Performance Examination of Concentric Tube Spiral Coil Heat Exchanger for Heat Transfer Analysis

Abhinav Giri *, Shashi Chandra Sharma

Department of Mechanical Engineering, Acropolis Institute of Technology and Research,

Indore, Madhya Pradesh 453771, India.

*Corresponding Author E-mail: abhinavgiri17@gmail.com

ABSTRACT:

Hot fluid passes through the inner tube and cold fluid flows through the outer tube in an experimental study of a Concentric Tube Spiral Coil Heat Exchanger conducted in a Counter Current method. The temperature data was recorded while the flow rates in the inner tube and Annulus were altered five times each. To get total heat transfer coefficients as well as heat transfer coefficients for the inner tube and annulus, the Wilson Plot method is utilised. The Nusselt Number gained from the experiment was compared to the Nusselt Number obtained through the development of a mathematical model using Regression Analysis. The inner Nusselt Number was linked to Dean Number, while the Annulus Nusselt Number was linked to Modified Dean Number and a new Dimensionless Number called "M Number." The experimental data was well-fitting with the Theoretical one. The hydrodynamics (pressure drop) and heat transfer properties of the concentric tube spiral coil heat exchanger were also examined.

KEYWORDS: Concentric tube Spiral Coil Heat Exchanger, Dean Number, Modified Dean Number, M Number, Wilson Plot technique, Regression Analysis.

INTRODUCTION:

Spiral coil heat exchangers outperform straight tubes in heat transfer applications, according to a number of studies. Centrifugal force creates secondary flows that are normal (perpendicular) to the primary axial flow, which promotes fluid mixing and hence enhances heat transmission. Two vortices move fluid from the tube's inner wall to its centre and subsequently to the outer wall in the secondary flow. After reaching the outer wall, it returns to the inside wall. The secondary flow enhances the heat transfer rates as the fluid moves over the temperature gradient. Heat flux or constant wall temperature boundary conditions have been the focus of the majority of spiral coil heat exchanger research. A third boundary condition that has yet to be researched is the "Liquid to Liquid heat exchanger." To reduce the risk of radiation from the outside annulus, the outer annulus wall was insulated with cerawool coating.

Advantages:

1. Spiral coil heat exchangers have a higher heat transfer rate than straight tube heat exchangers.

2. Heat transmission surface area is bigger and the structure is compact.

Applications:

1. In industries, heat exchangers using spiral coils are commonly utilised. Nuclear power plants, heat recovery systems, food processing businesses, and other industries commonly use spiral coil heat exchangers.

2. In a barge-mounted nuclear reactor system where nuclear energy is used for desalination of sea water, a heat exchanger with spiral coil is employed for residual heat removal.

In curved pipes, centrifugal motion forces the faster-flowing core parts of the flow outwards, while slower areas near the wall are driven inwards where the pressure is lower, resulting in secondary flow at right angles to the primary flow. If the curvature is significant, secondary flow completely changes the axial velocity distribution, resulting in a significant increase in resistance.

A. Nomenclature

A        Surface area of tube (m²)

U        Overall Heat transfer coefficient 

C         Constant in Eq.

E         Effectiveness

d_i Inner tube inner diameter (m)

ρ Density (Kg/m³)

d_o Inner tube outer diameter (m)

ν Kinematic viscosity (m²/s)

D_i Outer tube inner diameter (m)

µ Dynamic viscosity (N-s/m²)

D_o Outer tube outer diameter (m)

Re Reynolds Number

D_h Hydraulic diameter (m)

De Dean Number

a Curvature ratio

De^’ Modified Dean Number

P Pitch (m)

M Mujawar Number

Ṁ Mass flow rate (Kg/s)

Nu Nusselt Number

Ṽ Volume flow rate (LPM)

Pr Prandlt Number

Q Heat transfer rate (J/s)

θ_m LMTD (°C)

h Heat transfer coefficient (W/m²K)

R_c Curvature radius (m)

k Thermal conductivity (W/m K)

n Number of turns of coil

L Length (m)

∆P Pressure drop (Kg/cm²)

V Velocity (m/s)

f Friction factor

Cp Specific heat (J/kg.k)

Subscripts

i inner o outer

h hot c cold

II. OBJECTIVES:

The objectives of this study were;

a. Experimentally assess the heat transfer characteristics of a spiral coil heat exchanger in counter flow method.

b. Compare and contrast the experimental and theoretical outcomes.

c. To determine the efficiency of a heat exchanger.

d. The pressure drop inside the inner tube of a spiral coil heat exchanger must be determined.

III. Experimental Setup:

Fig 1: Line diagram of concentric tube spiral coil heat exchanger

Components:

Concentric tube Spiral coil heat exchanger

Electrical heater

Pressure Gauges

Thermocouples

Contactor

Submersible Pump

Measuring Pot

Storage Tank

Rota meter

Dimmer stat

Temperature Indicator

Flexible PVC

Control Valve

Electrical wires

Stirrer

PumpConstruction of concentric tube spiral coil heat exchanger

Because Copper has a high thermal conductivity, the tubes of the heat exchanger are built of copper to maximise heat transfer. The following parameters are taken into account when building a concentric tube spiral coil heat exchanger.

