Numerical simulation of transpiration cooling through porous material

Abstract

SUMMARYTranspiration cooling using ceramic matrix composite materials is an innovative concept for cooling rocket thrust chambers. The coolant (air) is driven through the porous material by a pressure difference between the coolant reservoir and the turbulent hot gas flow. The effectiveness of such cooling strategies relies on a proper choice of the involved process parameters such as injection pressure, blowing ratios, and material structure parameters, to name only a few. In view of the limited experimental access to the subtle processes occurring at the interface between hot gas flow and porous medium, reliable and accurate simulations become an increasingly important design tool. In order to facilitate such numerical simulations for a carbon/carbon material mounted in the side wall of a hot gas channel that are able to capture a spatially varying interplay between the hot gas flow and the coolant at the interface, we formulate a model for the porous medium flow of Darcy–Forchheimer type. A finite‐element solver for the corresponding porous medium flow is presented and coupled with a finite‐volume solver for the compressible Reynolds‐averaged Navier–Stokes equations. The two‐dimensional and three‐dimensional results at Mach number Ma = 0.5 and hot gas temperature THG=540 K for different blowing ratios are compared with experimental data. Copyright © 2014 John Wiley & Sons, Ltd.

Effect of Turbulence and Roughness on Coupled Porous-Medium/Free-Flow Exchange Processes

“…The transfer fluxes and state variables at the interface are model output. In contrast to other models, which use Richards equation (Defraeye 2011), consider only one-phase flow (Dahmen et al 2014), do not include turbulence (Davarzani et al 2014), or are more of theoretical nature (Discacciati and Quarteroni 2009;Lemos 2009;Rybak et al 2015), this concept includes two fluids phases inside the porous medium and models non-isothermal component transfer with an adjacent turbulent, roughness-affected free flow.…”

“…A better understanding of the interactions between free flow and flow in porous media is critical for a variety of applications in different fields, like medical science (Chauhan et al 2011), building physics (Defraeye et al 2010), aerospace engineering (Dahmen et al 2014), food processing (Verboven et al 2006), and agriculture Fujimaki et al 2006). In many of these applications, the processes in the two domains are strongly coupled.…”

“…Considering two different domains is desirable from a physical point of view. Because the free-flow processes act on smaller spatial and temporal scales than the porous-medium processes, the two-domain approach allows for the detailed modeling of the free flow while still applying simplifying assumptions to the porous medium (Dahmen et al 2014;Mosthaf et al 2014;Defraeye 2011). These different temporal and spatial scales also motivate different numerical treatments of the subdomains (Rybak et al 2015;Arbogast et al 2007).…”

“…These different temporal and spatial scales also motivate different numerical treatments of the subdomains (Rybak et al 2015;Arbogast et al 2007). The effects of coupling turbulent freeflow models to Richards or Darcy-Forchheimer models have been both studied theoretically and applied to heat transfer and drying problems, see Defraeye et al (2010), Dahmen et al (2014), Lemos (2009) and Pedras and Lemos (2001).…”

Mathematical modeling of transpiration cooling in cylindrical domain

“…Coupling of porous medium flow to the fluid flow is a field of research which lacks in both theoretical investigations and practical application of numerical tools, that is, there has been no approach of performing a fully coupled simulation of transpiration cooling so far [19]. The problem was defined such that a porous segment surrounded the converging part of the nozzle, which has the highest heating load of the nozzle.…”