Trang 1 MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION GRADUATION THESISMAJOR: AUTOMOTIVE ENGINEERING TECHNOLOGYHo Chi Minh City, July 2023INV
INTRODUCTION
Background
Currently, automotive aerodynamics is a very popular problem, studied both by experimental method in the wind tunnel and simulation on comercial code For the purpose of reducing aerodynamic drag (although the main drag of a car is wheel resistance), reduce wind noise, minimize noise emission and limit force unwanted lifting in the high-speed region For racing cars, people also designed aerodynamic component to increase the car’s downforce on the road and stabilize the car's cornering ability The study of the aerodynamics of cars also has features that are different from airplanes, such as: the shape of a car consists of faces slope, the car is running on the ground at a lower speed, the motion of the car is less steps free and less aerodynamically affected than an airplane
Although expensive and frequently performed late in the development process, wind tunnel tests are frequently a useful technique for analyzing a vehicle's aerodynamic performance As a result, it is challenging to make any changes Full-scale wind tunnel tests might be replaced or supplemented by simulation techniques like CFD (Computational Fluid Dynamics) software, which offer the ability to make changes early in the development process
Figure 1: Audi TT problem without spoiler
Figure 2: Flow around Tesla Model S.
Objective
The investigation of the Mercedes-Benz C180's aerodynamic characteristics is the primary goal of this thesis Commercial CFD codes will be used to carry out this The vehicle's drag coefficient and local flow field information are simulated, and the flow process is examined That might offer knowledge for designing the aerodynamic shapes of passenger cars However, there is no modeling or simulation of the engine compartment due to the intricacy of the cabin's components.
Challenges
How is drag force affected?
How is the behavior of air flow over the vehicle?
How is lift force affected?
Scope
The influence of crosswind and exterior shape will not be covered by the scope of this thesis
No physical tests will be performed; instead, computer simulations will be run using commercial CFD codes, which do not account for temperature changes or variations in air density
The simulations will be conducted at a fixed speed of 140 km/h (38.89 m/s); it has been decided to run CFD simulations at that particular speed.”
Method
The method for this thesis is as follows:
A CFD simulation includes three parts:
Pre-processing entails mesh creation, CAD cleanup, and boundary condition setup
To create a surface mesh, the model's surface cannot have any holes or shoddy surface connections The preprocessing is done using Simcenter Star-CCM+, software that is frequently employed in the automotive industry for CFD simulation To be able to describe the flow in the domain, Simcenter Star-CCM+ needs to solve the governing equations Simcenter Star-CCM+ will state all of the case's input data, including the boundary conditions and turbulence model The visualization and post-processing are done using Simcenter Star-CCM+
LITERATURE REVIEW
Domestic research and foreign research
Due to labour shortage, paper research about external veicle aerodynamic still restricted There are some typical papers such as
“NGHIÊN CỨU LỰC CẢN KHÍ ĐỘNG CỦA Ô TÔ CON” by author Nguyen Thanh Quang and his partner in 2019 They compared the aerodynamic characteristics of the sedan and hatchback designs of the Mazda 3 Using Ansys Fluent software to simualte and conducting case study between 2 versions of Mazda 3
Conclusion: By using Ansys Fluent software to build simulation models, assign constraints force the same assumption as when the car is moving on path from which the aerodynamic resistances can be calculated direct impact on the car, visually simulated by images and graphs Through these results we can obtain optimal solutions to improve the shape and minimize the aerodynamic drag on car when the car is in motion This reduction helps we save fuel significantly and make the vehicle move more stable
“Mô phỏng đặc tính khí động lực học mô hình xe buýt lắp ráp tại Việt Nam” by author Dang Tien Phuc and his parter in 2018 This paper examines the aerodynamic characteristics of a bus model by examining the speed and pressure distributions Numerical investigations were done using the model The Reynolds-averaged Navier- Stokes (RANS) equations, coupled with the Realizable k- model and CFD software, were used to simulate the bus's aerodynamic properties The analysis's findings demonstrated the presence of time-averaged velocity, magnitude, and static pressure fields in the flow fields surrounding the bus model The study's findings are illustrated with graphics and the calculation simulation value , which improves understanding of the bus model's aerodynamic properties The findings also lay the groundwork for future studies on improving bus exteriors to reduce aerodynamic forces and bus fuel usage
Conclusion: This paper presents the results of the simulation of aerodynamic characteristics for the vehicle model bus, using the RANS equation in combination with the Realizable k- model for the simulation CFD The calculation results
14 simulate the value within the reference value range Besides, this paper also illustrates clearly the distribution of pressure and velocity around the above model different planes Research results are the premise to perform special simulation calculations aerodynamics through numerical simulation CFD will solve the problem of gas experiments At present, the automotive aerodynamics laboratory in our country is still very limited Through the calculation results, it helps the next studies to improve the vehicle shape bus to reduce aerodynamic drag as well as reduce fuel consumption
In the world, there was so many piece of research about external vehicle aerodynamic The research that go into the evaluation of the impact of aerodynamic drag have the ability to apply in practice, some typical works such as:
“Analysis of Aerodynamic Performance of Tesla Model S by CFD” by author Qi- Liang WANG and his partner in 2017 The author analyzing the aerodynamic performance of Tesla Model S by Star-CCM+
Conclusion: For the purpose of referencing the aerodynamic design of passenger cars, the analysis of flow characteristics and the mechanism of air drag reduction is extremely important However, due to time constraints, this paper is unable to analyze the inner flow field, wind noise, etc.; we hope to do so in the future.[6]
“A Review paper on Aerodynamic Drag Reduction and CFD Analysis of Vehicles” by author Subhasis Sarkar and his partner Aerodynamics is the most important factor when it comes to resistive forces affecting the vehicle When a vehicle is moving through a fluid medium, it is important.There are many causes of this resistance, such as lift, side force, and drag Lowering aerodynamic drag will enhance comfort by reducing the car's overall fuel consumption in addition to enabling a higher top speed The aforementioned elements are essential when it comes to passenger cars These factors determine an automobile's appeal as well and form the basis of its marketing strategies For the reasons listed above, many researchers are constantly working to improve the features of cars.[9]
Conclusion: They have come to the conclusion that the primary cause of a vehicle's fuel consumption, power loss, and top speed is aerodynamic drag.
Theory of fluid mechanics
Fluid dynamics (gas and liquid) describes the motion of a fluid in terms of energy, momentum, and mass In this study, the flow field around a vehicle is solved using a commercial CFD tool The program resolves the governing equations for fluid flow for a limited number of cells in a generated grid domain
The three laws of conservation with the assumptions of incompressible and isothermal flow constitute a basic method for characterizing the flow field Due to the fact that the temperature is relatively low and the velocity is less than Mach number 0.3 Ma = 0.3 ≈
100 (m/s) during the simulation of the flow field, it is possible to make the assumption that the density and viscosity are constant
Conservation of mass – equal amount of mass enters and leaves the control volume.[3]
Conservation of linear momentum (Newton’s 2 nd law of motion) relationship between pressure, momentum, and viscous forces The incompressible Navier-Stokes equations are a class of non-linear partial differential equations that make up this group of formulas.[3] ρg −∂p
Conservation of energy (1 st law of thermodynamics) - the system's overall energy level remains constant.[3]
T = temperature, k = coefficient of thermal conductivity, Φ= viscous dissipation function
There will be changes in the flow field as a result of the turbulent, stochastic, three- dimensional, and time-dependent flow The Navier-Stokes equations (Eq 2) must be time averaged in order to handle this, as explained in Section 2.5.2
Various forms of resistance are encountered by a car as it travels along a road, Figure 3.”The sum of the rolling resistance, gravitational resistance, acceleration resistance, and aerodynamic drag resistance constitutes the overall resistance force on a moving object with constant velocity These opposing forces must be overcome in order to move the vehicle forward Eq (4) is used as the equation of motion to express the total resistance.[8]
Figure 3: Resistance on a passenger car.[4]
Since CFD calculations are done on flat roads and the inclination resistance is velocity independent, it is possible to ignore it The predominant resisting force at lower velocities is the rolling resistance For velocities above 70 km/h the aerodynamic drag will be the dominating resistance because that a relationship between the drag and the square of the speed Although it slightly increases with total resistance, rolling resistance is
