**Published at : ** 09 May 2023

**Volume :** **IJtech**
Vol 14, No 3 (2023)

**DOI :** https://doi.org/10.14716/ijtech.v14i3.5811

Ibrahim, A.Q., Alturaihi, R.S., 2023. Numerical Investigation for Single-Phase and Two-Phase Flow in Duct Banks with Multi Types of Vortex Generators.

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Adnan Qahtan Ibrahim | 1. Department of Mechanical Engineering, Faculty of Engineering, University of Babylon, Hilla, Babylon, 51002, Iraq, 2. Automotive Department, College of Engineering/AL-Musaib, University of Babylon, |

Riyadh Sabah Alturaihi | 1. Department of Mechanical Engineering, Faculty of Engineering, University of Babylon, Hilla, Babylon, 51002, Iraq |

Abstract

This paper examines the numerical work of the thermal convection over
tube banks with winglets through the heat exchanger in two parts under
turbulent conditions. The first section investigates the influence of two-phase
(water and air) flow on the performance of two kinds of vortex generators
(Delta and Rectangular) winglets across the oval tube banks. The second section
studied the performance of four types of winglets (Delta, Rectangular, Zikzak,
and Sinusoidal wavy), circular and oval tubes, forward and downward
configurations, and various angles of attack (15°, 20°,
and 25°) in
two-phase flow. Delta winglets provide the highest performance at an attack
angle of 15° for oval tube banks in a two-phase flow with a moderate turbulent
flow rate.

Duct Banks; Heat exchanger; Sinusoidal winglets; Zikzak winglets

Introduction

In numerous industrial processes, heat convection is essential in
heating and cooling operations. At high flow velocities, a two-phase flow is
utilized to minimize pressure losses in the duct. Over the last two decades, researchers have
focused on winglets' ability to generate interconnected vortices or swirling
flow parallel to the flow orientation. These winglets have been studied to enhance the Heat convection effectiveness of various heat
exchangers via air- or gas-side heat transfer. (Fiebig,
1998; Fiebig, Valencia,
and Mitra, 1993) explained flow
with winglets could lead to a massive increase in heat convection coefficient
in the laminar duct flows, increasing transverse vortex generators (VGs). It
was found that an inline tube configuration enhanced the heat convection rate
by 55–65 %, with a comparable pressure drop of 20–45 %. Lau, Meiritz, and
Ram (1999) published the results of an experimental
work investigating the movement in a turbulent duct flow with heat and momentum
using Vortex generators. Oval tubes have several advantages over circular tubes
in lowering pressure drop and reducing the wake zone. As a result, when vortex
generators are combined with oval tubes, it is possible to get increased
thermal performance without considerably raising the pressure drop (He and Zhang, 2012). Compared to the Baseline instance, the vortex generator exhibits
a promising improvement in *et al.,* 2003; Biswas, Mitra, and Fiebig, 1994). The overall heat transfer
coefficient for both laminar and turbulent flows increases as the number of
pairs of VGs increased, based on the number of rows difference (Syaiful *et al.,* 2017). The geometry of the
tube banks impacts the thermo-hydraulic characteristics of a fin and tube heat
exchanger (FTHE) directly (Sahel, Ameur, and Mellal,
2020) and a reduction in the heat convection coefficient as the flat
tube's size increases (Sahel, Ameur, and Boudaoud,
2019). A study by Susanto *et al.*
(2020) showed that the heat transfer rate improves more smoothly; where
the influence of convection walls is minimal, the local Nusselt number (Nu)
grows and the velocity profile increased marginally. The addition of flat
vortex generators increases the heat convection coefficient by approximately
62.53% (Sahel, Ameur, and Alem, 2021).
Augmentation of heat convection occurs with curved rectangular winglet VGs for
flow in a rectangular channel (Naik, Tiwari, and Kim,
2022) and for flow across three rows of cylindrical tubes installed on a
flat plate with height-averaged (Nu) and perimeter-averaged (Nu) variances along
the height of a cylinder. (Naik and Tiwari, 2017; Naik
and Tiwari, 2018). With upstream rectangular winglet pair positions,
performance is improved (Naik and Tiwari, 2020a).
In recent years, researchers have investigated several additional areas for
vortex generator forced convection enhancement, including the addition of
bulges, dimples, and punched delta winglets as vortex generators are all
geometric features. The collected data indicate that a tube incidence angle of
20° is the optimal structure for eliminating the hot areas among the tubes and
increasing the heat convection coefficient by 13% according to the base
scenario (Abdoune *et al.,* 2021). It
is known that tube diameter and height variances impact the convection heat
coefficient value (Susmiati *et al.,* 2022).
Inserts of various models to Vortex generators (Oneissi
*et al.,* 2018; Tang et al., 2016; Boonloi
and Jedsadaratanachai, 2016), the use of combined winglets (Tamna *et al.,* 2016), delta winglets with
Nanofluids (Ahmed *et al.,* 2017),
built-in interrupted delta-winglet (Wu *et al.,*
2016), the application of VGs to various kinds of heat exchangers (Garelli *et** al.,* 2019; Song
and Tagawa, 2018), and enhancement of heat convection have been
documented for angles of attack ranging from 0° to 45o. In contrast, the heat
convection coefficient decreases for angles of attack ranging from 135° to 180° (Afshari, Zavaragh, and Nicola, 2019). In this study, the air is used
as a second phase with water to increase vortex generators' efficiency by
reducing pressure loss in the duct.

