This course starts with a theoretical overview of the famous Navier-Stokes equations and how to simpllify them in order to get easier, yet insightful, potential equations for fast analysis.
This course starts with a theoretical overview of the famous Navier-Stokes equations and how to simpllify them in order to get easier, yet insightful, potential equations for fast analysis.
Then we will focus in using these equations to derive the Vortex Panel Method (we'll cover all maths aspects also) and code it in Matlab. With that in hands, we will perform several analysis of generic airfoils to better understand how key design characteristics affect the overall results.
On the next section, we'll go from 2D world to 3D, analysing wings now. Similarly, we'll start with a theoretical review of the Weissinger method for general wings (we'll cover all maths aspects also) and then we'll create a Matlab code to simulate the designs. We'll invistigate how several key parameters, such as sweep, aspect ratio, twist and others, can affect the overall behavior of wings.
Finally, we'll include viscous effects on the Weissinger method for a more robust analysis, including flow separation and stall.
This course is filled with real examples and is a more hands-on approach on the analysis of airfoils and wings. If your are an engineering student, aviation enthusiast, industry or academic engineer or just want to learn more about how to apply Aerodynamic theory, this is the right course for you.
Hello and welcome. Let's get to know each other and take a look what we will learn in this course.
References for further studies:
Fundamentals of Aerodynamics - John D. Anderson Jr.
Aerodynamics for Engineers - John J. Bertin
Foundations of Aerodynamics: Bases of Aerodynamic Design - Kuethe and Chow
The Matlab version used in this course is 2020a. But if you follow the step by step instructions you can use any version after 2012a.
We'll learn how to simplify the famous and difficult Navier-Stokes equations to more simple maths in order to allow a fast approach in analyzing airfoils.
There are several elementary flows (source, sink, uniform, vortex, etc). In this section will learn how to derive and work with the uniform and vortex flow. Those are the ones that will be used in the future Vortex Panel Method we'll derive.
In part 1 of the airfoil theory, the goal is to introduce the geometric characterisitcs and explain the physiscs behind lift generation.
We'll also introduce the pressure coefficient concepts to pave the way to the airfoil analysis to be done on part 2.
This part 2 will focus on the viscous theory and in the analysis of several design characteristics of airfoils.
- NACA airfoils characteristics
- Camber
- Thickness
- Leading edge radius
- Flap deflection
We will work on the theoretical derivation of the linear varying Vortex Panel Method. A lot of maths in this section, but it will greatly help our coding in the next lesson.
The main sources for this section derivations are:
1- Foundations of Aerodynamics: Bases of Aerodynamic Design - Arnold M. Kuethe / Chuen-yen Chow - 4th Ed - section 5.10
2- Fundamentals of Aerodynamics - John D. Anderson - 3rd Ed - section 1.5
After the paved theoretical background from last lesson, let's get into Matlab and code our Panel Method for airfoil analysis.
The first part is dedicated to the airfoils' drawing. We'll cover NACA 4 and 5 digit airfoils as well as general shapes that can be loaded via an Excel spreadsheet.
The second part is dedicated to defining and checking the panel geometry as defined in out theoretical lesson.
The third part is dedicated to calculating the linear coefficients from the A matrix and solve for zero normal velocities at the panels to determine the circulation and therefore, the lift, drag and moment coefficients.
The last part is just to help the flow visualization by computing the streamlines around the airfoil.
If you have a MATLAB version newer then 2016, you can open the live script (.mlx), otherwise, use the normal script (.m) VPM_lin
This lesson focus on the derivation of the Weissinger Method ofr the commputation of general planform wings. The references used are:
BERTIN, J. J.; CUMMINGS, R. M. Aerodynamics for engineers. 5. Ed. Englewood Cliffs, NJ: Pearson Prentice Hall, 2009.
PHILLIPS, W. F.; SNYDER, D. O. Modern adaptation of prandtl's classic lifting-line theory. Journal Of Aircraft. v.37, p. 662-670. Jul. 2000.
After the paved theoretical background from last lesson, let's get into Matlab and code our Weissinger Method for wing analysis.
Let's use our code to analyze several design characteristics of wings.
- Aspect Ratio
- Taper Ratio
- Sweep angle
- Geometric twist
- Aerodynamic Twist
This section aims in constructing a numerical optimizer for the wing geometry (Aspect Ratio, taper, twist and sweep) in order to minimize drag and other constraints.
If you have a MATLAB version newer then 2016, you can open the live script (.mlx), otherwise, use the normal script (.m) WEISSINGER_MAIN
In this lesson we'll learn how to use a potential method to compute viscous flows of wings.
The refetence used in the decambering method is:
Mukherjee, Rinku & Gopalarathnam, Ashok & Kim, Sung. (2003). An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics from Known Section Data. 10.2514/6.2003-1097.
References for further studies:
Fundamentals of Aerodynamics - John D. Anderson Jr.
Aerodynamics for Engineers - John J. Bertin
Foundations of Aerodynamics: Bases of Aerodynamic Design - Kuethe and Chow
PHILLIPS, W. F.; SNYDER, D. O. Modern adaptation of prandtl's classic lifting-line theory. Journal Of Aircraft. v.37, p. 662-670. Jul. 2000.
Mukherjee, Rinku & Gopalarathnam, Ashok & Kim, Sung. (2003). An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics from Known Section Data. 10.2514/6.2003-1097.
The Matlab version used in this course is 2020a. But if you follow the step by step instructions you can use any version after 2012a.
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