Pierwsza strona - Strona główna - Wydział Mechaniczny · Pierwsza strona Introduction to Heat Exchangers What Are Heat Exchangers? Heat exchangers are units designed to transfer

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THERMODYNAMICS

Lecture 15: Heat exchangers

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Introduction to Heat Exchangers

What Are Heat Exchangers?Heat exchangers are units designed to transfer heat from a

hot flowing stream to a cold flowing stream.

Why Use Heat Exchangers?Heat exchangers and heat recovery is often used to improve

process efficiency.

dr hab. inż. D. Mikielewicz, prof. PGThermodynamics

Applications of Heat Exchangers

Heat Exchangersprevent car engine

overheating andincrease efficiency

Heat exchangers areused in Industry for

heat transfer

Heatexchangers areused in AC and

furnaces


Types of Heat Exchangers

There are three broad categories:The recuperator, or through-the-wall non storingexchangerThe direct contact non storing exchangerThe regenerator, accumulator, or heat storageexchanger


Recuperators


Types of heat exchangers

Shell and tube heatexchanger, 1 shell, 1 pass

Shell and tube HEa) 1 shell, 2 passes, b) 2 shells, 4 passes.


Direct Contact


Regenerators


Compact heat exchangers

Heat transfer surface/Volume of HE >700 m2/m3

Hydraulic diameter <5mm, laminar flow

Cores of compact HE:a) Fins on round and rectangular channelsb) Slab-fin (one-pass, muli-pass)


RECUPERATORSHeat transfer in recuperator can take place as steady-stateor transient. Transient heat transfer occurs during thestart-up or shut-down of devices or during the change ofload.

For the possibly simple mathematical description of heattransfer in the recuperator the following assumptions aremade:

· specific heat of both fluids is constant,

· overall heat transfer coefficient k is constant on the entireheat transfer surface,

· no heat losses to surroundings,

heat in the wall is conducted only in the direction normal to the flow.


The closed-type exchanger is the most popular one.One example of this type is the Double pipe exchanger.

In this type, the hot and cold fluid streams do not comeinto direct contact with each other. They are separated by a tube wall or flat plate.


Principle of Heat Exchanger

First Law of Thermodynamic: “Energy is conserved.”

generatedsin out

outin ewqhmhmdtdE

&&&&& +++⎟⎠

⎞⎜⎝

⎛−= ∑ ∑ ˆ.ˆ.

∑∑ −=outin

hmhm ˆ.ˆ. &&h

hphh TCmAQ Δ= ... &

ccpcc TCmAQ Δ= ... &

0 0 0 0

•Control Volume

Qh

Cross Section AreaHOT

COLD

Thermal Boundary Layer

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Q hot Q cold

Th Ti,wall

To,wall

Tc

Region I : Hot Liquid-Solid Convection

NEWTON’S LAW OF COOLING

( )dATThdQ iwhhx .. −= Region II : ConductionAcross Copper Wall

FOURIER’S LAWdrdTkdQx .−=

Region III: Solid –Cold LiquidConvection

NEWTON’S LAW OF COOLING

( )dATThdQ cowcx .. −=

THERMAL

BOUNDARY LAYER

Energy moves from hot fluid to a surface by convection, through the wall by conduction, and then by convection from the surface to the cold fluid.


Region I : Hot Liquid –Solid Convection ih

xiwh Ah

QTT.

=−( )ATThQ iwhhotx .. −=

Region II : ConductionAcross Copper Wall

i

o

copperx

rr

LkQ

ln

2. π=

LkrrQ

TTcopper

i

ox

walliwallo π2.

ln.

,,

⎟⎟⎠

⎞⎜⎜⎝

⎛

=−

Region III : Solid –Cold Liquid Convection oc

xcwallo Ah

QTT., =−( ) ocwallocx ATThQ −= ,

+

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

+⎟⎟⎠

⎞⎜⎜⎝

⎛

+=−occopper

i

o

ihxch AhLk

rr

AhQTT

.1

2.

ln

.1

π

( )chx TTAUQ −= ..1

1.

ln.

.

