Helical Double-tube HX

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Ideas for Creation of Compact HX!!!

Helical Double-tube HX

Secondary Flow in Helical Coils

• The form of the secondary flow would depend on the ratio of the tube diameters and other factors.

• A representative secondary flow pattern is shown below:

• Thirdly, this configuration should lead to a more standard approach for characterizing the heat transfer in the exchanger.

• The ratio of the two tube diameters may be one of the ways to characterize the heat transfer.

Heat Transfer in Helical Tubes

Acharya et al. (1992, 2001) developed the following two correlations of the Nusselt number, for Prandtl numbers less than and greater than one, respectively.

Heat Transfer in Helical Annulus

Nusselt numbers for the annulus have been calculated and correlated to a modified Dean number.

The modified dean number for the annulus is calculated as it would be for a normal Dean number, except that the curvature ratio used is based on the ratio of the radius of the outer tube to the radius of curvature of the outer tube, and the Reynolds number based on the hydraulic radius of the annulus.

Thus the modified Dean number is:

Helical Coils: Laminar flow

• De is Dean Number. De=Re (a/R)1/2.

• Srinivasan et al. (7 < R/a < 104):

• Manlapaz and Churchill:

• Correction for vp:

0.275

0.5

1 for 30

0.419 for 30 300

0.1125 for 300

c

s

Def

De Def

De De

0.5

2

0.52

0.18 /1.0 1.0

3 88.331 35 /

m

c

s

f a R De

f De

0.25

0.91c w

cp b

f

f

Helical coils: turbulent flow

0.250.5 2 2

0.00725 0.076 Re for 0.034 Re 300c

R R Rf

a a a

0.20.5 2 2

0.0084 Re for Re 700 and 7 10c

R R R Rf

a a a a

0.33Pr

Prc m

cp w

f

f

Annular flow in series & Tubular Flow in Parallel

1

21

11

1

1

1

11,2,

111ln

12

1

RPRR

RR

PTTT

UA

Q exoinoM

Two level Annular flow in series & Tubular Flow in Parallel

1,,

1,2,1 2 inwexmw

exoino

TT

TTR

1,2,

1,1,1

inwino

inwexo

TT

TTP

21,2,

,exwexw

exmw

TTT