Power Coefficient Research Articles

The influence of the rotor spacing distance and rotating speed ratio on the power production of dual rotor wind turbines using a modified two-way interaction blade element momentum method

The present study aims to develop an accurate and fast improved blade element method (BEM) with two-way rotor-rotor interaction model which can account for two-way rotor-rotor interaction and the influence of rotor spacing while most previous BEM models for co-axis dual rotor wind turbines (DRWT) ignore the rear to front rotor interaction effect. A modified BEM model distinct from computationally intensive Computation Fluids Dynamics (CFD) model, is proposed for DRWTs. Validation of the present model is conducted by comparing it with experimental data from referenced literature for both co- and counter-rotating configuration. In our case study, for both co- and counter-rotating configurations, the power coefficient (CP) maps exhibit a double-hump shape instead of a single peak on the power output -λ curve observed in a single rotor wind turbine system. This characteristic may lead the DRWT to a local CPmax condition rather than the global CPmax while pursing the optimum operational condition. Although the counter-rotating DRWT can achieve a higher CPmax for most rotor spacing ratio (S/R) cases, it exhibits inferior power output than the single rotor for the S/R = 0.1 case. The present model can serve as a rapid and accurate model for configuring and control strategy evaluating DRWTs.

Effects of endplate designs on the performance of Savonius vertical axis wind turbine

In aerodynamic studies, endplates or wingtip devices play a crucial role in enhancing the performance of airfoil blades and minimizing losses. This is particularly important for wind turbines, especially the drag-type Savonius turbine. This paper aims to investigate the effects of different endplate designs. Both experimental works and numerical simulations were conducted on a Savonius rotor with an aspect ratio of 1. A total of eight different endplate geometries and sizes were investigated. The mechanical torque and rotational speed were measured experimentally under various loads with an incoming wind speed of 5.89 m/s. The coefficient of torque (CT) and coefficient of power (CP) were calculated in both the experiments and simulations. The simulation was first validated using data from the literature, and flow characteristics were then scrutinized. The results indicate that the endplates greatly impact the turbine performance, with improvements of up to 299.7 % compared to a turbine without endplates from the experiment. The endplates help prevent flow leakage near the blade edges. In addition to tip losses reducing turbine performance, aerodynamic parasitic drag also contributed to a decrease in CP for the full endplate. The relationship between the aerodynamic parasitic drag with TSR is also reported. By implementing a well-designed endplate, these adverse effects can be mitigated.

Forest Canopy Height Estimation Combining Dual-Polarization PolSAR and Spaceborne LiDAR Data

Forest canopy height data are fundamental parameters of forest structure and are critical for understanding terrestrial carbon stock, global carbon cycle dynamics and forest productivity. To address the limitations of retrieving forest canopy height using conventional PolInSAR-based methods, we proposed a method to estimate forest height by combining single-temporal polarimetric synthetic aperture radar (PolSAR) images with sparse spaceborne LiDAR (forest height) measurements. The core idea of our method is that volume scattering energy variations which are linked to forest canopy height occur during radar acquisition. Specifically, our methodology begins by employing a semi-empirical inversion model directly derived from the random volume over ground (RVoG) formulation to establish the relationship between forest canopy height, volume scattering energy and wave extinction. Subsequently, PolSAR decomposition techniques are used to extract canopy volume scattering energy. Additionally, machine learning is employed to generate a spatially continuous extinction coefficient product, utilizing sparse LiDAR samples for assistance. Finally, with the derived inversion model and the resulting model parameters (i.e., volume scattering power and extinction coefficient), forest canopy height can be estimated. The performance of the proposed forest height inversion method is illustrated with L-band NASA/JPL UAVSAR from AfriSAR data conducted over the Gabon Lope National Park and airborne LiDAR data. Compared to high-accuracy airborne LiDAR data, the obtained forest canopy height from the proposed approach exhibited higher accuracy (R2 = 0.92, RMSE = 6.09 m). The results demonstrate the potential and merit of the synergistic combination of PolSAR (volume scattering power) and sparse LiDAR (forest height) measurements for forest height estimation. Additionally, our approach achieves good performance in forest height estimation, with accuracy comparable to that of the multi-baseline PolInSAR-based inversion method (RMSE = 5.80 m), surpassing traditional PolSAR-based methods with an accuracy of 10.86 m. Given the simplicity and efficiency of the proposed method, it has the potential for large-scale forest height estimation applications when only single-temporal dual-polarization acquisitions are available.

Experimental and computational investigations of flexible membrane nano rotors in hover

With reduced size, the flight Reynolds number of the nano rotor decreases, leading to a sharp drop in the aerodynamic efficiency of the nano rotor. Therefore, improving the aerodynamic performance of the nano rotor at low Reynolds numbers through flow control methods becomes imperative. In this study, from the perspective of bionics, flexible materials are employed in nano rotor design. Seven different layouts of flexible membrane rotor blades are designed and fabricated. The influence of leading and trailing edge flexibility, as well as membrane occupancy ratio on rotor blade propulsion characteristics, is explored through propulsion performance tests in hover.Results show that among several layouts proposed in this study, the layout with both reinforced leading and trailing edges of the flexible membrane nano rotor blade exhibits excellent propulsive performance. However, the propulsion performance of the flexible membrane rotors doesn't vary linearly with the ratio of membrane area to the whole rotor area. The appropriate ratio or flexibility can increase the propulsive performance of the rotor, especially at medium and high collective angles. At 7000 RPM and a 20° collective angle, the Figure of Merit of the flexible membrane nano rotor increases up to 4.2% when comparing with the nano rotor without membrane. This improvement becomes more significant with higher collective angles. The structural natural vibration characteristics of each flexible membrane with different layouts are analyzed through modal tests, ensuring the accuracy of the finite element model for flexible membrane rotors. Numerical analysis of the fluid-structure coupling of a flexible membrane rotor with different layouts indicates that rotor structural vibrations is highly consistent with fluctuation of aerodynamic parameters. The deformation of the flexible membrane under aerodynamic forces enhances local blade camber, but reduces angles of attack. This, subsequently, minimizes the size of laminar separation bubbles and the intensity of the blade tip vortices at high collective angles. Consequently, rotor power coefficients decrease, and overall aerodynamic performance improves.

The Aerodynamic Performance of a Novel Overlapping Octocopter in Hover

A novel octocopter with an overlapping rotor arrangement is proposed in this paper to increase the payload with a limited size. The aerodynamic performance was obtained by both experiments and numerical simulations with the rotor spacing ranging from 1.2 D to 2.0 D (L= 1.2 D, 1.4 D, 1.6 D, 1.8 D, 2.0 D). Also, the aerodynamic parameter was evaluated by the thrust, power consumption, thrust coefficient, power coefficient, and figure of merit (FM) in hover. Compared with a traditional co-axial octocopter, the results indicated that the overlapping octocopter at L= 1.8 D presented an increasing thrust up to 15.98%, and the FM increment was up to 6%. Additionally, the streamline distribution showed that the symmetry of the vortex movement in the downwash flow for the overlapping rotors will offset the rotor interference with an increase in thrust. Meanwhile, the vortex deformation resulting from the induced velocity from the upper rotor also led to an increase in power consumption. Finally, the optimal aerodynamic performance of the overlapping octocopter was obtained with a rotor spacing of L= 1.8 D at 1800 RPM.

Probing the Temperature-Dependent Thermal Conductivity of Violet Phosphorus via Optothermal Raman Spectroscopy.

The temperature-dependent thermal conductivity of violet phosphorus on a perforated SiO2/Si substrate has been investigated via optothermal Raman spectroscopy. The obtained temperature coefficients of the Tg mode and Ptub mode of the violet phosphorus sample are -0.01268 and -0.01789 cm-1 K-1, respectively. On the basis of the temperature coefficients and power coefficients, the thermal conductivity of the violet phosphorus has been calculated to be 44.642 ± 4.995 W/mK at room temperature, which is higher than that of other two-dimensional materials such as black phosphorus and MoS2 due to the effect of boundary scattering and the phonon mean free path. Additionally, the thermal conductivity of violet phosphorus decreases as a power exponential function of the temperature, which is primarily associated with the phonon mean free path and phonon group velocity. This work provides a scientific foundation for thermal management and heat dissipation in designing micro-nano devices with violet phosphorus.

