Development of a consistent and conservative Eulerian  Eulerian algorithm for multiphase flows


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1 Development of a consistent and conservative Eulerian  Eulerian algorithm for multiphase flows Ana Cubero Alberto SanchezInsa Norberto Fueyo Numerical Fluid Dynamics Group University of Zaragoza Spain 6th OpenFOAM Workshop Penn State University, June 2011 File version: 14 Jun 11
2 Introduction Motivation Simulation of fluidized beds Chemical reactor with solid particles and a fluid, which together have fluidlike properties Issues: Bed hydrodynamics Heat transfer Mass transfer Combustion (homogeneous, heterogeneous)
3 Introduction Outline Development of a consistent and conservative Eulerian  Eulerian algorithm for multiphase flows Motivation EulerianEulerian multiphase equations Formulations: OpenFOAM alphaintensive Conservative Consistent Momentum Interpolation Results Illustration and comparison Fluidized beds
4 Equations 2. Heating Eulerian multiphase equations Multiple fluids (continua) share the space Fraction of shared space is the volume fraction The exchange mass, momentum and other properties as they move 1. Drag and turbulence dispersion 3. Drying (H2O) 5. Heterogeneous combustion (CO, CO2) Water Coal Char Ash 4. Pyrolisis (CH4)
5 Equations The Eulerian multiphase equations Phasemass conservation r p ρ p t + (r p ρ p v p ) (Γ r p r p )= x p and q are phases r is volume fraction x is a massexchange process (eg, drying) q ṁ x qp mx qp is mass transfer rate (kg/s) from phase p into phase q due to process x
6 Equations The Eulerian multiphase equations Conservation of a variable ϕ p r p ρ p φ p t + (r p ρ p v p φ p )+ (r p Γ φ p φ p )= = f φ qp(φ q φ p )+ ṁ x qpφ x + Sp φ q x q f is an interphase transport coefficient ϕ x is the value of ϕ in the donor phase in massexchanging process x Examples of ϕ: velocity, enthalpy/temp, water, volatile matter...
7 Approaches Related OpenFOAM efforts Alphaintensive formulation in OpenFOAM (twophaseeulerfoam) (Alpha is the volume fraction in OpenFOAM) EulerEuler gassolid flow solver for OpenFOAM, under development by Alberto Passalacqua (Politecnico di Torino/Iowa State University)
8 Approaches The alphaintensive formulation Oliveira and Issa, Weller, Rusche Motivation: Division of (nonconservative form) of the mom eqs by alpha, for preventing numerical difficulties when phase fractions tend to zero
9 Approaches Shortcomings 1. Nonconservative 2. Division by α requires setting an arbitrary min value 3. Momentum eq s not fully solved 4. Density presumed constant 5. Two phases (As implemented in twophaseeulerfoam)
10 Approaches Proposed approach CIPSAmultiPhaseEuler; C for consistent IPSAbased, with pressure [correction] from global mass conservation (IPSA: InterPhase Slip Algorithm, DB Spalding, Imperial College, circa 1982) PISOlike solution algorithm
11 Approaches Advantages CIPSAmultiPhaseEuler; C for consistent Consistent: steady state independent from relax coeffs and timestep size IPSAbased, with pressure [correction] from global mass conservation Equations solved in conservative form PISOlike solution algorithm Fully implicit, eqs fully satisfied at each time step
12 Approaches Other features Variable density (suitable for combustion) Multiple phases, inc Kinetic Theory of Granular Flows Heat and species conservation equations
13 Algorithmics Algorithm (IPSAPISO) 1. Calculate interfacial terms, constitutive relations, etc. 2. Build all U equations (for consistency in drag term) 3. Solve U equations 4. Calculate fluxes 5. Build p equation from overall mass continuity ( r p =1) 6. Solve p equation 7. Correct velocities 8. Build r p equations 9. Solve r p equations 10.Normalize so that r p =1; r p min=1.0e Goto 1 unless converged
14 Algorithmics Phase segregation with CIPSA Prompted Oliveira and Issa to develop alphaintensive form, because it did not converge in conservative form: [...] the standard method fails altogether because of the effect of phase segregation Solid volume fraction Solid volumetric flux Mixture velocity
15 Algorithmics Consistent Momentum Interpolation Extension to multiphase flows of CMI by Cubero and Fueyo Enhancement to Rhie and Chow s procedure Robust, prevents wiggles and checkerboard profiles, even for small time steps Results independent of time step and relaxation coeff Compact numerical interpolation, even for higher order temporal schemes Details (singlephase flows): Cubero, A, Fueyo N A compact momentum interpolation procedure for unsteady flows and relaxation. Numerical Heat Transfer, B. 52: (23).
