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Experimental investigation of heat transfer and fluid flow behaviour in multiple square perforated twisted tape with square wing inserts heat exchanger tube

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Abstract

The present work deals with experimental investigation of heat transfer and fluid flow characteristics of multiple square perforated twisted tape with wing inserts in a heat exchanger tube. The range of selected geometrical parameters are, perforation width ratio (a/WT) of 0.083–0.333, twist ratio (TL/WT) of 2.0–3.5, wing depth ratio (Wd/WT) of 0.042–0.167 and number of twisted tapes (TP) of 4. The Reynolds number (Ren) selected for experimentation ranges from 5000 to 27,000. The maximum heat transfer and friction factor enhancement was found to be 6.96 and 8.34 times that of plane tube, respectively. The maximum heat transfer enhancement is observed at a a/WT of 0.250, TL/WT of 2.5, and Wd/WT of 0.167.

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Abbreviations

a :

Perforated width, m.

a/W T :

Perforation width ratio, dimensionless

A o :

Area of orifice plate, m2

A p :

Area of pipe, m2

C p :

Specific heat, J/kg K

C d :

Coefficient of discharge, dimensionless

D :

Hydraulic diameter of pipe, m

f rs :

Friction factor rough surface, dimensionless

f ss :

Friction factor plain tube, dimensionless

H :

Head difference, m

h :

Heat transfer coefficient, W/m2 K

k :

Thermal conductivity of air, W/m K

L :

Tube length, m

\( \dot{m} \) :

Mass flow rate, kg/s

Nu rs :

Nusselt number rough tube, dimensionless

Nu ss :

Nusselt number plain tube, dimensionless

(∆P) o :

Pressure drop across orifice plate, Pa

(∆P) d :

Pressure drop according to Darcy’s equation, Pa

∆P :

Pressure drop, Pa

Pr :

Prandtl number, dimensionless

Q u :

Useful heat transfer, W

Re n :

Reynolds number, dimensionless

T pm :

Mean pipe temperature, K

T fm :

Mean fluid temperature, K

T i :

Inlet temperature, K

T o :

Outlet temperature, K

T L :

Twist length, m

T L /W T :

Twist ratio, dimensionless

V :

Air flow velocity, m/s

W T :

Width of tape, m

W d :

Wing depth, m

W d /W T :

Wing depth ratio, dimensionless

PCR :

Perforated conical ring

WPT :

Winglet perforated tapes

β :

Orifice diameter to the pipe diameter ratio, dimensionless

ρ :

Density, kg/m3

η :

Performance evaluation factor, dimensionless

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Author information

Authors and Affiliations

  1. School of Mechanical and Civil Engineering, Shoolini University, Solan, India

    Amar Raj Singh Suri & Anil Kumar

  2. Department of Mechanical Engineering, DIT University, Dehradun, India

    Rajesh Maithani

Authors
  1. Amar Raj Singh Suri
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  2. Anil Kumar
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  3. Rajesh Maithani
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Corresponding author

Correspondence to Rajesh Maithani.

Appendix

Appendix

Mass flow rate:

$$ \dot{m}={C}_d{A}_o\left[\frac{2{\rho}_o{\left(\Delta P\right)}_o}{1-{\beta}^4}\right] $$
$$ \frac{\delta \dot{m}}{\dot{m}}={\left[{\left(\frac{\delta {C}_d}{C_d}\right)}^2+{\left(\frac{0.5\delta {\rho}_o}{\rho_o}\right)}^2+{\left(\frac{\delta {A}_o}{A_o}\right)}^2+{\left(\frac{\delta {\left(\Delta P\right)}_o}{{\left(\Delta P\right)}_o}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta \dot{m}}{\dot{m}}={\left[\left(6.25\times {10}^{-4}\right)+\left(4.449\times {10}^{-6}\right)+\left(3.26\times {10}^{-5}\right)+\left(5.102\times {10}^{-7}\right)\right]}^{0.5} $$
$$ \dot{m}=0.0257 $$

Hence, uncertainty in mass flow rate measurement is 2.57%.

