This work is in the context of the safety-system development for the new generations of nuclear power plants. We wish to model the turbulent flow inside an industrial passive-safety device, the in-vessel flow limiter, based on the fluidic-diode principle [1]. Our goal is to design and optimize its shape. This shape optimization would need a lot of computations, each one with a specific mesh relative to the evaluated shape, followed by a statistical treatment. In order to avoid the time consuming phase of re-meshing, we use the Fictitious Domain approach. Using an in-house industrial software, we face the constraint to not being able to modify the physical-problem governing equations in the code. Taking into account this fact, we choose the Penalized Direct Forcing method, a merge of the Penalty and Direct-Forcing (DF) methods [2]. It consists in a penalized forcing term, written in a DF formulation, added to the governing equations for taking into account the immersed boundaries. Considering industrial turbulent-flow problems computed by RANS approach and not-resolved boundary layers, we need an appropriate immersed wall treatment. An immersed power-lawbased wall model is chosen because its ability to model the velocity profile inside the whole boundary layer [3]. This is important due to the non-uniform distribution of the forced-node distances to the immersed wall. Moreover, this wall model has the advantage to be explicit and to not rely on an iterative procedure for the friction velocity determination. Therefore, coming from our previous directional linear interpolation technique [2], we have implemented the power law approach into our PDF method. Using a Finite-Element version of our PDF method, we validate this approach on analytical-test cases and present our results concerning the in-vessel flow limiter industrial-test case.