Introduction

Kazakhstan, with a 0.2% share of the world economy, meets its energy demands almost exclusively from fossil fuels (88.72%), of which 77.7% is thermal coal [1]. The issue of efficient and clean coal combustion is a high priority globally [2]. The share of renewable energy is increasing in developed countries to mitigate climate change and conserve valuable resources. However, renewable energy sources are often unsustainable and, without efficient energy storage solutions, cannot fully meet people’s and industries’ needs [3]. In the long term, coal will remain a crucial thermal power resource due to its abundant global reserves and competitive prices [4, 5]. As of 2017, coal accounted for 66.5% of heat and power generation. Despite various influencing factors, the global share of coal has remained at 40% over the past 40 years [6]. Efficient and clean coal combustion remains a global priority [7].

In Kazakhstan, 60% of energy consumption is derived from coal combustion. Given the large reserves and production of low-cost solid fuels, coal power generation continues to play a significant role [8]. Kazakhstan occupies the 2nd place globally by indicator territory and has a population density of approximately one person per square kilometer. The population gasification program is conducted in those areas where there are gas fields [9]. Comprehensive gasification across Kazakhstan will require substantial financial investment. Consequently, coal remains a primary heating source, especially in low-capacity boilers. In rural areas, heat is generated through low-power fixed-bed coal boilers. These boilers have grate systems that do not control harmful emissions or combustion chamber temperatures effectively, a problem unsolved for decades [10].

Low-power (0.3–3 MW) boilers used for low-quality coal combustion have low efficiency in the range of 30%–60%, although they are capable of 70%–80% efficiency. With low coal quality and without modification of the low-capacity boiler system, design, the economics, heat dissipation, and harmful emissions control will not be maintained [11, 12]. Fixed-bed coal furnace technology has evolved since the beginning of the nineteenth century. To date, the combustion chamber design of these boilers has not changed much. Most of the research has focused on coal-dust technologies [13,14,15]. Typical drawbacks of grate system coal boilers include dispersion of very small coal particles by flue gases into the atmosphere, and heavier unburned fine coal particles not carried away by flue gases settling into the ash tank. As much as 15%–30% of combustion products are emitted into the environment as ash, ranging from 0.04 to 0.40 mg/m3 in ambient air in populated areas [16, 17].

The classical design of small-capacity fixed-bed coal boilers uses a grate to accommodate the burning coal mass. Air is supplied from beneath the grate and is drawn through the grid holes by the pressure differential between the chimney outlet and the combustion chamber, according to Bernoulli’s principle. This arrangement is convenient for operation but does not optimize boiler heat transfer efficiency due to the lack of additional air supply equipment. As a result of these drawbacks, approximately 10% of coal remains unburned (up to 3% dispersed by flue gases and 7% as ash). Additionally, due to the high airflow speed (up to 1.5 m/s), the coolant has a limited residence time in the heat exchanger, causing most of the heat to be carried away through the chimney and into the atmosphere.

To increase the efficiency of small-capacity fixed -bed coal boilers, an improved boiler design has been proposed [18,19,20]. The improved design features a solid metal plate instead of a grate, preventing the loss of unburned fine coal particles into the ashtray. Airflow is controlled by vertical air distributors within the coal layer, which have horizontal radial openings. The exclusion of air supply through the grate reduces the airflow speed by a factor of 2–2.5, prolonging the heat exchanger residence time. This arrangement prevents the dispersion of unburned fine coal particles, allowing for their complete combustion and the release of additional heat.

Objective of the study:

To improve the fixed-bed solid-fuel (coal) combustion efficiency of small-capacity industrial boilers by improving the design, parameters, and operating modes.

Tasks:

  • Numerical simulation of velocity and gas temperature field distributions in a fixed-bed coal combustion boiler.

  • Experimental study of the airflow jet coverage area in a fixed layer of coal depending on the diameter of the nozzle and the pressure of the supplied air.

  • Comparative evaluation of fixed coal layer combustion according to the proposed scheme and the classical scheme in a laboratory-scale low-power boiler.

