CFD in Heat Transfer Equipment Professor Bengt Sunden Division of Heat Transfer Department of Energy Sciences Lund University email: bengt.sunden@energy.lth.se
CFD? CFD = Computational Fluid Dynamics; Numerical solution methodology of governing equations for mass conservation, momentum and heat transfer Focus on thermal issues; Computational Heat Transfer or Numerical Heat Transfer more appropriate names
Flow and Heat Transfer in Heat Transfer Equipment - Governing Equations, steady state, Reynolds averaging 0 j j U x j i j i j j i j i j i j u u x x U x U x x p U U x t u x T x T U x j j j j j Pr
Turbulence Models Zero-equation models One-equation models Two-equation models Reynolds stress models Algebraic stress models Large Eddy Simulations (LES) Direct Numerical Simulations (DNS)
Turbulence models, RANS based Standard k-ε model RNG k-ε model Realizable k-ε model Standard k-ω model SST k-ω model Reynolds Stress Model v 2 f
Turbulence Models - Wall Effects Wall Functions Approach Low Reynolds Number Modelling
j i j i j k t j j j x U u u x k x k U x ) Pr ( ) ( k f C x U u u k C x x U x j i j i j t j j j 2 2 1 ) Pr ( ) ( EXAMPLE OF A TWO-EQUATION TURBULENCE MODEL Low-Re version k- model
EXAMPLE OF A TWO-EQUATION TURBULENCE MODEL Low-Re version k- model, turbulent kinematic viscosity t f 2 Ck / μ t = ρν t
Damping functions Abe et al. model f * y 1 exp( ) 14 2 1 Re 5 3/ 4 t exp Ret ( ) 200 2 * 2 y Ret 2 f 1 exp( ) 1 0.3exp ( ) 3.1 6.5 Re t k 2 u n y *
The general equation Arbitrary variable t x j u j x j x j S
NUMERICAL METHODS FOR PDEs -General Purpose FDM - finite difference method FVM - finite volume method FEM - finite element method CVFEM - control volume finite element method BEM -boundary element
Control volume method-fvm B th ds n V U j dv dv S dv V x j V x j x j V Divergence theorem U ds ds S dv S S V
Discretization - Sum over all the CV faces U ds ds S dv S S V O Ae I Sum up nf nf C D S V f f f f 1 f 1
Computational grid and a control volume Two-dimensional case N n W w P e E s S
Terms to be determined Convection flux C f Diffusion flux D f Scalar value at a face Φ f
CONVECTION-DIFFUSION TERMS CDS - central difference scheme UDS - upstream scheme HYBRID - hybrid scheme Power law scheme QUICK van Leer
PRESSURE - VELOCITY COUPLING SIMPLE (Semi-Implicit-Method-Pressure- Linked-Equations) SIMPLEC (SIMPLE-Consistent) SIMPLEX (SIMPLE-extended) PISO (Pressure-Implicit-Splitting- Operators) SIMPLER (SIMPLE-revised)
General algebraic equation, 2D case a P P = a E E + a W W + a N N + a S S + b
Discretization - grid Cartesian grid Body-fitted grid Unstructured grid
A typical multi-block BFC grid 3 2 y/e 1 0 0 2 4 6 8 10 x/e
Why multi-block? To ease the grid-generation of complex geometries Natural way for domain decomposition used by parallel computation Better cache usage: smaller blocks are easier to fit in the cache
Strategy for multi-blocking Keep most of the single-block code unchanged Same way of thinking as a single-block code Hide the multi-blocking from the enduser to ease the implementation of physical models Introduce no difference in the results
Grids - examples y/e 3 2 1 Orthogonal-mb 0-4 -3-2 -1 0 1 2 3 4 5 x/e6 3 y/e 2 1 Non-Orthogonal-mb 0 0 2 4 6 8 10 x/e 3 y/e 2 1 Non-Orthogonal-sb 0 0 2 4 6 8 10 x/e
Effect of multi-blocking On final results On convergence Execution speed
COMMERCIAL CFD COMPUTER CODES ANSYS FLUENT ANSYS CFX STAR CCM+ COMSOL PHOENICS NUMECA CONVERGENT OPEN FOAM In-house codes
Examples of CFD in Heat Transfer Plate heat exchangers Radiators Impinging jet Impinging jet in cross flow
Ways to adopt CFD in heat exchanger analysis and design 1) entire heat exchanger. a) detailed simulations with large scales meshes, b) local volume averaging or porous media approach including distribution of resistances 2) Modules or group of modules are identified and streamwise periodic or cyclic boundary conditions are imposed
