THERMODYNAMICS Lecture 15: Heat exchangers

Transcription

1 HERMODYNAMICS Leture 5: Heat exangers Pierwsza strona

2 Introdution to Heat Exangers Wat Are Heat Exangers? Heat exangers are units designed to transfer eat from a ot flowing stream to a old flowing stream Wy Use Heat Exangers? Heat exangers and eat reovery is often used to improve proess effiieny Pierwsza strona

3 dr ab inż D Mikielewiz, prof PG ermodynamis Appliations of Heat Exangers Heat Exangers prevent ar engine overeating and inrease effiieny Heat exangers are used in Industry for eat transfer Heat exangers are used in AC and furnaes

4 dr ab inż D Mikielewiz, prof PG ermodynamis ypes of Heat Exangers ere are tree broad ategories: e reuperator, or troug-te-wall non storing exanger e diret ontat non storing exanger e regenerator, aumulator, or eat storage exanger

5 dr ab inż D Mikielewiz, prof PG ermodynamis Reuperators

6 dr ab inż D Mikielewiz, prof PG ermodynamis ypes of eat exangers Sell and tube eat exanger, sell, pass Sell and tube HE a) sell, 2 passes, b) 2 sells, 4 passes

7 dr ab inż D Mikielewiz, prof PG ermodynamis Diret Contat

8 dr ab inż D Mikielewiz, prof PG ermodynamis Regenerators

9 Compat eat exangers Heat transfer surfae/volume of HE >700 m 2 /m 3 Hydrauli diameter <5mm, laminar flow Cores of ompat HE: a) Fins on round and retangular annels b) Slab-fin (one-pass, muli-pass) dr ab inż D Mikielewiz, prof PG ermodynamis

10 dr ab inż D Mikielewiz, prof PG ermodynamis RECUPERAORS Heat transfer in reuperator an take plae as steady-state or transient ransient eat transfer ours during te start-up or sut-down of devies or during te ange of load For te possibly simple matematial desription of eat transfer in te reuperator te following assumptions are made: speifieatofbotfluidsisonstant, overall eat transfer oeffiient k is onstant on te entire eat transfer surfae, no eat losses to surroundings, eat in te wall is onduted only in te diretion normal to te flow

11 dr ab inż D Mikielewiz, prof PG ermodynamis e losed-type exanger is te most popular one One example of tis type is te Double pipe exanger In tis type, te ot and old fluid streams do not ome into diret ontat wit ea oter ey are separated by a tube wall or flat plate

12 dr ab inż D Mikielewiz, prof PG ermodynamis Priniple of Heat Exanger First Law of ermodynami: Energy is onserved de dt m& ˆ in m& ˆ out + q& + w& s + e& in out generated Q Q Am & C p p Am & C m& ˆ in m& ˆ out Control Volume Cross Setion Area COLD Q HO ermal Boundary Layer

13 HERMAL BOUNDARY LAYER Energy moves from ot fluid to a surfae by onvetion, troug te wall by ondution, and ten by onvetion from te surfae to te old fluid Region III: Solid Cold Liquid Convetion NEWON S LAW OF COOLING dq ( x ow )da i,wall o,wall Region I : Hot Liquid- Solid Convetion Q ot Q old NEWON S LAW OF COOLING dq ( )da Region II : Condution Aross Copper Wall x iw FOURIER S LAW d dq x k dr Pierwsza strona

14 dr ab inż D Mikielewiz, prof PG ermodynamis Region I : Hot Liquid Solid Convetion i x iw A Q ( )A Q iw ot x Region II : Condution Aross Copper Wall i o opper x r r L k Q ln 2 π L k r r Q opper i o x wall i wall o 2π ln,, Region III : Solid Cold Liquid Convetion o x wall o A Q, ( ) o owall x A Q, o opper i o i x A L k r r A Q 2 ln π ( ) x U A Q ln + + old i opper i o o i ot o r k r r r r r U U e Overall Heat ransfer Coeffiient [W/m 2 K] 3 2 R R R Q x + + U A ΣR r o r i

