Study the effect of using a dual rotor system on the performance of horizontal axis wind turbines using CFD

0 Introduction

Wind energy is the second most expanding renewable energy after solar energy.Globally, wind energy production reached 1,021 GW by the end of 2023, Egypt represents around 0.20 % with total capacity of 2,062 MW[1], however Egypt seeks to increase the integration of wind energy production due to its exceptional geographical coordinates, especially in the Gulf of Suez, Egypt has wind speeds ranging from 5 to 10 m/s [2].

Wind turbine development started in the 19th century and with time designs were improved, and wind turbine capacities increased rapidly.Today’s HAWT have an average capacity of about 3 MW for onshore projects with a projected capacity of 5.5 MW by 2035 and 8 MW for off-shore with a projected capacity of 17 MW by 2035 [3].

Theoretically, according to Betz’s limit, the maximum energy that can be captured from an airstream by a wind turbine is 59.3 % in a single-rotor configuration.But in real-life conditions, the actual power coefficient value is less than the theoretical power coefficient value due to several reasons like wake losses and aerodynamic losses in the hub region.Dual-rotor wind turbine (DRWT) configuration was introduced to harness more wind energy achieving higher efficiency.Ideally, the Cp can exceed the Betz limit reaching up to 64 % because of using an auxiliary rotor to harvest more energy [4].

The aim is to enhance the efficiency of (HAWT), this is done by adding an auxiliary rotor rectifying the inefficiencies of the root area of the main rotor.While(DRWT) have been explored in previous studies,this work stands out by offering:

1) Optimization of key design parameters interchangeably, like diameter ratio, blade numb er, free steam velocity, and tip speed ratio.

2) Results show significant improvement up to 36.75 %in the power coefficient (Cp) compared to singlerotor systems.

3) Results practical relevance as it applies to highpotential places in Egypt, such as the Gulf of Suez.

4) Study the impact of auxiliary rotor on the primary rotor to identify trade-offs in performance and flow dynamics, especi ally with interchange between the number of front rotor blades and the diameter ratio.

These contributions not only add to our understanding of DRWTs, but also provide practical insights for their use in real-world situations.

1 Literature review

DRWTs have two rotors that can be on the same side or with the nacelle between them, those rotors can have similar or different diameters, also the two rotors may rotate in the same direction known as co-rotating (CODRWT) or maybe in the opposite directions known as counter-rotating (CR-DRWT).In a blade element momentum analysis of the co-rotating and counterrotating wind turbines by Amoretti et al.[5], counterrotating DRWT was found to harvest more energy than co-rotating DRWT by 4.3 % and to harvest mo re energy and power by 10.6 % compared to the single rotor wind turbine (SRWT).

Abdel Karim et al.[6] found that due to the decrease of the interaction between the front and rear rotor by increasing the axial distance, an increase in the front rotor performance and a decrease in the rear rotor performance occurs leaving the overall perfor mance of the CO-DRWT and CR-DRWT not affected by this change, this was further shown in a numerical study on aerodynamics of the CRDRWT by Mokhtar et al.[7], it was found that there is a negligible difference in changing the axial distance between the rotors.

As the wind speed increases more power output can be generated by the turbine.Each turbine has a designed operating range of wind speeds, the lower limit is the cut-in speed and the upper limit is the cut-out speed.The generated power will increase cubically with the increasing of wind speed until it reaches the turbine-rated wind speed from which the output power will stay relatively the same until the wind speed reaches the cut-out speed[8].Another important aspect is the tip speed ratio (TSR or λ), which is the ratio between the rotor blade tip speed and the freestream velocity, if it’s too low the wind turbine could stall,and if it’s too high there will be damage to the turbine and reduced rotor efficiency.So, to get the maximum power coefficient it’s recommended to work with the optimum tip speed ratio which depends on the number of blades,the smaller number of blades will have an optimum value higher compared to another rotor with a greater number of blades [9].For 2-blade rotors, the optimal tip speed ratio is around 6.28, while it can reach 5.45 for a threebladed rotor [10].

The effect of using more blades in a wind turbine has been examined by Adeyeye et al.[11] considering several physical and financial aspects like physical balance, cost,weight, rotor vibration, noise, wake effect, and storm resilience, and it was found when the number of blades increases, the solidity increase which in high freestream velocities can make the rotor act as a wall in which the wind doesn’t pass through decreasing the harvested energy dramatically, so the higher numb er of blades can be used in low free stream velocities in which it has a high effi-ciency, on the other hand using lower number of blades like 2 blades will decrease the efficiency by around 3 %compared to the 3 blades variation with the same diameter.

