A new model approach is presented in this work for including convective wall heat losses in the direct quadrature method of moments (DQMoM) approach, which is used here to solve the transport equation of the one-point, one-time joint thermochemical probability density function (PDF). This is of particular interest in the context of designing industrial combustors, where wall heat losses play a crucial role. In the present work, the novel method is derived for the first time and validated against experimental data for the thermal entrance region of a pipe. The impact of varying model-specific boundary conditions is analyzed. It is then used to simulate the turbulent reacting flow of a confined methane jet flame. The simulations are carried out using the DLR in-house computational fluid dynamics code THETA. It is found that the DQMoM approach presented here agrees well with the experimental data and ratifies the use of the new convective wall heat losses model.

References

References
1.
Pope
,
S.
,
1985
, “
PDF Methods for Turbulent Reactive Flows
,”
Prog. Energy Combust. Sci.
,
11
(
2
), pp.
119
192
.
2.
Valiño
,
L.
,
1998
, “
A Field Monte Carlo Formulation for Calculating the Probability Density Function of a Single Scalar in a Turbulent Flow
,”
Flow, Turbul. Combust.
,
60
, pp.
157
172
.
3.
Pozorski
,
J.
, and
Minier
,
J.-P.
,
2006
, “
Stochastic Modelling of Conjugate Heat Transfer in Near-Wall Turbulence
,”
Int. J. Heat Fluid Flow
,
27
(
5
), pp.
867
877
.
4.
Gerlinger
,
P.
,
2017
, “
Lagrangian Transported MDF Methods for Compressible High Speed Flows
,”
J. Comput. Phys.
,
339
, pp.
68
95
.
5.
Fiolitakis
,
A.
,
Ess
,
P. R.
,
Gerlinger
,
P.
, and
Aigner
,
M.
,
2014
, “
Modeling of Heat Transfer and Differential Diffusion in Transported PDF
,”
Combust. Flame
,
161
(
8
), pp.
2107
2119
.
6.
Yadav
,
R.
,
Kushari
,
A.
,
Eswaran
,
V.
, and
Verma
,
A. K.
,
2014
, “
A Detailed Validation Study of Multi-Environment Eulerian Probability Density Function Transport Method for Modeling Turbulent Nonpremixed Combustion
,”
ASME J. Eng. Gas Turbines Power
,
136
(
8
), p.
081506
.
7.
De
,
A.
,
Dongre
,
A.
, and
Yadav
,
R.
,
2013
, “
Numerical Investigation of Delft-Jet-in-Hot-Coflow (DJHC) Burner Using Probability Density Function (PDF) Transport Modeling
,”
ASME
Paper No. GT2013-95390.
8.
Lee
,
J.
,
Jeon
,
S.
, and
Kim
,
Y.
,
2015
, “
Multi-Environment Probability Density Function Approach for Turbulent CH4/H2 Flames Under the MILD Combustion Condition
,”
Combust. Flame
,
162
(
4
), pp.
1464
1476
.
9.
Lee
,
J.
, and
Kim
,
Y.
,
2012
, “
DQMOM Based PDF Transport Modeling for Turbulent Lifted Nitrogen-Diluted Hydrogen Jet Flame With Autoignition
,”
Int. J. Hydrogen Energy
,
37
(
23
), pp.
18498
18508
.
10.
Akroyd
,
J.
,
Smith
,
A. J.
,
McGlashan
,
L. R.
, and
Kraft
,
M.
,
2010
, “
Numerical Investigation of DQMoM-IEM as a Turbulent Reaction Closure
,”
Chem. Eng. Sci.
,
65
(
6
), pp.
1915
1924
.
11.
Abbrecht
,
P. H.
, and
Churchill
,
S. W.
,
1960
, “
The Thermal Entrance Region in Fully Developed Turbulent Flow
,”
Am. Inst. Chem. Eng.
,
6
(
2
), pp.
268
273
.
12.
Lammel
,
O.
,
Stöhr
,
M.
,
Kutne
,
P.
,
Dem
,
C.
,
Meier
,
W.