Hypothesis:

Increasing the number of coal-fired boilers using forced-air jets to the fixed coal layer will reduce air pollution and energy costs by ensuring complete coal combustion.

Materials and Methods

Design and Operation of the Advanced Laboratory-Scale Low-Power Boiler

To improve the efficiency of small industrial solid-fuel (coal) boilers (0.24–0.58 W), a laboratory-scale boiler was developed without a fire grate heating device, allowing the air jet to be fed by a fixed horizontal layer under pressure through multiple perforations (Fig. 1).

Fig. 1
figure 1

Scheme of the laboratory-scale fixed-bed coal boiler without a fire grate for coal combustion by feeding air into the fixed layer

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A laboratory-scale model of the boiler was developed without a fire grate, allowing the air jet to feed under pressure through multiple perforations in the vertical drainage tubes under the fixed-bed coal, which is located on a metallic plate (Fig. 1). The perforations on the vertical drainage tubes are horizontal with respect to the radius of the tube. The drainage tubes are closed at the top, and the airflows are directed horizontally. The numbers of drainage tubes and perforations depend on the cross-sectional area of the boiler combustion chamber. Therefore, when determining the parameters of the combustion chamber to ensure complete combustion, it is important to determine the diameter of the holes and the air pressure in the drainage tubes.

The proposed device provides air efficiently throughout the boiler combustion chamber. The airflow is directed horizontally in the form of a pressure jet to avoid air shortages in the combustible fuel layer. There is no airflow zoning between the jets due to the uniform and complete fuel combustion. The flue gas is directed upward by a gradual increase in pressure within the combustion zone. The flue gas movement rate is reduced by an order of magnitude compared to the classical combustion scheme (using a fire grate system boiler) due to the lack of upward airflow through the fire grate. Because the proposed method does not include a fire grate to supply airflow, the temperature of the system can be regulated with the airflow. To compare the fixed coal layer combustion under the existing and proposed schemes, the laboratory-scale boiler was designed to allow the installation of either a standard fire grate or a blank metal plate (Fig. 2).

Fig. 2
figure 2

Diagrams of boiler and the overall appearance of the air injector system a Classical scheme with grate; b advanced scheme with no grate; c air injector system; 1—flue; 2—boiler circuit; 3—water; 4—furnace chamber; 5—central air intake pipe; 6—coal layer; 7—horizontal air injection pipes; 8—base of combustion chamber; 9—air intake fan; 10—air intake line; 11—grate; 12—door; 13—flat plate; 14—flue cap

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The standard grate and blank steel plate had the same external dimensions of 190 mm × 230 mm. The blank plate was 10 mm thick and had a 45 mm diameter hole in the center. The air injection pipe passed through this opening. The base of the pipe was connected to the fan supplying the injection air.

The tests were conducted by combusting coal in the boiler with different air supply methods: the classical method through the grate and the method without a grate, using injectors into the coal layer. Research on different coal combustion methods was conducted on different days, maintaining the same ambient temperature. In each method, 10 kg of Shubarkol-branded coal with the same granulometric composition was used [21, 22]. A theoretical calculation using a mathematical model was made to determine the initial velocity field and gas temperature in the combustion chamber for the two coal combustion methods.

Numerical Simulations of Velocity and Gas Temperature Field Distributions in a Fixed-Bed Coal Boiler

Mathematical Model

The mathematical model is based on the Reynolds averaged Navier–Stokes, (RANS) equations, which consist of the following governing equations [23]:

Continuity equation:

$$\frac{{\partial u_{i} }}{{\partial x_{i} }} = 0$$
(1)

Momentum equation:

$$\frac{{\partial u_{i} }}{\partial t} + \frac{{\partial \left( {\rho u_{i} u_{j} } \right)}}{{\partial x_{j} }} = \frac{{\partial \left( { - \rho \overline{{u_{i}^{,} u_{j}^{,} }} } \right)}}{{\partial x_{j} }} - \frac{\partial P}{{\partial x_{i} }} + \frac{\partial }{{\partial x_{j} }}\left( {\mu \left( {\frac{{\partial u_{i} }}{{\partial x_{j} }} + \frac{{\partial u_{j} }}{{\partial x_{i} }}} \right)} \right) + f$$
(2)