16 Algorithmics CMI: essence (1)
17 Algorithmics CMI: essence (2)
18 Algorithmics CMI: essence (3)
19 Algorithmics Sample results Riser+elbow Solid density: 240 kg/m3; fluid density: 1.2 kg/m3 Inlet conditions: Us = 1.0 m/s; alpha_solid=0.001; Uf = 3.1m/s deltat = 1.0e3 s, 1.0e4 s Domain and gas velocity Mesh detail
20 Algorithmics Solid volume fraction Solid density 24 kg/m3, fluid 1.2 kg/m3 Using IPSA and both classic MI and Consistent MI IPSA + Momentum Interpolation CIPSA: IPSA + Consistent MI
21 Algorithmics Solid volume fraction IPSA + Momentum Interpolation CIPSA: IPSA + Consistent MI
22 Algorithmics Alphaintensive solution deltat=1.0e4s, restart from previous OpenFOAM alphaintensive
23 Algorithmics Solid volume fraction in the bed Temporal evolution Note timestep dependence of IPSA+MI solid mass / Kg IPSA+CMI deltat=1.0e3 IPSA+CMI deltat=1.0e4 IPSA+MI OFMI deltat=1.0e3 IPSA+MI OFMI deltat=1.0e time / s IPSA + MI CIPSA: IPSA + Consistent MI
24 Results::circulating beds Simulation of a dilute bed 5meter riser Initial conditions Only gas Developed flow Kinetic theory of granular Text flows (KTGF) for solid viscosity and pressure Outlet Air Solid SyamlalO Brien model for constitutive relations and drag Inlet
25 Results::circulating beds Dilute fluidized bed: results Solid volume fraction Solid vertical velocity Solid viscosity Particle cluster......going down......ktgf calculated Text
26 Results::circulating beds Animation Solid volume fraction Solid vertical velocity Solid viscosity Text
27 Results::circulating Tarea 2/9: Modelos Multifásicos/Modelado beds de configs Dense bed simulation 11meter riser Initial conditions Only gas Developed flow Kinetic theory of granular Text flows (KTGF) for solid viscosity and pressure Air Outlet Solid SyamlalO Brien model for constitutive relations and drag Inlet
28 Results::circulating beds Dense bed, results (t=18s) Solid volume fraction Solid vertical velocity Text Solid viscosity
29 Results::circulating Tarea 2/9: Modelos Multifásicos/Modelado beds de configs Animation Solid vertical velocity Solid volume fraction Solid viscosity Text
30 Results::circulating beds Dense bed: average flow fields Coreannulus structure Solid volume fraction Solid vertical velocity Text
31 Results::circulating beds Dense bed: average fields Radial profiles at 5.6 m Coreannulus structure Solid volume fraction Text Solid vertical velocity
32 Results::circulating beds From the start With initial r_solid=1.0e30 (low, algorithmically demanding) Solid vertical velocity Solid volume fraction Solid viscosity Text
33 Results::bubbling beds A bubbling bed Two solid phases: alpha, alpha2 Volume fractions Velocities
34 Results::bubbling beds FluentOpenFOAM comparison Fluent OpenFOAM 0.5s 1.0s 1.5s 2.0s 3.0s 5.0s 10s 15s 20s
35 Further work WIP/Further work Full integration of heat, mass transfer, chemical reaction (via Cantera) Validation Vol frac solid Mass frac CH4 Mass frac ash Gas temperature (Pneumatic transport regime)
36 6th OpenFOAM Workshop Penn State University, June 2011 Thank you Ana Cubero Alberto SanchezInsa Norberto Fueyo Numerical Fluid Dynamics Group University of Zaragoza Spain Funding acknowledgements: Fundacion Ciudad de la Energia (Government of Spain), project OXYCFD Spanish Ministry for Science and Innovation, CONSOLIDER INGENIO 2010, project CSD
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