An Effectiveness Analysis of the Pulsed Resonant Fuel Combustion in the Processes of Steel-Casting Ladle Drying and Warming

This paper reports a technique of the pulsed resonant fuel combustion in the processes of drying and heating steel-casting ladles, devised to save fuel. The research method is based on the initiation of pulsations when burning fuel at a frequency equal to the frequency of natural fluctuations within the working volume of the ladle, which leads to the resonance of pulsations. This study aimed to define a technique to effectively burn fuel and to confirm a decrease in fuel consumption in the process of the pulsed resonant combustion. The experimental and industrial studies involving 8 drying operations and 5 ladle heating operations have established the possibility to comply with the normative requirements in line with the technological instructions at the level of 80‒100 %. The possibility to search for the pulsed resonance frequencies under industrial conditions has been confirmed, despite the negative impact of high temperatures, acoustic interference, and inertia of the equipment. The feasibility of a pulsation unit has been determined, as well as the possibility to steadily maintain, during the drying process, the required resonance frequencies of gas pulsations. A more intensive course of the drying process has been observed, which makes it possible to shorten the process duration and, accordingly, to reduce fuel consumption. The high excitability of resonance frequencies in the ladle during heating has been detected, due to the short length and volume of the section of a gas pipeline between the pulsation unit and burner compared to the drying bench. The warm-up intensity was noticeably higher than that of drying due to the lower end temperature of the lining (777‒910 °C instead of 900‒1,120 °C) and the lack of moisture evaporation. Using the pulsed resonant fuel combustion mode at the posts of intensive heating of ladles for melting makes it possible to force the heating by the resonant pulsation of the torch. During pulsed resonant combustion, the usable utilization of fuel heat increases markedly, which leads to an increase in the drying and heating processes efficiency and corresponding fuel economy. The decrease in the consumption of natural gas when drying the ladles amounted to 2.7÷26.1 %; at the warm-up ‒ 19.5÷37.8 %. These data indicate the energy efficiency of the pulsed resonant combustion and the feasibility of implementing a burning technique in the processes of ladle drying and warming.


Introduction
Among major fuel consumers in steelmaking are foundry bays for the preparation of steel-casting ladles, namely, for the processes of ladle drying and warming, which in some cases use scarce and expensive natural gas.
The cost of natural gas for drying, for example, a single ladle with a capacity of 160 tons, is up to 3,000 m 3 ; for warmingup to 2,000 m 3 . As the ladle capacity increases, the consumption of natural gas increases accordingly.
One of the areas in fuel economy is to devise efficient techniques to burn fuel, thereby providing better combustion with less underburning and better utilization of the heat generated from fuel combustion. Such technologies include pulsed combustion.
Interest in pulsations is due to their positive impact on the characteristics of technological and energy processes. The use of pulsations in most cases begins with the impact on the combustion process of fuel by exciting the fluctuations in the gas and air flows participating in the combustion. The most effective manifestation of pulsations should be expected under resonance modes, that is, when the frequency of forced oscillations, which cause pulsations, coincides with the natural frequency of oscillations within the working volume of a firebox, a furnace, or a technological unit.
Given this, it is a relevant task to develop and implement an economical pulsed resonant fuel combustion technology in the processes of steel-casting ladle drying and warming.

Literature review and problem statement
In the total volume of processes of steel-casting ladle drying and warming, taking into consideration all drying and warming techniques, more than 80 % involve fuel combustion products. At the same time, the drying and warming with combustion products have a series of drawbacks: a low fuel heat utilization rate, the pollution of workplaces and the environment, the occurrence of thermal defects in the ladle lining, and so on.
To eliminate these deficiencies, it is recommended to regulate the supply of fuel, providing a "soft" mode of heat treatment. It is proposed to introduce additional partitions into the ladle cavity that could intensify the heat exchange [1][2][3], which, however, does not resolve the issue. It is possible to use the pulsed mode of fuel combustion [4], as well as the use of heat recovery [5], regenerative burners [6][7][8], and so on. However, according to our analysis, all these techniques were not used to dry and warm the steel-casting ladles and their application is problematic.
The above technical solutions do not fully eliminate the shortcomings in the ladle drying and warming by combustion products.