Research on Aerodynamic Performance of Asynchronous-Hybrid Dual-Rotor Vertical-Axis Wind Turbines

This study analyzes the performance degradation of traditional hybrid wind turbines under high blade-tip-speed ratio conditions and proposes solutions through two-dimensional Computational Fluid Dynamics (CFD) simulations. It also introduces the design of two innovative asynchronous-hybrid dual-rotor wind turbines. The results indicate a remarkable 98.5% enhancement in torque performance at low blade-tip-speed ratios with the hybrid wind turbine model. However, as the blade-tip-speed ratio increases, it leads to negative torque generation within the inner rotor of the conventional design, resulting in a reduction of the power coefficient by up to 13.1%. The introduction of the new wind turbine design addresses this challenge by eliminating negative torque at high blade-tip-speed ratios through adjustments in the inner rotor’s operating range. This modification not only rectifies the negative torque issue but also enhances the performance of the outer rotor in the leeward region, consequently boosting the overall power coefficient. Moreover, the optimized inner rotor configuration effectively disrupts and shortens the wake length by 16.7%, with this effect intensifying as the rotational speed increases. This optimization is pivotal for enhancing the efficiency of multi-machine operations within wind farms.

Study on aerodynamic and coupled motion response characteristics of floating vertical axis wind turbine

ABSTRACT To improve the efficiency of a floating VAWT (FVAWT), the aerodynamic and coupled motion response characteristics of 5MW Φ-type FVAWT are studied in fully coupled system. Based on the computational fluid dynamics (CFD) method, the dynamic fluid body interaction (DFBI), overlapping grid and dynamic mesh technique are adopted for numerical simulations. Under wind-wave coupling conditions, the power coefficient (Cp) and motion response of FVAWTs with different tip speed ratios (TSR) and height-todiameter ratios (η) are analysed. The mechanism of platform heave motion on torque Q generation of VAWT is explored. The results show that the FVAWT with height-to-diameter ratio of 1.2 and tip speed ratio of 5 has optimal aerodynamic and motion performance. Under the optimal tip speed ratio, the Cp of the offshore FVAWT is 5.21% higher than that of the land VAWT. As the floating platform rises, the torque of wind turbine decreased correspondingly, and vice versa.

Mitigating thermal stratification in lakes/reservoirs through wind-powered air diffusers.

Thermal stratification can cause various water quality issues in large water bodies. To address this, a new wind-powered artificial mixing system is designed and experimentally tested for various Savonius rotor combinations (three-stage and four-stage rotors). These turbines directly utilize wind energy to draw air into the water column for aeration, bypassing the need for electrical conversion. The rotor performances were tested in terms of power and torque coefficients. Additionally, these rotors were tested for artificial mixing efficiencies in a specially designed water tank that can mimic thermal stratification typically observed in an actual water supply reservoir. Among the rotors, the three-stage rotor with a 60° phase shift was found to exhibit superior power and torque coefficients, achieving a power efficiency value of 0.14. As for the mixing efficiency, the four-stage rotor with a 45° phase shift excelled in mixing efficiency, reaching 95%. PRACTITIONER POINTS: A new wind-powered artificial mixing system is designed and tested for various Savonius rotor combinations. While keeping the total rotor height constant, the three-stage Savonius rotor class shows superior performance against the four-stage Savonius rotor class in terms of power and torque efficiency. Apart from the rotor performance results, the four-stage Savonius rotors show greater artificial mixing efficiency than the three-stage Savonius rotors. Single-pump/diffuser artificial destratification system exhibits better mixing efficiency than multiple-pump/diffuser systems.

Effect of hills on wind turbine flow and power efficiency: A large-eddy simulation study

This study investigates the influence of topography on wind turbine flow and power efficiency. Specifically, a standalone wind turbine is positioned at the top of idealized two-dimensional hills, and the effects of hill geometry and turbine position are systematically investigated. Various parameters are studied, including hill slope, distance between the leeward side of the hill and the turbine, turbine hub height, and hill size. Overall, it is observed that the turbine wake is consistently stronger in the hill cases compared to the flat case. This is attributed to two characteristics of hill flows: (1) the negative streamwise velocity gradients on the leeward side of the hills and (2) the reduced turbulence above the hilltops and hill wake regions. In addition, it is observed that the turbine induction factor is consistently increased in the hill cases compared to the flat case, while the turbine power and thrust coefficients are reduced. In practice, this means that turbines on the hills produce less power output than those on flat terrain for an equivalent wind potential, with the potential decrease in power output reaching more than 20% for certain cases. Altogether, the results offer new insights into the effect of topography on turbine power efficiency. In addition, the study identifies clear relationships between the turbine power coefficient, the induction factor, the overall maximum deficit, and the base flow pressure gradient. These relationships could potentially be used to predict the change in power efficiency based on the wake flow or the base flow. Overall, the results show a clear connection between the turbine power efficiency and the turbine wake development.

