Physical Modelling Flashcards
What is a physical model?
A physical model is a small-scale copy of a full-scale (prototype) system
What are the 3 types of similarity?
Geometric, Kinematic and Dynamic
Describe common denotation used in physical modelling
()P = prototype value
()M = model value
()R = Ratio of ()P/()M, scale
Describe Geometric Similitude
Involved length (L) only. The flow pattern in model and prototype must have similar shapes There must be a constant ratio between corresponding lengths: 𝐿𝑟 = 𝐿𝑝/𝐿𝑚
Surface roughnesses must be scaled geometrically.
What is the area scale in terms of length scale?
Lr^2
What is the volume scale in terms of length scale?
Lr^3
Describe Kinematic similarity
Involve length (L) and time (T) only.
There must be a constant ratio between corresponding velocities and
accelerations in the model and prototype
The time scale can be expressed in terms of the length and velocity
scales
Describe Dynamic similarity
Involves mass (M), length (L) and time (T)
There must be a constant ratio between corresponding forces
in the model and prototype
Corresponding forces act in the same direction
What is complete dynamic similarity?
If we can satisfy any 2 of the 3 types of similitude, the 3rd type is automatically satisfied
Typically we build a model which looks like the prototype. We use scaling criteria involving forces to ensure dynamic similitude. As a result we get kinematic similitude so flow in the model replicates prototype flow.
Complete dynamic similarity means that there is a constant ratio between corresponding forces in model and prototype
Why do we get incomplete dynamic similarity?
Complete dynamic similarity is usually unachievable because:
Our choice of fluid is restricted
- Difficult to vary density and viscosity in a controlled manner (Water is commonly used as it is cheap, non-flammable and non-toxic)
- Acceleration due to gravity is fixed
Thus complete dynamic similarity can only be achieved with a full-sized
model
When is Reynold’s scaling used?
Closed conduit flows (pipes)
– Viscous forces (e.g. friction) are most important
– Pressure forces are scaled automatically
When is Froude’s scaling used?
Free surface flows (e.g. lakes, rivers, oceans)
– Gravity forces are most important
– Pressure forces are scaled automatically
Describe the relationship found in Froude scaling
Ur = sqrt(Lr)
Describe the relationship found in Reynold’s scaling
Ur = 1/Lr
Name 3 examples of scaling
(not Reynolds or Froude)
Mach Scaling, Weber Scaling, Euler Scaling
What are the positives and negatives of physical modelling?
Good for small localised regions, particularly where the flow is 3D, complex and violent, e.g. breakwaters and energy dissipators
Good for public relations; easy to relate to by specialist and non-specialists.
Can model turbulence, but correct scaling of turbulence is no guaranteed.
Modelling of gravity driven flows is relatively simple, but flows driven by the Coriolis force, wind and density differences are difficult to scale.
Models are not easy to modify.
Very expensive
Take time to build and operate
Typically impractical to store
Model faults are easy to identify
Not usually transportable
What are the positives and negatives of numerical modelling?
Good for extensive regions e.g. rivers and floodplains where the flow is essentially 1D (e.g. rivers) or 2D (e.g. estuaries) and gentle.
Produces attractive colour plots, but these can be difficult to relate to the prototype situation.
There is no complete mathematical description of turbulence.
Flow driven by winds, density differences and the inclusion of the Coriolis force are routinely modelled.
Easy to modify, inexpensive, easy to build, easy to distribute.
Once a model has been set up for a job, it can be easily re-used
Risk of using blind as a “black box” making faults less obvious
