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Thermohydraulic performance of thermal system integrated with twisted turbulator inserts using ternary hybrid nanofluids

  • Omer A. Alawi EMAIL logo , Haslinda Mohamed Kamar EMAIL logo , Mayadah W. Falah , Omar A. Hussein , Ali H. Abdelrazek , Waqar Ahmed , Mahmoud Eltaweel , Raad Z. Homod , Nadhir Al-Ansari and Zaher Mundher Yaseen
Published/Copyright: March 4, 2023
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Abstract

Mono, hybrid, and ternary nanofluids were tested inside the plain and twisted-tape pipes using k-omega shear stress transport turbulence models. The Reynolds number was 5,000 ≤ Re ≤ 15,000, and thermophysical properties were calculated under the condition of 303 K. Single nanofluids (Al2O3/distilled water [DW], SiO2/DW, and ZnO/DW), hybrid nanofluids (SiO2 + Al2O3/DW, SiO2 + ZnO/DW, and ZnO + Al2O3/DW) in the mixture ratio of 80:20, and ternary nanofluids (SiO2 + Al2O3 + ZnO/DW) in the mixture ratio of 60:20:20 were estimated in different volumetric concentrations (1, 2, 3, and 4%). The twisted pipe had a higher outlet temperature than the plain pipe, while SiO2/DW had a lower T out value with 310.933 K (plain pipe) and 313.842 K (twisted pipe) at Re = 9,000. The thermal system gained better energy using ZnO/DW with 6178.060 W (plain pipe) and 8426.474 W (twisted pipe). Furthermore, using SiO2/DW at Re = 9,000, heat transfer improved by 18.017% (plain pipe) and 21.007% (twisted pipe). At Re = 900, the pressure in plain and twisted pipes employing SiO2/DW reduced by 167.114 and 166.994%, respectively. In general, the thermohydraulic performance of DW and nanofluids was superior to one. Meanwhile, with Re = 15,000, DW had a higher value of η Thermohydraulic = 1.678.

Nomenclature

Ag

silver

Al₂O₃

aluminum oxide

CMC

containing carboxymethyl cellulose

CoTs

co-twisted tapes

C p

specific heat capacity (J/kg K)

CTs

counter-twisted tapes

Cu

copper

CuO

copper oxide

D h

hydraulic diameter (m)

DW

distilled water

f

friction factor

Fe

iron

FOM

figure of merit

k

thermal conductivity (W/m K)

L

pipe’s total length (m)

04-03-2023 m ̇

mass flow rate (kg/s)

MgO

magnesium oxide

MWCNTs

multi-walled carbon nanotubes

nf

nanofluids

np

nanoparticles

Nuavg

average Nusselt number

PCM

phase change material

PEC

performance assessment criteria

P out

pressure outlet (Pa)

PP

plain pipe

Pt

platinum

Re

Reynolds number

SiO₂

silicon dioxide

SST

shear stress transport

SWCNTs

single-walled carbon nanotubes

T in

inlet fluid temperature (K)

TiO2

titanium dioxide

T out

outlet fluid temperature (K)

TP

twisted pipe

TPF

thermal performance factor

T w

wall temperature (K)

ZnO

zinc oxide

α

twist ratio

β

width/depth

η

enhancement Index

ρ

density (kg/m3)

Φ

mass fraction of nanoparticles

µ

dynamic viscosity (Ns/m2)

1 Introduction

1.1 Study background and motivation

Pipes are the thermal system to exchange (dissipate) the heat from different engineering, industrial, and manufacturing applications. Tremendous energy is extensively consumed using heat exchangers in power plants, heating, and cooling systems, leading to global warming. New heat-exchanging systems with better thermal efficiency are needed in this matter [1,2]. Heat can be transported by three mechanisms: active, passive, and compound [3]. The active method uses external energy sources like mechanical support, resulting in a more complex/heavy system and higher production costs [4]. Meanwhile, the passive method utilizes the internal energy of the system to enhance heat transport efficiency by changing the flow pattern of the circulating medium or selecting high thermal conductivity fluids [5]. The combination of twisted-tape inserts and nanofluid is the technical solution within a heat exchanger [6]. Despite the significant advantages of applying the passive approach, such as higher heat transfer performance, low cost, and less maintenance, it still shows higher pressure loss [7,8]. As a result, the compound approach incorporates active and passive procedures into a single system.

1.2 Adopted literature review on nanofluid-based twisted pipes

Laboratory work and numerical simulations were performed using the passive methodology to evaluate the thermal efficiency of twisted-tape tubular heat exchangers [9]. Khoshvaght-Alabadi et al. [10] tested experimentally three twist ratios (α = 0.33, 0.67, and 1) with different values of width/depth for peripheral cuts (β = 0.33, 0.5, 0.67, 1, 1.5, 2, and 3) and three metallic nanofluids (Cu/distilled water [DW], Fe/DW, and Ag/DW). A maximum enhancement of 18.2% was identified using Ag/DW compared with base fluid, while the maximum rise in the pressure drop is only 8.5%. Also, 25 and 39 mm pitch wire coil turbulators were examined experimentally in heat transfer and pressure loss in the presence of Al2O3/DW in different concentrations [11]. The increase in heat transfer was larger when a 25 mm pitch wire coil was used in the fluid than when a 39 mm pitch wire coil was used. Meanwhile, the friction factor of the heat exchanger with turbulators was greater than that of the heat exchanger without turbulators. Furthermore, TiO2/DW nanofluid was tested in twisted-tape inserts in a dimpled pipe [12]. The maximum thermo-hydraulic performance of 1.258 was attained by inserting twisted tape with a twist ratio of 3 and 0.15vol%-TiO2/DW in a dimple angle of 45°. The heat transfer and CuO/DW nanofluid flow were simulated through a helical profiled pipe under turbulent single-phase and two-phase scenarios [13]. The most excellent performance efficiency coefficient in a tube with one twisted tape was 2.18, but it was 2.04 in a tube with two twisted tapes under the conditions of two-phase flow, Re = 36,000 and 4vol%-CuO/DW. The turbulent flow and heat transfer of a non-Newtonian aqueous solution containing carboxymethyl cellulose (CMC) and CuO nanoparticles in plain and helical profiled tubes were numerically investigated [14]. The averaged total thermal performance criterion using a twist ratio of 5 and 1.5% nanofluids was 2.02, with an enhancement of 38% relative to that at a twist ratio of 83 and 0.1% nanofluids. The effects of twisted-tape inserts on heat transfer parameters and pressure drop using graphene oxide nanofluid were computationally discussed and optimized through an artificial neural network and genetic algorithm [15]. Based on the results, the optimal inputs are Re = 19,471, the twist pitch is 0.0376, and the volume fraction is 0.0383, producing Nu of 263.57 and a friction factor of 0.0725.

Meanwhile, investigators need much attention to evaluate nanocomposites inside pipes with twisted-tape turbulators. The hydrothermal properties (Nuavg = 132%) and (f = 55%) increased by reducing the twist ratio, reducing the V-cut width ratio, and increasing the V-cut depth ratio in the presence of Al2O3@TiO2/DW [16]. Maddah et al. [17] concluded that applying Al2O3@TiO2 hybrid nanofluid inside a double pipe heat exchanger modified with twisted-tape insertion increased the exergy efficiency. A higher V-cut depth or lower width ratio yielded more heat transfer and pressure drop in the presence of DW-based Al2O3 and phase change material (PCM) nanofluids and Al2O3 + PCM hybrid nanofluids [18]. Bahiraei et al. [19] analyzed the entropy generation of graphene–platinum (Gr@Pt) hybrid nanofluid in double co-twisted tapes (CoTs) and double counter-twisted tapes (CTs) with various twisted ratios. The CoTs were recommended based on the outcomes since they demonstrated a reduced entropy production rate. Also, experimental reports on Al2O3@MgO hybrid nanofluid utilizing a tapered wire coil turbulator were investigated by Singh and Sarkar [20]. They observed that the maximum value of thermal performance factor (TPF) was 1.69 for D-type wire coil. The heat transfer properties, pressure loss, and hydrothermal efficiency were experimentally examined using various V-cut twisted-tape and tapered wire coil configurations in the presence of Al2O3@MWCNT hybrid nanofluid [9]. For all arrangements, the performance assessment criteria (PEC) and figure of merit (FOM) were found to be >1. The V-cut twisted tape with a twist ratio of 5, a depth ratio of 0.5, and a width ratio of 0.5 represented the maximum values of PEC and FOM, whereas the least values were found in C- and D-type tapered wire coil. The thermal performance of MoS2–Ag/DW hybrid nanofluid was tested inside a solar collector having wavy strips in the absorber tube [21]. The results revealed that using composite nanofluid with a 5% concentration in a twisted strip with a height of 40 mm provided the highest heat transfer rate. Moreover, the energy (η th), exergy (η ex), and PEC of DW-based MWCNT-MgO hybrid nanofluid were discussed inside a parabolic solar collector having a symmetrical twisted turbulator [22]. Their two-phase mixed model showed that the values of PEC are more than 1 for all cases. In addition, for case of φ = 3%, as Re increased from 10,000 to 25,000, η th and η ex were enhanced by 45.98 and 31.67% for pitch ratio (PR) = 1 and 0.25, respectively. In another numerical study, the maximum value of PEC is 4.7 and belongs to Re = 12,000 for a pipe with a lower number of turns (case 2), where Φ = 1% [23]. They utilized ((CH2OH)2)/Cu–SWCNT hybrid nanofluid with different volume concentrations and Reynolds numbers. In this regard, the simulation of ternary hybrid nanofluids is carried out by suspending six different nanoparticle combinations and four different surface profiles of regenerative evaporative coolers [24]. Compared with the flat surface, the maximum energy performance, coefficient of performance, and exergy efficiency were 30, 10.68, and 0.29%, respectively. Moreover, the performances of different water-based binary hybrid nanofluids (Al2O3–Cu, Al2O3–CNTs, Al2O3–graphene, Cu–graphene, and Cu–CNTs, CNTs + graphene) and tri-hybrid nanofluids (Al2O3–Cu–CNTs–water, Al2O3–Cu–graphene, Al2O3–CNTs–graphene, Cu–CNTs–graphene–water) at 100 W and 0.9vol% were tested for single‐phase natural circulation loop [25]. It can be observed that the ternary nanofluid shows better performance than the binary nanofluids [26,27]. The ternary nanofluids have a lower reduction in mass flow rate, higher enhancement in effectiveness, and higher reduction in the entropy generation rate as compared to water [28].

1.3 Research novelty and objectives

According to the previous studies and works of researchers, it can be easily recognized that less attention was paid to the problems of twisted tapes using ternary hybrid nanofluids. Accordingly, one of the motivations of the current research is to examine a new type of twisted tape based on ternary hybrid nanofluids. In the current research, single nanofluids (Al₂O₃/DW, SiO₂/DW, and ZnO/DW), hybrid nanofluids (SiO2 + Al2O3/DW, SiO2 + ZnO/DW, and ZnO + Al2O3/DW) in the mixture ratio of 80:20, and ternary nanofluids (SiO₂ + Al2O3 + ZnO/DW) in the mixture ratio of 60:20:20 were compared with different volumetric concentrations (1, 2, 3, and 4%). The shear stress transport (SST k-ω) three-dimensional turbulence model was used to solve the thermohydraulic performance. The favorable properties (heat transfer) and negative properties (frictional pressure drop) were optimized to select the practical working fluids in engineering systems. The previous experimental and numerical investigations on nanofluids as working fluids in twisted pipes are summarized in Table 1.

