2 Literature and theory
3.1 Description of the burner to be modeled
The burner modeled in this thesis is a 20 kW gas burner. It is a part of an apparatus rig standing in the laboratory at the Department of Energy and Process, consisting of fuel and air supply, burner and a combustion chamber. To the rig it is also possible to connect a diluent flow to the fuel supply. The apparatus has been widely used for experimental studies the last 10-15 years [3, 15, 21]. A schematic overview of the whole rig is given in Figure 15, and pictures of the rig and the swirl burner is attached in Appendix C.
Figure 15: Schematic view of the apparatus rig [15]
The actual burner modeled in this thesis was designed by Øystein Spangelo, when working on a scaling problem of swirl burners in his Ph.D. [3]. The burner consists of an inner gas tube from where fuel gas is injected into the air flow through gas nozzles which consists of drilled holes in the gas tube. The air flows through the annulus, from now on
referred to as the burner tube, surrounding the gas tube where it is given a swirl by a vane swirl generator. The fuel air mix is then introduced into the combustion chamber by a converging conical section. The NOx reducing technique implemented in this burner is the swirl generator. The aim of this swirl generator is to decrease the temperature and the partial pressure of oxygen by creating a central toroidal recirculation zone as described in chapter 2.2. The swirl number was set to approximatelyS ≈1.285, calculated from equation [3]:
Figure 16: Diagram of the swirl burner [3]
The burner was originally designed to work in the power range of 5-20 kW, but in practice it has proven difficult to operate in that range [3]. Problems like flame stability and lift off have been observed depending on what combustion chamber that is used. In an un-cooled combustion chamber problems with instability have been observed at low flow rates of fuel and air (5-10 kW). When using a water-cooled combustion chamber, the problem with stability becomes worse. In this type of combustion chamber, lift off and subsequently blow off occurred at high flow rates using propane as fuel. With
methane as fuel, the flame could not be stabilized at all. These results are of interest when deciding at what power output the burner should be modeled and simulated. The stability observations made by Øystein Spangelo are summarized in Table 3.
Table 3: Stability observations of the 20 kW swirl burner [3]
3.2 Simulation setup
The main goal of this thesis is, with the help of CFD, to investigate how the NOx
emission changes when implementing partial premixing in a gas burner. It is therefore important to establish different scenarios, and to make some assumptions about the operating conditions.
Because of the stability and lift off problems at some of the power outputs, it was decided to run simulations at a power output of 10 kW with propane as fuel to ensure that the scenario is physical possible. To minimize factors other than partial premixing that effect the NOx emission, the excess air and the nozzle velocity were set constant. The excess air was fixed at 3 vol% O2, and the nozzle velocity was held constant by changing the nozzle area (Denoted as Anozzle in Table 4). The velocity in the burner tube is assumed to change so little that it will not affect the emissions. For more information about the constant velocity calculations see appendix A.1.
The mass flow of fuel and air with a power output of 10 kW was found by solving equations (3-2) and (3-3):
Where P is the power output, LHVfuel is the lower heating value for propane given in chapter 2.3, φ is the overall combustion equivalence ratio and nair is the amount of mole air in a stoichiometric propane-air combustion.
In collaboration with supervisor Professor Johan Hustad, it was decided to limit the amount of simulations to eight different premixed air-fuel ratios ( air
fuel
m
m ). The ratios simulated were 0, 1/2, 1, 3/2, 2, 3, 7/2 and 4. Different properties for the different air-fuel ratios are given in Table 4.
Table 4: Properties for different air-fuel ratios at 10 kW
air
0 0.003891029 0.0002156567 39.27 100 ∞
0.5 0.003762746 0.0003234850 69.149 56.6 31.1
1 0.003675372 0.0004313130 99.298 39.5 15.5
1.5 0.003567544 0.0005391420 129.448 34.3 12.4
2 0.003459716 0.0006469700 159.597 24.6 7.8
3 0.003244059 0.0008626270 219.896 17.9 5.2
3.5 0.003136231 0.0009704550 250.046 15.7 4.4
4 0.003028402 0.0010782840 280.195 14.0 3.9
5.8 0.002856726 0.0012499660 331.343 10.1 2.7
The air-fuel ratio of 5.8 is the highest possible ratio before reaching the upper
flammability limit and is included here for comparison. In practice this air-fuel ratio is too dangerous to operate at with a view to flash back and explosion risk.
3.3 Implementation of CFD
The modeling of the burner was carried out by using the CFD software FLUENT.
FLUENT is a commercial computer program for modeling fluid flow and heat transfer in complex geometries, and the code is programmed in a C-language. The governing
equations are solved by means of iterations with the help of the models described in chapter 2.4.
