4th World Hydrogen Technologies Convention, 2011, Glasgow, U.K.
Paper ID: 0021
DIRECT NUMERICAL SIMULATION OF HYDROGEN IMPINGING JET FLAME
USING FLAMELET GENERATED MANIFOLD REDUCTION
K.K.J. Ranga Dinesh1, X. Jiang1, J.A. van Oijen2
1
Engineering Department, Lancaster University, LA1 4YR, UK
2
Combustion Technology, Department of Mechanical Engineering, Eindhoven University of
Technology, 5600 MB Eindhoven, The Netherlands
ABSTRACT
A hydrogen-air nonpremixed impinging jet flame is
studied using three-dimensional direct numerical
simulation (DNS) and flamelet generated manifold
(FGM). The simulations are used to investigate the
buoyancy instability and the spatial and temporal
patterns of the near-wall flame temperature. The
computational domain employed has a size of 4 jet
diameters in the streamwise direction and 12 jet
diameters in the cross-streamwise directions. The
results presented in this study were performed using
a Cartesian grid with 528×528×528 points.
Reynolds number used was Re=2000 , based on the
inlet reference quantities. The spatial discretisation
was carried out using a sixth-order accurate
compact finite difference scheme and the
discretised equations were advanced using a thirdorder accurate fully explicit compact-storage
Runge-Kutta scheme. Results shows that the
combustion-induced buoyancy leads to the
formation of both inner and outer vortical structures
in the primary and wall jet regions. Moreover, DNS
results suggest that the near-wall vortical structures
play an important role in the temperature field.
INTRODUCTION
The environmental issues concerning the reduction
of CO 2 emission from power-generating systems
have prompted researchers towards new
consideration of alternative fuel sources for energy
conversion. Considerable effort is being directed
towards updating safety codes and preparation for
production, distribution, and retail of hydrogen as a
consumer energy source [1]. Particularly hydrogen
combustion received much attention because of the
need for a clean alternative energy source. The
exclusion of harmful emissions such as CO, CO2 ,
soot and unburned hydrocarbons makes combustion
of hydrogen perfect for clean combustion. Various
investigations have focused on development of an
infrastructure for the future hydrogen economy
involving safety standards [2], flame stability [3],
fuel variability [4] etc. In addition, near-wall
combustion of hydrogen and hydrogen-enriched
syngas as a research topic has gained an increasing
amount of attention in recent years due to its usage
in a range of combustion systems such as
combustion engines, gas turbine combustors and
other industrial processes. In the context of nearwall combustion, the study of hydrogen impinging
jet is of particular interests. Because of the wealthy
flow phenomena involved and the geometric
simplicity, hydrogen-air impinging flame can be
considered as a benchmark for the development and
validation of near-wall models for hydrogen and
hydrogen enriched syngas combustion.
Direct numerical simulation (DNS) has emerged as
a promising technical tool to simulate turbulent
combustion problems, in which all relevant
continuum scales are resolved. Arguably, DNS
technique along with detailed chemical kinetics can
discover vital scientific and technological issues,
which can be used for model development of other
simulation techniques. Mahalingam et al. [5]
performed the three-dimensional DNS of turbulent
nonpremixed flame including finite rate chemistry
and heat release effects. Since then various groups
focused on DNS of nonpremixed combustion and
analysed the turbulence chemistry interaction, fuel
variability, flame stabilisation, local extinction and
auto ignition etc. Dabireau et al. [6] performed a
one-dimensional
simulation
of
hydrogen
combustion interacting with an inert wall. Hawkes
et al. [7] also carried out scalar intermittency of
CO/H 2 planer jet flame using DNS and more
recently Gruber et al. [8] studied turbulent flamewall interaction for hydrogen-air premixed flame
using DNS. Pitsch [9] has further demonstrated the
importance of investigation on near-wall
combustion using DNS. Since many practical
combustion chambers have closed geometry, the
DNS technique can be effectively used to develop
more efficient and accurate near-wall models for
hydrogen and hydrogen enriched syngas
combustion when large eddy simulation and
Reynolds averaged Navier-Stokes modelling
techniques for more complex and high Reynolds
number combustion problems are employed. To
achieve this task, here we present a fundamental
investigation on hydrogen impinging jet aiming to
identify the combustion-induced buoayncy effcts
and near-wall heat transfer using direct numerical
simulation and detailed chemical kinetics. The
detailed chemical kinetics have been employed
through the flamelet-generated manifold (FGM)
method [10], which takes both the chemistry and
Page 1 of 6
4th World Hydrogen Technologies Convention, 2011, Glasgow, U.K.
the most important transport processes into account.
This is a first step of our long-term objective, which
is to investigate the flame characteristics of
hydrogen enriched syngas mixtures and near-wall
vortical structures and convective wall heat transfer
including surface chemistry effects using DNS and
FGM approach.
GOVERNING EQUATIONS
The instantaneous conservation equations for mass,
momentum, energy, mixture fraction and the
transport equation of the progress variable in nondimensional form can be written as follows:
 (  u j )