An alternative to fuel combustion products is found in electric heating elements, microwave radiation, infrared radiation, application of a vacuum, as well as other technical solutions. The alternative technologies significantly complicate the processes of ladle drying and warming in comparison with conventional techniques and, in some cases, require the use of non-standard expensive equipment. The alternative technologies are rather energy-intensive.
Given this, using the pulsed fuel combustion is of interest [9], including mechanical engineering [10][11][12] and rocket engineering [13], which could significantly reduce the fuel underburning and increase the intensity of heat output from combustion products, which indicates the prospects and demand for a given direction. However, all the studies carried out do not concern the drying and warming of steel-casting ladles. This work highlights the pulsed resonant combustion technique [14], at which the most effective pulsation frequencies (the most effective in reducing the underburning and in the intensification of heat release) are achieved at minimal energy costs for the generation of pulsations.
To assess the feasibility of using the pulsed resonant fuel combustion, it is necessary to have the appropriate equipment for the process, to confirm the possibility of finding the pulsed resonance frequencies under industrial conditions, taking into consideration high temperatures, acoustic interference, and the equipment inertia. This information has not been revealed in the scientific literature.

The aim and objectives of the study
The aim of this study was to assess the effectiveness of the pulsed resonant fuel combustion in the processes of steel-casting ladle drying and warming.
To accomplish the aim, the following tasks have been set: -to adapt the pulsed resonant fuel combustion at existing steel-casting ladle drying and warming benches and to design the appropriate equipment for the processes; -to conduct an experimental-industrial study at the drying and warming posts and to compare the results on the drying and warming of regular ladles based on conventional technologies without pulsation; -to analyze the thermal balances of steel-casting ladle drying and warming processes based on the results from the experimental-industrial study in order to determine the energy efficiency of the pulsed resonant fuel combustion in comparison with a conventional combustion technology without pulsations.

The equipment and adaptation of the pulsed resonant fuel combustion method
The study method is based on the initiation of pulsations when burning fuel at a frequency equal to the frequency of natural fluctuations within the working volume of a ladle, which leads to the resonance of the pulsations. The principal diagram of the bench for the pulsed resonant fuel combustion in a steel-casting ladle is shown in Fig. 1. Fig. 1. The principal diagram of a bench for drying the steel-casting ladles through the pulsed resonant fuel combustion: 1 -ladle; 2 -burner; 3 -cover; 4 -gas pipeline to discharge combustion products; 5 -gas pipeline; 6 -air pipeline; 7 -pulsation unit; 8 -acoustic probe; 9 -preamp; 10 -spectrum analyzer; 11 -controlling element; 12 -rheostat; 13 -straightener The spectrum of oscillation frequencies in a ladle is recorded by acoustic probe 8. The signal from the probe is transmitted through preamp 9 to spectrum analyzer 10, where the working frequency of natural oscillations is selected. Based on the magnitude of a working frequency, controlling element 11 sets, through rheostat 12, the predefined DC voltage on the electric motors in the pulsation unit. This enables the pulsators' rotation at a speed corresponding to the oscillation natural frequency within the working volume of the ladle.

Experimental and industrial study of the pulsed resonant combustion
The study was carried out at 160-ton steel-casting ladles. The general view of the bench for drying steel-casting ladles and the arrangement scheme of the pulsation unit are shown in Fig. 2.
The bench includes the racks that host the ladle and a turning cover with a burner. The pulsations of gas flow are created by a pulsation unit installed on the gas pipeline, fabricated in the form of a mechanical pulsator with a cylindrical gas flow interrupter [15].
A schematic of the equipment to enable the pulsed resonant fuel combustion at the drying post is shown in Fig. 3.
The lining of the ladle was dried after the complete replacement of the working layer. The test results are given in Table 1 (Hregular ladle).
