Effect of the Darcy number on the energy flow and operating conditions of a thermoacoustic porous-medium system. (English) Zbl 1219.80072
Summary: In this paper, a simplified porous medium thermoacoustic system is modeled to observe its energy interaction characteristics and identify its operating conditions mainly as a function of porous medium Darcy number. The governing Darcy-Brinkman momentum equation and energy equation are simplified and linearized by using a first order perturbation analysis. Similar perturbation analysis is usually used to solve the linear thermoacoustic problem in the low Mach number limit. Simplified momentum and energy equations are solved, in the frequency domain, in order to obtain the expressions of the fluctuating velocity \((u_{1})\) and temperature \((T_{1})\). Time averaged and space averaged heat fluxes and work fluxes are calculated using the expressions of fluctuating velocity and temperature. The effects of the drive ratio (DR), Darcy number \((Da_{\delta })\), temperature gradient (\(\nabla T_{m}\)), and frequency \((f)\) on the heat flux, work flux, and operating conditions are discussed and graphically presented.
MSC:
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 76S05 | Flows in porous media; filtration; seepage |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76Q05 | Hydro- and aero-acoustics |
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