Increasing the number of blades increases the solidity which has two major effects are increa sing the friction loss and torque as per Eltayesh et al.[12], but that doesn’t mean that a higher number of blades can’t be used as in reality it depends of the optimum required working conditions for the turbine which isn’t only about achieving the maximum power coefficient but also include the aerodynamic flow around blades,number of blades and the operating TSR if the application requires lower TSR then using a higher number of blades will be viable and would give higher Cp.

Diameter ratio (DR) is one of the most important parameters in DRWT, as it has a significant influence on the downwind rotor’s power extraction, adding an upstream auxiliary rotor with a smaller diameter compared to the main rotor grants much more kinetic energy extraction from the moving wind, but it must be considered that increasing the area of the auxiliary rotor increases its performance on the cost of the rear main rotor’s performance which is overshadowed by the front rotor.When using a freestream wind velocity of 10 m/s,DRWT with diameter ratios of 0.5 and 0.25 had the highest overall performance [13].

In his research Jenkins et al.[14], found that using a larger downstream rotor compared to the upstream rotor in a DRWT system increases the rotation speed of the downstream rotor since it’s exposed to the full freestream velocity, also the blade velocity and power output of DRWT system increases with the increase of wind speed.

Modern HAWT doesn’t reach the Betz limit due to several losses, a significant amount of this deficiency is caused by the aerodynamic losses in the blade root area which has relatively thick airfoils with low aerodynamic performance used for structural stability and accounts for the bottom 25%of the rotor.Rosenberg et al.[15] presented a DRWT concept in which the auxiliary rotor’s size is 25 % of the main rotor size and axially aligned with it, an increase in power by around 4.6 % is produced while comparing wakes it was found that the concept is more efficient in energy extraction in the main rotor’s root area.

The performance of a DRWT system was numerically studied by Mokhtar et al.[7] with different three diameter ratios between the rear auxiliary rotor and front main rotor which (DR = 0.75, DR = 1, and DR = 1.5) were numerically investigated.The highest power coefficient resulted from the first case in which the auxiliary downwind rotor diameter is larger than the main rotor diame ter,resulting in a power coefficient increase of around 13.3 %compared to the SRWT at the optimum tip speed ratio λ = 5.In contrast, when the diameter ratio increased to 1.5 the power coefficient decreased compared to the SRWT.

2 Numerical model

Each The 3-D flow for the DRWT model is computationally studied using ANSYS Fluent 21.The velocity and pressure fields were coupled using the Coupled scheme, while the pressure interpolation was done in the second order and a second-order upwi nd scheme was used for solving the momentum equations.The threedimensional mass conservation or continuity equation at a point for unsteady, compressible fluid with no body forces [16].With the fluctuating velocity fields present in turbulent flows, there are variations where momentum,energy, and the species concentration transported are combined allowing for the fluctuation of the transported amount.To get an exact governing equations solution would be nearly impossible so it can be modified with assumptions to remove the tiny scales which gives several modified equations that are computationally easier to solve which in return lowers the costs.The resulting equations also contain new unknown variables which can be determined using turbulence models concerning known variables.

General recommendations and previous studies in the field of wind turbines consider either the k-ε model or the k-ω model with their variants since they provide high accuracy results, however k-ε models calculation and running requirement s are lower and with easier convergence,this study will use the realizable k-ε model as it provides the best performance of k-ε models[17] and it has demonstrated the ability to handle complex flow features that are frequently encountered in wind turbine aerodynamics such as rotat ional effects flow separation and high strain rates.The realizable variant is more appropriate for flows with significant curvature and rotation than the standard k-ε model because it includes an exact representation of the transport equation for the dissipation rate and an improved formulation for the turbulent viscosity.Similar aerodynamic studies have extensively validated this model which is renowned for offering a good balance between computational efficiency and accuracy.Additionally, it is a solid option for examining the dual-rotor configuration in this study due to its accuracy in forecasting turbulent flow characteristics surrounding rotating systems.Citations of earlier studies that used this model serve to further support its suitability for the current study.For this study the realizable k-ε turbulence model was selected because it is robust in handling free-stream turbulence effects which are crucial for wind turbine aerodynamics, and it performs better when simulating high Reynolds number flows.The k-ε model is more appropriate for simulating large-scale flows with high separation and reattachment regions which are frequently seen in wind turbine rotors and is less sensitive to near-wall grid resolution than the k-ω SST model.For analyzing the intricate interactions in a dual-rotor system the realizable k-ε model is a viable option because it provides dependable accuracy and enhanced computational efficiency for large domains.In comparison to the k-ω SST model these features and the fact that it has been widely validated in aerodynamic studies make the realizable k-ε model a better choice for the current study.The k-ε model outperformed the other turbulence models put to the test, particularly in the mid and far wake regions.This model is more predictive than standard models because it uses a modified epsilon equation to account for various turbulence scales [18].

