Thermo-Fluid Dynamics of Flue Gas in Heat Accumulation Stoves: Study Cases

Transcription

1 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

2 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

3 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

4 Description of Physical Problem Genelar Features of heat accumulation stoves historical heat accumulation stove Sfruz a scheme of one modern stove Boston, 04 Sep

5 Thermal Power [KW] Description of Physical Problem Burning Process of Woody Material V, T V, T time Boston, 04 Sep

6 curve E [m] Description of Physical Problem Burning Process of Woody Material Temporal evolution of Reynolds number Sharp Curve Turbulent motion IRe = x/d = DE A 1.0 DP/g Apii x/d [-] Boston, 04 Sep

7 Boston, 04 Sep 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 Turbulent energy eq. Turbulent Dissipation energy eq. where 2 k C T +

8 Theory of Turbulence and of Heat Transfer Theory of Turbulence: Wall Functions Wall d w u d dw w dw we will see also the influence that the choice of mesh can have on the results Boston, 04 Sep

9 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

10 Study Case One: Straight Steel Pipe Boston, 04 Sep

11 temperature [ C] temperature [ C] Result: straight steel pipe The physical model Straight steel pipe: physical model Thermotechnical characteristics stainless steel black steel thickness [mm] th 4 Sect emissivity [-] Top Side Bot. conductivity [W/mK] :00 0:30 1:00 1:30 2:00 2:30 0 tempo 1 [hh:mm] 2 tempo [h] Boston, 04 Sep st 1 Sect nd 2 Sect rd 3 Sect

12 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 Ra Boston, 04 Sep Pr

13 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

14 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: Eq M1 M2 M3 M h 2 u 0 10 x [m] M3 Boundary Layer [mm] Free Triangular [mm] D.O.F M1 M2 M3 M4 M1 No h BC M4 M2 h FL 1.0 h BC M3 No h BC M4 h FL 0.25 h BC x [m] Boston, 04 Sep

15 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 Top Side Bottom x [m] M1 M2 M3 M4 T T lower thermocouple lateral thermocouple Boston, 04 Sep x [m]

16 Study Case Two: Refractory Pipes Boston, 04 Sep

17 V [m/s] T [C ] V [m/s] T [C ] Result: refractory pipes Refractory Pipes: physical models configuration A Thermotechnical 4.0 characteristics 950 Tf refractory calcespan density 1.0 [kg/m 3 ] heat cap. 0.0 [J/kgK] conductivity 50[W/mK] emiss. [ ] t [min] configuration B Tf t [min] Boston, 04 Sep

18 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 Te Tf t [min] 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

19 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 Te Gf10 Te t [min] Gf3 Te Gf6 Te t [min] t [min] Boston, 04 Sep

20 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 t [min] t [min] Gf6 Te5 Boston, 04 Sep

21 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

22 THANKS FOR YOUR ATTENTION Boston, 04 Sep