Numerical Study of Biomass Combustion Using a Transient State Approach

Abstract

The behavior of the temperature and velocity, as well as the mass fraction of water (H₂O) and wood inside a combustion chamber under specific operating conditions, were numerically investigated using a transient state model. For the computational fluid dynamics (CFD) simulation, the software Ansys Fluent 2024 R2 was used to analyze a turbulent flow in two dimensions. The species transport with volumetric responses and eddy dissipation were included in the combustion simulation. The study was conducted for the first 150 s. The findings show that in the lower and upper zones of the combustion chamber close to the walls, the temperature rises over time. The velocity between the outlets rises over time. Due to the fact that the wood goes through a process that reduces the amount of wood and produces H₂O, it exhibits the opposite behavior for the mass fractions of wood and H₂O.

1. Introduction

In the past few decades, energy demands have increased due to the increase in population, industrialization, and the quality of life of people. This led to an increase in greenhouse gas (GHG) and municipal solid waste (MSW) [1,2,3].

In 2021, 56% of the world’s population resided in urban areas [4], and it is expected that this number will rise to 68% by 2050 [5].

This expected increase in the population residing in urban areas can lead to an increase in urban solid waste (USW) and GHG [6]. So, it is important to have strategies to transform this amount of MSW to protect the environment from pollution and, at the same time, create an optimized process that can utilize the planet’s resources to ensure human and animal quality of life and reduce GHG emissions. The use of MSW appears to be a good alternative that can help reduce the use of fossil fuels and for energy production [7].

Numerical models are often used in thermal processes because they can provide accurate predictions of how a system will behave under different conditions [8]. While experience can certainly be valuable in understanding the thermal process, it can be difficult to account for all of the variables involved in a complex system [9]. Numerical models, on the other hand, can take into account a wide range of factors, including temperature, pressure, and fluid flow, to provide a detailed understanding of how a system will behave. This information can be used to optimize system performance and simulate different scenarios, allowing for testing without the need for costly physical prototypes.

Green and alternative fuels, such as syngas, which contain carbon monoxide (CO), hydrogen (H₂), carbon dioxide (CO₂), and other gases), have been directed to secure energy globally amidst environmental concerns over the past decade [10,11,12].

Silva et al. [13] presented a study of the technological potential to produce energy from biomass residues in Portugal. They studied two cases: pellet production and the use of farm cattle manure. For pellet production, they concluded that the potential is significant, mainly due to forestry. However, the major costs involve obtaining the raw material, transportation, and power used during the production stages. The utilization of farm cattle manure, on the other hand, is far from reaching its full potential.

Ramos et al. [14] reviewed thermal conversion techniques of biomass for producing biofuels and other biomass-derived products, which have the potential to replace fossil-based fuels. They found that the main issues in these conversion techniques stem from the size, shape, moisture, and heterogeneity of the biomass, necessitating pre-treatment. They also noted that various pre-treatment processes exist, and the choice of treatment depends on the biomass stream and thermal conversion scheme.

Costa et al. [15] analyzed energy conversion in a thermal power plant using residual forest biomass as fuel. The results indicated that the primary potential for improvement lies in decreasing the moisture content of the residual biomass.

Sun et al. [16] studied the effects of a wide screening of crushed biomass pellets on temperature, heat release, gaseous pollutant emissions, and heat transfer in a co-fired circulating fluidized bed (CFB). They concluded that a higher biomass share leads to more uniform temperature profiles, lower gaseous emissions, and improved bed-to-wall heat transfer.

The three primary products obtained from biomass are liquid fuels (ethanol, methanol, biodiesel, etc.), solid fuels (char, biochar, etc.), and gaseous fuels (syngas) [17].

The transformation of urban solid waste (USW) into energy involves four stages: drying, pyrolysis, combustion, and gasification [18,19].

In the drying process, the water present in the fuel is removed and converted into steam. Pyrolysis occurs in the absence of oxygen (O₂) and decomposes the biomass into its constituent elements through heat application [20]. Combustion involves the oxidation of substances from or resulting from biomass and releases heat to maintain the reactor temperature, favoring gasification reactions [21].