A Comparison of a Three Blade and Five Blade Wind Turbine in Terms of the Mechanical Properties Using the Q-Blade Software

يمكن لتوربينات الرياح المنتشرة في مزارع الرياح على نطاق المرافق أن تدعم تلبية رغبات الطاقة المستقبلية وتقليل انبعاثات ثاني أكسيد الكربون عن طريق تقليل متطلبات الطاقة من الوقود الأحفوري. مع ارتفاع درجة حرارة الهواء على مدار اليوم، تزداد سرعة الرياح بسبب تدرجات درجة الحرارة، والتي تنتج تدرجًا في الكثافة / الضغط، مما يؤدي إلى حركة الهواء التي تواجهها توربينات الرياح. اعتمادًا على تضاريس الأرض، يمكن أن تواجه الرياح وتوجه في الوديان بين التلال وفوقها حيث تتدفق وتتبع منحنيات الأرض. تنتج هذه التضاريس زيادة في سرعة الرياح في القمم والتلال. في هذا العمل، تم تصميم شفرة دوار توربينات الرياح الأفقية الصغيرة للعمل في ظل سرعة الرياح المنخفضة، باستخدام برنامج (Q-Blade). استنادًا إلى نظرية عنصر الشفرة (BEM). مع الجنيح NACA3712. تم استخدام دوار ثلاثي الشفرات ودوار بخمس شفرات بناءً على نوع التوربين وحجم الدوار لتوليد الطاقة الميكانيكية من طاقة الرياح. تم إجراء مقارنة وتحليل قوة التوربين ومعامل القدرة ومعامل عزم الدوران عند سرعة رياح منخفضة ((1m/s-8m/s وتم الحصول على نتائج دقيقة للغاية. وجد أن أفضل أداء يمكن أن يعمل فيه دوار توربيني ثلاثي الشفرات بقدرة توربينية تبلغ (955W) كما تم الحصول على قدرة التوربين ((582W للدوار خماسي الشفرات. وجد أن تصميم توربينة رياح أفقية صغيرة بخمس ريش أفضل من التوربين بثلاث ريش ومناسب للعمل في المناطق ذات سرعة الرياح المنخفضة وبكفاءة عالية مقارنة بحجم التوربين.

Effect of Cereal Consumption (Frugra®) on Autonomic Nervous System Function in Healthcare Workers Who Skip Breakfast.

In this study, we aimed to clarify the effects of breakfast intervention on autonomic nerve function in healthcare workers who skip breakfast. This cross-sectional, interventional study was conducted between January 2020 and December 2021. All participants were full-time healthcare workers who completed a self-administered questionnaire on fatigue and subjective symptoms and underwent noninvasive autonomic nerve function tests. "Skippers" were defined as individuals who ate breakfast <4 times per week, and "eaters" were those who ate breakfast >4 times per week. We introduced a cereal, Frugra (Calbee, Inc.), to skippers who opted for the breakfast intervention. Subsequently, they completed the questionnaire again and repeated the autonomic nerve function tests. Among 196 participants (age [mean±SD]: 29.8±7.8 y; 177 women and 19 men), 120 were categorized as skippers and 76 as eaters. In the skipper group, more participants were nurses, lived alone, and worked the night shift than in the eater group. The Chalder Fatigue Scale (CFS) score in the skipper group was higher than that in the eater group, although not significantly. Regarding autonomic nerve function, no significant differences were observed between the groups. In 50 skippers who opted for the breakfast intervention, the CFS score significantly decreased after 4 wk. Log low frequency and log coefficient of component variance total power significantly increased, whereas log high frequency increased, but not significantly, after the intervention. In conclusion, for healthcare workers who were breakfast skippers, the consumption of breakfast cereal reduced their fatigue level and improved their autonomic nervous system activity.

