View of Designing a Helical Coil Heat Exchanger

Designing a Helical Coil Heat Exchanger

1.Dr.Najeh Alali¹2. Engineer .Lubna Wnos¹ 3. MSc .Worod M. Jabar ¹

1College of Petroleum Engineering, Al-Ayen University, Thi-Qar, 64001, Iraq

ABSTRACT

Heat exchangers are the important engineering systems with wide variety of applications including power plants, nuclear reactors, refrigeration and air-conditioning systems, heat recovery systems, chemical processing , food industries and commonly used for heating of curde oil with steam during oil production. Helical coils have been used in wide variety of applications due to simplicity in manufacturing and its capacityaccommodate a large heat transfer area in a small space, with high heat transfer coefficients. Flow in curved tube is different from the flow in straight tube because of the presence of the centrifugal forces. These centrifugal forces generate a secondary flow, normal to the primary direction of flow with circulatory effects that increases both the friction factor and rate of heat transfer. The aim of this work is to design a helical coil heat exchanger through a scientific methodology that includes many steps to obtain an experimental HCHE, calculating the number of turns needed to obtain the required amount of heat exchanged between the operating fluids and determining the rest of the design factors for this exchanger .

Keywords: Helical coil Heat exchanger, secondary flow.

1. INTRODUCTION

During the flow of fluid in a curved pipe, a secondary motion of the flow is developed and it is superimposed on its primary stream flow.The curvature of helical coil induces centrifugal force, causing the development of the secondary flow Fig.1.The intensity of the secondary flow is dependent on the radius of the bend curvature (Rc) and Reynolds number (Re) based on the pipe diameter (D) and velocity (U).

Fig 1. Secondary flow developed due to curvature 2. LITERATURE REVIEW

It has been widely reported in literature that heat transfer rates in helical coils are higher as compared to a straight tube. The centrifugal force dueto the curvature of the tube results inthe secondary flow development which enhances the heat transfer. The first attempt has beenmade by Dean [1,2] to describe mathematically the flow in a coiled tube. A first approximation of the steady motion of incompressible fluid flowing through a coiled pipe with a circular cross-section is considered in his analysis. It was observed that the reduction in the rate of flow due to curvature depends on a single variable, K, which is equal to 2(Re)2r/R, for low velocities and small r/R ratio.

White [3] has continued the study of Dean for the laminar flow of fluids with different viscosities through curved pipes with different curvature ratios (δ). The result shows that the onset of turbulence did not depend on the value of the Re or the De. He concluded that the flow in curved pipes is more stable than flow in straight pipes. White also studied the resistance to flow as a function of De and Re. There was no difference in flow resistance compared to a straight pipe for values of De less than 11.6.

Prabhanjan et al.[4] reported an experimental investigation the purpose of this study was to determine the advantage of using a helically coiled heat exchanger versus a straight tube heat exchanger for heating liquids .The results showed that the heat transfer coefficient in helical coil is 1.16 times greater than that of straight tubes at 40 °C and the largest is 1.43 at 50 °C.

Rennie [5] studied the heat transfer characteristics of a double pipe helical heat exchanger for both counter and parallel flow. For dean numbers ranging from 38 to 350 the overall heat transfer coefficients were determined. The results showed that the overall heat transfer coefficients varied directly with the inner dean number but the fluid flow conditions in the outer pipe had a major contribution on the overall heat transfer coefficient. The study showed that during the design of a double pipe helical heat exchanger the design of the outer pipe should get the highest priority in order to get a higher overall heat transfer coefficient.