There exist several other commercial CFD programs on the market, for instance KFX, CFX, Comsol Multiphysics, PHOENICS and CFD-ACE. The reason why FLUENT was chosen as the modelling tool was because of the previous work done by Øystein Spangelo [3]. The modelling, simulations and verification against experimental data in Spangelo’s Ph.D. made it possible to model the partially premixed swirl burner within the time limit of this master thesis.
3.3.1 Description of the mesh
To reduce the complexity of the problem the burner was simplified to a two dimensional, axis symmetric mesh with approximately 21 000-25 000 quadratic cells. The mesh can be seen in Figure 18 and Figure 19. In addition, the swirl generator was modeled by defining a tangential velocity as an internal condition where the swirl generator is located. This was done by using an user defined function (UDF) written by Øystein Spangelo [3]. This UDF, written in C-language, multiplies the axial velocity in the cells where it is applied with a tangential angle to create a tangential velocity. The tangential velocity component is defined by equation (3-4), where uθis the tangential velocity, uxis the axial velocity and β is set to 60 degrees. The user defined function can be found in Øystein Spangelo’s doctoral thesis.
uθ =uxtanβ (3-4)
The original swirl burner has nozzles both upstream and downstream of the swirl burner.
This geometry proved difficult to simulate in FLUENT, due to pressure difference
between the gas and burner tube upstream the swirl generator allowing air to seep into the and ignite the fuel inside the gas tube. The problem with the air flowing into the gas tube is visualized in Figure 17. Because of this problem the upstream nozzles in the model were removed, leaving only nozzles downstream of the swirl generator. In order to be able to model the burner as a two dimensional axis symmetric problem, the nozzles were simplified to one hole downstream the swirl generator. The area of the hole is listed as Anozzle in Table 4.
Figure 17: Contours of: a) the mass fraction of C3H8 and b) The static pressure in the burner; 10 kW
@ 3% O2 in the flue gas, mair mfuel =0 with two nozzle holes
When utilizing these simplifications, the CPU time and memory required to reach convergence are greatly decreased.
a) b)
Figure 18: Computational mesh used for the 20 kW swirl burner
The mesh was created in GAMBIT, a mesh preprocessor that interacts with FLUENT.
The mesh is structured and created with higher density in areas where the flow is expected to have large gradients, for instance around the fuel nozzles and in the
recirculation zones. The number of cells in the mesh depends on the area of the nozzles, because of the increased area with high density cells with increasing nozzle area.
When constructing a mesh it is important to minimize the numerical diffusion (false diffusion). If possible, a structured, quadrilateral mesh with a low skewness should be constructed. A normalized measure of the skewness is defined as follows [6]:
max max , min
Where θmaxand θmin are the maximum and minimum angles (in degrees) between the edges of the element, and θeq is for quadrilateral elements 90˚. By
definition, 0≤QEAS ≤1, where QEAS =0 describes an equilateral element, and QEAS =1 describes a completely degenerate (poorly shaped) element. For the mesh constructed in this thesis, maximum QEAS <0.39 and the average QEAS <<0,1 which is regarded as an excellent mesh quality [6].
Figure 19: Close-up of the swirl burner with nozzle area calculated for mair mfuel =0
Air Fuel & air
Placing of the swirl generator
3.3.2 Boundary conditions
The calculations were carried out by using the same boundary conditions as in the simulations performed by Øystein Spangelo. These conditions are a model of a water-cooled combustion chamber, and have proven satisfactory in previous calculations [3].
The operating pressure was set to 1.01x105 Pascal. The fuel and air flows and different nozzle areas are given for different premixing ratios in Table 4. In Appendix D there is enclosed an excel sheet with dimensions of the swirl burner. The hydraulic diameters for the gas tube, burner tube and the flue gas outlet are respectively 11.5 mm, 20.5 mm and 100 mm. The temperatures were set to 298 K for the incoming fuel and air and 650 K for the flue gas. The bottom of the combustion chamber (left side of Figure 18), the burner tube and the gas tube are all set to insulated steel. On the water-cooled sidewall, the material is steel and the temperature is set to 373 K (boiling water). The conical top and the exhaust pipe is uncooled steel with a constant temperature of 650 K. The temperature is set constant here because of the ambient air’s cooling effect. At the outlet the gauge pressure was set to 50 Pascal. When performing experiments in a laboratory there is set a gauge pressure to prevent ambient air to seep into the combustion chamber and change the amount of excess air in the flue outlet. This is of no concern when simulating on the computer, but is included in the model to make it as realistic as possible.
