Thermo-Fluid Dynamics of Flue Gas in Heat Accumulation Stoves: Study Cases Scotton P. Rossi D. University of Padova, Department of Geosciences Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston Boston, 04 Sep 2012 1
Description of Physical Problem; Theory of Turbulence and of Heat Transfer; Results of straight steel pipe straight refractory pipe curved refractory pipe Boston, 04 Sep 2012 2
Description of Physical Problem Genelar Features of global system flue gas rad. heat exchanges conv. heat exchanges rad. heat exchanges conv. heat exchanges refractory walls of room air suply combustion Barberi Srl Boston, 04 Sep 2012 3
Description of Physical Problem Genelar Features of heat accumulation stoves historical heat accumulation stove Sfruz a scheme of one modern stove Boston, 04 Sep 2012 4
Thermal Power [KW] Description of Physical Problem Burning Process of Woody Material V, T V, T time Boston, 04 Sep 2012 5
curve E [m] Description of Physical Problem Burning Process of Woody Material Temporal evolution of Reynolds number Sharp Curve Turbulent motion IRe = 28400 x/d = 1.4 1.3 DE A 1.0 DP/g Apii 0.7 0.4 0.1-5 15 35 x/d [-] Boston, 04 Sep 2012 6
Boston, 04 Sep 2012 7 Theory of Turbulence and of Heat Transfer Theory of Turbulence: Transport Equations Reynolds-averaged Navier Stokes eq. F u u I p u u u u t u T ' ' 0 u k k T P k k u t k k C P k C u t k T 2 2 1 Turbulent energy eq. Turbulent Dissipation energy eq. where 2 k C T +
Theory of Turbulence and of Heat Transfer Theory of Turbulence: Wall Functions Wall d w u d dw w dw 11.06 we will see also the influence that the choice of mesh can have on the results Boston, 04 Sep 2012 8
Theory of Turbulence and of Heat Transfer Theory of Heat Transfer conduction q i k T x i Heat transfer is guaranteed from three terms: convection q h A T s T radiation q A 4 T s heat flux by conduction Equation of heat transfer Equation of mass conservation.. the conserved property is the total energy not the heat T Cp : t t T T p t u T q S u p Q v 0 H k T u qr u 0 heat flux by radiation p Boston, 04 Sep 2012 9
Study Case One: Straight Steel Pipe Boston, 04 Sep 2012 10
temperature [ C] temperature [ C] Result: straight steel pipe The physical model Straight steel pipe: physical model Thermotechnical characteristics stainless steel black steel thickness [mm] 0.2 2.0 30 20 th 4 Sect emissivity [-] 0.1 0.95 0 Top Side Bot. conductivity [W/mK] 17 50 0 0:00 0:30 1:00 1:30 2:00 2:30 0 tempo 1 [hh:mm] 2 tempo [h] Boston, 04 Sep 2012 11 120 90 60 120 100 80 60 40 st 1 Sect nd 2 Sect rd 3 Sect
Result: straight steel pipe Straight steel pipe : 2D axial symmetry model The geometry Conv. Cooling h Nu k L c Q out + p with the boundary conditions: 1. Inflow + Temperature at the inlet face Q in + T 2. Pressure + Outflow at the outlet face 3. Convective cooling on the outer surface using the coefficient Nu k h L c where Nu 0.6 0.387 Ra Boston, 04 Sep 2012 12 1 6 0.559 1 Pr 9 16 8 27 2
Result: straight steel pipe Straight steel pipe : 3D model The geometry Conv. Cooling h Nu k L c Q out + p with the boundary conditions: 1. Inflow + Temperature at the inlet face 2. Pressure + Outflow at the outlet face 3. Convective cooling on the outer surface 4. Buoyancy forces: + F g T R T R Q in + T Boston, 04 Sep 2012 13