1. Heat transport is affected by the curvature ratio..

2. The effect of coil pitch on heat transfer.

3. Influence of No. of turns of coil on Overall heat transfer coefficients.

To preserve smoothness on the inner surface of the tubes, very fine sand particles were filled within the tubes during the bending process and cleaned out with compressed air. During the bending procedure, great care was taken to preserve the coil's round cross section. The tube ends were soldered, and the two ends were taken from coiled tubes.

Dimensional Parameters:

Geometrical Parameters	Dimensions
Inner diameter of inner tube (di)	8mm
Outer diameter of inner tube (do)	10mm
Inner diameter of outer tube (Di)	17mm
Outer diameter of outer tube (Do)	19mm
Inner curvature Radius (Rc)i	147mm
Outer curvature Radius (Rc)o	155mm
Stretch Length (L)	3992mm
Inner curvature ratio (ai)	0.0272
Outer curvature ratio (ao)	0.0548
Pitch (b)	100mm
Number of turns (n)	4
Tube Material	Copper

Range of Parameters:

1. Inner Tube Flow Rate: (4, 5, 5.5, 6, 7) LPM

2. Outer Tube Flow Rate: (4, 4.5, 5, 5.5, 6) LPM

3. Inner Tube Inlet Temp. (Hot Water): 50°C,55°C,60°C,65°C,70°C

4. Outer Tube Inlet Temp. (Cold Water): 25°C

5. Inner Tube: Hot Water

6. Outer Tube: Cold Water

7. Arrangement: Counter Flow

Experimental Procedure:

As previously stated, flow rates in the annulus and inner tube were changed five times. The temperature of the hot water was likewise changed five times, while the cold water temperature remained fixed. For counter current arrangements, all conceivable combinations of these flow rates in both the annulus and the inner tube were evaluated. There were a total of 125 trials as a result of this. Temperature data was taken every 10 minutes to ensure that a steady condition was reached. The intake and output temperatures of water were measured using thermocouples inserted into flexible PVC tubing. Because all of the thermocouples were made from the same wire rolls, temperature measurements were extremely consistent.

IV. CALCULATIONS:

Mass flow rate of Hot water (Kg/s):      Ṁ_h= Ṽ_hxρ_h

Mass flow rate of Cold water (Kg/s):    Ṁ_c=Ṽ_cxρ_c

Velocity of Hot water (m/s):                 V_h = Ṽ_h/1000 x A_h

Velocity of Cold water (m/s):                V_c= Ṽ_c/1000 x A_c

Heat transfer rate of Hot Water (J/s):      Q_h= Ṁ_hxC_px (T_hi-T_ho)

Heat transfer rate of Cold Water (J/s):   Q_c = Ṁ_cxC_px (T_co-T_ci)

Average Heat transfer rate (J/s):             Q_avg = Q_h+Q_c/ 2

Overall Heat transfer coefficient (W/m²K): U_o=Q_avg/A_ox LMTD

“The annular side (ho) and inner side (hi) heat transfer coefficients were determined using the Wilson Plot Technique as reported by Rose" [8]. The Wilson plot allows us to compute heat transfer coefficients based on the overall temperature differential and the rate of heat transfer without the requirement for a wall temperature. While attempting to measure the temperature of the wall, this method was used to avoid disrupting flow patterns and heat transfer. Wilson plots are created by calculating the total heat transfer coefficients for a set of trials (125) in which one fluid is kept constant while the other is varied. The heat transfer coefficients in the annulus and inner tube should behave in a fluid velocity-dependent manner.

h = CVⁿ Where n=0.8 [8]

Curve fitting was used to acquire the values for the exponent (n) and constant (C). It was possible to compute the inner and outer heat transfer coefficients. For each mass flow rate, the technique was repeated. This resulted in 50 Wilson plots (25 for inner tube and 25 for annulus).

Fig 2: Wilson Plot

The Effectiveness of heat exchanger was calculated by

Dimensionless numbers:

1. Reynolds number (Re) = (ρ*V*D/µ)

2. Dean number (De) = (ρ*V*D/µ)*a^0.5

3. Modified Dean number (De^’) = ((ρ*V/µ)*((Do²-Di²)/(Do+Di))*((Do-Di)/R)^0.5

4. Mujawar number (M) = (Re^0.64)/(0.26*a^0.18)

The Friction factor was calculated using ITO correlation [11]

Then the pressure drop was calculated using Darcy -Weisbach formula and theoretical and experimental pressure drop was compared.

