# Three-Dimensional CFD Model Development and Validation for Once-Through Steam Generator (OTSG): Coupling Combustion, Heat Transfer and Steam Generation

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

## 3. Mathematical Model

#### 3.1. Fireside (Combustion CFD Model)

#### 3.2. Waterside (Multiphase CFD Model)

#### 3.3. Coupling between Waterside (Multiphase CFD) and Fireside (Combustion CFD)

- Heat fluxes (from Fireside);
- Heat transfer coefficient and Temperature (from Waterside).

## 4. CFD Model Setup

#### 4.1. Geometrical Model

- 1.
- The structural members (beams, etc.) inside the furnace were not modeled. They do not take part into the fluid flow simulation, and the effect of their presence is assumed to be negligible;
- 2.
- The inlet boundaries of the simulation are the air inlet duct to the windbox and the fuel pipe inlet. It is assumed that the flow is steady and homogeneous;
- 3.
- For this particular case, the burner model consists of the two burner tips. One half circle is type 1 burner tips and another half circle is the type 2 burner tips according to the burner manufacture drawings. Type 1 burner tips direct the fuel jet inward (Figure 5) while Type 2 burner tips jet the gas parallel to the centerline or slightly outward (Figure 6).
- 4.
- The outlet of the simulation was cut off after the end point of stack where the flue gas exit joins with the stack. Atmospheric pressure was applied at the stack outlet;
- 5.
- All furnace surfaces were assumed to be adiabatic with a specific radiant emissivity;
- 6.
- For the sake of simplicity, the geometry of finned tubes was not considered in the geometry model. The computational time would be substantially increased without this simplification. Instead, the equivalence diameter approach for finned tubes was adopted, thus the physical shape of individual fins is not included in the solid model.

