SlideShare a Scribd company logo
1 of 8
Download to read offline
Aerodynamics analysis around
       a car by CFD



          Hayato Suzuki
Forecast

Recently, automobile industry started utilizing computer
simulations like CFD(Computational Fluid Dynamics) to
develop and design car body. Previously, it prepared actual
car body model, and it evaluated car body aerodynamic
character by running wind tunnel test. To prepare actual car
body model takes time and cost. Therefore, it tended to
decrease wind tunnel test and increase computer simulation.
But, to re-enact actual car running had difficulty in CFD, and it
had some problems like computational result accuracy.
Outline

I use an open source simulation software which name is
OpenFOAM. Here is how to simulate. First, I get the 3D data of
a car. I can not make whole car body 3D model on my own. So
I get it from web. Next, I decide a size of virtual wind tunnel
and position of car model in it. After that, I generate some grids
for calculation, it is called “mesh”. Next, I set boundary
condition like inlet of air flow. After that, I execute a simulation.
 Finally, I display a result by visualize software called
“paraView” after finished simulation. It can display stream line,
cut by X or Y or Z axis, and so on.
Motivation and Problem Statement

Past CFD were a lot of simulations when a car running straight
line, but they were not so real. First, a car model is not real.
For example, it is too simple, its appearance like box. Or, it has
only car body, no tires. My car model is normal sedan car.
Second, my simulation software is open source and free
software. It name is OpenFOAM. Past business engagement
simulation software are too expensive. OpenFOAM was made
possible simple simulation of student level like me. Finally, I
use k-omegaSST turbulent model. It is hybrid turbulent model
k-epsilon and k-omega. Past CFD were a lot of standard k-
epsilon model. It can calculate quickly. But, accuracy is not so
good. K-omegaSST can realize more good accuracy.
Methods

First, creating a model data. Creating 3D or 2D model by CAD
data. This model will be simulation objective. Second, mesh
generation. CFD expresses calculational space in mesh. This
number of mesh is very important for accuracy. A lot of mesh
provide good accuracy, but it needs long calculation time. So I
must find good balance. Third, running calculation. My
laboratory has super computer. In CFD, calculation time is
very long. So I need high spec computer. Finally,
visualization. Calculation result is difficult for human eyes to
understand.
Results

Pressure around a car. High pressure is looked front of car. But
low pressure is looked over a car. It is negative pressure.
Results

This is air stream line graphic. It is not easy for us to
understand. So I will fix it.
Summary

From CFD simulation, I can look air flow around a car. And, I
can find high pressure point around a car.

Additional, I want to calculate drag force and lift force. They are
important for aerodynamics. I will write them on my thesis.

But, this is low quality simulation. To save time, I reduce mesh
numbers. So I want to do more high quality simulation. Two
graphics shows air flow and pressure around a car. But they
are not easy to understand. So I will fix graphics to post it on
my thesis.

More Related Content

Similar to Week9

Aerodynamics analysis around_a_car_by_cfd
Aerodynamics analysis around_a_car_by_cfdAerodynamics analysis around_a_car_by_cfd
Aerodynamics analysis around_a_car_by_cfds1160120
 
CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...
CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...
CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...IOSR Journals
 
AUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYS
AUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYSAUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYS
AUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYSIAEME Publication
 
ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...
ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...
ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...IAEME Publication
 
IRJET- CFD-A Trend in Automobile Aerodynamics Technology
IRJET- 	  CFD-A Trend in Automobile Aerodynamics TechnologyIRJET- 	  CFD-A Trend in Automobile Aerodynamics Technology
IRJET- CFD-A Trend in Automobile Aerodynamics TechnologyIRJET Journal
 
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...IJRES Journal
 
[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...
[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...
[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...Geon-Hong Kim
 
Use of cfd in aerodynamic performance of race car
Use of cfd in aerodynamic performance of race carUse of cfd in aerodynamic performance of race car
Use of cfd in aerodynamic performance of race carDesignage Solutions
 
Project_Overview_ecopy
Project_Overview_ecopyProject_Overview_ecopy
Project_Overview_ecopyDavid Beck
 
A machine learning model for average fuel consumption in heavy vehicles
A machine learning model for average fuel consumption in heavy vehiclesA machine learning model for average fuel consumption in heavy vehicles
A machine learning model for average fuel consumption in heavy vehiclesVenkat Projects
 
