Numerical investigation of radiative transfer during oxyfuel combustion of hydrogen and hydrogen enriched natural gas in the container glass industry

The substitution of natural gas with hydrogen is one way to eliminate direct CO2 emissions. However, oxyfuel combustion of hydrogen or hydrogen enriched natural gas leads to different exhaust gas properties due to a changed composition compared to conventional combustion. In combustion simulation, the emissivity of a gas mixture is usually approximated using a Weighted Sum of Gray Gases (WSGG) model. Most of the existing WSGG models have been validated for natural gas combustion with air or oxyfuel and are therefore not applicable to hydrogen-oxyfuel combustion. CFD simulations showed, that none of the investigated WSGG models is able to predict the radiative heat transfer for all considered combustion scenarios with appropriate accuracy. In addition, in container glass manufacturing more than 95% of the heat flux to the glass surface is transferred by radiation because of the high process temperatures. Due to the changed gray gas emissivity, the high content of water vapor leads to a different emission spectrum of the exhaust gas. The influence of the changed emission spectrum on radiative heat transfer and the penetration depth of radiation in the glass melt is investigated using a simulation model of a pilot plant and non-gray modelling of the radiation transport. The CFD simulations show slightly enhanced radiative heat transfer to the glass and a slightly deeper penetration depth especially for wavelength below 2.2 μm for hydrogen-oxyfuel combustion.


Introduction
With the European Green Deal, the European Union established the goal of Europe becoming the first climate-neutral continent.In order to reach this goal, especially the energy-intensive industries need to eliminate their CO2 emissions [1].In container glass production, about 85% of the required energy is used for the melting process where soda, sand, glass shards and other ingredients are heated up to about 1450°C, refined and afterwards cooled to a temperature suitable for forming of glass containers.This is usually done in a natural gas-powered end fired glass furnace with air combustion and up to 20% electrical boosting.For a CO2-neutral container glass production different approaches are being followed.One is an all-electric furnace with a cold top, another possibility is to substitute natural gas with green hydrogen or hybrid solutions [2].Both ways eliminate the energy-related CO2 emissions.In addition, the raw-material related emissions need to be considered as well.These emissions can locally be avoided with a carbonate free batch composition.This will be studied in a pilot hybrid glass melting furnace which is being built as part of the BMWK founded ZeroCO2Glas project.This paper focuses on the substitution of natural gas with hydrogen oxyfuel with a conventional batch composition and the effects coming with it regarding heat transfer.
In many technical plants, radiative heat transfer is the dominant heat transfer mechanism due to the high process temperatures [3].Since experiments evaluating the radiative heat transfer between surfaces through a scattering, absorbing and emitting gaseous media are often hard to realize, the radiation modeling is an important alternative.Due to the high dependencies of the radiative properties on the wavelength, temperature and spatial direction, the accurate calculation of heat transfer can easily cause large computational costs.The recent literature regarding the accuracy of CFD simulation of combustion systems mainly focuses on the influence of turbulence-chemistry interaction.Radiation is often modeled using a gray approach or an optical thin simplification.These approaches can lead to an underprediction of up to 100°C of temperature depending on the conditions or inaccurate calculation due to spectral variations of the radiative properties [4].In addition, many gray models were only developed and validated for natural gas-air combustion [5].

Hydrogen combustion
Due to the different gas properties of hydrogen compared to natural gas, many combustion properties differ as well.Table 1 shows an overview of the important properties for hydrogen and methane, the main component of natural gas.The water vapor content in the flue gas for oxyfuel combustion with an air ratio of λ=1 rises with the hydrogen content in the fuel gas up to 100% while the CO2 proportion decreases until 0%.For combustion with air the maximum H2O content of 34.7% is reached with pure hydrogen as fuel gas.The emission spectrum of water and carbon dioxide differ, which leads to a change in the gray gas emissivity calculated according to Alberti [8].