Currently, nearly 40% of the global population relies on biomass combustion equipment for heating and cooking. Projections indicate an increase to 62–91% by 2040. A central priority in Europe’s strategic vision for a prosperous, modern, competitive, and climate-neutral economy is to maximize the use of renewable energy sources, including biomass combustion [22].

Several studies have been conducted on how to improve biomass combustion models to achieve better predictions. Su et al. [23] investigated the combustion of corn stover in a 130 t/h grate boiler experimentally and numerically. Their work provided guidance for more accurate modeling, optimization, and design of grate boilers.

Milijasevic et al. [24] developed a mathematical model for CFD simulation that considers parameters such as fuel properties, combustion kinetics, and fluid dynamics. This model enables predictions of temperature, species concentrations, and soot particle emissions. The results offer insights into how moisture content affects combustion performance.

Sakib and Birouk [25] introduced a comprehensive chemical mechanism comprising 168 species and 5068 reactions to enhance combustion process predictions. The results demonstrated improved accuracy in predicting biomass combustion and addressed limitations of partially premixed combustion models, particularly in forecasting NO_x emissions.

Morais et al. [18] studied the effects of viscosity, temperature, and velocity on the final composition of syngas. They concluded that the maximum temperature inside the gasifier remains nearly constant with changes in inlet velocity. However, variations in inlet temperature and viscosity resulted in significant changes in velocity. Additionally, fluctuations in inlet temperature impacted the turbulent fields.

This research builds on a model used by Morais et al. [18] and continues a previous study [26] to assess how the flow inside the combustion chamber changes over time. The goal is to understand how certain characteristics—such as velocity and temperature, as well as the composition and yield of gas—develop over time. Subsequently, the results obtained in this study will be compared with those obtained by Morais et al. [18] for steady-state conditions.

2. Materials and Methods

The software used in this study was Ansys Fluent 2024 R2, which utilizes governing equations in the form of differential equations to simulate fluid behavior in specific scenarios. CFD simulations have become one of the most effective techniques for solving a wide range of engineering problems, offering significant advantages over other approaches, such as analytical and experimental methods, e.g., [27,28].

The 2D combustion chamber geometry used in this study is shown in Figure 1. Wood is introduced through two side inlets, and combustion products exit through two outlets (upper and lower).

For the simulations, the standard K-epsilon turbulence model (2 equations) was chosen as it remains one of the most used models for simulations of turbulent flows due to its simplicity and robustness, despite presenting some limitations that may affect its accuracy, particularly in the simulation of complex flows. Species transport and the wood-volatile-air mixture (available in Fluent) with atomic content CH_2.382O_1.075 were used. Volumetric reactions with eddy-dissipation were applied, and the discrete phase was activated to examine particle behavior from a Lagrangian perspective. In this study, particles were injected only at the start (time = 0 s) with an initial velocity of 0.6 m/s and temperature of 300 K.

The numerical solutions were obtained using a coupled method with a Courant number of 1.

In the side inlets, a velocity condition (velocity-inlet) was applied with a velocity of 0.6 m/s and a temperature of 300 K. A turbulent intensity of 10% and a viscosity ratio of 10 were also specified.

A pressure condition (pressure outlet) was used at the outlets, ensuring that the pressure was equal to atmospheric pressure. A non-slip condition was defined on the walls, and it was assumed that the walls were adiabatic, meaning there was no heat or matter exchange between the system and the surrounding environment.

The combustion chamber dimensions are shown in Figure 2. The combustion chamber is represented on a laboratory scale with the purpose of studying combustion phenomena by collecting data regarding the temperature, velocity, and composition of the yield gas produced. In the inlets, wood, and air are introduced with a ratio of 0.7 to 0.3.

In CFD, the volatiles are combined into a single “artificial” species, typically represented as $C_x{H}_y{O}_z$ [29].

A single-step reaction model was used. The reaction equation is [30]:

$$C_x{H}_y{O}_z + \left(x + {\displaystyle \frac{y}{4}} - {\displaystyle \frac{z}{2}}\right) O_2 \to x C{O}_2 + {\displaystyle \frac{y}{2}} H_{2}O$$

(1)

Species transport with volumetric reactions and eddy dissipation gives us the following equation:

Wood_vol + 1.058 O₂ → CO₂ + 1.191 H₂O

(2)

From Equations (1) and (2), we can calculate the values of x, y, and z to find the atomic content of the wood used while keeping the stoichiometry of the reaction. We can then conclude that the single-step reaction model is:

CH_2.382O_1.075 + 1.058 O₂ → CO₂ + 1.191 H₂O

(3)

which is the same as what Buligins et al. used [31].