17 assumed to be constant for velocities below 100 km/h, as shown in Figure 4 Aerodynamic resistance is shown as a function of velocity
Figure 4: Aerodynamic drag and rolling resistance versus velocity.[4]
Form and friction force are two components of the aerodynamic drag force (9 ) The friction force is acting in a direction tangential to the surface, while the form (pressure) drag is acting in a direction normal to the surface Because of its size and shape, a passenger car is thought to have a bluff body, which favors form drag This implies that the flow field will have a large wake and vortices The pressure differential between the vehicle's front and back ends up creating form drag The air flow slows down near the surface and eventually separates from the body due to friction on the surface, which is a source of energy loss.[8]
“Because the pressure distribution over the body is not symmetrical and the pressure on the rear will be lower than in the front, there will be a rearward-directed drag force Due to Bernoulli’s Equation, Eq (5), as can be seen, the front's high pressure peak predicts that the velocity will be low and stagnant at that point The pressure decreases as the velocity increases further down, at the window roof transition, this correspond to to the Bernoulli’s
H D + IJ KL + H@ℎ1 = H + IJ LL + H@ℎ2 (5) Where: p = static pressure of fluid at cross section,
* = density of flowing fluid, g = acceleration due to gravity,
V = mean velocity of fluid flow at cross section,
18 h = elevation head of the center of the cross section
The friction force, which is equal to the sum of all shear forces in the fluid, is produced by shear stresses between the fluid and the surface of the body The areas with attached flow make up the majority of the friction drag.[3]
Figure 5: Pressure distribution on the surface of automotive.[3]
Regardless of size or speed, the drag coefficient, a dimensionless number that describes a vehicle's aerodynamic resistance, is a helpful tool when comparing various vehicle shapes.[4] The Eq (6) can be used to express the drag coefficient According to section 2.2.1, the drag coefficient has two parts: a frictional component and a form component
When air streams around a body with no separation in the flow field, there will be a pressure difference between the upper and lower parts, causing the air on the upper surface to travel farther to reach the end of the vehicle The difference in travel distance will affect the fluid's speed; a longer distance will produce a higher speed and lower pressure.[4]
On a vehicle, the pressure will be higher underneath and lower at the top, this gives the lifting force (9 W ) The lift coefficient, which describes the lift generated on the body and is expressed as a dimensionless coefficient, in Eq (7)
The pressure coefficient is a helpful metric for comparing incompressible flows ( Z ), see Eq (8) The surface pressure's deviation from the freestream pressure is described by the pressure coefficient ( Z ) There is only one Z for each and every point in the flow field or on the surface Z ought to be equal to one in order to calculate the surface's stagnation pressure Instead, if Z is equal to 0, this denotes a low pressure area with a high
20 risk of separation In Eq (8) the pressure coefficient is expressed in terms of pressure
L I \ J \L=- ]^_`a ,bcdd bc ,[, \ (8) Where: p is the pressure at the point at which pressure coefficient is being evaluated,
H e is pressure in the freestream,
* e is the freestream fluid density, f e is the freestream velocity of fluid
Induced drag, also referred to as vortex drag, is a significant source of drag that is brought on by lift-induced geometry, such as a wing profile On occasion, it is also referred to as a trailing vortex Even the pressure differential between the car's underbody and roof can result in induced drag The total of the additional viscous drag and the vortex motion brought on by higher kinetic energy is known as induced drag.[3]
Flow separation
A boundary layer forms near the fluid's surface as a body moves through it under the influence of viscous forces Laminar or turbulent boundary layers are both possible Calculating the Reynolds number will reveal the type of boundary layer; see Eq (9) The flow becomes turbulent when the Reynolds number is high.[3] gh = Iij k (9)
As air moves over a submerged body's surface, the pressure gradient of the boundary layer decreases (see Figure 8) When the gradient of the velocity profile (boundary layer) reaches zero, the flow will separate As the flow divides, the air loses its connection to the surface and begins to form eddies Increased drag, more specifically pressure drag, will result from this, so a delay in flow separation would have been more advantageous in terms of overall drag.[3]
Figure 8: A visual representation of the boundary layer's velocity profile The final profile shows separated flow in reverse flow.
