Modelling interfacial heat transfer in a 2-phase flow in a packed bed

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1 Modelling interfacial heat transfer in a 2-phase flow in a paced bed Dariusz ASENDRYCH, Paweł NIEGODAJEW Institute of Thermal Machinery Częstochowa University of Technology, Poland 1

2 Outline Motivation - CCS Experiment Test facility, Measuring procedure Results Interfacial heat transfer coefficient Conclusions / Perspectives 2

3 Motivation global warming / climate change CO 2 emission has to be reduced high energy efficiency + renewables - not enough solution - CCS (carbon capture & storage) 3

4 Motivation CCS (carbon capture & storage) Strategic Program: Advanced Technologies for Energy Conservation Contract SP/E/1/67484/10 Development of a technology for highly efficient zero-emission coal-fired power units integrated with CO2 capture. 4

5 CFD model of CO 2 capture installation decarbonised flue gas CO 2 geometry following the experimental facility (IChPW) unsteady 2D axisymmetric absorber heat exchanger stripper (desorber) porous zone - randomly filled with 6mm Raschig rings liquid-gas 2-phase flow flue gases heat countercurrent streams Eulerian model laminar flow gravity-driven liquid flow fluids: flue gases (including CO 2 ) aqueous MEA solution exothermic reaction Raschig rings tools: Ansys Gambit / Fluent 5

6 CFD model of a paced bed decarbonised flue gas CO 2 pressure outlet absorber heat exchanger stripper (desorber) liquid source flue gases heat porous zone 3D model - 0.5m high, 0.1m diameter structured mesh with refinement of highgradient regions - the vicinity of axis at the top of the column grid tests - choice of grid size (55, 138, 325, 540 th. cells) pressure inlet 6

7 Eulerian 2-fluid model of nonisothermal reactive flow 7

8 8 Continuity equation S ) u ( ) ( t = ρ + α ρ α Momentum conservation Governing Equations α = 1 Volume fraction iquid holdup Pressure drop coefficient ( ) n g 2 g 2 l l l l l 2 l u h h a 4 3 g u a h = ρ ε ξ ρ µ n g l l g s G C g = µ µ ρ ρ ξ ɺ ɺ ( ) ( ) ( ) ( ) + = T B r u u u p u u g M M t α ρ α ρ α α µ α ρ

9 Governing Equations Species mass fraction transport equation ( α t ρ Species flux due to diffusion J i, Y i, =α ρ ) + ( α ρ u D i,m Y i, Y i, D i,t Flux of species produced due to heterogeneous reaction R i = M i f C MEA C CO2 ) = α J i, T T + R i Energy equation ( α ρ h ) + ( α ρ u h ) = λ T + Q + S t e, Heat released due to reaction S e, r h f,i = i M i R model required 9

10 Interfacial heat transfer 10

11 Experimental setup Measured quantities: o gas inlet temperature o gas outlet temperature o liquid inlet temperature o liquid outlet temperature o humidity o gas flowrate o liquid flowrate abview data acquisition and post-processing 11

12 Experimental setup Pacing material properties Raschig rings Operating parameters used in experiment parameter symbol unit value inner diameter D in [mm] 5.0 outer diameter D out [mm] 6.0 height H [mm] 6.4 void fraction (porosity) ε [%] 80.7 specific surface area a [m 2 /m 3 ] 864 parameter symbol unit value inlet liquid load u [m 3 /m 2 /s] inlet gas load u G [m 3 /m 2 /s] inlet liquid temperature T,in [ºC] inlet gas temperature T G,in [ºC] 21±1 12

13 Interfacial heat transfer The heat flux transferred from the liquid phase Qɺ Qɺ = Qɺ + Qɺ + Qɺ ex vap loss The heat flux exchanged between phases ( ) = dqɺ = a S h T T dx Qɺ = Qɺ ex ex ex G 0 0 G Qɺ ex = h a V col T (I) interfacial heat transfer coefficient 13

14 Interfacial heat transfer The elementary heat flux absorbed by the gas phase dqɺ G = mɺ G cp d T where dx G d TG = T G water mass flux including water vapour mass flux Integration gives x mɺ = mɺ + mɺ G air vap T Qɺ dqɺ mɺ mɺ c dx mɺ mɺ c T x G 1 G = G = vap + air p = air + vap p G Assumingequalityofheatfluxesgives Nu h d cp TG 1 h= mɺ air + mɺ vap a V T 2 col e = 1 d e =a (II) 14

15 Results heat flux proportional to gas flow rate and temeperature difference Nu slightly dependent on liquid superficial velocity which becomes especially evident for the lowest loads varying Nu with temperature difference - the assumption of constant contact area between phases 15

16 Development of the heat transfer coefficient Nusselt number inertia gravity viscosity thermal diffusion buoyancy surface tension 16

17 Development of the heat transfer coefficient liquidreynoldsnumber gas Reynolds number Re Re G = u ρ a µ ug = 1 d p ρ ( ε) µ G G d p ε = 6 1 a Galileo number (gravity vs viscosity) Prandtl number (thermal & viscous diffusion rates) Grashof number (buoyancy vs viscosity) Ga Pr Gr= ρ g d e ε = µ 2 1 ε ( ) c = µ 3 g dl β T ν 2 G 3 Eötvös number (gravity vs surface tension) 17

18 Development of the heat transfer coefficient Nu= Re Re Ga Ga Pr Eoɺɺ Gr A B C D E F G G G 18

19 Development of the heat transfer coefficient Asendrych, Niegodajew- Modelling interfacial heat transfer 19 in a paced bed 19

20 Summary Conclusions Nusselt number is strongly dependent on the gas load, noticeably dependent on the temperature difference between phases and slightly dependent on the liquid load the correlation for Nusselt number taing into account the effects of inertia, gravity, surface tension, viscous force represented by Reynolds, Galileo and Eötvös numbers was proposed the proposed correlation for Nusselt number fits the experimental data with very good accuracy Perspectives the further research wor is needed to provide better understanding of the heat transfer processes in complex geometrical constraints in the further study the impact of the wetting efficiency will be analysed as this parameter may contribute to the interfacial heat transfer it is planned to continue the wor in a new test facility allowing to study much wider gas and liquid loads as well as different random pacing element types and sizes Asendrych, Niegodajew- Modelling interfacial heat transfer 20 in a paced bed 20

21 Acnowledgements PREUDIUM 6: Experimental investigation of interfacial gas-liquid heat exchange under the countercurent flow through the paced bed OPUS 8: Two-phase flow modelling in complex geometrical structures Asendrych, Niegodajew- Modelling interfacial heat transfer 21 in a paced bed 21

22 Than You for Your Kind Attention Comments, Questions? 22

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