In the discrete phase, the particle type was considered to be combusting, and the injection type was considered surface (inlet).

2.1. Governing Equations

In the present work, a numerical model is adapted to simulate the flow inside of a combustion chamber, considering the continuity, momentum, energy, turbulence, and species equations.

2.1.1. Continuity

For a two-dimensional flow, the continuity equations for the gas and solid phases are:

1.

Gas phase:

$${\displaystyle \frac{\partial \left(\varphi {\rho }_g\right)}{\partial t}}+\nabla \left(\varphi {\rho }_g{u}_g\right)=S_{sg}$$

(4)

2.

Solid phase:

$${\displaystyle \frac{\partial \left(\left(1-\varphi \right){\rho }_s\right)}{\partial t}}+\nabla \left(\left(1-\varphi \right){\rho }_s{u}_s\right)={-S}_{sg}$$

(5)

where ϕ is the fraction of voids present in the bed, $\rho$ represents the density, and $u$ the velocity. The subscript $g$ represents the gas phase, $s$ the solid phase, and $sg$ the transition from solid to gas. The fraction of voids can be calculated by:

$$\varphi ={\varphi }^0{\displaystyle \frac{V_0}{V}}={\varphi }^0\left[1-a_1\left(R_{dry}^0-R_{dry}\right)-a_2\left(R_v^0-R_v\right)-a_3\left(R_{wood}^0-R_{wood}\right)\right]$$

(6)

$$\varphi S_{sg}=R_{evp}+R_v+R_{wood}$$

(7)

V₀ is the initial volume, and V is the particle volume. a₁, a₂, and a₃ are coefficients equal to 0 or 1 according to the appearance of moisture (R_evp), devolatilization (R_v) and burning of the wood (R_wood), which appears in the form of the source term $S_{sg}$.

2.1.2. Momentum

The momentum equation for the gas phase is:

$${\displaystyle \frac{\partial \left(\varphi {\rho }_g{u}_g\right)}{\partial t}}+\nabla \left(\varphi {\rho }_g{u}_g{u}_g\right)=-\varphi \nabla P_g+\varphi {\rho }_{g}g-\beta \left(u_g-u_s\right)\nabla \varphi {\tau }_g$$

(8)

where β is the gas-solid interphase drag coefficient [14],$g$ is the gravity, $\nabla P$ the variation of the pressure, and ${\tau }_g$ is the stress tensor for the gaseous phase. β can be calculated as follows [26].

$$\beta =150{\displaystyle \frac{{\left(1-\varphi \right)}^2{\mu }_T}{\varphi d_p^2}}+1.75{\displaystyle \frac{{\rho }_g\left(1-\varphi \right)\left|u_g-u_s\right|}{d_p}}$$

(9)

The stress tensor for the gas phase can be calculated using the following expression:

$${\tau }_g= {\mu }_g\left[\nabla u_g+ \nabla u_g^T\right]-{\displaystyle \frac{2}{3}}{\mu }_T\left(\nabla u_g\right)$$

(10)

$${\mu }_T={\mu }_g+{\mu }_t$$

(11)

$\mu$ is the dynamic viscosity. ${\mu }_T$ is the total viscosity and ${\mu }_t$ is the turbulent viscosity.

For the solid phase, the momentum equation is:

$${\displaystyle \frac{\partial \left(\left(1-\varphi \right){\rho }_s{u}_s\right)}{\partial t}}+\nabla \left(\left(1-\varphi \right)\varphi {\rho }_s{u}_s{u}_s\right)=-\left(1-\varphi \right)\nabla P_s+\left(1-\varphi \right){\rho }_{s}g-\beta \left(u_g-u_s\right)\nabla \left(1-\varphi \right){\tau }_s$$

(12)

The stress tensor for the solid phase ${\tau }_s$ is calculated as follows:

$${\tau }_s=\left( {\mu }_b-{\displaystyle \frac{2}{3}}{\mu }_s\right)\nabla {\mu }_s+{\mu }_s\left(\nabla u_s+u_s^T\right)$$