2.1 Computational model

In this study, the design of Akay et al.[19] was used which is a three-bladed NREL S826 airfoil wind turbine model with a rotor diameter of 0.9 m shown in Fig.1.

Fig.1.The Rotor Model.

The airflow surrounding the turbine blades is efficiently analyzed by the model using the MRF approach for domain which is crucial for comprehending the turbines performance characteristics.Symmetric boundary conditions are used by the MRF model at the domains inlet and exit sides.To simulate the flow entering and leaving the turbine system and guarantee that the analysis represents actual operating conditions this configuration is essential.Blade Element Momentum (BEM) theory and CFD are combined in numerical research to assess the effi-cacy of the MRF approach.To accurately simulate the aerodynamic performance and replicate the dual-rotor wind turbines operating environment the boundary conditions employed in this study were carefully chosen.To guarantee correct flow field initialization a velocity inlet was placed at the upstream boundary to supply a consistent wind profile that matched the turbines rated wind speed.A pressure outlet condition was used at the downstream boundary to permit airflow to freely exit reducing numerical instabilities and reflections.To depict an open domain and prevent interference with the flow field slipwall (symmetry) conditions were applied to the top and lateral boundaries.Viscosity effects were taken into consideration by treating the hub surfaces and turbine blades as non-slip walls.

The main cylindrical domain boundaries used for the numerical model range from 7.8 Di1 downstream of the rotor to 3.3 Di1 upstre am of the rotor, with the crosssection radius of the cylindrical domain being 4.4 Di1[19] as in Fig.2, where Di1 is the main rotor diameter.Wind speed input is 10 m/s in the upstream part of the domain.The effect of the tunnel walls was neglected in the current computations utilizing a very large computational domain where the rotor calculations were done in a stable environment.

The DRWT model comprises of the front auxiliary rotor and rear main rotor, where the S826 airfoil was used in all the cases of the auxiliary front rotor with the twoblade, three-blade, or four-blade variations.Both the front and rear rotors were simulated with different variations of input parameters to obtain the optimum DR, wind speed,and number of blades.The validated numerical SRWT model was used for the DRWT as shown in Fig.3, also Table 1 shows the different diameters used for the auxiliary rotor and the resulting diameter ratio.

Fig.2.SRWT Computat ional Domain.

Fig.3.DRWT computation al model.

Table 1 Rotors Diameters and Diameter Ratio.

Di1/mDi2/mDR 0.90.2250.25 0.90.450.5 0.90.6750.75

2.2 The meshing of SRWT and DRWT models

The meshing was modeled using the ANSYS meshing tool.Table 2 shows the data for all models where the meshing quality was defined through mesh skewness and aspect ratio.For SRWT, 4.25 million cells were used to mesh the model with an average mesh skewness of 0.25 and an average aspect ratio of 1.92.For DRWT, the number of cells was between 5.5 million to 7 million cells based on the size of the rear rotor according to the diameter ratio with an average mesh skewness of 0.245 and an average aspect ratio of 1.91.Assuring the precision and quality of the numerical simulation,the computational maximum mesh skewness in this study is within the permissible range of 0.9-0.95.For CFD analyses this range is well within the suggested bounds.Five inflation layers with a default growth rate of 1.2 and an initial thickness of 0.00017 were included in the mesh.The free stream velocity Vo = 10 m/s allowed for the maintenance of the maximum Y+ value at 70.

The Mesh independence was done on the 4 blade DR = 0.75 case which has the highest number of cells where the power coefficient of different cases with different number of cells ranging from around 3.6 million elements to nearly 8 million elements were calculated, and Fig.4 shows that as the number of elements exceeds 7 million cells there is littl e to no change in the resulting power coefficient.

2.3 Setup of SRWT and DRWT Solutions

DRWT and SRWT simulations both used the realizable k-ε turbulence model.The Navier-Stokes non-linear equations (RANS) were translated into a series of algebraicequations with a pressure-based solver by the ANSYS Fluent 2021 R1 numerical solving method, the realizable k-ε turbulence model was used to validate the present results with those of Akay et al.[19].The long solving time was the result of the large number of cells of the mesh which will improve the accuracy and give good numerical results.One model was done for the SRWT and nine models were done for the DRWT depending on the number of blades (2, 3, and 4) and diameter ratio (0.25, 0.5, and 0.75).The inlet freestream velocity was based on three freestream velocities (5, 7.5, and 10 m/sec).The tip-speed ratio (λ) variation is in the range between 2 and 8 was used to get the variation of rotating domain angular velocity.The performance was studied by CP calculation at each value of λ.The goal of the study was to get the optimum value of CP for DRWT concerning SRWT based on the variation of the investigated parameters.For the solution of pressure-velocity coupling in ANSYS, the coupled scheme was chosen.The pressure and momentum equations were solved using a second-order upwind.

