Author's personal copy Numerical simulation of turbulent combustion in porous materials ☆ Marcelo J.S. de Lemos Departamento de Energia, IEME, Instituto Tecnológico de Aeronáutica, ITA, 12228-900, São José dos Campos, SP, Brazil abstract article info Available online 6 August 2009 Keywords: Porous burner Combustion Radiation Ceramic foam Turbulence modeling This paper presents one-dimensional simulations of combustion of an air/methane mixture in porous materials using a model that explicitly considers the intra-pore levels of turbulent kinetic energy. Transport equations are written in their time-and-volume-averaged form and a volume-based statistical turbulence model is applied to simulate turbulence generation due to the porous matrix. Four different thermo- mechanical models are compared, namely Laminar, Laminar with Radiation Transport, Turbulent, Turbulent with Radiation Transport. Combustion is modeled via a unique simple closure. Preliminary testing results indicate that a substantially different temperature distribution is obtained depending on the model used. In addition, for high excess air peak gas temperature is reduced and the flame front moves towards the exit of the burner. Also, increasing the inlet flow rate for stoichiometric mixture pushes the flame out of the porous material. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Combustion in inert porous media has been extensively investi- gated due to the many engineering applications and demand for developing high-efficiency power production devices. The growing use of efficient radiant burners can be encountered in the power and process industries and, as such, proper mathematical models of flow, heat and mass transfer in porous media under combustion can benefit the development of such engineering equipment. Accordingly, the advantages of having a combustion process inside an inert porous matrix are today well documented in the literature [1–8], including a recent review on lean-combustion porous burners [9]. Hsu et al. [10] points out some of its benefits including higher burning speed and volumetric energy release rates, higher combustion stability and the ability to burn gases of a low energy content. Driven by this motivation, the effects on porous ceramics inserts have been investigated in Peard et al. [11], among others. Turbulence modeling of combustion within inert porous media has been conducted by Lim and Matthews [12] on the basis of an extension of the standard k–ε model of Jones and Launder [13]. Work on direct simulation of laminar in premixed flames, for the case when the porous dimension is of the order of the flame thickness, has also been reported in Sahraoui and Kaviany [14]. Further, non-reactive turbulence flow in porous media has been the subject of several studies [15–17], including many applications such as flow though porous baffles [18], channels with porous inserts [19] and buoyant flows [20]. In such line of work, intra-pore turbulence is accounted for in all transport equations, but only non- reactive flow has been previously investigated in [15–20]. Motivated by the foregoing, this paper extends the previous work on turbulence modeling in porous media to include simulation of reactive flows. Computations are carried out for inert porous material consider- ing one-dimensional turbulent flow and a two-energy equation model. In addition, four different thermo-mechanical models are here compared, namely Laminar Flow, Laminar Flow with Radiation Transport, Turbulent Flow and Turbulent Flow with Radiation Transport, being the last two models derived from the work in [15–20]. As such, this contribution compares the effects of radiation and turbulence in smoothing temperature distributions within porous burners. 2. Mathematical model As mentioned, two of the thermo-mechanical models here employed, involving turbulent flow with and without radiation transport, are based on the “double-decomposition” concept [15,16], which has been also described in detail in a book [17]. In that work, transport equations are volume-averaged according to the Volume Averaging Theorem [21–23] in addition to using time decomposition of flow variables followed by standard time-averaging procedure for treating turbulence. As the entire equation set is already fully available in the open literature, these equations will be just reproduced here and details about their derivations can be obtained in the aforementioned references. Essentially, in all the above-mentioned work the flow variables are decomposed in a volume mean and a deviation (classical porous media analysis) in addition of being also decomposed in a time-mean and a fluctuation (classical turbulent flow treatment). International Communications in Heat and Mass Transfer 36 (2009) 996–1001 ☆ Communicated by W.J. Minkowycz. E-mail address: delemos@ita.br. 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.07.006 Contents lists available at ScienceDirect International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt