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Optimization of heat and fluid flow over curved trapezoidal winglet pair type vortex generators with one-row and three-row


Passive heat transfer enhancement methods are frequently chosen to achieve higher thermo-hydraulic performances in engineering applications because they do not require external energy. One of the most popular passive methods for increasing heat transfer and improving the cooling effects of heat transfer surfaces is the use of vortex generators (VGs). However, the pressure drop generated by the usage of VGs must be controlled. This work is interested in the number (one, three) and geometric dimensions of VGs in the rectangular channel. Numerical optimization studies are carried out for heat and fluid flow over curved trapezoidal winglet pair (CTWP) type VGs for one-row and three-row to obtain optimum geometric dimensions of one-row and three-row of CTWP types VGs in the rectangular channel under incompressible and turbulent flow and conjugate heat transfer assumptions. Heat transfer and pressure drop values are compared in terms of \(j/{j}_{0}\) (the ratio of Colburn factor with CTWP to without it) and \(f/{f}_{0}\) (the ratio of friction factor with CTWP to without it), respectively. The optimization problems are solved with no constraints in the workflows. Multi-Objective Genetic Algorithm (MOGA) is used for the computations where the maximization of \(j/{j}_{0}\) and minimization of \(f/{f}_{0}\) are the two objective functions. Thermo-hydraulic performances (\(R=(j/{j}_{0})/(f/{f}_{0})\)) of the studied cases are also compared. The optimization variables are inclination angle (α), attack angle (β), width / length ratio (b / a), height of the VG (h), interval between VG pair’s front edges (\({S}_{1}\)) for both one-row and three-row cases, also longitudinal spacing between each VG pair (\({S}_{L}\)) is added as an optimization variable for three-row case. It is found that three-row of CTWP type VGs can increase \(j/{j}_{0}\) also increase \(f/{f}_{0}\), i.e., heat transfer enhancement is obtained with a pressure drop increment disadvantage and it is possible to achieve 24.05% heat transfer enhancement with the penalty of 17.27% pressure drop increment as compared to one-row of CTWP type VGs. Furthermore, the fact that the pressure drop has the maximum value does not mean that the heat transfer value is the maximum.

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Data Availability

Solutiıon data can be provided if it is requested.



vortex generator length (mm)

\({A}_{c}\) :

cross-sectional area of channel (m2)

\({A}_{p}\) :

heated copper plate area (m2)

\({A}_{t}\) :

total heat transfer area (m2)

b :

vortex generator width (mm)

\({c}_{p}\) :

specific heat capacity (kJ/kg-K)

\({D}_{h}\) :

hydraulic diameter (mm)

f :

Darcy friction factor

\({f}_{0}\) :

Darcy friction factor of smooth channel (without VGs)

\({f}^{+}\) :

difference of average friction factor (%)

h :

average heat transfer coefficient (W/m2-K), height of the VG (mm)

H :

height of the channel (mm)

j :

average Colburn factor

\({j}^{+}\) :

difference of average Colburn factor (%)

\({j}_{0}\) :

average Colburn factor of smooth channel (without VGs)

k :

thermal conductivity (W/m-K)

L :

length of the channel (mm)

\({\dot{m}}_{air}\) :

mass flow rate of air (kg/s)

\({Nu}_{ave}\) :

average Nusselt number

Pr :

Prandtl number

\(q^{{\prime\prime}}\)  :

heat flux (W/m2)

Q :

heat transfer value (W)

R :

overall performance factor

\(Re\) :

Reynolds number defined the inlet of the channel

\({S}_{1}\) :

interval between vortex generator pair’s front edges (mm)

\({S}_{2}\) :

distance between vortex generator pair’s front edge and inlet of the channel (mm)

\({S}_{L}\) :

longitudinal spacing between each vortex generator pair (mm)

t :

thickness of vortex generator (mm)

\({T}_{w}\) :

base temperature of heated copper plate (K)

\({T}_{i}\) :

inlet temperature of the channel (K)

\({T}_{o}\) :

outlet temperature of the channel (K)

\({V}_{i}\) :

inlet velocity (m/s)

\({y}^{+}\) :

non-dimensional wall distance

\({y}_{max}^{+}\) :

maximum \({y}^{+}\) value in the walls

\({s}_{max}\) :

maximum skewness value of the mesh for mesh quality

W :

width of the channel (mm)

\(\rho\) :

density (kg/m3)

\(\mu\) :

dynamic viscosity of air (kg/m s)

β :

attack angle (°)

α :

inclination angle (°)

\(\Delta P\) :

pressure drop value of inlet and outlet regions (Pa)

\(\Delta T\) :

temperature difference in the inlet and outlet of the channel (K)

\({\Delta T}_{lm}\) :

logarithmic average temperature difference (K)












logarithmic mean












smooth channel


Computational Fluid Dynamics


Curved Trapezoidal Winglet Pair

DOEs :

Design of Experiments


Multi-Objective Genetic Algorithm


Reynolds – Averaged Navier Stokes


Re-Normalization Group


Vortex Generators


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Correspondence to Muhammet Nasıf Kuru.

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Kuru, M.N. Optimization of heat and fluid flow over curved trapezoidal winglet pair type vortex generators with one-row and three-row. Heat Mass Transfer (2023).

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