Table 2 Meshing Table for SRWT and DRWT.

Modeling DR FR B Aspect Ratio SRWT4,253,9200.251.92 DRWT 0.2525,592,6450.241.90 35,596,5690.241.90 45,600,0620.241.90 0.526,095,5080.241.90 36,111,6200.251.91 46,129,1930.251.91 0.7526,933,7030.251.91 36,951,6260.251.91 46,998,6450.251.93 Number of Mesh Elements Average Mesh Skewness

Fig.4.Mesh Grid Independence Curve.

3 Results and discussions

The first step was to perform the CFD validation by comparing the resulting power coefficient (Cp) values of the created SRWT model with the experimental and computational results of [19].Power Coefficient (Cp) can be described as the ratio between the actual produced power by the wind turbine and the total power of the wind stream at a certain velocity, it’s also a representation of the wind turbine efficiency.

The SRWT CFD simulation results for (Cp) a nd(λ)are shown in Fig.5.The (Cp) results nearly align with the experimental results of Akay et al.[19] with an absolute average error margin of 7 % as shown in Table 3.

The main goal of DRWT is to harvest more wind energy by solving the inefficient wind harvesting at the blade root area due to the bad aerodynamic properties in it by adding an auxiliary rotor with a smaller diameter which will also enhance the mixing in the wake flows and achieving a faster velocity recovery which solves the problem of power loss in the wake region in SRWT and leading to the higher power output of DRWT [7].

As discussed in the literature review the counterrotating DRWT system will be used to get the maximum power that can be harvested, also the distance between rotors will not be used as a parameter as it does not affect the results so the distance between rotors will be fixed and will be 0.75Di1 which equals to 0.675 m [7].

After running 196 simulation cases, the power coeffi-cient was calculated.The influence of four different parameters on the performance of the DRWT will be discussed in detail, the parameters are:

1) Number of blades for the auxiliary front rotor(B = 2, B = 3, and B = 4).

2) Free stream velocity(Vo=5 m/s, Vo=7.5 m/s, and Vo = 10 m/s)

3) Diameter ratio ‘‘DR” =Auxiliary Rotor Diameter /Main Rotor Diameter (DR = 0.25, DR = 0.5, and DR = 0.75).

4) Tip Speed Ratio λ (Ranging from 2 to 8) which is applied on all cases.

Fig.5.The relationship between tip-speed ratio(λ)and power coefficient(CP) of SRWT from CFD versus the experimental results.

Table 3 Maximum Two Cp Values for Both CFD and Experimental at Vo = 10 m/s.

λ CFD CPExperimental Data CP 5 0.4030.4318 6 0.4180.4375

3.1 Effect of adding 2 blades auxiliary rotor

With tip speed ratio ranging from 2 to 8,Figs.6-8 show three scenarios where the power coefficient for the three varieties of diameter ratios in a dual-rotor system with 2 blades auxiliary front rotor in the three free speed velocity variations as shown in Table 4.Due to the smaller diameter of the auxiliary rotor (FR), it has a lower capability of harnessing the wind energy, On the other hand, flow obstruction by the auxiliary rotor decreases the power coefficient of the rear main rotor (RR) compared to SRWT system, while the combined overall power coeffi-cient of the dual-rotor system is the sum of the power coefficients of the front and rear rotors.As the auxiliary rotor diameter increase it gains a higher capability to harvest wind energy and a higher flow obstruction for the rear rotor.

Comparing the three results of different diameter ratios in Fig.6(d)reveals that the best result for two-bladed auxiliary rotors at a free stream velocity of 5 m/s occurs at DR = 0.25 and λ = 5 as shown in Table 5.

Fig.6.Power coefficient of auxiliary 2 blades front rotor, rear main rotor, DRWT, in comparison to SRWT with the variation of TSR for Vo = 5 m/s.

Fig.7.Power coefficient of auxiliary 2 blades front rotor, rear main rotor, DRWT, in comparison to SRWT with the variation of TSR for Vo = 7.5 m/s.

