Experimental and computational study of the aerodynamics of an ahmed body

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EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE AERODYNAMICS OF AN AHMED BODY

MARIA FERNANDA DÁVILA RESTREPO

Graduation Project presented to opt for Mechanical Engineering Degree

Advisor

OMAR DARÍO LÓPEZ MEJÍA, Ph.D.

Co-Advisor

LUIS ERNESTO MUÑOZ CAMARGO, Ph.D.

UNIVERSIDAD DE LOS ANDES ENGINEERING FACULTY

MECHANICAL ENGINEERING DEPARTMENT BOGOTÁ

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List of Tables

Table 1. Wind Tunnel Test Section dimensions ... 9

Table 2. Ahmed Body dimensions of the resultant geometry ... 9

Table 3. DIfferent Domains for computational studies ... 18

Table 4. Domain of the computational case ... 19

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List of Figures

Figure 1. Ahmed Body designed for the study ... 9

Figure 2. Model of the Ahmed Body designed for manufacture ... 10

Figure 3. Front part of the Ahmed body ... 10

Figure 4. Rear part of the Ahmed Body ... 11

Figure 5. Exploded view of the Ahmed Body structure... 11

Figure 6. Front and Rear parts with assembled hoses ... 12

Figure 7. Lower Acrylic assembled with the legs of the model. Legs attached to the MDF base of the Wind Tunnel test section ... 12

Figure 8. Assembly of the front, central and rear parts. ... 12

Figure 9. Final Ahmed Body ... 13

Figure 10. Multitube variable inclination manometer (Barlow, 1999) ... 14

Figure 11. Millimeter paper for multitube manometer ... 14

Figure 12. Multitube variable inclination manometer used in the present study ... 15

Figure 13. Final setup for wind tunnel test ... 15

Figure 14. U- tube manometer ... 16

Figure 15. Domain created in CAD with Ahmed Body inside ... 19

Figure 16. Symmetrical part of the "Wall Ahmed Body" ... 19

Figure 17. Parts created for future boundary conditions ... 20

Figure 18. Densities created to refine the mesh ... 20

Figure 19. Final mesh used for the computational simulation ... 20

Figure 20. Determinant Quality Check of the Mesh ... 21

Figure 21. Drag coefficient for different Reynolds numbers (Bayraktar, 1998) ... 22

Figure 22. Pressure distribution in Ahmed Body (Bayraktar, 1998) ... 23

Figure 23. Pressure Contour on symmetry plane ... 23

Figure 24. Flow Visualization ... 26

Figure 25. Zoom of the rear part visualization ... 27

Figure 26. Zoom of the front part visualization ... 27

Graph 1. Pressure over the polyline exported from CFD Post ... 22

Graph 2. Pressure over the polyline ... 23

Graph 3. Velocity outside the boundary layer ... 24

Graph 4. Pressure Coefficient for the experimental measurements ... 24

Graph 5. Velocity graph from experimental measurements ... 25

Graph 6. Comparison of experimental and computational pressure coefficients ... 25

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Nomenclature

Symbols

𝐶𝑝: 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡

𝑔: 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛

𝑃𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙: 𝑠𝑡𝑎𝑡𝑖𝑐 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 𝑡𝑢𝑛𝑛𝑒𝑙 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑃𝑖𝑡𝑜𝑡 𝑡𝑢𝑏𝑒

𝑃𝑑𝑦𝑛𝑖: 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐴ℎ𝑚𝑒𝑑 𝑏𝑜𝑑𝑦

𝑃𝑠𝑡𝑖: 𝑠𝑡𝑎𝑡𝑖𝑐 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐴ℎ𝑚𝑒𝑑 𝑏𝑜𝑑𝑦

𝑃_{𝑡𝑜𝑡𝑎𝑙}: 𝑡𝑜𝑡𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑃𝑖𝑡𝑜𝑡 𝑡𝑢𝑏𝑒

𝑇: 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 𝑡𝑢𝑛𝑛𝑒𝑙

𝑉𝑖: 𝑤𝑖𝑛𝑑 𝑠𝑝𝑒𝑒𝑑 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑖𝑛𝑡𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑠𝑢𝑟𝑔𝑎𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐴ℎ𝑚𝑒𝑑 𝑏𝑜𝑑𝑦

