I recirculate back to my BK from my CFC. I catch the initial water to clean with in a large plastic tub. When my BK hits about 120, I have a tee that goes to a small sump pump. The pump is in a small kid pool with frozen gallon jug ice and a small amount of water. Takes about 4-5 frozen gallon jugs. It cools the rest of my batch to whatever pitch temp I want. It cut my consumption by a ton. I do 20 gallon batches, so it was taking me forever and a lot of usage. I think you could do something with a tee mounted to both tap and pump ice water. I'd just make it tall enough to be above your pump and easy to turn the valves on the tee. Plus the pump has hose threads. The water that doesn't get used in the cleaning, gets frozen in jugs and used again.
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