Large eddy simulations of the UMD line burner with the conditional moment closure method

Abstract

The conditional moment closure (CMC) method is applied in combination with large eddy simulations (LES-CMC) to the UMD line burner configuration. This corresponds to a low-strain, buoyant diffusion flame. The low strain rate conditions are representative of fire conditions and the aim of the study is to evaluate LES-CMC results, including radiative effects. Only conditions far from extinction are studied. The weighted sum of grey gases model (WSGGM) for radiation is applied in mixture fraction space. Results are compared to what is obtained when radiation is taken into account as a local loss term in the conditional heat release rate, with prescribed radiative fraction. It is shown that the conditional scalar dissipation rate (CSDR) profile in mixture fraction space and the spatial terms in the transport equations for the conditional quantities have a major impact with the non-local WSGGM approach, while this is not the case in adiabatic simulations, nor in the radiative fraction approach. In the latter, only the value of the CSDR at stoichiometric is important, making this approach less sensitive. However, the latter are not well suited for extinction simulations.

Introduction

Thanks to the remarkable rise in the available computational power, the LES approach has become very popular in turbulent combustion simulations. A major advantage is that large-scale turbulence effects are captured and models for the sub-grid scale (SGS) eddies are universal in nature. In non-premixed combustion in particular, turbulence governs the mixing of fuel and oxidizer. This is one reason why LES has been popular for fire simulations. Related to this, the very important phenomenon of entrainment, i.e., the mixing of air into the flame zone and into the smoke plume, is much better resolved in LES than with RANS, because the large scale unsteadiness and the puffing phenomenon are captured. This explains why LES is the default approach for turbulence in the two most widely used CFD codes for fire simulations, namely FDS [1] and FireFOAM [2].

Whereas the effect of turbulence in turbulent reacting flows, and in fires in particular, is known to be very important, an important observation in fire configurations is the relatively large size of the flame region, compared to lab-scale (jet) flames. The size of fuel involved at the inlet is of the order of tens of centimeters and flames can easily be more than 1 m high. This has implications on the fineness of the computational mesh: given that computational domains are large in volume, mm size mesh cells cannot be afforded. Hence, this can pose issues with respect to the resolution of turbulence. The effect of turbulence in turbulent reacting flows, and in fires in particular, is known to be very important. In the present study, we use the Smagorinsky model [3]. Moreover, turbulence – chemistry interaction (TCI) and turbulence – radiation interaction (TRI) are important to consider. With respect to TCI, there are many options [4]. One option is the use of the conditional moment closure (CMC) method, as developed in Ref. [5]. Some examples of LES-CMC simulations of turbulent flames are [[6], [7], [8], [9], [10]]. An important advantage of this technique is the potential to include finite-rate chemistry effects. It is important to note that all configurations in Ref. [[6], [7], [8], [9], [10]] deal with jet flames, i.e., the flow field is mainly momentum-driven by a strong injected fuel (and/or air) flow and combustion takes place where mixing leads to close to stoichiometric conditions. In fires, the situation is fundamentally different: the momentum of the injected fuel and oxidizer flows is weak. The actual flow field is driven by buoyancy, which is created through the high-temperature region, as a consequence of the combustion process. This leads on the one hand to much stronger feedback loops in this overall process, but the low velocities also induce longer residence times and lower scalar dissipation rates, and hence lower mixing rates. The lower values are illustrated below for the test case under consideration (Fig. 11) and they have a very strong impact, particularly when radiation is taken into account. To the best of the authors’ knowledge, it is the first time that LES/CMC is applied to a fire related configuration.

The slow mixing rate also makes the impact of the radiation source term more pronounced, as already reported in Ref. [11]. This was also confirmed in Ref. [12], illustrating again strong coupling between the different phenomena. Through the impact on the buoyancy, this also affects the flow and mixing fields in physical space more strongly than when these are mainly determined by the momentum of the injected flows (as is the case in jet flames). This is illustrated below for the test case under consideration (Fig. 9). To the best of the authors’ knowledge, it is the first time that this aspect is studied in the context of CFD simulations for a fire related flame.

As mentioned above, there are limitations to the possible fineness of the CFD mesh in fire simulations. Yet, due to the large domains, simulations are computationally expensive. Hence, in order to reduce the computational expenses, combustion modelling in fires has relied mostly on simplified global 1-step or 2-step chemistry mechanisms. These are coupled with the eddy dissipation concept (EDC), or eddy dissipation model (EDM), combustion modelling approach. On the other hand, phenomena like extinction, re-ignition, minor species or soot, are known to strongly depend on chemical kinetics. Due to the strong coupling of phenomena, these might also affect radiation. While in principle the EDC model is capable of handling finite-rate chemistry, to the best of the authors' knowledge this has not been applied yet in fires. Reaction rates are determined from the turbulent mixing time scale, while the mixed-is-burnt assumption is made for chemical kinetics [[13], [14], [15], [16], [17]]. Extinction and re-ignition models have been implemented with EDC separately, such as in Refs. [13,14]. In Ref. [13], a strong sensitivity of the results is reported on the critical temperature of the re-ignition model. This suggests it is worthwhile to investigate more advanced models. One approach to include detailed chemistry is the application of the flamelet model, such as in Ref. [18] (where a 1-step mechanism was used), and more recently [[19], [20], [21]]. Interestingly, in Ref. [18] two models have been evaluated for the conditional scalar dissipation rate (CSDR), which represents the mixing rate of fuel and oxidizer. It was determined that the CSDR model has a stronger impact in fires than in jet flames. The effect was observed for temperature and velocity fields. It is suggested in Ref. [18] that this would be due to the laminar-to-turbulent transition in fires, jeopardizing the assumption of statistical independence of mixture fraction and scalar dissipation rate (SDR). Regardless thereof, it has been illustrated in Ref. [12] that the CSDR model indeed has a strong impact, in particular for low SDR values, if radiation is taken into account in a non-local manner in mixture fraction space. This is confirmed in the study at hand when radiation is taken into account through the WSGGM model, comparing results with the classical AMC model [22] to what is obtained with a uniform CSDR profile (Fig. 4). Hence, the mentioned impact of the CSDR shape is shown to be significant in such conditions, even without the presence of the laminar-to-turbulence transition zone. To the best of the authors’ knowledge, it is the first time this is illustrated in fire related simulations.

