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A Dynamic LES Model for Turbulent Reactive Flow with Parallel Adaptive Finite Elements

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Energy for Propulsion

Part of the book series: Green Energy and Technology ((GREEN))

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Abstract

An adaptive finite element method (FEM) is used for the solution of turbulent reactive flows in 3-D utilizing parallel methods for fluid dynamic and combustion modeling associated with engines. A dynamic LES method permits transition from laminar to turbulent flow without the assumptions usually required for turbulent sublayers near wall area. This capability is ideal for engine configurations where there is no equilibrium in the turbulent wall layers and the flow is not always turbulent and often in transition. The developed adaptive FEM flow solver uses “h” adaptation to provide for grid refinement. The FEM solver has been optimized for parallel processing employing the message passing interface (MPI) for clusters and high-performance computers.

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Abbreviations

~:

Designates a Favre-averaged variable

–:

Designates a grid-filtered variable

c:

Sound speed (m/s)

\( C_{p} \) :

Specific heat capacity at constant P (J/kg.K)

\( C_{vm} \) :

Vreman fixed SGS eddy viscosity coefficient

\( C_{DVMG} \) :

Vreman dynamic SGS eddy viscosity coefficient

Dj:

Diffusion coefficient of the jth species \( \left( {{\text{m}}^{ 2} / {\text{s}}} \right) \)

\( D_{k} \) :

Turbulent diffusion coefficient \( \left( {{\text{m}}^{ 2} / {\text{s}}} \right) \)

E:

Total internal energy (J/kg)

\( f_{k,j} \) :

Body forces \( \left( {{\text{N/m}}^{ 3} } \right) \)

\( f_{drop} \) :

Body forces related to particulate or droplets in flow \( \left( {{\text{N/m}}^{ 3} } \right) \)

\( H_{j} \) :

Enthalpy of species j (J)

\( H_{oj} \) :

Enthalpy of formation (J)

P:

Pressure (Pa)

Pr:

Molecular Prandtl number

\( { \Pr }_{\text{sgs}} \) :

SGS eddy Prandtl number

Pr DVMG :

Vreman dynamic SGS eddy Prandtl number

\( Q_{j} \) :

Subtest-scale heat flux vector

\( q_{i} \) :

Heat flux vector

Re:

Reynolds number

\( {\tilde{\text{S}}}_{\text{ij}} \) :

Strain rate tensor \( \left( {\frac{\text{N}}{{{\mathrm{m}}^{ 2} }},{\mathrm{kg/m}}\,{\text{s}}^{ 2} } \right) \)

Sc:

Schmidt number

Sct:

Subgrid-scale turbulent Schmidt number

\( T \) :

Temperature (K)

\( T_{ij} \) :

Subgrid test-scale stress tensor

\( t_{ij} \) :

Grid-scale (resolved scale) shear stress \( \left( {\frac{\text{N}}{{{\mathrm{m}}^{ 2} }},{\mathrm{kg/m}}\,{\text{s}}^{ 2} } \right) \)

\( u_{i} \) :

Velocity component (m/s)

\( \Upsilon _{j} f_{j} \) :

Body force term for the \( j{\text{th}} \) component

\( \dot{w}_{chem}^{j} \) :

Chemical reaction

\( \dot{w}_{spray}^{j} \) :

Spray evaporation

\( \partial {\text{t}} \) :

Discrete time step size (s)

\( \kappa \) :

Coefficient of thermal conductivity \( \left( {{\text{W}}/{\text{m K}}} \right) \)

\( \rho \) :

Density (kg/m3)

\( \Upsilon ^{j} \) :

Mass fraction (jth species) \( \left( {\frac{{\rho^{j} }}{\rho }} \right) \)

\( \tau_{ij} \) :

Subgrid-scale stress tensor

μ:

Fluid viscosity \( \left( {{\text{Pa s}}} \right) \)

\( \upmu_{\text{sgs}} \) :

Turbulent eddy viscosity

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Acknowledgements

The DOE’s Office of Energy Efficiency and Renewable Energy (EERE) Advanced Combustion Program (Gurpreet Singh and Leo Breton) is supporting this effort. Los Alamos National Laboratory, an affirmative action/equal opportunity employer is operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the US Department of Energy (DOE) under contract DE-AC52-06NA25396. Los Alamos National Laboratory strongly supports academic freedom and a researcher’s right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness.

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Authors and Affiliations

  1. Los Alamos National Laboratory, T-3 Division, Los Alamos, USA

    Jiajia Waters & David B. Carrington

  2. Purdue University Northwest, Hammond, IN, 46323, USA

    Xiuling Wang

  3. NCACM, Department of Mechanical Engineering, University of Nevada Las Vegas, Las Vegas, USA

    Darrell W. Pepper

Authors
  1. Jiajia Waters
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  2. David B. Carrington
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  3. Xiuling Wang
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  4. Darrell W. Pepper
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Corresponding author

Correspondence to Darrell W. Pepper .

Editor information

Editors and Affiliations

  1. ACRI, The CFD Innovators, Los Angeles, California, USA

    Akshai K. Runchal

  2. Department of Mechanical Engineering, University of Maryland, Department of Mechanical Engineering, College Park, Maryland, USA

    Ashwani K. Gupta

  3. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Abhijit Kushari

  4. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Department of Aerospace Engineering, Kanpur, Uttar Pradesh, India

    Ashoke De

  5. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Department of Mechanical Engineering, Chicago, Illinois, USA

    Suresh K. Aggarwal

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Waters, J., Carrington, D.B., Wang, X., Pepper, D.W. (2018). A Dynamic LES Model for Turbulent Reactive Flow with Parallel Adaptive Finite Elements. In: Runchal, A., Gupta, A., Kushari, A., De, A., Aggarwal, S. (eds) Energy for Propulsion . Green Energy and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-7473-8_9

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  • DOI: https://doi.org/10.1007/978-981-10-7473-8_9

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