Thermal performance intensification of a circular heat exchanger tube integrated with compound circular ring–metal wire net inserts

Accepted Manuscript Title: Thermal performance intensification of a circular heat exchanger tube integrated with compound circular ring–metal wire net inserts Authors: Amit Bartwal, Abhishek Gautam, Manoj Kumar, Chidanand K. Mangrulkar, Sunil Chamoli PII: DOI: Reference:

S0255-2701(17)30910-8 https://doi.org/10.1016/j.cep.2017.12.002 CEP 7136

To appear in:

Chemical Engineering and Processing

Received date: Revised date: Accepted date:

8-9-2017 2-12-2017 2-12-2017

Please cite this article as: Amit Bartwal, Abhishek Gautam, Manoj Kumar, Chidanand K.Mangrulkar, Sunil Chamoli, Thermal performance intensification of a circular heat exchanger tube integrated with compound circular ring–metal wire net inserts, Chemical Engineering and Processing https://doi.org/10.1016/j.cep.2017.12.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermal performance intensification of a circular heat exchanger tube integrated with compound circular ring - metal wire net inserts Amit Bartwala, Abhishek Gautamb, Manoj Kumara, Chidanand K. Mangrulkarc, Sunil Chamolia* Mechanical Engineering Department, DIT University, Dehradun, Uttarakhand, India.

b

Mechanical Engineering Department, Tula’s Institute, Dehradun, Uttarakhand, India. c

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a

Mechanical Engineering Department, Visvesvaraya National Institute of

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Technology (V.N.I.T.), Nagpur, India. Email: [email protected] Ph: +91 – 9897870171

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Abstract

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Graphical abstract

Numerous studies have been recorded in developing the miniature heat transporting devices by the use of passive heat transfer enhancement technique. In the same context, a new novel

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insert geometry has been developed, which can enhance the convective heat transfer rate by the disruption of the thermal boundary layer. The circular ring with wire net inserts has been selected as the heat transfer enhancement insertion devices in the present research work. Three values of wire net grades (G = 4, 9, and 16) and the three values of pitch ratios (PR = 2, 3, and 4) are selected to investigate their effects on heat transfer (Nu), friction factor (f),

and thermal enhancement factor (TEF), respectively. The air is used as the working fluid in the turbulent flow regime for which Reynolds number (Re) ranges from 5000 – 40, 000. Significant enhancement over the smooth tube has been reported in terms of heat transfer and pressure drop. The maximum heat transfer enhancement of around 3.35 over the smooth tube

and G = 9. The statistical correlations for Nu, and f also presented.

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is obtained for the PR = 2, and G = 16. The maximum TEF of 2.84 is retrieved for the PR = 3,

Keywords: Nusselt number; Reynolds number; Friction factor; Pitch ratio; Grade of metal

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wire net; Thermal enhancement factor. Nomenclature Surface area of the test section (m2)

PR

Pitch ratio

a/D

Triangle side length to tube diameter

Pr

Prandtl number

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A

α

Angle of attack

b/di

Circumferential contact length to tube

d

Heat transfer rate (W) Heat transfer rate by air (kJ)

Qconv

Heat transfer rate by convection (kJ

Ring internal diameter (m)

Re

Reynolds number

D

Pipe outer diameter (m)

TEF

Thermal enhancement factor

DR

Diameter ratio

T

Temperature (K)

e/di

Height to tube inner diameter ratio

To

Outlet temperature (K)

f

Friction factor

Ti

Inlet temperature (K)

G

Grade of metal wire net

Tb

Bulk mean temperature (K)

Convective heat transfer coefficient

Tw

Local wall temperature (K)

Twm

Mean wall temperature (K)

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h

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Blockage Ratio

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BR

Qair

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inner diameter ratio

A

Q

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ratio

(W/m2K)

Thermal conductivity of air (W/mK)

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k L

Length of test section (m)

TR

Twist ratio

m

Mass flow rate of fluid (kg/s)

V

Mean velocity of fluid (m/s)

N

Number of twisted tapes

Greek letters

Ni

Number of perforated holes

µ

Dynamics viscosity of working fluid (Ns/m2)

Nu

Nusselt number

ɳ

Thermal enhancement factor

p

Pitch of circular rings (m)



Cylindrical co-ordinate

Patm

Atmospheric pressure (Pa)

ρ

Density of working fluid (kg/m3)

∆Po

Pressure drop at orifice plate (Pa)

Subscripts

∆P

Pressure drop across the test section

s

Smooth

(Pa) Pitch to projected length ratio

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p/pl

1. Introduction

The passive techniques of heat transfer enhancement are more popular and widely used

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for performance improvement of many heat transporting devices. In this methodology, few inserts are used in the flow passage to promote the flow turbulence, which correspondingly

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enhances the convective heat transfer rate. The passive methods of heat transfer enhancement

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are more beneficial over the active methods and can be directly implemented in the heat

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exchangers with without any additional pumping power. In the last decade, several studies on

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the passive techniques of heat transfer enhancement have been reported. Kumar et al. [1-2] used the circular perforated ring, hollow circular ring disk (SHCD) to enhance the thermal

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performance of a circular tube. Singh et al. [3] experimentally investigated the heat transfer enhancement using multiple twisted tapes and solid ring inserts. They reported the thermal

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enhancement factor (TEF) in the range of 1.46 – 1.61. Kumar et al. [4] studied the heat

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transfer and flow characteristics of a protruded surface heat exchanger tube. They found the maximum heat transfer enhancement of 3.42 of the smooth tube. Sheikholeslami et al. [5] studied the heat transfer and pressure loss in an air to water double pipe heat exchanger using

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a typical circular - ring (TCR) and perforated circular-ring (PCR) turbulators, and found that PCRs show low heat transfer enhancement than CRs. Tu et al. [6] explored the role of a small pipe inserts in a circular tube used for the heat transfer enhancement at a constant heat flux. They reported the enhancement in heat transfer and friction factor over the smooth tube in the range from 2.09 – 2.67, and 1.59–1.85, respectively. Bhuiya et al. [7] investigated

experimentally the heat transfer performance and friction factor characteristics of a circular tube fitted with twisted wire brush inserts. They reported the enhancement in heat transfer around 2.15 times of the plain tube. Ibrahim et al. [8] experimentally investigated the heat transfer characteristics of a tube embedded with full length helical screw elements of different twist ratios and helical screw inserts with different spacer length. They found that

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there is no increase in Nu with the increase of Re and with the decrease in TR and spacer

length, respectively. Kongkaithpaiboon et al. [9] presented the effect of circular-ring

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tabulators (CRT) on the heat transfer and fluid friction characteristics in a heat exchanger tube. Heat transfer rate in the tube fitted with CRTs are augmented around 57% to 195%

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compared to that of a plain tube. Moreover, the research results also reveal that the CRTs

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with the smallest pitch and diameter ratios offer the highest heat transfer rate and pressure

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drop. Promvonge et al. [10] studied the influence of an inclined vortex rings (VR) on the heat

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transfer augmentation in a uniform heat-fluxed tube. The aim of using the VRs is to create counter-rotating vortices inside the tube, which help to increase the turbulence intensity and

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promote the efficient fluid mixing. Thianpong et al. [11] experimentally investigated the heat transfer, friction factor, and thermal performance characteristics of a tube equipped with

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twisted-rings (TRs) and found that most TRs yield lower Nu and f than the typical circular rings. Kongkaitpaiboon et al. [12] used perforated conical-ring (PCR) as the turbulence-

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promoter device for enhancing the heat transfer rate in a heat exchanger system. They found that the PCRs can enhance the convective heat transfer rate more efficiently than the typical

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CR. Promvonge et al. [13] studied the heat transfer, friction factor, and enhancement efficiency characteristics in a circular tube fitted with conical-ring turbulators and a twistedtape swirl generator. The experimental results reveal that the tube fitted with the conical-ring and twisted-tape provides Nu values of around 4 -10%, and the enhancing efficiency of 4-8% higher than that with the conical-ring alone. Eiamsa-ard et al. [14] studied the heat transfer,

flow friction, and thermal performance factor characteristics of a tube fitted with deltawinglet twisted tape. The influence of oblique delta-winglet twisted tape (O-DWT) and straight delta-winglet twisted tape (S-DWT) arrangements was also reported. Nu, f, and TEF in a tube with the O-DWT are, respectively, 1.04–1.64, 1.09–1.95, and 1.05–1.13 times of those in the tube with typical twisted tape (TT). To make a better perspective of the heat

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transfer enhancement insertion devices and that are relevant to the present research work are

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depicted in Table 1.