 0,
t
x j
(  u j )
t

( a   )
 (  u j uk )
xk
gj
Fr
(1)

p
1  jk

xk Re xk
(2)
 0,
 e  (  euk ) ( puk )


t
xk
xk
1

T

(
)
Re Pr M 2 (  1) xk xk
gu
1  (u j jk )

 (  a   ) k k  0,
Re xk
Fr
( Y ) (  uk Y )
1
  Y


(
)
t
x k
Re Pr xk C p xk
(3)
(4)
Y  0,
 (  Z )  (  uk Z )
1
  Z


(
)  0,
t
x k
Re Pr xk C p xk
p
T
M2
(5)
(6)
In Eqs. (1)-(6), t stands for time, u j is the velocity
components in the x j direction, e stands for total
energy per unit mass, p for pressure, λ for heat
conductivity, CP for specific heat at constant
pressure, μ for dynamic viscosity, γ is the ratio of
Paper ID: 0021
decade, which simplify the description of the
chemical kinetics. These reduction methods have
been formulated by observing that a typical
combustion contains many chemical processes with
a much smaller time scale than the flow time scales.
These fast chemical processes may be decoupled
and assumed to be in steady state. The systematic
reduction technique [11], the intrinsic low
dimensional manifold (ILDM) approach [12], and
the computational singular perturbation method
[13] are the major reduction techniques that have
been developed based on the above noted
assumptions. A drawback of most reduction
methods is that they are based on chemistry only,
and transport processes are not taken into account
in constructing a manifold. While this may not be a
problem in areas where the temperature is high and
hence chemistry is dominant, it may lead to
increasingly large errors in regions where the
temperature is relatively low and transport becomes
as relevant as chemistry [14].
Among numerical combustion models proposed for
such reacting flows, the flamelet concept has
attracted great interest, for both non-premixed and
premixed turbulent combustion [15]. The so-called
flamelet-generated manifold (FGM) method [10]
not only based on chemical assumptions, but also
considers the most important transport processes. It
shares the idea with the flamelet approach that a
more-dimensional flame can be considered as an
ensemble of one-dimensional (1D) flames. In the
FGM method a manifold is constructed by using
1D laminar flamelets, which can be used in
subsequent flame simulations. In the present study,
the FGM database has been generated for H2-air
flame based on counter-flow non-premixed
flamelets. The mass fraction of H 2 O is selected as
the progress variable. The database contains the
variables as a function of the mixture fraction
Z and the progress variable Y such that:
Y  YFGM (Y , Z )
kg / m3 s
(7)
Rg 
J / kgK
(8)
J / kgK
(9)
RgFGM
(Y , Z )
CP  CPFGM (Y , Z )
h  CPT  (h  CP )

FGM
FGM
(Y , Z )
J / kg
(10)
specific heats, ωY is the source term of the
progress variable, ρ is the density, subscript a
stands for the ambient and M, Pr, and Re represent
Mach number, Prandtl number, and Reynolds
number respectively.
(12)
 