Advait Project Report
Advait Project ReportAdvait Project Report
Advait Project ReportAdvait Patel
 
Engineering + Programming portfolio
Engineering + Programming portfolioEngineering + Programming portfolio
Engineering + Programming portfolioJosephDonnelly14
 
Application of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptx
Application of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptxApplication of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptx
Application of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptxMohammadAbdullah1811
 
carla advanced Artificial Intelligence module
carla advanced Artificial Intelligence modulecarla advanced Artificial Intelligence module
carla advanced Artificial Intelligence modulejerlinhemnath03
 
Development of the required components of a performance vehicle model to stud...
Development of the required components of a performance vehicle model to stud...Development of the required components of a performance vehicle model to stud...
Development of the required components of a performance vehicle model to stud...Kayalarasan Kanagasabai
 
Presentation1
Presentation1Presentation1
Presentation1IaaC
 
Caleb Vanderpleog Resume and Academic Summary
Caleb Vanderpleog Resume and Academic SummaryCaleb Vanderpleog Resume and Academic Summary
Caleb Vanderpleog Resume and Academic SummaryCaleb VanderPloeg
 

Similar to Week9 (20)

Aerodynamics analysis around_a_car_by_cfd
Aerodynamics analysis around_a_car_by_cfdAerodynamics analysis around_a_car_by_cfd
Aerodynamics analysis around_a_car_by_cfd
 
CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...
CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...
CFD Simulation for Flow over Passenger Car Using Tail Plates for Aerodynamic ...
 
AUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYS
AUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYSAUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYS
AUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYS
 
ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...
ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...
ADVANCED TOOL FOR FLUID DYNAMICS-CFD AND ITS APPLICATIONS IN AUTOMOTIVE, AERO...
 
IRJET- CFD-A Trend in Automobile Aerodynamics Technology
IRJET- 	  CFD-A Trend in Automobile Aerodynamics TechnologyIRJET- 	  CFD-A Trend in Automobile Aerodynamics Technology
IRJET- CFD-A Trend in Automobile Aerodynamics Technology
 
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
 
[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...
[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...
[OFW 14] Prediction of Flow Characteristics by Applying Machine Learning of S...
 
Use of cfd in aerodynamic performance of race car
Use of cfd in aerodynamic performance of race carUse of cfd in aerodynamic performance of race car
Use of cfd in aerodynamic performance of race car
 
Project_Overview_ecopy
Project_Overview_ecopyProject_Overview_ecopy
Project_Overview_ecopy
 
A machine learning model for average fuel consumption in heavy vehicles
A machine learning model for average fuel consumption in heavy vehiclesA machine learning model for average fuel consumption in heavy vehicles
A machine learning model for average fuel consumption in heavy vehicles
 
Advait Project Report
Advait Project ReportAdvait Project Report
Advait Project Report
 
Engineering + Programming portfolio
Engineering + Programming portfolioEngineering + Programming portfolio
Engineering + Programming portfolio
 
Application of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptx
Application of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptxApplication of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptx
Application of Simulation Modeling-Mohammad Abdullah-181-15-2051-PC-B .pptx
 
Krishankant Sharma Portfolio
Krishankant Sharma PortfolioKrishankant Sharma Portfolio
Krishankant Sharma Portfolio
 
full report
full reportfull report
full report
 
carla advanced Artificial Intelligence module
carla advanced Artificial Intelligence modulecarla advanced Artificial Intelligence module
carla advanced Artificial Intelligence module
 
Lecture 7
Lecture 7Lecture 7
Lecture 7
 
Development of the required components of a performance vehicle model to stud...
Development of the required components of a performance vehicle model to stud...Development of the required components of a performance vehicle model to stud...
Development of the required components of a performance vehicle model to stud...
 
