Coupled simulation and validation of a utility-scale pulverized coal-fired boiler radiant final-stage superheater

Journal Pre-proofs Coupled simulation and validation of a utility-scale pulverized coal-fired boiler radiant final-stage superheater Ryno Laubscher, Pieter Rousseau PII: DOI: Reference:

S2451-9049(20)30033-0 https://doi.org/10.1016/j.tsep.2020.100512 TSEP 100512

To appear in:

Thermal Science and Engineering Progress

Received Date: Revised Date: Accepted Date:

28 August 2019 17 February 2020 18 February 2020

Please cite this article as: R. Laubscher, P. Rousseau, Coupled simulation and validation of a utility-scale pulverized coal-fired boiler radiant final-stage superheater, Thermal Science and Engineering Progress (2020), doi: https:// doi.org/10.1016/j.tsep.2020.100512

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Coupled simulation and validation of a utility-scale pulverized coal-fired boiler radiant final-stage superheater Ryno Laubscher a, b, Pieter Rousseau a a Department

of Mechanical Engineering, Applied Thermal-Fluid Process Modelling Research Unit, University of Cape Town, Library Rd, Rondebosch, Cape Town, 7701, South-Africa b Corresponding

author. Tel: +27 72 436 9979, E-mail address: [email protected]

Abstract The paper presents a coupled modelling methodology that employs a three-dimensional finite volume method computational fluid dynamics model to solve the boiler flue gas side, and a 1D FVM network approach to model the steam side flow and heat transfer of a final-stage radiant superheater. The CFD model includes the necessary upstream components that affect the thermal performance of the superheater, including combustion and heat transfer in the furnace and platen superheater. The methodology is applied to a 620 MWe drum-type boiler of which the superheater was instrumented with thermocouples measuring the outlet steam temperatures on the different elements. This was augmented with boiler process data that was extracted from the distributed control system (DCS) for steady-state operation at 99 % and 65 % boiler loads. The results show that the approach can capture the details of the temperature maldistribution between legs in the same heat exchanger, between elements in the same leg and between the inner and outer loops of the same element for different load cases. It also captures the steam flow maldistribution between the inner and outer loops. On the flue gas side the results show that for the part-load case, the high gas temperature and velocity zones are less uniformly distributed compared to the full load case and also less symmetric than in the full load case. The calculated total heat transfer rates for the evaporator, platen superheater and final superheater compare well with the experimental values for both the 99 % and 65 % maximum continuous rating load cases. This shows that the coupled simulation models can capture the overall thermal performance of the three heat exchangers modelled here with good accuracy.

Keywords: Computational fluid dynamics, process-modelling, co-simulation, pulverized coal-fired boiler, radiant heat exchangers

1. Introduction The addition of intermittent renewable energy sources onto national electrical grids increases the pressure on conventional coal-fired power plants to change their operating modes from baseload to flexible electricity production [1]. This includes low-load operation, during which the boiler is required to operate for extended periods at loads below the minimum design value, and quick response operation, where it is required that the boiler increases its steam production rates substantially over a short period. One of the major issues associated with low-load and quick response operation of conventional baseload coal-fired units is the induced thermal stresses on boiler pressure part components. Superheater elements are especially prone to localized overheating and superheater tube failures amounts to approximately 40 % of all boiler emergency shutdowns worldwide [2]. During low-load

operation, superheaters experience lower steam flow rates which result in insufficient heat extraction from the tube walls by the steam. Poor heat removal could lead to high metal temperatures, and in turn to tube ruptures. Furthermore, low steam flow rates in manifolds and tubes could result in steam side maldistribution due to insufficient steam-side pressure drop, which would further exacerbate the localized overheating of the tubes. A sudden increase or reduction in plant load would result in rapid changes in pressure part metal temperatures, which induces dynamic thermal stresses due to large temperature gradients in boiler tubes and thick-walled components. Boiler heat exchangers that are typically prone to localized overheating during such operating conditions are the platen and pendant type superheaters [3] exposed to the direct radiant heat flux of the combustion gases in the upstream furnace. Heat transfer to the platen and radiant pendant superheaters (usually the heat exchanger located directly behind the platen superheater) is mainly driven by tri-atomic gas and particle radiation, with the convective heat transfer portion usually small compared to the total heat transfer rate. Radiative heat transfer incident on these heat exchangers is not only a function of the gas and particles adjacent to the heat exchanger banks but also of the radiation incident from upstream gas volumes located in the furnace. Radiation heat transfer absorbed by the superheaters, which originates from upstream zones, is referred to as direct radiation. Convective superheaters, as the name suggests, have a convective portion of the total heat transfer which is comparable or even higher than the radiation portion due to the geometric arrangement of the tube banks. As boiler load is reduced, the amount of flue gas produced during the combustion of the coal particles decreases due to reduced fuel feed rates. The convective heat transfer in convective superheaters, therefore, scales nearly linear with plant load as it is flue gas flow rate and temperaturedependent. This is not the case for radiant superheaters, as the radiation effects are not flue gas flow rate dependent but rather gas temperature, gas composition, particle temperature, particle concentration and particle composition dependent. One could, therefore, expect higher radiant superheater metal temperatures at reduced loads compared to the 100 % load case. It is crucial to be able to estimate metal temperatures in radiant superheaters at various loads to reduce plant downtime, determine safe operating limits and estimate residual life of critical pressure parts. To determine the effect of flexible operation of coal-fired units on the radiant superheater metal temperatures with sufficient accuracy requires detailed mathematical models able to capture the 3D gas side heat flux distribution, steam side flow distribution and heat transfer within heat exchanger elements and adjacent manifolds. Previously, numerous researchers have investigated the thermal performance of boiler superheaters using 0D and 1D process modelling approaches to investigate dynamic and steady effects and 3D CFD (computational fluid dynamics) to study fluid flow profiles and heat flux distributions in boiler gas paths. Recently Hajebzadeh et al. [4] developed a 0D mathematical model of an entire boiler plant using the log mean temperature difference (LMTD) method and empirical correlations for radiative and convective heat transfer to model the thermal performance of the radiant heat exchangers. The direct radiation leaving the furnace, which is incident on the radiant superheaters, was calculated as the average furnace heat flux times the superheater frontal area. Starkloff et al. [5] built a 1D finite volume method (FVM) dynamic model of a tower-type coal-fired plant’s water and flue gas circuit and applied the model to investigate flexible operation. The convective heat transfer was modelled by using a simple 0D equation which uses an empirical constant based on heat exchanger geometry and a flue gas mass flow rate scaling constant. The radiative heat transfer was calculated using the Hottel equation for gas radiation. The direct radiation emitted from the furnace

