Speeding up a fan running in 'dumb' mode

I’m looking for feedback about how to get a computer cooling fan to spin with higher RPM. (It’s a fully ‘dumb’ connection – this is a 120mm fan in an under-the-desk air purifier, so no thermostat or CPU control). This was the sort of fan that the manufacturer used – but that fan was really noisy and I’m replacing it with a quieter fan.

The replacement fan is a 3pin fan, but also had a ‘hard drive’ style power connector that only used two wires (red/black). So, I do know that the manufacturer didn’t get clever – it’s a fan that can be controlled (yellow wire+red/black) OR run without control (red/black). The air filter has a 2pin header, and I snipped and soldered to old 2pin connector in its place.

So, as things stand, the fan has a replacement 2pin connector on it, and is plugged into the power supply and spinning. But it’s spinning a lot slower than I’d like.

So, can anyone suggest a way to get the fan to spin faster? I figured that I’d ask here since someone has probably done something similar on their computer’s case fans. Thanks!