Presentation1
Presentation1Presentation1
Presentation1
 
Caleb Vanderpleog Resume and Academic Summary
Caleb Vanderpleog Resume and Academic SummaryCaleb Vanderpleog Resume and Academic Summary
Caleb Vanderpleog Resume and Academic Summary
 

Recently uploaded

Beyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry InnovationBeyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry InnovationSafe Software
 
Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)
Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)
Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)Mark Simos
 
Unraveling Multimodality with Large Language Models.pdf
Unraveling Multimodality with Large Language Models.pdfUnraveling Multimodality with Large Language Models.pdf
Unraveling Multimodality with Large Language Models.pdfAlex Barbosa Coqueiro
 
Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024BookNet Canada
 
Vertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering TipsVertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering TipsMiki Katsuragi
 
Install Stable Diffusion in windows machine
Install Stable Diffusion in windows machineInstall Stable Diffusion in windows machine
Install Stable Diffusion in windows machinePadma Pradeep
 
My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024The Digital Insurer
 
Streamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupStreamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupFlorian Wilhelm
 
Story boards and shot lists for my a level piece
Story boards and shot lists for my a level pieceStory boards and shot lists for my a level piece
Story boards and shot lists for my a level piececharlottematthew16
 
Connect Wave/ connectwave Pitch Deck Presentation
Connect Wave/ connectwave Pitch Deck PresentationConnect Wave/ connectwave Pitch Deck Presentation
Connect Wave/ connectwave Pitch Deck PresentationSlibray Presentation
 
SIP trunking in Janus @ Kamailio World 2024
SIP trunking in Janus @ Kamailio World 2024SIP trunking in Janus @ Kamailio World 2024
SIP trunking in Janus @ Kamailio World 2024Lorenzo Miniero
 
"ML in Production",Oleksandr Bagan
"ML in Production",Oleksandr Bagan"ML in Production",Oleksandr Bagan
"ML in Production",Oleksandr BaganFwdays
 
Scanning the Internet for External Cloud Exposures via SSL Certs
Scanning the Internet for External Cloud Exposures via SSL CertsScanning the Internet for External Cloud Exposures via SSL Certs
Scanning the Internet for External Cloud Exposures via SSL CertsRizwan Syed
 
Artificial intelligence in cctv survelliance.pptx
Artificial intelligence in cctv survelliance.pptxArtificial intelligence in cctv survelliance.pptx
Artificial intelligence in cctv survelliance.pptxhariprasad279825
 
WordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your BrandWordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your Brandgvaughan
 
Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?Mattias Andersson
 
Unleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding ClubUnleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding ClubKalema Edgar
 
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...Patryk Bandurski
 
What's New in Teams Calling, Meetings and Devices March 2024
What's New in Teams Calling, Meetings and Devices March 2024What's New in Teams Calling, Meetings and Devices March 2024
What's New in Teams Calling, Meetings and Devices March 2024Stephanie Beckett
 
DevoxxFR 2024 Reproducible Builds with Apache Maven
DevoxxFR 2024 Reproducible Builds with Apache MavenDevoxxFR 2024 Reproducible Builds with Apache Maven
DevoxxFR 2024 Reproducible Builds with Apache MavenHervé Boutemy
 

Recently uploaded (20)

Beyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry InnovationBeyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
Beyond Boundaries: Leveraging No-Code Solutions for Industry Innovation
 
Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)
Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)
Tampa BSides - Chef's Tour of Microsoft Security Adoption Framework (SAF)
 
Unraveling Multimodality with Large Language Models.pdf
Unraveling Multimodality with Large Language Models.pdfUnraveling Multimodality with Large Language Models.pdf
Unraveling Multimodality with Large Language Models.pdf
 
Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
Transcript: New from BookNet Canada for 2024: BNC CataList - Tech Forum 2024
 
Vertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering TipsVertex AI Gemini Prompt Engineering Tips
Vertex AI Gemini Prompt Engineering Tips
 
Install Stable Diffusion in windows machine
Install Stable Diffusion in windows machineInstall Stable Diffusion in windows machine
Install Stable Diffusion in windows machine
 
My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024
 
Streamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupStreamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project Setup
 
Story boards and shot lists for my a level piece
Story boards and shot lists for my a level pieceStory boards and shot lists for my a level piece
Story boards and shot lists for my a level piece
 
Connect Wave/ connectwave Pitch Deck Presentation
Connect Wave/ connectwave Pitch Deck PresentationConnect Wave/ connectwave Pitch Deck Presentation
Connect Wave/ connectwave Pitch Deck Presentation
 
SIP trunking in Janus @ Kamailio World 2024
SIP trunking in Janus @ Kamailio World 2024SIP trunking in Janus @ Kamailio World 2024
SIP trunking in Janus @ Kamailio World 2024
 
