  An a priori reduced order method based on the proper generalised
decomposition (PGD) is proposed to compute parametric solutions involving
turbulent incompressible flows of interest in an industrial context, using
OpenFOAM. The PGD framework is applied for the first time to the incompressible
Navier-Stokes equations in the turbulent regime, to compute a generalised
solution for velocity, pressure and turbulent viscosity, explicitly depending
on the design parameters of the problem. In order to simulate flows of
industrial interest, a minimally intrusive implementation based on OpenFOAM
SIMPLE algorithm applied to the Reynolds-averaged Navier-Stokes equations with
the Spalart-Allmaras turbulence model is devised. The resulting PGD strategy is
applied to parametric flow control problems and achieves both qualitative and
quantitative agreement with the full order OpenFOAM solution for
convection-dominated fully-developed turbulent incompressible flows, with
Reynolds number up to one million.
