# All entries for Wednesday 28 March 2007

## March 28, 2007

### Party!– Recipe for 'Kickstart'

Milla & I have come up with a simple but rather addictive kickstart drink. It goes…

1 part vodka, 2 parts cranberry juice, 2 parts pineapple juice, 2 parts lemonade

### PhD Work– 28/03/07

09:46

rs01-02-07 still appears to be stable although the recirculation development is different to the other sims (although stable). Will just need to leave that running for now.

In the meantime, I can get on with the MT03-01 simulations in preparation for Juice’s work.

I also need to assess the full Reynolds number grid requirements before the meeting on Monday

• Calculate the grid requirements for full and 0.1 Re simulations
• Look at MT03-01 simulations

17:00

Have set running mt03-01-18 again which uses 50% fluctuations. Once this is established, I will run 19 & 20 with 75% & 100% fluctuations resp. (As detailed in the recent paper on LES BF Step)

Will now get on with working out grid requirements for LES runs for full and 0.1 Re in preparation for Monday’s meeting.

Grid Requirements

Full Re

For the full Re case, Bernard (2003) gives the friction velocity at the apex of the bump (I.e. the point of maximum wall shear) to be of the order of 0.535m/s. This would equate to a wall unit size of around 2.719×10-6m or 27 microns.

As LES requires the following:

dx+ < 100, dy+ < 1, dz+ < 20

this gives the following grid limits:

dx < 2.7mm, dy < 27 microns, dz < 0.54mm

Assuming that these grid spacings will be used throughout the domain (which is true as a starting point and we will try to compress the grid later to save resources):

nx = 10m/2.7mm = 3700
ny = 1m/27microns = 15000
nz = 0.5m/0.54mm = 925

This equates to a grid mesh of 5.134×1010 (that is 51,340 million nodes!) Clearly, even with some grid expansion, it would be almost impossible to bring the requirements down to the region of 1-10 million nodes.

0.1 Re

Using semi-empirical theory, the wall shear stress at the inlet is likely to be around 0.002 Pa which will probably increase by a factor of 2.5 near the bump apex to around 0.0057 Pa. This equates to a friction velocity of 0.068m/s thus giving a wall unit as 0.2mm.

Using the same grid requirements as above, we can estimate the grid spacings to be:

dx < 20mm, dy < 0.2mm, dz < 4mm

This gives the number of grid nodes as:

nx = 10m/20mm = 500
ny = 1m/0.2mm = 2000
nz = 0.5m/4mm = 125

Thus giving a total mesh size of 125 million. Still big but much closer to feasible.

Savings can be found by relaxing the dy+ requirement to <3 rather than <1. This will reduce the mesh count by a factor of 3 to 41.6 million.

Further savings can be found by reducing the length of the domain to 8m so reducing the mesh count by 1.2 to 34.7 million.

By also reducing the domain in z from 0.5m to 0.3m (slightly larger than the boundary layer thickness) this reduces the mesh count by 1.67 to 20.7 million.

This is still too large but by assuming that we can relax the wall shear stress estimates at the apex to be equal to those at the inlet, this gives a mesh of 300×1000 x 75 so a count of 22.5 million. Applying the above savings (which add up to a factor of 6, we get a mesh count of around 3.5-4 million.

Using a mesh of 4.5 million for extra nodes gives an estimated run time of 180 days (6 months) without the use of 2D preliminary start-up simulation.

## March 2007

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