Tip Loss Research Articles

Rotor Blade Performance Analysis with Blade Element Momentum Theory

Abstract In order to optimally explore and utilize wind energy, an optimal design of wind turbine propeller blades needs to be obtained. Therefore, a computational method to analyze and optimize the performance of the blades needs to be developed. For that purpose, a computational method based on the Blade Element Momentum (BEM) theory is developed in the present study. In this method, the propeller blade is divided into several elements and it is assumed that there is no aerodynamic interaction amongst the elements. Furthermore, the equations from momentum and blade element theories are combined to obtain equations which are useful in blades design process. In the analysis, tip and root losses proposed by Prandtl are also implemented. The computation results are validated using Qblade software. A good agreement can be found from comparison of the results computed from the developed BEM and QBlade.

Detailed flow measurement of the field around tidal turbines with and without biomimetic leading-edge tubercles

This paper focuses on implementing detailed flow measurement using advanced Particle Image Velocimetry (PIV) system to investigate the flow mechanism of leading-edge tubercles on tidal turbine blades. Two approaches have been applied: one is 2D PIV to map the flow separation around the blade sections at different radial positions; and the other is Stereo PIV to conduct a volumetric measurement in the wake field to reveal the tip vortex development and also velocity distribution. The research presented in this paper further demonstrates that the leading-edge tubercles can enable the flow to remain attached to the blades and weaken the three dimensional effect which can lead to efficiency loss or the so-called “tip loss”. Based on these phenomena that have been observed and concluded from the tests, the mechanism by which leading-edge tubercles can provide additional torque and thrust for a tidal turbine has been explained within this paper.

Analysis of a tip correction factor for horizontal axis turbines

AbstractIt is imperative to include three‐dimensional tip flow corrections when using low‐order rotor models that rely on the flow independence principle to compute the blade forces. These corrections aim to account for the effect of pressure equalization at the tips and the accompanying spanwise pressure gradients on the outboard sections, by reducing the computed axial and tangential forces as the blade tips are approached. While Glauert‐type corrections are conventionally employed for actuator disc‐type computations, alternative corrections are required for actuator line computations as they use a finite blade representation. We present actuator line computations of the Model Rotor Experiments in Controlled Conditions (MEXICO) rotor to investigate tip corrections. Using the tip correction factor proposed by Shen et al. (Wind Energy 2005; 8:457–475), the actuator line computations show an improvement in accuracy over similar computations undertaken without a tip correction factor included. Further improvement to the blade loading is achieved by recalibrating the tip correction factor using data extracted from blade resolved computations of the model rotor experiments in controlled conditions rotor. From the rotor resolved computations, the tip loss (reduction in the blade loading on the outboard sections) is found to be more aggressive in the tangential direction than the axial direction. To account for this, we recalibrate the tip correction factor separately in the axial and tangential directions to develop new directionally dependent tip corrections. The resulting actuator line computations show a further improvement in accuracy of the tangential blade loading, resulting in better prediction of the rotor power. Copyright © 2017 John Wiley & Sons, Ltd.

Darrieus wind turbine blade unsteady aerodynamics: a three-dimensional Navier-Stokes CFD assessment

Energized by the recent rapid progress in high-performance computing and the growing availability of large computational resources, computational fluid dynamics (CFD) is offering a cost-effective, versatile and accurate means to improve the understanding of the unsteady aerodynamics of Darrieus wind turbines, increase their efficiency and deliver more cost-effective and structurally sound designs.In this study, a Navier-Stokes CFD research code featuring a very high parallel efficiency was used to thoroughly investigate the three-dimensional unsteady aerodynamics of a Darrieus rotor blade. Highly spatially and temporally resolved unsteady simulations were carried out using more than 16,000 processor cores on an IBM BG/Q cluster. The study aims at providing a detailed description and quantification of the main three-dimensional effects associated with the periodic motion of this turbine type, including tip losses, dynamic stall, vortex propagation and blade/wake interaction. Presented results reveal that the three-dimensional flow effects affecting Darrieus rotor blades are significantly more complex than assumed by the lower-fidelity models often used for design applications, and strongly vary during the rotor revolution. A comparison of the CFD integral estimates and the results of a blade-element momentum code is also presented to highlight strengths and weaknesses of low-fidelity codes for Darrieus turbine design.The reported CFD results may provide a valuable and reliable benchmark for the calibration of lower-fidelity models, which are still key to industrial design due to their very high execution speed.

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

AbstractAerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.

Nonlinear blade element-momentum analysis of Betz-Goldstein rotors

Blade element-momentum theory is a fundamental tool of wind turbine aerodynamics but several of its basic assumptions are not easily examined. By applying the theory to ideal Betz-Goldstein (BG) rotors, two important aspects of the theory are investigated. We prove for the first time that Glauert's inclusion of the tip loss factor in the angular and axial momentum equations is exact for BG rotors. Then we derive, also for the first time, the nonlinear contributions to the angular momentum balance when the rotor has a finite number of blades. The most important nonlinearity is the induced azimuthal velocity of the blades combined with that of the trailing vorticitiy. The derivation follows the recent formulation for the tip loss factor (F) by Wood et al. [1] in terms of the azimuthal variations in the induced velocities due to the trailing vortices. