1. Introduction
Solid fuel combustion is one of the main sources of thermal energy used for heating purposes by the individual and commercial sector in Poland. According to data from 2018 [
1], 35.7% of Polish households were heated by heating devices using solid fuels. Heat provided by thermal plants was delivered to 40.4% of Polish households. The Energy Regulatory Office in Poland reported [
2] that in 2019 solid fuel combustion was responsible for 80.2% of the heat generated by the commercial sector. Moreover, 9.2% of the heat generated by the commercial sector originated from solid biomass burning. Nowadays changes in thinking about the environment cause the replacement of fossil fuel by renewable fuels like biomass. From one year to another the amount of heat generated by fossil fuel burning decreases and is replaced by different types of renewable sources of energy. Solid biomass share in energy production from renewable sources in Poland was equal to 67.9% in 2017. European Union average for the mentioned magnitude was 42% in the same year [
3]. This means that solid fuel burning for some time will be still the main source of heat generation.
One of the main methods for solid fuel combustion for domestic and industrial boilers is realized in fixed bed conditions. Computational Fluid Dynamic (CFD) modeling is often used to simulate packed bed burning. Fixed bed combustion modeling can be divided into two main groups. The first group is concerned with a small-scale, when a combustion process is realized in a range of heating power equal from over a dozen to tens of kilowatts. The mentioned group may belong to one-dimensional models focused on the phenomena that occurred during combustion of a single grain of a fuel. The second one deals with a huge scale, where obtained heating power from fixed bed combustion equals from few to tens megawatts.
Scharler et al. [
4] raised the issue of how the low power log stove burning modeling focused on CO concentration in the flue gas. Wiese et al. [
5] have been dealing with a transient simulation of pellet burning with the application of a discrete element model in CFD calculations for a 13 kW stove. Mehrabian et al. [
6] and Gomez et al. [
7] are concerned with numerical modeling of the thermally thick approach of biomass burning. Gomez et al. [
8] also have been using the mentioned approach for a 27 kW domestic boiler working conditions modeling. In other works [
9,
10] he also modeled emissions of harmful compounds during fixed-bed biomass burning in a 60 kW domestic boiler by steady and transient analysis. Similar transient modeling connected with the analysis of the chemical composition of exhausts was realized by Mehrabian et al. [
11] in a laboratory-scale biomass fixed bed batch. Collazo et al. [
12] also have been working on a transient simulation of a pellet wood burning for a laboratory combustor. He was targeting a temperature distribution at different points in the bed. Researchers from Clausthal University of Technology and Silesian University of Technology [
13,
14] were involved in numerical modeling of coal burning in small-scale retort boilers. They analyzed possibilities of the perfecting of domestic boiler construction in terms of pollution limitation and optimization of temperature distribution inside a combustion chamber. Chaney et al. [
15] modeled a 50 kw packed bed biomass boiler in terms of investigating the optimization of the combustion performance and NO
x emissions. A new approach of packed bed biomass burning was presented by Chapela et al. [
16]. His Eulerian-fouling model is computationally less expensive and shows a better response to the experimental data.
Tu et al. [
17,
18] modeled a 32 MW woodchip-fired grate boiler work with different operating conditions directed on NO
x reduction mechanisms. Silva et al. [
19] were concerned about 34.6 MW biomass grate-fired boiler modeling. He was focused on an analysis of temperature, velocity, and species field of exhaust gas within a boiler, which provided to the optimization of the burning process. Moving grate biomass boilers models realized in two different scales (250 kW and 4 MW) were analyzed by Rezeau et al. [
20] and Bermúdez et al. [
21] in terms of composition and temperature distribution of flue gas. Klason et al. [
22] analyzed a radiation heat transfer process in two various scales (10 kW and 50 MW) during biomass burning in fixed bed furnaces. He has obtained a gas temperature profile inside the combustion chamber located above a fixed bed with the assumption of constant temperature for furnace walls. Moreover, he investigated the accuracy of a solution for different radiation heat transfer models.