Evaluation of an experimental prototype in an aerodynamic tunnel with characteristics of a small wind turbine with two blades

The experimental consideration of wind turbines in an aerodynamic tunnel is a powerful alternative to determine the performance of these equipment, both to assimilate their behavior in operation, and to identify constructive and aerodynamic aspects, aiming to convert these characteristics to the real turbine. In the understanding described in this work, the aerodynamic characteristics of the prototype were evaluated, the static torque for the different flow speeds and the power coefficient was estimated based on the concept of variation in the amplitude of movement of the drying when crossing the turbine at different speeds of the flow. The results are compared with the values achieved analytically. The research theory predicted the aerodynamic and structural event, investing numerical and experimental tools. The present work constituted the first experimental event to evaluate the aerodynamic performance of the research project. At this stage, the experimental assessment of static torque was carried out, analyzing the aerodynamic wake of the prototype and determining the RPM curves for the attached wind speeds. The perspective is that it will be possible to describe a new process to, based on the correlation coefficients, determine a curve of the amount of energy granted by a source in a reliable unit of time through simulation or prototyping before starting the survey of real module equipment.

Optimizing a vertical axis wind turbine with helical blades: Application of 3D CFD and Taguchi method

Vertical axis wind turbines (VAWT) with helical blades are being interested in urban areas due to the low dependency on the wind direction and also due to low noise production. In spite of good self-starting and smooth operation as the advantages of this type of turbine, its optimizing has not been reported in literature yet and is the subject of this research. A primary investigation by 3D computational fluid dynamics (CFD) to simulate the air flow about the above type of VAWT in the first step showed the importance of three design variables of tip speed ratio, helical angle, and airfoil chord length. However, in the second step, CFD runs were very time consuming and costly. For considering five values for each design variable, 53=125 cases had to be simulated by 3D CFD. Thus, by the use of Taguchi method and with definition of an orthogonal array named L-25, the number of required 3D CFD simulations reduced from 125 to 25. Then, the optimum values of variables were obtained as 1.33 for the tip speed ratio, 30 degrees for the helical angle, and 0.4 m for the airfoil chord length. At the optimum point, the average power coefficient increased to 0.17542. The presented research is novel for optimizing VAWT with helical blades.

Investigating the Structural and Power Performance of a 15 MW Class Wind Energy Generation System under Experimental Wind and Marine Loading

The global transition to renewables in response to climate change has largely been supported by the expansion of wind power capacity and improvements in turbine technology. This is being made possible mainly due to improvements in the design of highly efficient turbines exceeding a 10 MW rated power. Apart from power efficiency, wind turbines must withstand the mechanical stress caused by wind–hydro conditions. Such comprehensive structural analysis has rarely been performed previously, especially for large-scale wind turbines under real environmental conditions. The present work analyzes the energy production and structural performance of an NREL-IEA 15 MW wind turbine using measured wind and hydro data. First of all, an optimum operating range is determined in terms of the wind speed and blade pitch angle to maximize the power coefficient. Then, at this optimum range, a detailed breakdown of the forces and moments acting on different components of the wind turbine is presented. It was found that wind speeds of 9 to 12 m/s are best suited for this wind turbine, as the power coefficient is at its maximum and the mechanical loads on all components are at a minimum. The loads are at a minimum due to the optimized blade pitch angle. The bending force on a monopile foundation (fixed on the seabed) is found to be at a maximum and corresponds to nearly 2000 kN. The maximum blade force is nearly 700 kN, whereas on the tower it is almost 250 kN. The maximum force on the tower occurs at a point which is found to be undersea, whereas above-sea, the maximum force on the tower is nearly 20% less than the undersea maximum force. Finally, seasonal and annual energy production is also estimated using locally measured wind conditions.

Experimental and numerical investigation of Zephyr-type wind turbine

The search for more environmentally friendly energy sources has been prompted by growing environmental concerns. In this regard, wind energy can be an alternative viable source of energy for world electricity demand supply. Despite of their benefits in terms of simplicity of manufacture, independency on wind direction and good starting ability in turbulent flow, Savonius wind turbines as a vertical axis wind energy converter are not recommended for large-scale power generation because of their poor performances. This research emphasizes on the performance improvement of a Zephyr wind rotor (ZWR). Experimental tests were conducted in a wind tunnel for different Reynolds numbers. Maximum power coefficient of 0.074 was recorded for Re = 158,000 corresponding to V∞ = 10 m s−1 at a tip speed ratio of λ = 0.99. Numerical study was carried out with the use of Ansys Fluent 17.0 software through transient 3D simulations investigating the optimization of the ZWR rotor blades and stator vanes with the aim of performance betterment. Maximum power coefficient of 0.168 was found with 8-bladed ZWR with 12 stator vanes. Aerodynamic properties were also improved.