(Y , Z ) W / mK
Where R g ,h stand for gas constant and enthalpy.
CHEMISTRY AND FLAMELET
GENERATED MANIFOLDS
NUMERICAL DETAILS
In order to reduce the computational cost, several
methods have been developed during the last
(Y , Z )
kg / ms
(11)
FGM
The flame temperature is calculated by linearising
the enthalpy around the state on the manifold,
which leads to an explicit expression.
In the present work, a non-premixed hydrogen
impinging jet has been simulated using DNS. Three
dimensional time dependent Navier-Stokes
Page 2 of 6
4th World Hydrogen Technologies Convention, 2011, Glasgow, U.K.
Paper ID: 0021
equations in the Cartesian coordinate system have
been solved in non-dimensional form. The
computational domain employed 4 jet diameters in
the streamwise direction and 12 jet diameters in the
cross-streamwise directions. The results presented
in this study were performed using a uniform
Cartesian grid with 528  528  528 points resulting
approximately 147 million nodes. The Reynolds
number used was Re  2000 based on the inlet
reference quantities. The Prandtl number Pr and the
ratio of specific heats  vary according to the FGM
table. The discretisation of the governing equations
includes the high-order numerical schemes for both
spatial discretisation and time advancement. The
spatial derivates in all three directions are
discretised using a sixth-order accurate compact
( Pade) finite difference scheme [16]. Solutions for
the spatial discretised equations are obtained by
solving the tridiagonal system of equations. The
spatial discretised equations are advanced in time
using a fully explicit low-storage third order
Runge-Kutta scheme [17]. The time step was
limited by the Courant number for stability and a
chemical restraint.
The computational domain contains an inlet and
impinging wall boundaries in the streamwise
direction where buoyancy term effect. At the
inflow, the flow was specified using the NavierStokes
characteristic
boundary
conditions
(NSCBC) [18] with the temperature treated as a
soft variable. At the inlet, the mean streamwise
velocity was specified using a hyperbolic tangent
profile. External unsteady disturbances were
artificially added for all three-velocity component
at the inlet in sinusoidal form. The non-slip wall
boundary condition is applied at solid wall at
ambient temperature, which is also assumed
impermeable to mass. At the impinging wall
boundary, the mixture fraction is assumed zerogradient corresponding to the impermeability, while
the progress variable for chemistry is taken as zero
at the wall boundary.
RESULTS AND DISCUSSION
This section presents detailed descriptions of the
buoyancy effects and near-wall flame structures of
hydrogen impinging jet flame. Comparisons
between the buoyant and non-buoyant cases for the
velocity field, mixture fraction and temperature are
firstly reported. Subsequently variation of near-wall
temperature and Nusselt number distributions are
presented, aiming for further derivation of the nearwall combustion for the hydrogen non-premixed
flame.
(a)
(b)
Figure 1: (a) nonpremxied manifold for source
term of the progress variable and (b) scatter plot of
the flame temperature in the mixture fraction space.
Squares (in red) denote DNS data and circles (in
blue) denote experimental data
Figure 1 (a) and (b) shows a nonpremixed manifold
for the source term of the progress variable and
scatter plot of the flame temperature versus mixture
fraction at one jet diameter in the streamwise
direction. The nonpremixed manifold of source
term of the progress variable, which results from
one-dimensional flamelet calculations and which
serve as an input for the 3D DNS is shown in
mixture fraction and progress variable space. For
figure 1(b), the experimental data have been taken
from Sandia hydrogen jet flame [19], and are
denoted by circle. As seen in figure 1 (b), DNS data
shows relatively high peak temperature and an
overpredicted profile compare to experimental data
mainly due to turbulence-chemistry interaction and
different
flow
conditions
between
two
configurations. Furthermore, the mixture fraction in
the FGM is based in a non-reactive scalar with
unity Lewis number (to prevent preferential
diffusion effects) and the mixture fraction in the
experiment is based on species mass fraction [19].
This might be another reason for the shift in the
mixture fraction where temperature has its
