There are a few common cooling technologies that use a semi-closed loop, not completely closed. It's a recycled loop of water with loss. Structures such as cooling towers mist the cooling water over a waterfall-like system with fans blowing over it. They use make-up supplies from municipal water to refill evaporative losses and provide "free" cooling.

There are also heat exchanges that mist water over the air it pulls in to lower the air temperature. Data centers use these all the time.

Look into adiabatic cooling.

For something truly shocking look into "once through cooling". It's being/been phased out but is a disgusting waste of water.