Finding friction factor for low temperature helium flow through serrated type plate-fin heat exchanger using CFD

B V Shah 1, A K Sahu2, N Mamgain 2, S V Jain 3, P Shrama4

1Bhakti Consultants, Gandhinagar, India 2Institute for plasma research, Bhat Village, Gandhinagar. Gujarat, India

3 Institute of Technology, Nirma University, Ahmedabad, Gujarat 4 Indus Institute of Engineering and Technology, Rancharda, Kalol , Gujarat, India

*E-mail : bhagyashri.parikh@yahoo.com , aksahu@ipr.res.in

Abstract: Serrated type plate-fin heat exchangers are good for high heat transfer coefficients due to high turbulence. But the serrated type gives larger pressure drop than that of other types. These can be used suitably for helium plant application, where high thermal effectiveness is important, but at the design

phase it should be ensured that pressure drop is not high and it should be about few tens of mbar. The present analysis has been done to find friction factor and pressure drop for a segment of plate-fin exchanger of helium plant considering empirical co-relations of Manglik and Bergles and computational fluid

dynamic (CFD) software. This heat exchanger is designed for 2-stream counter-flow configuration with serrated fins and for operation with temperature range between 7 to 4.5 K, at pressure 4 bar for hot helium stream and 1.2 bar for cold helium stream. Serrated fins of thickness 0.2 mm, has been used.

Calculated pressure drop, based on empirical co-relations, for this heat exchanger for both streams is less than 10 mbar. The pressure drop, found from CFD analysis is higher than that found from empirical co-relations. This paper will discuss in detail the method and results of CFD & co-relation based analysis.

INTRODUCTION

CONCLUSIONS

REFERENCES

For serrated fins, friction factor, f, is given by MB [1] correlation as below for 120<Re<104

(Reynold no. of our applications fall in this range),

Thermal effectiveness and pressure losses of heat exchangers are some of the

important parameter which decides the efficiency of helium refrigerator/liquefier.

To achieve high thermal effectiveness, serrated type plate-fin heat exchangers

(PFHE) are used.

Serrated type PFHEs provide higher heat transfer coefficient due to generation of

high turbulence,

It gives higher pressure drop also.

We will be using serrated type PFHEs for the exchangers required in the cold box

of helium refrigerator/liquefier (HRL), being designed and developed at IPR.

The heat exchanger (named as HE8 and shown in figure 1) will have operating

temperature range of 4.4 to 7 K and this heat exchanger is analysed in this paper

for estimation of friction factor and pressure drops.

To find friction factor and pressure drop there are different correlations and here,

Manglik and Bergles (MB) [1] correlation is used.

MB correlation is valid for larger range of Reynold No. (120 < Re < 104).

For validation of this correlation CFD analysis has been done to find friction

factor. The counter-flow configuration with process parameters are as in table 1 for

the heat exchanger which is designed for HRL.

CFD analysis of this 2-stream (He/He) plate fin heat exchanger is carried out to

analyse the internal flow and friction factor.

For finding friction factor by MB correlation, average property value is used,

where as in CFD, realistic fluid property variation can be taken into account.

Hence for better comparison, a temperature range (100 to 110 K) is chosen,

where, fluid properties are nearly constant and using same geometric

configuration and keeping all other parameters same, CFD modelling and

analysis has been done to find pressure drop and friction factor.

As the whole heat exchanger modeling, meshing and analysis will need large no.

of elements (more than 200 million elements), symmetric boundary condition

with a small segment of heat exchanger is modelled and analysed.

Initially, to establish the minimum size of the heat exchanger required for

accurate result, different small segments were tried.

Grid-independence test is also done to find minimum size of element required for

reliable results.

Design of PFHE[2]

The PFHEs are a stack of hot and

cold fluid layers arranged

alternately to have high heat

transfer and parting sheets

between layers separate the flow.

[3,4].

MODELING AND ANALYSIS WITH CFD

DESIGNED DIMENSIONS OF PFHE

Grid independence test, Selection of Turbulence Model and boundary condition

Figure 3: (a) Model with 2-layer and 108.8 mm long & (b) Model with elements

Table 3: Options of Solution technique

Figure 6: Pressure drop variation w.r.t different Reynold No.s for 108.8 mm long model

Process parameters Cold side Hot side

Temperature

Inlet/Outlet

4.408 K/5.662K 5.982 K/5.255 K

Pressure 1.2 bar 4 bar

Mass flux 3.55 kg/(m2.s) 9.38 kg/(m2.s)

Figure 1: Sectional view of HE8

Figure 2: Different parts of thermal section

Overall designed parameters of heat exchanger are given in table 2. Figure 1 and 2

show main parts of heat exchanger.

