WHAT IS CFD
CFD stands for Computational Fluid Dynamics.
It is a way of generating a computer simulation of fluid flow in real time.
It consists of analyzing all forces on individual particles in the fluid. The forces can consist of gravity, viscosity, friction, surface tension, shear forces, density etc. (Nothing to do with the standard hydraulic empirical formulas.) The resultant of these forces on each particle is distributed to surrounding particles, and so on. The resulting equations must also satisfy the conservation of mass, momentum and energy.
This means millions of calculations for each frame of a video to determine how far, and in what direction, each particle will move in a given time frame. If there are 25 frames/second, a ten second video will have 250 frames, with millions of calculations for each frame.
Each fluid particle is called a cell. The smaller the cell the more accurate the simulation, (generally).
The division of the fluid into cells is called a mesh. There are millions of cells in the mesh.
The cells can be a combination of hexahedral, tetrahedral, prismatic, pyramidal or polyhedral elements.
It is a hugely time consuming process if you wish to use it in any serious way. For instance I did a CFD simulation of a much simpler thing than that shown above, and using 16 cores of computing power it took 30 hours to get a result. (and a similar amount of time to analyse the result).
However I could then read the pressure, velocity, and depth anywhere in the simulation, and all in pretty colours. But this is a huge overkill for the design of a simple box gutter.
The simulation you see above took 4 hours of computer calculation, because I used a very coarse mesh. However the result is good enough to visualize what is going on, and to prove a point.
ANALYZING THE RESULTS
The above simulation is very pretty, but not very good at measuring any meaningful depths. So lets take a closer look at the mesh.
The important things to note are:-
a) The deepest flow is at the upstream end, because the water surface must always fall in the direction of the flow.
b) The flow over the brink is 0.7*critical depth. This is a hydraulic principle of a free outfall from an open channel.
c) The downpipe does not flow full. The flow is restricted by the entry throat diameter.
WHAT ARE THE CODE RESULTS
The simulation is based on 11 L/s, with a 300mm wide box gutter, and no slope.
From the Plumbing Code, Fig I1 gives the gutter depth for no slope as 170, and with 1:200 slope, depth = 145 mm.
AS3500.3 Fig I1 for 11 L/s
From fig I3, for a DP dia of 125, flow = 11 L/s rainwater head details are :-
- depth of water = 112
- Total depth of RWH = 187,
- and length of RWH, at BG depth of 145 (1:200) = 173
From Fig I6 :-
Critical depth “Loc” = 52 mm
0.7 * critical depth = 37
PLOTTING THE RESULTS ON THE MESH
The background grid is 100mm spacing, so you can visually check the dimensions, and confirm I am not pulling any legs.
The Code does not give any values for the freeboard, maybe this is because the freeboard may vary with width and flow, as in some other plumbing Codes.
However I find that a value of about 60mm seems to work. This gives a water depth of 110 mm.
The total gutter depth, and rain water head dimensions are also plotted to the code sizes.
As you can see, there is remarkable agreement with the Plumbing Code.
So we can all go away with a warm inner glow, knowing that a CFD simulation agrees with the Plumbing Code.
BTW my free programs also give the same results.