation Premium code. The code employs immersed boundary method to create a Cartesian mesh. The sliding mesh feature was employed to simulate the rotation of the fan at atmospheric conditions. The code employs κ-ε model with Two-Scales Wall Functions approach as the turbulence model. The numerical algorithm implemented is the SIMPLE-R, modified. The second-order upwind discretization scheme is used to approximate the convective fluxes while the diffusive terms are approximated using the central differencing scheme. The time derivatives are approximated with an implicit first-order Euler scheme.

     The numerical model for the fan had 816,994 cells of which 209,421 cells were at the solid-fluid interface. Two mesh controls were employed to refine the mesh near the blades of the fan and at the boundary of the stationery and the rotating domains. The results were indeed, mesh independent. Due to the fact that this was an internal flow problem, domain independence test was not applicable. The mesh and the computational domain is shown in Fig. 2. The curved teal arrow represents the direction of rotation of the fan. The blue arrows represent the pressure boundary conditions at the inlet and at the outlet of the fan assembly. The straight teal arrow represents the force of gravity (the arrow is inverted).

Fig. 2, The mesh and the computational domain.

     The pressure and velocity plots are shown in Fig. 3-4.

Fig. 3, Pressure contours.

Fig. 4, Velocity contour

     Thank you very much for reading. If you would like to collaborate on research projects or want a tutorial for the setup of the numerical simulations such as this one, please reach out.

Update 01

     CAD files are available here.

Computational Fluid Dynamics Analysis of a Symmetrical Wing, Update 01

     This post is about the computational fluid dynamics analysis of a wing. The wing analyzed employed the NACA 0021 section throughout. The wing had a span of 4 m and a chord length of 1 m. The Reynolds number was kept at 3,000,000. The software employed was SolidWorks Flow Simulation Premium.

     The mesh had a total of 385,064 cells of which 84,826 cells were in contact with the wing surface, as shown in Fig. 1. The results are, indeed, mesh independent. Mesh controls were employed to refine the mesh near the wing surface. The computational domain employed was of cylindrical shape.

 

Fig. 1, The computational mesh around the wing.

 

     The velocity variation at various angles of attack around the wing cross-section is shown in Fig. 3 while the pressure variation on the wing surface is shown in Fig. 4. The results were validated against experiments conducted by [1].

 

Fig. 2, Velocity variation around the wing at 0-25 degree AOA, 5 degree increments.

 

Fig. 3, Pressure variation at the wing surface at 0-25 degree AOA, 5 degree increments.

     The purpose of this blog is maintain my online portfolio. I did this analysis because I realized I haven't written anything of this nature before. All of my previous simulations and/or blog entries were from the propulsion, renewable energy and turbo-machinery areas.
 

     Update 01

     CAD files are available here.

 

    
     Thank you for reading. If you would like to collaborate on research projects, please feel free to contact.

     [1] Fernando A. Rocha, Adson A. de Paula, Marcos d. Sousa, André V. Cavalieri, and Vitor G. Kleine, "Lift enhancement by wavy leading edges at Reynolds numbers between 700,000 and 3,000,000," Proceedings of the 2018 Applied Aerodynamics Conference, AIAA AVIATION Forum, Atlanta, GA, 2018.

     https://doi.org/10.2514/6.2018-3816

SolidWorks Flow Simulation: Internal Variable Velocity Inlet Boundary Condition

     This post is about an internal computational fluid dynamics simulation. The Simulation was performed in a pipe with a diameter of 1 in. The length of the inlet was 8 in away from the intersection. The two outlets were 4 in away from the intersection and were at an angle of 120° from the inlet, respectively. The flow entered the pipe in pulses with a period of 0.2 s. The peak velocity was at 2 m/s and the minimum velocity was kept at 0 m/s. This simulation setup can be analogous to the opening/closing of an IC engine valve simulation or simulation of cardiovascular systems etc.

     The part used in the simulation and the simulation setup is available here, as shown in Fig. 1.

Fig. 1, Part geometry.

 

     The mesh is shown in Fig. 2. The simulation assumed 2D simplification, to save time and computational resources. The mesh had a total of 15,512 cells. A simulation time step of 0.00625 s was employed.

 

Fig. 2, The computational mesh.

 

     The velocity profile at 0.9 s is shown in Fig. 3.

 

Fig. 3, Velocity Streamlines colored by velocity magnitude, superimposed by velocity vectors.

 

     An animation of the results is shown below. The results are, indeed, mesh and time independent.

 

 

     Thank you for reading. Reach out to collaborate in research projects.