−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

+⎟⎟⎠

⎞⎜⎜⎝

⎛

+=coldicopper

i

oo

ihot

o

hrkrrr

rhrU

U = The Overall Heat Transfer Coefficient [W/m2.K]

321 RRRQTT x

ch ++=−

U =1

A .ΣR

ro

ri


Calculating U using Log Mean Temperature

coldhot dQdQdQ =−=

ch TTT −=Δch dTdTTd −=Δ )(h

hphh dTCmdQ ..&=

ccpcc dTCmdQ ..&=

Hot Stream :

Cold Stream:⎟⎟⎠

⎞⎜⎜⎝

⎛−=Δ

cpc

chph

h

CmdQ

CmdQTd

..)(

dATUdQ ..Δ−=−⎟⎟⎠

⎞⎜⎜⎝

⎛+Δ−=Δ c

pchph CmCm

dATUTd.1

.1...)(

∫∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛+−=

ΔΔΔ

Δ

2

1

2

1

..1

.1.)( A

Acpc

hph

T

TdA

CmCmU

TTd

( ) ( ) ( )[ ]outc

inc

outh

inhch TTTT

qAUTT

qAU

TT

−−−−=Δ+Δ−=⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ ...ln

1

2

∫∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ+

Δ−=

ΔΔΔ

Δ

2

1

2

1

..)( A

Ac

c

h

hT

TdA

qT

qTU

TTd

⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔΔ−Δ

=

1

2

12

ln.

TT

TTAUQ

Log Mean Temperature


CON CURRENT FLOW

⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔΔ−Δ

=Δ

1

2

12

lnTT

TTTLn

731 TTTTT inc

inh −=−=Δ

1062 TTTTT outc

outh −=−=Δ

COUNTER CURRENT FLOW

1062 TTTTT inc

outh −=−=Δ

731 TTTTT outc

inh −=−=Δ

( ) ( )Ln

cpc

Ln

hph

TATTCm

TATTCm

UΔ−

=Δ

−=

...

... 10763

&&&&

T1T2

T4 T5

T3

T7 T8 T9

T10

T6

Counter - Current Flow

T1 T2T4 T5

T6T3

T7T8 T9

T10

Parallel Flow

Log Mean Temperature evaluation

T1

A

1 2

T2

T3

T6

T4 T6

T7 T8

T9

T10

WallΔT1

ΔT2

Δ AA

1 2


T1

A

1 2

T2

T3

T6

T4 T6

T7 T8

T9

T10

Wall

lmih TAhQ Δ=

ΔTlm =(T3 −T1) − (T6 −T2)

ln(T3 −T1)(T6 −T2)

lmoc TAhQ Δ=

ΔTlm =(T1 −T7) − (T2 −T10)

ln(T1 −T7)(T2 −T10)


Nu = f (Re, Pr, L / D , μ b / μ o )

DIMENSIONLESS ANALYSIS TO CHARACTERIZE A HEAT EXCHANGER

μρ..Dv

kCp μ.

kDh.

Nu = a.Reb .Pr c•Further Simplification:

Can Be Obtained from 2 set of experiments

One set, run for constant Pr

And second set, run for constant Re

)( TTAkQ w −=δ

h

Nu =Dδ


•For laminar flowNu = 1.62 (Re*Pr*L/D)

•Empirical Correlation

14.0

3/18.0 .Pr.Re.023.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

o

bLnNu

μμ

•For turbulent flow

•Good To Predict within 20%•Conditions: L/D > 10

0.6 < Pr < 16,700Re > 20,000


Fouling

( ) ( ) ( ) ( )hh

h

c

c

c

hhcc

AAR

RA

RA

AkAkkA

αηηηαη λ0000

11

111

++++=

==

Fluid R(m2K/W)Sea water and treated water 0.0001boiler feed-water (<50oC)Sea water and treated water 0.0002boiler feed-water (>50oC)River water 0.0002-0.001Combustion oil 0.0009Refrigerants 0.0002Steam 0.0001

http://images.google.com/imgres?imgurl=www.nasact2001.org/Pictures/roller%2520coaster.jpg&imgrefurl=http://www.nasact2001.org/Youth.htm&h=521&w=441&prev=/images%3Fq%3Droller%2Bcoaster%26svnum%3D10%26hl%3Den


Overall heat transfer coefficient

( ) ( )( )

( ) ( )oo

oio

i

i

i

ooii

AAR

Ldd

AR

A

AkAkkA

απλα1

2/ln1

111

++++=

==

Fluid-combination k(m2K/W)Water-water 850-1700Water-oil 110-350Steam condenser (water in tubes) 1000-6000Ammonia condenser (water in tubes) 800-1400 Alcohol condenser (water in tubes) 250-700 Finned tubes (water in tubes,air cross-flow) 25-50

http://images.google.com/imgres?imgurl=www.nasact2001.org/Pictures/roller%2520coaster.jpg&imgrefurl=http://www.nasact2001.org/Youth.htm&h=521&w=441&prev=/images%3Fq%3Droller%2Bcoaster%26svnum%3D10%26hl%3Den


