CFD Simulations AC2-10

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Test Data

CFD Simulations

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Internal combustion engine flows for motored operation

Application Challenge AC2-10   © copyright ERCOFTAC 2024

CFD Simulations

Introduction

The TU Darmstadt engine has been investigated by three different groups using LES (Large Eddy Simulation) and hybrid URANS(unsteady Reynolds-averaged Navier-Stokes)/LES. These research groups are located at Technische Universit\"{a}t Bergakademie Freiberg (TUBF), Universit\"{a}t Duisburg-Essen (UDE) and Technische Universit\"{a}t Darmstadt (TUD). In the follow, the different approaches will be presented, including general information about the code and the physical modelling, computational domain and mesh treatment, initial and boundary conditions and computational requirements. Additional and detailed information can be found in the scientific papers listed in Table \ref{tab:simulations}.

Overview of simulation

Test data for the motored case is available at three different operating points. A test case considering an engine speed of 800 RPM is investigated in the numerical studies, which are summarized in Table \ref{tab:simulations}.

Table 3: Summary of simulations carried out at 800 RPM

Group	Approach	CFD Code / Publication
TUBF	URANS / LES	Ansys CFX R16.0 / Buhl et al. [9, 10]
UDE	LES	OpenFoam-2.3.x / Janas et al. [21]
TUD	LES	KIVA-4mpi / He et al. [20]

Further, simulations were carried out by Nguyen et al. \cite{Nguyen2016} and Baumann et al. \cite{Baumann2014}, which are not part of this comparison.

CFD codes

In the following, the governing equations, turbulence modelling and solver are described for the three different CFD codes.

Ansys CFX R16.0

For this compressible case, the filtered governing equations for mass, momentum and total enthalpy ${(H=h(T,p)+0.5u_{j}^{2})}$ are solved. They are defined as:

${{\dfrac {\partial {\overline {\rho }}}{\partial t}}+{\dfrac {\partial \left({\overline {\rho }}{\widetilde {u}}_{j}\right)}{\partial x_{j}}}=0}$	(4.1)
${{\dfrac {\partial \left({\overline {\rho }}{\widetilde {u}}_{i}\right)}{\partial t}}+{\dfrac {\partial \left({\overline {\rho }}{\widetilde {u}}_{i}{\widetilde {u}}_{j}\right)}{\partial x_{j}}}=-{\dfrac {\partial {\overline {p}}}{\partial x_{i}}}+{\dfrac {\partial }{\partial x_{j}}}\left(\left(\mu +\mu _{t}\right){\dfrac {\partial {\widetilde {u}}_{i}}{\partial x_{j}}}\right)}$	(4.2)
${{\dfrac {\partial \left({\overline {\rho }}{\widetilde {H}}\right)}{\partial t}}-{\dfrac {\partial {\overline {p}}}{\partial t}}+{\dfrac {\partial \left({\overline {\rho }}{\widetilde {u}}_{j}{\widetilde {H}}\right)}{\partial x_{j}}}={\dfrac {\partial }{\partial x_{j}}}\left(\lambda {\dfrac {\partial {\widetilde {T}}}{\partial x_{j}}}+{\dfrac {\mu _{t}}{Pr_{t}}}{\dfrac {\partial {\widetilde {h}}}{\partial x_{j}}}\right)}$	(4.3)

with the thermal conductivity ${\lambda }$ and the turbulent Prandtl number ${Pr_{t}}$ (set to 0.9 in the following). A non-density-weighted filtered variable is denoted by ${\overline {\Phi }}$, while ${\widetilde {\Phi }}$ is the density-weighted filtered variable. This system is complemented by the filtered equation of state for perfect gases, defined as:

${{\overline {p}}={\overline {\rho }}{\dfrac {R}{W}}{\widetilde {T}}}$

(4.4)

with the molecular weight ${W}$ and the universal gas constant ${R}$. The eddy viscosity (${\mu _{t}}$) is calculated based on the scale-adaptive simulation (SAS-SST) turbulence model \cite{Menter2010}. In case of insufficient spatial or temporal resolution (for a SRS), it reverts to the SST model \cite{Menter1994} and maintains a valid base of modelling. Its key element is the von K\'arm\`an length scale \cite{Rotta2010} (${L_{vK}}$), introduced into the scale-determining ${\omega }$ equation. In unstable flows, ${L_{vK}}$ adjusts the eddy viscosity to a level which allows the formation of a turbulent spectrum \cite{Menter2010,Travin2002,Schaefer2010,Lucius2010}. ${L_{vK}}$ is defined as

${L_{vK}=\kappa {\dfrac {\sqrt {2{\widetilde {S}}_{ij}{\widetilde {S}}_{ij}}}{{\widetilde {u}}''}}}$

(4.5)

with

${{\widetilde {S}}_{ij}={\dfrac {1}{2}}\left({\dfrac {\partial {\widetilde {u}}_{i}}{\partial x_{j}}}+{\dfrac {\partial {\widetilde {u}}_{j}}{\partial x_{i}}}\right){\text{,}}\quad {\widetilde {u}}''={\sqrt {{\dfrac {\partial ^{2}{\widetilde {u}}_{i}}{\partial x_{k}^{2}}}{\dfrac {\partial ^{2}{\widetilde {u}}_{i}}{\partial x_{j}^{2}}}}}}$

(4.6)

and the von Kármán constant ${\kappa }$.

ANSYS CFX R16.0 is a node-based, conservative and time-implicit finite-volume code \cite{Raw1996,Raithby1979,VanDoormaal1984}. The mass flow is evaluated such that a pressure-velocity coupling is achieved \cite{Rhie1983}. The discrete systems of equations are solved using a coupled algebraic multi-grid method \cite{Raw1996}. To minimize numerical diffusion, a second-order scheme in space \cite{Travin2002} and a second-order backward scheme in time are used.

OpenFOAM-2.3.x

The following governing equations for mass, momentum and absolute internal energy are solved on a moving grid:

${{\dfrac {\partial {\overline {\rho }}}{\partial t}}+{\dfrac {\partial \left({\overline {\rho }}{\widetilde {u}}_{j}\right)}{\partial x_{j}}}=0}$

(4.7)

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Contributed by: Carl Philip Ding,Rene Honza, Elias Baum, Andreas Dreizler — Fachgebiet Reaktive Strömungen und Messtechnik (RSM),Technische Universität Darmstadt, Germany

Contributed by: Brian Peterson — School of Engineering, University of Edinburgh, Scotland UK

Contributed by: Chao He , Wibke Leudesdorff, Guido Kuenne, Benjamin Böhm, Amsini Sadiki, Johannes Janicka — Fachgebiet Energie und Kraftwerkstechnik (EKT), Technische Universität Darmstadt, Germany

Contributed by: Peter Janas, Andreas Kempf — Institut für Verbrennung und Gasdynamik (IVG), Lehrstuhl für Fluiddynamik, Universität Duisburg-Essen, Germany

Contributed by: Stefan Buhl, Christian Hasse — Fachgebiet Simulation reaktiver Thermo-Fluid Systeme (STFS), Technische Universität Darmstadt, Germany; former: Professur Numerische Thermofluiddynamik (NTFD), Technische Universität Bergakademie Freiberg, Germany

Front Page

Description

Test Data

CFD Simulations

Evaluation

Best Practice Advice

© copyright ERCOFTAC 2018