Fig.8.Power coefficient of auxiliary 2 blades front rotor, rear main rotor, DRWT, in comparison to SRWT with the variation of TSR for Vo = 10 m/s.

Fig.7 shows the effect of changing the free stream velocity to 7.5 m/s,and applying this change on the three different diameter ratios for the DRWT, the power coefficients of the front auxiliary rotor and the rear main rotor are slightly better compared to the Vo = 5 m/s case, leading to an overall higher combined power coefficient of the DRWT system, again Fig.7 (d) shows that the best result for two-bladed auxiliary rotors at Vo = 7.5 m/s occurs at DR = 0.25 and λ = 6.

Table 4 DRWT with 2-Blade Auxiliary Rotor at Vo=5 m/s showing the Different Overall Maximum Cp.

DRλ FR Cp % VS SRWT Overall Cp %VS SRWT 0.25560.78 %21.22 %0.476+18.00 %662.87 %24.01 %0.473+13.12 %0.5549.36 %36.62 %0.460+14.02 %647.29 %44.05 %0.454+8.66 %0.75550.76 %50.80 %0.3971.56 %645.10 %64.75 %0.3779.86 %RR Cp % VS SRWT Overall Cp

Table 5 DRWT with 2-Blade Auxiliary Rotor at Vo = 7.5 m/s showing the Different Overall Maximum Cp.

DRλ FR Cp % VS SRWT Overall Cp %VS SRWT 0.25559.17 %19.40 %0.490+21.43 %660.56 %21.79 %0.492+17.65 %0.5548.00 %35.21 %0.471+16.80 %645.46 %42.07 %0.470+12.47 %0.75549.41 %49.66 %0.407+0.93 %643.32 %63.03 %0.3926.36 %RR Cp % VS SRWT Overall Cp

Table 6 DRWT with 2-Blade Auxiliary Rotor at Vo = 10 m/s showing the Different Overall Maximum Cp.

DRλ FR Cp % VS SRWT Overall Cp %VS SRWT 0.25558.33 %18.37 %0.497+23.30 %659.40 %20.54 %0.502+20.06 %0.5547.31 %34.39 %0.477+18.29 %644.48 %40.96 %0.479+14.56 %0.75548.68 %49.03 %0.413+2.29 %642.35 %62.05 %0.4004.40 %RR Cp % VS SRWT Overall Cp

Changing the free stream velocity to Vo = 10 m/s shows values that are higher than the previous scenarios at the same diameter ratios, The best result for two-bladed auxiliary rotors at free stream velocity of 10 m/s occurs at DR = 0.25 and λ = 6 as shown in Table 6.

From the three scenarios for 2-blade auxiliary rotor and after comparing the highest results from each which occurs at DR = 0.25 with SRWT, it was found that when Vo = 10 m/s DRWT gives the largest maximum power coefficient Cp for DRWT as in Fig.9.In Fig.10 the three different sizes for the 2-blade auxiliary rotor and the free stream obstruction effect in different diameter ratios are shown, D R = 0.25 has the lowest effect allowing the rear main rotor to harness more wind energy.

3.2 Effect of adding 3 blades auxiliary rotor

Fig.9.Power Coefficients of DRWT with 2-Blade Auxiliary Rotor for 3 DR Values in Comparison to SRWT with Variation of TSR.

Fig.10.Rear Main Rotor Harvesting of Freestream Wind Energy in 2-Blade Auxiliary Rotor Configuration(a)DR=0.25,(b)DR=0.5,and(c)DR = 0.75.

A second set of scenarios concerning the effect of using 3 blade auxiliary front rotor on the power coefficient for three varieties of diameter ratios in a dual-rotor system with three different free speed velocities in TSR range from 2 to 8,compared to the case in 2 blade rotor with the same diameter ratio, the front rotor has a higher power coeffi-cient and this is due to the extra blade which increases the rotor’s ability to harness wind energy, and subsequently the obstruction effect on the rear main rotor power increases causing a lower power coefficient as shown in Table 7.

However, there is a noticeable increase in the power coefficient compared to the 2 blade scenarios at the same diameter ratio and freestream velocity.Table 7 shows a comparison between the highest Cp values for this scenario, and Fig.11 (d) shows that the best result for threebladed auxiliary rotors at Vo = 5 m/s occurs at DR = 0.25 and λ = 5 as shown in Table 8.

Fig.12 (d) shows that the best result for three-bladed auxiliary rotors at Vo = 7.5 m/s occurs at DR = 0.25 and λ = 5.

