I am modelling flow at one segment of annulus (bladeless) using software FLUENT 4.5 (structural mesh). When I use the cyclic rotational boundary conditions and cylindrical velocity formulation, I was not able to switch on the higher order discretisation scheme for velocity (at EXPERT\SOLUTION-PARAMETERS). Where is the mistake?

FLUENT 4.5: Since the annulus is bladeless, you don't need to turn on MULTIPLE ROTATING REFERENCE FRAMES under EXPERT->OPTIONS. This is the reason you could not use EXPERT->SOLUTION-PARAMETERS/HIGHER ORDER SCHEME. Use STEADY CORIOLIS FORCE in EXPERT->OPTIONS and set your rotational speed in EXPERT->BODY-FORCES

Maybe, I should describe the task more in details. The annulus is bladeless, but it consist of the three fluids, where the first is stationary, middle fluid rotates with constant omega and the last is stationary again. It is something like bladeless axial compressor or pump. Only one rotational segment is modeled, i.e. the rotational cyclic boundary conditions are used. As you mentioned in your message, if only single rotating frame is considered for entire domain, there is no problem with switching to higher discretisation scheme. The problem appeared only in case, where the multiple rotating frames of reference are used. It is necessary to say, that my task is solved in cylindrical velocity formulation, as is described in users guide.

Maybe, is it possible, that FLUENT 4.5 is not able to use the higher discretisation scheme in case of multiple rotating frames of reference?

Yup, higher order discretization for momentum was never implemented with the multiple reference frames model in FLUENT 4.5. This is not an issue in FLUENT 5, so you will have to spatially resolve your FLUENT 4.5 model i.e. grid refinement.

Since your "pump" is bladeless, why have you chosen the MRF model? Since it is an annulus, the fluid does not need to be set as moving because it would get it's inertia from the walls. Specify a rotational velocity on the walls.