combustion gases was not accounted for. Rousseau and Gwebu [6] developed a dynamic radiant pendant superheater model. They used a quasi-2D approach, where the steam side was discretized along its flow path and the flue gas was divided into control volumes, which corresponded to the volume surrounding each longitudinal set of tubes in the cross-flow heat exchanger. The heat transfer was, similarly to [4], modelled using the LMTD approach and the direct radiation not accounted for. The previously mentioned 0D/1D research does not consider any 3D effects on the gas side, which contribute significantly to the thermal performance of the radiant heat exchangers. 3D CFD simulations enable the influence of the upstream combustion chamber fluid flow and heat transfer phenomena on the downstream heat exchangers to be included. Currently, coal-fired boiler CFD studies are focused primarily on combustion dynamics. The complete simulation of the water and gas side dynamics in a 3D CFD model would require extensive computational resources. More applicable models of heat exchangers and their internal flow medium are therefore utilized [3]. 3D simulation of the water circuit would not necessarily offer more accurate predictive capabilities compared to 1D modelling approaches which use empirical pressure drop and heat transfer correlations. Traditionally, in CFD boiler simulations platen superheaters are modelled as zero-thickness walls with fixed thermal boundary conditions [8]. Pendant superheaters and other heat exchangers (such as economizers) are usually approximated as porous zones with imposed flow resistances and heat extraction rates, which are incorporated as source terms in the momentum and energy conservation equations [9]. These simplified approximations of the water circuit dynamics in the 3D CFD simulations are unable to capture any waterside flow and heat transfer effects and, from a thermal-hydraulic pointof-view, over constrains the model and makes the approach unsuitable for flexibility studies. Avagianos et al. [7] used Aspen Plus to model the boiler heat exchangers’ performance of an actual lignite-fired boiler. The purpose was to investigate heat exchanger off-design performance. [7] used the process parameters as boundary conditions for CFD models of the flue gas side. The CFD models were in turn used to estimate heat fluxes to the membrane walls and convective heat exchangers. These heat flux results were fed back to a thermodynamic model to estimate off-design performance through a decoupled iterative technique. One approach to incorporate the waterside thermal-hydraulic effects, without the need for modelling all the tubes and pipework explicitly in CFD, is to perform coupled simulations. Coupled simulations entail solving the gas side of the boiler using a 3D CFD code and the water circuit using a 1D process simulation code. Modliński et al. [3] developed a 1D macro heat exchanger model (MHEM) which was coupled to a 3D CFD code to simulate the steam and gas side fluid flow and heat transfer of a pendant-type reheater. The CFD model included the combustion chamber dynamics and heat exchangers upstream of the reheater. The MHEM discretized the heat exchanger zone in the CFD model into multiple small porous zones. Given the gas temperature, velocity and gas composition in each porous zone the respective convective and radiative heat transfer coefficients were calculated and, in turn, the heat extraction rate using an LMTD method. The radiative component is accounted for by using an empirical correlation which calculates an effective radiation heat transfer coefficient which is a function of wall emissivity, flue gas and particle emissivity, gas temperature in the porous zone and the calculated tube wall outer temperature. Therefore, this approach only accounts for the radiation being emitted by the immediate gas volume in the porous zone. The analyzed reheater [3] is located sufficiently far downstream from the combustion chamber that the direct radiation from the furnace gases are insignificant and thus not included in the study.

Park et al. [10] performed a steady-state analysis of the heat transfer in an 800 MWe tangentially-fired pulverized coal boiler by co-simulating a 3D CFD model of the gas side with a 1D process model of the evaporator, superheaters and downstream heat exchangers. All heat exchangers were modelled using the porous zone approach. Chen et al. [11] developed a coupled simulation model of a 1000 MWe oncethrough pulverized coal-fired unit. In this study, the effect of coupling and decoupling the waterside and gas side simulations on the predicted tube metal temperatures were investigated. Similar to the previous studies, the porous zone approach was used to approximate the heat sink terms in the heat exchanger zones. Schuhbauer et al. [12] developed a coupled simulation approach and applied it to model a 1010 MWe once-through hard coal-fired boiler. Porous zone approximations were used to simulate the heat extraction of the heat exchanger gas volumes. Similarly to [3], the standard porous zone approach was adjusted to include the effect of adjacent gas and particle radiation heat transfer. It was found that by adjusting the porous zone models to compensate for the gas and particle radiation, the combustion chamber exit gas temperature was still higher than the expected value. The reason being that the radiation heat transfer emitted from the combustion chamber into the superheater and reheater zones was not accounted for because the heat exchanger walls were not explicitly modelled. The incident upstream radiation could therefore not interact with the heat exchangers. Schuhbauer et al. [12] accounted for the direct radiation leaving the furnace and absorbed by the superheaters using manually applied source terms. To accurately capture the thermal performance of the radiant superheaters at various loads, and to use the model to investigate metal temperatures during flexible operation, the model should properly account for the gas, particle and direct radiation. To accomplish this the radiant superheater walls should be modelled explicitly rather than using porous zones, and the walls should be used as the interface between the 3D and 1D models. The current paper presents the development, use and validation of a steady-state coupled modelling methodology that employs the 3D FVM to solve the combustion and heat transfer (convective and radiative) of the boiler flue gas side, and a 1D FVM approach to model the steam side flow and heat transfer of a radiant superheater. The 3D gas side and 1D steam side simulations interface at the walls of the radiant superheater elements. The superheater walls are thus explicitly modelled in the CFD simulation rather than using the zero thickness or porous zone approaches. To validate the modelling approach a 620 MWe drum-type boiler’s final stage radiant superheater was selected as a case study. The selected superheater was instrumented with 28 thermocouples measuring the outlet steam temperatures per transverse element. These are used to validate the predicted gas side heat flux distribution and steam side flow distribution at 99 % and 65 % boiler loads. Along with the thermocouple readings, boiler process data was extracted from the distributed control system (DCS) for a period of five hours per load case to further validate the model’s performance and determine input boundary conditions such as air and fuel flow rates. The CFD model of the gas side includes the necessary upstream components which affect the thermal performance of the final stage radiant superheater, including combustion and heat transfer in the furnace and platen superheater. The CFD model of the furnace and superheaters was developed in ANSYS Fluent® 19.2 and the 1D flow and heat transfer of the steam side was modelled using Flownex SE® 2018. The two simulation codes were coupled using an ANSYS Server Interface and the coupled simulation iterations and convergence was managed by custom developed Python scripts.

2. Case study boiler The current coupled simulation model was developed for an actual 620 MWe pulverized coal-fired subcritical drum-type boiler. The unit has a maximum continuous rating (MCR) of 477 kg/s highpressure steam supplied at 165 bar(a) and 540 °C. Additionally, the boiler has a reheat line which supplies low-pressure steam at 540 °C and 40 bar(a). Fuel and combustion air is fed via 36 wall-fired swirl burners. 2.1 Description of case study boiler and superheater The boiler under consideration has a two-pass flue gas flow path configuration. A flow diagram of the water circuit and the flue gas flow path is shown in figure 1. The water-cooled combustion chamber is constructed from fully welded vertical membrane tube walls. The platen superheater contains 20 parallel tube sheets (across the width of the boiler), with each tube sheet containing 28 steam paths (tubes). The platen superheater tubes have an outside diameter of 38 mm and an average wall thickness of 6 mm. The platen superheater has a transverse pitch of 1143 mm and a longitudinal gap between successive tubes of 1 mm. Due to the small longitudinal gap, the superheater was modelled as flat plates in the CFD model, with a thickness equal to the tube external diameter.

Figure 1: Diagram of the flue gas flow path and water circuit of case study boiler The process simulation consists of a detailed final-stage superheater model including the inlet and outlet manifolds. The final-stage superheater is located downstream from the platen superheater. The inlet steam to the final superheater is fed from the secondary attemperator, which in turn is fed from the platen superheater outlet manifolds and the spray water line. The final superheater is constructed with four legs each consisting of 7 transverse tube sheets, where each tube sheet contains 32 parallel steam paths, with a single downward and upward pass. Each of the four legs’ steam temperatures is controlled separately and therefore the steam mass flow rate and temperature at the inlet of each leg is different. The superheater has a cross-parallel flow arrangement between the flue gas and steam, with a transverse pitch of 800 mm between tube sheets and a longitudinal gap of 1 mm between successive tube rows. As mentioned each tube sheet has 32 parallel steam flow paths per pass, with increasing tube length from the innermost to the outer most tube. The arrangement of parallel steam paths also enables the tight longitudinal gap between successive tubes. Like the platen superheater, the final-stage

superheater was modelled in the CFD simulation as flat panel walls with a thickness equal to the tube external diameter. The outside diameter of the final-stage superheater is 44.5 mm. The tube sheets have three sections with each section having a different wall thickness as shown in figure 2.