, and
Aigner
,
M.
,
2012
, “
Experimental Analysis of Confined Jet Flames by Laser Measurement Techniques
,”
ASME J. Eng. Gas Turbines Power
,
134
, p.
41506
.
13.
Löwe
,
J.
,
Probst
,
A.
,
Knopp
,
T.
, and
Kessler
,
R.
,
2016
, “
Low-Dissipation Low-Dispersion Second-Order Scheme for Unstructured Finite Volume Flow Solvers
,”
AIAA J.
,
54
(
10
), pp.
2961
2971
.
14.
Reichling
,
G.
,
Noll
,
B.
, and
Aigner
,
M.
,
2013
, “
Development of a Projection-Based Method for the Numerical Calculation of Compressible Reactive Flows
,”
AIAA
Paper No. 2013-1003.
15.
Fox
,
R. O.
,
2003
,
Computational Models for Turbulent Reacting Flows
,
Cambridge University Press
, Cambridge, UK.
16.
Möbus
,
H.
,
Gerlinger
,
P.
, and
Brüggemann
,
D.
,
2001
, “
Comparison of Eulerian and Lagrangian Monte Carlo PDF Methods for Turbulent Diffusion Flames
,”
Combust. Flame
,
124
(
3
), pp.
519
534
.
17.
Pope
,
S. B.
,
1976
, “
The Probability Approach to the Modelling of Turbulent Reacting Flows
,”
Combust. Flame
,
27
, pp.
299
312
.
18.
Gerlinger
,
P.
,
2005
,
Numerische Verbrennungssimulation
,
Springer
, Berlin.
19.
Villermaux
,
J.
, and
Devillon
,
J.
,
1972
, “
Representation de la coalescence et de la predispersion des domaines de segregation dans un fluide par un modele d'interaction phenomenologique [representation of the coalescence and the predispersion of segregation domains in a fluid With a phenomenological interaction model]
,”
Second International Symposium on Chemical Reacting Engineering
, Amsterdam, The Netherlands, May 2–4, pp. 1–13.
20.
Wang
,
L.
, and
Fox
,
R. O.
,
2004
, “
Comparison of Micromixing Models for CFD Simulation of Nanoparticle Formation
,”
Am. Inst. Chem. Eng.
,
50
(
9
), pp.
2217
2232
.
21.
Raman
,
V.
,
Pitsch
,
H.
, and
Fox
,
R. O.
,
2003
, “
Quadrature Moment Method for the Simulation of Turbulent Reactive Flows
,”
Annu. Res. Briefs
, pp.
261
275
.
22.
Wilcox
,
D. C.
,
1988
, “
Reassessment of the Scale-Determining Equation for Advanced Turbulence Models
,”
AIAA J.
,
26
(
11
), pp.
1299
1310
.
23.
Raithby
,
G.
, and
Schneider
,
G.
,
1979
, “
Numerical Solution of Problems in Incompressible Fluid Flow: Treatment of the Velocity Pressure Coupling
,”
Numer. Heat Transfer
,
2
(4), pp.
417
440
.
24.
Kazakov
,
A.
, and
Frenklach
,
M.
,
1994
, “
Reduced Reaction Sets Based on GRI-Mech 1.2
,” University of California at Berkley, Berkley, CA, accessed Oct. 22, 2018, http://www.me.berkeley.edu/drm/
25.
Yin
,
Y.
,
Nau
,
P.
,
Boxx
,
I.
, and
Meier
,
W.
,
2015
, “
Characterisation of a Single-Nozzle Floy Model Combustor Using kHz Laser Diagnostics
,”
ASME
Paper No. GT2015-43282.
26.
Gövert
,
S.
,
Mira
,
D.
,
Zavala-Ake
,
M.
,
Kok
,
J.
,
Vázquez
,
M.
, and
Houzeaux
,
G.
,
2017
, “
Heat Loss Prediction of a Confined Premixed Jet Flame Using a Conjugate Heat Transfer Approach
,”
Int. J. Heat Mass Transfer
,
107
, pp.
882
894
.
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