Radiative transfer and the WSGG model
The Weighted Sum of Gray Gases model is a global approach for calculating the gray emissivity ε of gases according to formula (1).Where T is the Temperature, κ is the absorptivity, p the pressure and s the optical path length [5].Hottel and Sarafim [9] proposed the approximation in 1970 and many authors modified the model and parameter sets since then.The gray emissivity of gases or gas mixtures is thereby calculated as the sum of partial intensities using usually four or five (j) gray gases plus one transparent one.The radiative properties of these gray gases are assumed constant over the whole spectrum [5].
The temperature dependence of factor aε,I is normally approximated by but it is also possible to use any other function.The values for bε,i,j and κi are nowadays usually obtained by fitting the emissivity to Line-by-line calculations.In earlier papers different methods like exponential wide band modelling or spatial integration of the radiative transfer equation (RTE) were used to calculate an emissivity as reference [5].In a participating medium like the flue gas of a combustion absorption, emission and scattering take place.(3) When it comes to computational costs the advantage of using the WSGG model is, that the integration over the spectrum happens before solving the RTE, so the RTE only needs to be solved once for every direction needed to determine the radiation field.The LBL method on the other hand computes an emissivity for every line of the spectrum resulting in the need of solving the RTE for each of the lines for every direction [10].For modelling of complex industrial applications, the WSSG model often is chosen and delivers accurate estimates [11].Most WSGG formulations offer different sets of parameters depending on the gas composition in the cell.The composition is generally characterized by the molar ratio of the partial pressure of H2O to the partial pressure of CO2, figure 2 shows the molar ratio of the flue gas as a function of the hydrogen content in the fuel gas [5].hydrogen admixtures Many WSGG authors proposed WSGG formulations with improved accuracy for natural gas-oxyfuel combustion or operating points of special interest.A choice of relevant WSGG models are listed in table 2. ANSYS Fluent, as used for the calculations in this paper, computes the emissivity with the WSGG coefficients proposed by Smith [12] or Coppalle [13] depending on the Temperature [14].Due to the varying molar ratio considered in Bordbar's 2014 formulation and the consideration of all molar ratios in his 2020 formulation, these are the two models which will be compared to the commonly used Smith/Coppalle and the LBL based calculation by Alberti in the following.

Radiative properties of glass melts
The probably most significant property of glass is its permeability to visible light.When it comes to industrial glass production, the rapid change of the absorption over the wavelength has a significant influence on the overall process.Figure 3 shows the spectral absorption over the spectrum obtained with the transmission method for a flint glass with 0.02 wt% Fe2+.The radiative properties of a flint glass are mainly determined by the Fe2+ absorption bands since it nearly does not contain Cr2O3 [21].In Figure 3, the sudden increase in absorption at a wavelength of about 2.75 μm is particularly noticeable.The glass melt is therefore transmissive for lower wavelengths and more impervious for radiation of longer wavelengths.Water vapor has more bands at lower wavelength and emits more radiation in the transmissive band of the glass.The typical mean free path lm of photons in a clear silicate flint container glass melt for the more transparent spectral region is about 20 cm [22].The refractive index of the glass melt is assumed to be 1.5 according to Rubin [23].

Description of the test cases
In the following section the CFD test cases are described.

Test case for WSGG Model testing
For comparison of the selected WSGG models a test case was set up.For the 3D CFD simulation, the geometry and the refractory material properties of a pilot glass melting furnace were used.The ceiling is located 1 m above the glass bath and has a fixed temperature of 1773 K and an emissivity of 0.5.The glass surface is 1700 K and the fuel gas in between has a fixed temperature of 2000 K.The fuel gas emissivities were calculated using the WSGG parameters of the selected models for a mean beam length s of 0.899 m, according to the definition in ANSYS Fluents Theory Guide [14] where V is the volume considered and A is the area of the surrounding walls, see formula (4).The volume and absorbing area were obtained from the geometry of a planned pilot glass melting furnace.
The target value of the calculation is the heat flux density on the glass surface.

Test case for radiative transfer in the glass melt
For evaluating the radiative transfer in the glass melt the CFD model was extended to include the glass melt.The depth of the glass bath is 0.75 m as in the planned pilot melting furnace.The radiation transport in the glass melt was modelled with the non-gray Discrete Ordinates Method.To consider the variation of the absorption by the glass melt over the wavelength, three non-gray bands were implemented, as recommended in the ANSYS Fluent Users Guide [24].The absorption coefficients of the gas for the three bands were obtained from Line-by-Line calculations of the HITEMP 2010 [25] database and are listed in table 3. Due to the high computational costs of these calculations in this paper only natural gasoxyfuel and hydrogen-oxyfuel were considered for the comparison of the radiation transport in the glass melt.The glass surface was treated as Coupled Wall being semi-transparent for radiation.