As mentioned, recently, the steady flamelet model approach [21] has been used for the test case at hand, namely the UMD line burner [23,24], described in more detail below. A strong under-estimation of temperature has been reported. It was suggested in Ref. [21] to be due to the presumed β-PDF shape or the mixture fraction variance model, but most importantly it was stated that this requires further study. It was also concluded in Ref. [21] that an unsteady flamelet model would be more suited, because low SDR values imply long response times, which is not consistent with the steady state assumption. This approach has recently been considered in Refs. [19,20]. The use of (unsteady) flamelet models in fires is clearly work in progress, deserving further study.

This further motivates the use of the conditional moment closure (CMC) [5], as is done in the present study. LES-CMC is a high-end modelling approach that has, as mentioned above, been applied successfully for extinction and re-ignition in jet flame configurations [6,7,10]. It is capable of handling detailed finite-rate chemistry and has the potential to be used for the prediction of fire extinction. On the other hand, the conditioning procedure introduces an additional dimension, mixture fraction in non-premixed combustion, which renders the model expensive. Except for the spatial transport terms in the transport equations for the conditional quantities, the CMC equations resemble the unsteady flamelet equations. The application of CMC in fires is rare, which can be attributed to the large computational domains used in fire simulations. One example is [25], where CMC was coupled with RANS in an enclosure fire scenario. In Refs. [25], it was argued that the spatial terms in the CMC equations are required to accurately model CO concentrations in the post flame regions and that consequently the steady flamelet model does not lead to accurate results there. This further motivates the use of CMC in the present study. As mentioned above, CMC models have been evaluated mostly in jet flame configurations, with strong turbulence and high (conditional) SDR values. Consequently, it remains to be seen how well the various sub-models perform in fire applications, particularly because in Ref. [25] the impact of the CSDR shape on minor species was reported. This confirms again the importance of the CSDR shape, as mentioned above [18].

The present study aims to provide some insight into the impact of various aspects of the CMC approach, combined with LES, for fire CFD simulations, using the UMD line burner as fire related configuration. The findings of the accompanying CMC-0D study [12], which effectively focuses on the impact of the chemistry mechanism, the CSDR shape and the radiation modelling approach on extinction within the unsteady laminar flamelet concept approach for conditions representative of the UMD line burner, are used in order to reduce the number of CFD simulations and as assistance to interpret the results. However, because the case at hand does not exhibit much extinction, most results are presented first with the 1-step chemistry mechanism of [26], in order to reduce computing times. Comparison to the ARM 2 mechanism [27] confirms that the findings are not affected by the choice in chemistry mechanism here from a qualitative point of view. For radiation, two approaches are compared, imposed in mixture fraction space in the CMC energy equation, as described in Ref. [12]: 1) an approach where the experimentally measured radiative fraction is imposed, locally in mixture fraction space as a prescribed reduction of the local conditional HRR; 2) the WSGGM approach. The latter model has already been applied with EDC on the UMD line burner in Ref. [13], showing results in very good agreement with experiments. Moreover, the WSGGM is gaining popularity recently within the fire community [13,[19], [20], [21]]. Nevertheless, it is important to also assess results with prescribed radiative fraction, as reported below.

The case under study is the UMD line burner, developed at the University of Maryland [23,24]. It is a target case of the IAFSS working group MaCFP (‘Measurements and Computations of Fire Phenomena’) [28] to study fire extinction. The case features a buoyancy driven, methane-fueled fire with a controlled co-flow of a nitrogen/oxygen mixture. Extinction is reached by increasing the nitrogen levels in the co-flow. In this study, no extinction simulations have been conducted. Only the fully burning flame is considered, with the oxidizer being air. The aim is to evaluate the LES-CMC approach, before moving towards extinction in future work.

From the above it is clear that the study conducted in Ref. [12] is strongly connected to the present work. Therefore, the main findings from Ref. [12], used for the explanation of certain observations in the present study, are summarized first:

• The shape of the CSDR in mixture fraction space (uniform versus bell-shaped) does not have a strong impact on the results in adiabatic conditions, or when the radiative fraction model is applied, as long as the value for the CSDR at stoichiometry is the same for different CSDR models. This is because the reaction rate and the radiative source in the radiative fraction model are narrow spikes around stoichiometry.

• The shape of the CSDR in mixture fraction space has a strong impact on the results when the WSGGM and the RADCAL-based radiation model are used, even if the value of the CSDR at stoichiometry is the same for different CSDR models. The reason is that the radiative source term in these cases remains significant further away from stoichiometry.

• The ARM2 chemistry mechanism [27] yields almost identical results as the much more expensive GRI3 mechanism [29] for the quantities in the present study. It is therefore also studied here in one section (as the intent is to investigate extinction phenomena in future work).