Figure 9: Flow layers on the top of the bus.[4]
2.3.1 Separation on a passenger car and wake creation
Because of the passenger car's uneven body, which causes the flow to separate, the flow is asymmetrical around the vehicle Quasi-two dimensional and three dimensional separations are two different types of separations that can happen On edges that are perpendicular to the flow, like the edge between the grill and hood, quasi-two
22 dimensionality occurs This type of separation is characterized by intense turbulence The flow can reattach further downstream if there is a surface to reattach to after separation This type of separation takes place at the back of the vehicle and leaves a sizable wake in its wake.[4]
Figure 10: Flow around vehicle and wake region.[4]
The other type of separation, which is three-dimensional, happens at the A and C pillars and other edges where the air flows at an angle Vortices start to develop and move in a streamwise direction These kinds of trailing vortices are referred to as "induced drag" The circulation is determined by the shape of the edge where separation takes place and the direction that air moves from a high pressure region to a low pressure region
Figure 11: Induced drag on a Mercedes-Benz C180
The friction from the surface causes a fluid flowing along a body to slow down closest to the body As a result of the increased pressure brought on by the decreased
23 velocity, the fluid is being slowed down more than it is being propelled forward When this occurs, the fluid closest to the surface changes course and separates Where the separation occurs, a wake is formed with a lower pressure than the surroundings Increased drag resistance results from a combination of lower pressure behind the body and higher pressure in front of it Delaying the separation will reduce both the drag and the size of the wake.[8]
Figure 12: Separation and reattachment of the flow.[4]
2.3.2 Body of vehicle and its concepts
The drag coefficient of a car is between 0.3 and 0.4 The notions of the vehicle body are supported by a number of theories Any fluid, whether it be gas or liquid, that comes into contact with a solid body will try to keep the object from moving in the other direction The geometry of the object has a significant impact on the body's aerodynamics The size of the object that experiences drag and lift is primarily determined by the fluid The cross sectional shape of the object affects form drag Height above the earth
This includes the car experiencing more down force, which aids in the vehicle's ability to hold to the ground The flow of air under the vehicle's body will increase if the distance between its cross section and the ground is decreased This will lower the pressure underneath the car and result in more down force, which helps to maintain stability while the vehicle body is moving under fluid Ground effect is another name for this downward force.With the lower ground clearance, it can be raised By adding skirts next to the vehicle body, the down force values can also be raised Following graph shows that lift and the drag verses ground clearance for a model with the generic underbody tunnel
24Figure 13: Velocity against the ratio height over length.[4]
2.4.Introduction Simcenter Star-CCM+ and digital model Mercedes-Benz C180 2.4.1 Simcenter Star-CCM+
Simcenter STAR-CCM+ is a multiphysics computational fluid dynamics (CFD) simulation tool that gives CFD engineers the ability to simulate the complexity of products operating in real-world settings and explore their potential
A fully integrated user interface will increase your productivity
Discover everything with this unified software Pre-processing, meshing, multiphysics modeling, data analysis, photorealistic visualization, and VR are all included in Simcenter STAR-CCM+
Adapt to the most difficult applications
Go far beyond heat transfer and fluid flow in terms of physics You can run even the most complicated multiphysics CFD simulations using this fully integrated solver platform
Automated meshing and pre-processing of complex geometries can cut down the week-long preparation time for simulations to just a few hours Spend your time creating better products by using cutting-edge technologies like automated CAD cleanup, surface wrapping, and automated high-fidelity meshing
Leverage powerful end-to-end, code-free workflow automation and fully embedded designexploration
Utilize automated simulations throughout CFD-based design exploration
Figure 15: Reality model of Mercedes-Benz C180
These are dimensions of Mercedes-Benz C180
Table 1: Dimensions of Mercedes-Benz C180
Ride height (ground clearance) 157 mm
28Figure 16: Vitural model of Mercedes-Benz C180
Compuatational fluid dynamics (CFD)
CFD is a numerical approach for calculating and analyzing fluid dynamics In order to solve the governing equations numerically, the physical domain is divided into small finite volume parts Since almost all flows are turbulent, it is possible to simulate the turbulence using so-called turbulence models in order to save computer resources The governing equations and turbulence models are presented in the sections that follow
