# Presentation: 226793

## Interaction of Turbulence, Chemistry, and Radiation in Strained Nonpremixed Flames

**Chun Sang Yoo, Hong G. Im**
- Department of Mechanical Engineering
- University of Michigan
**Yi Wang, Arnaud Trouvé**
- Department of Fire Protection Engineering
- University of Maryland
**Sponsored by the DOE SciDAC Program**
**http://purl.org/net/tstc**

## Outline of Presentation

**Introduction**
**Role of DNS in Combustion Science (a brief version)**
**Overview: ****T****erascale High-Fidelity ****S****imulations of ****T****urbulent ****C****ombustion with Detailed Chemistry (TSTC)**
**Research Highlights* (work led by U. Michigan)**
**Computational: Improved Navier-Stokes Characteristic Boundary Conditions (NSCBC)**
**Science: Counterflow Diffusion Flames with Soot and Radiation Models**
**Ongoing/Future Work **
**	**** ****	****	**********More TSTC Research Highlights: Poster Session***
***	******	******	******	******WED21: Trouvé and Wang (Maryland)***
***	******	******	******	******WED22: Rutland and Wang (Wisconsin)***

**Notes:**
Evatt Hawkes yesterday gave an excellent presentation regarding the role of DNS
Disclaimer: what I’m gonna talk about is not terascale simulation results, but rather a modest sized DNS studies that were necessary towards our grand goal of turbulent combustion DNS with an emphasis of spray, soot, and radiation.  

## DNS: A Computational Microscope

**A diagnostic tool to study the fundamental physics of turbulent reacting flows**
- Full access to temporally/spatially resolved information.
- Allows identification of key paths for relevant phenomena, such as turbulence-chemistry interaction
**A benchmark tool to develop and validate physical submodels used in macro-scale simulations of engineering-level systems         (LES with embedded DNS)**

*DNS*

*Physical*
*Models*

*Engineering-level*
*CFD Codes*

**A KIVA-3V engine simulation**

**Formation of edge flames in **
**a turbulent counterflow**

**Notes:**
This is a slightly different version of what Evatt showed yesterday, for those who missed his presentation yesterday.
To recap what he said, the role of DNS is basically two-fold: (a) a computational diagnostic tool to understand the fundamental physics 
by allowing fully resolved information
That allows us to identify key reaction paths for phenomena of interest.
Secondly, it provides a useful benchmark dataset to develop and validate physical submodels for larger scale simulations such as LES or RANS.
With the petascale computing on the horizon, there is even more increased importance in DNS as an embedded subgrid scale model for LES simulation, as Evatt discussed yesterday.

## . S3D0: F90 MPP 3D

**. S3D0: F90 MPP 3D**
**. S3D1: GrACE-based**
**. S3D2: CCA-compliant**

**Software architecture**

**. IMEX ARK**
**. IBM**
**. AMR**

**Numerical algorithms**

**. Thermal radiation**
**. Soot formation**
**. Spray dynamics**

**Physical models**

**SciDAC**
**CCA**

**Post-processors: **
**In-situ visualization Feature tracking**

**SciDAC**
**CMCS**
**SDM**

**MPP S3D**

**Hong G. Im, University of Michigan**
**Arnaud Trouvé, University of Maryland **
**Chris Rutland, University of Wisconsin**
**Jackie Chen, Sandia National Labs**

**T****erascale High-Fidelity ****S****imulations of ****T****urbulent **
**C****ombustion with Detailed Chemistry (TSTC)****  **
**http://purl.org/net/tstc**

**SciDAC**
**CFRFS**

**Notes:**
So we have started a multi-university collaboration program about four years ago, to develop the next-generation DNS capabilities based on the S3D platform.  
The main tasks of the university PIs are to develop advanced physical models including radiation, soot formation and liquid spray. 
Along the way, we have also benefitted through interdisciplinary SciDAC project in implementing other software, numerical algorithms, and post-processing schemes by other SciDAC partners.