The researchers also employed the passive heat transfer methodology in other heat

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transporting devices and reported the improved thermal performance [36 - 44]. Based on the

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foregoing literature, the effective design of heat exchangers is more beneficial to be used as

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the heat transporting equipment in chemical industries. Moreover, many different novel

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inserts were investigated by researchers and significant performance enhancement was also reported. It is also noticed that the enhanced heat transfer always accompanied with a

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significant friction penalty, which in turn decreases the overall system performance. The vortex generators so far reported can enhance the heat transfer by promoting the efficient

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fluid mixing and ruination of the thermal boundary layer [15 – 23, 25, 37-38], but the more flow blockage increases the pressure drop. Thus it is necessary to develop some new devices

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which can impact on both the wall and core flow phenomenon, and can also generate a low pressure drop. Moreover, the literature survey explicitly revealed that the convective heat

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transfer studies using wire mesh inserts have not been adequately investigated and thus provide an idea to do study in this area. This provide a strong motivation to develop new kind of insert geometries are design and developed, which can promote the efficient hot and cold fluid mixing and also produce a low friction penalty. In this context in the present study, a simple and cost effective methodology is developed using wire meshes for heat transfer

augmentation in a circular tube heat exchanger with air as working fluid. The mesh inserts can’t insert solely into the circular tube thus the wire screens are welded on a thin circular ring. The idea behind making a compound insert that the circular ring can generate the longitudinal vortex which increases the fluid residence time and the wire mesh can guide the cold fluid towards the heated wall. These two aspects can significantly enhance the

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convective heat transfer and also the wire mesh will not impart high pressure drop. Moreover,

due to extend the reliability of the system stainless steel meshes can be implemented for real

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applications in heat exchanger, as the steel meshes are more effective in terms of maintenance. In the present study the effect of three pitch ratios (PR = 2, 3, and 4) and three

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grade of metal wire net (G = 4, 9, and 16) on Nu, f, and TEF are investigated and presented in the form of tables and graphs. The turbulent air flow regimes are considered for which Re

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ranges from 5000 – 40000.

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2. Experimental Investigations

In this study, experimental approach is pursued to explore the heat transfer and

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friction characteristics in a circular heat exchanger tube embedded with the circular ring and metal wire net. The experimental data like fluid flow rate, the pressure difference across the

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fluid, inlet and outlet temperature of the fluid and surface temperature of the tube are collected by varying the geometrical parameters and operating conditions of the system.

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2.1 Experimental setup

The experimental setup is associated with an open loop flow system that has been

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fabricated and designed to conduct the experiments to collect the data for heat transfer and fluid flow characteristics in a heat exchanger tube. Schematic diagram of the experimental setup is shown in Fig. 1. It consists of test tube together with exit and entrance sections, a control valve, a calibrated orifice plate, a suction blower and the instruments that have been used for the measurement of temperatures and pressure drop. The temperature measurement

at the various locations is carried out by means of T-type thermocouples with copper constantan having the accuracy of ±0.1oC and range from -100oC to 1100oC, while a digital micro-manometer with accuracy of 1Pascal for pressure drop measurement within test tube and a U-tube manometer for mass flow rate.

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The copper pipe (flow and test section) is 6000 mm long. The main purpose of using the calming section is to provide fully developed flow at the inlet of the test section. The test

section is 1400 mm long with the outer and inner diameters of the pipe are 70mm, and 68mm,

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respectively. The heating over the tested tube is provided with the wrapped nichrome wire on

the tested tube surface. The flux over the tube is maintained at 750 W/m2 with the

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arrangement of variac and ammeter. In order to suppress the heat losses to the environment,

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the tested tube is insulated from outside surface by glass wool and polyethylene foam. The

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total 21 T-Type thermocouples are placed over the tube surface at equidistant locations so as

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to record the wall temperature. The inlet and outlet temperature of the air are measured with the 1, and 3 thermocouples that are placed at the inlet and outlet of the test section.

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The flow arrangement is provided with blower contained 3 HP motor regulated with 3ɸ power supply. A flow measurement device is attached in between the test section and blower

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which consists of an orifice plate and a U-tube manometer filled with water as a manometric

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fluid. A flow control wall is also attached adjacent to the blower for the purpose of controlling and varying the fluid flow rate. To measure the pressure drop across the test

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section of heat exchanger tube, a digital micro manometer has been provided. 2.2. Insert geometry and flow parameters The insert geometries comprise two parts, one part is the circular ring and the other part is circular ring with metal mesh. The circular rings are fabricated from a GI wire of 3 mm diameter and the outer diameter of the circular ring are kept 66 mm by taking a sufficient

clearance for the assembly insertion inside the test section. The metal mesh is characterized by the number of square blocks formed in 10 mm × 10 mm mesh size. The idea of selecting the mesh geometry and their sizes are totally based on the ease of fabrication and their availability. The mesh matrixes that are easily available are selected for making the inserts. Fig. 2a represent the criterion of mesh grade selection and the number of square meshes are

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counted on a 10mm × 10mm mesh sheet using steel rule. Total 3 grades are selected defined

as 4, 9, 16, respectively. The assembly of insert is represented in Fig.2b. Total nine

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combinations of insert geometries are tested at different flow Re. The definition of

dimensionless geometric parameters PR and G and pictorial view of the inserts are

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represented in Fig. 2.

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3. Data reduction

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The data recorded at the steady state for each test run are the temperatures of tube wall,

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air inlet, air outlet, and the differential pressure drop across tested tube, and the pressure head at the orifice meter. Total time of experiment for a single of geometrical parameters is around

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9 hours. The heat balance between the air ( Qair ) and heat input ( QVI ) is found to be within

   (5  7%) 

(1)

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 Q VI  Q air   Q VI

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the range of 5-7% for all experimental runs.

A heat calibration test has been implemented between winding of coil and heat gain by air,

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for the heat supplied and the carrying heat. There is 5 -7% variation observed between the heat supplied by winding and the heat absorbed by the working fluid. Due to convection and radiation heat loss from the test section to atmosphere, the actual heat transfer rate is computed by the heat absorbed by air. By considering only forced convection, it is assumed that the heat absorbed by the fluid is taken for the internal convective heat transfer coefficient

calculation. The energy balance between convective heat transfer through the tube and heat gained by air flowing inside the tube is written as:

Qair = Qconv

(2)

Where  C p (To  Ti ) Qair  m

For the heat exchanger wall, the convective heat transfer is given by:

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Qconv  hATwm  Tb 

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(3)

(4)

Where Tb stands for the bulk mean temperature of the air and is calculated by the following

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Ti  To 2

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Tb 

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relation

(5)

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Tw is the local wall temperature. Twm is the average temperature of the total thermocouple

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placed on the wall surface and defined as:

(6)

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T  Twm    w   21 

The convective heat transfer rate and Nu are calculated as:

m C p (To  Ti )

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h

A (Twm - Tb )

h.D k

(8)

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Nu 

(7)

The Re and f are calculated using the following expressions:

Re 

 VD 

(9)

f 

P 

 

 L  V 2  D 2  

  

(10)

The thermal enhancement factor (TEF) estimated by:  Nu Nu  s TEF    1   f f s  3 

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(11)

4. Smooth tube validation and experimental uncertainty Validation

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4.1.