Figure 2: Arrangement of final-stage superheater 2.2 Experimental data capturing and processing To validate the results generated using the simulation models, DCS data and thermocouple readings were collected. The present subsection briefly discusses data collection, sensor installation and data processing. The selected boiler was operated in steady-state at approximately 99 % and 65 % MCR for a period of 5 hours per load case, during which time various boiler process parameters were recorded. These process values were used to calculate boundary condition inputs such as air and fuel flow rates using a mass and energy balance analysis which considered various boiler heat losses taken from the design schedules of the unit. The measured main steam and attemperator flow rates along with the manifold pressures and steam temperatures were used to calculate the experimental heat loads of the three considered heat exchangers. These are the evaporator, platen superheater and final-stage superheater, with the results presented in table 1.

Table 1: Experimentally calculated boiler heat exchanger heat loads Heat exchanger Boiler heat load (MCR) Evaporator (MW) Platen superheater (MW) Final-stage superheater (MW)

Mean (Maximum, Minimum) 65 % 99 % 345 (376, 323) 538 (552, 518) 169 (174, 146) 213 (220, 198) 56 (60, 42) 74 (86, 68)

To validate the ability of the process and CFD models to capture the 3D gas side heat flux distribution incident on the final-stage superheater, 28 thermocouples were installed on the outlets of each finalstage superheater tube sheet. The 32 parallel steam paths from one heat exchanger tube sheet feed into a stub header. From the stub header, two 4" pipes feed the final-stage superheater outlet manifolds. The thermocouples were mounted on one of the stub-to-outlet manifold intermediate pipes per element. For legs A and B, the thermocouples were installed on the outer loop outlet pipe and for legs C and D on the inner leg outlet pipe. Figure 3 indicates the pipes on which the thermocouples are

installed. Figure 3: Locations of the installed thermocouples and photograph of installation (thermocouple locations are shown in orange and blue)

3. Model development In order to reduce the utilized computational resources, the left-hand and right-hand sides of the furnace CFD model was simulated separately as symmetric models and coupled with its respective final superheater leg 1D process models. In other words, the left-hand side CFD model and process models

for legs A and B was co-simulated separately from the right-hand side CFD model and the process models for legs C and D. 3.1 Steam side process modelling A 1D discretized process model of the final-stage superheater steam circuit includes conduction through the pipe walls, internal forced convection, frictional and bend pressure losses, obstruction pressure losses and manifold steam flow distribution. The external wall heat flux obtained from the CFD model is applied as an input boundary condition to the 1D process model. The steam mass flow rate, inlet steam temperature and pressure for each leg were used as boundary conditions for the process model. 3.1.1 Governing equations The steam side governing equations are solved using the commercial software package Flownex SE® 2018. This software solves the 1D discretized transport equations for systems-level thermal-hydraulic applications and offers the ability to build detailed 1D heat transfer and fluid flow models of complex problems. In the present work, the steam side is modelled as a two-phase mixture (or superheated steam, depending on the process conditions) based on the homogenous two-phase approximation. The homogenous two-phase model assumes that the two-phases are distributed evenly across the crosssectional flow area of the domain [13]. This mixture model approach uses three conservation equations and assumes the fluid properties, phase velocities and temperatures to be equal per cross-sectional slice of the 1D fluid domain. Based on these assumptions, the homogenous volume fraction 𝛼𝐻 and mixture density 𝜌𝑀 [kg/m3] is expressed as 𝛼𝐻 =

𝜌𝐿𝑥

(1)

𝜌𝐿𝑥 + 𝜌𝐺(1 ― 𝑥)

𝜌𝑀 = (1 ― 𝛼𝐻)𝜌𝐿 + 𝛼𝐻𝜌𝐺

(2)

where 𝑥 is the mixture quality and the subscripts 𝐿,𝐺 denotes the liquid and gaseous phases respectively. Using the mixture density, the 1D transport equations for a control volume can be written as follows [14]: Mass conservation: ∂ ∂ (𝜌𝑀𝐴) + (𝜌𝑀𝐴𝑢) = 0 ∂𝑡 ∂𝑠

(3)

Momentum conservation: 1∂ 1∂ ∂𝑝 𝜏𝑊𝑃 ∂𝑧 (𝜌𝑀𝐴𝑢) + (𝜌𝑀𝐴𝑢2) = ― ― ― 𝜌 𝑀𝑔 𝐴∂𝑡 𝐴∂𝑠 ∂𝑠 𝐴 ∂𝑠

(4)

Energy conservation: ∂ ∂𝑧 1∂ 1∂ 1 ∂ ∂𝑝 𝑄𝑊 (𝜌𝑀ℎ𝑀) + (𝜌𝑀𝐴𝑢ℎ𝑀) + (𝜌𝑀𝑢2) + (𝜌𝑀𝑢3𝐴) = + ― 𝑔𝜌𝑀𝑢 ∂𝑡 𝐴∂𝑠 2∂𝑡 2𝐴∂𝑠 ∂𝑡 𝑉 ∂𝑠

(5)

where 𝐴 [m2] is the cross-sectional flow area, 𝑢 [m/s] is the 1D velocity, 𝑝 [Pa] is the mixture’s pressure in the control volume, 𝜏𝑊 [Pa] is the wall shear stress, 𝑃 [m] is the flow duct perimeter, 𝑔 [m/ s2] is the gravitational acceleration constant, 𝑧 [m] is the change in elevation from the inlet to the outlet of the control volume, ℎ𝑀 [J/kg] is the mixture enthalpy, 𝑉 [m3] is the volume of the control volume and 𝑄𝑊 [W] is the total incoming heat transfer through the wall boundaries. The total incident heat transfer rate for the process model is obtained from the results of the CFD wall heat flux distributions. The internal forced heat transfer coefficient and wall conduction are solved along with the conservation equations based on the following heat transfer formulation: 𝑄𝑊 =

(6)

𝑇𝑊,𝑒𝑥𝑡 ― 𝑇𝑀

(

)

ln (𝑟𝑒𝑥𝑡/𝑟𝑖𝑛𝑡) 1 + ℎ𝑖𝑛𝑡𝑃∆𝑠 2𝜋𝑘𝑡𝑢𝑏𝑒∆𝑠

where 𝑇𝑊,𝑒𝑥𝑡 [K] is the mean external wall temperature, 𝑇𝑀 [K] is the mean internal fluid mixture temperature, ∆𝑠 [m] is the length of the control volume, ℎ𝑖𝑛𝑡 [W/m2K] is the internal two-phase forced convection coefficient, 𝑟𝑒𝑥𝑡 [m] is the external radius of the tube, 𝑟𝑖𝑛𝑡 [m] is the internal radius of the tube and 𝑘𝑡𝑢𝑏𝑒 [W/mK] is the thermal conductivity of the tube material. The internal forced convection coefficient is calculated using the well-known Dittus-Boelter correlation [15]: ℎ𝑖𝑛𝑡 = 0.023𝑅𝑒0.8𝑃𝑟0.4

(7)

3.1.2 Superheater and manifolds model As indicated earlier, each tube sheet of the final-stage superheater consists of 32 tubes in parallel that each makes one downward and one upward pass across the flue gas flow duct. All 32 tubes are different in length and have different variations of tubes thickness along the flow direction. The tube wall thicknesses are increased along the steam flow direction to compensate for the reduced strength of the tube material as the steam temperature rises. At the junctions the different tube sections as welded and the internal shoulder due to the different tube thicknesses is machined, to create a smooth transition. To limit the size of the 1D network model each tube sheet was subdivided into only eight zones (shown in figure 4 by different colouring) based on the variations in tube thicknesses and whether it is situated in the outer or inner loop (flow path), as shown in figure 4. Each of the eight zones is represented by a single flow component, which is representative of 16 steam tubes in parallel. The free flow area of the representative pipe element is the same as the total of the 16 tubes in parallel and its length is equal to the average length of the 16 tubes that it represents. For each of the four legs A, B, C and D the inlet and outlet manifolds along with interconnecting piping are also included in the process model as seen in figure 5. To accurately account for the steam side pressure drops the frictional, bending and obstruction losses were specified as secondary loss coefficients per pipe component. The complete process model comprises of all four Legs A, B, C and D, each represented by a model such as the one shown in figure 5. The average steam temperature and internal heat transfer coefficients from the heat transfer components of each representative pipe element are passed on to the CFD model as thermal boundary condition inputs. The process model, in turn, receives the average heat flux per zone (8 zones per tube sheet x 28 tube sheets) as boundary value inputs to the heat transfer components of the process model.