Parameters Specifications

Type of fin Serrated fin or off-set

type fin

Hot stream: Fin

thickness/height

/density

0.2 mm/6mm/787

fins/m

Cold stream:

Fin

thickness/height

/density

0.2 mm/8 mm/787

fins/m

Fin serration

length for both

streams

3.2 mm

No of cold

layers/hot layers 14/7

Fin Material Al3003

Mass

flux(𝑚) cold side 3.55 kg/(m2.s)

Mass

flux(𝑚) hotside 9.38 kg/(m2.s)

Length/Width/H

eight

417 mm/300 mm/195

mm

Pressure

drop(Hot

side/cold side)

32.77 Pascal/23.55

Pascal

Figure 4: Grid independence test Figure 5: Results with different turbulence

models

The solution technique

options chosen for the

analysis of different

domains is shown in

Table 3.

Parameters Options chosen for solution technique

Scheme Pressure-velocity coupling scheme-simple

Model Simple, k-𝜖 Turbulent model

Inlet input condition Mass flow and temperature inlet

Outlet input condition Pressure outlet

Material Fluid-Helium, Solid-Aluminium

Discretization Second order up winding scheme

Figure 6 shows (with data of table 4) the deviation of 9 % in cold side friction factor and 15 % in hot side

friction factor for our designed mass flow rate.

So it shows that the co-relation used for design data are acceptable as per CFD analysis.

Figure 3 (a) shows model with fluid for a cold layer with a hot layer separated by a partition sheet.

It is 108.8 mm long having 34-rows or serrations of fins along the length and 2-fins along the

width of 3.38 mm. Figure 3 (b) shows the mesh generation for 108.8 mm long model. It has1.6

million elements with skewness 0.88, minimum element size 0.16 mm and maximum element size

0.32 mm.

Cold layer He mass flow rate(10-5

kg/sec)

4.70 9.40 12.5 18.8

Hot layer He mass flow rate(10-5

kg/sec)

8.4 16 22 33

Table 4: Different mass flow rate used for CFD analysis

Further, results obtained for hot and cold fluid with CFD analysis are compared with that

obtained from co-relation for different lengths of 38.4, 51.2, 75 and 108.8 mm with 4 fins

along the width and with different mass flow rates given in table 4.

As shown in the figure 7 (a) ,7(b) with data table 5, the friction factor in hot stream and cold

stream obtained from CFD analysis are matching with the co-relation based friction factor

within 10-15% deviation for designed mass flow rate.

Figure 7: Friction factor variation with respect to Re, (a) for hot stream and (b) for cold

stream

Length Mass flux f(c)(CFD

)

f(c)(Co-re) Deviatio

n (%)

f(h)(CF

D)

f(h)(co

-re)

Deviati

on (%)

108.8

mm

9.38 kg/(m2.s)

for H stream

3.55 kg/(m2.s)-

for cold stream

0.016 0.014 12 0.010 0.0088 12

The velocity contours and pressure contours are shown in figure 8.

Figure 8: Velocity and Pressure contours

ANALYSIS OF DIFFERENT DOMAINS WITH NON-

LINEAR HELIUM PROPERTY VARIATION

Pressure drop variation with non-linear fluid property variations (density, specific heat,

thermal conductivity and viscosity) of helium is analysed with CFD.

Geometry and mesh generation is same as given in figure 3 (a) and (b).

For full length of 416 mm, pressure drop values (table-6) based on CFD can be compared

with that from co-relation based results (table-2).

It shows about 50% deviation. This large deviation is due to the fact that co-relation

based result uses average properties of helium fluid.

Model

Length

(mm)

(width 3.38

mm)

Mass

flux(C)kg/sec/m2

Mass flux (H)

kg/sec/m2

Pressure drop hot

(Pa)

Pressure

drop

cold(Pa)

38.4 3.55 9.38 2.75 1.28

51.2 3.55 9.38 3.61 1.71

75 3.55 9.38 4.03 2.155

416 3.55 9.38 24.66 16.29

In the present study, validation of pressure drop estimations of counter flow PFHE with

serrated fin operating with He/He is carried out. CFD simulation of different portion of

heat exchanger is done and following conclusions are drawn.

With constant properties of Helium, friction factor is found to be about 15% higher if

estimated by CFD compared to Manglik and Bergles co-relation based results.

In the design, about 20% margin on pressure drop should be considered if pressure

drops are estimated based on Manglik and Bergles co-relation based methods.

The deviation is lower for higher Re No. For non-linear fluid property variation, the

CFD results found to be lower than found through co-relation based method.

