RANS Simulation of the Turbulent Flow Field in the Vicinity ... - wseas.us

NEW ASPECTS of FLUID MECHANICS, HEAT TRANSFER and ENVIRONMENT

RANS Simulation of the Turbulent Flow Field in the Vicinity of the Ahmed Reference Car Model Khalid M. Saqr

Md Nor Musa

High-Speed Reacting Flow Laboratory, Faculty of Mechanical Engineering Universiti Teknologi Malaysia, 81310 Skudai Johor Darul'Takzim, MALAYSIA [email protected]

Department of Thermofluids, Faculty of Mechanical Engineering Universiti Teknologi Malaysia, 81310 Skudai Johor Darul'Takzim, MALAYSIA [email protected] considers some application of wind turbine to harness the energy dissipated in this flow field. The vast majority of literature available on studying the flow around passenger vehicles is exclusively concerned about optimizing the drag coefficient and the vehicle frontal area [4-11]. The scope of the present study is rather different; we are concerned about the characteristics of the flow in the vicinity of the vehicle to explore the possibility of recovering the waste kinetic energy due to the aerodynamic drag. To give an indication on the order of magnitude of such energy, equation (1) has been solved for different values of frontal area and drag coefficient (i.e. different car models) and plotted in Fig. 1 against vehicle speed for a distance of 1 km.

Abstract— This paper describes the results of a RANS based numerical simulation of the flow field around the Ahmed references car model in the cruising conditions. The main objective of this analysis is to qualitatively identify the availability of kinetic energy around a cruising vehicle. The spatial gradients of pressure, turbulence and velocity fields are reported in the three dimensional, time independent Cartesian space around the car model. The region where the flow kinetic energy reaches to maximum values were identified and were found to be near to the turbulent wake downstream the vehicle. Keywords-Ahmed car model; CFD; pressure energy; kinetic energy; turbulence energy

-1

Vehicle Speed (m.s )

INTRODUCTION

250 200

C ci en t(

d

0.270

100

)

150

0.265

50

0.260 1.6

1.5

1.4

Vehic le

0.255 1.3

Fron tal

1.2

1.1

1.0

Area , A (m 2 f )

0.9

0.250

Figure 1. Energy loss in the aerodynamic drag vs.

A f , Cd and vr

The energy loss in aerodynamic drag is dissipated from the pressure energy, resulting from the vehicle motion, to the viscosity level of surrounding air through turbulent wakes that form and travel in the vicinity of the vehicle. As indicated in Fig. 1, the order of magnitude of the aerodynamic energy of a vehicle ranges in between 50 and 400 KJ for speeds corresponding to 65 km/h and 94 km/h, respectively. However, this amount of dissipated energy becomes enormous if one thinks about a fleet of different vehicles traveling continuously along a highway, for instance. Thus, vertical-axis wind turbine units, installed on the roadsides of lengthy highways, would have the potential

A f is the vehicle frontal projected area,

Cd is the coefficient of drag for the vehicle, vr is the relative vehicle velocity and d a is the distance traveled by the vehicle. The focus of the present study is on the characteristics of turbulent flow around vehicles, where the energy represented by U a is lost. The significance of such study arise when one

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300

0

where U a is the energy required to overcome the aerodynamic drag,

350

Aerodynamic

Energy (KJ)

400

Co ef fi

The energy required by different classes of passenger vehicle to counter the aerodynamic drag is approximately in between 13% and 23% of the vehicle's total energy demand according to a recent investigation by Burgess and Choi [1]. Although there are countless researches, driven by the global trends of oil price, to cut down such energy requirements, it is almost impossible for these researches to achieve their objective with the growing consumer demands for larger interior spaces in passenger vehicles. Modern semi-vans, mini busses, and FWD passenger vehicles have lower aerodynamic drag coefficient, except in the same time they have larger vehicle frontal area. This means that the energy required to overcome the aerodynamic drag (in both windy and windless driving conditions) is almost constant. This can be evidently shown by observing the following equation, which was proposed by Hucho [2]and Redsell et al [3]: (1) U a = 0.5 ρA f Cd vr2 d a

18 19 20 21 22 23 24 25 26

Dr ag

I.