(13)

$${\mu }_b={\displaystyle \frac{4}{3}}\left(1-\varphi \right){\rho }_s{d}_P{g}_o$$

(14)

$${\mu }_s={\displaystyle \frac{4}{5}}\left(1-\varphi \right){\rho }_s{d}_p{g}_o\left(1+e\right)\sqrt{{\displaystyle \frac{{\Theta }_s}{\pi }}}+{\displaystyle \frac{10{\rho }_s{d}_P\sqrt{\pi {\Theta }_s}}{96\left(1+e\right)ϵg_o}}{\left[1+{\displaystyle \frac{4}{5}}{g}_o\left(1-\varphi \right)\left(1+e\right)\right]}^2$$

(15)

P_s and g_o are the solid pressure and the radial distribution function, respectively [26]. ${\mu }_b$ is the bulk viscosity, ${\mu }_s$ is the solid shear viscosity $e$ is the restitution coefficient. P_s and g_o can be calculated using the following expressions:

$$P_s= \left(1-\varphi \right){\rho }_s{\Theta }_s+2\left(1+e\right){\left(1-\varphi \right)}^2{g}_o{\rho }_s{\Theta }_s$$

(16)

$$g_o={\displaystyle \frac{3}{5}}{\left[1-{\left({\displaystyle \frac{\left(1-\varphi \right)}{{\left(1-\varphi \right)}_{max}}}\right)}^{{\displaystyle \frac{1}{3}}}\right]}^{-1}$$

(17)

The granular temperature is a pseudo-temperature (Θ_s) as is given by:

$${\displaystyle \frac{3}{2}}{\Theta }_s={\displaystyle \frac{1}{2}}⟨u_s^{\prime }{u}_s^{\prime }⟩$$

(18)

$$u_s^{\prime }=\zeta {\left({\displaystyle \frac{2k}{3}}\right)}^{0.5}$$

(19)

$u_s^{\prime }$ is the fluctuating velocity of the particle and can be calculated by turbulence kinetic energy, using $\zeta$, which represents a random number that will obey the Gauss distribution and will have a value between 0 and 1, and $k$ represents the thermal conductivity [26].

2.1.3. Energy Equations

For the gas phase, the energy equation is:

$${\displaystyle \frac{\partial \left(\varphi {\rho }_g{c}_{pg}{T}_g\right)}{\partial t}}+\nabla \left(\varphi {\rho }_g{u}_g{c}_{pg}{T}_g\right)=\nabla \left({\lambda }_g.\nabla T_g\right)+A_s{h}_s^{\prime }\left(T_g-T_s\right)+S_{T_g}-S_r$$

(20)

where $S_r$ is the volumetric net radiation losses. $S_{T_g}$ is the source term of the energy equation for gas. $c_{pg}$ is the specific heat of the gas at constant pressure, $T_g$is the temperature of the gas, $A_s$ is the surface area between gas and solid, $h_s^{\prime }$ is the convective heat transfer coefficient between solid and gas, and $T_s$ the temperature of the solid, and λ_g is the thermal dispersion.

For the solid phase, the energy equation is:

$${\displaystyle \frac{\partial \left(\left(1-\varphi \right){\rho }_s{c}_{ps}{T}_s\right)}{\partial t}}+\nabla \left(\left(1-\varphi \right){\rho }_s{u}_s{c}_{ps}{T}_s\right)=\nabla \left(k_{eff}.\nabla T_s\right)+{\left(\nabla q_r\right)-A}_s{h}_s^{\prime }\left(T_g-T_s\right)+S_{T_s}$$

(21)

where $\nabla q_r$ is the radiative flux density and $k_{eff}$ is the effective thermal conductivity.