Comparison of counter-current and co-current heat exchangers

Interesting is comparison of cocurrent flow with a counter-current flow at same values of overall heat transfer coefficient k and A. In both cases the following holds

ALMTDkQ =&

Let’s introduce the following notation:

ic,oc,

oc,ih,

ic,ih,

ic,oc,

TTTT

TTTT

−−

=−−

= RP

Ψ = = =+−

−−

− +

&

&log

log

QQ

wspolpr

przeciwpr

wspolpr

przeciwpr

ϑϑ

R 1R 1

ln1 P

1 PR

ln1

1 P(R 1)

That will enable to develop the following ratio:


It results from the figure that the thermal load of co-currentrecuperator is lower than thermal load of counter-currentrecuperator. Only in case of values R=0 or P=0 these loads are same.

Such conditions corresponds to the constant temperature of one offluids (its phase change). The counter-current is always better thatco-current from the point of view of used heat transfer surface.

In other words in case of counter-current the fluid can be heated to a higher temperature than in case of co-current flow.

Comparison of counter-current and co-current heat exchangers


Multi-pass and cross-flow HEThe mean temperature difference in arbitrary recuperator is:

current-counterlog,TΔ=Δ FT

The method of calculation of recuperator is based on thefact that on the basis of knowledge of inlet and outlettemperature of both fluids the values of P and R aredetermined. Then from the chart F=F(P,R) the value of F isfound, which enables for calculation of mean temperaturedifference at a prior determination of mean temperaturedifference fopr the case of the counter-current.

R)P,(FF = P 1< R ≠ 1

currentcounter−Δ=

,logTkFQA&

Then the heat transfer surface is calculated from the relation


Correction coefficients F for shell and tube HE:a) One shell, multiple of two-passes (2, 4, 6, ...)b) Two shells, multiple of four-passes (4, 6, 12 ...)

Multi-pass and cross-flow HE


Correction coefficients for cross-flows HE of 1-pass with non-mixing fluids.

Correction coefficients for cross-flows HE of 1-pass with one mixing fluid and one non-mixing fluids.

Multi-pass and cross-flow HE


Design procedure

1. Formulation of thermal balance

• one temperature can be determined from here

• the rate of heat in HE can be determined

2. Selection of flow orientation, approximate distribution of temperatures and calculationof logarithmic mean temperature difference

3. Initial assumption of the heating surface (diameter of tubes) and flow of fluid aroundthem

• inside tubes should be the more aggressive fluid, giving fouling with high pressure

• on external side of tubes is the flow with higher viscosity, with smaller pressure drop

• external diameter from the range: 10 … 15… 25 … 40 mm

• wall thickness from the range 0 … 2.5 mm (due to strength of material)

• assumption of the spatial pitch, i.e. parallel, hexagonal (highest packing), concentric,

• assumption of the ratio s/dz


Design procedure

4. Initial assumption of flow velocity inside tubes (from experience) and determination ofthe number of tubes assuming that the flow must be turbulent and fouling would not appear,

5. calculation of heat transfer coefficients on both sides of tubes. When the ratioα1/α2 < 4 … 5 then the finned surface for a worse α should be considered.

6. Calculation of heat transfer surface (the one with worse heat transfer)

7. Check on hydraulic resistance, if these are too high then return to step 3.

• pumping power, parameter N/Q = 0.5 … 1 %, if outside that range then calculationsmust be repeated for other parameters.


Design procedure8. Final establishing of HE geometry with account of:

• thermal compensation

• technological conditions of manufacturing and assembly, sometimes transport

• necessity and possibility of cleaning

• possibility of repair (exchange of tubes or their sealing)

• total costs (reliability)

9. Strength calculations in accordance to standards

• if p< 1.4 MPa and temperatures < 150 oC no compensation required

• elastic compessator (up to 800 kPa)

• free head (expensive, difficult access to sealings, leaks may not be detected)

• throttle (p<10 bar, for small shell diameters, cause of leaks)

• bended tubes

• individual throttles on the tubes


Design procedure

10. Final calculations of assumed version of design

11. Schematic of pipelines and connection into the system

12. Design drawings

13. Calculation and determination of characteristics





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Pierwsza strona - Strona główna - Wydział Mechaniczny · Pierwsza strona Introduction to Heat Exchangers What Are Heat Exchangers? Heat exchangers are units designed to transfer