Heat gain:

$$ {Q}_u=\dot{m}{C}_p\left({T}_o-{T}_i\right)=\dot{m}{C}_p\Delta T $$
$$ \frac{\delta {Q}_u}{Q_u}={\left[{\left(\frac{\delta \dot{m}}{\dot{m}}\right)}^2+{\left(\frac{\delta {C}_p}{C_p}\right)}^2+{\left(\frac{\delta \left(\Delta T\right)}{\left(\Delta T\right)}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta {Q}_u}{Q_u}={\left[{\left(\frac{\delta \dot{m}}{\dot{m}}\right)}^2+{\left(\frac{\delta {C}_p}{C_p}\right)}^2+{\left(\frac{\delta \left(\Delta T\right)}{\left(\Delta T\right)}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta {Q}_u}{Q_u}={\left[\left(6.7081\times {10}^{-4}\right)+\left(9.9007\times {10}^{-9}\right)+\left(1.13\times {10}^{-4}\right)\right]}^{0.5} $$
$$ \frac{\delta {Q}_u}{Q_u}=0.0277 $$

Hence, uncertainty in heat gain is 2.77%.

Heat transfer coefficient:

$$ h=\frac{Q_u}{A_p\left({T}_{pm}-{T}_{fm}\right)}=\frac{Q_u}{A_p\left(\Delta {T}_{fm}\right)} $$
$$ \frac{\delta h}{h}={\left[{\left(\frac{\delta {Q}_u}{Q_u}\right)}^2+{\left(\frac{\delta {A}_p}{A_p}\right)}^2+{\left(\frac{\delta \left(\Delta {T}_{fm}\right)}{\left(\Delta {T}_{fm}\right)}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta h}{h}={\left[\left(7.784\times {10}^{-4}\right)+\left(2.166\times {10}^{-6}\right)+\left(2.764\times {10}^{-5}\right)\right]}^{0.5} $$
$$ \frac{\delta h}{h}=0.284 $$

Hence, uncertainty in heat transfer coefficient is 2.84%.

Reynolds number:

$$ \mathit{\operatorname{Re}}=\frac{\rho VD}{\mu } $$
$$ \frac{\delta Re}{\mathit{\operatorname{Re}}}={\left[{\left(\frac{\delta \rho}{\rho}\right)}^2+{\left(\frac{\delta V}{V}\right)}^2+\left(\frac{\delta D}{D}\right){+}^2{\left(\frac{\delta \mu}{\mu}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta Re}{\mathit{\operatorname{Re}}}={\left[\left(6.66\times {10}^{-7}\right)+\left(1.5129\times {10}^{-4}\right)+\left(8.76\times {10}^{-7}\right)+\left(2.543\times {10}^{-7}\right)\right]}^{0.5} $$
$$ \frac{\delta Re}{\mathit{\operatorname{Re}}}=0.01237 $$

Hence, uncertainty Reynolds Number is 1.23%.

Nusselt number:

$$ {Nu}_{rs}=\frac{hD}{K} $$
$$ \frac{\delta {Nu}_{rs}}{Nu_{rs}}={\left[{\left(\frac{\delta h}{h}\right)}^2+{\left(\frac{\delta D}{D}\right)}^2+{\left(\frac{\delta K}{K}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta {Nu}_{rs}}{Nu_{rs}}={\left[{(0.0284)}^2+{(0.000936)}^2+{\left(4.16\times {10}^{-4}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta {Nu}_{rs}}{Nu_{rs}}=0.02841 $$

Hence, uncertainty Nusselt Number is 2.84%.

Friction factor

$$ {f}_{rs}=\frac{2{\left({\Delta }_p\right)}_dD}{4\rho L{V}^2} $$
$$ \frac{\delta {f}_{rs}}{f_{rs}}={\left[{\left(\frac{\delta V}{V}\right)}^2+{\left(\frac{\delta \rho}{\rho}\right)}^2+{\left(\frac{\delta D}{D}\right)}^2+{\left(\frac{\delta L}{L}\right)}^2+{\left(\frac{\delta {\left({\Delta }_p\right)}_d}{{\left({\Delta }_p\right)}_d}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta {f}_{rs}}{f_{rs}}={\left[{\left(\frac{0.1}{8.13}\right)}^2+{\left(\frac{0.001}{1.225}\right)}^2+{(0.000936)}^2+{\left(\frac{0.1}{1400}\right)}^2{\left(\frac{0.01}{1.94}\right)}^2\right]}^{0.5} $$
$$ \frac{\delta {f}_{rs}}{f_{rs}}=0.01339 $$

Hence, uncertainty Friction Factor is 1.33%.

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Suri, A.R.S., Kumar, A. & Maithani, R. Experimental investigation of heat transfer and fluid flow behaviour in multiple square perforated twisted tape with square wing inserts heat exchanger tube. Heat Mass Transfer 54, 1813–1826 (2018). https://doi.org/10.1007/s00231-018-2290-x

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