To validate the fidelity of the data generated with the test rig, a smooth tube is validated with the correlation of Dittus-Boelter equation for Nu and modified Blasius equation for f. These

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correlations are defined as:

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Nu  0.023  Re 0.8  Pr 0.4

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f  0.316  Re 0.25

(12)

(13)

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Fig. 3a. represent a comparison between the experimental and predicted values of Nu and f for the smooth tube. A good agreement between the experiment and theoretical values are

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recorded with an average absolute deviation of 3.03% and 3.48% for Nu and f, respectively,

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this assures the correctness of the collected data. To assess the repeatability of the tests, the data for heat transfer is generated for

different days at different heat fluxes and depicted in Fig 3b. The Nu is plotted for the various

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range of Re which indicates good repeatability in the heat transfer data. It is observed that the variation in the Nu is within ± 10% at different heat flux, which shows the good repeatability in the experiments conducted. 4.2.

Uncertainty analysis

An error relevant to the experimental results has been carried out on the basis of uncertainty analysis proposed by Kline and McClintock [26]. The maximum uncertainties calculated for the non-dimensional parameters are, ±6% for Re, ±5% for Nu and ±10% for f, respectively. 5. Results and discussion

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The heat transfer rate and pressure drop of a tube integrated with circular ring combined with metal wire net inserts of various configurations have been analyzed and the

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results are compared with the smooth tube. The effect of PR, G, and Re on Nu, Nu/Nus, f, f/fs, and TEF are reported in the form of graphs and tables.

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5.1. Numerical investigation

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To study the mechanism of heat transfer in tubes embedded with solid rings alone and

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solid rings with mesh inserts are studied and presented for single set of geometrical and flow

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parameters. The study being done for G = 9, PR = 3, and Re = 5000. The tube embedded with

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solid rings as the base case and tube with solid rings with mesh as the modified case are modeled in design software. A 3-D computational fluid domain is considered in the present

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case and the governing equations are solved by RANS model. The RANS model (RNG k- ɛ) is used in the present simulations. The fluent module of ANSYS software is used for analysis.

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The unstructured mesh is generated for the present case using ICEM module of ANSYS software and the result independency are observed after 1.67 × 105 cells, thus these grids are

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used for analysis. A velocity inlet boundary condition at the inlet and a temperature equal to 300 K is prescribed. The hydraulic diameter is equal to the inner diameter of the pipe. At the outlet, the zero-gradient boundary condition is imposed. The no-slip condition is applied at the walls of the rings and pipe surface. A uniform heat flux of 750 W/m2 is applied on the tube wall by implementing the same experimental condition described in section 2. The governing equations (continuity, momentum and energy) for the incompressible fluid are

solved by using boundary conditions. The governing equations are presented as appendix. The pressure and velocity are coupled with SIMPLE algorithm and second order upwind scheme is implemented for all the variables (momentum, energy, turbulent kinetic energy, and turbulent dissipation rate). The convergence for the energy, velocity components, k, ɛ, and continuity are 10-9, 10-7, 10-7, 10-7, and 10-6, respectively. The prime objective of the

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numerical analysis is to demonstrate the aspects of performance improvement with rings and mesh inserts. This flow pattern helped to discuss the physical behavior of the flow when it

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passes from meshes. The numerical methodology adopted in the present case is presented in Table. 3.

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The contour plots of the velocity field, turbulent kinetic energy, temperature field and

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flow structure inside the tube embedded with solid rings alone and with meshes are shown in

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Figs. 4 – 7. The velocity field inside the tube at various axial locations is depicted in Fig. 4. It

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is clearly observed that for a common axial flow with the highest velocity in the centre core is observed for the tube with solid rings alone and a high velocity is also observed near to the

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wall due to the presence of rings near to wall. The centre core fluid part is nearly undisturbed for the solid rings alone (Fig. 4a), in contrast to this for rings with mesh the centre core is also

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disturbed due to the insertion of meshes and a high velocity in the domain is observed for

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solid rings with meshes (Fig. 4b). It is also observed from Fig. 4b that the fluid is spread into number of main streams at contour 1, 3 and 5 at Fig. 4b and this phenomenon are attributed to the flow partition effect of the meshes. This velocity behavior supports the more turbulence

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inside the tube and thus accommodates high heat transfer for solid with mesh inserts. Moreover, this high velocity in the centre core imparts more fluids towards the heated wall and exhibits a high heat transfer rate from the tube surface. To have a better perspective of high turbulence inside the tube with mesh inserts a Fig. 5 depicted the turbulent kinetic energy (TKE) inside the tube with inserts. It is clearly

observed from Fig.5 that the TKE is low in the tube with solid rings alone than the tube with solid and mesh inserts. As in such conditions, flow disturbance in the centre core is undisturbed, thus flow turbulence is low. For the tubes inserted with solid rings with meshes, high turbulence kinetic energies are found in the centre core. The high TKE is observed in the wake of mesh and this is attributed due to the flow separation associated with the mesh

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insertion in the solid ring. The magnitude of high TKE for solid ring with mesh can easily noticed in Fig. 5b. Further, this indicates that the turbulence intensities within solid ring alone

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tubes are low, resulting in insignificant temperature changes (Fig. 6a).

The thermal field at different axial positions for solid ring alone and with mesh is presented

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in Fig.6. The contours of thermal field are agreed well with the velocity and TKE contours

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presented in the Figs. 4-5. The presence of solid ring and meshes induced a recirculation

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flow, for solid ring alone the recirculation flow is observed near the wall (Fig. 8), while for

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the solid ring with mesh, the series of recirculation flow also observed around the mesh (Fig.9). It is evident that the each stream of recirculation flow is induced as the incoming

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flows pass over inserts. The recirculation flows improve flow mixing between the main flow regions and the walls, indicating by the higher core temperature just behind the inserts. The

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thermal fields for the mesh inserts are more uniform than the solid ring alone and this

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attributed to the thinned thermal boundary layer, which imparts high heat transfer rate. To have better understanding of the nature of velocity, thermal and TKE inside the tube, the

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contours at a transverse plane (X/D = 2) is presented in Fig. 7. It is observed that the high velocity and TKE is observed for the solid ring with mesh than solid ring alone. The thermal fields for the solid ring with mesh clearly evident the high heat transfer rate due to the efficient mixing of cold and hot fluid. The efficient fluid mixing for the solid ring with mesh case is due to the series of recirculation generated (Fig. 9). To support the aspect of efficient fluid mixing and high TKE due to the generation of

recirculation vortex in the fluid flow, the fluid structure inside the tube is depicted in Figs 8 – 9. The flow behavior inside the tube for solid ring is represented in Fig. 8. It is clear seen that a recirculation vortex is generated behind the ring in the flow stream direction, which

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intends to hot and cold fluid mixing near to wall, which in turn thins the thermal boundary layer. The generation of recirculation vortex also delayed the fluid residence time in the tube

and provides more time for fluid mixing. It is also observed that the core flow is undisturbed

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for the solid ring alone case. The flow behavior inside the tube with solid rings with meshes

is presented in Fig. 9. The fluid flow behavior for solid ring with mesh is completely different

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from the solid ring alone. There are series of recirculation vortex generated behind the

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meshes, which significantly increase the turbulence inside the tube and promotes efficient

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fluid mixing. The aspect of flow pattern is well agreed with the TKE and thermal fields

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demonstrated in Figs. 5 – 6. On comparing the flow pattern of solid ring and solid with mesh form Figs 8-9, it is observed that for solid alone, there is only one vortex appear behind the

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ring but for the second case at the same position two additional flow vortex appears. In addition, a series of two vortexes appear behind the mesh, where flow separation occurs. This

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kind of complex fluid behavior inside the tube with solid rings with meshes increases the

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convective heat transfer.