Page 3 of 6
4th World Hydrogen Technologies Convention, 2011, Glasgow, U.K.
Paper ID: 0021
maximum value. Despite this discrepancy between
DNS and experimental data values, both profiles
are consistent and show similar shape distribution
for hydrogen-air nonpremixed flame.
(a)
(a)
(b)
Figure 2: Instantaneous velocity vector field (a)
without buoyancy and (b) with buoyancy at t=12.0
Comparisons are made between two cases: a nonbuoyant case and a buoyant case. The focus here is
to demonstrate the buoyancy effects with moderate
Froude number (Fr=2.0) in a flow regime where
both buoyancy and momentum are important. The
effects of buoyancy on the dispersion of hydrogen
and its flame temperature distribution at the
primary jet and wall jet have been identified.
The cross-sectional instantaneous velocity vector
fields with and without buoyancy is shown in figure
2. The instantaneous velocity fields exhibit large
difference in the shear layers of the primary jet and
vortex formation at the wall jet. For the buoyant
case, large vortical structures started to form in the
flow field and thus affect the flow structure. The
buoyancy instability leads to form large vortical
structures, which are convected by the momentum
of the primary jet stream as well as by the
momentum of the secondary wall jet.
(b)
Figure 3: Contour plots of instantaneous mixture
fraction (a) without buoyancy and (b) with
buoyancy at t=12.0
Figures 3 and 4 show the contour plots of
instantaneous mixture fraction and flame
temperature with and without buoyancy at t=12.0.
Both mixture fraction and temperature distributions
exhibit large difference between two cases due to
formation of inner and outer vortical structures [20]
at the primary and wall jet regions. The formation
and convection of buoyancy induced vortical
structures lead to an irregular mixture fraction
distribution and flame structure particularly at the
primary jet and wall jet regions. A large head
vortex can be seen at the end of the wall jet flame
for the buoyant case and vortical structures such as
the head vortex are important characteristics of
impinging jets. For both cases, the maximum nondimensional temperature at the stoichiometric
region (stoichiometric mixture fraction = 0.0285)
reaches T=8.7, which is around 2550K.
Page 4 of 6
4th World Hydrogen Technologies Convention, 2011, Glasgow, U.K.
(a)
(b)
Figure 4: Contour plots of instantaneous flame
temperature (a) without buoyancy and (b) with
buoyancy at t=12.0
Figure 5: Instantaneous Nusselt number
distribution at the impinging wall at t=12. Here
solid line represents the buoyant and circles
indicate the non-buoyant case
Paper ID: 0021
Figure 6: Instantaneous Nusselt number
distribution at the impinging wall with buoyancy at
t=12(red solid line), 14(dashed blue line) and
16(dashed-dotted green line)
The distribution of Nusselt number (Nu), which is
dimensionless number that measures the
enhancement of heat transfer from a surface that
occurs in a real situation, compared to the heat
transfer that would be measured if only conduction
could occur. Figures 5 and 6 show the Nu
comparison between non-buoyancy and buoyancy
cases at t=12 and Nu variation at three different
time steps t=12, 14 and 16 for the buoyant case. All
three lines indicate distributions for the buoyant
case (t=12, 14,16) and circles indicate distribution
for the non-buoyant case (t=12). The Nu
distributions exhibit wider temperature distributions
with respect to time. Furthermore, Nu distributions
show more fluctuations for the buoyant case
compare to more smooth and narrow temperature
variation in the non-buoyant case.
(a)
(b)
(c)
Figure 7: Instantaneous near-wall temperature
distribution at t=12 (a), 14(b) and 16(c)
Figure 7 shows the corresponding near-wall
temperature distributions at t=12, 14 and 16. The
temperature distributions indicate the growth of
higher flame temperature on the surface of the wall,
which results in more prominent heat transfer
Page 5 of 6
4th World Hydrogen Technologies Convention, 2011, Glasgow, U.K.
effects. Further analysis of mean wall heat flux
such as averaged heat flux along the wall including
surface chemistry effects should provide vital
information
on
near-wall
heat
transfer
characteristics for the hydrogen combustion.
CONCLUSION
Direct
numerical
simulations
(DNS)
of
nonpremixed hydrogen flame with flamelet