The abovementioned research connected with the fixed bed modeling is concerned mainly with the emission of harmful compounds during solid fuel combustion. Moreover, there has been raised the issue of the temperature distribution occurring in the combustion chamber and inside a packed bed of fuel. Researchers do not relate achieved results of temperature distribution to prepare an in-depth analysis of the heat transfer process in modeled heating devices. The issue of heat transfer phenomenon occurring in a wall neighborhood and free-room of a combustion chamber during fixed-bed combustion still has not been deeply recognized like it is realized in other types of thermal devices used for different industrial applications, like heat treatment furnaces [
23,
24,
25], heat storage systems [
26,
27,
28], or heat exchangers [
29,
30,
31]. So far available results concerned about the packed bed burning assumed a temperature of combustion chamber walls as a boundary condition. Then a constant wall temperature was present for each wall of the combustion chamber or separately, at particular elements of modeled furnaces. Computational grids used in computational models were suitable for free-room analysis like bulk gas temperature and chemical composition. Grids used in the previous research were not capable of heat transfer analysis that occurred on combustion chamber walls. This was caused by the size of grid elements located near the combustion chamber wall (dimensionless wall distance y
+ >>1) being too high to obtain an appropriate solution of heat flux at the wall of the combustion chamber. Moreover, so far available packed bed burning models used wall functions for simulating the near-wall region (k-ε model of turbulence). The mentioned approach does not show sufficient accuracy for viable modeling of conditions that occurred near combustion chamber walls which are necessary for modeling a heat transfer process.
3. Results and Discussion
A comparison of exhaust gas temperature obtained during experimental and numerical research is shown in
Figure 4. The temperature distribution is presented at four different heights of the combustion chamber representing properties obtained in three crucial parts of the chamber (two located in the burner neighborhood—bottom part, one halfway up, and one at the top of the chamber). It showed that the temperature of exhausts obtained during experimental measurements was lower relative to the numerical modeling. Especially it is well visible in the bottom part of the combustion chamber, where a temperature difference is much higher relative to higher parts of the chamber. The biggest divergence was obtained in the axis of the stand (above a burner). The highest noticed difference is equal to about 350 °C and was obtained for each of the analyzed cases. The temperature distinction decreases along the chamber radius in a wall direction. At a point located 5 cm away from the wall the temperature disparity for experimental and numerical analysis is lower and equals about 50 °C. A temperature distribution obtained during numerical modeling is getting closer to the experimental results as exhausts are moved away from the fixed bed in the vertical direction. Occurred temperature overestimation results from numerical modeling as an effect of the application of the Eddy Dissipation Model (EDM) of combustion [
40,
41]. EDM assumes that the realized combustion process is complete, which affects the temperature overestimation. Extermination of the mentioned phenomenon requires an application of the Eddy Dissipation Concept (EDC) model, which is an extension of EDM [
42,
43]. The EDC model is highly computationally expensive due to including a detailed chemical mechanism in a turbulent flow [
44].
Table 4 presents a comparison obtained for a few basic parameters connected with the combustion chamber working conditions during numerical modeling and experimental research for each of the analyzed cases. It is a heat flow transferred to the cooling water, the temperature of exhaust gas at the outlet from the domain, the temperature of cooling water at the outlet from the test stand, the cooling water temperature difference between outlet and inlet of the test stand, oxygen and carbon dioxide mass fraction in exhausts leaving the domain. Due to the inability of exhaust gas mass flow at the outlet from the combustion chamber during experimental research, the mentioned magnitude was compared with a result of analytical calculations. Time-averaged data collected during experimental research for each case separately comply with the results of numerical modeling. The amount of exhaust gas obtained during numerical simulations is consistent with analytical calculations. Collected parameters show convergence between numerical modeling and experimental validation.