The thermal dispersion (λ_g) can be given by [18]:

$${\lambda }_g=k_{eff,0}+0.5 d_p{u}_g{\rho }_g{c}_{pg}$$

(22)

with

$$k_{eff,0}=\varphi \left(k_f+h_{r\upsilon }∆l\right)+{\displaystyle \frac{\left(1-\varphi \right)∆l}{\frac{1}{\left(\frac{k_f}{l_{\upsilon }}+h_{rs}\right)}+\frac{l_s}{k_s}}}$$

(23)

where $k_{eff,0}$ is the initial effective thermal conductivity, $k_f$ is the thermal conductivity of the fluid, $h_{r\upsilon }$ represents the radiative heat transfer coefficient, $∆l$ is the variation of the length between phases, $l_{\upsilon }$ is the length of the gas phase and $l_s$ is the length of the solid phase, and $k_s$ represents the thermal conductivity of the pure solid. The radiative flux density is [26]:

$$\nabla q_r=-{\displaystyle \frac{16\sigma T^2}{K}}\left(\nabla T^2\right)+ {\displaystyle \frac{16\sigma T^3}{3K}}\left({\nabla }^{2}T\right)$$

(24)

$$l_s={\displaystyle \frac{2d_p}{3}}$$

(25)

$$l_{\upsilon }=0.151912∆l\left({\displaystyle \frac{k_f}{k_{air}}}\right)$$

(26)

$$h_{r\upsilon }=0.1952{\left(1+{\displaystyle \frac{\varphi \left(1-ϵ\right)}{2\left(1-ϵ\right)}}\right)}^{-1}{\left({\displaystyle \frac{T_s}{100}}\right)}^n$$

(27)

$$h_{rs}=0.1952 d_p\left({\displaystyle \frac{ϵ}{2-ϵ}}\right){\left({\displaystyle \frac{T_s}{100}}\right)}^n$$

(28)

$$∆l=0.96795 d_p{\left(1-\varphi \right)}^{-1/3}$$

(29)

$$k_{air} \left(T_g\right)=5.66\times {10}^{-5}{T}_g+1.1\times {10}^{-2}$$

(30)

where $\sigma$ is the Stefan-Boltzmann constant, $K$ is the thermal conductivity, and k_air is the air thermal conductivity.

$$n=1.93+0.67\mathit{exp}\left(-{\displaystyle \frac{\left(m_g^{.}-0.39\right)}{0.054}}\right)$$

(31)

n is a parameter related to the fuel storage conditions. S_Tg and S_Ts are, respectively, the source term of the energy equation for gas and solid.

$$S_{T_g}=-R_{evp} h_{f,CO}$$

(32)

$$S_{T_s}=-R_{evp} {\displaystyle \frac{M_{CO}}{M_{{CO}_2}}} \left[h_{f{,CO}_2}-h_{f,CO}\right] \left[{\displaystyle \frac{Y_{CO}}{2}}-1\right]$$

(33)

${\displaystyle \frac{M_{CO}}{M_{{CO}_2}}}$ represents the ratio between the molar masses of CO and CO₂, $h_{f{,CO}_2} \mathrm{a}\mathrm{n}\mathrm{d} h_{f,CO}$ are the enthalpy of the formation of CO₂ and CO, respectively, and $Y_{CO}$ is the mole fraction of CO.

2.1.4. Turbulence

The k − ε turbulence model introduces two new variables to the system of equations, namely the turbulent kinetic energy (k) and the dissipation of turbulent kinetic energy (ε). The equations that allow us to determine these two variables are:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho k{u}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right) {\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(34)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \epsilon \right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho \epsilon u_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right) {\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+C_{\epsilon 1}{\displaystyle \frac{\epsilon }{k}}\left(G_k+C_{\epsilon 3}{G}_b\right)-C_{ϵ2}\rho {\displaystyle \frac{{\epsilon }^2}{k}}+S_{\epsilon }$$

(35)

$$G_k={\mu }_t\nabla u_g.\left[\nabla u_g+\nabla u_g^T\right]-{\displaystyle \frac{2}{3}}\nabla u_g\left({\mu }_t\nabla u_g+{\rho }_{g}k\right)$$

(36)

G_k is the turbulence kinetic energy. C_s1, C_s2, σ_k, and σ_s are constants with values equal to 1.44, 1.92, 1, and 1.3, respectively. $G_b$ represents the generation of turbulent energy due to buoyancy effects and $Y_M$ represents the production of turbulent kinetic energy due to mean velocity gradients.

2.1.5. Species Equations

1.

