What is the best way to teach CFD/suitable lecture material to undergraduate students in Department of Mechanical Engineering?
1.1 Strategies for Incorporating CFD into Undergraduate Curriculum
In the previous section, an effort was made to present the list of CFD‐related concepts and tools hierarchically. This effort was in anticipation of the current section, in which a hierarchy of CFD curriculum profiles from low to high is described. In this fashion, the modular CFD elements can naturally be identified for inclusion in an appropriate setting. For example, in the lowest profile setting, precomputed CFD solutions are to be used to illuminate fundamental fluid dynamic phenomena, and therefore only some elements of the concept hierarchy are invoked (in this case, post‐processing). The objective in this section is to present a number of examples, drawing where possible on existing curricula. This allows us to present the accompanying syllabi, some brief descriptions of sample homework problems and projects, and lessons learned on the development and continuing evolution of these existing courses.
1.1.1 CFD Light
This represents the lowest profile inclusion of CFD in an undergraduate curriculum. In such a case, an instructor of an introductory or intermediate fluid mechanics course uses pre‐computed CFD simulations in order to reinforce fundamental concepts. With the availability of free high‐quality visualization software (e.g., Paraview and VisIT), this approach is relatively straightforward to introduce into an existing curriculum, provided a repository of solutions has already been generated.
Students would be able to download the CFD solution files and use them to study fluid flow in and around various geometries. This approach would help eliminate software cost, and also introduce more realistic engineering simulations into the undergraduate curriculum while avoiding long simulation times and resources and instruction needed to conduct such simulations.
1.1.2 CFD Moderate
At this level of CFD instruction, CFD modules are used to augment course material, by substituting the module into an existing lecture‐form fluid mechanics or aerodynamics course, or into the accompanying lab unit of the course. The CFD content is heavier than in the CFD light scenario, in that here, the students are expected to compute the solutions before analyzing them. As the examples below will suggest, this approach often makes use of free or in‐house inviscid aerodynamic solvers (i.e. panel and vortex lattice codes) in order to compute flows and predict forces on lifting surfaces. For further information, please consult the [Eldredge et al.][1].
1.1.3 CFD Heavy
In this format, CFD is taught as a stand‐alone course, and therefore more emphasis is placed on teaching fundamental concepts of CFD. The U.S. Air Force Academy created this course nearly a decade ago, and the course has been continuously evolving since then. The course topics are largely presented to the students “just in time” as projects and assignments require a given knowledge set. The course topics include:
Ø Potential flow review
Ø Panel methods review
Ø Vortex lattice methods
Ø Introduction to CFD concepts
Ø Computer system overview
Ø Vector algebra review
Ø Governing equations of fluid motion review
Ø Levels of governing equations (assumptions and simplifications)
Ø Finite differencing/finite volume/finite element approaches
Ø Truncation error
Ø Stability, consistency, convergence, and CFL number
Ø Stability analysis
Ø Modified equation
Ø Classification of PDEs
Ø Algorithm types (explicit, implicit)
Ø Steady and unsteady flow
Ø Time integration
Ø Boundary conditions (far field, solid surfaces, matching PDE types)
Ø Grid generation (structured, unstructured, Cartesian, overset, topology, transformed coordinates)
Ø The solution process (initial conditions, convergence, stability/robustness)
Ø Grid independence
Ø Time accuracy
Ø Turbulence models (RANS, LES, DES), model types (eddy viscosity, stress transport)
Ø Flow visualization
Ø Parallel computing
Ø Optimization approaches
Specifically, we learned the following aerodynamic concepts while performing these projects:
Ø Boundary conditions and their relationship to flow type (viscous or inviscid)
Ø Boundary layer thickness, growth, and velocity profiles
Ø Importance of understanding boundary‐layer theory while doing CFD (sublayer types and thicknesses, pressure gradients, etc.)
