CFD Approach For Modeling High and Low Combustion in a Natural Draft Residential Wood Log Stove

The 3D model is divided into three parts: fluid flow, chemical mechanism and heat transfer. Model equations are listed in a paragraph presenting the governing equations. Fig. 1 shows half of the 3D geometry with a symmetry plane to reduce the computational domain and the corresponding boundary conditions. Special attention is given to the gas phase. The heterogeneous reactions are considered negligible in the oxidation zone as oxygen reacts much faster with the generated gas from pyrolysis.

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Figure 1. Geometry and boundary conditions

2.1 Governing equations

The time averaged gas phase equations for steady turbulent flow can be expressed as:

$\frac{\partial}{\partial \mathbf{x}_{\mathbf{j}}}\left(\rho \mathbf{u}_{\mathbf{j}} \Phi\right)=\frac{\partial}{\partial \mathbf{x}_{\mathbf{j}}}\left(\Gamma_{\Phi} \frac{\partial \Phi}{\partial \mathbf{x}_{\mathbf{j}}}\right)+\mathbf{S}_{\Phi}$      (1)

where Φ, Γ_Φ and S_Φ are respectively the representative dependent variables, the effective diffusion coefficient and the source term for the gas phase respectively as shown in equation (1). Replacement of Φ with a value of 1 yields the continuity equation, while a substitution with u, v and w represents the momentum equation in the x, y and z directions, and substitution of Φ with T, k, ω and y yields respectively the equations of energy, turbulent kinetic energy, dissipation rate of the turbulent kinetic energy and species transport. In this work, the following models were selected: Eddy Dissipation Concept (EDC) Model for turbulent combustion reaction, discrete ordinates model for radiation heat transfer, and k-ε equations for the turbulence model.

Eddy dissipation concept model. For a solid fuel such as wood, it is not possible to provide a mixture equivalent to that obtainable with a gas or a volatile liquid. It requires that each carbon atom or hydrogen waits its turn in the queue before being oxidized. When the first flies off the solid surface as volatilized product from when heated by combustion, then the neighbor becomes available to fly off next, and so on. This process delays the oxidation of the log mass and therefore decreases the efficiency of heat production. It has been confirmed by a number of researchers [3], [4], [5], [6] and [7] that, in the residential stove, the combustion reaction can be regarded as approaching equilibrium. Furthermore, it is reasonable that, in the wood pyrolysis process, each substance to form a particle is uniformly released. Concerning homogeneous reactions, a combined model is used. The finite rate Eddy dissipation concept model computes both the Arrhenius rate and the Eddy dissipation rate and uses the lower of the two. The combustion mechanism of Westbrook and Dryer [10] is used here; it consists of the partial oxidation of tar and light hydrocarbons (Reactions (R1), (R5), and (R6)), the complete oxidation of carbon monoxide (Reaction (R2)) and hydrogen (Reaction (R4)) and the dissociation of carbon dioxide (Reaction (R3)) which is significant at high temperatures.

Chemical kinetics used here is based on a global reduced mechanism, with the following reactions:

CH₄ +1,5 O₂ → CO + 2 H₂O                    (R1)

CO + 0,5 O₂ → CO₂                       (R2)

CO₂ → CO + 0,5 O₂                   (R3)

H₂ + 0,5 O₂ → H₂ O                    (R4)

C₂ H₂ + 2,5 O₂ → 2 CO₂ + H₂ O                  (R5)

C₂ H₄ + 3 O₂ → 2 CO₂ + 2H₂ O              (R6)

The kinetic rates for the mechanism are listed in Table 1.

Table 1. Parameters for Arrhenius rates

The advantage is that it requires less computation time, but it is limited to six (6) stages. In this EDC model, the total space is divided into smaller spaces to account for reaction, called fine structures. The reactions are assumed to take place in these fine structures. These models are described in more detail in the theory section of the user’s guide for the commercial code FLUENT ™.

The volatile stream composition is defined by selecting appropriate species and setting their mole fractions. The equilibrium system for homogenous combustion consists of 8 species (CH4, CO, CO2, C2H2, H2, H2O, C2H4 and O2).