V. MATHEMATICAL MODEL

The heat transfer characteristics of fluid at various mass flow rates and temperatures were investigated in Experimentation. A correlation is created that accurately represents the heat transfer in the above circumstance. Correlation is a mathematical equation that divides a set of terms into a set of usable constant numbers and values. Both the inner and outer sides of the correlation were created. The Nusselt number and Dean number have an internal association, while the Nusselt number and Modified Dean number and M number have an exterior correlation.

For the correlation the mathematical model was first developed by using the Buckingham’s π theorem method. The variables and the constants are clubbed together to form correlation in the form of Nusselt number. The independent variables such as d_i,D_c,V_h,γ,µ_h,k_h,Cp_h,ρ_h were taken where h is the dependent variable depends on these variables.

The dimensional relation obtained from Buckingham’s π theorem is

Nu_i = C₁ x De_i^axPr_i^b x γ^c..................(inner side correlation)

Nu_o= C₂ x De^’_o^axPr_o^b x γ^c...................(outer side correlation)

Nu_o= C₃ x M_o^axPr_o^b x γ^c..................(outer side correlation)

In this model γ is non dimensionless pitch. Now for Nusselt number correlation the properties of water were taken at bulk mean temperatures where in total 125 observations were included to increase the precision of correlation. The values of indices (a,b,c) for above three correlation were obtained by using Regression analysis. The final correlation so obtained were

Nu_i = De_i^0.5559x Pr_i^-0.2170 x γ^0.299    ..............(Eq.1)

Nu_o= De^’_o^0.0012x Pr_o^-5.1478 x γ^-5.2257...........(Eq.2)

Nu_o= M_o^0.0018x Pr_o^-5.1478 x γ^-5.224............(Eq.3)

Eq.1 represents the correlation for hot water flowing through inner tube whereas other two correlation (Eq.2 &Eq.3) for cold water flowing through annulus tube.

VI.  RESULTS AND DISCUSSION

A] Inner Nusselt Number

Fig. 3 Inner Nusselt Number v/s Inner Dean Number (Temperature 50^oc)

The Figure 4 depicts the inner Nusselt numbers (with 5 percent errors). At each Dean number, these are the average inner Nusselt numbers. The data is then compared to the mathematical model that has been built. The actual results and theoretical values were found to be in good agreement, indicating that the heat transfer correlations developed for spiral coils may be utilized to predict the inner heat transfer rate in a double-pipe spiral coil heat exchanger.

Fig. 4 Inner Nusselt Number v/s Inner Dean Number (Temperature 70^oc)

From the above two fig. we can see that the experimental data and the theoretical values are in good agreement for higher Inlet temperature of hot fluid and thus the heat transfer rate increases with increase in inlet temperature.

B] Annulus Nusselt Number

Fig. 5 Annulus Nusselt Number v/s Modified Dean Number (Temperature 50^oc)

The annular Nusselt number was associated with the Modified Dean number (De'o). The coil data is consistent with the correlation, however neither the Dean number nor the Reynolds number can accurately describe the hydrodynamics of flow through a spiral coil. As a result, a new dimensionless number, M, might be employed. The majority of theoretical work has been done for Dean numbers in the low range, which do not span the full laminar area in coiled tubes.

Fig. 6 Annulus Nusselt Number v/s M Number (Temperature 50^oc)

Furthermore on developing correlations with Modified Dean number and M number it was found out that the heat transfer coefficient increased with the second correlation.

C] Friction factor:

Fig. 7 Friction Factor v/s Inner Reynolds Number

The friction factor (f) is a function of Reynolds number (mass flow rate of fluid flowing through inner tube) and decreases as Reynolds number increases, as shown in Fig. 8.

Comparison of Experimental pressure drop and theoretical pressure drop

Fig. 8 Pressure Drops in Experiments verses Theoretical Pressure Drops

The above graphs shows that the experimental and theoretical pressure drop using ITO correlations[11] are found out to be in good agreement and hence the pressure drop for this setup is validated.

VII. CONCLUSIONS:

Five variable mass flow rates in the inner and annulus tubes in a counter flow manner were used in an experimental study of a twin pipe (concentric tube) spiral coil heat exchanger. The Nusselt number obtained through experimentation and that gained through the development of a mathematical model were found to be very similar. Furthermore, the value of indices acquired by means of regression analysis of models developed using MATLAB software demonstrates that m number indices are larger than Dean number indices, implying that hydrodynamics is roughly studied captured by M number. The pressure decrease is found to be in good agreement with the experimental and theoretical results.

VIII. CONFLICT OF INTEREST:

The authors have no conflicts of interest regarding this investigation.

IX. ACKNOWLEDGMENTS:

The authors would like to thank Acropolis Institute of Technology & Research, Indore for their kind support during thermal analysis and all other lab studies.

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Received on 06.02.2022            Accepted on 02.07.2022

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Research J. Engineering and Tech. 2022;13(1):1-9.

DOI: 10.52711/2321-581X.2022.00001