The three governing equations of fluid dynamics—continuity, momentum, and energy—describe the behavior of the flow and are also covered in Section 2.1 They come from fundamental physical principles, such as the conservation of mass, energy, and momentum Numerical simulations are necessary because these equations become quite complex and cannot be resolved analytically
The differential equations are discretized into large systems of algebraic equations in order to be solved numerically in a CFD simulation The energy equation can be ignored if the flow is incompressible, isothermal, and the vehicle moves at a constant temperature
Navier-Stokes equation Consider the Navier-Stokes equations as the force equilibrium of an infinitesimally small volume element They are derived from Newton's second law In order to convert stresses into velocity components, the Navier-Stokes equations are typically expressed for an incompressible Newtonian fluid with constant viscosity An incompressible fluid has zero velocity divergence, while a Newtonian fluid has a linear stress versus strain rate curve In Eq (10), three partial non-linear differential equations, one for each velocity vector, can be used to express the Navier-Stokes equations.[2]” ρg −∂p
Continuity equation The continuity equation, which has the form Eq (11) can be written, is based on the idea that the mass is unbreakable
Since it is assumed that the flow is incompressible, the continuity equation will be
The Continuity equation provides four unknowns, u, v, w, and p, along with the
Navier-Stokes equation These four unknowns will be resolved using differential equations
Figure 17: Workflow of Computational Fluid Dynamics[2]
Analytical solutions to the non-linear partial differential equations are not possible The Reynolds decomposition, also known as Reynolds Average Navier Stokes (RANS), is
31 the most straightforward method for solving these equations and analyzing the flow The RANS approach divides the instantaneous velocity and pressure into two parts: an average part and a fluctuating part, represented by Eqs (13) and (14) respectively no = D p n qr s (13) p = H̅ + p’ u = no + u’ (14) v = u̅ + v’ w = vw + w’
Inserting Reynolds decomposition into Navier-Stokes equation (x-direction) and will result in new fluctuating terms in the continuity equation xyw x + xzw x$ + x{w x| = 0 (15) ρg − x}w x + x x ~μ xyw x − ρu′oooo€ + x$ x ~μ xy x$ − ρu′v′ooooo€ + x| x ~μ xyw x| − ρu′w′oooooo€ = ρ •yw •‚ (16)
Eq (16) now consists of new unknown terms like pn′u′ooooo, also called for
Reynolds stresses A so-called closure problem is created when the number of unknowns exceeds the number of equations; the additional stress terms must be modeled in order to obtain a closed equation system In order to do this, turbulence models are used.[2]
2.5.3 Turbulence flow and turbulence modelling
Calculating the turbulent flow in CFD simulations is the most challenging step An irregular, erratic, turbulent flow changes both in time and space With existing computer capacity it’s impossible to solve Eq (10) and (12) exactly Turbulence models can be used to calculate the flow field with less computing power Such a model will alter the equations and only take into account the turbulence's average effects A fluctuation term and an average term will then be applied to the flow, this can be done using Reynolds Average Navier Stokes (RANS) A better option will provide a more accurate solution than a turbulence model, which can never provide an exact solution The model to use depends on the computing power available and the required level of accuracy k -ƒ model The k -ƒ model is the turbulence model that the automotive industry uses the most, this is a result of the model's robustness, which provides secure convergence The model provides a good
32 overview of the flow field, but the accuracy is not very good in regions with large velocity and pressure gradients The k -ƒ model is an Eddy Viscosity model, which means that the turbulence is modeled by adding the turbulence viscosity, 8 / It uses a semi-empirical approach, based on how the kinetic energy k , is transported and its dissipation rate The transport equation for k is derived exact while the transport equation for ƒ is derived from physical reasoning The given location eddies gets their kinetic energy, k = „
… ( †′oooo + ‡′ … oooo + … ˆ′ … ooooo ) from the main flow The energy becomes internal energy after being transmitted into smaller eddies Since the k -ƒ model is a RANS-model and is using time average terms, the model will fail to detect gradient differences over very brief time steps A new model known as the k -ƒ SST model has been developed in order to more precisely solve the flow problem Additionally, this model modified the linear constitutive equation and gave the modified model a new name the SST (shear-stress transport) k -ƒ model The transformed equation looks similar to the one in the k -ƒ model, but adds an additional non-conservative cross diffusion term containing the dot product ‰Š ‰ˆ Eq (17) describes the connection between kinetic energy, dissipation rate, and turbulent viscosity.[2]