Plate Heat Exchanger Gasketed plate-and-frame heat exchanger
Surface Configurations of Plate Heat Exchangers cross-corrugated surfaces PHE
Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces PHE
Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces
Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces unit cell
Reynolds number Definition: Re = 2m/ 2m Re 2 mw Re w 2 m 2m Re w w Re
Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces
Plate Heat Exchangers : cross-corrugated surfaces, hexahedron cells and boundary layer grid
Plate Heat Exchangers - cross-corrugated surfaces Re = 3000-5000 Grid density ~ 89 500-985 000 computational cells
Plate Heat Exchangers - cross-corrugated surfaces; Flow distribution
Plate Heat Exchangers - cross-corrugated surfaces; whole plate calculations - flow field in neighborhood of contact points
Plate Heat Exchangers - cross-corrugated surfaces; Fanning friction factor
Plate Heat Exchangers - cross-corrugated surfaces; Heat transfer coefficient
Surface Configurations of a Compact Heat Exchanger - triangular duct with bumps for regenerators
Secondary flow velocity vectors in a cross- sectional plane midway over a bump in a triangular duct
Radiator in vehicles
Radiator flat tubes and multilouvered fin geometry H w H P
Radiator porous media concept
Copper fin brass tube in a radiator - brazing joint
Copper fin brass tube in a radiator - brazing joint
Brazing joints in radiators - example temperature distribution
Multilouvered fin - sketch
Setup in Numerical Solution
Grid structure - inlet section
Grid structure - louver section
Grid structure - flow reverting section
Computed results - louvered fins (a) Velocity at Re Lp = 171 ( U = 2.5m/s ) (b) Temperature at Re Lp = 171 (c) Velocity at Re Lp = 513 ( U = 7.5 m/s ) (d) Temperature at Re Lp = 513
Computed results louvered fins (a) Velocity at Re Lp = 376 ( U=5.5 m/s ) (a) Temperature at Re Lp = 376 ( U=5.5 m/s ) (c) Velocity vektors at Re Lp =376
Computed results louvered fins
Impinging jet Re=20,000 D V2F CALC-MP V2F Fluent 4D
Mean velocities comparisons with ANSYS FLUENT CALC-MP Fluent U V
Turbulence properties - Comparison with Fluent CALC-MP Fluent TKE ED
Nusselt number on the impingement wall 200 150 Exp. Lee et al. V2F Fluent V2F CALC-MP Nu 100 50 0 0 1 2 3 4 5 r/d
Jet Impinging on a Flat Surface 100 Nu 90 80 70 60 50 Present simulation (EASM) Present simulation (V2F Durbin 1995) Exp. Gau & Lee (1992) Exp. Schlunder (1977) Exp. Gardon (1966) Re = 11000, H/B = 4.0 40 30 20 10 0 0 2 4 6 8 10 12 14 16 18 x/b The secondary peak of the Nusselt number is predicted faithfully, using V2F.
Impinging jet in cross flow Impingement cooling Aircraft vertical take off and landing
Flow structure with cross flow Jet Cross Flow Y X Z
Flow at the symmetry plane M = 0.1 M = 0.2
Flow at two cross sections X = 1.5D X = 20D 4 4 3 3 y/d 2 y/d 2 1 1 0-4 -2 0 2 4 z/d 0-4 -2 0 2 4 z/d Jet flow (Re = 20,000) Cross flow
RANS Horse shoe vortices LES Y/D = 3.2 Jet flow (Re = 20,000) Cross flow Y/D = 2.3
Reynolds stresses uu uv RANS LES
Nusselt number at symmetry line 250 200 M = 0.1 LES V2F 150 Nu 100 50 0 5 6 7 8 9 10 11 12 13 14 15 x/d
TOPICS NOT TREATED Implementation of boundary conditions Complex geometries Adaptive grid methods Local grid refinements Solution of algebraic equations Convergence and accuracy Parallel computing
Summary CFD might be a useful tool in engineering R & D in heat transfer Arbitrary geometries can be handled decently but may require a huge amount of grid points Computer demanding for complete real geometries Turbulence modeling is critical or a weakness