#### 4.2. Mesh Generation

#### 4.3. Solution Strategy

## 5. Results and Discussion

#### 5.1. Validation

#### 5.2. Coupling

#### 5.3. Results

## 6. Cost and Benefit of CFD Approach

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Charles, E.; Baukal, J. The John Zink Hamworthy Combustion Handbook; CRC Press: Boca Raton, FL, USA, 2013. [Google Scholar]
- Khoshhal, A.; Rahimi, M.; Alsairafi, A.A. The CFD Modeling of NOx Emission, HiTAC and Heat Transfer in an Industrial Boiler. Numer. Heat Transf. Part A Appl.
**2010**, 58, 295–312. [Google Scholar] [CrossRef] - Thornock, J.N.; Spinti, J.P.; Hradisky, M. Evaluating the NOx Performance of a Steam Generator for Heavy Oil Production; American Flame Research Committee: Houston, TX, USA, 2014. [Google Scholar]
- Liu, B.; Wang, Y.-H.; Xu, H. Numerical Study of the Effect of Staged Gun and Quarl on the Performance of Low-NOx Burners. J. Energy Eng.
**2016**, 142, 04015040. [Google Scholar] [CrossRef] - Ye, K.; Zhang, Y.; Lin, J.; Li, N.; Yang, Y.; Li, Z.; Hao, J.; Chen, Y. CFD Analysis of the Primary Side in a Helical-Coil Once-Through Steam Generator. In Proceedings of the 2017 25th International Conference on Nuclear Engineering, Shanghai, China, 2–6 July 2017. [Google Scholar] [CrossRef]
- Liu, B.; Bao, B.; Wang, Y.; Xu, H. Numerical simulation of flow, combustion and NO emission of a fuel-staged industrial gas burner. J. Energy Inst.
**2017**, 90, 441–451. [Google Scholar] [CrossRef] - Singha, A.; Forcinito, M. Emission Characteristic Map and Optimization of NOx in 100 MW Staged Combustion Once-Through-Steam-Generator (OTSG). In Proceedings of the AFRC Indsutrial Combustion Symposium, Salt Lake City, UT, USA, 17–19 September 2018. [Google Scholar]
- Singha, A.; Forcinito, M. Modelling Different Aspects of Once though Steam Generators. In Proceedings of the NAFEMS World Congress (NWC), Quebec City, QC, Canada, 17–20 June 2019. [Google Scholar]
- Drosatos, P.; Nikolopoulos, N.; Kakaras, E. An in-house built code incorporated into CFD model for the simulation of boiler’s convection section. Fuel Process. Technol.
**2020**, 202, 106333. [Google Scholar] [CrossRef] - Echi, S.; Bouabidi, A.; Driss, Z.; Abid, M.S. CFD simulation and optimization of industrial boiler. Energy
**2019**, 169, 105–114. [Google Scholar] [CrossRef] - Du, Y.; Wang, C.; Lv, Q.; Li, D.; Liu, H.; Che, D. CFD investigation on combustion and NOx emission characteristics in a 600MW wall-fired boiler under high temperature and strong reducing atmosphere. Appl. Therm. Eng.
**2017**, 126, 407–418. [Google Scholar] [CrossRef] - Kang, M.S.; Jeong, H.J.; Massoudi Farid, M.; Hwang, J. Effect of staged combustion on low NOx emission from an industrial-scale fuel oil combustor in South Korea. Fuel
**2017**, 210, 282–289. [Google Scholar] [CrossRef] - Schluckner, C.; Gaber, C.; Landfahrer, M.; Demuth, M.; Hochenauer, C. Fast and accurate CFD-model for NOx emission prediction during oxy-fuel combustion of natural gas using detailed chemical kinetics. Fuel
**2020**, 264, 116841. [Google Scholar] [CrossRef] - Shih, T.H.; Liou, W.W.; Shabbir, A.; Yang, Z.; Zhu, J. A new k-ϵ eddy viscosity model for high reynolds number turbulent flows. Comput. Fluids
**1995**, 24, 227–238. [Google Scholar] [CrossRef] - Carvelho, M.G.; Farias, T.; Fontes, P. Predicting radiative heat transfer in absorbing, emitting and scattering media using the discrete transfer model, in FiveLand. In Fundamentals of Radiation Heat Transfer; ASME: New York, NY, USA, 1991; pp. 17–24. [Google Scholar]
- Coppalle, A.; Vervisch, P. The total emissivities of high-temperature flames. Combust. Flame
**1983**, 49, 101–108. [Google Scholar] [CrossRef] - Westbrook, C.K.; Dryer, F.L. Chemical kinetic modeling of hydrocarbon combustion Prog. Energy Combust. Sci.
**1984**, 10, 1–57. [Google Scholar] [CrossRef] - ANSYS Fluent Theory Guide; Ansys, Inc.: Canonsburg, PA, USA, 2014.
- Kurul, N.; Podowski, M.Z. On the modeling of multidimensional effects in boiling channels. In Proceedings of the 27th National Heat Transfer Conference, Minneapolis, MN, USA, 28–31 July 1991. [Google Scholar]
- Askari, E. Development, Validation and Application of Population Balance Models in Eulerian Approach for Bubbly Flow Reactors. Ph.D. Thesis, Sherbrooke University, Sherbrooke, QC, Canada, 2018. [Google Scholar]
- Rabiee, R. Analysis of Heat Transfer by Boiling and Condensation Inside a Horizontal Heat Pipe. Ph.D. Thesis, Sherbrooke University, Sherbrooke, QC, Canada, 2019. [Google Scholar]
- ANSYS CFX Theory Guide; Ansys, Inc.: Canonsburg, PA, USA, 2014.
- Ishii, M.; Zuber, N. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J.
**1979**, 25, 843–855. [Google Scholar] [CrossRef] - Tomiyama, A.; Celata, G.; Hosokawa, S.; Yoshida, S. Terminal velocity of single bubbles in surface tension force dominant regime. Int. J. Multiph. Flow
**2002**, 28, 1497–1519. [Google Scholar] [CrossRef] - Behzadi, A.; Issa, R.I.; Rusche, H. Modeling of dispersed bubble and droplet flow at high phase fractions. Chem. Eng. Sci.
**2003**, 59, 795. [Google Scholar] - API Standard 560; Fired Heaters for General Refinery Service; Energy API: Washington, DC, USA, 2016.
- Li, R.; Yamaguchi, A.; Ninokata, H. Computational Fluid Dynamics Study of Liquid Droplet Impingement of Erosion in the Inner Wall of a Bent Pipe. J. Power Energy Syst.
**2010**, 4, 327. [Google Scholar] [CrossRef] [Green Version] - Charles, E.; Baukal, J. The Industrial Burners Handbook; CRC Press: Boca Raton, FL, USA, 2003. [Google Scholar]