[1] Manglik, Raj M., and Arthur E. Bergles. "Heat transfer and pressure drop correlations for

the rectangular offset strip fin compact heat exchanger."Experimental Thermal and Fluid

Science 10.2 (1995): 171-180.

[2] Barron R F Text book of cryogenic heat exchanger. Philadelphia: Taylor & Francis

Publication; 1999.

[3] I L, Ranganayakulu C, Shah R K. Numerical study of flow patterns of compact plate fin

heat exchangers and generation of design data for offset and wavy fins. Heat Mass Transfer

2009; 52: 397283.

[4] R.K. Shah and D Sekulic, Fundamentals of Heat Exchanger Design.J. Wiley & Sons,

New York, 2003.

[5] Sharma P, Design of 2-Stream (He/He) Plate-Fin Heat Exchanger for Helium

Refrigeration and Liquefaction Plant. Major Project Report, Nirma University, 2014.

Table 6: Pressure drop results from CFD analysis for non-linear property variations

Table 1:Operating parameters of HE8

ANALYSIS RESULTS: PRESSURE DROP AND FRICTION FACTOR

CALCULATION ALONG THE LENGTH

The heat exchanger has a counter-flow arrangement and the flow channel is

characterized by the presence of periodic interruptions in the form of serrated fins.

The working fluid is helium gas in both hot and cold side.

One hot layer is sandwitched between two cold layers are used in the design of HE8.

The geometry and the dimensions of plate fin heat exchanger used in the present

study is obtained from the analytical design made by Sharma [5].

The Reynolds number, for hot or cold stream, is calculated by using , 𝑹𝒆 =𝑮𝒅𝒉

𝝁

𝐺 =𝑚

𝐴𝑥 = core mass velocity (or flux),

dh =4𝑠𝑕𝑙

(2 𝑠𝑙:𝑙𝑕:𝑕𝑡 ):𝑡𝑠 = Hydraulic diameter [6]

𝐴𝑥 =The frontal free flow area, 𝜇 =Viscosity of fluid

Figure 4 shows for cases with no. of elements > 12.5 mollion, the variation in pressure drop is less

than 5 %.

Hence, further analysis is done with element size corresponding to this meshing and it has 0.16 mm

as minimum element dimension and 0.32 mm as maximum dimension.

In the present study, analysis is done with different turbulence models (Figure 5 ).

It shows (with a model having length of 38.8 mm and width 3.38 mm) that the results obtained

with standard k-ε model follows the pattern of co-relation results.

Hence, standard k-ε model is used for further analysis.

10-P3-240

PRESSURE DROP CALCULATIONS BASED ON CO-

RELATIONS

Table 2: HE8 designed parameters [5]

(a) (b)

(a) (b)

Table 5: Friction factor comparison

Domains chosen for modelling and analysis with constant helium property

Modelling and Grid generation

For useful comparison of friction factor estimated through MB co-relation and CFD analysis,

temperature range of helium fluid is taken as 100 to 110 K

Other parameters kept constant as in HE8.

Further as the no. of elements will be large, a smaller segment which can represent the HE8 is

considered for modelling and analysis.

To find the appropriate element size, suitable for this analysis, grid independence test is also done

(figure 4).

CFD analysis with different solution options are carried out with constant Helium properties to

select the best solution technique. With these different sizes of HE segments are modelled and

analysed for 100 to 110 K temperature range.

Later, the CFD analysis is carried out with non-linear variations of Helium properties in the

temperature range of 4.5 to 7 K for HE8

Here, s is spacing between fins, h is fin height, l is fin serration length and t is fin thickness

Total drop in pressure for hot or cold stream, is expressed as,

∆𝑃𝑡𝑜𝑡𝑎𝑙= ∆𝑃𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙 + 𝛥𝑃𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙, where ∆𝑃𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑎𝑙=4𝑓𝐿𝐺2

2𝜌𝐷ℎ , Here, f is fanning friction

factor, 𝜌 𝑖𝑠 density of fluid, 𝛥𝑃𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙= 𝜌𝑔𝛥𝐻 (not considered here)

𝐽 = 0.6522𝑅𝑒;0.5403𝑠

ℎ

;0.1541 𝑡

𝑙

0.1499 𝑡

𝑠

;0.0678

1 + 5.269x10;5𝑅𝑒1.340𝑠

ℎ

0.504 𝑡

𝑙

0.546 𝑡

𝑠

;1.055 0.1

[6] Kays W M and London A L ,Compact Heat Exchangers, 2nd ed., McGraw-Hill, New

York,1964.Joshi, H.M., and Webb, R.L., Prediction of Heat Transfer and Friction in the

Offset Strip Fin Array, International Journal of Heat and Mass Transfer. 30, 69 84, 1987