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to harvest a significant amount of waste kinetic energy and probably use it for road illumination or infrastructure. After the objectives and significance of the present study were highlighted, a brief literature review will precede the description of the mathematical formulation and the simulation model of the flow field. Then, the results are presented and discussed in the context of the above introduction in the last section of the paper.

where U i is the mean velocity tensor, xi is the position vector, u ′j ui′ is the temporal average of fluctuating velocity,

P is the mean static pressure, μ is the molecular viscosity and

∂xi ⎠ The local air density was calculated based on a fixed value for the operating pressure, which equals to the ambient pressure. In other words, the air flow was assumed to be incompressible. This assumption was made after ensuring the inlet Mach number is less than 0.3 in all cases [32]. The equations of the standard k − ε turbulence model, in tensor notation, are [31]: Equation for the turbulence kinetic energy ⎡⎛ ⎤ ∂U i ∂k ⎞ (3) ρU j = τ ij − ρε + ∂ ⎢⎜⎜ μ + μT ⎟⎟ ∂ε ⎥ ∂x j ∂xi ∂x j ⎣⎢⎝ σ k ⎠ ∂x j ⎦⎥

LITERATURE REVIEW

II.

A careful glance at the recent literature on the simulation of flow around passenger vehicles reveals several noteworthy elements, which are significant while considering the objectives of the present study. These elements are briefly summarized as: A. Standard Car Models Several standard car models are used to represent the effect of geometry on the aerodynamic characteristics of vehicles. The most well established standard car model is the Ahmed car model [11-15]. This model has been extensively investigated by experiments and numerical simulation. Thus, it was chosen to represent an arbitrary car model in the present study.

2 ⎝ ∂x j

where

σk

τ ij

is the Reynolds stress,

μT

is the eddy viscosity,

is a closure coefficient that has a unity value, and

ρU j

∂ ∂x j

⎡⎛ μT ⎢⎜⎜ μ + σε ⎣⎢⎝

⎞ ∂ε ⎤ ⎟⎟ ⎥ ⎠ ∂x j ⎦⎥

(4)

2 The eddy viscosity is expressed as μ T = ρC μ k

ε

(5)

Values for the closure coefficients are based on Launder and Spalding [33]. IV.

SIMULATION MODEL

A. Geometry and Flow Configurations

MATHEMATICAL MODEL

The flow field around the Ahmed car model was represented by the steady-state Reynolds averaged Navier Stokes (RANS) equations. These equations can be written in the Cartesian tensor form as [31]: ∂U i (1) =0 ∂xi

(

)

∂ ∂P ∂ (2μS ij ) U jU i + u ′j u i′ = − + ∂x j ∂xi ∂x j

(2) Figure 2. Geometry and dimensions of Ahmed car model

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is

ε ∂U i ε2 ∂ε − Cε 2 ρ = Cε 1 τ ij k k ∂x j ∂x j +

C. Validation of Computational Techniaues Several studies validated RANS computational approach with different variants of the k − ε turbulence models in simulating the flow around Ahmed car models [27-30]. The fundamental problem of turbulence was quite obvious in such validations where no specific turbulence model showed optimum prevalence over other models in describing the flow field.

ρ

ε

the dissipation rate. Equation for the dissipation rate of turbulence kinetic energy

B. Turbulence Modeling The computational domain of the flow around passenger vehicles, when treated in full scale, is relatively large. Thus, the most computationally economic class of turbulence models is the eddy viscosity models. This approach in considering the turbulence flow of the case in hand is quite evident in both classical [16-19] and modern [4, 9, 20, 21] CFD literature. Some recent trends, inline with the rapid growth of computational resources in personal computing units, include the application of higher order closure turbulence models [22, 23] and some filtering approaches such as LES [24, 25]and DES [13, 26].

III.

⎛ ⎞ S ij is the strain rate expressed as 1 ⎜ ∂u i + ∂u j ⎟ . ⎜ ⎟

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The dimensions of the Ahmed car model is showin in Fig. 1. The slant angle selected for the present simulation is 28o. These dimensions are reported in [11, 34-37]. The Flow was allowed to flow in the direction shown in Fig. 1 with a total velocity corresponding to a vehicle speed of 80 km/h. The flow domain dimensions were set as in Fig. 2. The height of the flow domain was set to be approximately ten orders of magnitude of the height of the car model, while width and length of the flow domain were set to be four times of their corresponding model dimensions. The total volume of the flow domain was 4.33 m3.

generated due to the relative car movement. While on the side walls of the car model, the static pressure takes negative values due to the high-velocity of air, as it is detailed in the next section.