## S3D: MPP DNS Code

**S3D code characteristics:**
**Compressible reacting Navier-Stokes, total energy, species equations**
**Fortran 90, MPI domain decomposition**
**Highly scalable and portable on all modern architectures**
**Numerical algorithms:**
**8****th**** order non-dissipative spatial finite difference, 10****th**** order dealiasing filter**
**4****th**** order explicit RK integrator with error monitoring**
**Additive 4****th**** order RK integrator for stiff chemistry**
**Improved boundary conditions to allow transverse velocity, flame passage through boundary, or solid walls***

**Physical models:**
**Lewis number, mixture averaged, or multi-component transport**
**Detailed gas-phase chemical kinetics**
**	****(Chemkin-compatible)**
**All thermodynamic properties are functions of T, p, and Y****i**** **
**Radiative heat transfer (discrete ordinate / discrete transfer method)***
**Soot formation* **
**Lagrangian spray model***
***	*************Recent Contributions from the SciDAC TSTC Project***

**Notes:**
The main code base is S3D, developed at Sandia through the BES support over the past decade. 
The code features a compressible N-S solver with high-order spatial differentiation and temporal integration, and detailed description of chemical reaction and transport.
The red colors, again, indicate some of our recent contributions toward the code capabilities through the TSTC project.

## Characteristic Boundary Conditions 

**A “pre-requisite” issue for high-quality turbulent combustion DNS**
**Historical Development**
**General nonreflecting outflow boundary conditions**
**	****(Engquist and Majda 1977, Hedstrom 1979)**
**Pressure damping for Navier-Stokes equations**
**	****(Rudy & Strikwerda 1980, 1981)**
**Inviscid characteristic theory for Euler equations (Thompson 1987,1990)**
**Navier-Stokes characteristic boundary conditions (NSCBC) - Viscous conditions (Poinsot & Lele 1992)**
**Multi-component reacting flows (Baum et al. 1994)**

***Applications to turbulent and reacting flows have revealed problems of spurious pressure waves, numerical instabilities.***
**Reaction source terms (Sutherland & Kennedy 2003)**

**Notes:**
When we started on some realistic turbulent combustion simulations, we have run into some “pre-requisite problem.”  
There was a series of historical development in this issue for the past decades, and this issue was considered done in aeroacoustics community.
But when it comes to reacting flow simulations, people have still encountereed numerous problems.  
One such example as an effort to alleviate this problem was the consideration of reaction source terms, recently studied by Sutherland and Kennedy,
which I will revisit later.
So we wanted to look into this issue more carefully, and it turned out to be quite a serious research issue.

## Characteristic Waves

**inflow**

**outflow**

***L******i***** : characteristic wave with ***********i ***
**    ****(wave velocities, **********1*****= *****(*****u************c*****)*****, ***********2****=**********3****=**********4****=*****u*****, **********5****= (*****u*****+*****c*****)****)**

**Computational**
**domain**

**flow**

## Locally One-Dimensional Inviscid (LODI) Relations

**Neglecing**** transverse convection, viscous, and reactive terms**
**The**** incoming  *****L******i*****’s****  can be determined at both inflow and outflow boundaries using LODI relations**
**Hard inflow boundary conditions**** yield large spurious wave reflections : ****nonreflecting conditions are needed**

**Inflow boundary**

**Outflow boundary**

## Generalized NSCBC for Transverse, Viscous, Reacting Flows

**LODI relations are no longer valid****: transverse, viscous, reaction terms must be considered in *****L******i******’s***

**Conventional LODI**

**Improved BC**

**Outflow boundary conditions (at *****x = l******x*****)**

**Spatial :**

**Temporal :**

**Low-Ma asymptotic expansion yields:**

## Test 1: Vortex-Convection

**Incompressible inviscid vortex**
**Conditions**
**Three different boundary conditions**
**BC1 : conventional LODI with **
**BC2 : keep all the transverse terms**** ****(*****a *****= 0.0****)**
**BC3 : improved BC with pressure and transverse damping (*****a *****= *****M= *****0.05****)**