Gas phase:

$${\displaystyle \frac{\partial \left(\varphi {\rho }_g{Y}_{ig}\right)}{\partial t}}+\nabla \left(\varphi {\rho }_g{u}_g{Y}_{ig}\right)=\nabla \left[D_{ig}\nabla \left(\varphi {\rho }_g{Y}_{ig}\right)\right]+S_{Y_g}$$

(37)

2.

Solid phase:

$${\displaystyle \frac{\partial \left[\left(1-\varphi \right){\rho }_s{Y}_{is}\right]}{\partial t}}+\nabla \left[\left(1-\varphi \right){\rho }_s{u}_s{Y}_{is}\right]=S_{Y_s}$$

(38)

where Y_ig denotes the mass fraction of species, Y_is is the mass fraction of particle compositions, and D_ig is the fluid dispersion coefficient. Source terms of species equations for gas and solid phases are calculated individually for each species and particle composition [26].

3. Results

Transient simulations were performed to investigate the flow characteristics inside the combustion chamber over time (from 0 to 150 s). Due to the combustion chamber geometry, symmetry in the results was expected, as there is an axis of symmetry at the center of the combustion chamber. For this reason, the simulations were conducted using only half of the geometry.

A grid independence test was conducted using five different grids. Based on the results, a grid with 123,125 nodes and 122,128 elements was selected. This grid was chosen due to its superior quality metrics, which included an average element quality of 0.983, an average aspect ratio of 1.017, an average skewness of 0.019, and an average orthogonal quality of 0.998. Additionally, it exhibited one of the lowest simulation times among the tested grids.

Figure 3 shows the temperature variation over time for three time steps (10, 75, and 150 s). The temperature begins to increase in the upper part of the combustion chamber (10 s) until nearly the entire combustion chamber reaches the maximum temperature of 2180 K (150 s). This high maximum temperature can be attributed to the adiabatic nature of the combustion chamber walls, and because the model does not consider the latent heat of the water vapor, it can lead to an overestimation of the maximum temperature. It is noticeable that the temperature near the inlets remains low (<400 K) throughout the simulation period, and at 150 s, there is a central area between the two inlets and in the upper zone of the combustion chamber with lower temperature values.

Figure 4 shows the variation of velocity over time. The results show that at early stages (10 s), the maximum temperature values are present near the two outlets, but at late stages (150 s) the higher velocities are seen between the two outlets in the central zone of the combustion chamber, and the velocity on the lower outlet is higher than at the upper outlet. It is also visible that at the inlets, the velocity remains almost equal to the mean velocity for each instant.

When compared with the results obtained by Morais et al. [18] for steady-state conditions, it can be observed that at t = 150 s, the contours of temperature and velocity are similar. For temperature contours, lower values are seen near the two side inlets, with higher values near the combustion chamber walls. Higher velocity values are found between the outlets.

Figure 5 and Figure 6 show the variation of two species (wood and H₂O) over time. The highest concentration of wood is initially located at the inlets, and as time progresses, it also appears in the central area of the upper zone of the combustion chamber. The behavior of H₂O follows a pattern similar to the temperature profile observed in Figure 2. At 150 s, the areas with a higher concentration of wood correspond to those with a lower concentration of water, and vice versa. This is expected as the wood (reactant) undergoes a process that results in the production of water (product).

When comparing the results obtained at t = 150 s with those from Morais et al. [18], it can be observed that in both studies, the contours of H₂O mass fraction and temperature exhibit similar behavior. The zones with higher wood concentrations correspond to those with lower water concentrations, as the wood (reactant) undergoes a process that leads to the formation of water (product).

Patel et al. [32] also demonstrated that the contours of H₂O mass fraction and temperature behave similarly. Zones with higher lignite (reactant) concentrations correspond to zones with lower H₂O (product) concentrations, and vice versa.

Three lines were drawn on the geometry, as shown in Figure 7, to study the behavior of wood and H₂O mass fraction, temperature, and velocity values over 150 s.

Figure 8 shows the variation in wood mass fraction at 10, 75, and 150 s along the three lines. Positions 0 and 1.66 m correspond to the axis of symmetry and the wall, respectively.

For line 1, at 10 s, the wood mass fraction is 0.06 at the axis of symmetry and 0.68 near the wall; at 75 and 150 s, the mass fraction is 0.64 and 0.68, respectively, at the axis of symmetry, while near the wall it reaches 0.70.