**Figure 16.**Flue gas streamlines with drop pressure contour profile on the convention box with (

**a**) and without fins (

**b**) on Second Tubes.

**Figure 20.**CO concentration distribution in the convection section-[CO] volume average = 6.84 [ppm].

Item | Description |
---|---|

Size | Pilot scale |

Firing rate | 1.7 MW |

Burner type | Free-Jet |

Target steam quality | 80% |

Parameter | Value |
---|---|

Fuel inlet mass flow | 0.0345 kg/s |

Combustion air inlet mass flow | 0.67 kg/s |

Combustion air inlet temperature | 75 ${}^{\xb0}$C |

Fuel inlet temperature | 40 ${}^{\xb0}$C |

Stack outlet pressure | Atmospheric |

Component | mol. % | |
---|---|---|

Hydrogen | ${\mathrm{H}}_{2}$ | 0.04 |

Methane | ${\mathrm{CH}}_{4}$ | 92.46 |

Ethane | ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$ | 5.85 |

Propane | ${\mathrm{C}}_{3}{\mathrm{H}}_{8}$ | 1.64 |

**Table 4.**Five-step combustion mechanism [17].

Reaction | Arrhenius Expression |
---|---|

${\mathrm{CH}}_{4}+\frac{3}{2}{\mathrm{O}}_{2}\to \mathrm{CO}+2{\mathrm{H}}_{2}\mathrm{O}$ | ${R}_{i,1}=1.0\times {10}^{10}\mathrm{exp}\left(\frac{-125,604}{RT}\right){\left[C{H}_{4}\right]}^{-0.3}{\left[{O}_{2}\right]}^{1.3}$ |

${\mathrm{C}}_{2}{\mathrm{H}}_{6}+\frac{5}{2}{\mathrm{O}}_{2}\to 2\mathrm{CO}+3{\mathrm{H}}_{2}\mathrm{O}$ | ${R}_{i,2}=1.0\times {10}^{12}\mathrm{exp}\left(\frac{-125,604}{RT}\right){\left[{C}_{2}{H}_{6}\right]}^{0.1}{\left[{O}_{2}\right]}^{1.65}$ |

${\mathrm{C}}_{3}{\mathrm{H}}_{8}+\frac{7}{2}{\mathrm{O}}_{2}\to 3\mathrm{CO}+4{\mathrm{H}}_{2}\mathrm{O}$ | ${R}_{i,3}=1.0\times {10}^{12}\mathrm{exp}\left(\frac{-125,604}{RT}\right){\left[{C}_{3}{H}_{8}\right]}^{0.1}{\left[{O}_{2}\right]}^{1.65}$ |

$\mathrm{CO}+\frac{1}{2}{\mathrm{O}}_{2}\to {\mathrm{CO}}_{2}$ | ${R}_{i,4}=1.0\times {10}^{14}\mathrm{exp}\left(\frac{-167,472}{RT}\right)\left[CO\right]{\left[{H}_{2}O\right]}^{0.5}{\left[{O}_{2}\right]}^{0.25}$ |

${\mathrm{H}}_{2}+\frac{1}{2}{\mathrm{O}}_{2}\to {\mathrm{H}}_{2}\mathrm{O}$ | ${R}_{i,5}=1.0\times {10}^{15}\mathrm{exp}\left(\frac{-100}{RT}\right)\left[{H}_{2}\right]\left[{O}_{2}\right]$ |

**Table 5.**Governing equations of Fireside [18].

Equation | Formulation |
---|---|

Continuity (single-phase) | $\frac{\partial \rho}{\partial t}+\nabla \xb7\left(\rho \mathbf{U}\right)=0$ |