2.2 Numerical scheme

The computational model uses a 3D steady-state solver and a second-order discretization scheme where gradients and derivatives are evaluated through the Green-Gauss method. Table 2 summarizes the characteristics of the solver. For the discretization of all conservative equations (momentum, continuity, energy, mixture fraction, turbulent kinetic energy, turbulent kinetic energy dissipation rate and mass fraction of chemical species), a second-order upwind scheme was used [9], [10] and [11]. In this discretization scheme, quantities at the cell faces are determined by assuming that the cell-center values represent an average value and hold throughout the entire cell; the face quantities are identical to the cell quantities.

Table 2. Solver parameters

4.1 Geometry and grid

The computational domain of the 3D geometry used in this study includes unstructured grid of tetrahedral mesh elements as seen at Fig.5. A grid independent study was performed with coarse, medium and fine grids. The results for the velocity field at the symmetry plane of the combustion chamber show a small difference between the medium and fine grids. The medium grid with 934 705 nodes was selected for this CFD analysis. The initial boundary conditions for the flow are shown in Fig.1.

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Figure 5. Tetrahedral grid

4.2 Validation cases

The validation study is to simulate two types of stove operating conditions defined by the Environmental Protection Agency (EPA) as follows: category 1: Low combustion (low burn) and category 4:  high combustion (high burn) as seen at Table 3. In this paper, only the high and low combustion are presented but temperature and species contours are shown only for category 4 (high combustion).

Indeed, prior to complex simulations, it is necessary to know the behavior of the computer code for this type of physics and thus to evaluate the accuracy of results that can be achieved. In our validation, the CFD results were compared with experimental values that were ​​obtained specifically for this validation study.

These comparisons have thus helped to refine the methodology as it was possible to identify the strengths and weaknesses of the code, and make adjustments as necessary.

Table 3. Different burning categories

Tables 4, 5 and 6 summarize all the operating conditions presented in this study. The air flow distribution as input to the model is estimated as follows at the high burn category:

• 88% for the primary air,

• 12% for the secondary air.

Table 4. Calculation assumptions

Table 5. Overall operating conditions

For each simulated case, a flow calculation must be done to adjust the natural draft in the chimney to meet the value of the overall equivalence ratio Ф. Therefore the Ф is set by changing the draft at the exit of the chimney to adjust the air feed rate and the fuel rate. The calculations are based on the detailed measurements done for the composition of combustion products and temperature distribution inside the combustion chamber. The results are compared with the experimental data to better understand the effects of temperature and Ф on the CO/CO₂ ratio.

Chimney draft (outlet pressure) varies within a range of 1.5 Pa (0.006 in H₂O) to 31.1 Pa (0.125 in H₂O). The fuel rate is evaluated experimentally (mass change of consumed wood logs), although only the gas phase is considered. The fuel volatile composition at the wood log boundary is listed in Table 6.

Table 6. Composition of Volatiles at wood log boundary

The CFD model was calibrated and validated using operating conditions and experimental measurements available in the Combustion Laboratory at Université Laval. Numerical results are in acceptable agreement with the experimental data. The CFD model is capable of describing the fluid dynamics and chemical processes taking place in the overall combustion process, capturing known phenomena like air velocity, temperature distribution and chemical species concentrations. However, since the model was developed in the framework of a commercial code, it can also handle more complex geometries and operating boundary conditions. Therefore, it can be used for the analysis and optimization of existing stove and for relatively quick evaluations of new designs. In future works, the combustion of solid biomass will be taken into consideration knowing that is generally assumed to be a multi-stage process (drying, gasification/pyrolysis, homogeneous combustion of the released volatiles, and heterogeneous combustion of the char residue). The CO/CO₂ ratio of the heterogeneous reactions for biomass combustion will also be investigated in the future, including the effect of the homogeneous reactions.

The integration of this multi-step model in an accurate and stable manner with moderate computational requirements will be one of the next ambitious steps. Furthermore, a model for the generation of NOx-emissions from fuel-N using several precursor species would be introduced.