Results and discussion
The following section discusses the results of the CFD

Results of WSGG model testing
Figure 4 shows the radiation heat flux received by the glass surface for different WSGG formulations.When comparing figure 4 (a) and (b) it becomes clear that oxyfuel combustion results in a higher heat flux to the glass bath.This is due to the higher content of radiating gas components.However, the lower exhaust gas volume is not considered in this calculation.For both, oxyfuel and air combustion, the WSGG model by Smith/Coppalle shows a deviation of at least 10 to 22 kW.This is equal to 5-12% for oxyfuel and 7-14% for combustion with air.The heat flux is thereby underestimated for oxyfuel and overestimated for air fuel.pure water vapour at 1 atm were given.This explains the great deviation of the predicted heat flux for combustion with air.None of the tested models can be safely used for all considered combustion scenarios.

Results of radiation transport in the glass melt
In total, 15.9 kW/m 3 more radiation is absorbed by the glass melt when switching to hydrogen-oxyfuel combustion, while just considering the different flue gas composition at the same temperature.To evaluate the origin of the increased heat flux, the radiation received by a horizontal area in dependence of the glass bath depth is shown in figure 5.It becomes clear that the biggest difference in the heat flux occurs in Band 0, where for hydrogen-oxyfuel at the surface 21 kW/m 2 more are absorbed by the glass melt.In addition, the radiation penetrates the glass slightly deeper for fuel gas composition of hydrogenoxyfuel combustion.The difference in radiation heat flux is significantly lower for Bands 1 and 2.

Conclusion and outlook
None of the evaluated WSGG Models delivers suitable results for all investigated operating points.To enable all combustion scenarios to be calculated with one model, new coefficients need to be fitted, especially for water vapor at different partial pressures, or different WSGG Models need to be combined.The simulation of the radiation depth with the three gray bands in the glass melt shows a slightly increased heat transfer for hydrogen-oxyfuel compared to natural gas oxyfuel.This is mainly caused by radiation at wavelengths below 2.2 μm.The obtained difference needs to be evaluated further regarding its impact on the formation of the flow in the glass melt.

Figure 2 .
Figure 2. Molar ratio of H2O to CO2 for the flue gas of combustion of natural gas with different hydrogen admixtures Many WSGG authors proposed WSGG formulations with improved accuracy for natural gas-oxyfuel combustion or operating points of special interest.A choice of relevant WSGG models are listed in table 2. ANSYS Fluent, as used for the calculations in this paper, computes the emissivity with the WSGG coefficients proposed by Smith[12] or Coppalle[13] depending on the Temperature[14].

TheFigure 4 .
Figure 4. Radiative heat flux received by the glass surface calculated with different WSGG formulations for different H2-contents in the fuel gas for (a) oxyfuel and (b) combustion with air

Figure 5 .
Figure 5.Comparison of incident radiation heat flux near the glass surface due to the gas radiation This is consistent with the differences in the emissivity shown in table 3.
[1] European Comission 2019 Communication from the comission to the european pariliament, the european council, the european economic and social committee and the committee of the regions The European Green Deal [2] Matthias Leisin 2019 Energiewende in der Industrie: Potentiale und Wechselwirkungen mit dem Energiesektor, Branchensteckbrief der Glasindustrie Bericht an Bundesministerium für Wirtschaft und Energie [3] Wang P, Fan F, Li Q 2014 Accuracy evaluation of the gray gas radiation model in CFD simulation Case Studies in Thermal Engineering vol 3 [4] Moest M F, Haworth D C 2016 Radiative Heat Transfer in Turbulent Combustion Systems (Springer) ed F A Kulacki 40th UIT International Heat Transfer Conference (UIT 2023) Journal of Physics: Conference Series 2685 (2024) 012032

Table 2 .
Overview of recent or commonly used WSGG Models

Table 3 .
Emissivity calculated by Line-by-Line calculations for the three gray bands for an optical path length of 0.899 m