CFD Simulations AC2-09

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Application Challenge AC2-09   © copyright ERCOFTAC 2024

Overview of CFD Simulations

All the calculations presented below were obtained within the MOLECULES FP5 project Contract N° G4RD-CT-2000-00402 by the team of the Institute of Thermal Machinery, Częstochowa University of Technology. The computations were performed with BOFFIN-LES code developed at Imperial College by the group of Prof. W.P. Jones. BOFFIN-LES computer code utilizes a boundary conforming general curvilinear coordinate system with a co-located storage arrangement. It incorporates a fully implicit formulation and is second order accurate in space and time. For the convection terms an energy conserving discretization scheme is used and matrix preconditioned conjugate gradient methods are used to solve the equations for pressure and velocity etc. The CFD simulations are all LES predictions with various subgrid scale models and turbulence/combustion interaction approaches and neither RANS nor URANS methods are studied in this document.

In the LES calculations two models of turbulence/combustion interaction were applied: steady flamelet model and simplified Conditional Moment Closure (CMC) neglecting the convection term in physical space (The CMC module was developed by Prof. E. Mastorakos from Cambridge University). In both cases the standard subgrid-scale (SGS) Smagorinsky model was used. Then in order to evaluate the importance of the subgrid-scale models the LES calculations were also performed using steady flamelet and dynamic (Germano) SGS model.

SIMULATION CASE CFD1

Solution Strategy

In the CFD1 the steady flamelet concept was applied with the standard Smagorinsky SGS model for turbulence.

Computational Domain

The CFD1 results were obtained with computational meshes 80×80×160 nodes. The computational domain at the inlet and outlet plane extended to 5.5D and 18.3D respectively in both horizontal directions. The length of the domain was equal to 50D. The mesh was stretched in axial direction by exponential function and in radial directions by hyperbolic tangent function. The grid refinement studies for the LES calculations showed that the grid resolution with 80×80×160 nodes in the proposed computational domain is sufficient and further grid refinement leads to minor changes of the statistically converged parameters. The computational domain is shown in Fig.4.

Boundary Conditions

The boundary conditions in the inlet plane were assumed to be as follows:

• the mean and RMS profiles of the axial velocity component were interpolated from experimental data - Fig.3 presents comparison of the experimental data with boundary profiles applied in computations; the random disturbances, introduced as a white noise, were scaled by RMS profile and next they were superimposed on the mean profile;
• the mean and RMS values of the radial velocity components were assumed equal to zero;
• the mixture fraction was assumed equal to 1.0 in the main jet; 0.27 in the pilot jet and zero in the co-flowing air.

At the lateral boundaries the axial velocity was assumed equal to the velocity of coflowing air (0.9 m/s) while the remaining components were equal to zero. At the outlet the convective type boundary conditions were assumed which do not require specification of any variables.

Application of Physical Models

In the most general case modeling of the combustion processes is very expensive computationally since together with the solution of the flow field it requires solution of additional transport equations for particular N species (e.g. CO, CO₂, H₂O, H₂, etc.) produced in chemical reactions. The transport equations for species have the following form:

${\frac {\partial \rho Y_{k}}{\partial t}}+{\frac {\partial \rho u_{i}Y_{k}}{\partial x_{i}}}={\frac {\partial }{\partial x_{i}}}\left(\rho D_{k}{\frac {\partial Y_{k}}{\partial x_{i}}}\right)+{\dot {\omega _{k}}}\quad k=1,2,\dots ,N\qquad (1)$

where

$\rho$	is the density
$u_{i}$	is the velocity component
$Y_{k}$	is the mass fraction of species $k$
${\dot {\omega _{k}}}$	is the reaction rate (speed of creation/destruction of a given species)
$D_{k}$	is the diffusion coefficient usually taken the same (denoted by $D$) for each species and defined as $\rho D=\mu /Pr$, where $\mu$ is the molecular viscosity and $Pr$ is the Prandtl number.

SIMULATION CASE CFD2

(as per CFD 1)

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Contributed by: Andrzej Boguslawski — Technical University of Częstochowa

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Description

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© copyright ERCOFTAC 2024