Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
216 Figure 8 depicts the temperature distribution along the
tunnel roof wall when steady state condition is reached. For small lh ratios the temperature distribution are more
homogeneous, the radiation effect are less evident and the detected temperatures are the highest. When lh raises
the distance between surfaces and duct reduces and the central part of the roof walls is heated by radiation,
significantly. The introduction of the thermal shield decreases the temperature values and distribution are
more homogeneous.
x l
θ
0.25 0.5
0.75 1
1.4 1.45
1.5 1.55
1.6 1.65
lh = 1.00 lh = 1.46
lh = 2.00 lh = 2.27
lh = 3.26 lh = 4.00
With Thermal Shield
Fig. 8. Temperature profiles of tunnel roof surface for different lh at steady state condition with thermal shields
In Figure 9 results are presented in terms of average dimensionless temperature of the tunnel side walls for
different lh ratios and investigate the influence of the thermal shields.
As described, the introduction of the thermal shield tends to decrease the temperatures evaluated on the
tunnel side walls and this behavior is more evident as lh augments.
y h
θ
0.25 0.5
0.75 1
1.1 1.2
1.3 1.4
1.5 1.6
lh = 1.00 lh = 1.46
lh = 2.00 lh = 2.27
lh = 3.26 lh = 4.00
With Thermal Shield
Fig. 9. Dimensionless temperature profiles of tunnel side surface for different lh ratios at steady state condition for the configuration with
thermal shields s = 0.007 m
Figure 10 shows the Nusselt number profile depending on time for the base configuration with
thermal shields for different values of the underbody total width, L. Nusselt number raises as L decreases
although differences are not so significant.
In this way, it is possible to focus the attention on simpler models characterized by small L and reduce
computational times.
τ
Nu
1 2
55 60
65 70
L
tot
= 0.60 m L
tot
= 0.70 m L
tot
= 0.85 m L
tot
= 0.90 m L
tot
= 1.00 m
With Thermal Shield
Fig. 10. Nusselt number profile depending on time for the base configuration with thermal shields for different values of L
Figures 11 are referred to the base configuration characterized by lh = 2.27 with thermal shields and
describes the behaviour of the system by changing the distance of the under-body from the road surface. Figure
10a depicts the Nusselt number profiles for different values of H. It is observed that for the largest value of H
the steady state condition is not reached.
Nu rises as H grows although differences are not much evident.
The steady state condition, moreover, is detected for larger dimensionless times as H augments.
Figure 11b presents the results in terms of temperature distribution along the tunnel roof wall.
From the figure it is easy to observe two relative maximum. This behaviour is related to presence of the
convective cells rising from the heated duct. The maximum values are attained at xl = 0.3 and 0.7,
respectively and profiles are perfectly symmetric.
The highest maximum values of dimensionless temperature are detected for H = 0.009 m because the
fluid flows difficultly in the tunnel and in correspondence of the inlet and outlet sections.
The minimum value of the dimensionless temperature is detected at xl = 0.5.
IV. Conclusion
A numerical simulation of a two-dimensional model of a car underbody has been carried out taking into
account the effects of the natural convection and radiation.
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
217
τ
Nu
1 2
55 60
65 70
H = 90 x 10
-3
m H = 120 x 10
-3
m H = 150 x 10
-3
m H = 240 x 10
-3
m H = 360 x 10
-3
m
With Thermal Shield
a
x l
θ
0.25 0.5
0.75 1
1.485 1.49
1.495 1.5
1.505 1.51
1.515 1.52
H = 90 x 10
-3
m H = 120 x 10
-3
m H = 150 x 10
-3
m H = 240 x 10
-3
m H = 360 x 10
-3
m
With Thermal Shield
b Figs. 11. Influence of the distance from the road surface, H: a Nusselt
numbers profile depending on time; b temperature distribution along the tunnel roof surface at the steady state condition
The model represents the section close to the catalyst component and the interaction of the underbody with the
exhaust system, represented by a heated duct, and the road surface was investigated by changing different
aspect ratios.
The under-body problem was solved by means of FLUENT. Results showed that Nusselt number increases
as lh ratio and H rise. The introduction of the thermal shields above the exhaust system reduces the calculated
average temperatures and this effect is more significant for larger lh ratios; the steady state condition is detected
for larger times. The temperature of the tunnel roof surface and side walls augments as lh and H decrease
and for H = 0.36 m the steady state condition is not observed.
Acknowledgements
This work was supported by a Legge 5 Regione Campania grant.
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Authors’ information
1
Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università degli Studi di Napoli,
via Roma 29, 81031 Aversa, Italy.
2
Elasis S.C.p.A. – FPT, via Ex Aeroporto, 80038 Pomigliano d’Arco – Italy.
3
Department of Plastical Processes and Heat Treatment, Faculty of Materials Science and Engineering,
“Gh. Asachi” Technical University of Iasi, 63 Mangeron Blvd., Iasi, Romania.
Special Issue on Heat Transfer, February 2011
Manuscript received and revised January 2011, accepted February 2011 Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved
218
Optimization of Turbulence and Radiation Models for an Improved Prediction of Non-Premixed Turbulent Flames
C. Pfeiler, C. J. Spijker, H. Raupenstrauch
Abstract – Turbulent combustion of gaseous fuels is of importance especially for the steel industry. To predict details on the concentration fields, an accurate modeling of turbulence and
temperature is required. If industrial scale combustion has to be predicted, the dimension of the geometry leads to a limit of models that can be used efficiently. Therefore, an optimization of
turbulence and radiation models has been performed. The accuracy of the realizable k-epsilon and the Reynolds Stress model RSM for the turbulence and the Discrete Transfer Radiation
Model DTRM and the Discrete Ordinate model DO for radiation are compared. The combustion system is a non-premixed diluted methane flame Sandia flame D. The stationary
laminar flamelet model together with the GRI-Mech 3.0 mechanism was applied. A modification of the empirical turbulence model constant C
2
helped to get better correlation with the experimental data. The DO radiation model, applying fewer rays, gives similar but faster results
than the DTRM model. Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved. Keywords:
Burner, Combustion, Flamelet, Radiation, Sandia Flame D, Turbulence
I. Introduction