Momentum (single-phase) | $\frac{\partial}{\partial t}\left(\rho \mathbf{U}\right)+\nabla \xb7\left(\rho \mathbf{U}\mathbf{U}\right)=-\nabla p+\nabla \xb7{\overline{\overline{\tau}}}_{\mathrm{effi}}$ |

Reynolds stress tensor | ${\overline{\overline{\tau}}}_{\mathrm{effi}}=\left({\mu}_{\mathrm{lam}}+{\mu}_{\mathrm{t}}\right)\left(\nabla \mathbf{U}+\nabla {\mathbf{U}}^{T}\right)-\frac{2}{3}\left(\rho k+\left({\mu}_{\mathrm{lam}}+{\mu}_{\mathrm{t}}\right)\nabla \xb7\mathbf{U}\right)\overline{\overline{I}}$ |

Realizable k-$\u03f5$ model | $\frac{\partial}{\partial t}\left(\rho k\right)+\nabla \xb7\left(\rho \mathbf{U}k\right)=\nabla \xb7\left(\frac{\mu}{{\sigma}_{\mathrm{k}}}\nabla k\right)+{G}_{k}+{G}_{b}-\rho \u03f5-{Y}_{M}+{S}_{k}$ |

$\frac{\partial}{\partial t}\left(\rho \u03f5\right)+\nabla \xb7\left(\rho \mathbf{U}\u03f5\right)=\nabla \xb7\left(\frac{{\mu}_{\mathrm{t}}}{{\sigma}_{\mathrm{ffl}}}\nabla \u03f5\right)+\rho {C}_{1}S\u03f5-\rho {C}_{2}\frac{{\u03f5}^{2}}{k+\sqrt{\nu \u03f5}}+{G}_{\u03f5}\frac{\u03f5}{k}{C}_{3\u03f5}{G}_{b}+{S}_{\u03f5}$ | |

${C}_{1}=max\left[0.43,\frac{\eta}{\eta +5}\right]$, $\eta =S\frac{k}{\u03f5}$, $S=\sqrt{2{S}_{ij}{S}_{ij}}$ | |

Energy equation | $\frac{\partial}{\partial t}\left(\rho E\right)+\nabla \xb7\left(\rho \mathbf{U}E\right)=\nabla \xb7(k+{k}_{t}\xb7\nabla T)+\nabla \xb7(\tau \xb7\mathbf{U})+\nabla \xb7\left(p\mathbf{U}\right)+{S}_{r}+{S}_{k}$ |

DO model | $\nabla \xb7\left(I(\overrightarrow{r},\overrightarrow{s})\right)\overrightarrow{s}+(a+{\sigma}_{s})I(\overrightarrow{r},\overrightarrow{s})=a{n}^{2}\frac{\sigma {T}^{4}}{\pi}+\frac{{\sigma}_{s}}{4\pi}{\int}_{0}^{4\pi}I(\overrightarrow{s},\overrightarrow{{s}^{\prime}})d{\mathrm{\Omega}}^{\prime}$ |

Species transport equation | $\frac{\partial}{\partial t}\left(\rho {m}_{l}\right)+\nabla \xb7\left(\rho \mathbf{U}{m}_{l}\right)=\nabla \xb7\left((\rho D+\frac{{\mu}_{t}}{{\sigma}_{m}})\nabla m\right)+{R}_{l}$ |

EDM model | ${R}_{i,r}={\nu}_{i,r}^{\prime}{M}_{w,i}A\rho \frac{\u03f5}{k}{\mathrm{min}}_{\Re}\left(\frac{{Y}_{R}}{{\nu}_{\Re ,r}^{\prime}{M}_{w,\Re}}\right)$ |

${R}_{i,r}={\nu}_{i,r}^{\prime}{M}_{w,i}AB\rho \frac{\u03f5}{k}\left[\frac{{\mathrm{\Sigma}}_{p}{Y}_{p}}{{\mathrm{\sum}}_{j}^{N}\nu {\u2033}_{j,r}{M}_{w,j}}\right]$ |

