Free Shear Layer Between Two Different Streams — Lesson 3

This lesson covers the concept of laminar free shear flows, focusing on the free shear layer between two streams with different velocities. It explains how a velocity gradient forms when two different streams meet and continue in the axial direction. The lesson introduces the concept of similarity variables used by Blesius to solve this problem and explains how to write down the similarity variable. It also discusses the boundary layer equation and how to solve it using similarity variables. The lesson further delves into the boundary conditions for each layer and the use of asymptotic approach to true stream velocities. It also explains the use of numerical methods like finite difference method, finite volume method or finite element method to solve the boundary layer equation. The lesson concludes with a discussion on the use of explicit and implicit methods to discretize the boundary layer equation and the boundary conditions.

Video Highlights

00:30 - Introduction to free shear flows between two different streams with different velocities U1 and U2.
03:03 - Explanation of the boundary layer equation and its solution using similarity variables.
15:13 - Discussion on the use of numerical method and the division of domain into grid for solving the boundary layer equation.
17:30 - Explanation of the governing equation and the discretization scheme for solving it.
22:00 - Discussion on the use of explicit method for discretizing the boundary layer equation and the restrictions in choosing the value of delta X.
27:11 - Explanation of the use of implicit finite difference model for discretizing the boundary layer equation and its unconditional stability.
30:56 - Discussion on the boundary conditions for solving the boundary layer equation.

Key Takeaways

- The free shear layer between two streams with different velocities creates a velocity gradient.
- The concept of similarity variables, introduced by Blesius, is used to solve the problem of free shear flows.
- The boundary layer equation can be solved using similarity variables.
- Boundary conditions for each layer are important and the asymptotic approach to true stream velocities is used.
- Numerical methods like finite difference method, finite volume method or finite element method can be used to solve the boundary layer equation.
- Both explicit and implicit methods can be used to discretize the boundary layer equation.
- The boundary conditions are crucial in solving the boundary layer equation.