Experimental Methods

**The Geometric Model**

*2**.**1**. **Modelling of Flow and Boundary Condition*

The characteristics of the problem and
boundary condition for the single and two phase-flows can be shown in Figure 1.
The rectangular duct inlet is represented as the fluid inlet's superficial
velocities. The oval tube wall is exposed to constant heat flux, while the
outlet pressure is represented at the outlet of the rectangular duct. The
remaining portion of the duct walls is put to be adiabatic.

The heat
convection coefficient and the temperature distribution were investigated in
the duct by using various values for the discharges of water and air with
different shapes and positions of the vortex generators. ANSYS-Fluent 19.0 is
used to evaluate the flow characteristics of water flow and mixture (water-air)
flow through the banks of the tubes with vortex generators. Fluent shows temperature
distribution, pressure gradient, and velocity for two-phase and single-phase
flow through the tube banks.

Fluent is a fluid flow simulation software suite that solves fluid flow problems using computational fluid dynamics (CFD). It solves a fluid's governing equations by using the finite volume method. Fluent's fluid problem scheme is defined by momentum, mass, and energy conservation laws. This law defines a finite volume-based discretization of a partial differential equation. These parameters pass in the course of the rectangular duct for fluid flow over oval tube banks with and without winglets. Computational fluid dynamics (CFD) is the branch of fluid dynamics that investigates the issue by calculating and giving practical methods for reproducing natural flow by solving the governing equations numerically (Abdulnaser, 2009).

**Figure 1** Boundary
Condition

The boundary conditions of
the single-phase and two-phase flow systems are presented in Table 1.

**Table 1** Boundary conditions

Zone |
Fluid |
Energy |

Inlet |
Velocity |
293 k |

Tube walls |
No-slip |
21883.8 w/m |

Duct walls |
Symmetry |
Symmetry |

Winglets |
No-slip |
Adiabatic |

Outlet |
Pressure |
Adiabatic |

*2.2. The Geometry of the Testing Section*

In order to simulate the system, it has
been modeled as a 3-D model using Solid Works 2018 combined with Ansys
Workbench 19.0. The model has been drawn as a rectangular shape, and its
dimensions are (12 cm × 2 cm × 100 cm). The geometry of the testing section is
set to be fluid, as shown in Figure 2.
Using the diameter of the tube (D) as the characteristic length scale,
all dimensions of the duct are calculated as L = 10D, W = 1.2D, and H = 0.2 D,
respectively.