3.Nomenclature

A Area for heat transfer, m²

B outside diameter of inner cylinder, m C inside diameter of outer cylinder ,m D inside diameter of coil , m

𝐷𝐻𝑎𝑣𝑒𝑟𝑎𝑔𝑒𝑑𝑖𝑎𝑜𝑓 ℎ𝑒𝑙𝑖𝑥 ,𝑚

𝐷_𝐻1 𝑖𝑛𝑠𝑖𝑑𝑒𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑜𝑓ℎ𝑒𝑙𝑖𝑥, 𝑚 𝐷_𝐻2 𝑜𝑢𝑡𝑠𝑖𝑑𝑒𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑜𝑓ℎ𝑒𝑙𝑖𝑥, 𝑚 𝑑₀𝑜𝑢𝑡𝑠𝑖𝑑𝑒𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑜𝑓𝑐𝑜𝑖𝑙, 𝑚

𝐺_𝑆𝑚𝑎𝑠𝑠𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦𝑜𝑓𝑓𝑙𝑢𝑖𝑑𝑘𝑔/(𝑚²)(ℎ)

H height of cylinder , m

ℎ_𝑖ℎ𝑒𝑎𝑡𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑖𝑛𝑠𝑖𝑑𝑒𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡𝑡𝑢𝑏𝑒 𝑏𝑎𝑠𝑒𝑑𝑜𝑛𝑖𝑛𝑠𝑖𝑑𝑒𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟w/m².k

ℎ_𝑖𝑐ℎ𝑒𝑎𝑡𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑖𝑛𝑠𝑖𝑑𝑒𝑐𝑜𝑖𝑙𝑒𝑑𝑡𝑢𝑏𝑒 𝑏𝑎𝑠𝑒𝑑𝑜𝑛𝑖𝑛𝑠𝑖𝑑𝑒𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟, 𝑤/𝑚². 𝑘

ℎ_𝑖𝑜ℎ𝑒𝑎𝑡𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑖𝑛𝑠𝑖𝑑𝑒𝑐𝑜𝑖𝑙𝑏𝑎𝑠𝑒𝑑𝑜𝑛 𝑜𝑢𝑡𝑠𝑖𝑑𝑒𝑑𝑖𝑎𝑜𝑓𝑐𝑜𝑖𝑙, 𝑤/𝑚². 𝑘

ℎ₀ℎ𝑒𝑎𝑡𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡𝑜𝑢𝑡𝑠𝑖𝑑𝑒𝑐𝑜𝑖𝑙, 𝑤/𝑚². 𝑘 L length of helical coil needed to form N turns ,m M Mass flowrate of fluid, kg/m

N Theoretical number of turns of helical coil

n Actual number of turns of coil needed for given process heat duty q Volumetric flowrate of fluid , 𝑚³/h

r Average radius of helical coil taken from the centerline of the helix to the centerline of the coil , m

𝑅_𝑎𝑠ℎ𝑒𝑙𝑙𝑠𝑖𝑑𝑒𝑓𝑜𝑢𝑙𝑖𝑛𝑔𝑓𝑎𝑐𝑡𝑜𝑟 ℎ 𝑚² ℃ /𝑘𝑎𝑙 𝑅_𝑡𝑡𝑢𝑏𝑒𝑠𝑖𝑑𝑒𝑓𝑜𝑢𝑙𝑖𝑛𝑔𝑓𝑎𝑐𝑡𝑜𝑟 ℎ 𝑚² ℃ /𝑘𝑎𝑙 𝑣_𝑎𝑣𝑜𝑙𝑢𝑚𝑒𝑜𝑓𝑎𝑛𝑛𝑢𝑙𝑢𝑠 , 𝑚³

𝑣_𝑐𝑣𝑜𝑙𝑢𝑚𝑒𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑𝑏𝑦𝑁𝑡𝑢𝑟𝑛𝑠𝑜𝑓𝑐𝑜𝑖𝑙 , 𝑚³

𝑣_𝑓𝑣𝑜𝑙𝑢𝑚𝑒𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒𝑓𝑜𝑟𝑓𝑙𝑢𝑖𝑑𝑓𝑙𝑜𝑤𝑖𝑛𝑡ℎ𝑒𝑎𝑛𝑛𝑢𝑙𝑢𝑠 , 𝑚³

x thickness of coil wall , m 𝜇𝑓𝑙𝑢𝑖𝑑𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 , 𝑘𝑔/ 𝑚 ℎ 𝜌𝑓𝑙𝑢𝑖𝑑𝑑𝑒𝑛𝑠𝑖𝑡𝑦 , 𝑘𝑔/𝑚³ Nu Nusselt number Re Reynolds number Q heat load , kcal/h