𝑉𝑡𝑢𝑛𝑛𝑒𝑙: 𝑤𝑖𝑛𝑑 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑢𝑛𝑛𝑒𝑙 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑒𝑠𝑡𝑠

Greek Characters

𝛽: 𝑎𝑛𝑔𝑙𝑒 𝑡𝑜 𝑤ℎ𝑖𝑐ℎ 𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑡𝑢𝑏𝑒 𝑚𝑎𝑛𝑜𝑚𝑒𝑡𝑒𝑟 𝑖𝑠 𝑖𝑛𝑐𝑙𝑖𝑛𝑒𝑑

Δℎ: ℎ𝑒𝑖𝑔ℎ𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑈 − 𝑡𝑢𝑏𝑒 𝑚𝑎𝑛𝑜𝑚𝑒𝑡𝑒𝑟 𝑢𝑠𝑒𝑑 𝑡𝑜 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒

𝜌: 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑎𝑖𝑟 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 𝑡𝑢𝑛𝑛𝑒𝑙

𝜌_𝑎: 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑖𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑡𝑢𝑏𝑒 𝑚𝑎𝑛𝑜𝑚𝑒𝑡𝑒𝑟

𝜌𝑓: 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑡𝑢𝑏𝑒 𝑚𝑎𝑛𝑜𝑚𝑒𝑡𝑒𝑟

𝜎𝐶𝑝: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝐶𝑝

𝜎_𝑃_{𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙}: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑃_𝑎𝑡𝑚_{𝑡𝑢𝑛𝑛𝑒𝑙}

𝜎_𝑃_𝑑𝑦𝑛: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑃_𝑑𝑦𝑛

𝜎_𝑃

𝑠𝑡𝑖: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑃𝑠𝑡𝑖 𝜎_𝑃_{𝑡𝑜𝑡𝑎𝑙}: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑃_{𝑡𝑜𝑡𝑎𝑙}

𝜎𝑇: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡

𝜎𝑉𝑖: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑉𝑖

𝜎_𝑉: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 𝑉

𝜎_Δ_ℎ: 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑜𝑓 Δℎ

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1. Introduction

Nowadays, there is a global concern regarding the pollution generated because of fossil fuels. This concern has increased the interest in research related to the design of ground vehicles. As the years go by, it is a priority that cars become more efficient, avoiding fuel waste. Different researches work on alternative energies, improving engines, and design of better bodywork aerodynamics. Automotive aerodynamics focuses in the study of technological alternatives, in order to improve vehicle’s aerodynamic performance.

The study of automotive aerodynamics is approached using experimental techniques such as wind tunnels and road tests; or using computational techniques like “Computational Fluid Dynamics” (CFD). Experimental approaches can be very expensive, and for that reason, during the design process, CFD presents itself as a reliable solution. On the other hand, Ahmed Bodies have been widely used in the study of the aerodynamics of bluff body, which make experimentation cheaper. Ahmed bodies are simplified geometries, which are simple enough to allow accurate flow simulation and experimentation retaining important features of automobile bodies, such as the slant angle.

A fundamental problem encountered in the solution of aerodynamic problems is predicting the forces and torques that act on vehicles. One way of doing so is describing the flow pattern around the body and, for that purpose; equations of continuity, momentum and energy are used. Nevertheless, for complex geometries, it becomes a very complex problem. Experimental techniques were a couple of years ago, the most common method to analyze fluid behavior. Nevertheless, they had to be carried out in wind tunnels that were big enough to fit a real life size car. Consequently, ground vehicle research was too elevated and, as a result, alternatives such as bluff models and Computational Fluid Dynamics (CFD) were developed. CFD is a tool that uses numerical methods and algorithms to solve and analyze aerodynamic and flow current problems. This tool divides the domain in which the body is submerged in volumetric elements, forming a mesh. CFD has gained strength as one the best alternatives in the research of ground vehicle aerodynamics, due to the fact that it widens the range of operating conditions in which cars can be studied, including those of the atmosphere and those regarding the flow itself. Nevertheless, it has its disadvantages due to the high complexity that certain factors generate, like ground clearance, transient flow and separation regions.