**Figure 2** (a)
Computational domain for test section; (b) Vortex generator placement with oval
tube; (c) Four types of vortex
generators

*2**.**3**. **Mesh Generation*

Because there are so many mesh types to
choose from, it is essential to consider factors like flow field, geometry, and
complexity when choosing which mesh to use. The required CPU time, solution
accuracy, and convergence rate are all influenced by the size and kind of mesh (Bakker, 2006). In this work, the meshing
procedure is performed in the Ansys Workbench 19.0 application using
Quadrilateral structured grid elements. The meshing sizes for maximum and
minimum meshing sizes are set to be equal (0.001 m) for oval and circular
tubes, as shown in Figure 3. Table 2 shows how many elements and nodes each
situation in this study contains for oval and circular tubes, respectively.

**Table 2** The number of
elements and nodes

Case |
Nodes No. |
Elements No. |

Without Vortex |
202860 |
181440 |

Delta |
124767 |
624620 |

Rectangular |
124831 |
624663 |

Zikzak |
124826 |
624657 |

Sinusoidal |
134436 |
674249 |

**Figure 3** The Mesh of
oval tubes

*2**.**4**. **Grid independence*

A grid-independent solution is required to enhance the precision of the computations. The present work on grid independence consists of three parts: convergence index, grid refinement, and General Richardson. Two various winglet positions relative to the center of each tube are used. For forward (X = -1, Y = ±4), downward (X = 1, Y = ±4) of each tube with = 15° and Re = 3643.5.

**3****. ****Governing Equations **

The
challenge entails solving the flow field and heat convection problems
associated with a bank of oval and circular tubes fitted with winglets in a
rectangle duct under a transient state. Vortex
generators are added to the duct to improve heat transfer. A computational
examination is necessary because of how their addiction impacts the flow field
and heat convection. The flow field must be resolved to establish the ideal
heater diameter and form for the vortex generators.

*3**.**1**. **Continuity Equation *

*3**.**2**. **Momentum Equation*

*3**.**3**. **Energy Equation*

** **

**4****. ****Turbulence Model **

Models are utilized to have the capacity for characterizing and predicting the physics of the multiphase flow. Also, these models are suitable for different applications that have multiphase flow. Some demonstrating approaches are the Euler-Lagrange approach, the Volume of fluid approach, the Euler-Euler approach, and dispersed phase modeling. The Euler-Lagrange method is computationally expensive and is appropriate for flows with a small volume percentage of the dispersed phase. The (k-) standard model is utilized in place of the (k-) model in this work due to the (k-) model's poor prediction of rotating and swirling flows, as well as fully developed flows in the rectangular ducts (Shbeeb and Mahdi, 2016).

Also, the (k-) standard turbulence model will be used to simulate the
flow-through test section. The single and two-phase flows are modeled by
combining the model with various parameters based on the testing factors and the
outcomes of the experiments to compare and validate the CFD results (Vejahati *et al.,* 2009; Fluent, 2006).

**5****. ****Performance parameter **

where *j *is
the Colburn factor, and *f* is the coefficient of friction (Chu, He, and Tao, 2009).

**6****. ****Model validation **

The computational fluid dynamics model
validation by numerical simulations of flow through the heat exchanger with an
intake of the Reynolds number between 600 and 3000 were compared to the
numerical outcomes of (Fiebig, Valencia, and Mitra, 1993).

The maximum errors between the present model
findings and the numerical outcomes of (Fiebig, Valencia, and Mitra, 1993) are 4.35% for *Nu* and 5.825% for *f. *The model
validation results are shown in Figure 4. From the above analyses, the high
degree of agreement between these outcomes illustrates the model's reliability
in precisely forecasting the flow structure and heat convection properties.

