The Starting Flow in Ducts Filled with a Darcy–Brinkman Medium

Wang, C. Y.

doi:10.1007/s11242-008-9210-3

Cited by 10 publications

(6 citation statements)

References 8 publications

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“…Unlike external flows, these transient internal flows will asymptotically tend to a steady state at large times. We shall derive the exponentially decaying transient solutions using the eigenfunction expansion method, as has been applied by Wang [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…On assuming steady and uniform slip lengths, our problems for starting Couette flow between two parallel flat plates and between two coaxial cylinders, and starting pressure-driven flow through a parallel-plate, rectangular, circular, and annular channel are then presented in Sections 3-8. Figures 1,3,6,8,10,13,16 show the definition sketches for these problems.…”

Section: Introductionmentioning

confidence: 99%

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Starting flow in channels with boundary slip

2016

Meccanica

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This paper contains a collection of problems and their analytical solutions for starting flows under the effect of boundary slip in channels of various geometries. The startup flows examined in this work include: (i) plane Couette flow between two plates, (ii) rotary Couette flow between two coaxial cylinders, (iii) Poiseuille flow through a parallel-plate channel, (iv) Poiseuille flow through a rectangular channel, (v) Poiseuille flow through a circular channel, and (iv) Poiseuille flow through an annulus. It is first shown that, using a depletion layer to model the effective slip, the slip length may attain its steady state much faster than the starting flow will do. This supports the use of a constant Navier slip length in the present problems. Transient solutions are derived in the form of eigenfunction expansions, where the eigenvalues are determined, by solving the characteristic equations numerically, as a function of the channel geometry and the slip lengths. From the leading eigenvalue, it is found that the boundary slip will in general lengthen the transient period of a starting flow.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Starting flow in channels with boundary slip

2016

Meccanica

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“…Examples are the investigations of turbulent flow/porous media interaction by Breugem et al (2006), the study of instabilities in Poiseuille flow over a porous layer (Hill and Straughan 2008;Tilton and Cortelezzi 2008) and analysis of bioheat transport (Fan and Wang 2011). A similar formulation was used by Kuznetsov and Nield (2006), Wang (2008) and Habibi et al (2011) to directly derive an analytical solution for unsteady flow in a porous channel.…”

Section: Introductionmentioning

confidence: 99%

A Study of the Time Constant in Unsteady Porous Media Flow Using Direct Numerical Simulation

et al. 2014

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We consider unsteady flow in porous media and focus on the behavior of the coefficients in the unsteady form of Darcy's equation. It can be obtained by consistent volumeaveraging of the Navier-Stokes equations together with a closure for the interaction term. Two different closures can be found in the literature, a steady-state closure and a virtual mass approach taking unsteady effects into account. We contrast these approaches with an unsteady form of Darcy's equation derived by volume-averaging the equation for the kinetic energy. A series of direct numerical simulations of transient flow in the pore space of porous media with various complexities are used to assess the applicability of the unsteady form of Darcy's equation with constant coefficients. The results imply that velocity profile shapes change during flow acceleration. Nevertheless, we demonstrate that the new kinetic energy approach shows perfect agreement for transient flow in porous media. The time scale predicted by this approach represents the ratio between the integrated kinetic energy in the pore space and that of the intrinsic velocity. It can be significantly larger than that obtained by volume-averaging the Navier-Stokes equation using the steady-state closure for the flow resistance term.

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“…The accuracy can be improved by increasing N . Table 1 shows the convergence of the method for the square duct, where an exact series solution exists (Hooman and Merrikh 2006;Wang 2008b). We see only a few terms are needed for convergence.…”

Section: General Formulation and Approximationsmentioning

confidence: 98%