Modeling and Simulation of Complex Fluid Networks in the Flue Gas System of a Boiler

Abstract: Under the conditions of high demand for energy saving and environmental protection, the thermal power unit is required to phase out the traditional extensive operation mode—a method of oxygen-enriched combustion in a furnace, considering safety first. Achieving efficient and economic operation with an optimal proportion of air distribution in these thermal power units is crucial. The high-precision simulation equipment could provide an experimental basis for optimal operation of field units. This paper starts by improving the accuracy of simulation equipment. In this work, the method of dividing nodes and branches in the boiler was based on signal flow graph theory. According to the flow characteristics of the working substance, the method for calculating the node and branch pressure drop was analyzed and set up. Subsequently, a fluid network model of the multi-dimensional flue gas system was constructed. With the help of our self-developed simulation model and data-driven platform, a modular simulation algorithm was designed. The simulation analysis of the boiler showed the accuracy of the model.


Introduction
A decrease in electricity consumption has meant that the average utilization hours of thermal power units have decreased rapidly. Many thermal power units run at a low load for a long time, or the working conditions are adjusted frequently. Under severe environments, efficient and economic operation of the thermal power unit is important [1]. High-precision mathematical models can provide the necessary data support for operation optimization. The boiler equipment, especially the burning system, is a key component for achieving efficient operation optimization. An accurate description of the flow characteristics of a flue gas system has long-term significance. Many researchers have established many different types of flow-characterization models from different perspectives.
With the cold-flow model experiment, a cold test model was built to study gas flow characteristics in a boiler [2][3][4], potentially providing the basis for the design of a real boiler. Advanced measuring devices and methods were used to monitor the dynamic field of the boiler. The two-dimensional (2D) velocity field was reconstructed using the sound velocity distribution obtained by acoustic measurement [5]. An experimental investigation of the aerodynamic field in a four-cornered tangentially fired boiler was carried out using linear discriminant analysis (LDA) technology and a rotation method [6]. The powder velocity field in a boiler was set up using particle imaging velocimetry by dispersing tracer particles that followed the different motion of fluids in the two-phase particle flow field [7]. With the development of numerical simulation, the flow characteristics in a boiler could be simulated. Y. Zhou used the standard k-ε turbulence model to study the flow field of a tangentially fired boiler. The comparison error between the simulation result and test data was about In 1953, S.J. Mason proposed the signal flow graph that could be used to solve linear algebraic equations from topological graphs. The theory could be used for the analysis of feedback systems, solving linear equations, simulating linear systems and designing digital filters. The complex system was also described with nodes and directed segments with arrows [24]. With signal flow graph theory, nodes and branches can be used to describe the relationship of a device in a fluid network. However, the device not only corresponds to the nodes, but may also correspond to the branches. The connection between the devices may also correspond to both the nodes and branches.
The theory can be described as follows [25]: (1) When using the node to describe the device in a fluid network, it accurately reflects the change in pressure of the devices. The compressing process is neglected, such as the pumps and fans. (2) When using the node to describe the type of connecting pipeline among the devices, the pressure of the pipeline would change because it is under high pressure. The changing pressure could be calculated via the increasing number of nodes. (3) When using the branch to describe a connecting pipeline among the devices, it could reflect the change in mass and flow, and the change in pressure would be neglected. (4) When describing a device such as a valve, which mainly affects the change in mass and flow, the change in pressure could be obtained via node calculation. (5) There are three types of nodes in the signal flow graph: input, output and mixed nodes. During the setup of the model, the input and output nodes correspond to the boundary condition, which is usually atmosphere, or fluid with confirmed parameters, and so on. (6) The calculation of a mixed node is more complex. The impact from upstream and downstream of the node, and entering and out-flowing of the node, should be considered.
In this paper, the flow refers to mass flow. m i is the mass of the fluid and q mi is the flow of the branch passing through node i, which is defined where the flow entering the node is positive and that exiting is negative. q m,ext is the additional flow through node i, or the node characteristic correction. The magnitude of the positive and negative q mi value is the same. V i is the volume of node i, ρ i is the density of the fluid, p i is the pressure of node i and T i is the temperature.
Thus, the mass conservation equation of a single node can be described as follows: The length of the pipeline among the nodes and the node volume are constant. The density of the fluid varies with pressure and temperature, and the impact of the temperature is neglected. c i denotes the change of density with pressure, or the compressive energy of the working fluids. For the uncompressed fluid, dρ i /dp i = 0, and for the general fluid, the compressed coefficient is considered as a number close to zero. The relation between compressibility and flow is as follows: The flow and pressure of the pipeline inlet is described by: where C m is the admittance of the pipeline, which reflects the circulation resistance, and ∆p is the differential pressure of the pipeline inlet and outlet. The equation is nonlinear. The following is the result after Taylor series expansion, ignoring higher-order terms with an initial condition of zero: where B m is the admittance after linearization. Without considering the additional flow, the following results after linearization: B sm is the branch admittance that enters the node, and B sn is the branch admittance that exits the node. p j and q mi are the upstream and downstream node pressure with a relationship of: p i is the final pressure, and Equation (7) can be described as: Subsequently, the formula of node pressure p i can be obtained: After Laplace variation of Equation (7) under an initial condition of zero: p i is determined by the pressure of the final moment, and the upstream and downstream pressure. The equivalent transfer coefficient form among the nodes is the first-order inertia element.