5.2. Effect on heat transfer

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To show the superiority of the circular ring with metal wire net over the conventional

circular ring alone, a graph prepared and represented in Fig. 10, which inculcates the Nu, f, and TEF of both the inserts at a constant PR of 3. It is clear from Fig. 10 that for the complete range of Re the heat transfer rate for the solid ring with mesh is more than the ring alone. This is due to the fact that the rings alone are not capable of proving an efficient cold

and hot fluid mixing due to the undisturbed centre fluid core, which in turn produces low convective heat transfer for ring alone. The high aspect of convective heat transfer for solid ring with mesh is clearly demonstrated in Figs. 4- 9. The f of the ring integrated with mesh is higher than the ring alone due to the significant disturbance provided in the core flow with mesh inserts. The TEF of ring with mesh is higher than the ring alone for the complete range

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of Re and thus finally ensures the performance preeminence of ring with mesh over the ring alone.

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The variation of Nu and Nu/Nus with Re for different values of PR and G represented

in Fig. 11. From Fig. 11a-c, it is found that Nu is continuously increasing with Re for all sets

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of PR and G. This is due to the fact that high Re is responsible for enhancement in turbulence

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intensity, which improves the fluid mixing and in turn thins the thermal boundary layer. The

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heat transfer rates of the tubes embedded with solid ring with mesh inserts are higher than

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those of the plain tube because the presence of inserts imparts a higher tangential velocity in core tube and a thinner velocity boundary layer formed near the tube wall [6-7]. Moreover, it

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also observed that the Nu increases with the increase of G and decrease of PR and the maximum heat transfer is obtained for the high mesh density and minimum PR. The data

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trend supports that the smaller PR generates the strong recirculation vortex and also promote

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the efficient fluid mixing, which interrupts the thermal boundary layers along the heated tube resulting in higher heat transfer rate (Figs. 4-9). Further, it is also observed that the higher Nu is found for the lower PR values for all the G. This is attributed due to more number of inserts

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for lower PR, which exhibit more turbulent intensity in the tube and thus accounted high heat transfer rates. The enhancement in heat transfer as compared to the smooth tube for PR = 2 is 265% to 354%, for PR = 3 is 241% to 323%, and for PR = 4 is 226% to 303%, while for G = 4 it is recorded between 226% to 309%, for G = 9 it is 245% to 334% and for G = 16 it is 259% to 354%.

The comparison of Nu for the present case PR = 2 and G = 16 with previously published geometries are presented in Fig. 12. The Nu for the present insert solid ring – mesh is found to be more than most of the insert geometries selected for comparison. This shows the superiority of the solid ring – mesh inserts over other geometries.

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5.3. Effect on friction factor The f plays an imperative role in the efficient working of a heat exchanger. For the

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high values of f the TEF significantly decreases, thus it is very necessary to control the f in order to improve the thermal performance of heat exchangers. Effect of inserts with various mesh grades (G = 4, 9, and 16) and different pitch ratio (PR =2, 3, and 4) on friction factor (f)

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and friction factor ratio (f/fs) is demonstrated in Fig. 13a-d. As shown, friction factor

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insignificantly changes with the change of Reynolds number (Re), while f/fs ratio tends to

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increase with decreasing Reynolds number (Re). At a given Reynolds number (Re), friction

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factor (f) decreases as the pitch ratio (PR) decreases and mesh grade (G) increases. It can be

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easily noticed from Fig.13 that for G=16 f is maximum at PR = 2 as compared to other G and PR combinations. This is due to the maximum flow blockage provided by the dense mesh for

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this case. It is also observed that for the lower Re the f is maximum and as the Re increases, the value of f decreases as the fluid velocity increases with increasing Re. The maximum and

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minimum f can be seen for the PR = 2 and 4, respectively, as low PR means more number of insert geometries and thus high blockage and correspondingly the high friction penalty. From

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Fig. 13d, the enhancement in f by the use of circular ring with mesh as compared to the smooth tube for PR = 2 is 144% to 185%, for PR = 3 is 122% to 157% and for PR = 4 it is 108% to 139%, while for G = 4 it is recorded between 108% to 158%, for G = 9 it is 118% to 173% and for G = 16 it is 126% to 185%.

The pressure drop in term of f with the mesh inserts for PR = 2, and G =16 is compared with the previous geometries and demonstrated in Fig. 14. It is found that the friction factor for the present case is relatively lower than many cases and this is due to the less flow blockage associated with the mesh inserts. The passive heat transfer enhancement insertion devices like twisted tapes, vortex generators are capable to impart intensified vortexes in the core, which

IP T

exhibit very high heat transfer than the mesh inserts but they also accompanied a very high

pressure drop (Figs. 12-14). Thus, solely either high Nu or low f cannot predict the

SC R

comprehensive system performance. The comprehensive evaluation can be undertaken by considering both the functional parameters viz. heat transfer and friction penalty. The

U

comprehensive performance termed as TEF is discussed in the next section.

N

5.4. Effect on thermal enhancement factor

A

The influence of ring mesh inserts on TEF at constant pumping power is represented

M

in Fig. 15. The effect of PR and G on TEF at selected Re is depicted in Fig.15a. The TEF

ED

values increase with the increase of PR and G and attained a maximum value at PR = 3, and G =9 and thereafter it decreases. The graph subdivided into the dashed from A to E, A – B

PT

comprises data of Re = 5000, B-C comprises data of Re = 10000, C-D comprise data of Re = 25000, and D-E comprise data of Re = 35000. The high performance attributed due to the

CC E

efficient fluid mixing at G = 9 and the increase in flow reattachment points for the PR = 3. TEF for compound inserts with PR = 3 is found to be about 104.4% and 105.4% higher than

A

those at PR = 2, and 4, respectively. At PR of 3 and Re = 5000–35,000, TEF varied between 2.56 and 2.79, 2.67 and 2.84, and 2.59 and 2.82 for G of 4, 9, and 16, respectively. Furthermore, the maximum TEF of 2.84 is achieved by using the ring with mesh inserts at G = 9, and PR =3. A 3D contour plot prepared to show the most suitable TEF regime and represented in Fig. 15b, and it is found that the suitable TEF is from PR 2.5 to 3.5 and at G

=9, respectively. Thus, it can be concluded that the optimum geometry in the view point of energy saving at PR = 3 and G = 9 (Fig. 15b). In order to evaluate the advantage of solid ring – mesh inserts in the present work as heat transfer enhancement devices, the TEF results of the solid ring - mesh the highest

IP T

thermal performance factor (PR = 3 and G = 9) is compared with those of inserts, including multiple twisted tapes and solid rings [3], delta winglet-twisted tapes [14], coiled wire inserts

[28], twisted tape inserts placed separately from the tube wall [29], triple twisted tape [30],

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circular-rings and twisted tapes [31], vortex generator [32], and perforated vortex generator [45]. The comparison results are demonstrated in Fig. 16. It is clearly observed from the Fig.

U

16 that the present insert geometry is beneficial than many other geometries reported in Table

N

1. This clearly indicates the suitability of using mesh wire as insert geometries over the

M

6. Correlations for Nu and f

A

conventional passive insertion devices.

ED

In order to consider the comprehensive effect of the parameters Re, PR, and G, the correlations are developed for Nu and f as a function of these parameters using multi –

PT

variable regression analysis, respectively. The geometrical parameters considered are PR (2,

CC E

3, and 4) and G (4, 9, and 16), while the flow parameter considered is Re ranging from 5000 to 40000. The developed correlations for Nu and f are depicted in Equations (14) and (15), respectively.

(14)

f  0.85 Re 0.2965 PR 0.4089G 0.1108

(15)

A

Nu  0.02866 Re 0.8746 PR 0.2262G 0.0993

Fig. 17 shows that the deviations between the experimental data and the correlations predicted values of Nu and f are ±10% and ±11%, respectively.

Conclusions Thermal and fluid flow characteristics of a uniformly fluxed circular tube integrated circular ring with mesh inserts are investigated experimentally and numerically. From the present results, the conclusions can be drawn as follows:

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o The circular tube with metal wire net insert has a significant effect on TEF, including the Nu and f values, for Re ranges from 5000 – 40,000, and can be effectively used as

SC R

passive mode of enhancement for the thermal intensification in the commercial applications.

o Nu of a circular tube fitted with circular ring combined with metal wire net insert

U

increases with increasing Re as expected. The Nu increases with the decrease and

N

increase of PR and G, respectively, and attained maximum values at PR=2 and G =16.

