Ch. 10 Compact Heat Exchangers

Transcription

1 King Abdulaziz University Mechanical Engineering Department MEP 460 Heat Exchanger design Ch. 10 Compact Heat Exchangers April 2018

2 Ch. 10 Compact Heat Exchangers 1-Introduction 2-Tube-fin heat exchangers 3-Plate-fin heat exchangers 4-Examples

3 1- Introduction

4 Compact heat exchangers

5 Surface heat transfer area over volume α

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8 Tube fin compact heat exchangers

9 Tube fin compact heat exchangers Non-circular tubes

10 2- Tube fin heat exchangers continuous fins on flat tubes Continuous fins on circular tube Circular fins on circular tubes

11 Heat transfer and pressure drop for tube fin heat exchangers 1 = 1 + R fi + R U o A o h i η i A i η i A w + R fo + i η o A o 1 h o η o A o Overall surface efficiency η o η o = 1 A f A (1 η f) η f is the fin efficiency For h o outside (gas) heat transfer coefficient use Kays & London book in compact heat exchangers

12 Definitions Frontal area A fr Free Flow area A min = A ff σ = Free flow area Frontal area = A ff A fr Fin area/total area=a f /A o α = Surface area/volume Hydraulic diameter D h Mass velocity G= u max

13 Definitions Colburn j H factor j H = StPr 2 3 Re = GD h /μ Stanton Number St = Nu Re Pr = h ρc p V max = h C p G Mass velocity [kg/(m 2.s) G = ρv max = ρva fr A ff = m A ff = m σa fr Pressure drop Friction coefficient f ΔP = f L D ρ V2 2

14 Pressure drop gas side A: heat transfer area A fr Frontal area A ff Free flow area v i specifc volume at inlet v o specific volume at outlet v m mean specific volume = v i+v o 2 The above equation for pressure drop can be also written in terms of densities instead of specific volume v m = v i + v o 2 A A ff = σ = αv σa fr Fin area Total area = A f A α = A V

15 From Incropera 6 th edition Surface information(cf-7.0-5/8j) Circular fin on circular tubes

16 Typical data for tube fin heat exchangers (8.0-3/8T) Continuous fin on circular tubes

17 Surface information Hydraulic diameter D h σ = Free flow area Frontal area = A ff A fr Surface density α = β = A V Fin area Total area = A f A

18 Surface information

19 Evaluating overall heat transfer coefficient 1 = 1 + R fi + R U o A o h i η i A i η i A w + R fo + i η o A o Neglecting fouling resistances 1 U o = 1 U o = R w = ln (r o r i ) 2πkL 1 h i (A i A o ) + A oln (r o r i ) 2πkL + 1 h o η o 1 h i (A i A o ) + D iln (r o r i ) 2k (A i A o ) + 1 h o η o 1 h o η o A o Need to know the heat transfer area ratio A i /A o

20 Ratio of inside to outside heat transfer area A i = πd i L A o,p = πd o L Inside heat transfer area Outside heat transfer area without fins A i A o,p = D i D o A i = D i D o A o,p D i D o A o = A uf + A f = A o,p + A f Neglecting the area occupied by fins. i.e. A uf =A op A o,p = A o A f A i A o = D i D o 1 A f A o Fins

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22 Example 11.6 h i is given From frontal area A fr, and mass flow rate get G and Re Dh Get j from Kays & London graphs and h o Get fin efficiency for circular fins on circular pipe Get U o value Knowing q and q max get the effectiveness Knowing C r and the effectiveness get NTU From NTU=UA/C min calculate the heat transfer area A o Calculate the volume of the heat exchanger usingα = β = A o V Get the depth of the heat exchanger L form V=A fr L Calculate the number of rows of tubes

23 Surface: 8.0-3/8 T Continuous fins on circular tubes

24 Surface CF-8.72(c) Circular fins on circular tubes

25 CF-8.7-5/8J Circular fin on circular tubes

26 Heat transfer factor j and friction coefficient f for some tube-fin and plate- fin surface Ref.: Kays & London

27 Continuous fin with flat tube

28 Some of the data for plate-fin and tube fin compact heat exchangers

29 Pressure drop (Gas side) Δp = G2 2ρ i 4f L D h ρ i ρ σ2 ρ i ρ o 1 A t = 4L = A m D h heat transfer area min. flow area Δp = G2 2ρ i f A t A min ρ i ρ σ2 ρ i ρ o 1 D h = 4A min P L L = 4 A minl A t A t = 4L A min D h L A t =heat transfer area=p*l D h = 4A min /P A =heat transfer area P=perimeter A min min. flow area