Table 1

Previous experimental and numerical investigations on the use of nanofluids as working fluids in twisted pipes

Ref. Nanofluids Type of study Specifications Remarks
[10] Cu/DW, Fe/DW, and Ag/DW Experimental U-tube heat exchanger using spiky TT Maximum η at α = β = 0.33
[13] CuO–DW Computational One–two TT PEC = 2.18 (1-TT) and PEC = 2.04 (2-TT)
[14] CMC@CuO–DW Computational TT with H/D = 5, 10, 15, and 83 PEC = 2.02, using 1.5vol% and H/D = 5
[15] Graphene oxide–DW Computational TT with P/W = 7.03, 3.51, and 2.34 Maximum PEC value at P/W = 2.34
[16] Al2O3@TiO2–DW Experimental TT with different H/D, V-cut depth ratios, and V-cut width ratios TPF >1 for hybrid nanofluid for all modified twisted-tape inserts
[18] Al2O3@PCM–DW Experimental TT with different H/D, V-cut depth ratios, and V-cut width ratios A higher V-cut depth or lower width ratio yields more heat transfer and pressure drop
[19] GNPs@Pt–DW Computational TT with CoTs and CTs CTs reduced total entropy generation rate more than CoTs
[21] MoS2@Ag–DW Computational Simple, wavy, and twisted tapes Wavy and twisted tapes had the lowest and highest PEC
[22] MWCNT–MgO–DW Computational PSC integrated with TTs with various pitch ratios As Re increased from 10,000 to 25,000, η th and η ex were enhanced by 45.98 and 31.67% for PR = 1 and 0.25, respectively
[23] EG–Cu–SWCNTs Computational PTC integrated with helical axial fines The maximum PEC value was 4.7 and belonged to Re = 12,000 for a pipe with a lower number of turns (case 2), in which φ = 1%
Current study Al₂O₃/DW, SiO₂/DW, and ZnO/DW; SiO2 + Al₂O₃/DW and SiO₂ + ZnO/DW; and ZnO + Al₂O₃/DW, and SiO₂ + Al₂O₃ + ZnO/DW Computational Tilted TT with 45° DW showed higher η Thermohydraulic values than nanofluids

2 Numerical methodology

2.1 Physical model and numerical method

The basic configuration under examination is a plain pipe with L = 900 mm and D h = 20 mm. Meanwhile, the twisted pipe has the same total length and hydraulic diameter. The helical profile length, width, and path were 20 mm, 0.5 mm, and 30 mm, respectively. Meanwhile, the twisted-tape angle was 45°. Different heat transfer fluids such as DW, single nanofluids, hybrid nanofluids, and ternary nanofluids enter the heat exchangers under the conditions of T in = 303 K, different volumetric concentrations, and different Reynolds numbers. The external walls of plain and twisted-tape pipes were heated under a constant heat flux to study the heat transfer enhancement parameters.

The schematic diagram of the twisted-tape insert pipe is illustrated in Figure 1, along with the applied boundary conditions and the grid domain. Here, the input variables are the inlet temperature T in; the wall temperature T w; the inlet velocity v in; the outlet pressure P out, which is set to atmospheric pressure; and the different geometrical parameters. As for the output parameters, P in is set to be the pressure at the inlet, which is compared against P out, the pressure at the end of the twisted pipe, which is the relevant section of the simulation. Temperature T out is also taken at the end of the twisted pipe. The twisted tape does not cover the full length of the pipe because pressure outlets near obstacles can produce backflow errors, leading to poor convergence [29]. The pressure-based solver has been applied in this simulation. Meanwhile, the partial differential equations have been solved (discretized) by the second-order upwind method using ANSYS FLUENT 2020R1 software based on the finite volume method. All computational fluid dynamics simulations in this study are run with double-precision variables to avoid such inaccuracies. Iteration errors occur when solutions are not completely converged or oscillate between values. This error is frequently addressed by performing enough iterations to ensure convergence. Furthermore, the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) Consistent algorithm is implemented to couple the velocity and pressure. It should be noted that the convergence for the residual of mass and momentum and energy equations is considered below 10−3 and 10−6, respectively.

Figure 1 
                  Physical problem and computational domain of pipe with twisted-tape inserts.
Figure 1

Physical problem and computational domain of pipe with twisted-tape inserts.

2.2 Mathematical formulations and assumptions

The nanofluids employed to improve heat transport are typically diluted solid–liquid blends. These metallic particles can roughly be said to act like a fluid because they are fluidizable and ultrafine (less than 100 nm). The nanofluid can be considered a regular pure fluid if it is assumed that there is no motion slip between the discontinuous phase of the scattered ultrafine particles and the continuous liquid and that there is local thermal equilibrium between the nanoparticles and the fluid [30,31]. In this study, the effective single-phase flow works due to the above assumptions and hypotheses.

The nanofluid flow is assumed to be turbulent, incompressible, Newtonian, and steady-state conditions. In this study, compression work and viscous heating are not significant. The thicknesses of the inner and outer pipe walls are not considered. All the equations of continuity, motion, and energy for the pure fluid are directly extended to the nanofluid [32]:

Governing equation for mass:

(1) · ( ρ V ) = 0 ,

Governing equation for momentum:

(2) · ( ρ V V ) = P + · ( ( u + u t ) ( V + V T ) ) + ρ g ,

Governing equation for energy transport:

(3) · ( ρ C p V ) = · ( k eff T ) + ρ ϵ ,

where V is the mean velocity vector, K eff  =  K  +  K t is the effective thermal conductivity of covalent and non-covalent nanofluids, and ϵ is the energy dissipation rate.

The turbulent nanofluid flow in plain and twisted pipes was simulated in this work for Reynolds numbers ranging from 5,000 to 15,000. These simulations and the convective heat transfer coefficient were calculated using Menter’s two-equation SST k-ω turbulence model, which uses the benefits of the k-ω model and the k-ε model by defining weight functions [33,34]. Governing equations of the SST k-ω turbulence model are as follows:

Kinematic eddy viscosity:

(4) ν T = a 1 k max ( a 1 ω , S F 2 ) ,

Turbulence kinetic energy:

(5) k t + U j k x j = P k β * k ω + x j ( ν + σ k ν T ) k x j ,

Specific dissipation rate:

(6) ω t + U j ω x j = α S 2 β ω 2 + x j ( ν + σ ω ν T ) ω x j + 2 ( 1 F 1 ) σ ω 2 1 ω k x i ω x i ,

Closure coefficients and auxiliary relations:

(7) F 2 = tanh max 2 k β * ω y , 500 ν y 2 ω 2 ,

(8) P k = min τ ij U i x i , 10 β * k ω ,

(9) F 1 = tanh min max 2 k β * ω y , 500 ν y 2 ω , 4 σ ω 2 k C D k ω y 2 4 ,

(10) C D k ω = max 2 ρ σ ω 2 1 ω k x i ω x i , 10 10 ,

(11) ϕ = ϕ 1 F 1 + ϕ 2 ( 1 F 1 ) ,

α 1 = 5 9 , α 2 = 0 . 44 ,

β 1 = 3 40 , β 2 = 0 . 0828 ,

β * = 9 100 ,

σ k 1 = 0 . 85 , σ k 2 = 1 ,

(12) σ ω 1 = 0 . 5 , σ ω 2 = 0 . 856 ,

where S is the strain rate magnitude and y is the distance to the next surface. Meanwhile, α 1 , α 2 , β 1 , β 2 , β * , σ k 1 , σ k 2 , σ ω 1 , and σ ω 2 represent all model constants. F 1 and F 2 refer to the blending functions. Note that F 1 = 1 inside the boundary layer and 0 in the free stream.