Thermal transport equation for temperature:

$$\frac{\partial T}{{\partial t}} + \frac{{\partial \rho u_{j } T}}{{\partial x_{j} }} = \frac{{\partial \left( { - \rho \overline{{u_{j}^{,} T^{,} }} } \right)}}{{\partial x_{j} }} + \frac{\partial }{{\partial x_{j} }}\left( {D\frac{\partial T}{{\partial x_{j} }}} \right)$$
(3)

Turbulence kinetic energy:

$$\frac{\partial k}{{\partial t}} + u_{{\text{j}}} \frac{\partial k}{{\partial x_{{\text{j}}} }} = P_{{\text{k}}} - \beta^{*} k\omega + \frac{\partial }{{\partial x_{{\text{j}}} }}\left[ {\left( {\nu + \sigma_{k} \nu_{T} } \right)\frac{\partial k}{{\partial x_{{\text{j}}} }}} \right]$$
(4)

Specific dissipation rate:

$$\frac{\partial \omega }{{\partial t}} + u_{j} \frac{\partial \omega }{{\partial x_{j} }} = \alpha S^{2} - \beta \omega^{2} + \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\nu + \sigma_{\omega } \nu_{T} } \right)\frac{\partial \omega }{{\partial x_{j} }}} \right] + 2\left( {1 - F_{1} } \right)\sigma_{\omega 2} \frac{1}{\omega }\frac{\partial k}{{\partial x_{i} }}\frac{\partial \omega }{{\partial x_{i} }}$$
(5)

Species transport equation:

$$\frac{\partial C}{{\partial t}} + \frac{{\partial \left( {Cu_{j} } \right)}}{{\partial x_{j} }} = \frac{\partial }{{\partial x_{j} }}\left( {\gamma \frac{\partial C}{{\partial x_{j} }}} \right)$$
(6)

To describe the combustion process \(\text{A}+\text{B }\to \text{C}\), the equations for species transport have been added. To incorporate combustion (Eq. (6)) into the Navier–Stokes equations, it is essential to account for the interactions between fluid flow, chemical reactions, and heat (temperature) release [24].

Numerical Method

The iterative semi-implicit method for pressure-linked equations algorithm [25, 26] is used in computational fluid dynamics to solve the Navier–Stokes equations for incompressible flows. The pressure field is initially unknown, but necessary to calculate the velocity components. An iterative process is required to estimate the unknown pressure field, as follows.

  1. 1.

    Guess the pressure field p*;

  2. 2.

    Solve the momentum equation to obtain \({u}^{*},{v}^{*}\);

  3. 3.

    Solve the p′ equation;

  4. 4.

    Pressure correction step: \(p = p^{\prime } + p^{*}\);

  5. 5.

    Find the correct values of \(u {\text{and}} v, u = u^{\prime } + u^{*} , {\text{and}} v = v^{\prime } + v^{*} ;\)

  6. 6.

    Check for convergence by comparing the changes in the velocity and pressure fields against the predefined convergence criteria \(\epsilon\).

  7. 7.

    If convergence is not achieved, iterate through the previous steps until convergence is reached.

Numerical results for coal combustion in a small boiler.

Computational Geometry

Figure 3 is a schematic of the combustion chamber used in an experimental setup to analyze the process after the coal combustion. Dimensions and coordinates are annotated to ensure accurate reproduction and replicated from the real chamber. In the front view, the overall height of the chamber is 630 mm, the width of the bottom section is 400 mm, and the width of the top section is 100 mm. The side view shows a bottom section height of 420 mm, a middle section width of 150 mm and an overall height of 630 mm. These measurements are critical for calibrating airflow velocity and estimating temperature distribution. The schematic helps to accurately construct the experimental model and interpret data obtained from different combustion methods, providing consistent experimental conditions for reliable comparisons. The structured grid shown in Figs. 4, 5 and 6 was created using the minimal step size ∆x = 0.005 m = 5 mm. The given size of ∆x yields 9,531 nodes and 9,240 elements.