Testing the pulsed resonant fuel combustion at the bench of steel-casting ladle drying makes it possible to note the following: -the possibility to search for the pulsation resonance frequencies under industrial conditions has been confirmed, despite the negative impact exerted by high temperatures, acoustic interference, and the equipment inertia; -the pulsation unit has been found to operate rather sufficiently; the possibility to steadily maintain the necessary resonance frequencies of gas pulsations during the drying process has been established; -a more intensive course of the drying process has been noted, which shortens the process length and reduces fuel consumption accordingly; -the savings of natural gas under the pulsed resonant fuel combustion mode amounted, in comparison with the normative indicators, to 2.7÷26.1 %; -the test results allow us to recommend the pulsed resonant fuel combustion mode for the experimental introduction. a b Fig. 2. A steel-casting ladle drying bench: a -general view; b -pulsation unit arrangement scheme; 1 -gas pipeline; 2 -burner; 3 -cover; 4 -ladle; 5 -rack; 6 -gas pipelines to discharge combustion products; 7 -air pipeline; 8 -counter-load; 9 -cover turning mechanism; 10 -pulsation unit; 11 -power and control unit Fig. 3. Schematic of equipment for the pulsed resonant fuel combustion at the post of steel-casting ladle drying: 1 -ladle; 2 -burner; 3 -cover; 4 -gas pipeline to discharge combustion products; 5 -chromatographer; 6 -gas pipeline; 7 -air pipeline; 8 -bypass pipe; 9 -pulsation unit; 10 -radiation pyrometer; 11 -acoustic probe; 12 -preamp; 13 -thermocouple; 14 -potentiometers; 15 -spectrum analyzer; 16 -controlling element; 17 -rheostat; 18 -straightener; 19, 20 -flowmeters The scheme of equipment for the pulsed resonant fuel combustion at a ladle warming post is shown in Fig. 4.
Our experiments involved ladles after a long idling time, that is, the warming of the ladles started from a cold state. A ladle was placed on a mobile trolley in a horizontal position and moved towards the fencing (refractory) wall with a protruding burner, the HNP-9 type. The axis of the burner is located at a distance of 1/3 of the diameter of the ladle from the bottom edge. The results of the experiments are given in Table 2 (H -regular ladle). 4 -radiation pyrometer; 5 -acoustic probe; 6 -fencing wall; 7 -chromatographer; 8 -bypass pipe; 9 -flow meter;10 -gas pipeline; 11 -preamp; 12 -spectrum analyzer; 13 -controlling element; 14 -rheostat; 15 -pulsation unit; 16 -straightener; 17 -burner; 18 -air pipeline; 19 -flow meter The results of testing the system for the pulsed resonant fuel combustion at the post of steel-casting ladle warming allow us, in addition to the above features in the system operation at the drying post, to note the following: -the high excitability of resonance frequencies in a ladle due to the short length and volume of the section of a gas pipeline between the pulsation unit and burner compared to the drying bench; -a noticeable increase in the warm-up intensity compared to drying due to the lower end temperature of the lining (777-910 °C instead of 900-1,120 °C) and the lack of moisture evaporation; -the expediency of using the pulsed resonant fuel combustion mode at the posts of intensive warming of ladles for melting as the pulsed resonant mode makes it possible, along with the increased gas consumption, to force the warm-up by the resonance pulsation of the flame; 380V Table 1 Test results at the post of steel-casting ladle drying -the savings of natural gas at the warming post amounted to 19.5÷37.8 %, which allows us to recommend the pulsed resonant fuel combustion mode at the warm-up benches for experimental implementation.

Thermal balance analysis
An analysis of the thermal balances of the processes of steel-casting ladle drying and warming implied comparing the usable utilized heat and heat losses.
The usable unitized heat includes the consumption of heat for warming the working masonry Q w , the reinforcement row Q r , insulation Q in , casing Q cas , and for evaporating the moisture Q ev at drying. The remaining consumption of heat relates to losses: the loss of heat with outgoing gases Q out , from the chemical underburning of fuel Q ch , the heat transmission to the environment through the ladle lining Q htll and through the cover Q htc as well as the loss of heat to warm the cover Q c and the loss of heat by radiation into the gap between the top cut of the ladle and the cover Q rad (Fig. 3).
At the warm-up bench, instead of the losses of heat associated with the ladle cover (Q htc, Q c and Q rad ), the consumption part of the thermal balance includes the loss of heat associated with the fencing wall of the bench Q wb (Fig. 4).