The turbulent convective heat transfer and nanofluid flow are examined through several parameters as follows [35]:

Reynolds number:

(13) Re = ρ v D h μ ,

Prandtl number:

(14) Pr = μ C p k ,

Heat gain (W):

(15) Q Gain = m ̇ × C p × ( T out T in ) ,

Heat transfer coefficient (W/m2. K):

(16) h tc = Q Gain A × ( T ̅ w T ̅ f ) ,

Nusselt number:

(17) Nu avg = h D h k ,

Friction factor:

(18) f = 2 × Δ P × D h ρ × v 2 × L ,

Pressure drop:

(19) P = P in P out ,

Dittus–Boelter equation:

(20) Nu avg = 0 . 023 × Re 0 . 8 × Pr 0 . 4 ,

Blasius equation:

(21) f = 0 . 3164 Re 0 . 25 ,

Thermohydraulic performance:

(22) η Thermohydraulic = Nu TP Nu PP / f TP f PP 1 / 3 ,

where ρ, v, D h, and μ refer to the density, working fluid velocity, hydraulic diameter, and dynamic viscosity. C p and k are the specific heat capacity and thermal conductivity of the working fluid. Also, m ̇ refers to the mass flow rate and T out T in represents the outlet/inlet difference temperatures. TP and PP refer to twisted and plain pipes. A = π DL , T ̅ f = ( T out T in ) 2 , and T ̅ w = T w n .

3 Thermophysical properties of mono, hybrid, and ternary nanofluids

The thermophysical properties of single, hybrid, and ternary nanofluids were estimated empirically through a set of equations and models under 303 K. Nanofluids are preferred because nanoparticles have a larger surface-to-volume ratio than bulk materials [36], resulting in unique behavior. The suspension of nanoparticles into base fluids augments the thermophysical properties of heat transfer fluids [37]. In the literature, several studies have discussed the thermophysical properties of single and double nanofluids [38,39,40]. The development of innovative triple nanofluids has recently gained considerable interest [41,42]. In this research, three different nanomaterials, such as Al2O3, SiO2, and ZnO, were suspended in DW in different volumetric concentrations (1, 2, 3, and 4%) (Table 2). The hybrid nanofluids were SiO2@Al2O3/DW, SiO2@ZnO/DW, and ZnO@Al2O3/DW in the mixture ratio of 80:20. Meanwhile, the ternary nanofluids were SiO2@Al2O3 + ZnO/DW in the mixture ratio of 60:20:20. The current mixing ratios are optimized using Prandtl number values. As a result, the selected mixing cases have a higher Prandtl number than base fluids, resulting in improved heat transfer mechanisms. The density of single, hybrid, and ternary nanofluids can be predicted via the following set of equations [41]:

(23a) ρ nf = Φ np ρ np + ( 1 Φ np ) ρ DW ,

(23b) ρ nf = Φ np 1 ρ np 1 + Φ np 2 ρ np 2 + ( 1 Φ np 1 Φ np 2 ) ρ DW ,

(23c) ρ nf = Φ np 1 ρ np 1 + Φ np 2 ρ np 2 + Φ np 3 ρ np 3 + ( 1 Φ np 1 Φ np 2 Φ np 3 ) ρ DW .

Moreover, the specific heat capacity of single, hybrid, and ternary nanofluids can be predicted via the following set of equations [41]:

(24a) C p nf = Φ np ρ np C p np + ( 1 Φ np ) ρ DW C p DW / ρ nf ,

(24b) C p nf = Φ np 1 ρ np 1 C p np 1 + Φ np 2 ρ np 2 C p np 2 + ( 1 Φ np 1 Φ np 2 ) ρ DW C p DW / ρ nf ,

(24c) C p nf = Φ np 1 ρ np 1 C p np 1 + Φ np 2 ρ np 2 C p np 2 + Φ np 3 ρ np 3 C p np 3 + ( 1 Φ np 1 Φ np 2 Φ np 3 ) ρ DW C p DW / ρ nf .

As a result, the following equations may be used to estimate the thermal conductivity of single, hybrid, and ternary nanofluids [43]:

(25a) k nf 1 k DW = k np 1 + 2 k DW + 2 Φ ( k np 1 k DW ) k np 1 + 2 k DW Φ ( k np 1 k DW ) ,

(25b) k nf 2 k DW = k np 2 + 2 k DW + 2 Φ ( k np 2 k DW ) k np 2 + 2 k DW Φ ( k np 2 k DW ) ,

(25c) k nf 3 k DW = k np 3 + 2 k DW + 2 Φ ( k np 3 k DW ) k np 3 + 2 k DW Φ ( k np 3 k DW ) ,

(25d) k nf = ( k nf 1 Φ 1 + k nf 2 Φ 2 + k nf 3 Φ 3 ) Φ .

Similarly, the dynamic viscosity of single, hybrid, and ternary nanofluids may also be calculated using the equations as follows [43]:

(26a) μ nf 1 = μ DW ( 1 + 2 . 5 Φ 1 + Φ 1 2 ) ,

(26b) μ nf 2 = μ DW ( 1 + 2 . 5 Φ 2 + Φ 2 2 ) ,

(26c) μ nf 3 = μ DW ( 1 + 2 . 5 Φ 3 + Φ 3 2 ) ,

(26d) μ nf = ( μ nf 1 Φ 1 + μ nf 2 Φ 2 + μ nf 3 Φ 3 ) Φ .