Figure 4: CFD model cell zones of single superheater tube sheet and 1D process model (gas flow direction from right-to-left)

Figure 5: Process model of single superheater leg, with 7 tube sheets

3.1.3 Process inlet conditions for simulated load cases For calibration and validation purposes the unit was operated in near steady state at 99 %MCR and 65 %MCR boiler loads for an extended period of time. During these periods the required DCS and thermocouple readings were captured and post-processed to determine various parameters such as boiler fuel flow rate, heat exchanger heat loads and superheater steam temperature distributions. The DCS data is used to determine the inlet conditions for the process model and the thermocouple readings will be used to calibrate and validate the modelling methodology. Inlet boundary conditions for the process models of the final-stage superheater are specified at the spray water inlet and at the platen superheater outlet locations. The outlet boundary condition is specified at the outlet of the final superheater. For the inlet boundaries, the water and steam mass flow rates and temperatures are specified, whereas for the outlet boundary only the boiler outlet pressure is provided. The steam temperatures and mass flow rates at the outlet of the platen superheater are measured per leg. Therefore, the process models’ boundary conditions for each leg are specified individually based on the DCS data. Table 2 below shows the boundary conditions used for each leg in the process model of the final superheater. Table 2: Process model boundary conditions Boundary condition 𝟗𝟗 % 𝑴𝑪𝑹 case Platen superheater mass flow rate [kg/s] Platen superheater outlet steam temperature [K] Spray water mass flow rate [kg/s] Spray water temperature [K] Superheater outlet pressure [MPa] 𝟔𝟓 % 𝑴𝑪𝑹 case Platen superheater mass flow rate [kg/s] Platen superheater outlet steam temperature [K] Spray water mass flow rate [kg/s] Spray water temperature [K] Superheater outlet pressure [MPa]

Leg A

Leg B

Leg C

Leg D

121.5 774.4 0.9 520 16.2

112.2 757.2 0.88 520 16.2

116.3 757.8 0.33 520 16.2

119.3 781.6 1.02 520 16.2

80.7 780.8 1.95 498 15.8

67.3 798.8 4.72 498 15.8

70.7 780.5 3.33 498 15.8

78.5 783.6 2.03 498 15.8

3.2 Computational fluid dynamics modelling The CFD model of the boiler flue gas side includes 18 swirl burners, a symmetric model of the furnace, a symmetric model of the platen superheater and final-stage superheater. Figure 6 shows the computational domain. The simulation of the following processes is accounted for in the CFD model: turbulent fluid flow, species transport, solid-phase dynamics, solid-phase combustion, gas-phase combustion, convective heat transfer and radiative heat transfer. The homogenous (gas) phase is modelled using the Eulerian framework and the solid particles using the Lagrangian approach. The current subsection provides an overview of the modelling methodologies used for the CFD model of the gas side fluid flow and heat transfer.

Figure 6: Computational domain of CFD model, showing furnace, superheaters and burner geometries 3.2.1 Transport equations To approximate the fluid flow, species and temperature distributions in the furnace and cross-over pass (superheater cavity) the steady-state Reynolds averaged conservation equations of mass, species and energy are solved along with the Navier-Stokes momentum conservation equations. The Reynolds stress term which arises in the momentum equation due to the averaging operation of the instantaneous velocity term is approximated using the Boussinesq hypothesis and the turbulent species mass diffusion term is approximated using the turbulent viscosity and Schmidt number. Equations 8-11 show the conservation equations solved in the CFD code [16]. Mass conservation: ∂ (𝜌𝑢𝑖) = ∂𝑥𝑖

∑𝑆

(8) 𝑗

𝐽

Momentum conservation:

{[

]} ( (

) (

))

∂𝑢𝑗 ∂𝑢𝑖 2 ∂𝑢𝑖 ∂𝑢𝑖 ∂𝑢𝑗 ∂𝑢𝑘 ∂ ∂𝑃 ∂ ∂ 2 (𝜌𝑢𝑖𝑢𝑗) + + ― 𝛿𝑖𝑗 + + ― 𝜌𝑘 + 𝜇𝑡 𝛿 ― 𝐹𝑝 = 𝜇 𝜇𝑡 ∂𝑥𝑖 ∂𝑥𝑗 ∂𝑥𝑖 ∂𝑥𝑖 ∂𝑥𝑗 3 ∂𝑥𝑖 ∂𝑥𝑖 ∂𝑥𝑗 ∂𝑥𝑖 3 ∂𝑥𝑘 𝑖𝑗

Energy conservation:

(9)

{

}

∂ ∂ ∂𝑇 (𝑢𝑖[𝜌𝐸 + 𝑃]) = 𝜆𝑒𝑓𝑓 + 𝑆ℎ ∂𝑥𝑖 ∂𝑥𝑗 ∂𝑥𝑗

(10)

Species conservation:

((

)

)

𝜇𝑡 ∂ ∂ ∂ (𝜌𝑢𝑗𝑌𝑘) = 𝜌𝐷𝑘,𝑚 + (𝑌 ) + 𝜔𝑘 + 𝑆𝑘 ∂𝑥𝑖 ∂𝑥𝑗 𝑆𝑐𝑡 ∂𝑥𝑗 𝑘

(11)

In equations 8-11 𝜌 [kg/m3] is the mixture density and is determined using the ideal gas equation of state, 𝑢𝑖 [m/s] is the velocity of the fluid volume in the direction 𝑖 and 𝑆𝑗 [kg/m3s] is the mass source term which accounts for the mass transferred from the solid phase to the gaseous phase. 𝑃 [Pa] is the static pressure of the fluid, 𝐹𝑝 is the momentum source term due to momentum exchange between the particles and the gas phase and 𝜇 [Pa.s] is the fluid mixture dynamic viscosity. 𝐸 [J/kg] is the total energy of the fluid mixture, 𝑆ℎ [W/m3] is the energy source term which accounts for energy sources and sinks such as chemical reactions and radiation transport. 𝑌𝑘 is the species mass fraction of species 𝑘, 𝜔𝑘 [kg/m3s] is the net rate of production or destruction of species 𝑘 due to chemical reactions and 𝑆𝑘 [kg/ m3s] is the discrete phase mass source. The effective thermal conductivity is calculated as 𝜆𝑒𝑓𝑓 = 𝜆 + 𝑐𝑃𝜇𝑡/𝑃𝑟𝑡