generated manifold approach for the chemistry was
performed to elucidate the buoyancy effects and
near-wall combustion in a nonpremixed flame. The
main outcomes of the present investigation were the
following. Both inner and outer vortical structures
developed in the flow field of this moderately
buoyant case with Fr=2.0. The combustion-induced
buoyancy act as oscillators in the flow field and led
to the formation of self-sustained outer vortical
structures. In addition, the moderate buoyancy with
Fr=2.0 led to the development of inner vortical
structures. Vortex deformation occurs at the wall jet
region due to the geometry effects. The
comparisons between the buoyant flame and the
non-buoyant flame revealed that the two flames
have large differences at near flame region and
impinging wall regions. Velocity distributions
demonstrate buoyancy effects on flame dynamics
where the flow has a tendency of transition to
turbulence in the form of inner and outer vortical
structures. These vortical structures thus affect the
mixture fraction, progress variable and hence the
flame temperature through the flamelet calculation.
Further DNS studies with detailed chemical
kinetics are ongoing in order to investigate the
combustion-induced buoyancy effects by varying
the Froude number and combustion regimes
changes towards the wall for hydrogen
nonpremixed combustion.
ACKNOWLEDGEMENT
This research is funded by the UK EPSRC grant
EP/G062714/2.
REFERENCES
[1] G. Marban, T. Valdes-Solfs “Towards the
hydrogen economy”, Int. J. Hydrogen Energy, 32
(2007), pp 1625-1637.
[2] W. Houf, R. Schefer “Predicting radiative heat
fluxes and flammability envelopes from unintended
releases of hydrogen”, Int. J. Hydrogen Energy, 32
(2007), pp 136-151.
[3] R.W.Schefer “Hydrogen enrichment for
improved lean flame stability” Int. J. Hydrogen
Energy, 28 (2003), pp 1131-1141.
[4] F.C.A. Coghe “Behaviour of hydrogen enriched
non-premixed swirl natural gas flames”, Int. J.
Hydrogen Energy, 31(2006), pp 669-677.
Paper ID: 0021
[5] S. Mahalingam, J.H. Chen, L. Vervisch “Finite
rate chemistry and transient effects in direct
numerical simulations of turbulent non-premixed
flames” Combust. Flame, 102 (1995), pp 285-297.
[6] F. Dabireau, B. Cuenot, O. Vermorel, T. Poinsot
“Interaction of flames of H2/O2 with inert walls”
Combust. Flame, 135 (2003), pp 123-133.
[7] E.R.Hawkes, R. Sankaran, J.C. Sutherland, J.H.
Chen “Scalar mixing in direct numerical
simulations of temporally evolving plane jet flames
with skeletal CO/H2 kinetics” Combust. Flame, 31
(2007), pp 1633-1640.
[8] A. Gruber, R. Sankaran, E.R. Hawkes, J.H.
Chen “Turbulent flame-wall interaction: a direct
numerical simulation study” J. Fluid Mech., 658
(2010), pp 5-32.
[9] H. Pitsch “Shedding new light on a burning
question” J. Fluid Mech., 658 (2010), pp 1-4.
[10] J.A. van Oijen, L.P.H. de Goey “Modelling of
premixed laminar flames using flamelet generated
manifolds” Combust. Sci. Tech., 161 (2000), pp
113-137.
[11] N.Peters “In reduced kinetic mechanisms and
asymptotic approximations for methane-air flames”
(M.D. Smooke Ed.), Springer-verlang, Berlin, 384
(1991), pp 48-85.
[12] U. Mass, S, B. Pope “Laminar flame
calculations using simplified chemical kinetics
based on intrinsic low-dimensional manifolds”
Proc. Combust. Inst., 25 (1994), pp1349-1356.
[13] A. Massias, D. Diamantis, E. Mastorakos,
D.A. Goussis “An algorithm for the construction of
global reduced mechanisms with CSP data”
Combustion and Flame, 117(1999), pp 685-708.
[14] R.L.G.M Eggels, L.P.H de Goey
“Mathematically reduced mechanisms applied to
adiabatic flat hydrogen/air flames” Combust.
Flame, 100(1995), pp559-570.
[15] N.Peters “Turbulent combustion” Cambridge
Uni. Press. 2000.
[16] S.K. Lele “Compact finite difference scheme
with spectral-like resolution” J. of Comput.
Physics, 103 (1992), pp16-42.
[17] J.H. Williamson “Low-storage Runge-Kutta
schemes” J. of Comput. Physics, 35 (1980), pp 4856.
[18] T.J. Poinsot, S.K. Lele “Boundary-conditions
for direct numerical simulations of compressible
viscous flows” J. of Comput. Physics, 101 (1992),
pp 104-129.
[19] R.S.Barlow, C.D.Carter “Relationships among
nitric oxide, temperature and mixture fraction in
hydrogen jet flame” Combust. Flame, 104 (1996),
pp 288-299.
[20] X. Jiang, K.H. Luo “Combustion-induced
buoyancy effects of an axisymmetric reactive
plume” Proc. Combust. Inst., 28 (2000), pp 19891995.
Page 6 of 6