Table 2

Thermophysical properties of base fluids and nanomaterials at 303 K [44]

DW Al2O3 SiO2 ZnO
Density, ρ (kg/m³) 995.65 3,970 2,200 5,600
Specific heat, C p (J/kg K) 4178.8 765 703 495.2
Thermal conductivity, k (W/m K) 0.6182 40 1.2 13
Dynamic viscosity, μ (Ns/m²) 7.97 × 10−04 / / /

4 Results and discussion

4.1 Verification and validation with literature

Grid independence tests were carried out for three grid sizes to ensure that the simulations were independent of the grid size. Numerical instability caused by the mesh, or the model can occasionally impair the convergence. Discretization errors happen when the mesh is not precise or of appropriate quality, frequently representing the geometry incorrectly or failing to reflect the gradients present in the problem adequately. Four different grids were plotted against the Nusselt number (Nuavg) from the Dittus–Boelter equation (Figure 2a) and friction factor (f) from the Blasius equation (Figure 2b). Grids 1, 2, 3, and 4 were with a number of elements of 374,609, 228,925, 194,025, and 152,742. The average errors among grids 1, 2, 3, and 4 with Dittus–Boelter and Blasius equations were 4.233 and 2.102%, 3.244 and 4.773%, 3.124 and 5.843%, and 2.947 and 6.683%, respectively. The accuracy of Nuavg readings increased by decreasing the number of elements. Meanwhile, the accuracy of friction factor values showed completely different behaviors. Grid 2 was used to assess thermohydraulic performance as the main mesh domain in the simulation cases.

Figure 2 
                  Grid independence results between simulation and empirical correlations for DW: (a) average Nusselt number and (b) friction factor.
Figure 2

Grid independence results between simulation and empirical correlations for DW: (a) average Nusselt number and (b) friction factor.

The study of Eiamsa-ard et al. [45] was used as the validation reference. They experimentally discussed the heat transfer rate (Nuavg), friction factor (f), and thermal enhancement index (η) of DW flow in a tube fitted with twin twisted tapes. Their results demonstrated that the Nusselt number (Nuavg), friction factor (f), and thermal enhancement index (η) increase with decreasing twist ratio. In Figure 3(a and b), the experimental values of Nuavg and f were compared with the current numerical results. The average errors between the experimental and numerical results were 4.406% (Nuavg) and 10.497% (f), respectively.

Figure 3 
                  Comparison between the experimental [45] and numerical results: (a) average Nusselt number and (b) friction factor for DW.
Figure 3

Comparison between the experimental [45] and numerical results: (a) average Nusselt number and (b) friction factor for DW.

4.2 Thermophysical properties

The number of nanoparticles added to the base fluids significantly impacts the thermophysical properties of nanofluids. The thermophysical properties of single nanofluids (Al2O3/DW, SiO2/DW, and ZnO/DW), hybrid nanofluids (SiO2@Al2O3/DW, SiO2@ZnO/DW, and ZnO@Al2O3/DW) in the mixing ratio of 80:20, and ternary nanofluids (SiO2@Al2O3-ZnO/DW) in the mixture ratio of 60:20:20 were estimated using equations and correlations under the condition of 303 K. As shown in Table 3, density, thermal conductivity, and viscosity were increased by increasing the volumetric concentration. Meanwhile, the specific heat was decreased by increasing the volumetric concentration. ZnO/DW achieved the highest density enhancement with 18.554% and ZnO+Al2O3/DW with 16.946% at 4vol%. The highest drop in the specific heat was 14.514% by ZnO/DW, and the ternary nanofluid showed a slight decrement by about 1.518% at 4vol%. Also, the best improvement in thermal conductivity was presented by Al2O3/DW, ZnO/DW, and ZnO+Al2O3/DW by about 20.600, 17.785, and 14.830%, respectively, at 4vol%. The augmentation in the thermal conductivity of single, double, and triple nanofluids can be attributed to the nature of heat transport in nanoparticles and clustering phenomena, the Brownian motion of nanoparticles, and liquid layering at the particle interface [46]. Moreover, hybrid and ternary nanofluids reduced the undesired increment in the dynamic viscosity from 67.383 to 40.668 and 24.086%, respectively, at 4vol%. Meanwhile, the growth in dynamic viscosity of ternary nanofluids relative to DW can be credited to the other layer mixture in the triple nanofluid. As nanoparticle volume fraction increases, dynamic viscosity of nanofluids increases. Also, the increase in the viscosity of the triple nanofluid is attributed to the internal viscous stress and the formation of clusters in the fluid [47,48].

Table 3

Thermophysical properties of DW and different types of single, hybrid, and triple nanofluids at 303 K

Properties Al2O3/DW SiO2/DW ZnO/DW
1% 2% 3% 4% 1% 2% 3% 4% 1% 2% 3% 4%
ρ (kg/m³) 1021.694 1047.737 1073.781 1099.824 1007.694 1019.737 1031.781 1043.824 1041.694 1087.737 1133.781 1179.824
C p (J/kg K) 4058.513 3944.205 3835.443 3731.831 4103.833 4030.637 3959.150 3889.312 3980.775 3799.514 3632.976 3479.436
k (W/m K) 0.6949 0.7109 0.7286 0.7470 0.6412 0.6421 0.6457 0.6501 0.6817 0.6966 0.7127 0.7296
μ (Ns/m²) 8.79 × 10−04 9.84 × 10−04 1.12 × 10−03 1.30 × 10−03 8.79 × 10−04 9.84 × 10−04 1.12 × 10−03 1.30 × 10−03 8.79 × 10−04 9.84 × 10−04 1.12 × 10−03 1.30 × 10−03
SiO2 + Al2O3/DW [80:20] SiO2 + ZnO/DW [80:20] ZnO + Al2O3/DW [80:20]
1% 2% 3% 4% 1% 2% 3% 4% 1% 2% 3% 4%
ρ (kg/m³) 1010.494 1025.337 1040.181 1055.024 1014.494 1033.337 1052.181 1071.024 1037.694 1079.737 1121.781 1163.824
C p (J/kg K) 4094.669 4012.973 3933.609 3856.478 4078.562 3981.979 3888.856 3799.009 3996.083 3827.595 3671.737 3527.139
k (W/m K) 0.6509 0.6505 0.6526 0.6556 0.6483 0.6479 0.6500 0.6530 0.6807 0.6899 0.7003 0.7113
μ (Ns/m²) 8.51 × 10−04 9.16 × 10−04 9.96 × 10−04 1.09 × 10−03 8.51 × 10−04 9.16 × 10−04 9.96 × 10−04 1.09 × 10−03 8.51 × 10−04 9.16 × 10−04 9.96 × 10−04 1.09 × 10−03
SiO2 + Al2O3 + ZnO/DW [60:20:20] SiO2 + Al2O3 + ZnO/DW [50:30:20] SiO2 + Al2O3 + ZnO/DW [60:20:20]
1% 2% 3% 4% 1% 2% 3% 4% 1% 2% 3% 4%
ρ (kg/m³) 1017.294 1038.937 1060.581 1082.224 1017.294 1038.937 1060.581 1082.224 1017.294 1038.937 1060.581 1082.224
C p (J/kg K) 4069.528 4049.162 4028.796 4008.430 4069.528 4049.162 4028.796 4008.430 4069.528 4049.162 4028.796 4008.430
k (W/m K) 0.6583 0.6570 0.6582 0.6603 0.6583 0.6570 0.6582 0.6603 0.6583 0.6570 0.6582 0.6603
μ (Ns/m²) 8.31 × 10−04 8.70 × 10−04 9.14 × 10−04 9.65 × 10−04 8.31 × 10−04 8.70 × 10−04 9.14 × 10−04 9.65 × 10−04 8.31 × 10−04 8.70 × 10−04 9.14 × 10−04 9.65 × 10−04