Lines 2 (above line 1) and 3 (below line 1) display the same trend at each time point. The highest values appear near the axis of symmetry, and lower values near the combustion chamber walls.

Figure 9 shows the variation in H₂O mass fraction along the three lines at 10, 75, and 150 s. For line 1, the highest values occur between positions 0.17–0.21 m at 10 s and between 0.20 and 0.56 m at 75 and 150 s. The lowest values are found near the inlet and the axis of symmetry. For lines 2 and 3 at 75 and 150 s, lower values are near the axis of symmetry, with higher values near the combustion chamber walls.

Figure 8 and Figure 9 exhibit opposite behavior for wood and H₂O mass fractions over 150 s; areas with higher wood levels correspond to areas with lower H₂O levels. This is expected due to the primary reaction, where the amount of wood (reactant) decreases, leading to the formation of H₂O (product).

According to Figure 3 and Figure 4, the temperature and velocity at the upper outlet are not constant. The lowest temperature and highest velocity values occur near the symmetry axis.

Figure 10 illustrates the temperature and velocity values at the top and bottom outlets over time. The temperature changes such that, at 150 s, lower values are observed near the symmetry axis while higher values occur near the walls at the upper outlet, with the opposite behavior at the lower outlet. Overall, the maximum velocity at the upper outlet decreases over 150 s, while at the lower outlet, it decreases between 10 and 75 s and then increases between 75 and 150 s. As expected, near the walls, the velocity values are zero due to the non-slip condition.

Figure 11 shows the temperature variation along the three lines at 10, 75, and 150 s. The temperature variation along the three lines follows a pattern similar to the variation observed in the mass fraction of H₂O in Figure 9. Positions with higher temperature values correspond to higher H₂O mass fractions and vice versa.

Figure 12 illustrates velocity changes along the three lines at 10, 75, and 150 s. For line 1, velocities are 0.06, 0.66, and 0.58 m/s along the symmetry axis at 10, 75, and 150 s, respectively, while near the wall, the velocity remains 0.61 m/s across all time points.

Lines 2 (above line 1) and 3 (below line 1) follow the same trend across all time points, with the highest velocities near the symmetry axis and lower velocities near the combustion chamber walls.

Figure 8 and Figure 12 together show that locations with higher velocities also exhibit a greater mass fraction of wood.

When comparing the results obtained at 150 s with those from previous studies [18,32], it is evident that higher values of H₂O mass fraction are found in positions with higher temperatures. Based on the analysis of the data presented by Morais et al. [18], it can be concluded that in both studies, between the two side inlets, higher values of wood mass fraction correspond to positions with higher velocities.

4. Conclusions

The behavior of combustion inside a combustion chamber was studied under transient conditions. For the temperature field, it was observed that there is only a small variation between different time intervals, particularly between 75 and 150 s. The temperature near the inlets remains low (below 400 K) throughout the process, and at 150 s, a central area between the two inlets and the upper zone of the combustion chamber exhibits relatively lower temperature values.

For velocity, the values were higher at the outlets at the beginning of the process but gradually increased in the central zone of the combustion chamber, between the two outlets, as time progressed.

For the optimization and design of the combustion chamber, understanding temperature profiles can aid in selecting appropriate materials, while velocity profiles can help identify areas of low flow that may require design adjustments.

The mass fractions of wood and H₂O exhibit opposite behaviors. This can be explained by the fact that the wood fraction undergoes a process that produces water, leading to a reduction in the wood fraction. In regions with low temperatures, the amount of water is almost negligible.

The variation in the temperature field is qualitatively similar to the variation in the mass fraction of H₂O. From this, it can be inferred that, as described by the reaction rate equation, the reaction rate increases with temperature.

2D simulations facilitate sensitivity analyses by enabling the evaluation of various parameters’ effects on combustion and providing an overview of the evolution of temperature and the concentrations of chemical species. However, they have certain limitations. In contrast, 3D simulations aim to provide more realistic predictions, as transitioning to a 3D model offers a more comprehensive representation of real-world phenomena. Another limitation of this work is that the model does not account for the latent heat of water vapor, which could explain the higher-than-expected maximum temperature values. Additionally, the lack of comparison with experimental data limits the validation of the results and the ability to draw more definitive conclusions.