Model of the Single-Layer Tangentially Fired Boiler
The nozzle form of the tangential burner was a rectangular jet. The overall pressure drop included that of the primary airduct and that of the jet from burner to boiler. The flow resistance coefficient of the equivalent branch was obtained using the total pressure drop and the mass flow [26].

Pressure Drop of the Primary Airduct
In the primary airduct, the mixture of primary air and pulverized coal was a typical dilute gas-solid flow. There were two types of pressure drop: the working fluid acceleration pressure drop, and the frictional pressure drop. The latter was composed of two drops corresponding to the gas and solid phase.
The acceleration pressure drop can be described as: where µ is the powder concentration, ρ g is the gas density, v g is the gas velocity and v s is the solid velocity. The friction pressure drop is given by: where λ g is the equivalent friction coefficient of the gas phase,λ s is the equivalent friction coefficient of the solid phase, L is the length of the pipeline and d is the diameter of the pipeline.

Pressure Drop in Boiler
The nozzle form of the tangential burner was a rectangular jet. The pressure drop of the jet from burner to boiler could be calculated with jet speed along the direction of the nozzle.
The expanding angle of the jet can be calculated using: where x 0 is the distance from the jet origin to the nozzle, and b 0 is the nozzle radius. The relation between the two is as follows: where a is the empirical constant (related to the turbulence degree of the airflow and the uniform distribution of the velocity field at the nozzle), ω 0 is the initial speed of the nozzle and x is the distance measured to the nozzle. ω m is the speed at axis x from the nozzle, and ω x is the speed at axis x from the nozzle. y is the distance to the axis, and y bj is the distance between the axis and the boundary. The pressure drop is calculated based on the change in the jet velocity: where c 0 is the density of coal fines.