Fig. 3
figure 3

Computational geometry of the combustion chamber

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Fig. 4
figure 4

Computational grid

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Fig. 5
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Structured view of the computational grid

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Fig. 6
figure 6

Boundary conditions

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Experimental Study of the Airflow Jet Coverage Area in a Fixed Layer of Coal Depending on the Diameter of the Nozzle and the Pressure of the Supplied Air

A laboratory study was conducted to substantiate the aerodynamic parameters of the air supply to the fixed coal layer in the combustion chamber. The experiment was conducted on a specially designed device, shown in Fig. 7. The required air pressure in the injection pipeline is generated by a centrifugal fan driven by an electric motor. The required pressure was achieved by changing the fan speed. The fan rotated with a Delta VFD-L frequency inverter connected to the electrical circuit. The pressure (hydraulic drop) of the air in the supply line was controlled by a pressure gauge. By changing the pressure value on the pressure gauge, the speed of the electric fan motor through the frequency converter was controlled. This controlled data provided a timeline for converting the frequency to air pressure. The distance between the opposite walls parallel to the glass loading plates did not exceed the thickness of the vertical pressure tube. The airflow pipe had a predrilled radial hole of the required diameter according to the experimental plan. When pressure is generated in the tube, the air jet in the vertical plane can be evaluated by two indicators: the length of the jet along the axis, where it is marked as a function (Y1) dependent on the hole diameter (x1) and the air pressure in the pipeline (x2); or jet height as a function (Y2) also dependent on these two parameters. These functions assess the completeness of the coverage (coating) of the air jet, i.e., the elimination of the dead zone and the distance of the hole center from the upper surface of the coal layer. The third assessment function is jet width (Y3). This was determined by rotating the jet 90º: a container of parallel transparent glass plates ④ and an air distribution vertical tube with a side opening ⑤. This indicator estimated the distance between the openings, i.e., the distance between the vertical air delivery pipes. The multifactor experiment involved the following levels and intervals of factor variations (Table 1). The plan matrix and the variation levels of the experimental factors are presented in Table 2.

Fig. 7
figure 7

Device for studying airflow parameters in the coal layer a diagram of the device in the vertical plane; b diagram of the device in the horizontal plane; c general appearance of the device; 1—air supercharger (centrifugal fan); 2—pressure gauge; 3—frequency inverter; 4—container of parallel transparent glass plates; 5—air distribution vertical tube with side opening

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Table 1 Levels and intervals of independent factors
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Table 2 Planning matrix and variation levels
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Encoded value.

According to the experimental research task (comparative evaluation of fixed coal layer combustion according to the proposed scheme and the classical scheme in a laboratory-scale low-power boiler), the following indicators of fixed-bed coal combustion after the appearance of a flame on the surface of the formation were to be determined:

  • Flame temperature on the surface of the combustible coal layer.

  • Flue gas toxicity.

  • Percentage of unburned small particles of coal that entered the ash receptacle through the grate.

  • Ash analysis for the two coal combustion methods (classical and proposed).

The air supply to the coal bed (in the new combustion method) was controlled by a fan by changing the electric motor rotation frequency. The electric motor rotation frequency was controlled by a frequency inverter, and the air pressure was controlled by a pressure gauge located at the outlet of the fan (Fig. 8).

Fig. 8
figure 8

Regulation of the air supply to the air distribution nozzles a Overall view of the equipment; b equipment diagram; 1—air line; 2—pressure gauge; 3—fan; 4—automatic circuit breaker; 5—frequency converter; 6—electric meter

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The values for the electric motor rotation frequency corresponding to the pressure (in the pressure gauge) at the inlet to the main pipe (at the outlet of the fan) are presented in Table 3.

Table 3 Calibration of the speed of the electric motor shaft to the air injection pressure reading
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Determination of the flame temperature on the surface of the combustible coal layer The temperature of the flame on the surface of the coal layer was determined after complete combustion horizontally and vertically of the front-coal loading area. In this case, the cover on the front-loading area was opened for temperature measurement using a pyrometer, model C-20.3, with a measurement range of − 8  to 1250 °C (Fig. 9). Measurements were taken every 10 min according to the previously marked coordinates (Fig. 9a) with increments of 40 mm vertically and 50 mm horizontally. The obtained temperature measurements were recorded in a table according to the coordinate axes of the measurement and processed.

Fig. 9
figure 9

Fragments of flame temperature measurement on coal layer a Measurement scheme; b temperature measurement process with pyrometer; c measurement process with Fluke thermometer

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Determination of flue gas toxicity The toxicity of harmful impurities in the flue gases was measured with the Testo-300 gas analyzer according to the manufacturer’s procedure [27]. Prior to the measurement, the following operations were performed on the gas analyzer: condensate receptacle cleaning, dust filter inspection, zeroing of the gas and pressure values, and gas pipe leakage check. The measurement was conducted by leveling the flue gas probe so that its tip was at the center of the gas stream (the area where the gas temperature reaches the maximum, Max FT), as shown in Fig. 10.

Fig. 10
figure 10

Determination of the toxicity of flue gas a measurement scheme; b measurement process

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Determination of the percentage of unburned small particles of coal that entered the ash receptacle through the grate The percentage of unburned fine coal particles deposited in the ashtray through the grate was determined only for the classical method of combustion because there is no grate in the proposed method. The mass of the unburned fine coal particles was determined after extraction from the ashtray of the boiler (Fig. 11).

Fig. 11
figure 11

Determination of the fraction of unburned fine coal particles deposited in the ashtray through the fire grate 1—fire box chamber; 2—flame; 3—coal loading door; 4—fire grate; 5—unburned small coal particles which fall through the fire grate

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Ash analysis for the two coal combustion methods (classical and proposed) The analysis was conducted after each coal combustion method by extracting the accumulated ash from the combustion chamber. The samples obtained from the chamber were evaluated with a bomb calorimeter in the laboratory. These indicators estimated coal combustion completeness to determine the energy loss.

The fuel combustion heat was determined using an automatic isoperibolic combustion calorimeter with the bomb B-08 MA “K” in accordance with GOST 21261. The automatic calorimetric test was conducted in the calibration mode by burning the reference substance (benzoic acid K-3), and the combustion heat of the sample was determined in the range of 10–40 kJ. The ash content of the test combustion product was determined according to GOST 1461–75 by heating the remaining solid residue in a muffle furnace until a constant mass was reached, then cooling to room temperature and weighing. The determination of the total moisture of the test sample was conducted according to GOST 11014–2001 by drying at temperatures from 105  to 110 °C.

Results

Numerical Simulations of Velocity and Gas Temperature Field Distributions in a Fixed Coal Boiler

Based on the analytical calculation results, graphical interpretations of the mathematical models for the propagation of the velocity field and temperature over the fixed coal layer during combustion were obtained (Figs. 12, 13, 14).

Fig. 12
figure 12

Control line of starting velocity a t = 1 s; b t = 50 s; c t = 100 s

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Fig. 13
figure 13

Velocity profile a t = 1 s; b t = 50 s; c t = 100

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Fig. 14
figure 14

Temperature profiles in the computational geometry at a velocity of 1.5 m/s (Tinlet = 800 ℃ + 273.15 K = 1,073.15 K, Tmedium = 300 K) a t = 1 s; b t = 50 s; c t = 100 s

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The results are presented graphically in parallel for the classical method of combustion with air supplied through a fire grate (left side of Figs. 12, 13, 14) and the proposed method with air forced into the fixed coal layer under pressure (right side of Figs. 12, 13, 14). The coordinates of the reference line for which numerical results have been recorded are \(x = 0.4, y = - \,0.3\). The graphs in Figs. 12, 13 and 14 show speed profiles at different points in time (t = 1 s, 50 s, 100 s) depending on the range of x.

Figure 12 represents the beginning of the established combustion mode in the chamber: a reference line for a constant speed of 1.5 m/s (left) and a reference line for an initial speed of 0 m/s (right). The first velocity changes at the initial speed of 0 m/s were observed at t = 1 s on the side walls of the boiler. Subsequent changes in velocity, in the form of vortices, were observed throughout the computational geometry, with the maximum velocity first appearing on the right sidewall of the boiler.

