Hi all,
During a feedback session with our coaches, the project manager of Humasol, Wout Cordeel, asked us an interesting question whether the installation of a ram pump can help to extend the efficiency of a water turbine and if this solution would be more cost-efficient or not?
To evaluate a certain set-up, we start with a situation where a Laval turbine is driven by water that drops 70 meters. Suppose that the inlet water flow is 50 l/s and that we want to increase power with 10%.
Can we reach these requirements?
First we start by defining the power that the water can deliver to a Laval turbine with symmetric blades in function of the mass/volume flow: P = f(Q). We can see that we have a linear course so if we increase the volume flow with 10% we get approximately an increase of 10% on the power production of the generator.
Q_delivery = 0.1*50 l/s = 5 l/s = 432000 l/day (we want to pump around 5 l/s with our hydram pump)
Q_supply = 50 l/s + 5 l/s = 55 l/s = 3300 l/min (hydram inlet flow due to mass conservation)
Let’s say that:
H_supply = 14 m (the supply head of the hydram pump)
H_delivery = 14 m + 70 m = 84 m. Let’s take H_delivery = 100 m so that we include losses.
Let’s use a well-documented commercial ram pump for our installation: the Blake Hydram. In tables we can find:
Source: J.P.H.M. Tacke – Hydraulic Rams, a comparative investigation
V_pumped = 132 l/day for each l/min of supply water (the volume water pumped)
V_pumped = 132 (l/day)/(l/min) * 3300 l/min = 435600 l/day which is bigger then the desired situation.
Has this solution an increased cost efficiency?
So now we have found a ram pump that is able to lift the needed amount of water to our Laval supply reservoir we need to check if it’s not better to just built in a bigger Laval turbine. We suppose that the cost of the turbine set-up increase linearly with the power production.
Set-up cost of a Laval turbine: €12000
Set-up cost of a hydram: €1500
Set-up cost of the improved system without a hydram: 1.1*€12000 = €13200
Set-up cost of the improved system with a hydram: €12000 + €1500 = €13500
Conclusion:
We can clearly see that our solution requires quite unpractical supply values and a big hydram pump. We can even see that if our linear cost increment approximation is correct that the system doesn’t gain a better cost-efficiency.
If you have any remarks on the calculation, feel free to join me in the search for cost-efficient optimalisation solutions.
Cheers,
Alexander