4.3 Thermohydraulic enhancement of plain pipe

In this section, single, hybrid, and ternary nanofluids with 4vol% are tested in the plain pipe under different Reynolds numbers through various parameters, including outlet temperature, heat gain, heat transfer coefficient, average Nusselt number, friction factor, and pressure loss. The outlet temperature of the base fluid and nanofluids decreases by increasing the working fluid velocity inside the plain pipe (Figure 4a). The higher outlet temperature was presented by base fluid (DW); meanwhile, SiO₂/DW nanofluids show a lower T out value. This behavior is due to a change in nanofluid properties (i.e., density and dynamic viscosity) by increasing the Reynolds number at the constant volumetric fraction. The thermal system gains more heat by increasing the Reynolds number for base fluid and all types of nanofluids (single, hybrid, and ternary) (Figure 4b). ZnO/DW and Al2O3/DW nanofluids show the best energy gain. Meanwhile, base fluid and SiO₂+Al2O3+ZnO/DW offer the worst heat gain performance. Figure 4c and d exhibits the heat transfer enhancement parameters (h tc and Nuavg) for base fluid and nanofluids at different Reynolds numbers. h tc and Nuavg enhance by increasing Reynolds number for DW, single, hybrid, and ternary nanofluids. Al₂O₃/DW nanofluid shows a higher heat transfer coefficient. Meanwhile, SiO₂/DW nanofluid presents higher values of Nuavg. The heat transfer is enhanced by using higher nanoparticle volumetric fraction and nanofluids with better thermal conductivity. The condition of constant Reynolds number for base fluid and nanofluids leads to an increase in dynamic velocity and density values. Therefore, the lower temperature gradients enhance the heat transfer efficiency [35]. Figure 4(e and f) illustrates the pressure drop and friction factor values of DW, single, hybrid, and ternary nanofluids in 4vol% at different Reynolds numbers. The pressure loss increases as the Reynolds number increases, but the friction factor decreases. As shown in Figure 4e, DW presents the lower pressure loss against Re, and single nanofluids show higher pressure reduction values in the order of SiO2/DW, Al2O3/DW, and ZnO/DW, respectively. Because the friction factor is only determined by the Reynolds number, using different working fluids (DW and nanofluids) has no effect.

Figure 4 
                  Thermohydraulic parameters of plain pipe using DW, single, hybrid, and ternary nanofluids: (a) outlet temperature, (b) heat gain, (c) heat transfer coefficient, (d) average Nusselt number, (e) pressure loss, and (f) friction factor.
Figure 4

Thermohydraulic parameters of plain pipe using DW, single, hybrid, and ternary nanofluids: (a) outlet temperature, (b) heat gain, (c) heat transfer coefficient, (d) average Nusselt number, (e) pressure loss, and (f) friction factor.

4.4 Thermohydraulic enhancement of twisted pipe

In this section, single, hybrid, and ternary nanofluids with 4vol% are tested in the twisted pipe under different Reynolds numbers through various parameters, including outlet temperature, heat gain, heat transfer coefficient, average Nusselt number, friction factor, and pressure loss. The outlet temperature of the water and nanofluids decreases by increasing the working fluid velocity inside the plain pipe (Figure 5a), which can be attributed to short heat exchange duration. The higher outlet temperature was presented by base fluid (DW); meanwhile, SiO2/DW nanofluid shows a lower value of T out. The thermal system gains more heat by increasing Reynolds numbers for base liquid and all types of nanofluids (single, hybrid, and ternary) (Figure 5b). ZnO/DW and Al2O₃/DW nanofluids show the best energy gain. Meanwhile, water and SiO₂ + Al2O₃ + ZnO/DW show the worst heat gain performance. According to equation (15), and because the inlet temperature for DW and nanofluids has been fixed, three primary parameters are playing a major role in the system absorbing more heat and energy, which are mass flow rate, C p, and working fluid outlet temperature. Figure 5c and d exhibits the heat transfer enhancement parameters (h tc and Nuavg) for base fluid and nanofluids at different Reynolds numbers. h tc and Nuavg enhance by increasing Reynolds number for DW, single, hybrid, and ternary nanofluids. Al₂O₃/DW nanofluid shows a higher heat transfer coefficient. Meanwhile, SiO₂/DW nanofluid presents higher values of Nuavg. The use of twisted-tape turbulator has significantly influenced flow directions in heated pipes. The helical shape twisted-tape turbulator may induce swirl fluid flow in pipes and promote fluid mixing along the walls. Turbulators can be used to destroy turbulent fluid layers in twisted pipes, improving heat transfer performance [49,50]. However, this phenomenon might result in a larger pressure drop penalty in twisted pipes with nanofluids. The values of pressure drop and friction factor of DW, single, hybrid, and ternary nanofluids in 4vol% at various Reynolds numbers are shown in Figure 5(e and f). The pressure loss increases as the Reynolds number increases, but the friction factor decreases. As shown in Figure 5e, DW has a more minor pressure loss than Re, but single nanofluids have larger pressure reduction values in the order of SiO2/DW, Al2O3/DW, and ZnO/DW. Employing various working fluids, such as DW and different types of nanofluids, has little impact because the friction factor is solely dictated by the Reynolds number (Figure 5f). Furthermore, inserting twisted tape causes more significant pressure decreases. The increase in pressure drop with increasing Reynolds number is because of the rise in nanofluid viscosity, which produces more friction loss and a greater, more significant pressure drop [35].