(12)

with 𝜆 [W/mK] being the thermal conductivity of the gas mixture, 𝑐𝑃 [J/kgK] the specific heat of the gas and 𝑃𝑟𝑡 the turbulent Prandtl number which is set to a constant value of 0.85. In equation 9, 11 and 12 𝜇𝑡 is the turbulent viscosity which is calculated as 𝜇𝑡 = 𝜌𝐶𝜇𝑘2/𝜀, with 𝑘 as the turbulent kinetic energy and 𝜀 being the turbulence kinetic energy dissipation rate. 𝐶𝜇 and 𝑆𝑐𝑡 are model constants and the interested reader is advised to read [16] for more details. 3.2.2 Turbulence modelling To resolve the turbulence closure problem which is induced by the Reynolds averaging of the conservation equations a two-equation turbulence model was selected which solves for the 𝑘 and 𝜀 variables known as the realizable 𝑘-𝜀 model. The realizable 𝑘-𝜀 model has been used in numerous CFD studies of pulverized coal swirl burners such as [17], [18], [19]. The model generates higher accuracy results when compared to the standard 𝑘-𝜀 model for many engineering flow problems due to its enhanced model dissipation rate formulation which is more accurate for swirling and separating flows. These types of flow phenomena are abundant in a boiler, with highly anisotropic swirling flows around the burners and separated flows found at the nose of the furnace. 3.2.3 Combustion modelling Combustion within a pulverized coal burner can be divided into four steps namely: particle heating and moisture evaporation, particle devolatilization, char oxidation and gas-phase combustion. The model equations and constants used for the simulation of the coal combustion is shown in table 3. The fuel particles enter the combustion chamber through the primary air annulus (as seen in figure 6). Once in the domain, the particles heat up via convection and radiation to 373 K, at which point the moisture starts to evaporate off the particle. Once all the moisture is removed from the particle it heats to the devolatilization temperature which for the present model is set to 553 K [9]. The devolatilization rate is calculated using a single-rate kinetic model which is a function of the mass fraction of volatiles left in the particle and particle temperature. The kinetic rate model constants were taken from the work of Sheng

et al. [20]. After all the volatiles are removed from the particle the remaining carbon reacts with oxygen in the flue gas to form 𝐶𝑂. The rate of char oxidation in the present work is calculated using the diffusion-kinetics limited char oxidation model of Baum and Street [21]. The volatiles that are released into the freeboard react with oxygen in the flue gas to form more 𝐶𝑂 as well as 𝑁2, 𝐻2𝑂 and 𝑆𝑂2, while the 𝐶𝑂 reacts further to form 𝐶𝑂2. The gas phase reaction rates, in the present work, is calculated using the eddy dissipation finite-rate turbulence-chemistry interaction model. The selected gas-phase combustion model calculates three rates namely: chemical reaction rate, the rate of turbulent production eddies dissipation and the rate of dissipation of reaction eddies and use the minimum of the three for the source term in the species and energy transport equations. For the gas phase combustion model the modelling constants proposed by Spalding was used [22]. The combination of the diffusionkinetics limited char oxidation and the eddy dissipation finite-rate gas-phase combustion models was used by [17] successfully to simulate a utility-scale pulverized coal boiler. Furthermore, a good correlation was found between the temperature and gas species predicted by the CFD model and infurnace measurements. Table 3: Summary of combustion models used in the CFD model Model and reference Single-rate kinetic devolatilization model, Char oxidation

Equation/s 𝑑𝑚𝑣𝑜𝑙 = 𝑘𝑣𝑜𝑙[𝑚0,𝑣𝑜𝑙 ― 𝑚𝑣𝑜𝑙] 𝑑𝑡 ― 𝐸𝑎,𝑣𝑜𝑙 𝑘𝑣𝑜𝑙 = 𝐴𝑣𝑜𝑙exp ( 𝑅𝑇𝑃) 𝐶(𝑠) + 0.5𝑂2(𝑔)→𝐶𝑂(𝑔) 𝑑𝑚𝑐ℎ𝑎𝑟 𝑑𝑡 𝑅𝑑𝑖𝑓𝑓 =

= ― 𝐴𝑃 5 × 10 𝐷𝑃

𝑅𝑐 = 𝐴𝑐exp ( Volatile and CO combustion (reaction rate equations for EDM-FR model seen in [16])

𝜌𝑃𝑅𝑇𝑔𝑌𝑂2 𝑅𝑑𝑖𝑓𝑓𝑅𝐶

Constants 𝐴𝑣𝑜𝑙 = 2 × 105 s ―1 𝐸𝑎,𝑣𝑜𝑙 = 6.7 × 107 J/kmol 𝐴𝑐 = 0.0053 kg/m2sPa 𝐸𝑎,𝑐 = 8.37 × 107 J/kmol.

𝑀𝑂2 𝑅𝑑𝑖𝑓𝑓 + 𝑅𝐶 𝑇𝑔 + 𝑇𝑃 0.75

―12

(

― 𝐸𝑎,𝑐

2

)

𝑅𝑇𝑃)

Reaction 1: [𝐶𝐻3.51𝑂0.78𝑁0.1106𝑆0.0466]0.2 +1.03 [𝑂2]1.3→𝐶𝑂 + 1.75𝐻2𝑂 + 0.0553𝑁2 +0.0466𝑆𝑂2 Reaction 2: [𝐶𝑂]1 +0.5[𝑂2]1.3→𝐶𝑂2

Reaction 1: 𝐴𝑟 = 2.56 × 1011 𝑠 ―1 𝐸𝑎,𝑟 = 1.081 × 108 J/kmol Reaction 2: 𝐴𝑟 = 8.83 × 1014 𝑠 ―1 𝐸𝑎,𝑟 = 9.98 × 107 J/kmol

In table 3 𝑚𝑣𝑜𝑙 is the mass of volatiles released from the particle, 𝑚0,𝑣𝑜𝑙 is the initial volatile mass of the particle before combustion, 𝑘𝑣𝑜𝑙 /(s ―1) is the Arrhenius rate of the devolatilization reaction, 𝐸𝑎,𝑣𝑜𝑙 /(J/mol) is the activation energy of the reaction, 𝐴𝑣𝑜𝑙 /(𝑠 ―1) is the pre-exponential factor of the reaction, 𝑅 is the gas constant and 𝑇 /(K) the particle temperature. 𝐴𝑃/(m2) is the particle surface area, 𝑅𝑑𝑖𝑓𝑓 the rate coefficient for the oxygen diffusion and 𝑅𝑐 is the chemical reaction rate coefficient,

𝐷𝑃 /(m) is the particle diameter, 𝑇𝑔 the gas temperature surrounding the particle and 𝑇𝑃 the particle temperature. 𝐴𝑟 is the pre-exponential factor of the chemical reaction 𝑟 and 𝐸𝑎,𝑟 is the activation energy of reaction 𝑟. 3.2.4 Heat transfer modelling The heat transfer modelling in the CFD simulation is comprised of two sections namely particle and gas radiation modelling and heat exchanger boundary conditions (wall surfaces) modelling. The radiation transport in the CFD model was solved using the Discrete Ordinates Method (DO) with angular discretization set to four divisions in both discretization angles. Fuel, char and ash particles are responsible for approximately 65 ― 90 % of the total furnace heat flux [23] and the remainder is due to emission by the tri-atomic molecules in the flue gas mixture such as 𝐶𝑂2 and 𝐻2𝑂. During the combustion of the particles their emissivity and radiation scattering efficiency changes as a function of the ash constituents, volatile fraction and char fraction. Lockwood et al. [24] and Yin et al. [25] developed models which incorporate the changes in particle radiation properties and the interested reader is advised to read the mentioned papers. In the present work, constant particle radiation parameters were used. The particle emissivity was set to 0.9 and the scattering factor to 0.6 as proposed by Blackreedy et al. [26] and used by [18], [9]. The radiation emitted by the tri-atomic molecules was approximated using the domain-based weighted sum of gray gases model (WSGGM) which accounts for the radiation emitted by the 𝐶𝑂2 and 𝐻2𝑂 molecules [19], [27]. The evaporator and superheater walls were approximated as flat planar surfaces with assigned freestream temperatures, internal heat transfer coefficients, wall thicknesses, ash deposit thicknesses and material conductivities. The modelling approach made use of ANSYS Fluent® 19.2’s convection thermal boundary condition type. In the CFD model, the wall surface temperature exposed to the flue gas was calculated using equation 13, where 𝑇𝑠,𝑖 [K] is the 𝑖𝑡ℎ boundary cell face surface temperature, 𝑇𝑤𝑎𝑡𝑒𝑟 [K] is the free stream water/steam temperature inside the tubes, 𝑄𝑖𝑛,𝑖 is the net rate of heat flowing into the wall for the 𝑖𝑡ℎ boundary face, 𝐴𝑏,𝑐𝑒𝑙𝑙,𝑖 is the surface area of face 𝑖 and 𝑈𝑖 is the overall heat transfer coefficient for boundary face 𝑖. 𝑇𝑠,𝑖 = 𝑇𝑤𝑎𝑡𝑒𝑟 +