Tangential Boiler Model of Single-Layer with FourCorners
The signal flow graph model of the single-layer tangentially fired boiler was built as shown in Figure 1. S i is the node of pressure, and i is from 0 to 8. S 0 is the inlet pressure node of the air-powder pipe. S j is the outlet pressure node of the air-powder pipe, and j is from 1 to 4. S k is the pressure node of the injector, and k ranges from 5 to 8. S k reflects the position and pressure of the circle. Figure 1. Model of the single-layer tangentially fired boiler. Table 1 shows the structure and parameters of the 350 MW supercritical coal-fired units. Figure  2 is the hypothetical tangential structure for theoretical calculation.  On the simulation platform STS (Simulation Training System), which was designed independently, algorithms were designed to calculate the node pressure, the pressure drop of the air-powder pipeline and the jet flow. Figure 3 shows the module distribution and connection relationship in STS.  Table 1 shows the structure and parameters of the 350 MW supercritical coal-fired units. Figure 2 is the hypothetical tangential structure for theoretical calculation.  Figure 1. Model of the single-layer tangentially fired boiler. Table 1 shows the structure and parameters of the 350 MW supercritical coal-fired units. Figure  2 is the hypothetical tangential structure for theoretical calculation.  On the simulation platform STS (Simulation Training System), which was designed independently, algorithms were designed to calculate the node pressure, the pressure drop of the air-powder pipeline and the jet flow. Figure 3 shows the module distribution and connection relationship in STS. On the simulation platform STS (Simulation Training System), which was designed independently, algorithms were designed to calculate the node pressure, the pressure drop of the air-powder pipeline and the jet flow. Figure 3 shows the module distribution and connection relationship in STS. On the simulation platform, the response curves of key parameters with different inputs and external disturbance were studied, as shown in Figure 4.
(a-1) S0 ( a-2) S1, S2, S3, S4 (a-3) S5, S6, S7, S8   On the simulation platform, the response curves of key parameters with different inputs and external disturbance were studied, as shown in Figure 4. On the simulation platform, the response curves of key parameters with different inputs and external disturbance were studied, as shown in Figure 4.
(a-1) S0 ( a-2) S1, S2, S3, S4 (a-3) S5, S6, S7, S8   In the subfigures, the ordinate is absolute pressure and the unit is KPa. By changing the inlet pressure disturbance of the air-powder pipe, the response curves of the air-powder pipe outlet pressure and the injector pressure were studied.
It can be seen from the subfigures that the position and pressure of the tangential circle varied with the pressure of the separator outlet of the coal grinding machine (and the inlet of the air-powder pipeline). When the air-powder pipelines were blocked, the amplitude of the pressure varied. According to the curve in Figure 4d, on the same branch of the fluid network, the pressure change of the downstream node lagged behind the front node. The lag time was adjusted by c i in the node calculation process. In the subfigures, the ordinate is absolute pressure and the unit is KPa. By changing the inlet pressure disturbance of the air-powder pipe, the response curves of the air-powder pipe outlet pressure and the injector pressure were studied.

Tangential Boiler Model of the Direct-Current Burner with Intersecting Adjacent Multilayers
It can be seen from the subfigures that the position and pressure of the tangential circle varied with the pressure of the separator outlet of the coal grinding machine (and the inlet of the air-powder pipeline). When the air-powder pipelines were blocked, the amplitude of the pressure varied. According to the curve in Figure 4d, on the same branch of the fluid network, the pressure change of the downstream node lagged behind the front node. The lag time was adjusted by ci in the node calculation process.   The calculation of the pressure drop in the secondary airduct was relatively simple compared to the calculation of the pressure drop in the air-powder duct. This pressure drop was composed of the acceleration and friction pressure drops.

Tangential Boiler Model of the Direct-Current Burner with Intersecting Adjacent Multilayers
These pressure drops were calculated for the fluid in a single phase by: In the subfigures, the ordinate is absolute pressure and the unit is KPa. By changing the inlet pressure disturbance of the air-powder pipe, the response curves of the air-powder pipe outlet pressure and the injector pressure were studied.
It can be seen from the subfigures that the position and pressure of the tangential circle varied with the pressure of the separator outlet of the coal grinding machine (and the inlet of the air-powder pipeline). When the air-powder pipelines were blocked, the amplitude of the pressure varied. According to the curve in Figure 4d, on the same branch of the fluid network, the pressure change of the downstream node lagged behind the front node. The lag time was adjusted by ci in the node calculation process.   The calculation of the pressure drop in the secondary airduct was relatively simple compared to the calculation of the pressure drop in the air-powder duct. This pressure drop was composed of the acceleration and friction pressure drops.