The input part of the thermal balance includes the heat of fuel combustion. com ng , where B is the consumption of natural gas for drying or warming up a ladle, m 3 ; Q ng is the heat of natural gas combustion, MJ/m 3 . The output part of the thermal balance was determined as follows: 1) the consumption of heat to warm the working masonry: where M w is the weight of working masonry, kg; w t is the average temperature of the working masonry at the end of drying or warming, °C; ( ) w w 0 , are the mean heat capacities of the material for a working masonry, kJ/kg·K; t init is the initial temperature of ladle lining, °C; 2) the consumption of heat to warm the reinforcement row: where M r is the weight of the lining reinforcement row, kg; 3) the consumption of heat to warm the insulation: where M in is the mass of the thermal insulation, kg; where M cas is the weight of the ladle casing, kg; cas e t is the average temperature of the casing at the end of the process, °C; ( ) where M c is the cover weight, kg; c e t is the average cover temperature at the end of the process, °C; ( ) where с whc is the water heat capacity, kJ/kg·K; r is the specific consumption of heat to evaporate moisture, kJ/kg; 100 Here, ω init and ω e are, respectively, the initial and final relative humidity of the ladle lining, %; 7) the loss of heat with outgoing gases: where 1.1 is a factor that takes into consideration the air suction; V cp is the specific output of combustion products, m 3 /m 3 ; Table 2 Test results at the post of steel-casting ladle warming where CO ,  (11) where δ і is the thickness of the corresponding i-th layer of the lining, m; λ і is the thermal conductivity factor of a material of the i-th layer of the ladle lining at an average temperature per cycle of drying or warming, W/m·K; α os is the heat output ratio from the outer surface of the ladle casing, W/m 2 ·K; c sur t is the average, per cycle of drying or warming, the surface temperature of the ladle casing, °C; t ama is the temperature of the ambient air, °C; F is the average value of the area of the surface of the ladle lining (between the inner and outer surfaces), m 2 ; τ is the cycle duration of ladle drying or warming, h; 10) the losses of heat due to the heat transfer through the cover: where δ c is the thickness of the cover, m; λ c is the thermal conductivity factor of a cover's material at an average temperature per cycle, kJ/kg·K; α osc is the heat output ratio from the outer surface of the cover to the surrounding air, W/m 2 ·K; c c t is the average temperature of the cover per cycle, °C; F c is the surface area of the cover, m 2 ; 11) the losses of heat through the radiation into the gap between the top cut of the ladle and the cover: 4 6 l rad 5,67 3600 10 , 100 where 5.67 is the radiation factor of an absolutely black body, W/m 2 ·K 4 ; Т l is the average temperature in the volume of a ladle during drying, K; S is the area of the gap between the ladle and cover, m 2 ; D is the diaphragm factor. The heat losses associated with the fencing wall of the warming bench Q wb , which include warming the wall, heat transfer through the wall, and radiation into the gap between the wall and the ladle cut, which are in a horizontal position at the trolley (Fig. 4). These losses are determined from the difference between the heat input Q com (1) and the sum of heat consumption Q w (2), Q r (3), Q in (4), Q cas (5), Q out (9), Q ch (10) and Q htll (11).
The calculation of the thermal balances of the processes of steel-casting ladle warming has been performed in accordance with the recommended procedure given in work [16].
The ratio between the usable utilized heat and the loss of heat is shown in Fig. 5, 6; hence, the following conclusions can be drawn: -the usable utilization of heat during drying is on average 9.6 % higher under all experimental modes than that in the warming process, which is due to the additional consumption of heat to evaporate the moisture at drying; -the usable utilization of heat under the pulsed resonant fuel combustion in all experiments is higher than that when drying and warming a regular ladle (while drying the ladle, it is higher by 5.3-11.4 %, and when warmingby 4.9-7.2 %); -accordingly, the losses of heat under the pulsed resonant fuel combustion in a ladle are lower than those for a regular ladle, that is, at conventional burning. Comparing the cost items based on the average values of the usable utilization of heat for experimental modes, shown in Fig. 7, allows us to draw the following conclusions: -the most essential cost items in terms of the usable utilization of heat in the drying of the ladles are the consumption of heat to warm the working masonry Q w , the reinforcement row Q r , and the evaporation of moisture Q ev ; -the most essential cost items in terms of the usable utilization of heat when warming the ladles are the consumption of heat to warm the working masonry Q w and the reinforcement row Q r ; -the usable utilization of heat for all cost items at the pulsed resonant fuel combustion in prototype ladles exceeds the same cost items at the standard fuel combustion in a regular ladle. Fig. 7. Comparing the cost items of the usable utilization of heat when drying the ladles; Q w , Q r, Q in , Q cas are, respectively, the consumption of heat to warm the working masonry, reinforcement row, thermal insulation, and the ladle casing; Q ev -the heat used to evaporate moisture at drying; ■ -standard regime; -averages for the experimental modes Fig. 8. Comparing the cost items of the usable utilization of heat when warming the ladles; Q w , Q r, Q in , Q cas are, respectively, the consumption of heat to warm the working masonry, reinforcement row, thermal insulation, and the ladle casing; ■ -standard regime; -averages for the experimental modes The comparison of cost items based on the average values of heat losses for experimental modes is shown in Fig. 9, 10.