Ø Stagnation points and stagnation streamlines
Ø Flow separation and reattachment
Ø Laminar separation bubbles
Ø Airfoil/wing stall
Ø Airfoil pressure gradients as a function of angle of attack
Ø Airfoil surface and off‐surface pressures, circulation, and the resulting lift and
Ø drag variations with angle of attack
Ø The relationship between pressure gradients and flow separation
Ø Pressure and skin friction drag
Ø Unsteady vortex shedding
Ø The impact of wing‐tip vortices
Ø Compressibility effects at subsonic Mach numbers
Ø In addition, the following aerodynamic theories and concepts are taught to the students while they are performing their projects (or are learned in a prior course):
Ø NACA airfoil designations and data
Ø Potential flow theory
Ø Kutta‐Joukowski theorem
Ø Thin airfoil theory
Ø Lifting‐line theory
So, while many faculty members might have believed they were giving up a great deal by teaching computational aerodynamics to their students in lieu of the more traditional syllabus, we found that many of the same concepts were still covered, but in different (and project‐based) ways. The main idea behind the course design is to give students an exposure to the application as well as code development aspects of CFD. It also contains tutorials on the use of commercial CFD software (ANSYS Fluent). The outline of the course is as follows:
· Introduction and Background
o Conservation Laws and Model Equations
· Spatial Discretization
o Finite‐Difference Approximations
o Grid Convergence Studies
o Finite‐Volume Methods
· Solving Linear Systems
o Direct Methods
o Iterative Methods
o Preconditioning
· Time‐Marching Methods
o Some popular Time‐Marching Methods
o Implementation of Implicit Methods
o Stability
· Turbulence
o Direct Numerical Simulations
o Basics of Turbulence Modeling
o Some popular Turbulence Models
o Large Eddy Simulations
[1] Jeff D. Eldredge, Inanc Senocak, Paul Dawson, James Canino, William W. Liou, Ray LeBeau, Darren L. Hitt, Markus P. Rumpfkeil, and Russell M. Cummings, “A Best Practices Report on CFD Education in the Undergraduate Curriculum”, AIAA Fluid Dynamics Technical Committee.
Start with this and expand by adding in the links, as deemed necessary: https://en.wikipedia.org/wiki/Computational_fluid_dynamics. Make it practical and hands-on, with real examples and lab work. The undergrads must get their hands wet, literally and figuratively.
See also https://www.researchgate.net/post/Can_anyone_suggest_a_CFD_lecture_on-line_for_me_to_follow
Dr-Ali M Y A H
CFD concerns the solution of Navier-Stokes equations with computers to receive flows in an entire region. This often involves specifications of boundary conditions for e.g. relative velocities. For example , the 'Pouiseuille flow analytical solution' is a parabolic flow profile and the velocity at the boundary is zero, when following the flow, but often one wants a solution compared with a surface at rest/(fix surface or how you like to express it). Then, a large branch of CFD is turbulence, where often an additive decomposition is used with additional assumptions. I am not an expert, and not entirely updated into state of the art, but there are many solutions, however some results could also be captured without computers and C stands for computational, c.f. the splendid answer above from Dr Ian Kennedy.
The best way to teach CFD/suitable lecture material to undergraduate students in Department of Mechanical Engineering is go in details in concerned subjects like fluid mechanics and heat and mass transfer from Nptel lectures.
It is better to start with introduction to CFD which is teaching students different differential equations and how to solve them using a programming software like FORTRAN or MATLAB. Once students know the basic governing equations in CFD then they can understand CFD.
Honestly, I think that doing finite volume methods and the stuff that programs like Fluent uses might be beyond undergraduate class levels. its much more important to teach fundamentals instead of just training them up on some software tool.
I would recomend having some solid theory lectures followed with labs. The students could program their own simulations using simpler methods like vortex panels or other superposition methods. That way they really get their hands dirty with application of fundamental concepts, but the scale of the project is within reason of a single undergraduate semester.
Thank you for your wonderful contribution, Prof. Ian Kennedy, Dr-Ali Mohammed Yassen Al Hashemi ; Lena J-T Strömberg; Andrea Passariello; ; Dr. Sajad Hussain Din and Amin Ghorbanpour for your wonderful contribution.
1.1 Strategies for Incorporating CFD into Undergraduate Curriculum
In the previous section, an effort was made to present the list of CFD‐related concepts and tools hierarchically. This effort was in anticipation of the current section, in which a hierarchy of CFD curriculum profiles from low to high is described. In this fashion, the modular CFD elements can naturally be identified for inclusion in an appropriate setting. For example, in the lowest profile setting, precomputed CFD solutions are to be used to illuminate fundamental fluid dynamic phenomena, and therefore only some elements of the concept hierarchy are invoked (in this case, post‐processing). The objective in this section is to present a number of examples, drawing where possible on existing curricula. This allows us to present the accompanying syllabi, some brief descriptions of sample homework problems and projects, and lessons learned on the development and continuing evolution of these existing courses.
1.1.1 CFD Light
This represents the lowest profile inclusion of CFD in an undergraduate curriculum. In such a case, an instructor of an introductory or intermediate fluid mechanics course uses pre‐computed CFD simulations in order to reinforce fundamental concepts. With the availability of free high‐quality visualization software (e.g., Paraview and VisIT), this approach is relatively straightforward to introduce into an existing curriculum, provided a repository of solutions has already been generated.
Students would be able to download the CFD solution files and use them to study fluid flow in and around various geometries. This approach would help eliminate software cost, and also introduce more realistic engineering simulations into the undergraduate curriculum while avoiding long simulation times and resources and instruction needed to conduct such simulations.
