CFD calculation of convective heat transfer coefficients and validation Laminar and Turbulent flow
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1 CFD calculation of convective heat transfer coefficients and validation Laminar and Turbulent flow Subtask 3: Boundary Conditions by Adam Neale M.A.Sc. Student Concordia University Dominique Derome Concordia University Bert Blocken K.U.Leuven Jan Carmeliet K.U.Leuven/Technical University of Eindhoven
2 CFD Calculation of Surface Coefficients Part 1: Laminar Flow - Simulation of Forced Convection Part 2a: Turbulent Flow - Simulation of Forced Convection Wall boundaries Wall boundary - Analytical Validation - Semi-empirical Validation Part 2b: Turbulent Flow - Simulation of Natural Convection - Validation case for wall functions
3 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Cases Computational Domain : Y X Height = 0.05 m Length = 3.0 m Boundary Conditions : Inlet Conditions U av = 0.1 m/s U(y) = 3/2*U av *[1 4*(y/b) 2 ] m/s T = 283 K Wall boundaries Case (A): Constant Heat Flux (CHF) q w = 10 W/m 2 Case (B): Constant Wall Temperature (CWT) T w = 293K q w = 10 W/m 2 T w = 293K
4 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Mesh cells b = 0.05m L = 3m
5 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Boundary Conditions (B.C.) Case A (CHF): Velocity Inlet B.C. U av = 0.1 m/s U(y) = 3/2*U av *[1 4*(y/b) 2 ] m/s T = 283 K Wall B.C.: q w = 10 W/m 2 Pressure Outlet B.C. Wall B.C.: q w = 10 W/m 2 Case B (CWT): Velocity Inlet B.C. U av = 0.1 m/s U(y) = 3/2*U av *[1 4*(y/b) 2 ] m/s T = 283 K Wall B.C.: T w = 293K Wall B.C.: T w = 293K Pressure Outlet B.C.
6 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Case A, Constant Heat Flux: h c values 4 h c (W/m 2 K) T b n i= = 1 ( u b T ) U i av i b i h cref hc-ref h cc hcc h cb hcb Analytical X Position (m)
7 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Case B, Constant Wall Temperature: h c values 4 h c (W/m 2 K) h cref hc-ref h cc hcc hcb h cb Analytical X Position (m)
8 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Grid sensitivity analysis φ h φ 2h φ 4h φ 8h φ 16h Number of cells in the Y Direction Number of cells in the X Direction Smallest cell height (m) Smallest cell width (m) Total number of cells E E E E E *Initial mesh
9 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Richardson Extrapolation Using h c at 2.5m as a reference (i.e. φ h = h c ) Discretization error: ε d h φh 2 φ a 2h 1 Order of the scheme: a = φ2h φ4 log φh φ2h log ( 2) h Richardson grid independent solution: d Φ = φ h + ε h Finest mesh solution
10 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Case A: Grid sensitivity results Φ = h c (W/m 2 K) x=2.5m Richardson Relative error Relative Error (%) φ16h (300) φ8h (1200) φ4h (5100) φ2h (19800) φh (80400) 0.0 Grid (#cells)
11 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Case B: Grid sensitivity results Φ = h c (W/m 2 K) x=2.5m Richardson Relative error Relative Error (%) φ16h (300) φ8h (1200) φ4h (5100) φ2h (19800) φh (80400) 0.0 Grid (#cells)
12 CFD Calculation of Surface Coefficients Part 1 Laminar Flow Results Order of the scheme a d ε h Discretization Error (W/m 2 K) Finest mesh solution (W/m 2 K) Richardson Solution (W/m 2 K) Analytical solution h c (W/m 2 K) CHF x φh Φ CWT x
13 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow Part 2a: Turbulent Flow - Simulation of Forced Convection Part 2b: Turbulent Flow - Simulation of Natural Convection - (In)Validation of wall functions Wall boundary - Semi-empirical Validation
14 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow Universal Law-of-the-wall u u+ Equation (7) u+ Equation (10) u+ Spalding Equation (13) T+ Equation (8) T+ Equation (11) T y+
15 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow Guidelines for near-wall modelling Height of first cell above the wall 1) Laminar Sublayer (y + < 5) Low-Reynolds number modelling u+ Equation (7) u+ Equation (10) u+ Spalding Equation (13) T+ Equation (8) T+ Equation (11) u+ T+ 2) Buffer Region (5 < y + < 30) Not recommended ) Log-law Layer (30 < y + < 60) y+ Wall functions
16 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow Computational Domain Symmetry BC U = 0.5m/s T = 283 K Y Velocity Inlet BC Pressure Outlet BC H = 1m Wall BC - Constant Heat Flux X q w = 10 W/m L = 5m Note : Not to scale.