On the other hand, bluff bodies were created to provide experiments that can validate aerodynamic data, using simple geometries characterized by variable parameters, such as the slant angle. One such body is the Ahmed body, a bluff model of simple shape with basic aerodynamic properties of a vehicle. The first experimental measurements of a bluff body were carried out in 1978, trying to evaluate the influence of the slant angle in the range between 0° and 40° at a flow velocity of 40 m/s using a first prototype called Morel Body. Later, in 1984, Ahmed designed the actual “Ahmed Body” and performed tests with the same boundary conditions. Further authors such as Bayraktar then used a scaled model of the Ahmed body (4.7 times larger) to measure pressures and drag forces at full scale Reynolds numbers. Lienhart, in the year 2000, summarized all previous research and measured pressure distribution, velocity, and turbulence properties of the flow around the Ahmed Body. The design of an Ahmed body consists in determining the parameters for such important features, using modeling equations shown further on. Important features are chosen because they represent the region of the flow that generates more contributions to the car’s drag force. Modeling equations make an Ahmed body proportional to the wind tunnel section in which it will be tested. In the case of this graduation project, the wind tunnel used has a cross section area of 1mx1m. The design of an accurate Ahmed Body is crucial in order to avoid wall effects.

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For the present project, in order to design an Ahmed Body, several references were used (Ahmed, 1984) (H. Lienhart, 2000). The slant angle used is 25° and the Reynolds number is 1.17x106_{. In (H.}

Lienhart, 2000) the blockage ratio was 4%, therefore, the one used was 3.5%. For the CFD approach of the present project, a RANS model was used. RANS is a solution model which uses the averaged Navier Stokes equations. A mesh was generated with a combination of tetrahedral and prisms. The prism layer was created around the Ahmed body, with approximately 30 layers and an exponential growth. The final aim of the present study is to evaluate experimentally the aerodynamic behavior of the Ahmed Body and further on to test the ability of a CFD simulation to reproduce the experimental measurements.

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2. Objectives

2.1 General Objective

Design and implement an experiment and a computational simulation in order to study the flow and aerodynamic behavior of an Ahmed body.

2.2 Specific Objectives

 Study the theory of Ahmed Body design and carry out the calculations pertinent to determine its size.

 Design and build an Ahmed body with the parameters calculated.

 Carry out experimental tests on the Ahmed Body within the wind tunnel and measure variables such as pressure and velocity.

 Implement a CFD model in FLUENT in order to carry out simulations of the flow around the Ahmed body.

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3. Methodology

3.1 Experimental Technique

3.1.1 Ahmed Body Design

As it was mentioned before, the research done by (Bayraktar, 1998) and (H. Lienhart, 2000) were used as reference. The most important variable is the wind tunnel’s test section size. In both, Bayraktar and Lienhart, the tunnel used was 1.5 times bigger than the one available at Universidad de los Andes. For this reason, the first thing to do was to scale accordingly the different parameters.

Table 1. Wind Tunnel Test Section dimensions

The model’s dimensions were scaled by 1.5 and the resultant size is summarized in table 2.

Table 2. Ahmed Body dimensions of the resultant geometry

The resultant geometry for a 25° slant angle is shown in figure 1.

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The further step was to design a model that could be built easily and that allowed access to the measurement instrumentation. In order to measure static pressure on the surface of the body, it was necessary to add 4 mm diameter holes throughout the center plane of the model. The center plane was chosen because, in the simulation, a symmetry plan was established in order to save computational time. Those holes are to be connected with hoses to a manometer; therefore the model had to be hollow. On the other side, it had to be considered that the front and rear geometries had to be precise according to the CAD model, and for that purpose they were 3D printed. The resulting model designed for manufacture is shown in figure 2.