Where: T is the turbulent time scale
As mentioned an extra term ‰Š ‰ˆ, is included in the Navier-Stokes equation, see
Transport Equations: The transport equations for the kinetic energy k and the specific dissipation rate ω are:
/(*v) + ∇ (Hvu̅) = ∇ Œ(8 + • m 8 / )∇vŽ + m − *• ∗ ? ‘ (v − v ’ ) + “ m (20) Where:u̅ is the mean velocity,
? ‘ ∗ is the free shear modification factor,
? ‘ is the vortex stretching modification factor,
“ ‹ and “ m are the user speacified source terms,
0 ’ and v ’ are the ambient turbulence values that counteract turbulence decay
2.5.4 Boundary layers and wall functions
When a fluid moves along a body, a boundary layer is created very near the surface Near the surface, the flow's velocity is zero before it rises and reaches the freestream velocity The thickness of the boundary layer is determined by measuring the distance from the body to the location where the velocity reaches 99% of the freestream velocity The boundary layer can be divided into three categories, including laminar, turbulent, and a combination of both, as shown in Figure 10 The boundary layer is initially laminar when the body is first exposed to the fluid; however, as the fluid moves along the body, the boundary layer becomes turbulent A laminar boundary is preferred in some circumstances because it has less skin friction than a turbulent layer.[2]
“Three regions—the viscous sublayer, the buffer layer, and the fully turbulent log- law region—typically make up the near wall flow.The near wall region is displayed in Figure 18 and is plotted using semi-log coordinates The non-dimensional wall distance is represented by the symbol y+ on the y-axis, which is defined as in Eq (21)
Figure 18: Velocity profile in the near wall region for a turbulent boundary layer.[2]
Where: n ∗ is the friction velocity,
34 v is the kinematic viscosity and y is the height of the first cell
The boundary layer's velocity profile has been solved using wall functions The thickness of the first cell must have a ” = 1 in the normal case (without wall functions), but with wall functions, ” can range between 30 and 300 In Star-CCM+, there are two different types of walls: standard wall functions and non-equilibrium wall functions Assuming that the flow near the wall behaves fully turbulently, wall functions use the algorithm to resolve the gradients in the boundary layer When compared to standard wall functions, non-equilibrium wall functions are more sensitive to pressure gradients In domains with complex geometry and frequent separations with reattachments, the non- equilibrium wall function more accurately predicts the flow This is because it is possible to account for the effects of pressure gradients
2.5.5 Star-CCM+ set-up solver
Both pressure-based solvers and density-based solvers are available in the Star-CCM+ software This study used the pressure-based solver because it is appropriate for incompressible flows and low velocities The domain has been split up into different control volumes in order to resolve the flow The governing equations of each control volume are combined into an algebraic system, which is linearized and solved for each iteration The governing equations can be solved separately (SIMPLE or SIMPLEC) or coupled (COUPLED), depending on the algorithm used SIMPLE is preferred when the
35 simulation is steady state and the computer's processing power is limited COUPLED is a more dependable, secure method that offers better convergence There are additional requirements for the solver when running transient simulations; SIMPLEC or PISO are preferred in these simulations Instability may result from using SIMPLEC for a steady state simulation
Figure 20: Setup solver in Star-CCM+
To study the flow field, the domain must be divided into small cells, and the governing equations must be represented as integrals Each cell has six faces, and the motions of the cells around it affect how each cell flows Numerous techniques can be used to calculate the governing equations; in this study, the first and second order upwind methods have been used A first order upwind solution scheme is used to solve the governing equations, extrapolating the results from one neighbor cell in each direction Using two neighbor cells in each direction, the equations are solved using a second order upwind method The second order upwind method produces more precise results, but it uses more processing power
METHODOLOGY
Introduction
In the industry today, numerical simulations of the aerodynamic performance of vehicles are frequently used to assess and improve the vehicle design Such computational fluid dynamics (CFD) simulation results must be compared to test data, typically gathered from a wind tunnel, in order to be fully trusted When there are discrepancies between test and simulation, they are usually attributable to at least one of three broad categories:
2 The test object's uncertain geometrical representation
