In a traditional pipe organ, the dynamic range of both labial (flue) and lingual (reed) pipe ranks are strictly limited as each rank is tuned and voiced to a nominal windchest pressure. Changing this pressure not only affects the amplitude of the radiated sound but both the pitch and the timbre of the pipes. A new pipe construction with a blown open free tongue was proposed recently to overcome this limitation. Prototype pipes of the new construction were built and measurements were carried out on them at different blowing pressures. It was found that the new construction provides a pleasing stability of the pitch and a broad range of playable amplitudes; however, the timbre of the pipes changes significantly with the blowing pressure. To improve the design in the latter aspect, a physical model of the pipes needs to be established first. In this contribution the sound generation of the experimental pipes is simulated by time domain computations. The resonator and its interaction with the vibration of the tongue are simulated using both the truncated impedance model and the reflection function approach. Results of the temporal simulations and their comparison with measurements are presented.