Figure 3. A schematic of the flow domain

B. Three Dimensional Spatial Descretization The flow domain was discretized to 2.62×106 tetrahedral grid cells, with a minimum and maximum volumes of 4.26×10-8 m3 and 8.85×10-6 m3, respectively. The unstructured variable density grid was applied designed to let the smallest cells to be adjacent to the car model, and the larger cells to be located near to domain boundaries.

Figure 4. Static pressure contours at a height of 220 mm. Units in Pa

B. Dynamic Pressure The dynamic pressure can be mathematically represented as:

1 2 ρv (2) 2 where ρ and v is the fluid density and the flow velocity, PDyn =

C. Boundary Conditions The inlet and outlet boundary conditions were set to constant, fully developed inlet velocity and ambient pressure, respectively. The lower flow boundary and Ahmed car model walls were assigned a no-slip boundary condition, on the contrary from the upper and side boundaries of the flow domain which were assigned a free-slip boundary condition.

respectively. The kinetic energy can be expressed as:

1 (3) E K = mv 2 2 where m is the mass of the car model. Thus, the dynamic pressure around the car model can be taken as a meaningful representation of the kinetic energy distribution of the flow field. The dynamic pressure is plotted on an XZ plane in Fig. 5. The region where such pressure is at maximum value is bounded by the rectangle A in Fig. 5. While, in contrast, the region downstream the vehicle is characterized by minimum dynamic pressure. This is because of the highly turbulent wake in such region which dissipates the pressure energy.

D. Numerical Details A decoupled pressure-velocity, general purpose finite volume CFD solver was used to compute the flow field variables. The semi implicit method for pressure linked equations (SIMPLE) was used to decouple the pressure and velocity fields.

V.

RESULTS AND DISCUSSION

The solution convergence criteria was reached when the residuals of the momentum equation was reduced four orders of magnitude. The problem was solved on a 6 GB of RAM on a Core2Due Intel processor and a 64 bit Windows® operating system. The solution time was estimated to be approximately 13 hours. In this section we discuss the spatial distribution of pressure and velocity components at different 2D planes that describe the 3D flow field. A. Static Pressure The XZ contours of static pressure around the Ahmed car model are plotted in Fig. 4 at a height of 220 mm of the ground boundary. The regions where the static pressure are negative (i.e. vacuum) are indicated by green and sub-green colors. The region directly in front of the car model has a high positive static pressure, this is due to the pressure wave

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Figure 5. Dynamic pressure contours at a height of 220 mm. Units in Pa

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C. Turbulence Kinetic Energy Fig. 6 shows the turbulence kinetic energy (TKE) around the vehicle in the XZ plane at a height of 220 mm. The turbulent wake downstream the vehicle is quite obvious, and the shape of such wake is in good agreement with such available in literature. The turbulent wake is close to the region of maximum dynamic pressure (i.e. maximum kinetic energy) which is denoted by the region A in Fig. 5. In such region, the kinetic energy is dissipated to the viscosity level of the fluid through the turbulent eddies. Thus, it can be assumed that the drag force on an arbitrary object located in this region should be at maximum value.

Figure 8. Y Velocity distribution at different XY planes. Units in m.s-1

Figure 6. XZ Spatial distribution of TKE. Units in m2.s-2

D. X,Y and Total Velocity Distributions As another indication on the distribution of kinetic energy lost in the aerodynamic drag of the car model, the X and Y velocity components, as well as the total velocity are depicted on different planes in Fig. 7-9.

Figure 9. XZ Total velocity contours at a height of 220 mm. Units in Pa

The velocity contours in Fig. 7-9 show that the velocity increases around the car model in the downstream direction. The stagnation region where the turbulent wake exits has minimum values for X and Y velocity components as well as the total velocity. However, near to such turbulent wake, the maximum values for velocity are reached. VI.

A 3D numerical simulation of the flow field around the standard Ahmed car model was conducted, presented and analyzed. The objective of such simulation was to give a qualitative overview of the kinetic energy in the vicinity of a cruising vehicle. The spatial distributions of pressure, turbulence kinetic energy and velocity were observed at different planes around the car model. It was evidently shown that the regions where the flow kinetic energy is at maximum values are very near to the turbulent wake downstream the vehicle. The qualitative overview of the

Figure 7. X Velocity distribution at different XY planes. Units in m.s-1

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CONCLUSION

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ISBN: 978-960-474-215-8


flow kinetic energy described in the present study should be followed by a quantitative analysis to determine the gradients of dynamic pressure around a cruising vehicle. This is essential when considering any method of recovering the kinetic energy losses due to the aerodynamic drag of passenger vehicles.

[16]

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