Fig.13(d) show that the best result for three-bladed auxiliary rotors at free stream velocity of 10 m/s occurs at DR = 0.25 and λ = 5.From the three scenarios in the3-blade auxiliary rotor configuration,and after comparing the highest results from each scenario, the best result ‘‘as with the 2-blade rotor” occurs at DR = 0.25 and Vo = 10 m/s as shown in Fig.14 and Table 9.

Table 7 DRWT with 3-Blade Auxiliary Rotor at Vo = 5 m/s showing the Different Overall Maximum Cp.

FR Cp % VS SRWT DRλOverall Cp %VS SRWT 0.25549.78 %23.18 %0.513+27.05 %656.90 %26.27 %0.489+16.83 %0.5533.56 %45.03 %0.490+21.41 %636.01 %53.04 %0.464+10.95 %0.75527.03 %69.96 %0.416+3.01 %629.38 %86.13 %0.35315.51 %RR Cp % VS SRWT Overall Cp

Fig.11.Power coefficient of auxiliary 3 blades front rotor, rear main rotor, DRWT, in comparis on to SRWT with the variation of TSR for Vo = 5 m/s.

Table 8 DRWT with 3-Blade Auxiliary Rotor at Vo = 7.5 m/s showing the Different Overall Maximum Cp.

FR Cp % VS SRWT DRλOverall Cp %VS SRWT 0.25547.51 %21.41 %0.529+31.08 %653.81 %24.08 %0.511+22.11 %0.5531.72 %43.76 %0.502+24.51 %633.34 %51.16 %0.483+15.50 %0.75525.26 %69.08 %0.426+5.66 %627.09 %84.72 %0.36911.74 %RR Cp % VS SRWT Overall Cp

Fig.12.Power coefficient of auxiliary 3 blades front rotor, rear main rotor, DRWT, in comparis on to SRWT with the variation of TSR for Vo = 7.5 m/s.

Fig.13.Power coefficient of auxiliary 3 blades front rotor, rear main rotor, DRWT, in comparis on to SRWT with the variation of TSR for Vo = 10 m/s.

Fig.15 shows the three different sizes for the 3-blade auxiliary rotor and the free stream obstruction effect in different diameter ratios, DR = 0.25 causes the least obstruction just like in 2 bladed rotor case.

Fig.14.Power Coefficients of DRWT with 3-Blade Auxiliary Rotor for 3 DR Values in Comparison to SRWT with Variation of TSR.

Table 9 DRWT with 3-Blade Auxiliary Rotor at Vo = 10 m/s showing the Different Overall Maximum Cp.

FR Cp % VS SRWT DRλOverall Cp %VS SRWT 0.25546.37 %20.40 %0.538+33.24 %652.14 %22.83 %0.523+25.03 %0.5530.74 %43.03 %0.509+26.23 %631.90 %50.13 %0.493+17.97 %0.75524.29 %68.58 %0.432+7.13 %625.83 %83.84 %0.3789.66 %RR Cp % VS SRWT Overall Cp

Fig.15.Rear Main Rotor Harvesting of Freestream Wind Energy in 3-Blade Auxiliary Rotor Configuration (a) DR=0.25,(b)DR=0.5,and(c)DR = 0.75.

Table 10 DRWT with 4-Blade Auxiliary Rotor at Vo = 5 m/s showing the Different Overall Maximum Cp.

FR Cp % VS SRWT DRλOverall Cp %VS SRWT 0.25545.27 %24.95 %0.524+29.77 %659.13 %28.25 %0.471+12.61 %0.50526.44 %52.94 %0.487+20.62 %635.35 %60.88 %0.434+3.77 %0.75518.05 %83.61 %0.3971.65 %625.54 %99.83 %0.31225.37 %RR Cp % VS SRWT Overall Cp

3.3 Effect of adding 4 blades auxiliary rotor

The third set of scenarios concerning the effect of using 4 blade auxiliary front rotor on the power coefficient for three varieties of diame ter ratios in a dual-rotor system with three different free speed velocities in TSR range from 2 to 8.Table 10 shows the highest Cp values for this scenario, and Fig.16 (d) shows that the best result for three-bladed auxiliary rotors at Vo = 5 m/s occurs at DR = 0.25 and λ = 5, with noticeable increase in the power coefficient compared to the 2 & 3-blade scenarios at the same diameter ratio and freestream velocity but in case of λ = 6 the 4 blades scenario have lower Cp compared to the 2 & 3-blade scenarios as shown in Table 10.

Fig.17(d) is a comparison graph for the three diameter ratios DRWT power coefficients showing that the best result for 3-bladed au xiliary rotors at Vo=7.5 m/s occurs at DR = 0.25 as shown in Table 11.