"ML in Production",Oleksandr Bagan
"ML in Production",Oleksandr Bagan"ML in Production",Oleksandr Bagan
"ML in Production",Oleksandr Bagan
 
Scanning the Internet for External Cloud Exposures via SSL Certs
Scanning the Internet for External Cloud Exposures via SSL CertsScanning the Internet for External Cloud Exposures via SSL Certs
Scanning the Internet for External Cloud Exposures via SSL Certs
 
Artificial intelligence in cctv survelliance.pptx
Artificial intelligence in cctv survelliance.pptxArtificial intelligence in cctv survelliance.pptx
Artificial intelligence in cctv survelliance.pptx
 
WordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your BrandWordPress Websites for Engineers: Elevate Your Brand
WordPress Websites for Engineers: Elevate Your Brand
 
Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?
 
Unleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding ClubUnleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding Club
 
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
Integration and Automation in Practice: CI/CD in Mule Integration and Automat...
 
What's New in Teams Calling, Meetings and Devices March 2024
What's New in Teams Calling, Meetings and Devices March 2024What's New in Teams Calling, Meetings and Devices March 2024
What's New in Teams Calling, Meetings and Devices March 2024
 
DevoxxFR 2024 Reproducible Builds with Apache Maven
DevoxxFR 2024 Reproducible Builds with Apache MavenDevoxxFR 2024 Reproducible Builds with Apache Maven
DevoxxFR 2024 Reproducible Builds with Apache Maven
 

Week9

  • 1. Aerodynamics analysis around a car by CFD Hayato Suzuki
  • 2. Forecast Recently, automobile industry started utilizing computer simulations like CFD(Computational Fluid Dynamics) to develop and design car body. Previously, it prepared actual car body model, and it evaluated car body aerodynamic character by running wind tunnel test. To prepare actual car body model takes time and cost. Therefore, it tended to decrease wind tunnel test and increase computer simulation. But, to re-enact actual car running had difficulty in CFD, and it had some problems like computational result accuracy.
  • 3. Outline I use an open source simulation software which name is OpenFOAM. Here is how to simulate. First, I get the 3D data of a car. I can not make whole car body 3D model on my own. So I get it from web. Next, I decide a size of virtual wind tunnel and position of car model in it. After that, I generate some grids for calculation, it is called “mesh”. Next, I set boundary condition like inlet of air flow. After that, I execute a simulation. Finally, I display a result by visualize software called “paraView” after finished simulation. It can display stream line, cut by X or Y or Z axis, and so on.
  • 4. Motivation and Problem Statement Past CFD were a lot of simulations when a car running straight line, but they were not so real. First, a car model is not real. For example, it is too simple, its appearance like box. Or, it has only car body, no tires. My car model is normal sedan car. Second, my simulation software is open source and free software. It name is OpenFOAM. Past business engagement simulation software are too expensive. OpenFOAM was made possible simple simulation of student level like me. Finally, I use k-omegaSST turbulent model. It is hybrid turbulent model k-epsilon and k-omega. Past CFD were a lot of standard k- epsilon model. It can calculate quickly. But, accuracy is not so good. K-omegaSST can realize more good accuracy.
  • 5. Methods First, creating a model data. Creating 3D or 2D model by CAD data. This model will be simulation objective. Second, mesh generation. CFD expresses calculational space in mesh. This number of mesh is very important for accuracy. A lot of mesh provide good accuracy, but it needs long calculation time. So I must find good balance. Third, running calculation. My laboratory has super computer. In CFD, calculation time is very long. So I need high spec computer. Finally, visualization. Calculation result is difficult for human eyes to understand.
  • 6. Results Pressure around a car. High pressure is looked front of car. But low pressure is looked over a car. It is negative pressure.
  • 7. Results This is air stream line graphic. It is not easy for us to understand. So I will fix it.
  • 8. Summary From CFD simulation, I can look air flow around a car. And, I can find high pressure point around a car. Additional, I want to calculate drag force and lift force. They are important for aerodynamics. I will write them on my thesis. But, this is low quality simulation. To save time, I reduce mesh numbers. So I want to do more high quality simulation. Two graphics shows air flow and pressure around a car. But they are not easy to understand. So I will fix graphics to post it on my thesis.