Figure 2. Model of the Ahmed Body designed for manufacture

Front and Rear Parts of the Vehicle

For the front and rear parts, it was crucial that the surface was smooth and that the curves of the geometry complied with those of the calculations. For that reason, they were printed out in PLA polymer. The pieces had to be hollow, in order to be able to fit the hoses. Figure 3 shows the design of the front piece.

Figure 3. Front part of the Ahmed body

As it can be seen in figure 3, the front part is divided in half. The reason for this division is that 3D printers are usually not as big as to print a model as big as the Ahmed body. Therefore, the front and rear parts were designed with the help of Autodesk Inventor’s polymer tools, with which lips were created for the pieces to fit together.

In figure 3, one can notice the supports for the hoses along the symmetry plane. They allow the hoses to be in perpendicular position and avoid blockage of airflow. In addition, on the 4 corners, conical holes were made in order to attach the Ahmed body to the rest of the structure.

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Figure 4 shows the rear part of the Ahmed Body. The rear part, as well as the front part, is divided in half to facilitate 3D printing. It also has its supports for the hoses and holes to attach the rear part to the rest of the body.

Figure 4. Rear part of the Ahmed Body

Body’s Central Part

For the central part of the body, aluminum L profiles we cut to form a rectangular box. The walls of the box were made of 4mm-thick acrylic sheets. On the upper acrylic sheet, holes were also drilled along the symmetry plane to fit the hoses for pressure measurement. On the lower acrylic sheet, countersunk holes were made of 2 mm depth, in order to place the legs of the body.

The legs were made hollow with the intention of fitting all the hoses. The floor of the wind tunnel section is made up of MDF fiberboard. On the floor, countersunk holes were also drilled to fit the legs, but this time they were 20 mm deep, for the model not to vibrate with high wind speeds. The result is shown in figure 5.

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Manufacture Process

In figure 6, it is clear how the front and rear parts were assembled and the hoses were inserted.

Figure 6. Front and Rear parts with assembled hoses

In figure 7, one can see the assembly of the lower acrylic sheet with the four legs and the MDF base of the wind tunnel’s test section.

Figure 7. Lower Acrylic assembled with the legs of the model. Legs attached to the MDF base of the Wind Tunnel test section

Figure 8 shows how the front and rear parts were assembled with the central L profiles and further covered with the acrylic sheets.

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Finally, the lower acrylic with the legs were assembled with the rest of the body and all the hoses were inserted in their supports. The result is shown in figure 9. The hoses were left long, in order to be cut just before the wind tunnel test and avoid blockage.

Figure 9. Final Ahmed Body

3.1.2 Wind Tunnel Testing

In order to design the experiment, Barlow’s “Low Speed Wind Tunnel Testing” was used (Barlow, 1999). The common usages of the classification of low speed wind tunnels include those with maximum speed capability up to 135 m/s. The wind tunnel at Universidad de los Andes, TVIM 49-60-1x1 used in the present study, reaches a maximum wind speed of 60m/s. The variables to be measured were:

1. Angular Velocity of fan of the wind tunnel 2. Atmospheric Pressure outside the wind tunnel 3. Temperature outside the wind tunnel

4. Static pressure in the test section of the wind tunnel 5. Total pressure in the test section of the wind tunnel 6. Temperature in the test section of the wind tunnel 7. Static pressure distribution on the Ahmed body surface 8. Static Pressure in 4 points of the wake

Angular velocity of the fan is given by the variable- frequency drive. The equipment used for numbers 2, 4, and 5 for pressure measurement was:

 Pitot Tube:

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Temperature inside and outside the tunnel was measured with:

 Fluke 170 Multimeter with a type K thermocouple with a sensitivity of 41 µV/°C. Range -200 to 1350 °C.

Flow visualization was created with a steam generator of AERLOAB. It is a pressurized box with propylene glycol connected to a resistance rod that heats the oil until it evaporates.