3.3.3 Models used
3.3.3.1 Turbulence and combustion models
From the previous work done on the 20 kW swirl burner, it is concluded that Reynolds stress model (RSM) and flamelet models is the most appropriate respectively turbulence and combustion models [3]. The k-ε turbulence model can on the other hand be used to get more accurate initial conditions before introducing the RSM, and therefore lower the time used on iteration. The constants in the turbulence models are defined by FLUENT, and is not altered.
The flamelet look-up tables were calculated in FLUENT. This proved to be the most time consuming part of the simulations. A look-up table had to be made for each of the
different air-fuel ratios because of the composition change in the gas and burner tube.
The tables were created as non-adiabatic multiple strained flamelets using the chemical mechanism GRI-Mech 3.0, with 20 different species chosen by FLUENT [26]. A probability density function (PDF) is then calculated from the flamelet table.
3.3.3.2 The solver
The solver used for the computations, was a steady state pressure based implicit two-dimensional swirl solver. The pressure-based solver uses a solution algorithm where the governing equations are solved sequentially (i.e. segregated from one another). Because the governing equations are non-linear and coupled, the solution loop must be carried out iteratively in order to obtain a converged numerical solution, using a second-order
scheme. For the pressure interpolation the PRESTO! scheme were used due to
recommendation from FLUENT to use this scheme for swirling flows [6]. The difference
between a two dimensional swirl solver and a two dimensional solver is that the
circumferential component of velocity is included in the calculations for the swirl solver.
The convergence criteria based on scaled residuals was set to 10-4 for all the equations except the energy and radiation equations which was set to 10-6. Before solving the equations, a set of under-relaxation factors can be fixed. The under-relaxation of equations is used in the pressure-based solver to stabilize the convergence behaviour of the outer nonlinear iterations by introducing selective amounts of ϕ in the system of discretized equations. In a simple form, the new equation value,ϕ, can be written as follows when implementing the under-relaxation factor α:
ϕ ϕ= old + Δα ϕ (3-6)
These under-relaxation factors proved important when trying to reach the convergence criteria and a lot of effort had to be made to find appropriate values for these factors. An overview of the under-relaxation factors that gave convergence is given in Table 5.
Table 5: Under-relaxation factors used in the simulations
Pressure Density Body forces
0.7 0.3 0.7
Momentum Swirl velocity Turbulent Kinetic energy
0.3 0.4 0.5 Turbulent dissipation rate Turbulent viscosity Reynolds stresses
0.5 0.6 0.5
Pollutant NO Pollutant hcn Energy
0.95 0.95 0.99
Temperature P1 Progress variable
1 0.9 0.9 Mean mixture fraction Mixture fraction variance
0.9 0.8
3.3.3.3 NOx formation models
The NOx concentration is in FLUENT calculated in a postprocessor. The postprocessor uses rate models developed at the Department of Fuel and Energy at The University of Leeds in England as well as from the open literature [6]. In the calculations of the NOx
concentrations in this thesis, only models for thermal and prompt NOx formations are included. In addition a reburn mechanism is implemented, which includes the reduction of NOx formation by accounting for the reaction of NO with hydrocarbons.
FLUENT solves the mass transport equation for the NO species, taking into account convection, diffusion, production and consumption of NO and related species. This approach is completely general, being derived from the fundamental principle of mass conservation. The effect of residence time in NOx mechanisms, a Lagrangian reference
The convergence criteria based on scaled residuals was set to 10-6 for the transport equation dealing with NO species.
In the calculation of NO from the thermal mechanism, a quasi-steady assumption for the nitrogen concentration is assumed and the NO formation rate can be calculated as follows [6]:
Where ki,j is the rate constants for the elementary reactions (2-1), (2-2) and (2-3). The O2
and OH radical concentration is taken from the local species mass fraction in the flamelet model.
The prompt NOx formation rate is calculated from equation (3-8) [6]:
[ ]
Where f is a correction factor that incorporates the effect of the fuel type and equivalence ratio, kpr is the rate coefficient, a is the oxygen reaction order, Ea is the activation energy, R is the universal gas constant and T is the temperature.
3.3.4 Comparison of the calculations with previous work
As mentioned previously, there has been performed some work with the swirl burner in the past both experimental in the laboratory and CFD simulations in FLUENT. The results from the previous work can be used to validate accurateness of the CDF
calculations. In this chapter the results from the calculations of the swirl burner at 10 kW with mair mfuel = ⇒0 φlocal = ∞ performed here will be compared with previous
measurements and calculations made on the same burner.