A

The variation in Nu is more pronounced for high values of Re. The enhancement in

M

Nu over plain tube is in the range of 226% – 354%.

ED

o The f values decreases with increase in Re, and PR and increases with increase of G. The minimum f values obtained for PR = 4 and G =4. The enhancement in f over plain

PT

tube is in the range of 108% – 185%. o The recirculation of the fluid past the wire insert increases the Nu, along with increase

CC E

in the f values for wire mesh with different PR and G combinations.

o TEF of the modified tube tends to decrease with increasing Re. The PR = 3, G = 9

A

provides the highest TEF of about 2.84, resulting the higher thermal performance of the heat exchanger.

o Empirical correlations of Nu and f are in good agreement with the experimental observations with deviations of ± 10% for Nu and ± 11% for f. Appendix: Governing equations

Continuity equation y ui  = 0 x i

Momentum equation

     x j 

      u i' u 'j   

IP T

  u i u j      x j x i

SC R

y uiu j    p   x i x i x j

where ρ is the density of the fluid, and ui is a mean component of velocity in the direction xi, p is the pressure, μ is the dynamic viscosity, and u’ is a fluctuating component of velocity.

N

U

Energy equation

Pr

M



is the molecular thermal diffusivity and t 

ED

Where,  

CC E

PT

diffusivity.

A

A

  y ui T      t  T  x i x j  x j 

t Prt

is turbulent thermal

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IP T

perforated ring inserts. Experimental Thermal and Fluid Science 79 (2016) 168–174. [2] A. Kumar, S. Chamoli, M. Kumar. Experimental investigation on thermal

SC R

performance and fluid flow characteristics in heat exchanger tube with solid hollow circular disk inserts. Applied Thermal Engineering, 100 (2016) 227-236.

[3] V. Singh, S. Chamoli, M. Kumar, A. Kumar. Heat transfer and fluid flow

U

characteristics of heat exchanger tube with multiple twisted tapes and solid rings

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A

[4] P. Kumar, A. Kumar, S. Chamoli, M. Kumar. Experimental investigation of heat

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transfer enhancement and fluid flow characteristics in a protruded surface heat

ED

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PT

flow and heat transfer in air to water heat exchanger using perforated circular ring. Experimental thermal and fluid science 70 (2016) 185-195.

CC E

[6] W. Tu, Y. Tang, B. Zhou, L. Lu. Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube with small pipe inserts.

A

International Communications in Heat and Mass Transfer 56 (2014) 1-7.

[7] M.M.K. Bhuiya, M.S.U. Chowdhury, M. Islam, J.U. Ahamed, M.J.H. Khan, M.R.I. Sarker, M. Saha. Heat transfer performance evaluation for turbulent flow through a tube with twisted wire brush inserts. International Communications in Heat and Mass Transfer 39 (2012) 1505-1512.

[8] E.Z. Ibrahim, Augmentation of laminar flow and heat transfer in flat tubes by means of helical screw-tape insert, Energy Conversion and Management, 52 (2011) 250-257. [9] V. Kongkaitpaiboon, K. Nanan, S. Eiamsa-ard. Experimental investigation of convective heat transfer and pressure loss in a round tube fitted with circular ring turbulators. International Communications in Heat and Mass Transfer 37 (2010)

IP T

568-574.

[10] P. Promvonge, N. Koolnapadol, M. Pimsarn, C. Thianpong. Thermal performance

SC R

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U

[11] C. Thianpong, K. Yongsiri, K. Nanan, S. Eiamsa-ard. Thermal performance

N

evaluation of heat exchanger fitted with twisted-ring turbulators. International

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Communications in Heat and Mass Transfer 39 (2012) 861-868.

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[12] V. Kongkaitpaiboon, K. Nanan, S. Eiamsa-ard. Experimental investigation of heat transfer and turbulent flow friction in a tube fitted with perforated conical–rings.

ED

International Communications in Heat and Mass Transfer 37 (2010) 560-567. [13] P. Promvonge, S. Eiamsa-ard. Heat transfer behaviors in a tube with combined

PT

conical ring and twisted tape insert. International Communications in Heat and Mass Transfer 34 (2007) 849-859.

CC E

[14] S. Eiamsa-ard, K. Wongcharee, P. Eiamsa-ard, C. Thianpong. Heat transfer enhancement in a tube using delta winglet-twisted tape inserts. Applied Thermal

A

Engineering 30 (2010) 310-318.

[15] P. Promvonge, S. Eiamsa-ard. Heat transfer in a circular tube fitted with freespacing snail entry and conical –nozzle turbulators. International Communications in Heat and Mass Transfer 34 (2007) 838–848.

[16] S. Eiamsa-ard, P. Promvonge. Experimental investigation of heat transfer and friction characteristics in a circular tube fitted with V-nozzle turbulators. International Communications in Heat and Mass Transfer 33 (2006) 591–600. [17] S. Eiamsa-ard, P. Nivesrangsan, S. Chokphoemphun, P. Promvonge,Influence of combined non-uniform wire coil and twisted tape inserts on thermal performance

IP T

characteristics, International Communications in Heat and Mass Transfer, 37 (2010) 850–856.

SC R

[18] M. Rivier, P. Sébastian, T. Goli, G. Raffray, A. Collignan. Heat transfer enhancement of a circular tube heat exchanger fitted with an elliptic shaped turbulator

U

designed in the context of developing countries. Applied Thermal Engineering 81

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(2015) 92-101.

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[19] S. W. Chang, T. L. Yang, J. S. Liou. Heat transfer and pressure drop in tube with

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broken twisted tape insert. Experimental Thermal and Fluid Science 32 (2007) 489501.

ED

[20] S. Eiamsa–ard, N. Piriyarungrod, Thianpong, M. Pimsarn, K. Nanan. Heat transfer enhancement by tapered twisted tape inserts. Chemical Engineering and Processing:

PT

Process Intensification 96 (2015) 62-71. [21] S. Eiamsa–ard. Study on thermal and fluid flow characteristics in turbulent channel

CC E

flows with multiple twisted tape vortex generator. International Communications in Heat and Mass Transfer 37 (2010) 644–651.

A

[22] K. Nanan, C. Thianpong, P.Promvonge, S. Eiamsa-ard. Investigation of heat transfer enhancement by perforated helical twisted–tapes. International Communications in Heat and Mass Transfer 52 (2014) 106–112. [23] A. Saad, A. Sayed, El-Sayaed, E. Mohamed, A. Hamid, M.S. Mohamed. Experimental study of turbulent flow inside a circular tube with recirculation

interrupted fins in the stream wise direction. Experimental Thermal and Fluid Science 15 (1997) 1-15. [24] M.M.K. Bhuiya, A.S.M. Sayem, M. Islam, M.S.U. Chowdhury, M. Shahabuddin. Performance assessment in a heat exchanger tube fitted with double counter twisted tape inserts. International Communications in Heat and Mass Transfer 50 (2014) 25–

IP T

33.

[25] M.M.K. Bhuiya, M.S.U. Chowdhury, M. Saha, M.T. Islam. Heat transfer and friction

SC R

factor characteristics in turbulent flow through a tube fitted with perforated twisted tape inserts. International Communications in Heat and Mass Transfer 46 (2013) 49–

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57.

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[26] S.J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments,

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Mech. Eng. 75 (1953) 385–387.

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[27] P. Promvonge. Thermal augmentation in circular tube with twisted tape and wire coil turbulators. Energy Conversion and Management 49 (2008) 2949–2955

ED

[28] S. Gunes, V. Ozceyhan, O. Buyukalaca. Heat transfer enhancement in a tube with equilateral triangle cross sectioned coiled wire inserts. Experimental Thermal and

PT

Fluid Science 34 (2010) 684–691. [29] H. Bas, V. Ozceyhan. Heat transfer enhancement in a tube with twisted tape inserts

CC E

placed separately from the tube wall. Experimental Thermal and Fluid Science 41 (2012) 51–58.

