Physical Modelling

Question 1

What is a physical model?

Answer 1

A physical model is a small-scale copy of a full-scale (prototype) system

Question 2

What are the 3 types of similarity?

Answer 2

Geometric, Kinematic and Dynamic

Question 3

Describe common denotation used in physical modelling

Answer 3

()P = prototype value
()M = model value
()R = Ratio of ()P/()M, scale

Question 4

Describe Geometric Similitude

Answer 4

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.

Question 5

What is the area scale in terms of length scale?

Answer 5

Lr^2

Question 6

What is the volume scale in terms of length scale?

Answer 6

Lr^3

Question 7

Describe Kinematic similarity

Answer 7

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

Question 8

Describe Dynamic similarity

Answer 8

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

Question 9

What is complete dynamic similarity?

Answer 9

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

Question 10

Why do we get incomplete dynamic similarity?

Answer 10

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

Question 11

When is Reynold’s scaling used?

Answer 11

Closed conduit flows (pipes)

– Viscous forces (e.g. friction) are most important
– Pressure forces are scaled automatically

Question 12

When is Froude’s scaling used?

Answer 12

Free surface flows (e.g. lakes, rivers, oceans)

– Gravity forces are most important
– Pressure forces are scaled automatically

Question 13

Describe the relationship found in Froude scaling

Answer 13

Ur = sqrt(Lr)

Question 14

Describe the relationship found in Reynold’s scaling

Answer 14

Ur = 1/Lr

Question 15

Name 3 examples of scaling

(not Reynolds or Froude)

Answer 15

Mach Scaling, Weber Scaling, Euler Scaling

Question 16

What are the positives and negatives of physical modelling?

Answer 16

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

Question 17

What are the positives and negatives of numerical modelling?

Answer 17

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