In a strong swirling flow it is important to be able to model the central toroidal
recirculation zone (CTRZ) and the corner recirculation zone (CRZ). Figure 20 indicates the contours of the zero-axial velocity areas in the combustion chamber from the new calculations performed here and the old ones performed by Øystein Spangelo. In Figure 20 it can be seen that the new calculations manage to model the recirculation zones described in chapter 2.2.3. When comparing the new calculations with the old one, the recirculation zones seem more stretched out in axial direction and not as plump as in Spangelo’s calculations. The reason for these differences is not found, but since the same models and solvers are employed in the two calculations the source of the differences has
to be the flamelet look-up tables, the mesh, the nozzle geometry or the placing of the swirl generator.
Figure 20: Contours of zero-axial velocities: a)The new calculations in this thesis; b) Calculations by Øystein Spangelo, 10 kW @ 3% O2 with mair mfuel =0 [3]
CTRZ
As described in chapter 2.1, temperature is an important parameter considering NOx
emissions. A verification of the correctness of the calculated temperature should therefore be made. At the moment there exists no successful experimental measurement of the temperature distribution in the swirl burner. Spangelo investigated the possibility to use laser induced fluorescence (LIF) for temperature measurements, but the LIF was found too inaccurate [3]. One property that it is possible to compare the calculated temperature with is the adiabatic flame temperature for propane listed in Table 1 in chapter 2.3. The maximum calculated temperature should be below the adiabatic flame temperature because of for instance heat loss, recirculation zones, excess air in the flue gas or dissociation of the combustion products [20]. The adiabatic flame temperature for propane is 1994 ˚C. The maximum temperature calculated in FLUENT with the help of the models described in the previous chapter was 1706 ˚C (see Figure 29 in Appendix B).
Spangelo calculated a maximum temperature of 1700 ˚C. A temperature around 1700-1706 ˚C can therefore be a feasible temperature for the burner, but without experimental values no final conclusion can made about its correctness.
Another parameter that affects the NOx emissions is the shape of the flame. The size of the high temperature area will effect the emissions significantly. One way of to describe the flame shape is to look at the OH concentration in the combustion chamber. Formation of OH radicals takes place in the flame front and is in most flames present in relatively large concentrations. The OH radical is therefore, together with CH radical, a typical marker of the flame front [3]. Figure 21 and Figure 22 shows the results of Spangelo’s work with LIF measurements and calculations in FLUENT, respectively. Spangelo had some problems to reproduce the flame shape that was measured with the LIF. The range of the OH concentrations is satisfactory, but the flame shape in the calculation looks more like a “flower” and is far more divergent than the measured shape. This “flower”
shape can also be seen from the new calculations performed in this thesis (see Figure 23), a)
b)
CTRZ CRZ
calculations. It seems like the new calculations can model the flame shape better than the old one performed by Spangelo.
Figure 21: OH mole fractions in swirl burner measured with LIF, 10 kW @ 3% O2 [3]
Figure 22: OH mole fractions computed in FLUENT by Øystein Spangelo, 10 kW @ 3% O2 [3]
Figure 23: OH mole fractions computed in FLUENT,mair mfuel =0 10 kW @ 3% O2
The problem described in chapter 3.3.1 with air seeping into and igniting in the gas tube was not a problem when removing the nozzle upstream of the swirl generator. The contours of the C3H8 mass fraction and the static pressure is given in Figure 24.
Figure 24: Contours of: a) the mass fraction of C3H8 and b) The static pressure in the burner; 10 kW
@ 3% O2, mair mfuel =0 with one nozzle hole
a) b)
3.4 The effect of partial premixing on NOx emissions
In Figure 25 the NOx concentration from the simulations of the 10 kW swirl burner is plotted versus the different premixing ratios listed in Table 4. The quantity of the NOx
emission is different from the results found from experimental measurements. Spangelo measured a NOx concentration of approximately 26 ppmv when performing experiments with the swirl burner at 10 kW power output, three percent excess air and no premixing [3]. In the simulations, an emission of 0.5 ppmv was calculated. This difference was, as explained earlier, expected. The interesting thing is to see what effect partial premixing have on the NOx emission. This will be expounded in the following sections.
emission is different from the results found from experimental measurements. Spangelo measured a NOx concentration of approximately 26 ppmv when performing experiments with the swirl burner at 10 kW power output, three percent excess air and no premixing [3]. In the simulations, an emission of 0.5 ppmv was calculated. This difference was, as explained earlier, expected. The interesting thing is to see what effect partial premixing have on the NOx emission. This will be expounded in the following sections.