# Modélisation numérique

NSMB Code

In 1989, Navier Stokes Multi-Block (NSMB). This code has been created by european research laboratories in aerodynamicsuch as École Polytechnique Fédérale de Lausanne (EPFLausanne), KTH, CERFACS, IMFT, EADS, SAAB Military Aircraft, CFS Engineering, ETH-Zurich, IMFS de Strasbourg. Its was designed for parallel computing by solving blocks in parallel on different processors. NSMB enables to solve Navier-Stokes equations on a mesh divided in several blocks. Thanks to this approach, we can mesh the structure with a complex geometry

Simulation

Figure 2.1 – Problem scheme

During the first week, we worked on a 2D model SST k-omega. As a first step, we worked on a simulation where the two cylinders were immobile to study results on position cylinder and force coefficients.

# Turbulence models

Averaged equations for turbulence model are :

Boussinesq approximation is used to model Reynolds stress tensor :

It is a model with two equations on k and w :

For DDES kw-sst the model length scale is calculated as :

Model OES (Organised Eddy Simulation) is used when turbulence is not in equilibrium and enables to see Von Kármán effects. This model is based on the k epsilon model. Equations for k epsilon model are :

# 2D simulation

Parameters chosen for the 2D simulation are :
— Mach number 0.1285
— Reynolds 166 000
— Gas constant 43.25
— Timestep 0.00845
— CFL 1
— residue variable : density
— Tolerance 1e − 4
— Time scheme : implicit
— space scheme : centered

Eventually, we used a mesh where the second cylinder is free, enabling it to move axially upwards. This configuration represents the movement of cylinders in nuclear power plants in the coolant circuit. The following animation is what we have obtained with Tecplot, during one period ( 1000 snapshots ), with u* = 4 which is a supercritical regime.

# 3D simulation

For the 3D simulation, two turbulent models were given to us : OES model and DDES k omega-SST model.

Figure 2.2 – 3D Visualization with kw SST model

We have tested these two models to study the differences, the aim is to perform the 2D study on these 3D cases and follow the Kelvin-helmholtz structures.

Figure 2.3 – Slice on q criterion on the 3D model

We could represent the pressure coefficient around the second cylinder by using :

Then, we can plot the pressure coefficient around the second cylinder compared with NASA results :

Figure 2.4 – Pressure coefficient around the second cylinder compared with NASA results