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[30] M.M.K. Bhuiya, M.S.U. Chowdhury, M. Shahabuddin, M. Saha, L.A. Memon. Thermal characteristics in a heat exchanger tube fitted with triple twisted tape inserts. International Communications in Heat and Mass Transfer 48 (2013) 124–132. [31] S. Eiamsa-ard, V. Kongkaitpaiboon, K. Nanan. Thermohydraulic of turbulent flow through heat exchanger tubes fitted with circular-rings and twisted tapes fluid

dynamics and transport phenomena. Chinese Journal of Chemical Engineering 21 (2013) 585—593. [32] P. W. Deshmukh, R. P. Vedula. Heat transfer and friction factor characteristics of turbulent flow through a circular tube fitted with vortex generator inserts. International Journal of Heat and Mass Transfer 79 (2014) 551–560.

IP T

[33] S. Chokphoemphun, M. Pimsarn, C. Thianpong, P. Promvonge. Thermal

Journal of Chemical Engineering 23 (2015) 755-762.

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performance of tubular heat exchanger with multiple twisted-tape inserts. Chinese

[34] S. Skullong, P. Promvonge, C. Thianpong, M. Pimsarn. Heat transfer and turbulent

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flow friction in a round tube with staggered-winglet perforated-tapes. International

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Journal of Heat and Mass Transfer 95 (2016) 230–242

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[35] P.W. Deshmukh, S.V. Prabhu, R.P. Vedula. Heat transfer enhancement for laminar

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flow in tubes using curved delta wing vortex generator insert. Applied Thermal Engineering 106 (2016) 1415-1426. M.

Hatami, G.H.R.

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[36]

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Ahangar, D.D.

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[37]

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fins. Energy Conversion and Management 84 (2014) 533-540.

exchangers for ICEs exhaust waste heat recovery. Case Studies in Thermal Engineering 4 (2014) 53-64.

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[38]

M. Fakour, A. Vahabzadeh, D.D. Ganji, M. Hatami. Analytical study of

micropolar fluid flow and heat transfer in a channel with permeable walls. Journal of Molecular Liquids 204 (2015) 198-204.

[39]

M. Sheikholeslami, D.D. Ganji. Heat Transfer Improvement in a Double Pipe

Heat Exchanger by Means of Perforated Turbulators. Energy Conversion and Management 127 (2016) 112–123 [40]

M. Sheikholeslami, D.D. Ganji. Heat transfer enhancement in an air to water

heat exchanger with discontinuous helical turbulators. Experimental and Numerical

[41]

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Studies, Energy 116 (2016) 341–352.

M. Sheikholeslami, M.M. Bhatti. Forced convection of nanofluid in presence

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of constant magnetic field considering shape effects of nanoparticles. International Journal of Heat and Mass Transfer 111 (2017) 1039–1049.

H. M. Ali and A. Briggs. Condensation of ethylene glycol on pin-fin tubes:

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[42]

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effect of circumferential pin thickness and spacing. Applied Thermal Engineering 49

H. M. Ali and A. Briggs. Enhanced condensation of ethylene glycol on pin-fin

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[43]

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(2012) 9 -13.

tubes: effect of pin geometry. ASME J. of Heat Transfer 134 (2012) 011503. H. M. Ali and A. Briggs. Condensation heat transfer on pin-fin tubes: effect of

ED

[44]

thermal conductivity and pin height. Applied Thermal Engineering 60 (2013) 465-

PT

471.

[45] S. Chamoli, R. Lu, P. Yu. Thermal characteristic of a turbulent flow through a

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circular tube fitted with perforated vortex generator inserts. Applied Thermal Engineering 121 (2017) 1117–1134.

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[46] S. Chamoli, P. Yu, S. Yu. Multi-objective shape optimization of a heat exchanger tube fitted with compound inserts. Applied Thermal Engineering 117 (2017) 708 – 724.

[47] S. Pethkool, S. Eiamsa-ard, S. Kwankaomeng, P. Promvonge. Turbulent heat transfer enhancement in a heat exchanger using helically corrugated tube. International Communications in Heat and Mass Transfer 38 (2011) 340–347. [48] A. Harleß, E. Franza, M. Breuer. Experimental investigation of heat transfer and friction characteristic of fully developed gas flow in single-start and three-start

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corrugated tubes. International Journal of Heat and Mass Transfer 103 (2016) 538 -

A

CC E

PT

ED

M

A

N

U

SC R

547.

IP T SC R U N

A

CC E

PT

ED

M

A

Fig. 1. Schematic view of experimental setup.

IP T SC R

M

A

N

U

(a)

ED

(b)

A

CC E

PT

Fig. 2. (a) Front view of mesh insert, (b) isometric view of insert geometry.

100

0.045

Nu (Experiment) Nu (Dittus - Boelter) f (Experiment) f (Blausius )

90

0.04

80 Nu

IP T

70

0.035

50 f

U

40

15000

20000

M

10000

A

20

0.025

25000

30000

35000

ED

Re

CC E

PT

Fig. 3a. Comparison of experimental and theoretical values of Nu and f.

A

0.03

N

30

10 5000

SC R

f

Nu

60

0.02

150

-2

q = 300 W-m q = 500 W-m-2 q = 750 W-m-2 -2 q = 1000 W-m

IP T

90

SC R

Nu

120

30 20000

N

U

60

30000

40000

50000

M

A

Re

A

CC E

PT

ED

Fig.3b. Experimental repeatability for Nu at different heat fluxes.

60000

A ED

PT

CC E

IP T

SC R

U

N

A

M (a)

IP T SC R U N A M ED PT

(b)

CC E

Fig.4 . Contour plot of velocity fields at various transverse planes for (a) solid ring alone, (b)

A

solid rings with meshes at PR = 3, G = 9, and Re = 5000.

A ED

PT

CC E (a)

IP T

SC R

U

N

A

M

IP T SC R U N A M ED

(b)

PT

Fig.5 . Contour plot of turbulent kinetic energy at various transverse planes for (a) solid ring

A

CC E

alone, (b) solid rings with meshes at PR = 3, G = 9, and Re = 5000.

A ED

PT

CC E (a)

IP T

SC R

U

N

A

M

IP T SC R U N A M ED PT

(b)

Fig.6 . Contour plot of thermal field at various transverse planes for (a) solid ring alone, (b)

A

CC E

solid rings with meshes at PR = 3, G = 9, and Re = 5000.

SC R

IP T

Velocity

U

a (i)

N

Thermal

b (i)

A

CC E

PT

ED

M

A

field

a (ii)

b (ii)

SC R

IP T

TKE

b (iii)

A

N

U

a (iii)

M

Fig.7. Contour plots of velocity, thermal field and TKE at X/D = 2 for (a (i), a (ii), and a (iii)) solid ring alone, (b (i), b (ii), and b (iii)) solid rings with meshes at PR = 3, G = 9, and Re =

A

CC E

PT

ED

5000.

IP T SC R U N A

A

CC E

PT

ED

M

Fig. 8. Flow behavior in a tube embedded with solid ring alone at PR = 3 and Re = 5000.

A ED

PT

CC E (a)

IP T

SC R

U

N

A

M

IP T SC R U N A M

(c)

ED

Fig. 9. Flow behavior inside the tube embedded with solid ring with mesh at PR = 3, G = 9,

A

CC E

PT

and Re = 5000 (a) tube with two rings (b) partial view behind the mesh near to tube wall.

200

X

X

X

X

X

X

X

0.08 3 2.5

TEF

X

150

0.06

TEF

X

4 3.5

f

250

Nu

0.1

Nu: Solid ring (PR = 3) Nu: Solid ring with mesh (PR = 3, G = 9) f: Solid ring (PR = 3) f: Solid ring with mesh (PR = 3, G = 9) TEF: Solid ring (PR = 3) TEF: Solid ring with mesh (PR = 3, G = 9)

IP T

300

2

100

1

Nu f

0.04

0.5

10000

20000

40000

M

V1

30000

A

0

N

U

50

0

SC R

1.5

0 0.02

ED

Fig. 10. Comparison of experimental values of Nu, f , and TEF for circular ring and circular

A

CC E

PT

ring with mesh at constant PR of 3.