Figure 5 shows a distribution of wall temperature and a bulk-average temperature inside the chamber as a function of the domain height. The temperature of the combustion chamber wall is generally constant. It only comes to a small rising of temperature in the direction of the working medium flow (from bottom to the top of the domain), which is related to the heating of water used for test stand cooling. The average bulk temperature of exhaust gas is noticeably changing in subsequent parts of the domain.
The highest value is present in a direct neighborhood of a flame. It is following the obtained data concerning overall heat flux (sum of radiation and convection heat flux), which achieves maximum value in the mentioned area. The peak of the bulk temperature occurs in the area, where a deflector limits a flame length and smashes it horizontally. When fumes flow around a deflector, the average temperature deeply decreases. Right above a deflector comes the formation of an Eddy, which causes a significant cooling of flue gas (
Figure 6). Over regions of swirled flow, a visible increase of bulk temperature is present. It is caused by exhausts getting through from the flame dispersion zone to the mentioned area. In the horizontal cross-sections of the chamber located above 20 cm over a deflector, the average temperature of exhausts is gradually decreasing. Exhausts flow in the upper part of a chamber is more uniform than in the direct neighborhood of the deflector. When the gas has contact with the top surface of the combustion chamber it comes to obtain a backflow of a slight part of exhausts to the domain along heat transfer surface.
The local value of convection and radiation heat flux that occurred on the exhaust side of the combustion chamber wall along a domain height is present in
Figure 7. Radiation and convection heat flux magnitudes are varied along with the height of the chamber. The impact of the radiation for an overall heat transfer process is dominating in the direct neighborhood of a flame. As a distance from a burning area is increased away, a local amount of the radiation heat flux is substantially falling off. The distribution of convective heat flux does not show significant changes over the entire surface bounding the combustion chamber. Regional increases depend on changes in the local value of the Reynolds Number and a thickness of a boundary layer. Determination of percentage participation in the heat transfer phenomenon for radiation and convection shows that they are dependent mainly on a heat load. During coal combustion with a nominal power, radiation is responsible for about 61.7% of the overall heat transfer. When combustion was carried out with the half level of the nominal heat load, radiation achieved only 50% in the heat transmission. Radiation participation in the heat transfer during biomass combustion was equal to 58.6% and 47.5%, respectively, for 100% and 50% of the nominal power.
Radiation and convection heat transfer coefficient courses are various for distinct parts of the computational domain (
Figure 8). The radiation heat transfer coefficient achieves a peak in the direct neighborhood of a flame and vitally decreases in the upper part of the chamber, which is following in a radiation heat flux distribution. In the bottom part of the chamber, a radiation coefficient is uneven, which testifies with a differential level of the thermal load. A varied course of the convection heat transfer coefficient has occurred along with the domain height. In the direct neighborhood of the deflector, it comes to intense decreasing of
, which achieves a minimum value in the mentioned area. The convection heat transfer coefficient is increased in the area located above the deflector. After that,
is stabilized until a part of the domain, which is located 15 cm below the top surface of the domain. In the last part of the domain the top surface
achieves a maximum value. The peak value of the convection heat transfer coefficient is present also on the top surface of the combustion chamber. The main impact of the convection heat transfer is connected with the character of exhaust gas flow inside the combustion chamber (
Figure 6). Exhaust gas movement occurred along a sidewall of the chamber and was an effect of reversing flow realized for a part of exhaust gas, which is not directly conducted to the outlet. According to theory of heat transfer [
45,
46], Reynolds and Prandtl numbers are the main parameters used in the analytical description of the convection heat transfer coefficient.
Figure 9 shows a distribution of Reynolds number obtained during the research for analyzed cases.
A diameter of the combustion chamber is used as a characteristic linear dimension in Reynolds number definition. In the direct neighborhood of the combustion chamber sidewall, Reynolds number achieves value corresponding to a laminar or transitional flow. The effect is visible in the obtained value of which occurred during the mentioned types of fluid flow. A similar distribution of convection heat transfer coefficient between analyzed cases is connected with a lack of changes in Reynolds and Prandtl number distribution during fumes flow in the wall area.