30 3- Plat fin compact heat exchangers

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32 Kays & London heat transfer and pressure drop data for plate-fin and tube-fin heat exchangers Ch. 9

33 Plain fins Ch. 9 Kays & London

34 Strip fins Ch. 9 Kays & London

35 Louvered fins Ch. 9 Kays & London

36 Ch. 9 Kays & London

37 Circular tubes, continuous fins Flat tubes continuous fins Ch. 9 Kays & London

38 Circular tubes- circular fins Ch. 9 Kays & London

39 Flow inside circular and flattened tubes Ch. 9 Kays & London

40 Pressure drop for plat-fin heat exchanger Δp = G2 k 2ρ c + 1 σ + 2 ρ i 1 + f A ρ i i ρ o A min ρ 1 k e σ 2 ρ i ρ o Entrance Acceleration Friction Major loss Exit Average density can be found using 1 ρ = ρ i + 1 ρ o

41 Typical data for plate-fin compact heat exchanger

42 Surface tabulated data for plate-fin compact heat exchangers

43 Plate-fin compact heat exchanger (Gas-to-Gas HX) Calculate 1-Number of passes N p 2-Calculate volume between plates for side 1 and side 2 3-Calculate heat transfer area A 1, and A 2 4-Calculate A min1, A min2 5-Calculate G 1, and G 2 6-Calculate j 1,j 2, h 1 and h 2 7-Calculate U value Gas 8-Calculate Cr and NTU, then get 9-Calculate outlet temperatures 10-Calculate pressure drops for both sides Surface 1 Hydaulic diameter D h1 Plate spacing b 1 Fin thickness δ f1 Area/ volume between plate, β 1 Fin area/heat transfer area, ω 1 Length of the fin, l f1 2 =A 2 /V A fr1 L2 L1 Surface 2 A fr2 Air Hydaulic diameter D h2 Plate spacing b 2 Fin thickness δ f2 Area/ volume between plate, β 2 Fin area/heat transfer area, ω 2 Length of the fin, l f2 1 =A 1 /V

44 Calculating the heat transfer areas for side (1) and side (2) Assuming the number of passes in one side is N p and N p +1 on the other side, then the common edge length can be written in terms the pate spacing's b 1, b 2 and the plate thickness a as follows L c = N p b 1 + N p + 1 b N p + 1 a N p = L c b 2 2a b 1 + b 2 + 2a Volume between the plates for side (1) and side (2) V p1 = L 1 L 2 N p b 1 V p2 = L 1 L 2 N p b 2 Utilizing the relation between and the volume between the plates β 1 = A 1 V p1 β 2 = A 2 V p2

45 If 1 and 2 are calculated based on b 1, b 2 and a, then one can easily find the heat transfer areas A 1 and A 2 α 1 = A 1 V α 2 = A 2 V Where V is the total volume of the heat exchanger

46 Overall heat transfer for plate-fin heat exchanger 1 U 1 A 1 = 1 h 1 A 1 η 01 + R w + 1 h 2 A 2 η 02 A w = L 1 L 2 2(N p + 1) R w = a k w A w Conduction resistance η 01 = 1 A f1 A 1 (1 η f1 ) η 02 = 1 A f2 A 2 (1 η f2 ) η f = tanh (Ml f) Ml f M = 2h k f δ f l f is the length of the fin δ f is the fin thickness

47 Some types of plate fin Compact HX a) Plain triangular fin b) Plain rectangular fin c) Wavy fin d) Offset strip fin e) multi-louver fin f) Perforated fin

48 Fin types for plate fin compact heat exchanger

49 4-Examples

50 Air at p=1 atm T=400 K U =10 m/s Find h and Dp

51 Example 10.1

52 Example 10.1

53 Air at p=2 atm T=500 K U =20 m/s Find h and Dp

54 Example 10.2

55 Example 10.2

56 To=100 C Air at p=1 atm T=30 C m=1500 kg/s A fr =0.25 m 2 Find h and Dp

57 Example 10.3

58 Example 10.3

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