360 PR = 2, G = 4 PR = 2, G = 9 PR = 2, G = 16

330 300 270

Nu

240 210 180

IP T

150 120

60 30

0

7000

14000

21000

28000

(a)

240

42000

ED

Nu

210 180

PT

150 120

CC E

90 60 30

A

35000

M

270

A

PR = 3, G = 4 PR = 3, G = 9 PR = 3, G = 16

300

42000

N

330

35000

U

Re

SC R

90

0

7000

14000

21000

Re (b)

28000

35000

42000

330 PR = 4, G = 4 PR = 4, G = 9 PR = 4, G = 16

300 270 240

Nu

210 180

IP T

150 120

60 35000

42000

30

0

7000

14000

21000

28000

CC E

PT

42000

A

35000

ED

M

A

N

(c)

35000

U

Re

SC R

90

42000

4.25

PR = 2, G = 4 PR = 2, G = 9 PR = 2, G = 16 PR = 3, G = 4 PR = 3, G = 9 PR = 3, G = 16 PR = 4, G = 4 PR = 4, G = 9 PR = 4, G = 16

4 3.75

Nu/Nus

3.5 3.25

X

3

X 2.75

+

X +

X

X

X

+

+

+

+

+

N

2.5

10000

20000

M

0

A

2.25 2

X

U

+

X

IP T

+ X

SC R

4.5

30000

40000

ED

Re

(d)

PT

Fig. 11. Influence of G on Nu as a function of Re for (a) PR = 2, (b) PR = 3, (c) PR = 4, (d)

A

CC E

Variation of Nu/Nus with Re at different values of PR and G.

330 300 270 X

240

+

Present study Bhuiya et al. [30] Pethkool et al. [47] Gunes et al. [28] Bas and Ozceyhan [29] Eiamsa-ard et al. [31] Harleß et al. [48]

210

+

+

150

X X

+ 120

+

X X

X

90

+

X

X

+

60

U

X

5000

10000

15000

20000

25000

30000

A

0

N

30 0

IP T

+

SC R

Nu

+ 180

M

Re

A

CC E

PT

ED

Fig.12. Nu comparison of present insert geometry with previous reported inserts.

PR = 2, G = 4 PR = 2, G = 9 PR = 2, G = 16

0.0

f

0.08

0.0

f

0.06

0.0

IP T

0.04

0

7000

14000

21000

28000

35000

M

A

0.1

PR = 3, G = 4 PR = 3, G = 9 PR = 3, G = 16

0.04 0.03

0.01

PT

f

0.06

0.06

0.02

ED

0.08

0.07

0.05

N

(a)

42000

U

Re

f

0

SC R

0.02

,G=4 ,G=9 , G = 16

CC E

0.04

0.02

0

7000

14000

21000

28000

35000

42000

Re 0.07 (b) 0.06 0.05 0.04

f

0

42000

A

0

0.0

0.1

0.03 0.02

PR = 4 PR = 4 PR = 4

0.04

0.02

42000

0.07

0

0

PR = 4, G = 4 PR = 4, G = 9 PR = 4, G = 16

0.06 0.05

f

0.04

IP T

0.03 0.02

0

0

7000

14000

21000

28000

PT

ED

M

A

N

(c)

CC E

35000

U

Re

SC R

0.01

A

35000

42000

7000

14

2.4

PR = 2, G = 4 PR = 2, G = 9 PR = 2, G = 16 PR = 3, G = 4 PR = 3, G = 9 PR = 3, G = 16 PR = 4, G = 4 PR = 4, G = 9 PR = 4, G = 16

2.2

IP T

2

X +

SC R

f/fs

1.8

1.2

1

0

10000

+ X

+ X

+ X

+ X

N

+ X

A

+ X

20000

M

1.4

U

1.6

30000

+ X

+ X

40000

PT

ED

Re

(d)

Fig. 13. Influence of G on f as a function of Re for (a) PR = 2, (b) PR = 3, (c) PR = 4, (d)

A

CC E

Variation of f/fs with Re at different values of PR and G.

0.3 Present study Bhuiya et al. [30] Pethkool et al. [47] Gunes et al. [28] Bas and Ozceyhan [29] Harleß et al. [48]

0.27 0.24

+ 0.21

IP T

0.18

f

0.15

0.09 0.06

+

+

+

+

+

+

0

5000

10000

N

0.03 0

+

U

+

SC R

0.12

15000

20000

25000

30000

M

A

Re

A

CC E

PT

ED

Fig.14. Nu comparison of present insert geometry with previous reported inserts.

X

3.3 2.85

X

3.2

2.8

Re = 25000

4.2

TEF

2.7 2.65

X

4 3.8

X

3

X

3.6

X

2.6

X

X

1

1.5

2

Re = 5000

X

2.5

3

CC E

PT

ED

PR

A

N

2.6

A

X

2.8

2.4 2.4

X

M

2.45

3

U

3.2

2.5

2.75

2.9

2.7

2.8

2.65

2.7

2.6

2.6

2.55

D

3.4

2.55

E

Re = 35000

SC R

2.75

2.8

3.1

(a)

3.5

Re = 10000 C

X X 4

TEF

4.4

2.9

G=4 G=9 G = 16

IP T

2.85

4.6

2.5

B A

2.5

2.4 4.5

5

2.45

Re = 35000 Maximum TEF: 2.84 Minimum TEF: 2.68 2.86 2.84 2.66 2.68 2.70 2.72 2.74 2.76 2.78 2.80 2.82 2.88

2.82

IP T

2.80

TEF

2.78 2.76 2.74

SC R

2.72 2.70 2.68 2.66 14 12

2.0

G 10 8

U

2.5

3.0

6 4.0

PR

A

4

N

3.5

M

(b)

ED

Fig. 15. (a) Influence of G and PR on TEF as a function of Re, (b) Optimum geometry in

A

CC E

PT

view point of energy saving at PR = 3 and G = 9.

3

2.5 X

X

X

X

X

+

+

+

X

+

X

X

X

X

0.5

0

+ X

5000

IP T

[3] [14] [28] [29] [30] [31] [32] [45] Present study

10000

SC R

1

+

+

+

+

U

+

N

+

15000

A

1.5

20000

M

TEF

2

25000

30000

35000

ED

Re

Fig. 16. Comparison of the present TEF result with those of other modified heat transfer

A

CC E

PT

enhancement devices.

f (Exp) 0.02 350

0.03

0.04

0.05

0.06

0.07 0.02

300

f

+10%

0.03

-11%

-10%

IP T

250

Nu 150

U

100

N 50

100

M

0

150

200

250

300

ED

Nu (Exp)

CC E

PT

Fig. 17. Predicted data of Nu and f versus experimental data.

