CHE521 ADVANCED FLUID FLOW
| Course Code: | 5630521 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Chemical Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. YUSUF ULUDAĞ |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of the course students should be able to
- Develop basic equations of fluid flow through vector/tensor operations
- Obtain general solutions for creeping flows via eigenfunction expansions
- Apply regular and singular perturbations for pulsatile flow
- Solve steady shear flow problems involving non-Newtonian fluids through generalized Newtonian model
- Use linear viscoelastic constitutive models and interpret their physical significance for material characterization
- Apply nonlinear viscoelastic models to obtain relations for material functions
Course Content
Inviscid fluid, Euler equation, Bernoulli equation, Kelvin's theorem, irrational motion, Stoke's stream function, vorticity; analytical and numerical solutions of Navier-Stokes equation; creeping flow equation, introduction to lubrication theory; vorticity transport equation, laminar boundary layers, turbulent boundary layers; introduction to turbulence.
Course Learning Outcomes
- Vector/tensor manipulations, index notation, Reynold’s transport theorem, continuity equation
- Properties of stress tensor, Cauchy stress equation, mechanical and thermal energy balances, constitutive equations
- Navier-Stokes equations, steady and unsteady unidirectional flows, scaling terms in the Navier-Stokes equations
- Creeping flows, linearity of Stokes equations, streamfunctions, general solutions via eigenfunction expansions
- Regular and singular perturbations for pulsatile flow, lubrication theory, Reynold’s equation, slider block and cylinder problems
- Shear flow with viscous dissipation, concept of viscoelasticity and Deborah number. Shear-rate dependent viscosity in steady shear flow
- Invariant properties of tensors. Generalized Newtonian fluid models. Measurement of steady shear viscosity: Couette and cone-and-plate rheometers. Analytical solutions for generalized Newtonian fluids in simple shear flows
- Definition of normal stress differences in steady shear flows. Analysis of observable effects of normal stresses. Measurement of normal stress differences with cone-and-plate rheometers
- Linear viscoelastic properties: The complex modulus and complex viscosity. Linear viscoelastic constitutive equations: The Maxwell, Jeffreys and Kelvin models in differential and integral form
- Linear viscoelasticity with multiple relaxation times. Empiricisms for relating the linear viscoleastic properties to steady shear viscosity and normal stress differences: The Cox-Merz rule and Laun’s rule
- Limitations of linear viscoelastic models. Commonly observed “funy flow phenomena” in viscoelastic liquids. The need for nonlinear constitutive equations
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | Acquire knowledge in depth and breadth via scientific research in their field; evaluate, interpret and apply this knowledge. | ✔ | |||
| 2 | Are thoroughly informed about current techniques and methods of engineering, and their limitations. | ✔ | |||
| 3 | Complement and apply uncertain, limited or incomplete knowledge using scientific methods; are capable of integrating knowledge from different disciplines. | ✔ | |||
| 4 | Are aware of the new and developing applications of their profession; can study and learn about these applications when necessary. | ✔ | |||
| 5 | Can define and formulate problems relevant to their field, develop solutions to solve these problems and employ innovative methods for these solutions. | ✔ | |||
| 6 | Develop new and/or original ideas and methods; design complex processes and develop innovative/alternative solutions in design. | ✔ | |||
| 7 | Design and apply theoretical, experimental and model-based research; analyze and resolve complex problems that arise during this process. | ✔ | |||
| 8 | Can effectively function within intra- and interdisciplinary teams, can lead such teams and formulate solution approaches under complex situations; can work independently and assume responsibility. | ✔ | |||
| 9 | Can communicate verbally or in written form in a non-native language, at least at level B2 of the European Language Portfolio. | ✔ | |||
| 10 | Can communicate the progress and results of their studies systematically and clearly in oral or written form, in national or international forums related to their area or others. | ✔ | |||
| 11 | Are informed and aware of the limitations of social, environmental, health and safety-related and legal dimensions on engineering applications. | ✔ | |||
| 12 | Uphold social, scientific and ethical values in acquisition, interpretation and communication of data and in all activities related to their profession. | ✔ | |||