## Vorticity and Pressure

**LODI**

**Improved BC (*****a***** = 0.05****)**

**BC2 ****(*****a***** = 0.0****)**

***P***

**********

## Velocities

**LODI**

**Improved BC (*****a***** = 0.05****)**

**BC2 ****(*****a***** = 0.0****)**

***v***

***u***

## Temporal Pressure Variation

**Examine how the solution approaches the steady state**
**The L2-norm :**

**Temporal variations of the L2-norms**
**of pressure difference**

## Test 2: Ignition H2-O2 Mixture

**Case A: ****conventional LODI**
**Case B: include ****source terms**** in incoming *****L******i******’*****s (Sutherland & Kennedy 2003)**
**Case C: improved BC with *****a***** = 0.125 ****(scaling analysis) **

***Test 2: Ignition H******2******-O******2****** Mixture***

**Stoichiometric H****2****-O****2**** mixture**** diluted with 50% N****2**** by volume**
**2mm ******** 2mm (200 ******** 200 grid points)**
**Initial temperature and pressure, 300K and 1atm**
**Initial Gaussian temperature peak**

## Temperature and HO2

**Case A **
**(LODI)**

**Case B**
**(Sutherland**** ****& Kennedy)**

**Case C **
**(Improved BC)**

**Y****HO2**

**T**

## Test 3: Poiseuille Flow (Isothermal Wall)

**Viscous terms must be considered**
**Test cases**
**Case A: ****conventional LODI B.C. with **********1,exact**
**Case B: including only pressure damping term ****(*****a *****= 0.0****)**** **
**Case C: improved B.C. with *****a***** = 0.1**

**Temporal variation of pressure**

**The pressure level of Case A is increased**** because **********1,exact**** does not cancel out  all the viscous and heat flux effect **
**The velocity at the outflow boundary in Case B is not accurate: ****transverse damping term is needed **

## Test 4: Turbulent Reacting Counterflow

**Transverse terms cannot be ignored**
***a *****= 0.01**
**Use the steady laminar H****2********air nonpremixed counterflow flame as the initial condition**
**Turbulence inflow condition**
**Velocity fluctuations are superimposed**** on the mean inlet velocities.**
**Homogenous turbulence**

**(a) temperature**

**(b) vorticity**

## Strained Nonpremixed Flames with Soot and Radiation

**Motivation**
**Predictive tools for pollutant formation (soot, NOx)**
**Thermal radiation plays an important role, but has not been incorporated in high-fidelity simulations**
**Need better understanding of interaction between flow, chemistry, and heat transfer**
**Objectives**
**To develop high-fidelity DNS capabilities with advanced physical submodels for soot and radiation**
**Validate and assess the impact of the advanced physical models in a canonical configuration (flame-vortex)**
**Perform laboratory-scale simulations to answer science questions on turbulence-chemistry-radiation interaction (future work)**

## Radiation Models in S3D

**Based on gray gas assumption**
**Radiative heat flux:**
**Optically thin model (OTM)**
**Discrete ordinate method (DOM)**
**RTE solved in *****n***** discrete directions (ordinates)**
**S****n**** approx. ******** number of equations = ****n(n+2)/2**** (2-D)**
**S****2****: 4 eqs., and S****4****: 12 eqs.**
**Discrete transfer method (DTM)**
**	****RTE solved for *****n***** rays (ray-tracing)**

**Notes:**
Alternatively, the discrete transfer method (DTM) is composed of determining the intensity for each of N rays arriving at each surface element in an enclosure. The rays and their associated solid angles are equally distributed over the surface of a hemisphere centered over the receiving element. The point of origin of each ray is determined by finding the intersection of the ray with the enclosure boundary. The source function, temperature, and properties are usually assumed to be constant within a given volume element. The radiation transfer equation along each ray can be placed in the form of a recurrence relation,

where  is the ray intensity leaving boundary n+1 of a volume element and is equal to the ray intensity  crossing boundary n and attenuated along the path  within the element, plus the increase from the source function  within the element. 

## Performance of DOM/DTM

**MPI Scalability**

**Total radiative power**

**Relative error**

**DOM is found to be overall superior for the desired accuracy.**

**Notes:**
(Ask Chunsang about the test problem)
Relative error in radiative heat loss

## Soot Model (Two Equation Model)

**A semi-empirical two-equation model based on a flamelet approach (Young and Moss, 1995)**
**Soot number density**
**Soot volume fraction**

**Parameters**

**Notes:**
Although this is rather a simplified model based on the major species concentration, it still captures some essential physical subprocesses of soot formation: such as nucleation, coagulation, surface growth, and oxidation.

