CFD in Heat Transfer Equipment Professor Bengt Sunden Division of Heat Transfer Department of Energy Sciences Lund University

Size: px

Start display at page:

Download "CFD in Heat Transfer Equipment Professor Bengt Sunden Division of Heat Transfer Department of Energy Sciences Lund University"

Mervin Ryan
5 years ago
Views:

1 CFD in Heat Transfer Equipment Professor Bengt Sunden Division of Heat Transfer Department of Energy Sciences Lund University

2 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

3 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

4 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)

5 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

6 Turbulence Models - Wall Effects Wall Functions Approach Low Reynolds Number Modelling

7 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 ) Pr ( ) ( EXAMPLE OF A TWO-EQUATION TURBULENCE MODEL Low-Re version k- model

8 EXAMPLE OF A TWO-EQUATION TURBULENCE MODEL Low-Re version k- model, turbulent kinematic viscosity t f 2 Ck / μ t = ρν t

9 Damping functions Abe et al. model f * y 1 exp( ) Re 5 3/ 4 t exp Ret ( ) * 2 y Ret 2 f 1 exp( ) 1 0.3exp ( ) Re t k 2 u n y *

10 The general equation Arbitrary variable t x j u j x j x j S

11 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

12 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

13 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

14 Computational grid and a control volume Two-dimensional case N n W w P e E s S

15 Terms to be determined Convection flux C f Diffusion flux D f Scalar value at a face Φ f

16 CONVECTION-DIFFUSION TERMS CDS - central difference scheme UDS - upstream scheme HYBRID - hybrid scheme Power law scheme QUICK van Leer

17 PRESSURE - VELOCITY COUPLING SIMPLE (Semi-Implicit-Method-Pressure- Linked-Equations) SIMPLEC (SIMPLE-Consistent) SIMPLEX (SIMPLE-extended) PISO (Pressure-Implicit-Splitting- Operators) SIMPLER (SIMPLE-revised)

18 General algebraic equation, 2D case a P P = a E E + a W W + a N N + a S S + b

19 Discretization - grid Cartesian grid Body-fitted grid Unstructured grid

20 A typical multi-block BFC grid 3 2 y/e x/e

21 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

22 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

23 Grids - examples y/e Orthogonal-mb x/e6 3 y/e 2 1 Non-Orthogonal-mb x/e 3 y/e 2 1 Non-Orthogonal-sb x/e

24 Effect of multi-blocking On final results On convergence Execution speed

25 COMMERCIAL CFD COMPUTER CODES ANSYS FLUENT ANSYS CFX STAR CCM+ COMSOL PHOENICS NUMECA CONVERGENT OPEN FOAM In-house codes

26 Examples of CFD in Heat Transfer Plate heat exchangers Radiators Impinging jet Impinging jet in cross flow

27 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

28 Plate Heat Exchanger Gasketed plate-and-frame heat exchanger

29 Surface Configurations of Plate Heat Exchangers cross-corrugated surfaces PHE

30 Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces PHE

31 Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces

32 Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces unit cell

33 Reynolds number Definition: Re = 2m/ 2m Re 2 mw Re w 2 m 2m Re w w Re

34 Surface Configurations of Plate Heat Exchangers - cross-corrugated surfaces

35 Plate Heat Exchangers : cross-corrugated surfaces, hexahedron cells and boundary layer grid

36 Plate Heat Exchangers - cross-corrugated surfaces Re = Grid density ~ computational cells

37 Plate Heat Exchangers - cross-corrugated surfaces; Flow distribution

38 Plate Heat Exchangers - cross-corrugated surfaces; whole plate calculations - flow field in neighborhood of contact points

39 Plate Heat Exchangers - cross-corrugated surfaces; Fanning friction factor

40 Plate Heat Exchangers - cross-corrugated surfaces; Heat transfer coefficient

41 Surface Configurations of a Compact Heat Exchanger - triangular duct with bumps for regenerators

42 Secondary flow velocity vectors in a cross- sectional plane midway over a bump in a triangular duct

43 Radiator in vehicles

44 Radiator flat tubes and multilouvered fin geometry H w H P

45 Radiator porous media concept

46 Copper fin brass tube in a radiator - brazing joint

47 Copper fin brass tube in a radiator - brazing joint

48 Brazing joints in radiators - example temperature distribution

49 Multilouvered fin - sketch

50 Setup in Numerical Solution

51 Grid structure - inlet section

52 Grid structure - louver section

53 Grid structure - flow reverting section

54 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

55 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

56 Computed results louvered fins

57 Impinging jet Re=20,000 D V2F CALC-MP V2F Fluent 4D

58 Mean velocities comparisons with ANSYS FLUENT CALC-MP Fluent U V

59 Turbulence properties - Comparison with Fluent CALC-MP Fluent TKE ED

60 Nusselt number on the impingement wall Exp. Lee et al. V2F Fluent V2F CALC-MP Nu r/d

61 Jet Impinging on a Flat Surface 100 Nu Present simulation (EASM) Present simulation (V2F Durbin 1995) Exp. Gau & Lee (1992) Exp. Schlunder (1977) Exp. Gardon (1966) Re = 11000, H/B = x/b The secondary peak of the Nusselt number is predicted faithfully, using V2F.

62 Impinging jet in cross flow Impingement cooling Aircraft vertical take off and landing

63 Flow structure with cross flow Jet Cross Flow Y X Z

64 Flow at the symmetry plane M = 0.1 M = 0.2

65 Flow at two cross sections X = 1.5D X = 20D y/d 2 y/d z/d z/d Jet flow (Re = 20,000) Cross flow

66 RANS Horse shoe vortices LES Y/D = 3.2 Jet flow (Re = 20,000) Cross flow Y/D = 2.3

67 Reynolds stresses uu uv RANS LES

68 Nusselt number at symmetry line M = 0.1 LES V2F 150 Nu x/d

69 TOPICS NOT TREATED Implementation of boundary conditions Complex geometries Adaptive grid methods Local grid refinements Solution of algebraic equations Convergence and accuracy Parallel computing

70 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

International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May ISSN

International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 28 CFD BASED HEAT TRANSFER ANALYSIS OF SOLAR AIR HEATER DUCT PROVIDED WITH ARTIFICIAL ROUGHNESS Vivek Rao, Dr. Ajay