**Figure 4** Validation of the present model
with the germane work (Fiebig, Valencia, and Mitra, 1993) for various values of Re (a) *Nu* and (b) *f *

Results and Discussion

Figures 5 to 19 show the numerical
results of the increased water-air flow rates on the temperature gradient at
various locations in the duct with a constant electrical power of (110 W) as a
heat flux. In this study, the performance of VGs was investigated based on the
temperature gradient between the fluid flow and the surface of the tube bank,
which corresponded to the pressure loss inside the duct. The best performance
at the lowest temperature difference and the lowest pressure drops, with other
parameters remaining kept constant. The Nusselt number (*Nu*) was directly proportional to the coefficient of heat convection. When
the temperature gradient between single or two-phase flow and the surfaces of
tube banks increased, the heat convection coefficient decreased, and vice
versa. Also, the friction coefficients (*f*) were directly proportional to the pressure
drop in the duct, according to Equation 7.

*7**.**1**. Effect of the phase*

__7.1.1. Single-phase flow__

Figure
5 illustrates the temperature gradient between water flow and oval tube
surfaces at various locations in the duct without winglets, with Delta winglets, and with Rectangular winglets for three different water flow
rates (15, 17.5, and 20 L/min). Observed from this figure that the temperature
gradient decreased as the water flow rate increased. These results agree with Chu, He, and Tao (2009), and Haque and Rahman (2020) for reduced temperature
gradient at the water flow velocity increased; therefore, the heat convection
coefficient increased. When the water flow rate increases, the flow velocity
increases, ultimately enhancing the heat convection coefficient.

Figure
6 illustrates the entrance and exit pressure for water flow at many points in
the duct without winglets, with Delta winglets, and with Rectangular winglets
for three different water flow rates (15, 17.5, and 20 L/min). The pressure
loss in the duct raised as the discharge of water increased, and these results
agree with Chu, He, and Tao (2009). When the water flow
rate increases, the pressure drop decreases, which reduces the coefficients of
friction.

Adding
vortex generators to the duct can augment the heat convection coefficient by
raising the velocity of single-phase flow and the turbulence intensity within
the duct. As the flow velocity increases, the temperature gradient reduces.
When flow is oriented toward the oval tube's surface, the temperature gradient
is inversely proportional to flow velocity.

Figure
7a illustrates the fluctuation of a temperature gradient with Reynolds number
in water flow across the bank of oval tubes without winglets generators. Owing
to a decrease in the temperature gradient between the water flow and surfaces
of the oval tube, the heat convection coefficient improved as the Re number
raised.

Figure
(7b) represents the fluctuation of the pressure reduction with Reynolds number
in water flow over oval tube banks without winglets. As the Reynolds number
grew, the duct pressure losses were reduced.

Figure (7c) represents the Reynolds number performance parameter for water flow over oval tube banks without winglets. As the Re number climbed, the performance parameter improved because the pressure in the duct and the temperature gradient between the water flow and the surfaces of the oval tube decreased. The delta winglets' performance is greater than that of the other two vortex generators. These results concur with the reports of Haque and Rahman (2020), and Naik and Tiwari (2020b) which examined the influence of different vortex generator forms on heat flow in the duct and showed that Delta winglets provide the highest performance.

**Figure
5**
The temperature gradient between water flow and surfaces of an oval tube for
various water flow rates (15, 17.5, and 20 L/min) for single-phase flow (a)
without winglets (b) with Delta winglets (c) with Rectangular winglets

**Figure 6** Inlet and
Outlet pressure in the duct with an oval tube for single-phase flow (a) without
winglets (b) with Delta winglets (c) with Rectangular winglets

**Figure 7** (a) The temperature
gradient with
Delta and Rectangular winglets for single-phase flow over oval tube (b) Pressure
drop (c) Performance parameter

__7.1.2. Two-phase
flow__

Figure 8 indicates that at a
constant discharge of water, the temperature gradient between mixture
(water-air) flow and surfaces of oval tubes increased. At these points, the
airflow rate increases (8.33, 16.67, and 25 L/min) with a constant water flow and
heat flux. When the flow rate of water and air flow is increased without
winglets, the heat convection rate drops, and the temperature gradient becomes
less significant. The heat convection coefficient improved as the temperature
difference reduced because the winglets concentrated the working fluid on the
tube surface with Delta winglets and
Rectangular winglets
used in the duct.