Our comparison of the cost items related to heat losses leads to the following conclusions: -the most essential losses of heat in the processes of steel-casting ladle drying and warming are the losses of heat with outgoing gases Q out (on average, when drying the ladles, these losses amounted to 43.1 %; when warming -53.0 %); -in all experiments, the losses of heat with outgoing gases at the pulsed resonant fuel combustion in a ladle are lower than those during standard combustion (when drying the ladles, they are lower by an average of 6.9 %, when warming -by 4.0 %); -the pulsed resonant fuel combustion significantly reduces the losses of heat due to the chemical fuel underburning Q ch (on average, when drying the ladles, these losses amounted to 4.1 % while losses in a regular ladle were 7.4 %; at warming -3.5 % while losses in a regular ladle -6.1 %); -a certain increase in the heat losses associated with the drying bench cover (Q c and Q rad in Fig. 8) and the fencing wall of the warming bench (Q wb in Fig. 8) is due to the higher temperature level in experimental ladles at the pulsed resonant fuel combustion compared to conventional combustion in regular ladles (Tables 1, 2) Fig. 9. Comparison of cost items related to the losses of heat when drying the ladles: Q out -losses of heat with outgoing gases; Q ch -losses of heat from the chemical fuel underburning; Q htll -losses of heat due to the heat transfer through the ladle wall; Q htc -losses of heat through the heat transfer through the cover of the ladle; Q c -losses of heat to warm the cover; Q rad -losses of heat through the radiation into the gap between the top cut of the ladle and the cover; ■ -regular regime; -averages for experimental modes Fig. 10. Comparison of cost items related to the losses of heat when warming the ladles: Q out -losses of heat with outgoing gases; Q ch -losses of heat from the chemical fuel underburning; Q htll -losses of heat due to the heat transfer through the ladle wall; Q wb -losses of the heat related to the fencing wall of the warming bench; ■ -regular regime; -averages for experimental modes In general, our analysis of thermal balances of the experimental modes allows us to draw the following conclusions about the effectiveness of the pulsed resonant combustion: -the pulsed resonant combustion significantly increases the usable utilization of fuel, which leads to an increase in the efficiency of the drying and warming processes and the appropriate fuel savings; -the increase in the proportion of the usable utilization of heat is due to the increase in the accumulation of heat by the working masonry, reinforcement row, thermal insulation, and the ladle casing; -the pulsed resonant fuel combustion reduces the chemical underburning, which reduces fuel losses, increases the temperature within the working volume of the ladle, and intensifies the heat output; -the pulsed resonant fuel combustion mode considerably reduces the losses of heat with outgoing gases, which generally indicates the intensification of heat exchange within the working volume of the ladle.

Discussion of results of studying the effectiveness of the pulsed resonant fuel combustion in the processes of steel-casting ladle drying and warming
A technique of the pulsed resonant fuel combustion in the processes of steel-casting ladle drying and warming has been developed. The pulsed resonant combustion preserves the basic principles of conventional drying and warming technology. At the same time, it creates the prerequisites for more efficient combustion of fuel in the ladle with a reduction in the underburning (Fig. 9, 10), more intensive heat exchange between combustion products and the ladle lining, and more even heat treatment of the inner surface of the ladle (Fig. 7, 8).
In comparison with the standard technique of fuel combustion, our experimental studies have shown the rather high performance of the developed system and a decrease in the consumption of natural gas: when drying the ladles, 2.7÷26.1 % (Table 1), when warming -19.5÷37.8 % ( Table 2).