Figure 5 
                  Thermohydraulic parameters of twisted pipe using DW, single, hybrid, and ternary nanofluids: (a) outlet temperature, (b) heat gain, (c) heat transfer coefficient, (d) average Nusselt number, (e) pressure loss, and (f) friction factor.
Figure 5

Thermohydraulic parameters of twisted pipe using DW, single, hybrid, and ternary nanofluids: (a) outlet temperature, (b) heat gain, (c) heat transfer coefficient, (d) average Nusselt number, (e) pressure loss, and (f) friction factor.

4.5 Comparison of plain and twisted pipes

Figure 6 discusses the enhancements/improvements in the thermohydraulic parameters using plain and twisted pipes under 4vol% and Re = 900. In general, T out increases in the twisted pipe by about 1.056% relative to the plain pipe using the same working fluids. In both plain and twisted pipes, SiO₂/DW presents the lower increment in the outlet temperature, followed by Al2O3/DW, SiO₂ + Al2O3/DW, SiO₂ + ZnO/DW, ZnO/DW, SiO₂ + Al2O3 + ZnO/DW, and ZnO + Al2O3/DW. This can be attributed to the formation of rotational flow throughout the tube, good flow mixing, and subsequently better heat transfer in the twisted-tape tube. Also, heat gain increases in the twisted pipe by about 36.469% relative to the plain pipe using the same working fluids. ZnO/DW presents the best enhancements in the heat gain values with 39.259% (plain pipe relative to DW) and 38.914% (twisted pipe relative to DW) followed by Al₂O₃/DW with 35.841% (plain pipe relative to DW) and 35.406% (twisted pipe relative to DW). Moreover, hybrid (ZnO + Al2O3/DW) nanofluid shows 25.360% (plain pipe relative to DW) and 25.186% (twisted pipe relative to DW). Heat transfer parameters (h tc and Nuavg) enhance the twisted pipe by about 84.009% relative to the plain pipe using the same working fluids (DW and different nanofluids). Al2O3/DW presents best enhancements in the heat transfer parameter values with 33.427% (plain pipe relative to DW) and 34.928% (twisted pipe relative to DW). Meanwhile, lowest enhancements in the heat transfer parameters values are presented by SiO2 + Al2O3 + ZnO/DW with 13.122% (plain pipe relative to DW) and 13.720% (twisted pipe relative to DW). Heat transfer parameters improved as the Reynolds number increased due to the rising turbulence level in the twisted pipe and a higher mixing of the working fluid. Inserting twisted tapes inside the pipe significantly improved heat transfer (relative to plain pipe). The fluid moving through the small gaps has a more incredible velocity, resulting in a thinning of the thermal/velocity boundary layer and, consequently, an increase in heat transfer [50]. Moreover, the heat transfer depends on the changes in thermal conductivity values using different nanofluids and the increment in the Prandtl number for the same Re [51]. Furthermore, the hydrodynamic properties (ΔP and f) increase in the twisted pipe by 265.454% relative to the plain pipe using the same working fluids (DW and different nanofluids). SiO₂/DW presents the maximum augmentations in the hydrodynamic property values with 167.114% (plain pipe relative to DW) and 166.994% (twisted pipe relative to DW). Meanwhile, the lowest augmentations in the hydrodynamic property values are presented by SiO₂ + Al2O3 + ZnO/DW with 41.588% (plain pipe relative to DW) and 41.518% (twisted pipe relative to DW). Helical profiled pipe suffering of high-pressure loss because of the swirling flows and turbulent intensities due to the larger surface area, which enhanced the interaction of the pressure forces with inertial forces in the boundary layers. Meanwhile, the increased flow resistance created by the counter-collision of fluid streams is attributed to the more considerable friction losses [50]. This phenomenon may lead to the division of the cross-sectional area in the tube; thus, the flow velocity increases, and the complicated pipeline structure enhances the disturbance, which leads to the increase in the flow resistance [52].

Figure 6 
                  Thermohydraulic parameters of plain and twisted pipes using DW, single, hybrid, and ternary nanofluids at Re = 900 and 4vol%.
Figure 6

Thermohydraulic parameters of plain and twisted pipes using DW, single, hybrid, and ternary nanofluids at Re = 900 and 4vol%.

Figure 7(a and b) depicts the local Nusselt number against axial position for plain and twisted-tape pipes filled with various nanofluids at 4vol% and Re = 9,000. The collected data, comprising the bulk and wall temperatures, as well as the heat flow of the test area, could be used to compute the local Nusselt number. The results clearly reveal insignificant variations in the Nusselt number data of the nanofluids in the plain pipe under the fully developed condition of the turbulent flow region and the local Nusselt number in the thermally developing region because the local Nusselt number is somewhat enhanced [53]. Meanwhile, because the axial locations are measured at the helical cross sections of twisted-tape pipe, Figure 7(b) displays more variations than Figure 7(a).

Figure 7 
                  Comparison of the local Nusselt number and the non-dimensional axial distance (x/D) at Re = 9,000 and 4vol% of various nanofluid types: (a) plain pipe and (b) twisted tape pipe.
Figure 7

Comparison of the local Nusselt number and the non-dimensional axial distance (x/D) at Re = 9,000 and 4vol% of various nanofluid types: (a) plain pipe and (b) twisted tape pipe.