The temperature propagation process begins at the lower wall of the computational geometry, where the inlet boundary condition was specified, with a temperature of 800 °C. The temperature spread is observed as a parabola, heating the entire bottom of the designed geometry. By t = 25 s, the temperature reaches its maximum value. High temperatures were not recorded in the tapering section of the low-power boiler throughout the entire modeling process. With the increase in speed, instantaneous heating was recorded throughout the boiler. The steady state of temperature, i.e., its constant value, was achieved after 50 s.

According to the boiler combustion chamber temperature chart, heat is released faster into the atmosphere with the flue gases due to the high airflow rate through the flue. When coal is burned without a fire grate, the flue gas velocity increases by increasing the flame pressure above the fixed coal layer. Vertical airflow through the fire grate is absent in this case. As a result, the flue gas flow velocity initiates at the surface of the fixed coal layer and increases with the space temperature.

Air Currents in the Fixed Coal Layer

As a result of experimental data processing for air-current dimensions in the fixed coal layer, first-order multiple regression equations have been obtained for three indicators, as follows:

  • Air currents along the length of the fixed coal layer

$${L}_{\text{length}}=-42.354 + 0.659 P+ 13.058\;D$$
(7)

  • Air currents through the width of the fixed coal layer

$${L}_{\text{width}}=-42.866 + 0.562 P+ 14.175\; D$$
(8)

  • -Air currents through the height of the fixed coal layer

$$L_{{{\text{height}}}} = - 41.913 + 0.542P + 14.117\;D$$
(9)

Graphical interpretations of the regression equations are presented in Fig. 15. To estimate the optimal parameters in the regression equations, two-dimensional sections of dependencies were constructed with specified values of one of the variables (Fig. 16). If the hole diameter is 2 mm, the air pressure in the injection line shall be at least 2700 Pa. This pressure can only be obtained if the engine velocity is much higher than 2,946 rev/min (Table 3), which in turn results in high energy consumption and high emissions.

Fig. 15
figure 15

Graphical interpretations of multiple regression equations a air-current length; b air-current width; c air-current height

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Fig. 16
figure 16

Graphical dependencies of the functions on two-dimensional cross-section parameters

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At the minimum pressure value P = 1500 Pa and D = 3 mm, all three function values will be positive: \({L}_{\text{length}}\hspace{0.17em}=6.705\text{ mm}\); \({L}_{\text{width}}\hspace{0.17em}=8.089\text{ mm}; {L}_{\text{height}}=\hspace{0.17em}\)8.568 mm.

When the maximum air pressure value is P = 11,500 Pa and D = 5 mm, all three air jet indicators will have their maximum values: \({L}_{\text{length}}\) = 98.721 mm; \({L}_{\text{width}}\hspace{0.17em}=\hspace{0.17em}\)92.639 mm; \({L}_{\text{height}}\) = 90.002 mm. With a hole diameter of D = 4 mm, all three air jet values are closest to each other: all distances L for length, width, and height vary uniformly.

We determined that a hole diameter of less than 4 mm is not recommended, and the pipe pressure should be at least 1500 Pa. The distance between the two pipes should not be less than 20 mm when the pipes are parallel on the same plane. Depending on the capabilities of the air injection device and the locations of the injection pipes according to the specified limits, the third parameter should be adjusted.

Results of Experimental Studies of the Fixed-Bed Coal Combustion Process with Air Supplied via a Fire Grate or by Horizontal Air Distribution Devices Without a Fire Grate

The measured surface flame temperature distributions of the combustible coal layer are shown in Fig. 17.

Fig. 17
figure 17

Fixed-bed coal surface flame temperatures a by the classical method using a fire grate; b according to the proposed method without a fire grate

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The obtained temperature values verify the results of the theoretical numerical calculations. In conventional combustion, the vertical temperature is much higher than that in the proposed combustion method, whereas the horizontal temperature is higher in the proposed combustion method than In the classical method. This phenomenon can be explained as follows: in the classical method, the airflow passes through the ashtray and the fire grate, then enters the coal layer, where it participates in the oxidation process. The airflow then moves up the flue, mixing with the flue gas and carrying away part of the heat. In the proposed method, the airflow is horizontal inside the coal layer, and the heat flow is also directed toward the combustion chamber walls. The airflow then changes direction toward the areas with lower pressure, resulting in a vortex movement. Consequently, the flame temperature is elevated in the horizontal direction compared to the fire grate system, and heat distribution is more efficient due to the longer residence time of the flame in the combustion chamber.