A

0.05

0.06

A

50

0

f (Pred)

SC R

Nu (Pred)

0.04

+11%

200

0.07 350

I N U SC R

A

Table 1. The different swirl and vortex generators used in a circular tube heat exchanger. Parameters range

ED

M

Geometries

Singh et al. [3]

A

CC E

ring

PT

Multiple twisted tape with solid

Developed correlations

Results Nu/Nus

PR = 1 - 2

Nu  0.09653 Re 0.7834 N 0.0551 exp(0.0256 ln( N) 2 )TR 0.2127 4.12–4.91

y/w = 2 - 4

exp( 0.1696 ln(TR) 2 )

N=1-4

exp( 0.376 ln(TR) 2 )

Re = 6300–22500

  3.033 Re 0.0786 N 0.0188 exp(0.01063 ln( N) 2 )TR 0.1304

f/fs

η

18 - 36

1.62-1.32

6 - 70

0.55-1.09

f  1.073 Re 0.0786 N 0.0352 exp(0.1094 ln( N) 2 )TR 0.4696

exp( 0.0968 ln(TR) 2 )

Kongkaitpaiboon et al. [9]

DR =0.5 - 0.7

Nu = 0.354 Re 0.697 Pr 0.4 DR -0.555 PR -0.598

Circular ring turbulators

PR = 6 - 12

f = 0.715 Re -0.081 DR -4.775 PR -0.846

Re = 4000 - 20,000

 = 5.315 Re -0.078 DR1.031 PR -0.317

1.6 - 3

I N U SC R A M

BR = 0.1- 0.2

Nu = 0.165 Re 0.698 Pr 0.4 (BR + 1) 3.063 (PR + 1) -0.549

Inclined vortex ring

PR = 0.5- 2.0

f = 1.709 Re 0.209 (BR + 1)10.753 (PR + 1) -1.433

ED

Promvonge et al. [10]

2.2-4.2

5-36

1.03-1.4

1.3-1.5

4.5 - 7

0.7-0.95

CC E

PT

Re = 5000 - 26,000

PR = 4 - 12

Nu = 1.258 Re 0.606 PR -0.39 Ni -0.32 Pr 0.4

Perforated conical ring

Ni = 4- 8

f = 985.48 Re-0.368 PR -0.747 Ni-1.253

Re = 4000 - 20,000

 = 1.596 Re-0.067 PR -0.142 Ni-0.095

A

Kongkaitpaiboon et al. [12]

I N U SC R A M

y/w = 3.75 and 7.5

Nu = 1.356 Re 0.433 Pr 0.4 (d/D) -1.23 (y/w)-0.053

Combined conical ring and

Re = 6000 - 26,000

f = 24.87 Re -0.43 (d/D) -3.99 (y/w)-0.16

ED

Promvonge & Eiamsa-ard [13]

-

1.08-1.98

1.65-3.45

1.90-3.87

1.05-1.35

A

CC E

PT

twisted tape

-

Bhuiya et al. [24]

y/w = 1.95- 7.75

Nu  (0.0007 y 3  0.0077 y 2  0.0385y  0.4777)

Double twisted tape

Re = 6950 - 50,050

Re ( 0.0002y

3

0.0021y 2  0.0047y  0.5894)

Pr 0.33

f  (0.0009 y 3  0.1015y 2  1.0842 y  8.685) Re ( 0.00004y

3

 0.0015y 2 0.0165y 0.4722)

I N U SC R M

A PR= 4- 8

Nu  4.47 Re 0.5 Pr 0.4 (H / d) 0.382 ( y / w) 0.38

Wire coil with twisted tape

y/w = 4 and 6

f  338.37 Re 0.367 (H / d) 0.887 ( y / w) 0.455

ED

Promvonge [27]

3-6

30 - 75

0.9-1.55

3.75-6.75

0.9-1.39

1.63-4.34

1.2-1.8

PT

Re = 3000 -18000

PR = 1- 3

Coiled wire with triangular

a/D = 0.0714 and

cross-section

0.0892

A

CC E

Gunes et al. [28]

Bas & Ozceyhan [29]

Nu  0.598417 Re 0.745064 Pr 0.39 (P / D) 0.268374(a / D) 0.813205 1.25-2.55 f  83.70924 Re 0.305268(P / D) 0.388 (a / D)1.319018

Re =3500 - 27,000

y/w = 2- 4

Nu  0.4069 Re 0.586556 Pr 0.38 ( y / D) 0.443989(c / D) 0.055072

1.1-1.91

I N U SC R

Twisted tapes placed separately

c/D = 0.0178 and

from the wall

0.0357

f  6.544291Re 0.452085( y / D) 0.730772(c / D) 0.1579

A

Re = 5132 - 24,989 y/w = 1.92- 6.79

Triple twisted tape

Re = 7200 - 50,200

Nu  (0.0017 y 3  0.0179 y 2  0.0962 y  0.7734) Re ( 0.00002y

3

 0.0013y 2 0.0094y  0.05746)

1.75-3.8

1.88-4.2

1.25-1.45

2.5 – 4.5

17– 33.8

1.02-1.43

Pr 0.33

f  (0.0388y 3  0.2484 y 2  0.8462 y  17.685) Re ( 0.00005y

3

 0.0017y 2 0.0164y 0.5193)

CC E

PT

ED

M

Bhuiya et al. [30]

PR = 1.0- 2.0

Nu  0.326 Re 0.724 Pr 0.4 (l / D) 0.475 ( y / W) 0.406

Twisted tape with circular ring

y/w= 3- 5

f  13.99 Re 0.202 (l / D) 0.927 ( y / W) 0.619

A

Eiamsa-ard et al. [31]

Re = 6000 - 20000

  4.63 Re 0.111(l / D) 0.166 ( y / W) 0.199

I N U SC R

Deshmukh & Vedula [32]

p/pl = 1.4- 7.9

Vortex generator insert

e/ di = 0.09- 0.25 α = 15˚ - 45˚

Nu  0.46 Re 0.77 (p / p l ) 0.4 (e / d) 0.79 (0.125  (e / d) 2 ) 0.125

f  0.77 Re 0.14 (p / p l ) 0.59 (e / d)1.22 (0.125  (e / d) 2 ) 0.7

ED

M

A

Re = 10,000 - 45,000

PT

Chokphoemphun et al. [33]

A

CC E

Multiple twisted tape

y/w = 4 and 5 N = 1- 4

1 – 1.8

Nu  0.092 Re 0.65 Pr 0.4 ( N) 0.46

5 - 65

-

1.15–2.12

1.9–4.1

0.9-1.35

2.48-4.95

4-50

1.22-1.71

f  0.791Re 0.33 ( N) 0.873

Re = 5300 - 24,000

Skullong et al. [34]

BR = 0.1- 0.3

Nu  0.1844 Re 0.7682 PR 0.4 (BR ) 0.3097(PR ) 0.2536

Staggered winglet perforated

PR = 0.5- 1.5

f  4.318 Re 0.0634(BR ) 0.9139(PR ) 0.7134

tapes

Re = 4180 -26,000

  3.9023 Re 0106(BR ) 0.005 (PR ) 0.0158

I N U SC R M

A p/pl = 1.1- 6.2

Nu  0.99 Re 0.61 (p / d) 0.26 (b / di) 0.57 (tan ) 0.28

Curved delta wing vortex

b/di= 0.7- 1.3

f  2.87 Re 0.21 (p / d) 0.83 (b / di) (tan ) 0.19

A

CC E

PT

generator inserts

ED

Deshmukh et al. [35]

PR = 0.6- 3.2

 = 15˚- 75˚ Re = 250 – 1500

1.3 - 6

1.2– 150

-

I N U SC R

Table 2. Range of geometrical and flow parameters.

Parameter

Specification

Values

1.

Pitch ratio (PR)

Ratio of distance between two rings and

2, 3, and 4

ED

M

A

S. No.

PT

2.

A

CC E

3.

Grade (G)

Reynolds Number (Re)

diameter of circular ring (P/d) No of rectangular spaces in 10mm ×

4, 9, and 16

10mm area of metal wire net Flow parameter

5000-40000

I N U SC R

Table 3. Details of numerical methodology Parameters

Computational conditions

1.

Dimensional

3 – Dimensional

2.

Grid numbers

1.65 × 105

3.

Method

5.

Turbulence model

RNG k - ɛ with wall treatment

6.

Working fluid

Air

M

A

S. No

CC E

PT

ED

Finite volume

Prandtl number Pr = 0.73, ρ = 1.164 kg/m3, K = 0.02588 W/m. K, µ = 1.87 × 10-5 Pa. s and Cp = 1007 J/kg.

Wall condition

Constant heat flux

8.

Inlet

Velocity inlet

9.

Outlet

Pressure outlet

10.

Rings

Adiabatic wall

11.

Reynolds number

5000

A

7.

I 3

13.

Grade (G)

9

N U SC R

Pitch ratio (PR)

A

CC E

PT

ED

M

A

12.