3 Numerous test domains and boundary circumstances
Regarding item 1, significant progress has been made, with scale-resolving techniques being created and becoming practical with rising computational power The ability to ensure that the CAD data used as input to the simulations is representative of the actual test object has also improved with the development of 3D scanners, reducing some of the uncertainties surrounding item 2
Regarding item 3, using open road conditions, the numerical test domain for vehicle aerodynamic CFD simulations is typically a sizable rectangular cuboid with a uniform inlet flow, a moving ground plane, and a negligible blockage ratio This is in no way comparable to the test area of a wind tunnel, where the blockage ratio is typically in the 10% range, the flow is not perfectly uniform, and the movement of the ground relative to the car has to be simulated using a variety of techniques, typically only covering the area underneath and directly in front of the vehicle Inviscid flow-based correction techniques are frequently used to adjust the physical measurements in order to account for the difference brought on
40 by the interference from the wind tunnel
Figure 26: CFD simulation external vehicle aerodynamic[1]
Boundary conditions
Simcenter Star-CCM+ 2021.1.1 is the solver utilized for these simulations In order to provide a summary of the driving conditions during the simulation, a brief description of the boundary conditions is presented in this section; for reference, see Table 3 When simulating a road vehicle, the automotive industry uses a standard wind speed or driving
41 speed of 140 km/h (38.89 m/s), * ^`b = 1.225 0@/ – , and temperature of 15℃ This investigation also makes use of these characteristics Because the flow is incompressible at this velocity and the density can be assumed to be constant, the governing equations are pressure-based Another well-documented CFD simulation technique is the use of the k -ƒ
SST turbulence model together with non-equilibrium wall-functions when solving the RANS-equations in Star-CCM+, which will be utilized throughout this thesis
S URFACE /P ART M OVEMENT T YPE C ONDITION
Wind tunnel top stationary symmetry -
Wind tunnel sides stationary symmetry -
Wind tunnel ground transitional x- velocity wall 38.89 (m/s)
Wind tunnel inlet stationary velocity- inlet
Wind tunnel outlet stationary pressure- outlet
Guage pressure: 0.0 (Pa) turbulence length scale: 1
Vehicle stationary wall no-slip
Wheels rotational velocity (y- axis) wall no-slip
Frame) rotational velocity (y- axis) wall
Table 4 displays the rotational center for the wheel and MRF-zone boundary conditions
Simulation in Star-CCM+
Figure 28: Flow chart of simulation process
The total number of volume mesh cells is approximately 10 million The simulations uses the intel core i5-9300H with 4 cores and 32GB RAM It has been demonstrated that
44 performing the calculations for 2000 iterations is sufficient to provide low residuals values The first 500 iterations include computing the RANS equations in first order, and the following 1500 involve solving the numerical mesh in second order The final drag coefficient ( ) and lift coefficient ( W ) for simulation is determined by calculating the mean value of the last 200 iterations
RESULTS AND DISCUSSIONS
Force and power curves
Recall Eq (6) We have =0.255, A =2.232 calculate in Star-CCM+ and * 1.225 0@/ –
Substituting these numbers we have 9 = 0.35u In this thesis, I choose u 8.89 m/s
=>9 = 529.3 The Figure 32 showing the relationship between drag force and velocity
Figure 32: Curve of drag force
We have = 9 ∗ u Minimun power the vehicle need is 20584.447 N.m/s = 27.6
HP It means if the vehicle with low will save more fuel
Recall Eq (7) We have W =-0.96, A =2.232 calculate in Star-CCM+ and * 1.2250@/ –
Substituting these numbers we have 9 W = −1.31u In this thesis, I choose u 8.89 m/s =>9 W = −1985 With large down force makes the vehicle better road handling The Figure 33 showing the relationship between down force and velocity
Figure 33: Curve of down force
Figure 34: Lift coeffcient of front and rear wheels With front wheels W¢ = −0.08 =£ 9 W¢ = −180
Energy losses
Figures 35 and 36 depict the model with the so-called isosurface for zero total pressure; this irregular surface depicts the wake created by the vehicles A wake is a zone of intense turbulence and low pressure that denotes energy loss Wakes also form at the wheels, the mirrors, and on the underbody, as shown in the image Here, the isosurface is colored to identify the locations with the greatest turbulence
Figure 35: 3D view and front view
Figure 36: Side view and top view
The isosurface highlights areas where significant energy losses occur and add to the overall drag The asymmetric underbody design of the automobiles can be seen in the two figures as well as in the asymmetric wakes at the ends of the cars It is obvious that the wakes produced at the rear wheels interact with the base wake; therefore, by avoiding this interaction, significant reductions in drag can be made Despite the differences in the outward shapes of the cars, the wheels, the underbody, and the back end will all contribute most to the drag