The double effects of thermal and frictional properties should be considered in engineering applications. The thermohydraulic efficiency (η Thermohydraulic) was proposed to evaluate the total performance of plain and helical profiled pipes in more depth. The formula for calculating the (η Thermohydraulic) value is presented in equation (22). Overall, η Thermohydraulic > 1 for all tested working fluids (DW, single, hybrid, and ternary nanofluids) versus Reynolds numbers (Figure 8). When the Reynolds number is increased, the η Thermohydraulic rises quickly at first, then gradually declines. As a result, there is a crucial Reynolds number, and the largest value of η Thermohydraulic may be produced. The heat transfer augmentation effect supplied by the nanoparticle suspension is no longer noticeable at Reynolds numbers of 7,000 and 9,000 or greater than 15,000, and the impact of frictional pressure drop progressively rises, resulting in a decline in thermohydraulic efficiency values [52]. The negative effect of frictional pressure drop in the helical pipe on the η Thermohydraulic is the smallest. The heat exchanging effect caused by its disturbance is the maximum; therefore, the η Thermohydraulic value peaks at the moment. Different types of nanofluids show almost the same thermohydraulic trends/behaviors. In general, the suspension of nanoparticles in DW shows the opposing effects as follows [54]:

  1. increased thermal conductivity and nanoparticle collisions improve the heat transport rate,

  2. the increase in working fluid viscosity reduces fluid flow and, therefore, the heat transfer rate decreases.

Figure 8 
                  Thermohydraulic performance of plain and twisted pipes using DW, single, hybrid, and ternary nanofluids at 4vol%.
Figure 8

Thermohydraulic performance of plain and twisted pipes using DW, single, hybrid, and ternary nanofluids at 4vol%.

The current result indicates that improved thermal conductivity and increased nanoparticle collisions at the current range are more significant than the effect of increased viscosity. In this study, DW shows higher η Thermohydraulic values than nanofluids. DW achieves the highest η Thermohydraulic value at Re = 15,000 with 1.678. The lowest η Thermohydraulic value is achieved by SiO₂/DW at Re = 7,000 with 1.181.

4.6 Velocity contours and profiles

Figure A1 shows the velocity contours and profile of DW, single nanofluids (Al2O3/DW, SiO2/DW, and ZnO/DW), hybrid nanofluids (SiO2 + Al2O3/DW, SiO2 + ZnO/DW, and ZnO + Al2O3/DW), and ternary nanofluids (SiO2 + Al2O3 + ZnO/DW). Velocity contours of twisted pipe under different planes (slices), namely, P-1, P-2, P-13, P-14, and P-27 were presented at Re = 9,000. The five planes were chosen to represent various twisted-tape directions. Figure A1 indicates that the insertion of the twisted tape leads to the significant increase in the velocity of the flow near it. Moreover, figures illustrate that the velocity at the center of the tube near the twisted tape is larger, and consequently, the flow resistance increases. Clearly, because of the geometry of twisted tapes and the fluid having to overcome additional barriers to flow through the pipe, the ΔP of the twisted tape is greater than the smooth one.

5 Conclusions

Plain and tilted twisted-tape pipes were computationally evaluated via k-omega SST turbulence models in the 5,000 ≤ Re ≤ 15,000. Single nanofluids (Al₂O₃/DW, SiO₂/DW, and ZnO/DW), hybrid nanofluids (SiO₂ + Al₂O₃/DW, SiO₂ + ZnO/DW, and ZnO + Al₂O₃/DW) in the mixture ratio of 80:20, and ternary nanofluids (SiO₂ + Al₂O₃ + ZnO/DW) in the mixture ratio of (60:20:20) were estimated in different volumetric concentrations (1, 2, 3, and 4%). Other thermohydraulic parameters were studied, and the most significant conclusions are as follows:

  1. Thermophysical properties were estimated at 303 K. The higher increments in thermal density, thermal conductivity, and viscosity were 18.554% for 4vol%-ZnO/DW, 20.600% for 4vol%-Al₂O₃/DW, and 67.383% for 4vol%-Al₂O₃/DW, respectively. Meanwhile, the higher reduction in specific heat was presented by 4vol%-ZnO/DW with 14.514%.

  2. The average errors among grids 1, 2, 3, and 4 with Dittus–Boelter and Blasius equations were 4.233 and 2.102%, 3.244 and 4.773%, 3.124 and 5.843%, and 2.947 and 6.683%, respectively.

  3. SiO₂/DW recorded the lower outlet temperature at 4vol% and Re = 900 such as 310.933 K (plain pipe) and 313.842 K (twisted pipe).

  4. ZnO/DW presented the highest increment of heat gain at 4vol% and Re = 900 with 39.259% (plain pipe) and 38.914% (twisted pipe) relative to DW.

  5. Heat transfer parameters enhanced by about 86.978% when using SiO₂/DW at 4vol% and Re = 900 through twisted pipe relative to plain pipe.

  6. SiO₂/DW presented the higher pressure drop at 4vol% and Re = 900 with 167.114% (plain pipe) and 166.994% (twisted pipe) relative to DW.

  7. The plots of local Nusselt number versus the axial locations revealed insignificant variations in both plain and twisted-tape pipes using different types of working fluids.

  8. All tested heat transfer fluids showed η Thermohydraulic > 1. At Re = 900, DW recorded the best η Thermohydraulic with 1.496 followed by SiO₂/DW with 1.214. Meanwhile, the higher η Thermohydraulic value was 1.678 using water at Re = 15,000.

  1. Funding information: This work was funded by Universiti Teknologi Malaysia (UTM), operated by Research Management Center (RMC), under the Research University Grant number (06E10).

  2. Author contributions: Omer A. Alawi: conceptualization, formal analysis, writing – original draft; Haslinda Mohamed Kamar and Nadhir Al-Ansari: funding acquisition; Omer A. Alawi, Omar A. Hussein, Raad Z. Homod: investigation; Omer A. Alawi, Ali H. Abdelrazek, Waqar Ahmed: methodology; Haslinda Mohamed Kamar, Omer A. Alawi, Nadhir Al-Ansari: project administration; Haslinda Mohamed Kamar: supervision; Zaher Mundher Yaseen, Ali M. Ahmed, Mahmoud Eltaweel: writing – review and editing. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

Appendix

Figure A1 
                  Velocity profiles of DW, single, hybrid, and triple nanofluids under different planes at Re = 9,000.
Figure A1 
                  Velocity profiles of DW, single, hybrid, and triple nanofluids under different planes at Re = 9,000.
Figure A1 
                  Velocity profiles of DW, single, hybrid, and triple nanofluids under different planes at Re = 9,000.
Figure A1 
                  Velocity profiles of DW, single, hybrid, and triple nanofluids under different planes at Re = 9,000.
Figure A1

Velocity profiles of DW, single, hybrid, and triple nanofluids under different planes at Re = 9,000.

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Received: 2022-08-22
Revised: 2022-10-22
Accepted: 2023-01-02
Published Online: 2023-03-04

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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