Model | Type or/and Value |
---|---|

Turbulence | realizable k-$\u03f5$ model |

Wall function | non-equilibrium |

Radiation | DOM |

Gas absorption properties | grey-gas model |

Combustion | 5-step mechanism EDM/Finite rate model |

Heat Transfer towards Tubes | steam/water temperature and inside heat transfer coeff. |

Tube metal | emissivity = 0.85 |

Burner tile | adiabatic; emissivity = 0.65 |

Transition from the convection section to stack | adiabatic; emissivity = 0.65 |

Refractory walls of the radiant section and the convection section | adiabatic; emissivity = 0.65 |

Stack walls | adiabatic; emissivity = 0.65 |

**Table 7.**Governing equations of Waterside [22].

Equation | Formulation |
---|---|

Continuity | $\frac{\partial}{\partial t}\left({\rho}_{\mathrm{i}}{\alpha}_{\mathrm{i}}\right)+\nabla \xb7\left({\alpha}_{\mathrm{i}}{\rho}_{\mathrm{i}}{\mathbf{U}}_{\mathrm{i}}\right)={\mathsf{\Gamma}}_{ij}^{+}-{\mathsf{\Gamma}}_{ji}^{+}$ |

Momentum | $\frac{\partial}{\partial t}\left({\rho}_{\mathrm{i}}{\alpha}_{\mathrm{i}}{\mathbf{U}}_{\mathrm{i}}\right)+\nabla \xb7\left({\alpha}_{\mathrm{i}}{\rho}_{\mathrm{i}}{\mathbf{U}}_{\mathrm{i}}{\mathbf{U}}_{\mathrm{i}}\right)=-{\alpha}_{\mathrm{i}}\nabla p+\nabla \xb7\left({\alpha}_{i}{\overline{\overline{\tau}}}_{\mathrm{effi},i}\right)+{\mathbf{R}}_{\mathrm{i}}+{\mathbf{F}}_{\mathrm{i}}+{\alpha}_{\mathrm{i}}{\rho}_{\mathrm{i}}\mathbf{g}++({\mathsf{\Gamma}}_{ij}^{+}{\mathbf{U}}_{\mathrm{j}}-{\mathsf{\Gamma}}_{ij}^{+}{\mathbf{U}}_{\mathrm{i}})$ |

Reynolds stress tensor | ${\overline{\overline{\tau}}}_{\mathrm{effi},\mathrm{i}}=\left({\mu}_{\mathrm{lam},\mathrm{i}}+{\mu}_{\mathrm{t},\mathrm{i}}\right)\left(\nabla {\mathbf{U}}_{\mathrm{i}}+\nabla {\mathbf{U}}_{\mathrm{i}}^{T}\right)-\frac{2}{3}\left({\rho}_{i}{k}_{i}+\left({\mu}_{\mathrm{lam},\mathrm{i}}+{\mu}_{\mathrm{t},\mathrm{i}}\right)\nabla \xb7{\mathbf{U}}_{\mathrm{i}}\right)\overline{\overline{I}}$ |

Interfacial momentum exchange | ${\mathbf{R}}_{\mathrm{G}}=-{\mathbf{R}}_{\mathrm{L}}={\mathbf{R}}_{\mathrm{G},\mathrm{drag}}+{\mathbf{R}}_{\mathrm{G},\mathrm{lift}}+{\mathbf{R}}_{\mathrm{G},\mathrm{vm}}$ |

Liquid–gas exchange coefficient | $K=\frac{3}{4}{\rho}_{\mathrm{L}}{\alpha}_{\mathrm{G}}\frac{{C}_{\mathrm{D}}}{{d}_{32}}\mid {\mathbf{U}}_{\mathrm{G}}-{\mathbf{U}}_{\mathrm{L}}\mid ({\mathbf{U}}_{\mathrm{G}}-{\mathbf{U}}_{\mathrm{L}})+{\alpha}_{\mathrm{G}}{C}_{\mathrm{l}}{\rho}_{\mathrm{L}}{\mathbf{U}}_{\mathbf{r}}\times (\nabla \times {\mathbf{U}}_{\mathbf{L}})+{\alpha}_{\mathrm{L}}{C}_{\mathrm{vm}}{\rho}_{\mathrm{L}}\left(\frac{{D}_{L}{\mathbf{U}}_{\mathbf{L}}}{Dt}-\frac{{D}_{G}{\mathbf{U}}_{\mathbf{G}}}{Dt}\right)$ |