𝑄𝑖𝑛,𝑖

(13)

𝐴𝑏,𝑐𝑒𝑙𝑙,𝑖𝑈𝑖

For the evaporator walls, the water temperature was set equal to the saturation temperature at the drum pressure and for the platen superheater equal to the average of the experimentally measured inlet and outlet steam temperatures. The free-stream water temperature for the evaporator walls was therefore set to 625 K for the 100 % MCR case and 620 K for the 65 % MCR case and the mean water temperature in the platen superheater to 698 K for 100 % MCR case and 708 K for the 65 % MCR case. For the final-stage superheater, the water temperatures for the various zones (figure 4) were calculated with the aid of the 1D process models and transferred to the CFD model. The integrated 𝑄𝑖𝑛,𝑖 boundary cell face values that correspond with the zones shown in figure 4 per tube sheet, were transferred from the CFD model to the process model and used as thermal input boundary conditions. The effective heat transfer coefficient in equation 13 is calculated using the following relation. Note that this relation excludes the gas side thermal resistance (convection and radiation) seeing as the CFD simulation will calculate it.

𝑈𝑖 =

1 1 ℎ𝑖𝑛𝑡,𝑐𝑜𝑛𝑣

+

𝑡𝑤𝑎𝑙𝑙 𝜆𝑡𝑢𝑏𝑒

(14) +

𝑡𝑎𝑠ℎ,𝑑𝑒𝑝 𝜆𝑎𝑠ℎ,𝑑𝑒𝑝

In equation 14 above, ℎ𝑐𝑜𝑛𝑣 [W/m2K] is the internal convective heat transfer coefficient. For the furnace walls ℎ𝑖𝑛𝑡,𝑐𝑜𝑛𝑣 is the two-phase flow boiling convection coefficient [28] that was determined through simulation of a simplified water circulation process model of the drum, downcomers and water wall risers and applying the calculated experimental evaporator heat loads. The calculated evaporator tube side flow boiling heat transfer coefficient for the 100 % MCR case is 53610 W/m2K and for the 65 % MCR case 43996 W/m2K. Similarly, for the platen superheater a calculation was performed using the experimental values (steam mass flow rates and temperatures) as inputs to determine the mean internal single-phase forced convection coefficients. The calculated platen superheater steam side heat transfer coefficient for the 100 % MCR case is 4767 W/m2K and for the 65 % MCR case 2718 W/m2K. For the final-stage superheater the internal forced convection coefficient was determined by the cosimulated process model and transferred to the CFD model boundary conditions. In equation 14 𝑡𝑤𝑎𝑙𝑙 [m] and 𝑡𝑎𝑠ℎ,𝑑𝑒𝑝 [m] are the tube metal and ash deposit thicknesses respectively and 𝜆𝑡𝑢𝑏𝑒 [W/mK] and 𝜆𝑎𝑠ℎ,𝑑𝑒𝑝 [W/mK] are the tube metal and ash deposit thermal conductivities. The fouling resistances ( 𝑡𝑎𝑠ℎ,𝑑𝑒𝑝 𝜆 ) for the platen and final-stage superheaters were set to 0.0066 [𝑚2K/W] and 0.011 [ 𝑎𝑠ℎ,𝑑𝑒𝑝

2

𝑚 K/W] respectively [29]. The overall heat transfer coefficient (equation 14) was calculated by assuming a flat plate geometry. To compensate for the error between the actual heat transfer area (and fin efficiency for the furnace walls) and the flat plate area, the ash deposit thickness was adjusted to yield results that compare well with the experimental heat loads for the near full load case. The previously mentioned ash deposit thermal resistances corresponds closely to values found in the relevant literature for radiant superheaters located in a coal-fired boiler [30]. Values between 0.6 ― 0.9 have been used in literature ([31], [32]) for modelling wall emissivity of pulverized coal boiler furnaces. Various values in this range have been applied in the present work and the value of 0.85 was selected since it resulted in a calculated total evaporator heat transfer rate close to the value determined from the experimental data at 99 % MCR (table 1). The selected value is a typical value found in literature [26] and was applied in the CFD model to all heat exchanger boundary walls. 3.2.5 Numerical setup As mentioned earlier, only half of the boiler furnace and superheater cavity (and tube sheets) was modelled in the CFD in order to reduce computational costs. The simulations were solved on a numerical mesh of approximately 3.5 million cells. To ensure that the simulation solution procedure is numerically stable and to reduce numerical inaccuracies, the mesh’s orthogonal quality was kept above 0.25 and the aspect ratio below 15. The momentum, energy and species transport equations were discretized using the second-order upwind method for increased accuracy and the pressure equation was discretized using the PRESTO! scheme. It was assumed that the air-fuel ratio for all swirl burners are constant for each boiler load and with pulverized coal maldistribution between the burners was neglected. The velocity profiles used for the burner inlets were acquired from a detailed burner CFD model which included the swirl plates and other burner internals. The secondary air mass flow rate per burner for the 99 % and 65 % cases were set to 14.46 kg/s and 10.5 kg/s respectively. The primary airflow rates were set to 4.82 kg/s (99 % case) and

3.5 kg/s (65 % case). The mass flow rate of coal per burner for the two simulated load cases were set to 3.13 kg/s (99 % case) and 2.07 kg/s (65 % case). The primary air inlet temperatures for both load cases were kept constant at 373 K. The inlet air temperature for the secondary air was set to 577 K ( 99 % case) and 535 K (65 % case). 3.3 Coupling of simulation codes Flownex SE® 2018 in which the 1D process model was developed has the capability to exchange input and output data with ANSYS® with the aid of a built-in interface component. The component communicates with an idle server-mode Fluent instance with a preloaded case file (and data file if needed). Flownex SE® is pointed to the correct instance of Fluent® by using the location of the latter’s identification key file location (aaS_FluentID.txt). At present the Flownex SE®’s ANSYS interface component only runs the CFD simulation after a fully converged Flownex steady-state solution is obtained or after every converged transient iteration. In order to obtain simultaneous fully converged steady-state solutions for both the Flownex SE® process model and the Fluent CFD model using the twoway coupling, one would have to manually run multiple converged Flownex SE® steady-state simulations where after a preset number of Fluent iterations are solved. Only when both models have reached convergence can the coupled simulation be considered as converged. This would entail manually initiating each steady-state simulation in Flownex SE®. In the present work this was circumvented by developing an IronPython 2.7 script that automatically calls a preset number of Flownex SE® steadystate solutions, and after each converged steady-state solution also calls a preset number of Fluent® iterations. Figure 7 below shows the solution flow diagram for the coupled simulation. After convergence of each process model simulation, the relevant output parameters are transferred to the CFD thermal boundary input conditions via the ANSYS® interface component, and after each CFD simulation, the output parameters are transferred to the process model as inputs to the relevant process model components.