Flue Gas Toxicity

Flue gas measurements using the Testo-300 gas analyzer in the traditional boiler with a fire grate obtained the values given in Table 4. The measurements were conducted during the complete ignition of the coal layer. Similarly, the flue gas toxicity results for the proposed air injection method (at different pressures) are presented in Table 5.

Table 4 Flue gas toxicity for fire grate coal combustion
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Table 5 Flue gas toxicity for air injection in the coal bed
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In the traditional combustion scheme, the carbon monoxide (CO) content ranged from 1746 to 5383 mg/m3, and the carbon dioxide (CO₂) content ranged from 7.81% to 17.18%. In the proposed scheme, the CO content ranged from 1013 to 1233 mg/m3, and the CO2 content from 9.08% to 14.15%, respectively. Under the proposed coal combustion scheme, the CO and CO2 contents in the waste gases are 48% lower and 21% lower, respectively, than those in the traditional scheme. The new method of coal combustion results in more complete combustion compared to the traditional method.

Percentage of Unburned Small Particles of Coal that Entered the Ash Receptacle through the Fire Grate

The percentage of unburned fine coal particles that entered the ashtray of the boiler at the beginning of coal loading and before ignition depends on the size of the coal itself. Unburned particles, which are smaller than the slit of the fire grate, fall into the ashtray of the boiler. The mass of the unburned fine coal particles was determined by weighing. Due to the limited volume of the combustion chamber, the total mass (10 kg) of the coal was divided into two parts of 5 kg each. The results after weighing are presented in Table 6.

Table 6 Loss of fine coal through the fire grate
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The total coal loss (unburned) through the grate with a fractional composition of less than 10 mm in diameter when burning 10 kg of coal (in two 5-kg loads) was 11.83%, which exceeds the allowable standard for the grate system of up to 7% according to GOST 2093–82 [28]. This is due to the combustion of a small quantity of coal and the use of a fine-particle specimen.

Ash Analysis for the Classical and Proposed Coal Combustion Methods

The ash content, moisture content, and combustion heat values for ash samples from the two combustion methods and for the unburned coal are presented in Table 7.

Table 7 Test results of unburned coal and ash samples
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Ash as a percentage of total coal burned was 24% for the classical method using a fire grate- and 13% for the proposed method without a fire grate. The moisture content in the ash of the proposed method is half that of the ash of the classical combustion system.

Discussion

The following results were obtained: graphical interpretations of the mathematical models of gas velocity and temperature distribution in the fixed-bed coal combustion chamber of the low-power boilers; air flow models in the coal bed; dependence of the flame temperature on the surface of the combustible coal layer by feeding air through a grate and by horizontal air supply directly into the coal layer without a fire grate; comparative evaluation of flue gas toxicity for the classical and proposed combustion methods; percentage of unburned fine coal particles in the ashtray through the fire grate; and comparative ash assessments for the classical and proposed methods.

The graphical interpretations of the mathematical models of gas velocity and temperature distributions in the fixed-bed coal combustion chamber of a low-power boiler for the proposed method show better heat transfer than the traditional method by reducing the vertical component of the gas flow rate. The vertical component reduction is related to vortex formation in the combustion chamber above the coal layer. This makes it possible to increase the residence time of the flue gas in the chamber. The combustible components in the gas will also burn out due to the extended residence time, increasing the combustion efficiency and reducing the flue gas toxicity.

Most coal combustion modeling studies have focused on cyclone cell vortex combustion for coal dust [29, 30]. These boilers are designed for district heating and obtaining steam for turbines. Further development of coal combustion theory in small boilers is particularly necessary for a decentralized system where population density is low and district heating is impractical due to transportation loss. At present, new low-capacity boilers manufactured in Kazakhstan are focused on the forced supply of air and the use of selected coal, while mechanical losses due to the presence of the grate remain within the same limits [31].