Ishii–Zuber drag coefficient [23] | ${C}_{D}=max\{min[\frac{2}{3}\sqrt{\mathrm{Eo}},\frac{8}{3}],\frac{24}{\mathrm{Re}}(1+0.1{\mathrm{Re}}^{0.75})\}$ |

Energy | $\frac{\partial}{\partial t}\left({\rho}_{\mathrm{i}}{\alpha}_{\mathrm{i}}{h}_{\mathrm{i}}\right)+\nabla \xb7\left({\alpha}_{\mathrm{i}}{\rho}_{\mathrm{i}}{h}_{\mathrm{i}}{\mathbf{U}}_{\mathrm{i}}\right)=\nabla \xb7\left[\alpha \mathrm{i}\left({\mathbf{q}}_{\mathrm{i}}+{\mathbf{q}}_{\mathrm{i}}^{t}\right)\right]+{\alpha}_{\mathrm{i}}\frac{DP}{Dt}+({\mathsf{\Gamma}}_{ij}^{+}{h}_{\mathrm{j}}-{\mathsf{\Gamma}}_{ij}^{+}{h}_{\mathrm{i}})+{Q}_{i}+{q}_{\mathrm{wall}}^{\u2033}{A}_{\mathrm{wall}}^{\u2033}$ |

${\mathbf{q}}_{\mathrm{i}}=-\frac{{\lambda}_{i}}{{C}_{p,i}}\overrightarrow{\nabla}{h}_{\mathrm{i}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}{\mathbf{q}}_{\mathrm{i}}^{t}=-\frac{{\lambda}_{i}^{t}}{{C}_{p,i}}\overrightarrow{\nabla}{h}_{\mathrm{i}}$ | |

${\mathsf{\Gamma}}_{\mathrm{ij}}^{+}=\frac{{q}_{\mathrm{wall}}^{e\u2033}}{{h}_{tv}}A{\u2033}_{\mathrm{wall}}$ | |

${\mathsf{\Gamma}}_{\mathrm{ji}}^{+}=\frac{{h}_{\mathrm{int}}\left({T}_{\mathrm{sat}}-{T}_{b}\right){a}_{\mathrm{int}}}{{h}_{\mathrm{tv}}}$ | |

RPI boiling model | $q{\u2033}_{\mathrm{wall}}={q}_{\mathrm{wall}}^{c\u2033}+{q}_{\mathrm{wall}}^{e\u2033}+{q}_{\mathrm{wall}}^{q\u2033}$ |

${q}_{\mathrm{wall}}^{c\u2033}={h}_{c}({T}_{w}-{T}_{l})(1-{A}_{b})$ | |

${q}_{\mathrm{wall}}^{q\u2033}=\frac{2K}{\sqrt{\pi {\lambda}_{l}T}}({T}_{w}-{T}_{l})$ | |

${q}_{\mathrm{wall}}^{e\u2033}={V}_{d}{N}_{w}{\rho}_{\nu}{h}_{\mathrm{fv}}$ | |

Tomiyama lift coefficient [24] | ${C}_{l}=\left\{\begin{array}{c}min(0.288tanh\left(0.121\mathrm{Re}\right),f\left({\mathrm{Eo}}_{G}\right))\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4.pt}{0ex}}\phantom{\rule{4.pt}{0ex}}\phantom{\rule{4.pt}{0ex}}{\mathrm{Eo}}_{G}<4\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\hfill \\ f\left({\mathrm{Eo}}_{G}\right)\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}4\le {\mathrm{Eo}}_{G}\le 10.7\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}\hfill \end{array}\right.$ |