A numerical investigation of a new horizontal wind turbine performance for rural use

In this paper, a new configuration of a horizontal axis wind turbine with three blades for domestic electricity production on farms was numerically simulated. Three configurations were tested numerically: a standard single-blade wind turbine (STWT), a single wind turbine (SWT), and a tandem three-blade wind turbine (TWT) for rural use. For the tandem wind turbine, the effects of pitch angle and the distance between the blades were also investigated. The Gambit and Fluent 19.2 codes were, respectively, used to generate different meshes and determine various parameters. The resolution of the averaged Navier–Stokes equations (RANS) using a finite volume method was conducted. The k–[Formula: see text] realizable two-equation model was chosen for turbulence calculation. The obtained results showed that the maximum power coefficient (Cp) was 0.444 for one of the tandem configurations (TWT), compared to the conventional blade (STWT). The maximum Cp obtained in this study is slightly greater than the experimental results found in the literature. It has also been observed that the flow on these new turbines exhibits a complex phenomenon on both surfaces.

Energy Conversion by Helical Hydrokinetic Turbine in A Pipe

Hydrokinetic turbines are mechanisms designed for the purpose of utilizing the kinetic energy present in the movement of water bodies like rivers, tidal currents, or ocean currents, and transforming it into electrical power. These turbines function based on a principle akin to that of wind turbines; however, they are positioned underwater to harness the energy of the water flow. This study focuses on the fundamentals of hydrokinetic turbines and presents existing research. Additionally, simulations have been conducted to observe how the hydrokinetic turbine responds hydrodynamically inside a pipe. A three-bladed vertical-axis helical hydrokinetic turbine was installed within a circular conduit and subjected to analysis under varying flow conditions. The k-ω SST turbulence model was employed in the analyses. The results indicated that increasing the turbine's angular velocity initially raises the torque and the power coefficient until a peak is reached, after which the power coefficient decreases. The highest power coefficient was observed at a flow velocity of 2 m/s. Additionally, consistent with previous studies, the hydrokinetic turbine within the pipe surpassed the Betz limit.

Order of magnitude increase in power from flow-induced vibrations

Natural hydro environments such as rivers and ocean currents provide abundant and essentially free sources of kinetic energy. Although significant research has been devoted to harnessing this power through traditional turbine systems, there are also studies on the novel use of flow-induced vibration of a bluff body. The large oscillations of an elliptical cylinder resulting from the newly-discovered hyper branch have raised interesting questions about its potential as a source of effective renewable energy. This study investigates the power extraction characteristics of the hyper branch over a range of flow velocities. A factor-of-ten increase in the maximum time-mean power coefficient relative to an established flow-induced vibration system — the vortex induced vibration for aquatic clean energy converter is demonstrated. This suggests the possibility of a new and effective strategy to utilise flow-induced vibrations for energy generation and could help drive the commercial implementation and uptake of oscillating energy converters.

Joint vehicular power and RIS reflection coefficient optimization to maximize the minimum bit rate in VANETs

Reconfigurable intelligent surfaces (RISs) have recently gained significant attention for improving reliability in vehicular communications. However, ensuring reliable communication between far-distance vehicles remains a challenge. This work investigates an RIS-aided vehicular ad hoc network (VANET) in a road section where the distance between vehicles is too large for a single roadside unit (RSU) to provide reliable communication. We propose a novel RIS architecture where several RIS panels are connected by cables and each is equipped with a power amplifier. We then optimize vehicle power and RIS reflection coefficients to maximize the minimum bit rate of the VANET. Due to the non-convex nature of the formulated problem, we use fraction programming (FP) to reformulate it into a convex form, allowing solution using tools like CVX which is a MATLAB-based modeling system for convex optimization. The reformulated problem is then decoupled into subproblems. Block coordinate descent (BCD) is employed to optimize all variables alternately and obtain the joint optimal solution. Additionally, the alternating direction method of multipliers (ADMM) ensures that the phase shift of each reflecting element remains a unit vector. Finally, semidefinite relaxation (SDR) is used to solve the boolean quadratically constrained problem. Simulation results demonstrate the effectiveness of the proposed method and confirm that our architecture outperforms conventional approaches.