Reference frames
- 1. Reference frames A brief overview
- 2. Definition of Reference frame • A frame of reference is a set of coordinates that can be used to determine positions and velocities of objects in that frame; different frames of reference move relative to one another. • To put simply, it is the location from which an observer observes a physical phenomenon • Example : • For a person on a railway platform observing a train, the train moves. But for the person in the train, it appears like the platform moves. • Another way to look at it : the person in the train could even think that the train is stationary. Why?
- 3. Types of reference frames • Inertial reference frames – No acceleration arises • Non inertial reference frames – acceleration and pseudo forces arise What type of reference frame are these?
- 4. Reference frames in CFD • Mainly used in rotating flow simulation • Transforms an unsteady problem in stationary frame into a steady problem in moving frame • Result? – Obvious, steady equations are simpler to solve • Condition – steady rotational speed is needed. • If not? – Additional unsteady terms will appear, they have to be applied as a source term. What is velocity formulation and what are its types?
- 5. Coriolis force (What??) Identify the stationary and moving reference frame from this gif
- 6. FLUENT – Reference frames • Single rotating reference frame • Multiple rotating reference frame • Multiple reference frame model • Mixing plane model • Sliding mesh
- 7. Single rotating reference frame • Many problems permit the entire computational domain to be referred to as a reference frame • Wall boundary requirements: • Moving walls have no slip condition – relative velocity zero • Surface of revolutions – absolute velocity zero (components outside the reference frame)
- 8. Multiple rotating reference frame • Simplest approach for multiple zones • Steady state approximation – individual cell zones can have different rotational and/or translational speeds • Mesh remains fixed for computation – “Frozen rotor approach” • To be used for problems with weak rotor-stator interactions and not highly transient problems.
- 9. MRF – Interface formulation • Depends on velocity formulation being used. • Applies to velocity and velocity gradient, not for scalar quantities like pressure, temperature. Conformal mesh – define the interface between rotating and stationary zone as “interior” Non conformal mesh – define mesh interfaces separately as “interface”
- 10. Interface treatment – Relative velocity formulation • For a translational velocity 𝑣𝑡 𝑣 = 𝑣𝑟 + 𝑤 × 𝑟 + 𝑣 𝑡 The gradient of the above vector can be shown to be, The above transformation is what is used to transfer data pertaining to velocity and its gradients from the moving reference frame to the stationary/laboratory reference frame Note – Scalar quantities do not need any special transformation. The quantities are passed on from adjacent cells without loss of continuity
- 11. Interface treatment – Absolute velocity formulation • Governing equations in each subdomain written with respect to that subdomain’s reference frame • However velocity values are stored in the absolute frame • So no special transformation is required across the interface for velocity and its gradient • Scalar quantities – from adjacent cells
- 12. References 1. FLUENT manual – Theory guide, User guide, Tutorial guide 2. Google images 3. Introduction to Computational Fluid Dynamics – H. Versteeg and W. Malalasekera I have compiled the contents of this presentation from the above sources. You may choose to reproduce the same, however, please cite the references as and when needed Please try out the tutorial simulations from the manual so as to have a more comprehensive treatment of the concepts explained above. I sincerely hope that this small explanation has given a deeper understanding of reference frames, and we can be more intuitive about the same for future problems. Sincerely, Siddharth. N CFD Engineer
- 13. Thank you!