17 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow Meshes y ,000 cells y cells
18 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow Simulations Low-Re Simulations 1. Spalart-Allmaras Model 2. Standard k-ε Model 3. RNG k-ε Model 4. Realizable k-ε Model 5. Standard k-ω Model 6. SST k-ω Model 7. Reynold s Stress Model (RSM) Wall Function Simulations 1. Standard k-ε Model 2. Standard k-ω Model
19 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow u + Results 25 u Semi-Empirical Equation - Laminar Sublayer Semi-empirical Equation - Log-law Empirical Equation - Spalding (1961) k-e standard k-e RNG k-e realizable k-w standard k-w SST Spalart-Allmaras RSM WF - ke WF - kw y+
20 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow T + Results 16 T Semi-empirical Equation - Laminar Sublayer Semi-empirical Equation - Log-law k-e standard k-e RNG k-e realizable k-w standard k-w SST Spalart-Allmaras RSM WF - ke WF - kw y+
21 CFD Calculation of Surface Coefficients Part 2a Turbulent Flow h c Results 6 h c (W/m 2 K) k-e standard k-e RNG k-e realizable k-w standard k-w SST Spalart-Allmaras RSM k-e WF k-w WF Lienhard (2006) Eq Lienhard (2006) Eq X Position (m)
22 CFD Calculation of Surface Coefficients Part 2b Turbulent Flow Methodology for validation Part 2a: Turbulent Flow - Simulation of Forced Convection Part 2b: Turbulent Flow - Simulation of Natural Convection - (In)Validation of wall functions Wall boundary - Semi-empirical Validation
23 CFD Calculation of Surface Coefficients Part 2b Natural Convection (In)Validity of Wall Functions y = 3m Air, T initial = 293K Isothermal Hot Side y = 2.25m Cold Side T w1 = 298K y = 1.50m T w2 = 288K Y y = 0.75m 0m 0m X Isothermal X = 3m Note : Not to scale.
24 CFD Calculation of Surface Coefficients Part 2b Natural Convection Meshes y + 2 (22500 cells) y + 30 (900 cells)
25 CFD Calculation of Surface Coefficients Part 2b Natural Convection Velocity profiles Low-Re Velocity profile at y = 2.25 m, Hot side Spalding wall function equation 0.6 Velocity (m/s) Position (m)
26 CFD Calculation of Surface Coefficients Part 2b Natural Convection Velocity fields m/s Low-Re Modelling Wall Function
27 CFD Calculation of Surface Coefficients Part 2b Natural Convection Dimensionless velocity Low-Re: y=0.75m, Hot side Low-Re: y=1.50m, Hot side Low-Re: y=2.25m, Hot side WF: y=0.75m, Hot Side WF: y=1.50m, Hot Side WF: y=2.25m, Hot Side Spalding Wall Function Equation Low-Re: y=0.75m, Cold side Low-Re: y=1.50m, Cold side Low-Re: y=2.25m, Cold side WF: y=0.75m, Cold Side WF: y=1.50m, Cold Side WF: y=2.25m, Cold Side u y+
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