A simple way to confirm would be to test without the transistor and put two diodes in series with the solenoid to see if it still activates when directly connected across 12 V. The 2 diodes would simulate the voltage loss through the transistor in operation.
Not exactly. A darlington transistor has a two diode voltage drop across it's base/emitter leads, but the 'saturation' voltage drop across the emitter/collector leads should be .2 volts or so depending on collector current. Still it's a good idea to power the solenoid directly with +12vdc to see if it works at all and what current draw it consumes.
Without knowing the actual solenoid current, I played it save. ;^)
At 3A the TIP102 Vcesat is actually 2V max from the "On Characteristics" spec sheet which is why I approximated two diode drops (1.4V) which is still less then 2V.
If I am reading Figure 10 correctly, minimum is Vcesat 0.7V at 1A, 1.0V at 2A, 1.06V at 3A, 2V at 8A
Since it is a valve that is being driven, my assumption is there will be a large initial current with the solenoid?
For roador's benefit, whatever the Vcesat (voltage across the collector - emitter) ends up being, this is subtracted from the voltage that is available across the solenoid. To minimize Vcesat, you want to overdirve the current on the base. From Figure 10, the base current should be minimum of 1/250 of the collector current.
Which still brings us to the question, can the solenoid drive the valve with less then 12V? If not, one solution would be to increase the solenoid power supply voltage to compensate.