## Computational Configuration

**Calculation procedure**
**Generate 1-D diffusion flame profile (Oppdif)**
**Establish steady diffusion flame in counterflow**
**Superimpose initial vortex pairs**
**Velocity profile for a vortex**

## Parameters

| Parameter | Case A | Case B | Case C |
| --- | --- | --- | --- |
| u,max [cm/s] | 100 | 300 | 500 |
| u0 [cm/s] | 78 | 78 | 78 |
| uL [cm/s] | 78 | 78 | 78 |

**Three different vortex strength cases**
**Weak vortex : flame and soot are not extinguished**
**Medium vortex : extinguishes soot only**
**Strong vortex : extinguishes both flame and soot**

## Weak vs. Strong Vortex Cases

**Temperature**

***N*****soot**

***f*****v**

**Case**
**A**

**Case**
**C**

**Vorticity**

**Case**
**B**

## Integrated Nsoot and fv (Case B)

|  |  |
| --- | --- |

**Volume-integrated *****f*****v**** **
**in different temperature regions**

**Volume-integrated *****N*****soot**** **
**and flame volume**

**Soot number density depends strongly on the high-temperature flame volume **
**Soot volume fraction increases by surface growth at low temperature, fuel-rich regions**

## Effects of the Vortex Strength

|  |  |
| --- | --- |

**Comparison of integrated *****f*****v**** **
**for Cases A-C**

**Comparison of integrated *****N*****soot**** **
**for Cases A-C**

***Effects of the Vortex Strength***

**As vortex strength increases, more soot particles are convected into fuel rich zone**
**Case A: *****f*****v**** is more directly affected by the soot nucleation.**
**Case C: *****f*****v**** does not change much even the the soot nucleation (*****N*****soot****) is turned off.**

**Notes:**
All these results demonstrate the unique role of DNS by providing all the details within the fidelity of the submodels.  It also implies that the fidelity of the solution depends on the fidelity of individual submodels.

## Comparison of Radiation Models

**Total radiative heat loss with **
**OTM and DOM for Case  B**

**Radiative heat loss**
**During transient period, OTM overpredicts**** ****the radiative heat loss by up to a factor of two compared to DOM**
**Fidelity of radiation model is important in DNS **

## Ongoing/Future Work 

**Terascale Computing: 3D Turbulent Nonpremixed Counterflow**
**Flames with Radiation, Soot, and Water Spray**
**Integration of all the developed physical submodels**
**Test bench for numerical algorithms: boundary conditions, acoustic speed reduction (ASR)**
**Science issue: partial/total extinction and pollutant formation due to water spray interaction**
**Further To-Do List**
**Computational Development**
**Immersed boundary method **
**Adaptive mesh refinement**
**Chemistry reduction strategies**
**Physical Models**
**Detailed soot model**
**Radiation model (spectral) **
**Catalytic surface reaction**

**Enabling Technologies**
**Data-mining and visualization**
**Object-oriented code architecture for efficient management**

- DOE INCITE Project:
- 3D DNS of turbulent nonpremixed jet flame,
*J. H. Chen et al.*
*Sandia National Labs*

## Acknowledgments

**SciDAC TSTC**** ****Program****	**
**Hong G. Im (Michigan) **
**Chunsang Yoo, Ramanan Sankaran (SNL)**
**Christopher J. Rutland (Wisconsin)**
**Yunliang Wang**
**Arnaud Trouvé (Maryland)**
**Yi Wang**
**Jacqueline H. Chen (Sandia National Laboratories)**
**Scott Mason, Chris Kennedy, James Sutherland, Evatt Hawkes**
**Pittsburgh Supercomputing Center**
**Ravishankar Subramanya, Raghurama Reddy**
**DOE Computing Resources**
**National Energy Research Scientific Computing Center**
**Oak Ridge National Laboratory**
**Pacific Northwest National Laboratory**
**University of Oregon (the Tau Project)**
**Sameer Shende, Allen Malony**