The obtained models of air flow propagation in the fixed coal layer are aimed at determining the oxidization penetration capability based on air pressure and nozzle diameter. The three presented models characterize the distribution distances of the oxidizer (air) within a fixed coal layer, forming a combustion surface for each air supercharger. The axis of symmetry passes through the center of the nozzle opening. Equation (7) describes the length of the air jet in the coal bed on the horizontal and vertical planes passing through the axis of symmetry. Equation (8) describes the relationship between the width of the air jet on the horizontal plane, the diameter of the hole, and the pressure of the air passing through the axis of symmetry. Equation (9) describes the dependence of the jet coverage height on the hole diameter and the air pressure of the vertical plane passing through the axis of symmetry. The function values at certain controlled parameter values (hole diameter and air pressure) describe the distances between the mixed nozzle openings.

The temperature distribution of the combustible coal layer surface flame under the established combustion method shows that the temperature of the air supply through the grate is higher than that of the horizontal air supply directly into the coal layer without the grate. This phenomenon occurs because combustion in the proposed method occurs directly inside the coal layer where the air is supplied. It also shows a slower temperature spread due to the low vertical gas velocity. However, there are difficulties in measuring the temperature inside the coal layer related to equipment limitations and technical capabilities.

The comparative evaluation of flue gas toxicity in fixed-bed coal combustion reflects the advantages of the proposed method over the classical combustion method according to environmental regulations [32]. The new combustion method decreases CO values by 2–3 times and NO by twice the amount. The efficiency is more than 7% higher. However, these values should be verified in industrial boilers over an extended period. The percentage of unburned fine coal particles entering the ash pit through the grate in this study considered only the initial moment of coal loading. However, unburned or partially burned individual fine coal particles may also fall into the ash tank during boiler operation. Considering these losses, the proposed combustion method is even more efficient. All these losses are described in the scientific and technical literature when compiling the thermal balance of fuel combustion as heat loss from mechanical incompleteness of combustion. The value of this indicator depends on the design of the furnace and the particle size distribution of the fuel, with allowable losses of up to 8%. The results of the combustion tests showed average losses of 11.83%, which exceeds this standard, even though a standard grate was used. However, in the improved boiler design, the loss is zero.

A comparative assessment of the ash content for the classical and proposed methods of fixed-bed coal combustion also shows the advantage of the proposed oxidant supply method. When visually compared, the ash produced by the new coal combustion method had a light tint and a fine granulometric composition.

Conclusion

The hypothesis presented in this work suggests a way to improve the efficiency of fixed-bed coal combustion by distributing the oxidant (air) through the entire base of the combustion chamber and the height of the coal layer and by reducing the rate of movement of the combustible gas stream for better heat distribution in the chamber.

Graphical interpretations of the mathematical models for the gas velocity and its temperature profiles during fixed-bed coal combustion for an experimental laboratory-scale boiler (comparing the classical and proposed methods) are obtained.

Mathematical models were built to characterize the main parameters of the air jets (in height, width, and length) in a fixed coal layer based on a multifactor physical simulation experiment of the developed device.

Comparative indicators of flue gas toxicity for the classical and proposed methods of fixed-bed coal combustion in a low-power experimental boiler are obtained.

The distribution of the flame temperature on the external surface of the combustible fixed-bed coal layer is constructed based on the geometric coordinates of the chamber for the classical and proposed combustion methods.

Estimated losses from mechanical coal underburning in the classical combustion method using a fire grate were provided.

The coal combustion completeness was appraised by evaluating the ash produced under laboratory conditions for specific combustion heat, moisture content, and ash content for the classical and proposed methods of fixed-bed coal combustion in an experimental boiler.

Further research on the fixed-bed coal combustion process using a horizontal air supply delivered to the coal layer through special nozzles should focus on methods for mechanized coal loading and ash unloading for prolonged boiler operation. Additional research should also be conducted on a direct air injection combustion mechanism for low-grade coal.