1.1.2 CFD Moderate
At this level of CFD instruction, CFD modules are used to augment course material, by substituting the module into an existing lecture‐form fluid mechanics or aerodynamics course, or into the accompanying lab unit of the course. The CFD content is heavier than in the CFD light scenario, in that here, the students are expected to compute the solutions before analyzing them. As the examples below will suggest, this approach often makes use of free or in‐house inviscid aerodynamic solvers (i.e. panel and vortex lattice codes) in order to compute flows and predict forces on lifting surfaces. For further information, please consult the [Eldredge et al.][1].
1.1.3 CFD Heavy
In this format, CFD is taught as a stand‐alone course, and therefore more emphasis is placed on teaching fundamental concepts of CFD. The U.S. Air Force Academy created this course nearly a decade ago, and the course has been continuously evolving since then. The course topics are largely presented to the students “just in time” as projects and assignments require a given knowledge set. The course topics include:
Ø Potential flow review
Ø Panel methods review
Ø Vortex lattice methods
Ø Introduction to CFD concepts
Ø Computer system overview
Ø Vector algebra review
Ø Governing equations of fluid motion review
Ø Levels of governing equations (assumptions and simplifications)
Ø Finite differencing/finite volume/finite element approaches
Ø Truncation error
Ø Stability, consistency, convergence, and CFL number
Ø Stability analysis
Ø Modified equation
Ø Classification of PDEs
Ø Algorithm types (explicit, implicit)
Ø Steady and unsteady flow
Ø Time integration
Ø Boundary conditions (far field, solid surfaces, matching PDE types)
Ø Grid generation (structured, unstructured, Cartesian, overset, topology, transformed coordinates)
Ø The solution process (initial conditions, convergence, stability/robustness)
Ø Grid independence
Ø Time accuracy
Ø Turbulence models (RANS, LES, DES), model types (eddy viscosity, stress transport)
Ø Flow visualization
Ø Parallel computing
Ø Optimization approaches
Specifically, we learned the following aerodynamic concepts while performing these projects:
Ø Boundary conditions and their relationship to flow type (viscous or inviscid)
Ø Boundary layer thickness, growth, and velocity profiles
Ø Importance of understanding boundary‐layer theory while doing CFD (sublayer types and thicknesses, pressure gradients, etc.)
Ø Stagnation points and stagnation streamlines
Ø Flow separation and reattachment
Ø Laminar separation bubbles
Ø Airfoil/wing stall
Ø Airfoil pressure gradients as a function of angle of attack
Ø Airfoil surface and off‐surface pressures, circulation, and the resulting lift and
Ø drag variations with angle of attack
Ø The relationship between pressure gradients and flow separation
Ø Pressure and skin friction drag
Ø Unsteady vortex shedding
Ø The impact of wing‐tip vortices
Ø Compressibility effects at subsonic Mach numbers
Ø In addition, the following aerodynamic theories and concepts are taught to the students while they are performing their projects (or are learned in a prior course):
Ø NACA airfoil designations and data
Ø Potential flow theory
Ø Kutta‐Joukowski theorem
Ø Thin airfoil theory
Ø Lifting‐line theory
So, while many faculty members might have believed they were giving up a great deal by teaching computational aerodynamics to their students in lieu of the more traditional syllabus, we found that many of the same concepts were still covered, but in different (and project‐based) ways. The main idea behind the course design is to give students an exposure to the application as well as code development aspects of CFD. It also contains tutorials on the use of commercial CFD software (ANSYS Fluent). The outline of the course is as follows:
· Introduction and Background
o Conservation Laws and Model Equations
· Spatial Discretization
o Finite‐Difference Approximations
o Grid Convergence Studies
o Finite‐Volume Methods
· Solving Linear Systems
o Direct Methods
o Iterative Methods
o Preconditioning
· Time‐Marching Methods
o Some popular Time‐Marching Methods
o Implementation of Implicit Methods
o Stability
· Turbulence
o Direct Numerical Simulations
o Basics of Turbulence Modeling
o Some popular Turbulence Models
o Large Eddy Simulations
[1] Jeff D. Eldredge, Inanc Senocak, Paul Dawson, James Canino, William W. Liou, Ray LeBeau, Darren L. Hitt, Markus P. Rumpfkeil, and Russell M. Cummings, “A Best Practices Report on CFD Education in the Undergraduate Curriculum”, AIAA Fluid Dynamics Technical Committee.
Usually during undergraduate math courses the student learn numerical methods. In finite volumes method everything is about discretization of governing equations. Mass, energy, moment and species conservation in partial derivatives are the main subject and how they can turn them in algebraic equations using taylor series or any other method. But CFD is a very wide subject and just the rudiments could be taught in undergraduate courses.
First of all, you should learn numerical methods to discrete the equations and then programming the discrete equations and solve it. Or learning the CFD software like Ansys Fluent.
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