Figure 7: Coupled simulation solution flow chart The interface boundaries for the two simulation frameworks are the external tube surfaces of the final superheater. The steam side temperature, 𝑇𝑗𝑤𝑎𝑡𝑒𝑟, and internal forced convection coefficient, ℎ𝑗𝑖𝑛𝑡,𝑐𝑜𝑛𝑣, per tube sheet zone component 𝑗 (figure 4) are calculated via the process model. These values are sent to the CFD code as Fluent input parameters which in turn are used for the thermal boundary conditions. This is followed by doing 𝑀 steady-state CFD iterations. Once the CFD iterations are completed the areaweighted average wall heat fluxes 𝑞𝑗 are calculated and returned to the process model via Fluent’s output parameter functionality. The heat flux values are distributed to the relevant tube sheet zone heat transfer components in the process model. The complete co-simulation process is repeated 𝑁 times, until the CFD simulation is converged.

4. Results and discussion To evaluate the thermal performance accuracy of the modelling approach, a high-level comparison of the evaporator, platen superheater and final-stage superheater heat loads was performed where the simulation results are compared to the experimental values found in table 1. For the 99 % MCR case the evaporator, platen superheater and final superheater total heat transfer rates were calculated as 541 MW, 218 MW and 80 MW, which are within 0.6%, 2.3% and 8.1% respectively of the experimental values. For the 65 % MCR the heat loads were calculated as 357 MW, 152 MW and 59 MW, which are within 3.5%, 10.1% and 5.4% respectively of the experimental values. These results show that the coupled simulation models can capture the overall thermal performance of the three heat exchangers modelled here with good accuracy.

Figures 8 and 9 show the inlet and outlet flue gas temperature and inlet velocity distributions for the final-stage superheater for the 99 % MCR and 65 % MCR cases respectively. Since the inlet temperature and velocity distributions are found at the outlet of the platen superheater, the figures also show the positions of the platen superheater elements. For the 99 % MCR load case the gas temperatures and velocities form typical “M” shaped profiles, which are not unexpected. At the inlet plane, the high gas temperature zones are distributed uniformly over a relatively large area while at the outlet plane it is more concentrated and positioned higher up. The temperature and velocity profiles are also relatively symmetric around the centre line of the flue gas flow path.

Figure 8: 99 % MCR case flue gas temperature and velocity distribution For the part-load case, the high gas temperature and velocity zones are located lower down and are less uniformly distributed compared to the full load case. The temperature and velocity distributions are also less symmetric than in the full load case.

Figure 9: 65 % MCR case flue gas temperature and velocity distribution Figure 10 shows the predicted steam outlet temperatures together with the corresponding measured thermocouple values. As shown earlier in figure 3 the measurements were only taken for the outer loops of legs A and B and only for the inner loops of legs C and D.

Figure 10: Simulated and measured steam outlet temperatures For the 99 %MCR case the temperature profile of the simulated values compares well with the measured values of leg A (elements 1-7) and leg D (elements 22-28). For leg B (elements 8-14) and leg C

(elements 15-21), the predicted temperatures decrease from the outside towards the centre of the boiler, which is opposite to what is observed in the measurements. Similar trends are observed for the 65 %MCR case, but the difference between the simulated and measured values for leg B and leg C is more pronounced. A possible cause for the difference between the predicted and measured temperatures of legs B and C could be maldistribution of fuel flow rates to the individual burners, which was not accounted for in the current work. This possibility will have to be tested in future work by representing the fuel flow rates to different burners more accurately. This would shift the flame and incident flow profile on the heat exchanger. Another possible cause could be non-uniform ash deposition. Overall the model is able to predict the average steam outlet temperatures for all four legs with sufficient accuracy, as shown in table 4. Table 4: Predicted and measured averaged outlet steam temperatures 𝟔𝟓 % load case Predicted Measured (min, max) Leg A 550 547 (541, 551) Leg B 538 542 (534, 550) Leg C 514 524 (518, 528) Leg D 540 534 (530, 539)

Predicted 547 545 533 537

𝟗𝟗 % load case Measured (min, max) 544 (540, 548) 540 (536, 544) 527 (523, 531) 535 (532, 537)

Figure 10 shows that on average the measured outlet temperatures for legs A and B are higher than those of legs C and D which corresponds to the higher outlet steam temperatures shown in table 4. This is simply because for legs A and B the thermocouples are mounted on the outer loops while for legs C and D they are mounted on the inner loops. Since the coupled simulation provides results for both the inner and outer loops it can be compared directly for all the elements as shown in figure 11. Figure 11 shows that the outer loops have higher outlet temperatures for all tube sheets in all cases. This is partly due to the lower steam flow rates through the outer loops compared to the inner loops as well as higher heat fluxes incident on the outer loops. The inner and outer loops of each tube sheet enter a common stub header as seen in figure 2 and 3. Due to the large temperature difference between the inner and outer loops a significant temperature gradient will exist along the length of the stub header which would induce detrimental thermal stresses.

Figure 11: Comparison between the simulated steam outlet temperatures and mass flow rates for the inner and outer loops per tube sheet The predicted steam mass flow rates for the inner and outer loops are also shown per tube sheet in figure 11 (bottom). The results show very little maldistribution for the respective loops in each leg. However, there is a noticeable difference in mass flow rate between inner and outer loops of each tube sheet. This is due to the increased frictional pressure drop of the outer loop which has a longer pipe length as well as higher heat transfer, which results in a lower average density and higher velocity and in turn in a higher pressure drop. It is noted that the difference between the inner and outer loop mass flow rates and outlet steam temperatures is smaller for the lower load case, which would result in lower induced thermal stresses in the stub headers compared to the full load case temperatures. Figure 12 shows the heat flux surface contours for the final-stage superheater. Table 5 shows the total heat transfer rate for the inner and outer loops per leg (steam flow path). The difference in heat load between the inner and outer loops varies between 4 ― 20 % depending on position and boiler load, which coincides with the behaviour observed in figure 11 where the outer loop has a higher pressure drop and thus reduced mass flow rate.

Figure 12: Final-stage superheater heat flux Table 5: Leg-averaged inner and outer loop heat absorption rates Leg A (Inner) [MW] A (Outer) [MW] B (Inner) [MW] B (Outer) [MW]

Load case 65 99 7.63 10.48 7.92 11.1 6.67 9.12 7.48 9.58

Leg C (Inner) [MW] C (Outer) [MW] D (Inner) [MW] D (Outer) [MW]

Load case 65 99 6.11 7.68 7.01 9.6 7.79 11.12 8.09 12.14

5. Conclusions The paper presented a steady-state coupled modelling methodology that employs the 3D FVM to solve the combustion and heat transfer of the boiler flue gas side, and a 1D FVM approach to model the steam side flow and heat transfer of a radiant superheater. The results show that the approach can capture the details of the temperature maldistribution between legs in the same heat exchanger, between elements in the same leg and between the inner and outer loops of the same element for different load cases. This level of detail has not been captured before by other researchers and could be valuable to evaluate the temperature gradients occurring on the outlet manifolds at different loads. However, it requires calibration of the model with the aid of measurements by adjusting the fouling resistances. Furthermore, the cause of the difference in the trends observed on the inner legs have not been clarified satisfactorily and requires further attention. It is suspected that it is due to maldistribution in the pulverized fuel flow rates to different burners which is not accounted for in the present work and needs to be investigated further.

The detailed modelling approach also captures the steam flow maldistribution between the inner and outer loops of the respective elements and show that there is very little maldistribution between the elements. On the flue gas side the results show that for the part-load case, the high gas temperature and velocity zones are located lower down and are less uniformly distributed compared to the full load case. The temperature and velocity distributions are also less symmetric than in the full load case. The calculated total heat transfer rates for the evaporator, platen superheater and final superheater compare well with the experimental values for both the 99 % MCR and 65 % MCR load cases. This shows that the coupled simulation models can capture the overall thermal performance of the three heat exchangers modelled here with good accuracy.

