Single-Course Engelsk 5 ECTS

## Overall Course Objectives

To develop an analytical and physical understanding of the fundamental equations that govern fluid flow and solve them analytically in reduced form in a range of engineering and academic problems. The assumptions in the reduced forms of the equations and their implications on the obtained solutions will be carefully discussed and evaluated. The student will apply the solutions of the reduced equation on relevant engineering problems and evaluate the validity of the solutions based on the respective assumptions made.

See course description in Danish

Learning Objectives

• Explain and derive the basic conservation laws of fluid mechanics on differential form
• Apply tensor notation to describe flow kinematics and solve flow problems
• Explain and apply the analogy between momentum, heat and mass transfer
• Derive and solve simplified versions of the Navier-Stokes equations, such as the vorticity equation, Creeping/Stokes flow, potential flow, similarity solutions and the boundary layer equations
• Solve and analyze various corresponding simplified flow problems and identify problem formulations that even further simplify solutions of the reduced equations.
• Evaluate the validity and impact of the assumptions used to solve the flow problems
• Discuss the physical interpretation of these solutions
• Use the boundary layer approximation to solve simple boundary layer problems
• Apply the method of normal modes to simple problems of flow instability and identify flow settings with potential appearance of common instabilities
• Document a technical solution in writing in a short and precise form

Course Content

Derivation of the continuity equation, the Navier-Stokes equation and the energy equation on differential form. Tensor notation for describing flow kinematics. Analogies between transfer of momentum, heat and mass. Flow in ducts, boundary layers, free shear flows, Creeping/Stokes flows, potential flows. Similarity solutions and vorticity formulation of the Navier-Stokes equation. Linear instability analysis and laminar to turbulent transition. Theory will also be discussed in relation to industrial problems.

Recommended prerequisites

41312/41102/02631/02633/28864, Knowledge of basic fluid mechanics and basic knowledge of Matlab, Python or similar.
Knowledge of mathematics, specifically for solving partial differential equations (e.g. the chain rule, partial differentiation and integration, basic vector calculus including familiarity with Stokes’ and Gauss’ theorems).

Teaching Method

Lectures and problem solving. Feedback on exercises during the course.

Faculty

See course in the course database.

## Registration

Language Engelsk 13 weeks DTU Lyngby Campus 41320 Candidate Week 36 Week 49 Thurs 8-12
Price 9.250,00 DKK