15 dr ab inż D Mikielewiz, prof PG ermodynamis Calulating U using Log Mean emperature dq ot dq old dq d d d ( ) p d m C dq & p d mc dq & Hot Stream : Cold Stream: p p m C dq m C dq d ) ( da U dq + p p C m C m da U d ) ( ) ( A A p p da C m C m U d ( ) ( ) ( ) [ ] out in out in q A U q A U + ln ) ( A A da q q U d 2 2 ln A U Q Log Mean emperature

16 Log Mean emperature evaluation 2 Ln 2 ln CON CURREN FLOW 2 m& C& U A ( ) m& C& ( ) p 3 6 p 7 0 Ln A COUNER CURREN FLOW 2 Ln Wall 2 4 A A Parallel Flow in in 3 7 out out dr ab inż D Mikielewiz, prof PG ermodynamis Counter - Current Flow in out 3 7 out in 2 6 0

17 dr ab inż D Mikielewiz, prof PG ermodynamis Q A i lm 2 lm ( 3 ) ( 6 2 ) ln ( 3 ) ( 6 2 ) Wall A Q A o lm lm ( 7 ) ( 2 0 ) ln ( 7 ) ( 2 0 )

18 dr ab inż D Mikielewiz, prof PG ermodynamis DIMENSIONLESS ANALYSIS O CHARACERIZE A HEA EXCHANGER Nu f (Re, Pr, L / D, μ b / μ o ) D k vdρ μ C p μ k Furter Simplifiation: Nu are b Pr Can Be Obtained from 2 set of experiments One set, run for onstant Pr And seond set, run for onstant Re Nu D δ k Q A( ) w δ

19 dr ab inż D Mikielewiz, prof PG ermodynamis Empirial Correlation For laminar flow Nu 62 (Re*Pr*L/D) For turbulent flow Nu Ln 0023 Re 08 Pr / 3 μ b μ o 04 Good o Predit witin 20% Conditions: L/D > 0 06 < Pr < 6,700 Re > 20,000

20 Fouling dr ab inż D Mikielewiz, prof PG ermodynamis Fluid R(m 2 K/W) Sea water and treated water 0000 boiler feed-water (<50 o C) Sea water and treated water boiler feed-water (>50 o C) River water Combustion oil Refrigerants Steam 0000 ka k A k A + R + R λ ( η 0αA) ( η A) ( η A) ( η αa) R +

21 Overall eat transfer oeffiient Fluid-ombination k(m 2 K/W) Water-water Water-oil Steam ondenser (water in tubes) Ammonia ondenser (water in tubes) Alool ondenser (water in tubes) Finned tubes (water in tubes, air ross-flow) dr ab inż D Mikielewiz, prof PG ermodynamis ka k A i i ( αa) ( A) i + k A o R i o i + ( d / d ) ln o 2πλL i + R o + ( A) o ( αa) o

22 Comparison of ounter-urrent and ourrent eat exangers Interesting is omparison of ourrent flow wit a ounterurrent flow at same values of overall eat transfer oeffiient k and A In bot ases te following olds Q & k LMD Let s introdue te following notation: A,o,i P R,i,i,i,o,o,i at will enable to develop te following ratio: dr ab inż D Mikielewiz, prof PG ermodynamis Q& ϑ wspolpr log wspolpr Ψ Q& ϑ przeiwpr log przeiwpr ln P R+ PR R ln P(R+ )

23 Comparison of ounter-urrent and ourrent eat exangers It results from te figure tat te termal load of o-urrent reuperator is lower tan termal load of ounter-urrent reuperator Only in ase of values R0 or P0 tese loads are same Su onditions orresponds to te onstant temperature of one of fluids (its pase ange) e ounter-urrent is always better tat o-urrent from te point of view of used eat transfer surfae In oter words in ase of ounter-urrent te fluid an be eated to a iger temperature tan in ase of o-urrent flow dr ab inż D Mikielewiz, prof PG ermodynamis

