Direct numerical simulation of hydrogen impinging jet flame
using flamelet generated manifold reduction
Citation for published version (APA):
Ranga Dinesh, K. K. J., Jiang, X., & Oijen, van, J. A. (2011). Direct numerical simulation of hydrogen impinging jet flame using flamelet generated manifold reduction. In Proceedings of the 4th World Hydrogen Technologies Convention 2011, 14-16 September 2011, Glasgow, Scotland (pp. paper 0021-1/6)
Document status and date: Published: 01/01/2011
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DIRECT NUMERICAL SIMULATION OF HYDROGEN IMPINGING JET FLAME
USING FLAMELET GENERATED MANIFOLD REDUCTION
K.K.J. Ranga Dinesh
1, X. Jiang
1, J.A. van Oijen
21
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 third-order 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 emission from power-generating systems 2 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 asCO, 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 near-wall 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
2
CO/H planer jet flame using DNS and more recently Gruber et al. [8] studied turbulent flame-wall 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
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 non-dimensional form can be written as follows:
( ) 0, j j u t x ρ ρ ∂ ∂ + = ∂ ∂ (1) ( ) ( ) 1 Re ( ) 0, j j k jk k k k j a u u u p t x x x g Fr ρ ρ t ρ ρ ∂ ∂ ∂ ∂ + + − ∂ ∂ ∂ ∂ + − = (2) 2 ( ) ( ) 1 ( ) Re Pr ( 1) ( ) 1 ( ) 0, Re k k k k k k j jk k k a k eu pu e t x x T M x x u g u x Fr
ρ
ρ
λ
g
t
ρ
ρ
∂ ∂ ∂ + + ∂ ∂ ∂ ∂ ∂ − − ∂ ∂ ∂ − + − = ∂ (3) ( ) ( ) 1 ( ) Re Pr 0, k k k p k Y u Y Y Y t x x C x ρ ρ λ ω ∂ ∂ ∂ ∂ + − ∂ ∂ ∂ ∂ − = (4) ( ) ( ) 1 ( ) 0, Re Pr k k k p k u Z Z Z t x x C x ρ ρ ∂ λ ∂ + − ∂ ∂ = ∂ ∂ ∂ ∂ (5) 2 T p M ρ g = (6)In Eqs. (1)-(6), t stands for time, uj is the velocity components in the xj 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 specific heats, ωY is the source term of the progress variable, ρ is the density, subscript a stands for the ambient and M, Pr, andRerepresent Mach number, Prandtl number, and Reynolds number respectively.
CHEMISTRY AND FLAMELET
GENERATED MANIFOLDS
In order to reduce the computational cost, several methods have been developed during the last
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 O2 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: 3 ( , ) / FGM Y Y Y Z kg m s ω =ω (7) ( , ) / FGM g g R =R Y Z J kgK (8) ( , ) / FGM P P C =C Y Z J kgK (9) ( )FGM( , ) / P P h C T− = h C− Y Z J kg (10) ( , ) / FGM Y Z kg ms m m= (11) ( , ) / FGM Y Z W mK λ λ= (12)
Where R ,h stand for gas constant and enthalpy. g The flame temperature is calculated by linearising the enthalpy around the state on the manifold, which leads to an explicit expression.
NUMERICAL DETAILS
In the present work, a non-premixed hydrogen impinging jet has been simulated using DNS. Three dimensional time dependent Navier-Stokes
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 Prand the ratio of specific heats g 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 Navier-Stokes 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 zero-gradient 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 near-wall 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
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)
(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 non-buoyant case and a non-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.
(a)
(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 non-dimensional temperature at the stoichiometric region (stoichiometric mixture fraction = 0.0285) reaches T=8.7, which is around 2550K.
(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
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
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.
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