Comparing the three diameter ratios DRWT power coefficients showing that the best result for three-bladed auxiliary rotors at Vo = 10 m/s occurs at DR = 0.25 as shown in Fig.18(d) an d Table 12.

From the three scenarios in 4 blade auxiliary rotor configuration, and after comparing the highest results from each, it is found that the best results ‘‘similar to the 2,and 3 blade rotors” occur at DR = 0.25, and it was found that when Vo=10 m/s DRWT gives the largest maximum power coefficient Cp for DRWT using the 4-blade auxiliary rotor as shown in Fig.19.

Fig.16.Power coefficient of auxiliary 4 blades front rotor, rear main rotor, DRWT, in comparison to SRWT with the variation of TSR for Vo = 5 m/s.

Fig.17.Power coefficient of auxiliary 4 blades front rotor, rear main rotor, DRWT, in comparis on to SRWT with the variation of TSR for Vo = 7.5 m/s.

Table 11 DRWT with 4-Blade Auxiliary Rotor at Vo = 7.5 m/s showing the Different Overall Maximum Cp.

FR Cp % VS SRWT DRλOverall Cp %VS SRWT 0.25542.48 %23.22 %0.542+34.30 %655.22 %26.08 %0.496+18.71 %0.50524.10 %51.75 %0.501+24.16 %632.01 %59.08 %0.455+8.91 %0.75516.03 %82.72 %0.408+1.26 %622.56 %99.85 %0.32422.41 %RR Cp % VS SRWT Overall Cp

Fig.20 shows the three different sizes for the 4-blade auxiliary rotor and the free stream obstruction effect in different diameter ratios, and similar to the 2 and 3-blade scenarios, DR = 0.25 causes the least obstruction allowing the rear rotor to harness more wind energy from the freestream.

3.4 Results analysis and discussion

From the past sections, it was found that the best power coefficient improvements occur at a small diameter ratio and high freestream velocity since as stated before as the stream velocity increases, more power will be produced by the turbine, as with the smal ler diameter ratio less negative impact is imposed on the main rotor this is because the freestream blockage decrease and the remaining energy that can be harvested by the main rotor is higher.

Fig.18.Power coefficient of auxiliary 3 blades front rotor, rear main rotor, DRWT, in comparis on to SRWT with the variation of TSR for Vo = 10 m/s.

Table 12 DRWT with 3-Blade Auxiliary Rotor at Vo = 10 m/s showing the Different Overall Maximum Cp.

FR Cp % VS SRWT DRλOverall Cp %VS SRWT 0.25541.00 %22.25 %0.552+36.75 %653.13 %24.84 %0.510+22.03 %0.50522.88 %51.06 %0.509+26.06 %630.15 %58.06 %0.467+11.78 %0.75514.90 %82.23 %0.415+2.86 %621.00 %99.55 %0.33220.55 %RR Cp % VS SRWT Overall Cp

Fig.19.Power Coefficients of DRWT with 4-Blade Auxiliary Rotor for 3 DR Values in Comparison to SRWT with Variation of TSR.

Fig.20.Rear Main Rotor Harvesting of Freestream Wind Energy in 4-Blade Auxiliary Rotor Configuration (a) DR=0.25,(b)DR=0.5,and(c)DR = 0.75.

Comparing the effect of increasing the diameter ratio for the 4-bladed case at free stream velocity Vo = 10 m/s, we will see that at DR = 0.25 and λ = 5 the auxiliary front rotor represents around 43 % of the total power where the rear main rotor represents around 57 %, by changing the diameter ratio to 0.5 by consequence the participation of the front rotor increases by around 18 % leading to it representing 61 % of the overall power coefficient decreasing the representation of the rear rotor to 39 %only, and then at DR = 0.75 the front rotor represents the majority of the produced power with a whopping 83%while the rear rotor resides at merely 17%.The same applies to the different number of front rotor blades giving the same response.

The main reason to use an auxiliary rotor in this study is to be able to efficiently harvest some of the lost wind energy in the blade root area of the main rotor due to its inefficient aerodynamic for the sake of the construction integrity, so by adding a small rotor that covers the root area only, the main rotor will be affected slightly by the upstream rotor but it will be to harvest most of the energy it harvested before and with the addition of the harvested energy by the auxiliary rotor we get a much higher overall power coefficient compared to the SRWT case, so if the front rotor diameter increases it will directly impact the performance of the main rotor negatively leading to dwindling output power and defying the purpose of adding the front rotor in the first place.

