Some way of making distiller water is a must for a steam engine because of the mineral
and calcium in all drinking water. To made a distiller as you suggested by the drawing is
not practical because you did not include a condensing section. Using pressurized hot
water or contaminated steam to heat a separate evaporator is standard procedure. But
after boiling the water it must be condensed. Maybe an old car radiator with the cooling
water inside and the distillate on the outside would work. If you could insure the inside
of the radiator was clean , you could reverse the systems and it would function like all
the condensing towers used around the world. Just let the outside air cool the steam.
One other point, most modern evaporators work under vacuum to lower the flash point of the water being distilled. One way they do this is by connecting a waternozzle to the shell of the boiler(evaporator) as water passes through the nozzle it sucks a vacuum on the shell. This is similar to how a paint sprayer sucks paint from a can. The effect on lowering the pressure makes the water being heated flash to a vapor at a much lower temperature depending on the vacuum. It can be lowered to 120 degrees. The higher the vacuum the less heat needed. Of course this will depend on the availability of a good water source.
Offered by Gary.