Figure 9 represents the
inlet and outlet pressure in the duct for water-air flow at various points. At
these points, the airflow rate increases (8.33, 16.67, and 25 L/min) with a
constant flow rate of water and heat flux. The pressure losses without winglets
in the duct are reduced. Increased pressure drops compared to Delta winglets,
and Rectangular winglets are used in the duct that is not utilized. In
addition, the pressure drops in the duct are minimized due to growth in the
flow rate of water-air Delta winglets. This is in accordance with the findings
of Chu, He, and Tao (2009)
and Haque and Rahman (2020).

In addition, the pressure
drop is reduced when the discharge of mixture (water-air) flow is increased in
the absence of winglets. When rectangular VGs are
used in the duct, the pressure losses are more significant than not. In
addition, when the flow rate of water-air increases with rectangular winglets,
the pressure losses in the duct are decreased. There is good agreement with
that of Haque and Rahman (2020) and Naik
and Tiwari (2020b).

Adding winglets to the duct
can raise the surface velocity of water-air flow, raising the heat convection
coefficient by generating intense turbulence. The temperature gradient
decreases as the flow velocity increases. When the flow is directed toward the
surfaces of the oval tube, the temperature gradient is inversely related to the
flow velocity. The airflow rate increased from (8.33, 16.67, and 25 L/min) with
a constant flow rate of water and heat power of (110 W).

The effect of the Reynolds
number for water-air flow over oval tube banks in a turbulent region on heat
convection rate and pressure reduction is essential for optimal design and
location of vortex formation. Due to the decrease in pressure and temperature
gradient between water-air flow and surfaces of the oval tube in the duct, the
performance parameter was improved when the Re number of water was lowered. The
Re number of air grew as the air flow rate raised (8.33, 16.67, and 25 L/min),
but the water flow rate remained constant.

The variance of the
temperature gradient with Re number in water-air flow over oval tube banks
without winglets, with Delta winglets, and with Rectangular winglets are
represented in Figure 10. At a constant flow rate of water, the heat convection
coefficient increases as the temperature gradient between the water-air flow
and surfaces of the oval tube decreases.

The variance of the drop in
pressure with the Re number in water-air flow over oval tube banks without
winglets, with Delta winglets, and with Rectangular winglets are visualized in
Figure 11. When the Re number of water and air increased, the pressure drop
decreased in the duct with a constant flow rate of water.

The variance between the Re
number and performance parameter in the water-air flow over oval tube banks
with and without winglets is depicted in Figure 12. As water-air flow
increased, the performance parameter improved. Delta winglets offer the most
efficient performance. This is in agreement with the findings by Chu, He, and Tao (2009).

Figures 13,14, and 15
illustrate that the velocity contour for water flow and water-air flow without
winglets, with Delta winglets, and with Rectangular winglets are used in the
duct from Workbench 19.0 (ANSYS - Fluent 19.0) when a flow rate of air
increases (0, 8.33, 16.67, and 25) (L/min) respectively, with a constant flow rate of water.

**Figure 8 T**he temperature gradient between the flow of water and air with oval tube surfaces for two-phase flow (a) without winglets (b) with Delta winglets (c) with Rectangular winglets

**Figure 9** Inlet and Outlet pressure in the
duct with an oval
tube for two-phase flow (a) without winglets (b) with Delta winglets (c) with
Rectangular winglets

**Figure 10** The temperature gradient with Delta and Rectangular
winglets for two-phase flow over oval tube at (a) Q_{w}= 15 L/min (b) Q_{w}=
17.5 L/min (c) Q_{w}= 20 L/min

**Figure 11** Pressure drop with Delta
and Rectangular winglets for two-phase flow over oval tube at (a) Q_{w}=
15 L/min (b) Q_{w}= 17.5 L/min (c) Q_{w}= 20 L/min

**Figure 13** The velocity vector without
vortex generators (a) single-phase flow (b) two-phase flow at constant a flow
rate of water 15 Lpm with a flow rate of air 8.33 Lpm (c) 16.67 Lpm (d) 25 Lpm