Static pressure on the surface of the Ahmed body was expected to be between 100 and 1000 Pa so a multitube manometer as the one illustrated in figure 10 was used.

Figure 10. Multitube variable inclination manometer (Barlow, 1999)

A multitube manometer was built, in order to measure pressure on the surface of the Ahmed body with higher sensitivity. For high speeds, a 90° angle was used to decrease sensitivity but, for lower speeds were small pressures were expected, a 17° angle was used. The resolution of the manometer was 1 milimeter and the range was from 0 to 300mm. Then, 8 U- tube manometers were placed next to each other and filled with water with density of 998 kg/m3_{. This is shown in figure 11.}

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Finally, 16 hoses were attached to the U-tubes, each of them with their own push in fitting, in order to allow easy change between hoses of the Ahmed Body for experimentation. The multitube manometer built for the present study is shown in figure 12.

Figure 12. Multitube variable inclination manometer used in the present study

Measurement

The final experimental setup is shown in figure 13.

Figure 13. Final setup for wind tunnel test

Five experimental tests were conducted. In each of them, angular velocity of the fan of the wind tunnel was set up to:

1. 600 rpm 2. 650 rpm 3. 750 rpm 4. 850 rpm

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Calculated Variables

For static pressure at each of the points i on the surface, figure 14 shows the schematic. In equation 1, β is the angle of inclination of the manometer base, ρ_f is the density of the fluid used to measure pressure (in this case water and 998 kg/m3_{) and}_ρ

ais the air density (0,88 kg/m3 in Bogota).

Figure 14. U- tube manometer

𝑃_𝑠𝑡_𝑖= 𝑝₂− 𝑝₁= 𝛥ℎ𝑠𝑖𝑛𝛽𝑔(𝜌𝑓− 𝜌𝑎) Equation 1

Further on, density of the air has to be corrected. For that, ideal gas law will be used.

𝜌 =

𝑃𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙

𝑅𝑇 Equation 2

In order to estimate the wind speed outside of the boundary layer it is first necessary to calculate the dynamic pressure for such point.

𝑃

_𝑑𝑦𝑛_𝑖

= 𝑃

_{𝑡𝑜𝑡𝑎𝑙}

− 𝑃

_𝑠𝑡_𝑖 Equation 3

Finally, the wind speed outside of the boundary layer for each of the points is

𝑉

_𝑖

= √

2𝑃𝑑𝑦𝑛𝑖_𝜌 Equation 4

On the other hand, in order to be able to compare the pressure distribution for different tests with different speeds, the static pressure calculations are expressed dimensionless using the pressure coefficient.

𝐶

_𝑝

=

𝑃𝑠𝑡𝑖1−𝑃𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙 2𝜌𝑉𝑡𝑢𝑛𝑛𝑒𝑙2

Equation 5

Where Vtunnel is the wind speed of the test and it is calculated as:

𝑉

_{𝑡𝑢𝑛𝑛𝑒𝑙}

= √

2(𝑃𝑡𝑜𝑡𝑎𝑙−𝑃_𝜌𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙) =

√

2𝑃𝑡𝑢𝑛𝑛𝑒𝑙

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Uncertainty

The uncertainty of difference of height from which we calculate pressure is: 𝜎_Δℎ=𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

2 =

5𝑚𝑚

2 = 0.0025 𝑚

The uncertainty of the angle 𝛽 is:

𝜎_β=𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

2 =

1 ° 2 = 0.5°

There on, there is a propagation of the uncertainty. The uncertainty of the pressure measurement on the body’s surface is:

𝜎𝑃_𝑠𝑡𝑖 = √(𝜎Δℎ 𝜕𝑃 𝜕Δℎ)

2 + (𝜎𝛽

𝜕𝑃 𝜕β)

2

The uncertainty of the static pressure within the tunnel is given by the resolution of the barometer.

