Helically coiled heat exchanger 3

[rjw57]

Hello everyone,

I am involved in the analysis of some equipment which uses a helically coiled tubing heat exchanger. I have a number of great heat transfer resources in my possession. One of these (from Beggell House) has empirical correlations for heat transfer inside a helically coiled tube. What I cannot find is empirical correlations for the following:
1) Convective heat transfer on the outside of the helically coiled tube,
with this flow parallel to the centerline axis of the helix. Correlations would be for either co- or counter-current flow on the inside.
2) Pressure drop for case 1 above.
3) Pressure drop for flow internal to the tubing.

Any formulas, references or even a willingness to fax or mail any info (my cost) would be greatly appreciated.

Thank you all...

 

[Gianfranco]

Hi Robert,

1. You can use the Zukauskas's correlation for a bundle of tubes for in line arrangement:

Nu (outside) = C Re^n * Pr^0,36 * (Pr/Prw)^0,25

Where (SI notations):
Nu = Nusselt
Re = Reynolds (at v max)
Pr = Prandtl
w = wall
C n
Re < 100.000 0,27 0,63
Re >= 100.000 0,021 0,84

Properties evaluated at fluid temp. (indisturbed) except Prw
For details see:
- Ozisik, Heat Transfer - A Basic Approach, Mc Graw Hill
- E. Guyer - Handbook of Applied Therma Design, Ed. Taylor&Francis

The correlations for inside heat transfer coeff., introduce the:

Dean Number = (Dia. coil/dia. tube)

Laminar flow:
Nu = 0,76 + 0,065 * Dn^0,5 * Pr^0,175
Valid for 5 < Pr < 175
Nu = 0,913 Dn^0,476 Pr^02
Valid for 0,7 < Pr < 5

Turbolent flow:
Nu = 0,023 Re ^0,85 * (d/Dc)^0,1 * Pr^0,40

For details see:
- Rohsenow, Hartnett, Ganic - Handbook of Heat Transfer Fundamentals, McGraw Hill. ch. 7
- E. Guyer - Handbook of Applied Therma Design, Ed. Taylor&Francis

2. The outside friction factor

Dp= f N (ro*u max^2/2) * (muw/mu)
f = ( C1 + C2/( ( ST/D-1 )^n ) ) * Re^-m

where:
N = number or in line tubes
ro = density
muw = dynamic viscosity at wall temperature
C1= 0,176
C2 = 02*SL/D
ST = Dc = dia. coil
SL = Pitch of the coil
n = 0,43 +1,13*SL/D
m = 0,15

For details see as (1).

3. The inside friction factor is:

Laminar flow
f/fst = (1 - (1 - (11,6/Dn)^0,45 )^2,22 )^-1
valid for 11,6 < Dn < 2000

Turbolent flow
f*(Dc/d)^0,5 = 0,00725 + 0,076 * (Re * (d/Dc)^2 )^-0,25
valid for 0,034 < (Re * (d/Dc)^2 < 300
f = 16/Re
valid for (Re * (d/Dc)^2 < 0,034
f =,079 * ( d/Dc)^0,5 / ((Re * (d/Dc)^2 )^0,20
valid for (Re * (d/Dc)^2 > 6
For Dc/d > 860 there isn't any difference with the straight tubes.

where:
Dn = Dean Number = Re * (d/Dc)^0,50
Fst = 16/Re

For details see as (1).

I advise you to introduce the effectiveness approach in designing the heat exchanger: see ref. as (1) and (2).

Hoping this is useful to you.

Gianfranco

 

[rjw57]

Ciao Gianfranco,

Thank you for your quick reply. I was concerned about the use of straight tube bundle correlations. This would seem to me to be a problem involving a series-series type arrangement of unmixed(inside)-mixed (outside)cross-flow. Each pitch of the coil would represesnt a &quot;stage&quot; of crossflow in my mind. If this is what you are referring to for the effectiveness approach to the problem solution, then I understand what you mean. If not, could you please clarify.

Finally, I was not totally clear in my problem definition (to avoid too much detail). My real problem involves multiple coil diameters (4 to be exact). I assume you think that a tube bundle approach would still be appropriate, true?

Thanks again...
Bob

 

[Gianfranco]

Bob, thanks for &quot;Ciao&quot;.

Yes, your assumption << each pitch of the coil would represesnt a &quot;stage&quot; of crossflow>> seems correct to me.
The effectiveness approach avoids the use of correction factor F = f(P, R).

The effectivenss eps as follows:

eps = Ch * dTh /(Cmin *(th,1 - tc,1) = Cc * dTc /(Cmin *(th,1 - tc,1)
eps = 1- exp { [ exp (-Ntu^0,78 * Cmin/Cmax) - 1] / [Ntu^-0,22 * Cmin/Cmax] }

where:
DT = temp. difference
h = hot
c = cold
C = m Cp
Ntu = A *U/Cmin

The formula is valid for a cross-flow with both fluid unmixed.
For a multipass heat exchanger you can discretize the field flow and apply the formula for the single pass.
For details see:
- Kays and Crawford, Convective Heat and Mass Transfer, Mc Graw Hill.

Is the coil shaped on a cone's surface?
In this case you could taking into account 4 rings with different mean Dc.
If the ST > 2-3 I adivise you of approaching the heat transfer coefficient calculations as a single cylinder or a coil with 1 ring.

Ciao!

Gianfranco

 

[rjw57]

Hi Gianfranco,

I was reviewing some of your formulas yesterday. I am particularly interested in the following items and would like clarification if you would be so kind:

a) Dean Number = (Dia. coil/dia. tube)
b) Dn = Dean Number = Re * (d/Dc)^0,50
c) Fst = 16/Re

First, I think I see a discrepancy (possibly) in terminology in a) and b). Is one right and the other wrong, or does the Dean Number have different meanings in different contexts?

Second, and this is very important, can you confirm that Fst = 16/Re is correct? I have found indications that it should be 64/Re, a factor of 4 in pressure drop!

Thanks again for your time...
Bob

 

[Gianfranco]

Hello Bob,

I confirm you that Dn = Dean Number = Re * (d/Dc)^0,50. The first Dn's definition was incomplete: sorry.

I confirm that Fst = 16/Re
The author Mr. Ito, Friction Factor for Turbolent Flow in Curved Pipes, J. Basic. Eng. 81, 123, 1959, uses Fst that is equal to the Fanning's Friction factor cf.
You are saying the true: the conventional friction factor f, used in conjuncion with Moody diagram (originated on 1944), is = 64/Re.
I personally should use the Fanning formula.
But, seeing the hystorical confusion on Friction Factors, I advise you to check the result of algorithm f/fst for Dn < 11,6 when the tube can be assimilated at the straight tube.

I've checked my the previous message and I've found out an other fault on laminar Nu. The correlation is:

Nu = (0,76 + 0,065 * Dn^0,5 ) * Pr^0,175

Further details are in:

Seban, Mc Laughlin, Heat Transfer in Tube Coils with Laminar and Turbolent Flow, Int. J. Heat Mass Transfer, 6, 387, 1963.

Let me apologize to you for the two mistakes.

Did you set the simulation of the coil?

Gianfranco