Bringing order to nozzle changing

The heavens have opened at last !  From the middle of August until last week it has been very dry here with the water available for my Powerspout being less than 0.6 litre/sec; but a deep depression coming in from the Atlantic last week brought copious rain and has abruptly increased flow fourfold.

Although I have been looking forward to the winter rain coming, its suddenness has caught me on the back foot: in order to generate at all on a flow of 0.6 l/s, the SmartDrive had been set up with 18 pole stator and the rotor packed off maximally.  All this had to be changed and changed in the middle of a downpour: the 18 pole stator replaced with a 42 pole, the packing reduced and nozzles upped to match the greater flow available.

Despite my best efforts to have an orderly "take off" into each new water year when the rain comes, I have to admit I've failed this year.  I like to increase the nozzles in a steadily incremental way which matches as closely as possible the increasing flow. I don't like having to 'back track' to a smaller nozzle because I've put in too big a one. But a big element of getting things right is predicting how quickly the flow is going to increase and this year I've got it wrong; I've been beguiled by the torrent of water in the stream into which the turbine discharges (see pic below), and twice have put in too big a nozzle only to have to replace it with a smaller one within 24 hours.  I've been slow to follow my own adage that a source coming from a spring increases its output only gradually as ground water builds up; that I must not be misled by the early 'flashiness' of the run-off which appears in the stream.

In an attempt to bring a system to nozzle changing, I try to bring in a bit of measurement so the process becomes less of a guessing game.

For each nozzle I like to think I know what discharge the orifice will give; but in reality I know the accuracy of the figure will probably not be very good.  The lack of accuracy arises because the way of calculating the discharge involves a formula and that formula has rather too many inputs which are not known with great precision; the formula is:

Q  = CD x Anoz x √ (2g x Hn)

where: 
Q is the flow from the nozzle (m³/s)
CD is the discharge coefficient for the nozzle (dimensionless; I take its value to be 0.91)
Anoz is the cross sectional area of the orifice (m²)
Hn is the net head (m)
g is 9.81m/s²

The term which is easiest to tie down in this formula is Anoz. By using the taper gauge that EcoInnovation supply in their tool kit, or a 'small hole gauge' and a vernier calliper (see here), the diameter of an orifice can be fairly accurately measured, and from that the area calculated. 

The difficulty comes with the other two terms: CD and Hn; as the orifice size changes so will the values of these two terms; but it is too complicated to try to measure them for every size of orifice; it is easier to assume constant values and recognise this will introduce an inaccuracy to the value calculated for Q.

With this limitation in accuracy admitted, my orifices are so arranged as to have a difference in flow between one and the next of about 0.3 l/s.  The smallest orifice, Roman numeral # 1, is cut to deliver 0.3 l/s.  By keeping this nozzle permanently in the top nozzle position and bringing it into use only when there appears to be sufficient water to be able to use it, I can test whether the time has come to increase the bottom nozzle by another 0.3 l/s increment: - if I find that employing # 1 causes the header tank to stop overflowing, the time to up the bottom nozzle has not yet come; but if the header tank still overflows, I can up-size the bottom nozzle.

Intuition might say that employing nozzles of markedly different size in the top and bottom positions is a bad thing.  True, it will produce a vector thrust which has to be born by the bearing on which the shaft is carried; a vector thrust which is cancelled by an equal and opposite force if the two jets are equal in size.  But the size of this thrust when calculated at the bearing is small and is unlikely to be a factor in limiting its life. 

The more important consideration relates to the velocity of the water in the two jets; it may be counter-intuitive, but the velocity is actually the same.  This comes about because jet velocity relates only to net Head, not to orifice size.  So the two jets actually deliver water to the pelton cups at the same velocity even though one is delivering more mass of water than the other.  Having the same velocity, the relative velocity of each jet to the speed of the runner is the same for both jets and this is what is important for good pelton efficiency.

As I finish writing, it has not rained for over 24 hours; all today I've been running on nozzles # 1 and # VIII delivering respectively 0.3 and 1.6 l/s, and giving 448w into the grid; the header tank is still overflowing and the forecast is for no more rain for several days.  With that forecast, the likelihood is my next move will be to turn off # 1.

It's good to have a plan but better still would be to have more rain !