𝜎𝑃_{𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙} =

𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

2 =

0.01ℎ𝑃𝑎

2 = 0.5 𝑃𝑎

The uncertainty of the temperature measure within the tunnel is given by the resolution of the multimeter. 𝜎_𝑇 =𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

2 =

0.1°𝐶

2 = 0.05°𝐶 = 0.05𝐾

The uncertainty of the density calculation is then:

𝜎𝜌= √(𝜎𝑃_{𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙}

𝜕𝜌 𝜕𝑃_𝑎𝑡𝑚_{𝑡𝑢𝑛𝑛𝑒𝑙})

2 + (𝜎𝑇

𝜕𝜌 𝜕𝑇)

2

= √(0.5 ∗ 1 𝑅𝑇)

2

+ (273.2 ∗ −𝑃𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙 𝑅𝑇2 )

2

The uncertainty associated with the total pressure measured with the Pitot tube is: 𝜎_𝑃_{𝑡𝑜𝑡𝑎𝑙}=𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

2 = 0.5 𝑃𝑎

Therefore, the uncertainty propagation for the dynamic pressure is: 𝜎𝑃𝑑𝑦𝑛 = 𝜎𝑃𝑡𝑜𝑡𝑎𝑙+ 𝜎𝑃_𝑠𝑡𝑖

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𝜎𝑉𝑖= √(𝜎𝑃_{𝑑𝑦𝑛𝑖} 𝜕𝑉𝑖 𝜕𝑃_{𝑑𝑦𝑛𝑖})

2

+ (𝜎𝜌𝜕𝑉_𝜕𝜌𝑖) 2

= √(

𝜎𝑃_{𝑑𝑦𝑛𝑖}

(

√(𝑃𝑑𝑦𝑛𝑖_𝜌 ) √2𝑃_{𝑑𝑦𝑛𝑖} )₎ 2 + ( 𝜎𝜌 ( −

√(𝑃𝑑𝑦𝑛𝑖_𝜌 ) √2𝜌

)₎ 2

Furthermore, for the uncertainty of the pressure coefficient of each of the i points we first need the uncertainty of the wind speed of the test.

𝜎_𝑃_{𝑡𝑢𝑛𝑛𝑒𝑙} = 𝜎_𝑃_{𝑡𝑜𝑡𝑎𝑙}+ 𝜎_𝑃

𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙 = 1𝑃𝑎

𝜎_𝑉_{𝑡𝑢𝑛𝑛𝑒𝑙} =

√( 𝜎_𝑃_{𝑡𝑢𝑛𝑛𝑒𝑙}

( √(𝑃𝑡𝑢𝑛𝑛𝑒𝑙 𝜌 ) √2𝑃𝑡𝑢𝑛𝑛𝑒𝑙 )₎ 2 + ( 𝜎_𝜌 ( −√(𝑃 𝑡𝑢𝑛𝑛𝑒𝑙 𝜌 ) √2𝜌 )₎ 2 And finally,

𝜎_𝐶_𝑝= √(𝜎𝑃_𝑠𝑡𝑖 𝜕𝐶_𝑝 𝜕𝑃𝑠𝑡𝑖

) 2

+ (𝜎𝑃_{𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙}

𝜕𝐶_𝑝 𝜕𝑃𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙

) 2

+ (𝜎𝜌 𝜕𝐶_𝑝

𝜕𝜌) 2

+ (𝜎𝑉 𝜕𝐶_𝑝 𝜕𝑉𝑡𝑢𝑛𝑛𝑒𝑙)

2

𝜎𝐶_𝑝 = √(𝜎𝑃_𝑠𝑡𝑖 2 𝜌𝑉2 )

2

+ (𝜎𝑃_{𝑎𝑡𝑚𝑡𝑢𝑛𝑛𝑒𝑙} 2 𝜌𝑉2)

2

+ (𝜎𝜌(

2(Pst_i− Patm_tunnel) 𝜌2_𝑉2 ))

2

+ (𝜎𝑉(

4(Pst_i− Patm_tunnel)

𝜌𝑉3 ))

2

3.2 Computational Simulation

3.2.1 Computational Domain

In order to implement a computational simulation of the flow around the Ahmed body, it was first necessary to create the computational domain. Many different options were studied, including the ones shown in table 3.