24 Multi-pass and ross-flow HE e mean temperature differene in arbitrary reuperator is: F log,ounter-urrent F F(P, R) P< R e metod of alulation of reuperator is based on te fat tat on te basis of knowledge of inlet and outlet temperature of bot fluids te values of P and R are determined en from te art FF(P,R) te value of F is found, wi enables for alulation of mean temperature differene at a prior determination of mean temperature differene fopr te ase of te ounter-urrent en te eat transfer surfae is alulated from te relation Q& A kf dr ab inż D Mikielewiz, prof PG ermodynamis log, ounter urrent

25 dr ab inż D Mikielewiz, prof PG ermodynamis Multi-pass and ross-flow HE Corretion oeffiients F for sell and tube HE: a) One sell, multiple of two-passes (2, 4, 6, ) b) wo sells, multiple of four-passes (4, 6, 2 )

26 Multi-pass and ross-flow HE Corretion oeffiients for ross-flows HE of -pass wit nonmixing fluids Corretion oeffiients for ross-flows HE of -pass wit one mixing fluid and one non-mixing fluids dr ab inż D Mikielewiz, prof PG ermodynamis

27 dr ab inż D Mikielewiz, prof PG ermodynamis Design proedure Formulation of termal balane one temperature an be determined from ere te rate of eat in HE an be determined 2 Seletion of flow orientation, approximate distribution of temperatures and alulation of logaritmi mean temperature differene 3 Initial assumption of te eating surfae (diameter of tubes) and flow of fluid around tem inside tubes sould be te more aggressive fluid, giving fouling wit ig pressure on external side of tubes is te flow wit iger visosity, wit smaller pressure drop external diameter from te range: mm wall tikness from te range 0 25 mm (due to strengt of material) assumption of te spatial pit, ie parallel, exagonal (igest paking), onentri, assumption of te ratio s/d z

28 dr ab inż D Mikielewiz, prof PG ermodynamis Design proedure 4 Initial assumption of flow veloity inside tubes (from experiene) and determination of te number of tubes assuming tat te flow must be turbulent and fouling would not appear, 5 alulation of eat transfer oeffiients on bot sides of tubes Wen te ratio α /α 2 < 4 5 ten te finned surfae for a worse α sould be onsidered 6 Calulation of eat transfer surfae (te one wit worse eat transfer) 7 Cek on ydrauli resistane, if tese are too ig ten return to step 3 pumping power, parameter N/Q 05 %, if outside tat range ten alulations must be repeated for oter parameters

29 dr ab inż D Mikielewiz, prof PG ermodynamis Design proedure 8 Final establising of HE geometry wit aount of: termal ompensation tenologial onditions of manufaturing and assembly, sometimes transport neessity and possibility of leaning possibility of repair (exange of tubes or teir sealing) total osts (reliability) 9 Strengt alulations in aordane to standards if p< 4 MPa and temperatures < 50 o C no ompensation required elasti ompessator (up to 800 kpa) free ead (expensive, diffiult aess to sealings, leaks may not be deteted) trottle (p<0 bar, for small sell diameters, ause of leaks) bended tubes individual trottles on te tubes

30 dr ab inż D Mikielewiz, prof PG ermodynamis Design proedure 0 Final alulations of assumed version of design Semati of pipelines and onnetion into te system 2 Design drawings 3 Calulation and determination of arateristis

31 dr ab inż D Mikielewiz, prof PG ermodynamis

32 dr ab inż D Mikielewiz, prof PG ermodynamis

33 dr ab inż D Mikielewiz, prof PG ermodynamis

34 dr ab inż D Mikielewiz, prof PG ermodynamis