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Calculation of single phase pressure drop in heat exchangers considering the change of fluid properties along the flow path

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Abstract

The cost-optimized design of heat exchangers requires a fast but reliable calculation of pressure drop which makes a major contribution to running costs. For cocurrent and counter-current flow a simple approximating calculation method is presented, taking into account the variation of the fluid properties along the flow path. For any practical case reliable results are obtained only by calculating both the pressure drop and the local overall heat transfer coefficient at least at two points of the heat exchanger. In the special case of a gas in a turbulent flow and when, as usual, the major resistance to heat transfer is caused by the gas, it is sufficient to calculate only the pressure drop and at one point only. Pressure drops calculated exactly or by the proposed approximation compare well.

Zusammenfassung

Bei der Optimierung von Wärmeaustauschern ist zur Ermittlung der Betriebskosten eine schnelle und möglichst genaue Berechnung des Druckverlustes erforderlich. Es wird ein einfaches, für Gleich- und Gegenstrom gültiges Näherungsverfahren zur Berechnung des Druckverlustes hergeleitet, welches die Veränderlichkeit der Stoffwerte entlang des Strömungsweges berücksichtigt. Um in beliebigen, praktisch vorkommenden Fällen zuverlässige Ergebnisse zu erhalten, muß der Druckverlust und darüber hinaus der örtliche Wärmedurchgangskoeffizient an mindestens zwei Stellen des Wärmeaustauschers berechnet werden. Im Sonderfall eines turbulent strömenden Gases genügt es, allein den Druckverlust an nur einer Stelle zu berechnen, wenn, wie es meist der Fall ist, der Hauptwiderstand für den Wärmedurchgang auf der Gasseite liegt. Ein Vergleich von näherungsweise und exakt berechneten Beispielen liefert gute Ergebnisse.

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Abbreviations

A, a, B, b:

constants

Ċ:

product of specific heat and mass flow rate

c, D:

constants

d:

tube diameter (inside)

E:

a constant

F:

heat transfer area (with index q cross-section)

f:

variable heat transfer area beginning at the inlet

G, H, K:

constants

k:

local overall heat transfer coefficient

L:

length of flow path

l:

variable length of flow path beginning at the inlet

M:

a constant

M:

mass flow rate

n:

number of points in the Gaussian integration

Pr:

Prandtl-number

p:

pressure

R:

special gas constant

T:

absolute temperature

t, U:

constants

u:

a function (Appendix)

V:

ratio

w:

mean velocity in a cross-section

x:

dimensionless variable (def. in Eq. 64)

a:

local film coefficient for heat transfer

β :

exponent

δ :

finite difference

ζ :

dimensionless pressure drop

θ :

temperature

ξ :

dimensionless flow path or heat transfer area

ρ :

density

0, 1:

at inlet or outlet of stream under consideration

(0), (1):

determined with the fluid properties taken at P0 or p1, respectively

i:

counter for representative points in Gaussian integration

j:

special value (Appendix)

I, II:

these representative points

ρ, δ θ :

a function ofθ, Δ θ

p:

a function of p

P0 :

determined at p0

o:

when used withρ orζ: values at the pressure p0

q:

cross-section

M:

mean value

T:

at turbulent flow regime

L:

at laminar flow regime

In mean:

logarithmic mean value

Tm :

calculated with Tm

w:

at the wall

e:

estimated value

t:

true value

′:

cold stream

″:

area average mean value

*:

effective net value

References

  1. Roetzel, W.: Berücksichtigung veränderlicher Wärmeübergangskoeffizienten und Wärmekapazitäten bei der Bemessung von Wärmeaustauschern. Wärme- u. Stoffübertragung 2 (1969) 163/170.

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  2. Peters, D. L.: Heat-exchanger design with transfer coefficients varying with temperature or length of flow path. Wärme-u. Stoffübertragung 3 (1970) 220/226.

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  3. Gregorig, R.: Wärmeaustauscher. Aarau u. Frankfurt/M. H. R. Sauerländer & Co. 1959.

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  4. Geisler, K. W.: Leitertafel zum Bestimmen der Reibung bei Strömungen durch Rohrleitungen. Wärme 77, H. 1, März 1971, 21/22.

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  5. Taylor, M. F.: Prediction of friction and heat-transfer coefficients with large variation in fluid properties. Nasa TM X-2145, National Aeronautics and Space Administration, Washington, D.C., December, 1970.

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  6. Gröber, Erk, Grigull: Grundgesetze der Wärmeübertragung. Berlin/Göttingen/Heidelberg: Springer 1963. S. 205 und 215.

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  7. Roetzel, W.: Querangeströmte Rohrbündelwärmeaustauscher, Maschinenmarkt, Würzburg Jg. 76 (1970), Nr. 27-KW17, S. 523/526.

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Authors and Affiliations

  1. Chemical Engineering Group, Council for Scientific and Industrial Research, P.O. Box 395, Pretoria, South Africa

    W. Roetzel

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  1. W. Roetzel
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Roetzel, W. Calculation of single phase pressure drop in heat exchangers considering the change of fluid properties along the flow path. Wärme- und Stoffübertragung 6, 3–13 (1973). https://doi.org/10.1007/BF01270699

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  • DOI: https://doi.org/10.1007/BF01270699

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