Table 3. Different Domains for computational studies

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Table 4. Domain of the computational case

3.2.2 Mesh

The mesh was generated using the commercial software Ansys Icem. First, the geometry CAD was designed in Autodesk Inventor, in which, the domain was solid and the geometry of the Ahmed Body was carved into it.

Figure 15. Domain created in CAD with Ahmed Body inside

Further on, this geometry was cut in half in order to save computational cost, as it is shown in figure 16. The CAD geometry was then imported into Ansys ICEM, where different parts were created in order to simplify the process of boundary conditions. The part “Wall Ahmed Body” is shown in figure 16. The rest are shown in figure 17.

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Figure 17. Parts created for future boundary conditions

Additionally, two boxes of densities were created in order to be able to refine the mesh. They were made around the Ahmed Body part and in the near wake. The boxes of densities are shown in figure 18.

Figure 18. Densities created to refine the mesh

The resultant mesh is shown in figure 19.

Figure 19. Final mesh used for the computational simulation

As it can be seen in figure 19, prisms layers were created around the Ahmed Body. The first layer of the prisms was less than a millimeter high and the layers’ size grew exponentially. The purpose of the prism layers was being able to analyze up close the boundary layer. The quality of the mesh was evaluated and 98% of the elements had the best quality as shown in figure 20.

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Figure 20. Determinant Quality Check of the Mesh

3.2.3 Case Configuration

The simulation was run in the commercial software Ansys Fluent. The configuration consists on: 1. Solver:

a. Type: Pressure Based b. Time: Steady

2. Model:

a. Viscous: Spalart Allmaras 3. Materials:

a. Air (𝜌 = 0.88 𝑘𝑔/𝑚3) 4. Boundary Conditions:

a. Inlet: Velocity Inlet 40 m/s

b. Outflow: Pressure Outlet with gauge pressure 0 Pa.

c. Wall Ahmed, Wall Floor, Wall Lat, Wall Sup: Wall No slip d. Symmetry: Symmetry

5. Reference Values:

a. Density: 0.88 kg/m3_.

6. Solution Methods:

a. Pressure Velocity Coupling Scheme: Simple b. Spatial Discretization:

i. Gradient: Least Squares Cell Based ii. Pressure: Second Order

iii. Momentum: Second Order Upwind

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4. Results

4.1 Computational

4.1.1 Pressure

First, simulation results were compared to those in (H. Lienhart, 2000) in order to validate them. Figure 21 shows the reference’s drag coefficient for different Reynolds.

Figure 21. Drag coefficient for different Reynolds numbers (Bayraktar, 1998)

As it can be seen, figure 21 show equation:

𝐶𝐷= 0.2788 + 0.0915𝑒 −𝑅𝑒∙106

1.7971

The Reynolds number of the present simulation is:

𝑅𝑒 = 1.1𝑥106

Therefore, the expected drag coefficient according to the reference is: 𝐶_𝐷_{𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑} = 0,3265

The drag coefficient obtained in the simulation oscillated around 0,323. Therefore, it is considered that the results are valid. Graph 1 shows the pressure distribution in the center of the Ahmed body.

Graph 1. Pressure over the polyline exported from CFD Post

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Graph 2. Pressure over the Polyline

As it is shown in figure 22, from (Bayraktar, 1998), this is the expected pressure distribution for the upper part of the Ahmed body.

Figure 22. Pressure distribution in Ahmed Body (Bayraktar, 1998)

The behavior of the graph is expected to be like that because there is a maximum pressure point, on the stagnation point, followed by a pressure drop completing the front end. Then, there is a stable pressure point, where the geometry is straight and, finally, there is a great pressure drop where the rear end starts, representing the slant surface.

Additionally, the pressure contour on the symmetry plane was exported as it is shown in figure 23.