4.Experimental model:

Liquid A flows inside a 316 stainless-steel pipe coil, liquid Bin the annulus. The flowrates, the inlet and outlet temperatures, and the physical properties of the fluids are given in the table . The geometry of the HCHC is that shown in Fig 2, where B = 0.04 m , C = 0.06 m ,

D = 0.004 m , 𝑑₀=0.006 m

Table 1: Fluid properties

Liquid B Liquid A

Unit property

36 36

Kg/h Mass flowrate

30

℃ 130 Inlet temperature

50

℃ 97 Outlet temperature

1.00 1.00

kcal/(kg)(℃) Heat capacity

0.4075 0.419

Kcal/(h)(m)(℃) Thermal conductivity

5.76 1.89

Kg/m.h Viscosity

935 870

Kg/m3 Density

Fig 2 :Geometrical assumptions for designed helical coil heat exchanger A. calculate the shell-side heat transfer coefficient 𝐡_𝟎

1- The length of coil 𝐿 = 2𝜋𝑟 ²+ 𝑃² 𝑃 = 1.5 × 0.006 = 0.009𝑚

𝑟 = 𝐵 2+ 𝑑₀

r = 0.026m

𝐿 = 2𝜋 0.026 ²+ 0.009 ² L = 0.164N

2-The volume available for fluid flow in the annul 𝑣_𝑓 is:

𝑉_𝑓 = 𝑉_𝑎 − 𝑉_𝑐

Vc =(π/4)d0² P Va = (π/4)(C² –B²)PN

Va =( π/4)(0.062 -0.042)×0.009×N

= 1.413×10^-5 N

Vc =(π/4)(0.006)20.164 N

=4.635×10-6 N

𝑉_𝑓 = 1.413 × 10⁻⁵𝑁 − 4.635 × 10⁻⁶𝑁

=9.495×10^-6 N

3-The shell-side equivalent diameter is : De = 4𝑉_𝑓 /πd0L

De =(4)(9.495×10^-6 N)/(π)(0.006)(0.164N)

=0.0123m

4-The mass velocity of the fluid is : Gs = M/{(π/4)((C² –B²) – (DH22

-DH12

))}

DH1 = B + d0

= 0.04 + 0.006 = 0.046m DH2 = C - d0

=0.06-0.006 = 0.054m

Gs =36/{(π/4)((0.062-0.042) – (0.0542-0.0462))}

=38216.561 kg/(m²)(h) 5- The Reynolds number is : Re = (38216.561)×(0.0123)/(5.76)

=82

6-The heat transfer coefficient based on the outside the coil : h0 De/k = 0.6 N Re0.5

N Pr0.31

Pr = (1×5.76)/(0.4075) = 14.135

h0= (0.6)(0.4075)(82)^0.5(14.135)^0.31/(0.0123)

=410 kcal/(h)(m²)(℃)

B-Compute 𝒉_𝒊𝒐, the heat transfer coefficient inside the coil:

1-The fluid velocity is : U = q/𝐴_𝑓

Where A_f = ΠD²/4= π(0.004)²/4 =1.256×10^-5 m² q = M/p=36/870=0.041 m³/h u = (0.041)/(1.256×10^-5)

u=3264.331 m/h

2-The Reynolds number (tube-side) is then : Re=(3264.331)×(0.004) ×(870) /(1.89)

=6010.514 3- Using the Dittus-Boelter relationship, we calculate the heat transfer coefficient inside the straight tubes depending on the inside diameter:

Nu _DB = 0.023Re^0.8 Pr^0.4

ℎ_𝑖 = 0.023 × 0.419 × 6015.514 ^0.8× 4.511 ^0.4 0.004

=4642.162 kcal/(h)(m²)(℃) 4-Corrected for a coiled tube , this becomes:

ℎ_𝑖𝑐 = (4642.162)[1 + 3.5(0.004/0.05)]

=5941.967 kcal/(h)(m²)(℃)

5-The heat transfer coefficient based on the outside diameter of the coil is:

ℎ_𝑖𝑜 = (5941.967)(0.004/0.006)

= 3961.311kcal/(h)(𝑚²)(℃)

C- Calculate the overall heat transfer coefficient U:

The coil wall thickness x is : x = (d0 – D)/2

=(0.006 – 0.004)/2 =0.001m

Both 𝑅_𝑡 and 𝑅_𝑎are 8.2×10^-4(h)(m²)(℃)/kcal 1

𝑈 = 1 ℎ₀ + 1

ℎ_𝑖𝑜 + 𝑥

𝑘_𝑐 + 𝑅_𝑡+ 𝑅_𝑎 1/U = 1/410 + 1/3961.311 + 0.001/14 + 0.00082+0.00082

𝑈 = 277.118(h)(m2)(℃)/kcal

D-Determine the required area:

-The log mean temperature difference is :

∆𝑇_𝑡𝑚 = 130 − 50 − 97 − 30 𝑙𝑛 130 − 50 / 97 − 30

= 73.3℃

To account for counter flow , the correction factor from Fig 3 is 0.99 Where 𝑃 = ⁵⁰⁻³⁰

130−30 = 0.2

𝑅 = 130 − 97

50 − 30 = 1.65

Calculate the correction factor from Fig 3

So that, ∆𝑇_𝑐 = (0.99)(73.3)= 72.567 ℃ The heat load is :

Q =( 36)(1)(130-97) = 1188 kcal/h The required area:

A = (1188)/(277.118)(72.567)

E-Calculate the number of turns of coil required : N = A/(πd0(L/N))

N = (0.059)/(π)(0.006)(0.164) = 19.11 And: n=20

The height of the cylinder needed to accommodate 21 turns of coil is : H = 20×0.009 + 0.006 =0.186m

5. Conclusions

1- The study showed that the heat transfer coefficient inside the helical coil is high, so the overall heat transfer coefficient is also high despite that the laminar flow of the working fluid inside coil . The fluid flowing through curved tubes induces secondary flow in the tubes. This secondary flow in the tube has significant ability to enhance the heat transfer due to mixing of fluid.

2- The low flow rate of the operating fluids on the coil side and shell side so the straight tube heat exchanger can’t use because its low thermal efficiency.

3-The greatest advantage of the HCHE is that, the helical coil can accommodate greater heat transfer area in a less Space, with higher heat Transfer coefficients.

6.REFERENCES

[1] Dean, W. R. (1927). XVI. Note on the motion of fluid in a curved pipe. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 4(20), 208-223.

[2] Dean, W. R., (1928) “The streamline motion of fluid in a curved pipe”, Philosophical Magazine, Series 7, Vol. 5(30), pp. 673-95.

[3] White, C. M., (1929) “Streamline flow through curved pipes”, Proceedings of the Royal Society of London, Series A, Vol. 123(792), pp. 645-663.

[4] Prabhanjan, D. G., Raghavan, G. S. V., & Rennie, T. J. (2002). Comparison of heat transfer rates between a straight tube heat exchanger and a helically coiled heat exchanger. International Communications in Heat and Mass Transfer, 29(2), 185-191.

[5] Prabhanjan, D. G., Raghavan, G. S. V., & Rennie, T. J. (2002). Comparison of heat transfer rates between a straight tube heat exchanger and a helically coiled heat exchanger. International Communications in Heat and Mass Transfer, 29(2), 185-191.

[6] Alali, N.; Pishvaie, M. R.; Jabbari, H. A new semi-analytical modeling of steam-assisted gravity drainage in heavy oil reservoirs. J. Pet. Sci. Eng. 2009, 69 (3−4), 261−270.