7.1.4. Correction of Effective Turbulent Burning Velocity for Lean Hydrogen-air Mixtures

7.1.4.1. Purpose

In this multi-phenomena combustion model, more effects on flame acceleration at low turbulence are considered in the effective turbulent burning velocity, including:

• Laminar unstretched burning velocity considering effects of transient pressure and temperature.

• Flame surface area enlargement due to small-scale flame front wrinkling caused by Landau-Darriues (LD) and thermal-diffusive (TD) instabilities.

• Pressure effect on flame surface area enlargement due to small scale flame front wrinkling.

• Flame surface area enlargement due to self-induced turbulence driven by hydrodynamic instability.

• Local flame front curvature and the resulting stretch on laminar burning velocity.

• Flow turbulence in the unburned mixtures.

7.1.4.2. Model descriptions

GASFLOW-MPI input options below have to be selected.

iburn = 4, ; combustion progress variable transport for hydrogen-air mixtures

isourcexi = 2, ; models based on gradient of combustion progress variable

Laminar burning velocity

ilamfs : GASFLOW-MPI options for calculation of the laminar burning velocity: SL,0. (default: ilamfs =1)

Laminar burning velocity considering effects of pressure and temperature

ithetath: GASFLOW-MPI options for exponents to correct the laminar burning velocity. (default: ithetath = 1)

Flame wrinkling factor induced by Landau-Darriues (LD) and thermal-diffusive (TD) instabilities

ielp: GASFLOW-MPI options for flame wrinkling induced by TD instabilities. (default: ielp = 0)

flcri_radius0: GASFLOW-MPI input variable for flame front critical radius (cm). (default: flcri_radius0 = 110)

Flame wrinkling factor due to self-induced turbulence driven by hydrodynamic instability

iesturb: GASFLOW-MPI options for flame wrinkling induced by hydrodynamic instability. (default: iesturb = 0)

ifgeo: GASFLOW-MPI options for geometry effect.1: for sphere, 2: for tubes. (default: ifgeo = 1)

flcri_radius0: GASFLOW-MPI input variable for flame front critical radius (cm). (default: flcri_radius0 = 110)

esturb_phi: GASFLOW-MPI input variable for the coefficient of flame wrinkling factor. For near-stoichiometric mixtures: esturb_phi = 0.5 is recommended. For lean hydrogen/air mixtures, esturb_phi=1.0 is recommended. (default: esturb_phi = 1.0)

fgeo_coef: coefficient for tube (default: fgeo_coef = 0.5)

Flame stretch factor induced by local flame front curvature

ifstretch: GASFLOW-MPI options for flame stretch factor induced by local flame front curvature. (default: ifstretch = 0)

Turbulent burning velocity correlations

iturbflame: GASFLOW-MPI options for turbulent burning velocity correlation. (default: iturbflame = 0)

7.1.4.3. Input example

Combustion model

Input example for hydrogen flame acceleration in a tube

           iburn_malloc    = 1,     ; allocate memory for combustion restart calculation
           iburn           = 4,     ; combustion models based on progress variable for hydrogen-air mixtures
           ilamxi          = 1,     ; calculate laminar diffusion term in the xi equation
           iturbxi         = 1,     ; calculate turbulent diffusion term in the xi equation
           isourcexi       = 2,     ; 2: Gradient Model; 
           iturbflame      = 6,     ; options for the turbulent burning/flame velocity
           ilamfs          = 1,     ; options for laminar flame speed
           ithetath        = 1,     ; options for pressure and temperature correction of laminar flame speed
           ielp            = 1,     ; options for flame wrinkling induced by TD instabilities  
           iesturb         = 1,     ; options for flame wrinkling due to self-induced turbulence 
                                    ; driven by hydrodynamic instability
           ifstretch       = 1,     ; options for flame stretch factor induced by local flame front curvature
           ifgeo           = 2,     ; options for geometrical effect (1: sphere; 2: tube)

           fgeo_coef       = 0.35,  ; model constant for flame propagation in tubes
           flcri_radius0   = 275,   ; flame front critical radius (cm) used when iesturb = 1 and ielp = 1
                                    ; increase flcri_radius0 can slow down the pressure increase in the tube

           iref_unburnt = 2,
           jref_unburnt = 2,
           kref_unburnt = 400,
           Schmidt_turb = 0.9,

           xi_ignitdef(1:10,1) = 1, 2, 1, 2, 1, 2, 1, 0.0, 1e-5, 0, ; Ignitor Model

Initial turbulence conditions

The calculation results may be sensitive to the initial turbulent conditions. Below is the default values of turbulent kinetic energy and dissipation rate in GASFLOW-MPI.

           ; define the initial turbulent conditions
           turbdef(1:12,1) = 1, 10, 1, 13, 1, 401, 1, 1, 1, 0, 0.0, 0.0,
           tkeval          = 40,     ; initial turbulent kinetic energy
           epsval          = 30,    ; initial turbulent dissipation rate

Input file

Reference

[1] U. Maas, J. Warnatz, Ignition processes in hydrogen-oxygen mixtures, Combustion and Flame, Volume 74, Issue 1, 1988, Pages 53-69.

[2] Toshio Iijima, Tadao Takeno, Effects of temperature and pressure on burning velocity, Combustion and Flame, Volume 65, Issue 1, 1986, Pages 35-43

[3] ETTNER, F. Effiziente Numerische Simulation des Deflagrations-Detonations-Übergangs. PhD thesis, Technische Universität München, 2013.

[4] Bentaib, A., Chaumeix, N., 2012. SARNET H2 Combustion Benchmark Diluent: Effect on Flame Propagation Blind Phase Results. Tech. Rep., IRSN.

[5] Katzy P. Combustion model for the computation of flame propagation in lean hydrogen-air mixtures at low turbulence[D]. Technische Universität München, 2021.

[6] Wieland C H. Efficient Simulation of Flame Acceleration and Deflagration-to-Detonation Transition in Smooth Geometries[D]. Technische Universität München, 2022.

[7] J.K. Bechtold and M. Matalon. The Dependence of the Markstein Length on Stoichiometry. Combustion and Flame, 127(1-2):1906– 1913, 2001.

[8] Molkov V. Fundamentals of Hydrogen Safety Engineering, parts I & II. Free download e-book, bookboon.com, ISBN: 978-87-403-0279-0. 2012.

[9] Xiao H, Makarov D, Sun J, Molkov V. Experimental and numerical investigation of premixed flame propagation with distorted tulip shape in a closed duct. Combust Flame 2012;159:1523e38.

[10] Gostintsev YA, Istratov AG, Shulenin YV. Self-similar propagation of a free turbulent flame in mixed gas mixtures. Combust Explos Shock Waves 1989;24(5).

[11] S.C. Taylor. Burning Velocity and the Influence of Flame Stretch. PhD Thesis, University of Leeds, 1991.