Analyzing the effect of number of blades on the resulting power coefficient, we find that as the number of blades of the front rotor increase the output power of the rear main rotor decreases, this can be attributed to the same reason of increasing the diameter ratio since adding more blade means increasing the blockage on the main rear rotor leading to increasing performance for the front rotor and lower performance for the rear rotor, when changing the number of blades at DR = 0.25 and Vo = 10 m/s we can see that at λ = 5 the front rotor power coefficient increase by around 29 % by increasing the number of blades from 2 to 3, and increases by around 42 % by increasing number of blades from 2 to 4, the impact on the rear rotor differs with the diameter ratio, at high diameter ratio the impact of number of blades is much higher on the rear rotor where at λ = 5 the increasing of number of blades of the front rotor from 2 to 3 will cause a decrease in the rear rotor power coefficient by 38 % and if the number of blades of the front rotor increases to 4 the decrease in rear rotor power coefficient compared to the 2 rotor case will be whopping 65 % decrease showing the large impact of the number of blades on the power coefficient.

Fig.21.Comparison between the Highest Performing Cases for 2,3,and 4 Bladed DRWT Systems.

The highest power coefficient for the experimental SRWT case study and the SRWT CFD simulation validated in this study occurred at λ = 6 and Vo = 10 m/s with a slightly higher power coefficient compared to the power coefficient at λ = 5, after adding the front auxiliary rotor and studying the effect of changing the tips speed ratio with other parameters in the range of 2-8 and in agreement with previous studies that are discussed in the literature review the optimum tip speed ratio for the two blades case was around λ = 6 especially at higher free stream velocity cases as at Vo = 5 m/s the λ = 5 case is so slightly higher, and for the three and four blades case was at λ = 5 and the effect of the 4 bladed front rotor will be better at lower tip speed ratios in contrast with the two-bladed case in which the effect will be better at higher tip speed ratios,while the 3 bladed case lies in between them with good performance in high and low tip speed ratios.The effect of the tip speed ratio can be seen for front and rear rotors as the front rotor keeps nearly the same patterns in different diameter ratios and with different numbers of blades while the rear rotor will be negatively affected by the increasing diameter ratios as in the case of 4 blades it will have the lowest performance at any tip speed ratio.

Fig.21 shows the comparison between the best cases for each number of blades which occurs at freestream velocity Vo = 10 m/s, DR = 0.25.from this figure, we can see that as stated above the 4-bladed auxiliary front rotor will give the best and highest performance but at lower tip speed ratios in contrast with the 2-bladed case which will have the best performance at high tip sped ratios while the 3 bladed case lies in between them.The highest overall performance occurs at λ = 5 for the 4-blade case in which it has the highest overall power coefficient where Cp max=0.552 compared to Cp max=0.403 for SRWT with an increase of 36.75 %.

4 Conclusion

The performance of (DRWT) system was studied focusing on the parameters below on the turbine overall power coefficient:

1- Effect of Diameter Ratio (DR): The optimum diameter ratio was found to be DR = 0.25, which have minimum obstruction on the rear rotor while effectively harvesting energy from the root area of the main rotor.Increasing the diameter ratio results in higher front rotor performance but significantly diminishes the rear rotor efficiency.

2- Effect of Number of Blades (B): Increasing the blade count from 2 to 4 enhances the front rotor’s power coefficient by up to 42 %, but also leads to a 65 %reduction in the rear rotor’s power coefficient at higher diameter ratios so it is critical to balance rotor solidity and flow obstruction.

3- Effect of Free Stream Velocity (Vo): The highest power coefficient (Cp) was achieved at Vo = 10 m/s, aligning with wind conditions in the Gulf of Suez,increasing the velocity allows the system to harness more energy.

4- Effect of Tip Speed Ratio (λ): The optimal λ varies with the number of blades.For two-bladed systems,λ = 6 provides the best performance, while threeand four-bladed systems perform optimally at around λ = 5.Lower λ values are better suited for configurations with higher rotor solidity.

The study demonstrates that the DRWT system, optimized with DR = 0.25, B = 4, Vo = 10 m/s, and λ = 5,achieves a maximum Cp of 0.552, a 36.75 % improvement over single-rotor wind turbines (SRWTs).These findings provide valuable insights for designing efficient DRWT systems for real-world applications,particularly in regions with high wind speeds.

CRediT authorship contribution statement

Amr Mokhtar: Validation, Software, Resources.Mahmoud Fouad: Writing - review & editing, Supervision, Project administration, Conceptualization.Mohamed Rashed:Writing - review & editing, Supervision, Methodology,Investigation.Mostafa Mokhtar: Validation, Software,Resources.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This research received no exter nal funding.