Estimate current through inductor in DC circuit with PWM control
Ideally, a high-enough-frequency PWM circuit with a perfect switch and catch diode will give you \$ \alpha \$ times the current you'd get with 100% duty cycle (where 0\$ \le \alpha \le 1 \$ is the duty cycle ) . In this case, you've drawn the circuit as having an inductor without resistance, so the current would increase without limit.. So you need to include the DC resistance of the coil in your analysis.

Edit: Something is obviously screwed up with your model. Below is a simulation of startup from zero inductor current with good models of all the parts as you've shown, and 4kHz frequency and 50% duty cycle. 



The average current is about 1.428A. The ideal prediction was 50% of 7.5V/2.4 ohms or 1.56A, however there is some loss in the MOSFET and the diode. 

Your "experimental" data does not sound too far off, as I said there are losses in the diode and MOSFET (mostly the diode in this case). If you want a more ideal result you could replace the Schottky diode with another MOSFET (drive the coil with a half-bridge). 

If the Schottky Vf is 330mV at 0.5A and the MOSFET has 100mV across it when on, then with 20% duty cycle the voltage the R+L will see is +7.4V when on and -0.33V when off, for an average of 0.2 * 7.4 + 0.8 * -0.33 = 1.216V, so the average current will be 0.506A, which is very close to what the simulation shows.