6. Acknowledgements The authors would like to thank the staff of Eskom SOC Ltd for providing crucial data used for model validation and Ms Lethukuthula Vilakazi for collecting the on-site data. Computations were performed using facilities provided by the University of Cape Town’s ICTS HighPerformance Computing team: hpc.uct.ac.za Funding: The authors would like to thank Eskom EPPEI program for funding this project.

References [1]

G. Sankar, D. S. Kumar, and K. R. Balasubramanian, “Computational modeling of pulverized coal fired boilers – A review on the current position,” Fuel, vol. 236, no. September 2018, pp. 643–665, 2019.

[2]

D. Taler, M. Trojan, P. Dzierwa, K. Kaczmarski, and J. Taler, “Numerical simulation of convective superheaters in steam boilers,” Int. J. Therm. Sci., vol. 129, no. March, pp. 320–333, 2018.

[3]

N. Modlinski, K. Szczepanek, and D. Nabag, “Mathematical procedure for predicting tube metal temperature in the second stage reheater of the operating fl exibly steam boiler,” Appl. Therm. Eng., vol. 146, no. October 2018, pp. 854–865, 2019.

[4]

H. Hajebzadeh, A. N. M. Ansari, and S. Niazi, “Mathematical modeling and validation of a 320 MW tangentially fired boiler: A case study,” Appl. Therm. Eng., vol. 146, no. September 2018, pp. 232– 242, 2019.

[5]

R. Starkloff, F. Alobaid, K. Karner, B. Epple, M. Schmitz, and F. Boehm, “Development and validation of a dynamic simulation model for a large coal- fired power plant,” Appl. Therm. Eng., vol. 91, pp. 496–506, 2015.

[6]

P. G. Rousseau, E. Z. Gwebu, “Modelling of a Superheater Heat Exchanger with Complex Flow Arrangement Including Flow and Temperature Maldistribution,” Heat transfer Engineering, vol. 40, pp.862-878, 2019.

[7]

I. Avagianos et al., “Predictive method for low load off -design operation of a lignite fired power plant,” Fuel, vol. 209, no. April, pp. 685–693, 2017.

[8]

P. J. Edge, P. J. Heggs, M. Pourkashanian, and P. L. Stephenson, “Integrated fl uid dynamicsprocess modelling of a coal- fired power plant with carbon capture,” Appl. Therm. Eng., vol. 60, no.

1–2, pp. 242–250, 2013. [9]

V. Ranade and D. Gupta, Computational modelling of pulverzied coal fired boilers, 1st ed. Boca Raton: Taylor & Francis, 2015.

[10]

H. Y. Park, M. Faulkner, M. D. Turrell, P. J. Stopford, and D. S. Kang, “Coupled fluid dynamics and whole plant simulation of coal combustion in a tangentially-fired boiler,” Fuel, vol. 89, no. 8, pp. 2001–2010, 2010.

[11]

T. Chen, Y. Zhang, M. Liao, and W. Wang, “Coupled modeling of combustion and hydrodynamics for a coal-fired supercritical boiler,” Fuel, vol. 240, no. December 2018, pp. 49–56, 2019.

[12]

C. Schuhbauer, M. Angerer, H. Spliethoff, F. Kluger, and H. Tschaffon, “Coupled simulation of a tangentially hard coal fired 700 ° C boiler,” Fuel, vol. 122, pp. 149–163, 2014.

[13]

MTech, Flownex SE 2018 Theory Guide. Potchefstroom, 2018.

[14]

S. Levy, Two-phase flow in complex systems, 1st ed. USA: John Wiley & Sons, 1999.

[15]

Y. Cengel, Heat transfer: A practical approach, 2nd ed. USA: McGraw-Hill, 2003.

[16]

ANSYS, “ANSYS Fluent Theory Guide.” 2018.

[17]

M. Chernetskiy, A. Dekterev, N. Chernetskaya, and K. Hanjalić, “Effects of reburning mechanicallyactivated micronized coal on reduction of NOx: Computational study of a real-scale tangentiallyfired boiler,” Fuel, vol. 214, no. May 2016, pp. 215–229, 2018.

[18]

A. Đugum and K. Hanjalić, “Numerical simulation of coal-air mixture flow in a real double-swirl burner and implications on combustion anomalies in a utility boiler,” Energy, vol 170., pp. 942953, 2018.

[19]

N. Modlinski, “Computational modeling of a utility boiler tangentially-fired furnace retrofitted with swirl burners,” Fuel Process. Technol., vol. 91, no. 11, pp. 1601–1608, 2010.

[20]

C. Sheng, B. Moghtaderi, R. Gupta, and T. F. Wall, “A computational fluid dynamics based study of the combustion characteristics of coal blends in pulverised coal-fired furnace,” Fuel, vol. 83, no. 11–12, pp. 1543–1552, 2004.

[21]

M. Baum and P. Street, “Predicting the combustion behaviour of coal particles,” Combust. Sci. Technolodgy, vol. 3, no. 43, p. 231, 1971.

[22]

D. Spalding, “Mixing and chemical reaction in steady confined turbulent flames,” in Symposium (International) on combustion, 1971, vol. 13, no. 1, pp. 649–657.

[23]

P. Basu, C. Kefa, and L. Jestin, Boilers and burners: Design and theory, 1st ed. New York: Springer, 2000.

[24]

F. Lockwood, S. Rizvi, and N. Shah, “Comparative predictive experience of coal firing,” Proc Inst Mech Eng, vol. 200, pp. 79–86, 1986.

[25]

C. Yin and J. Yan, “Oxy-fuel combustion of pulverized fuels : Combustion fundamentals and modeling,” Appl. Energy, vol. 162, pp. 742–762, 2016.

[26]

R. Blackreedy et al., “Modeling pulverized coal combustion using a detailed coal combustion model,” Combust. Sci. Technolodgy, vol. 178, pp. 763–787, 2006.

[27]

G. D. Rago et al., “CFD analysis of a swirl stabilized coal combustion burner,” Energy Procedia, vol. 148, pp. 703–711, 2018.

[28]

Flownex, “Flownex SE 2018 Theory Guide.” 2018.

[29]

R. Laubscher and P. Rousseau, “International Journal of Heat and Mass Transfer Numerical investigation into the effect of burner swirl direction on furnace and superheater heat absorption for a 620 MWe opposing wall-fired pulverized coal boiler,” Int. J. Heat Mass Transf., vol. 137, pp. 506–522, 2019.

[30]

Y. Zhang, Q. Li, and Z. Zhou, Theory and Calculation of Heat Transfer in Furnaces, 1st ed. London: Elsevier Ltd, 2016.

[31]

T. Asotani, T. Yamashita, H. Tominaga, Y. Uesugi, Y. Itaya, and S. Mori, “Prediction of ignition behavior in a tangentially fired pulverized coal boiler using CFD,” Fuel, vol. 87, no. 4–5, pp. 482– 490, 2008.

[32]

M. Y. Chernetskiy, A. A. Dekterev, A. P. Burdukov, and K. Hanjalić, “Computational modeling of autothermal combustion of mechanically-activated micronized coal,” Fuel, vol. 135, pp. 443–458, 2014.

Ryno Laubscher: conceptualization, methodology, software, validation, formal analysis, investigation, writing – original draft, visualization. Pieter Rousseau: writing – review & editing, resources, conceptualization.

Highlights:    

Detailed co-simulation of 1D process and 3D CFD simulations Validation of simulation results using multiple steam temperature measurements Good correlation between simulated and measured steam temperatures Outer loop tubes have lower steam flow rates due to heat load and pressure drop