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Thursday February 6, 2020 at 12:30pm

In 2018 SOLIDWORKS introduced a new capability to their Flow software. This is called ‘Free Surface’ and opens up many more applications for users who need to simulate fluid behaviour where a gas and a liquid (or two immiscible liquids) share the same region of space without an intervening solid.

- Sloshing of tanks e.g. petrol tankers where the petrol does not completely fill the tank
- Filling of chambers e.g. a barrel being filled with oil
- Cistern emptying e.g. a toilet cistern flushing a toilet pan
- Fountains and jetting e.g. a water jet hosing a car
- Waves impacting static bodies e.g. a sea wall or the legs of an oil platform in the ocean
- Civil engineering hydraulics e.g. dams, weirs, orifices, valves, sluices
- Process engineering e.g. partially filled valves, orifices, pipes

The underlying technology is called the **‘Volume of Fluid’**
(VOF) method. In the case of air and water, this assigns a volume fraction of
air and water to each cell in the domain. The sum of the two fractions is
always 1, so calculating one fraction always implies the other. Where the
volume fraction is 0.5, there will be a free surface. Either side of this cell
the volume fraction will tend towards fully water or fully air. As with all
Flow simulations, the software calculates the mass and volume of fluids
entering and leaving each cell and conserves momentum, energy and mass. However,
the actual movement of the free surface is obtained using ‘transport equations’
driven by fluid momentum calculations and external boundary conditions including
gravity. More details are available in the Flow Simulation Technical Reference.

For those of us who struggle with understanding second order differential equations (most of us!) the proof of the pudding is in the eating, or in terms of Flow, the proof is whether the software actually works. There are plenty of fancy animations online that look impressive but I like to be sure of the technology before I recommend it to a customer – therefore I set myself a free surface challenge - based on a ‘Sharp Crested Weir’.

A Sharp Crested Weir is a well understood hydraulics problem which is taught in universities to civil engineers who need to design dams, splash pools, water courses and weirs. Below is an extract from one university lecture that is publicly available on YouTube.

The critical equation is derived from energy balances and takes the form …

Where...

- Q = volumetric water flow rate over the weir in m3/s g = gravity in m/s2
- L = the width of the weir (perpendicular to the water flow) in metres
- H = the ‘head’ of the weir i.e. the height of the upstream water level measured vertically from the top of the weir in metres
- P = the upstream height of the weir in metres
- X = a constant for a sharp crested weir = 1.5
- Cd =the ‘Discharge Coefficient’ that has been obtained by experimental work and variables H and P

The first step in simulating this is to build a simple model in SOLIDWORKS. This is for both the weir and 2 bodies to represent the water – upstream (with a head) and downstream as a splash pool. Since we will simulate a 2D slice, this can be done with simple extrudes ignoring any channel sides.

The dimensions used were:

- H = 400 mm
- P = 1000 mm
- L = 20 mm (i.e. the depth of the 2D computational domain)

Plugging these values into the equation gives a predicted
flow rate, **Q = 0.0095 m3/s**

The set up in Flow is quite simple …

I also enabled saving of important parameters that I want to display using the ‘Transient Explorer’. I did this in ‘Calculation Control Options’ and chose saving of ‘Volume Fraction of Water’ and ‘Immiscible Water’. This enables a very quick and easy way to create animations of the chosen parameters over time.

**The mesh in Free Surface simulations is very important.** As a
rough guide you need at least 5 cells across the width of each fluid stream. I
used a ‘Manual’ mesh and several local meshes.

A result at 1 sec after the water is release is shown below. The water is spilling over the weir and has generated a wave in the splash pool.

The graph above shows the volumetric flow rate of water over
the weir (Q). At 1 sec the flow rate is **0.0082 m3/s.**

The flow rate reaches a maximum value at 1.5 seconds of **0.0088 m3/s.**This is within 8% of the theoretical value. This is a great start, but is there
any reason for the small discrepancy? Is the theory correct or the simulation?

To answer that we need to understand the assumptions in the theory. The mathematical derivation (based on energy conservation) makes the assumption that the upstream flow is constant and sufficient to perfectly match the flow over the weir i.e. the surface of the water is at a fixed height (H and P are constants).

In contrast the Flow simulation is modelled as a tank with finite capacity so the water level slowly reduces. Furthermore, you can see from the animation below that the upstream water gently sloshes from end to end as a result of the initial release of the water.

Clearly we could extend the tank or even introduce more water upstream with an inlet boundary condition which would result in a higher flow rate over the weir giving an even closer match to the theory. However, I think it is informative to observe the sloshing effect.

This is just one of a number of Free Surface applications but the accuracy of the method gives confidence to apply the technology to more interesting situations like a more complex 3D weir (Cipolletti weir) with a downstream splash tank and a complex 3D outlet channel such as this.

You can even simulate the flushing of toilets!!!

(The video shows the water flushing the pan on a half model to make it easier to see)

**Andy Fulcher**

*
Solid Solutions Management - **Group Technical Director*

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