Mixture k-$\u03f5$ model [25] | $\frac{\partial}{\partial t}\left({\rho}_{\mathrm{m}}{k}_{\mathrm{m}}\right)+\nabla \xb7\left({\rho}_{\mathrm{m}}{\mathbf{U}}_{\mathrm{m}}{k}_{\mathrm{m}}\right)=\nabla \xb7\left(\frac{{\mu}_{\mathrm{t},\mathrm{m}}}{{\sigma}_{\mathrm{k}}}\nabla {k}_{\mathrm{m}}\right)+{P}_{k}^{\mathrm{m}}-{\rho}_{\mathrm{m}}{\u03f5}_{\mathrm{m}}+{S}_{k}^{\mathrm{m}}$ |

$\frac{\partial}{\partial t}\left({\rho}_{\mathrm{m}}{\u03f5}_{\mathrm{m}}\right)+\nabla \xb7\left({\rho}_{\mathrm{m}}{\mathbf{U}}_{\mathrm{m}}{\u03f5}_{\mathrm{m}}\right)=\nabla \xb7\left(\frac{{\mu}_{\mathrm{t},\mathrm{m}}}{{\sigma}_{\u03f5}}\nabla {k}_{\mathrm{m}}\right)+\frac{{\u03f5}_{m}}{{k}_{m}}\left({C}_{1\u03f5}{G}_{\mathrm{k},\mathrm{m}}-{C}_{2\u03f5}{\rho}_{\mathrm{m}}{\u03f5}_{\mathrm{m}}\right)+{C}_{\u03f53}\frac{{\u03f5}_{m}}{{\u03f5}_{k}}{S}_{k}^{\mathrm{m}}$ |

Model | Type or/and Value |
---|---|

Turbulence | Mixture k-$\u03f5$ model |

Drag coefficient | Ishii-Zuber |

Lift coefficient | Tomiyama lift coefficient |

Boiling | RPI model |

Bubble size model | constant (${\mathrm{d}}_{\mathrm{o}}=5\phantom{\rule{3.33333pt}{0ex}}\mathrm{mm}$) |

Assembly | No. Cells |
---|---|

Burner-Radiant section (Fireside) | 33 M |

Convective-Stack section (Fireside) | 6 M |

First Tubes (Waterside) | 12 M |

Second Tubes (Waterside) | 13 M |

Radiant Tubes (Waterside) | 14 M |

Assembly | Approximate Wall-Clock Time [h] |
---|---|

First Tubes (convection section) | 120 |

Second Tubes (convection section) | 300 |

Radiant Tubes | 320 |

Parameter | Field Data | CFD |
---|---|---|

Average radiant section flux [kW/m${}^{2}$] | 52.77 | 47.576 |

Flue gas temperature leaving the radiant section [${}^{\xb0}$C] | 1144 | 1152.18 |

Tube ID | Field Data [kW/m${}^{2}$] | CFD [kW/m${}^{2}$] |
---|---|---|

$\#1$ | 52.96 | 51.85 |

$\#2$ | 30.57 | 24.5 |

Tube ID | Field Data [kW/m${}^{2}$] | CFD (w/o Fins) [kW/m${}^{2}$] | CFD (with Fins) [kW/m${}^{2}$] |
---|---|---|---|

$\#3$ | 54.06 | 20.85 | 50.6 |

$\#4$ | 29.87 | 17.78 | 28.61 |

$\#5$ | 13.30 | 16.18 | 17.17 |

Tube Number | ${\mathbf{q}\u2033}_{\mathbf{intial}\phantom{\rule{3.33333pt}{0ex}}\mathbf{point},\mathbf{furnace}-5}\phantom{\rule{3.33333pt}{0ex}}[\mathbf{kW}/{\mathbf{m}}^{2}]$ | ${\mathbf{q}\u2033}_{\mathbf{first}\phantom{\rule{3.33333pt}{0ex}}\mathbf{iteration}}\phantom{\rule{3.33333pt}{0ex}}[\mathbf{kW}/{\mathbf{m}}^{2}]$ | ${\mathbf{q}\u2033}_{\mathbf{second}\phantom{\rule{3.33333pt}{0ex}}\mathbf{iteration}}\phantom{\rule{3.33333pt}{0ex}}[\mathbf{kW}/{\mathbf{m}}^{2}]$ |
---|---|---|---|