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4.1.2 Velocity

Graph 3 shows the velocity distribution outside the boundary layer.

Graph 3. Velocity outside the boundary layer

4.2 Experimental

For the experimental data measured, the calculations in 4.1.2 were carried out. After that, the uncertainty could be calculated for each of the measurements. For example, the uncertainty for point 1, when the wind speed of the tunnel was 30,28m/s is shown in table

Table 5. Uncertainty of point 1

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Graph 5. Velocity graph from experimental measurements

4.3 Comparison

The pressure distribution found computationally was also converted into dimensionless with the pressure coefficient in order to compare it with the ones found experimentally. Graph 6 shows the computational distribution as a continuous function and the experimental points with their uncertainty.

Graph 6. Comparison of experimental and computational pressure coefficients

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Graph 7. Velocity graph comparison between experimental and computational data

It can be seen that, for the experimental wind speed of 40,93 m/s, the computational graph (which was run at 40 m/s) fits almost perfectly.

4.4 Flow Visualization

In order to visualize the flow over the Ahmed body, a qualitative smoke test was carried out. Figure 24 shows how the boundary layer becomes thicker with the Z coordinate and also, the behavior in the rear part. It is clear that there is no separation of the flow along the inclined surface of the model due to the small slant angle used.

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Figures 25 and 26 show the rear and front parts up close.

Figure 25. Zoom of the rear part visualization

Figure 26. Zoom of the front part visualization

5. Conclusion

First of all, the main conclusion is that it was possible to build a successful Ahmed body, which could be used as a model for aerodynamic study of ground vehicles at Universidad de los Andes.

After studying the dynamics of the flow around an Ahmed body, both CFD and the wind tunnel tests have results that are in agreement to the ones found in the literature. The wind tunnel model proved to be very reliable, with insignificant uncertainty of approximately 3.21%. However, the multitube manometer is a tedious instrument to operate and, in order to achieve a low uncertainty, a high level of attention was needed. Therefore, in order not to affect the reproducibility of the experiment, a digital barometer with higher sensitivity is needed.

The computational data obtained with the simulation converged very close to the drag coefficient found in previous researches and it is considered satisfactory. Nonetheless, better approximations of the reference values and that of the turbulence intensity of the tunnel could make it more precise.

With the previous taken into account, the present study shows that both alternatives are useful in the study of a ground vehicle’s aerodynamics. CFD and the Ahmed body both represent solutions to the difficulty in studying the aerodynamics of objects of complex geometries or of considerable size. The research of alternatives such as the ones presented here is crucial, as it was mentioned before, due to the fact that conventional methods are so expensive that they make it hard to improve the aerodynamic efficiency of ground vehicles.

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6. Future Work

 For future research, it is suggested that the turbulence intensity is properly studied or measured in order to determine whether this could lower the difference between the computational and experimental data.

 Having already one successful CFD case, this should be used for future experimentation in order to better measure the wake.

 The flow in the lower part of the model should be studied with more detail.

References

Ahmed, S. R. (1984). Some Salient Features of the Time-Averaged Ground Vehicle Wake. SAE.

Barlow, J. R. (1999). Low Speed Wind Tunnel Testing. New York: John Wiley & Sons.

Bayraktar, I. (1998). Experimental and Computational Investigation of Ahmed Body for Ground Vehicle Aerodynamics. . Boston: SAE.

Beckwith, T. G. (2007). Mechanical Measurements. Pearson Prentice Hall.

Castro, N. X. (2012). Estudio Experimental y Computacional de la Aerodinámica de un Vehículo Comercial.

Bogotá.

H. Lienhart, C. S. (2000). Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model).

Erlangen.

Jiyuan Tu, G. (2008). Computational Fluid Dynamics: A Practical Approach. Boston: BK.

Ordoñez Romero-Robledo, C. (1961). Aerodinámica. México, D.F.: Unión Tipográfica Editorial Hispanoamericana.

Princeton. (2013). Drag of Blunt Bodies and Streamlined Bodies. Princeton.