T [ C] h mesh [mm] Result: straight steel pipe Straight steel pipe: 2D results M1 M2 The choice of the mesh dimensions are fundamental for the quality of the results. first of all, we have estimated the thickness of the first layer of cells adjacent to the wall with the equation: 8 6 4 2 0 Eq M1 M2 M3 M4 11.06 h 2 u 0 10 x [m] M3 Boundary Layer [mm] Free Triangular [mm] D.O.F 10 6 100 M1 M2 M3 M4 M1 No h BC 5.5 0.245 60 M4 M2 h FL 1.0 h BC 11.0 0.201 M3 No h BC 1.0 1.722 M4 h FL 0.25 h BC 1.0 1.713 20 0 10 20 x [m] Boston, 04 Sep 2012 14
result of 2D model T [ C] result of 3D model T [ C] Result: straight steel pipe Straight steel pipe: 3D results In the 3D model the buoyancy forces have been also considered: F g T It was possible to highlight the temperature differences at different positions in the cross section R T R upper thermocouple 100 60 20 Top Side Bottom 0 10 20 x [m] M1 M2 M3 M4 T T lower thermocouple lateral thermocouple Boston, 04 Sep 2012 15 100 60 20 0 10 20 x [m]
Study Case Two: Refractory Pipes Boston, 04 Sep 2012 16
V [m/s] T [C ] V [m/s] T [C ] Result: refractory pipes Refractory Pipes: physical models configuration A Thermotechnical 4.0 characteristics 950 Tf1 3.0 750 refractory calcespan 2.0 550 density 1.0 [kg/m 3 ] 2550 600 350 heat cap. 0.0 [J/kgK] 859 1000 150 conductivity 50[W/mK] 150 3.16 0.15 emiss. [ ] t [min] 0.95 0.70 configuration B 4.0 3.0 2.0 1.0 0.0 Tf1 50 150 t [min] 950 750 550 350 150 Boston, 04 Sep 2012 17
V [m/s] T [C ] Result: refractory pipes Refractory Pipes: numerical models configuration A Gf2 Gf1 Te1 Gf3 Te2 Gf4 Te3 Gf5 Te4 Gf6 Te5 Gf7 Gf8 Te6 Gf9 Gf10 Te7 4.0 3.0 2.0 1.0 0.0 Tf1 50 150 t [min] 950 750 550 350 150 with the boundary conditions: 1. Inflow + Temperature at the inlet face 2. Pressure + Outflow at the outlet face 3. Convective cooling on the outer surface 4. Buoyancy forces: F R g Boston, 04 Sep 2012 18
T [C ] T [C ] T [C ] Result: refractory pipes Refractory Pipes: numerical models configuration A Gf2 Gf1 Te1 Gf3 Te2 Gf4 Te3 Gf5 Te4 Gf6 Te5 Gf7 Gf8 Te6 Gf9 Gf10 Te7 800 600 400 200 0 Gf10 Te7 50 150 t [min] 800 600 400 Gf3 Te2 800 600 400 Gf6 Te5 200 200 0 50 150 t [min] 0 50 150 t [min] Boston, 04 Sep 2012 19
T [C ] T [C ] Result: refractory pipes Refractory Pipes: numerical models configuration A Gf2 Gf1 Te1 Gf3 Te2 Gf4 Te3 Gf5 Te4 Gf6 Te5 Gf7 Gf8 Te6 Gf9 Gf10 Te7 Those differences are significantly reduced introducing the radiation in participating media. 600 500 400 300 200 100 0 50 70 t [min] 800 600 400 200 0 50 150 t [min] Gf6 Te5 Boston, 04 Sep 2012 20
Result: refractory pipes Conclusions The very challenging experimental conditions (very high temperatures, very low pressures) induce to accept high errors of the order of 20% The choice of the mesh influences, in an important way, the numerical solution, in particular, near a wall, the choice of the mesh could influence, importantly, the heat transfer through the wall An important contribute on heat transport could be given from radiation absorption and emission phaenomena of particle fraction of the flue gas Boston, 04 Sep 2012 21
THANKS FOR YOUR ATTENTION Boston, 04 Sep 2012 22