Turbulence viscosity in front wheels at position [1.189694804939385, - 0.8184842916644133, -0.12765594367135213](m, m, m) equal 0,0921979 (Pa-s)
Turbulence viscosity in rear wheels at positon [4.611051029562188, - 0.8181319579195647, -0.04213486263553293](m, m, m) equal 0,219181 (Pa-s)
The ratio between rear and front wheels = s, D¦D§D s,s¦ D¦¨¦= 2.37 It shows that the drag in rear will bigger than front wheels
Flow analysis
Figure 38 shows the model's velocity magnitude at the lateral location of y = 0 Over the hood and roof, as would be expected, there is a region of high velocity There are low- speed areas with separate flows in between these regions According to Bernoulli’s equation, Eq (5), high velocity areas have low pressure, which could lead to separation
These figures are comparable to those of the isosurface in the earlier figures, where low speed regions may be found in the base wake
The wake can be considered to be more streamlined as an extension of the car to enhance pressure recovery and subsequently reduce drag The flow underneath the car is forced to flow around the wake area because it is accelerating close to the wake, which widens the low pressure area The vectors show recirculation in the wake because the air over the vehicle is moving more quickly
Overpressure is created when air strikes the object When the air reaches a fully assembled vehicle, the pressure is at its highest At the model's nose is Figure 41 The pressure there is referred to as the stagnation pressure, which is equivalent to a static pressure coefficient or , = 1
The likelihood that a forward-facing surface will produce overpressure and consequent drag increases with how perpendicular it is to the flow Similarly, a surface facing backward that is under pressure (has a negative pressure coefficient) will cause the vehicle to move backward, producing drag once more Try to minimize overpressure and underpressure peaks by reducing drag by smoothing the surface at peak locations and critical transitions
Figure 41: 3D view and front view
54 Figure 42: Side view and top view
The study of aerodynamics requires an understanding of streamlines The path a massless particle takes as it moves with the current is known as a streamline If we follow the body rather than going with the flow, it is simpler to picture a streamline The Figure
44, 45 and 46 shows the computed streamlines around the vehicle Because a moving particle is tracing the streamline, every point along the path's length has a velocity that is perpendicular to the streamline Because there is no normal component of the velocity along the path, mass cannot cross a streamline The mass contained between any two streamlines is constant over the entire flowfield We can use Bernoulli's equation to relate the pressure and velocity along the streamline The surface of the object is a streamline because no mass passes through the vehicle Aerodynamic forces are present as the vehicle travels through the air You could feel the aerodynamic force pushing against your hand if you put your hand out the window while driving Your hand seems to be passing through the air at the same speed as the car Whether you are in the car or standing on the corner, the forces acting on the vehicle are the same
Figure 44: Top view and bottom view of streamline
56 Figure 45: Side view of streamline
Figure 46: Front view and rear view of streamline
Accumulated drag
Accumulated drag coefficient plot demonstrating the progression of drag from the front of the vehicle profile moving backward to the rear part of the vehicle, emphasizing the step change in the drag in every shape of the vehicle
CONCLUSION AND FUTURE RESEARCH
Conclusion
This thesis shows that the numerical simulation of the external aerodynamics of the Mecedes-Benz C180 model by 3D scanning as well as of the real model now may be implemented by the average hardware resources The result of coefficient of drag in simulation different with the real one only 6.25% This is acceptable because we must apply the worst scenario when doing simulating
Also, the analysis of the flow characteristics and effect on the model are proving the drag being produced by the rear wheels are much more than twice time with respect to the front wheels The ratio of turbulence viscosity between rear and front wheels = s, D¦D§D s,s¦ D¦¨¦ 2.37 It is the same with the downforce between rear and front wheels = [–¨
This thesis also shows that the pressure distrution over the whole of the model could help the manufactuer predection for the first stage when design the new vehicle.
Future research
At the same time, due to the hasty time and limit of hardware, this thesis can not analyze the inner flow field with engine compartment modelling Also with the URANS (Unsteady Raynol Reynolds Averaged Navier Stokes) approach as well
Hopefully, it could perform in the future
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