The special features of the proposed method are the search for the resonance frequencies during pulsations. The result of testing the pulsed resonant fuel combustion has confirmed the possibility of finding the pulsation-resonance frequencies under industrial conditions, despite the negative impact of high temperatures, acoustic interference, and the equipment inertia. We have established the high enough operability of the pulsation unit, as well as the possibility to steadily maintain the necessary resonance frequencies of gas pulsations.
The results of tests at the post of steel-casting ladle warming indicate the expediency of using the pulsed resonant fuel combustion mode at the posts of intensive warming of ladles for melting. The pulsed resonant mode makes it possible to force the warming for melting by the resonance pulsation of the flame.
Our analysis of the thermal balances has confirmed that the pulsed resonant fuel combustion mode significantly increases the usable utilization of heat, which provides for an increase in the efficiency of the drying and warming processes and, accordingly, in the fuel savings compared to conventional combustion (Fig. 5, 6). The increase in the proportion of the usable utilization of heat occurs due to the increase in the accumulation of heat by the working masonry, reinforcement row, thermal insulation, and the ladle casing (Fig. 7, 8). The reduction in the chemical fuel underburning (Fig. 9, 10) contributes to the increase in the proportion of the usable utilization of heat. The pulsed resonant fuel combustion mode significantly reduces the losses of heat with outgoing gases, indicating the intensification of heat exchange within the working volume of the ladle (Fig. 9, 10).
The results of our research confirm that using the pulsed resonant fuel combustion is applicable in the processes of steel-casting ladle drying and warming.
The main limitation for the broad implementation of the pulsed resonant fuel combustion in the processes of steel-casting ladle drying and warming is the ability to adapt the technique. The technique must be adjusted in a specific production setting in compliance with acting technological instructions of drying and warming. At the same time, the existing technologies of the ladle drying and warming processes at different enterprises vary considerably depending on the type of lining and the equipment used.
The proposed technique could be advanced by designing an automated control system for the pulsed resonant fuel combustion, in compliance with the current drying and warming technology. An automated control system would make it easier to adapt the proposed technique to acting drying and warming technologies. The automated system could reduce the duration of search for the resonance frequencies and thus make it more energy-efficient.

Conclusions
1. A technique of the pulsed resonant fuel combustion in the processes of steel-casting ladle drying and warming has been developed, which makes it possible to adjust the pulsation to resonance frequencies and, by maintaining these frequencies, to ensure the most effective result of pulsation. The technique has been adapted to ensure that the consumption of the fuel burned and the time intervals are in accordance with technological instructions. The appropriate equipment for the processes has been designed: we have introduced a pulsator with a bypass pipe, a resonance frequency adjustment scheme to enable the necessary response to changes in the consumption of gas and fuel intervals in accordance with the technological instruction. The devised technique, while preserving the basic principles of the conventional drying and warming technology, creates the prerequisites for more efficient combustion of fuel in a ladle with the reduced underburning, for the intensification of heat exchange between combustion products and the ladle lining, and for more even heat treatment of the ladle.
2. The result of testing the pulsed resonant fuel combustion has confirmed the possibility of finding the pulsation-resonance frequencies under industrial conditions, despite the negative impact of high temperatures, acoustic interference, and the equipment inertia. We have established the feasibility of the pulsation unit, as well as the possibility to steadily maintain the necessary resonance frequencies of gas pulsations.
The results of tests at the post of steel-casting ladle warming indicate the expediency of using the pulsed resonant fuel combustion mode at the posts of intensive warming of the ladles for melting. The pulsed resonant mode makes it possible to force the warming for smelting by the resonance pulsation of the flame.
3. Our analysis of the thermal balances has confirmed that the pulsed resonant fuel combustion mode significantly increases the usable utilization of heat, which provides for an increase in the efficiency of the drying and warming processes and, accordingly, in the fuel savings compared to conventional combustion. The increase in the proportion of the usable utilization of heat occurs due to the increase in the accumulation of heat by the working masonry, reinforcement row, thermal insulation, and the ladle casing. The reduction in chemical fuel underburning contributes to the increase in the proportion of the usable utilization of heat. The pulsed resonant fuel combustion mode significantly reduces the losses of heat with outgoing gases, indicating the intensification of heat exchange within the working volume of the ladle.