Tangential Boiler Model of the Direct-Current Burner with Intersecting Adjacent Multilayers
These pressure drops were calculated for the fluid in a single phase by: The calculation of the pressure drop in the secondary airduct was relatively simple compared to the calculation of the pressure drop in the air-powder duct. This pressure drop was composed of the acceleration and friction pressure drops.
These pressure drops were calculated for the fluid in a single phase by: where ζ is the equivalent resistance coefficient. Considering the influence of secondary air, the result is shown in Figure 7.
Energies 2017, 10, 1432 9 of 12 where ζ is the equivalent resistance coefficient. Considering the influence of secondary air, the result is shown in Figure 7.
(a-1) S0 ( a-2) S1, S3 (a-3) S2, S4 (a-4) S5, S6, S7, S8 Compared with the simulation result in Figure 4, the influence of the outlet pressure of the coal-grinding machine on the pressure position of the tangential circle reduced. In the figures, the ordinate is also absolute pressure, and the unit is KPa. By changing the inlet pressure disturbance of the air-powder pipe, the curves of the air-powder pipe outlet pressure and the injector pressure were studied.

Overall Network Model
There were 5 pulverizing systems in the 350 MW supercritical units. The nodes are shown in Figure 8.  Compared with the simulation result in Figure 4, the influence of the outlet pressure of the coal-grinding machine on the pressure position of the tangential circle reduced. In the figures, the ordinate is also absolute pressure, and the unit is KPa. By changing the inlet pressure disturbance of the air-powder pipe, the curves of the air-powder pipe outlet pressure and the injector pressure were studied.

Overall Network Model
There were 5 pulverizing systems in the 350 MW supercritical units. The nodes are shown in Figure 8.

Simulation of the Overall Dynamic Model
The simulation curves under different inputs and disturbances are shown in Figure 9.

Simulation of the Overall Dynamic Model
The simulation curves under different inputs and disturbances are shown in Figure 9.

Simulation of the Overall Dynamic Model
The simulation curves under different inputs and disturbances are shown in Figure 9. In the subfigures, the ordinate is gauge pressure and the unit is Pa. The tangential circle pressure at different heights was studied. On comparing the simulation curves, it is evident that the influence of the outlet pressure fluctuation of the bottom separator on the tangential circle pressure was greater than that of the middle separator. The influence of the pressure fluctuation of secondary air on the tangential circle pressure was greater than that of the primary air.

Conclusions
By analyzing the characteristics of a mixture of wind and powder, a complex multi-dimensional fluid network model was built to describe the change in node pressure in the boiler under different ratios of wind to powder. Thus, the flow characteristics of the complex fluid in the boiler were obtained.
It is hoped that the research results will improve the accuracy of thermal-power-unit simulations and can be used for further research about optimal operation. The modeling method and process were described with the help of our self-developed simulation platform (STS). The simulation results showed that the model obtained can demonstrate the characteristics of the fluid network in a boiler. In the subfigures, the ordinate is gauge pressure and the unit is Pa. The tangential circle pressure at different heights was studied. On comparing the simulation curves, it is evident that the influence of the outlet pressure fluctuation of the bottom separator on the tangential circle pressure was greater than that of the middle separator. The influence of the pressure fluctuation of secondary air on the tangential circle pressure was greater than that of the primary air.

Conclusions
By analyzing the characteristics of a mixture of wind and powder, a complex multi-dimensional fluid network model was built to describe the change in node pressure in the boiler under different ratios of wind to powder. Thus, the flow characteristics of the complex fluid in the boiler were obtained.
It is hoped that the research results will improve the accuracy of thermal-power-unit simulations and can be used for further research about optimal operation. The modeling method and process were described with the help of our self-developed simulation platform (STS). The simulation results showed that the model obtained can demonstrate the characteristics of the fluid network in a boiler.