#1 | 9612 | 16,932 | 16,839 |

#2 | 9509 | 16,772 | 16,683 |

#3 | 9408 | 16,552 | 16,454 |

#4 | 9310 | 16,748 | 16,635 |

#5 | 9212 | 16,962 | 16,855 |

#6 | 9112 | 17,003 | 16,886 |

#7 | 12,073 | 16,689 | 16,581 |

#8 | 11,971 | 16,847 | 16,746 |

#9 | 11,871 | 16,821 | 16,709 |

#10 | 11,774 | 16,339 | 16,223 |

#11 | 11,676 | 16,629 | 16,518 |

#12 | 11,574 | 16,807 | 16,682 |

#13 | 15,361 | 17,739 | 17,629 |

#14 | 15,193 | 17,842 | 17,716 |

#15 | 15,029 | 17,969 | 17,850 |

#16 | 14,864 | 17,985 | 17,855 |

#17 | 14,701 | 18,022 | 17,897 |

#18 | 14,540 | 18,080 | 17,943 |

#19 | 19,421 | 17,351 | 17,249 |

#20 | 19,260 | 17,341 | 17,246 |

#21 | 19,094 | 17,395 | 17,291 |

#22 | 18,936 | 17,501 | 17,402 |

#23 | 18,783 | 17,516 | 17,425 |

#24 | 18,626 | 17,574 | 17,469 |

Absorbed Heat Rate at Radiant Section [MW] | Absorbed Heat Rate at Convection Section [MW] | Overall OTSG Efficiency % | |
---|---|---|---|

Field data | 0.71 | 0.834 | 90.8 |

CFD (w/o fins) | 0.735 | 0.617 | 79 |

CFD (with fins) | 0.735 | 0.806 | 90.6 |

Tube ID | Max. TMTs [${}^{\xb0}$C] Coil Design Datasheet | Max. TMTs [${}^{\xb0}$C] CFD |
---|---|---|

$\#1$ | 395.3 | 338.3 |

$\#2$ | 347.5 | 324.4 |

$\#3$ | 347.5 | 328.2 |

$\#4$ | 377.4 | 265.1 |

$\#5$ | 377.4 | 222 |

$\#6$ | 377.4 | 200 |

Zone # | Maximum [kw/m${}^{2}$] | Average [kw/m${}^{2}$] | CFF |
---|---|---|---|

$\#1$ | 30.56 | 19.7 | 1.5 |

$\#2$ | 68.5 | 28.15 | 2.43 |

$\#3$ | 129.4 | 59.07 | 2.91 |

Steam Quality | Bulk Velocity [m/s] | |
---|---|---|

BFW inlet (OTSG inlet) | 0% | 1.6 |

Radiant section outlet (OTSG exit) | 80% | 18 |

Project Type | Timeframe | Cost |
---|---|---|

Traditional design approach [28] | 2 years | $2 M |

CFD approach | up to 12 months | $500 K–$750 K (based on industrial experience) |

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## Share and Cite

**MDPI and ACS Style**

Askari Mahvelati, E.; Forcinito, M.; Fitschy, L.; Maesen, A.
Three-Dimensional CFD Model Development and Validation for Once-Through Steam Generator (OTSG): Coupling Combustion, Heat Transfer and Steam Generation. *ChemEngineering* **2022**, *6*, 23.
https://doi.org/10.3390/chemengineering6020023

**AMA Style**

Askari Mahvelati E, Forcinito M, Fitschy L, Maesen A.
Three-Dimensional CFD Model Development and Validation for Once-Through Steam Generator (OTSG): Coupling Combustion, Heat Transfer and Steam Generation. *ChemEngineering*. 2022; 6(2):23.
https://doi.org/10.3390/chemengineering6020023

**Chicago/Turabian Style**

Askari Mahvelati, Ehsan, Mario Forcinito, Laurent Fitschy, and Arthur Maesen.
2022. "Three-Dimensional CFD Model Development and Validation for Once-Through Steam Generator (OTSG): Coupling Combustion, Heat Transfer and Steam Generation" *ChemEngineering* 6, no. 2: 23.
https://doi.org/10.3390/chemengineering6020023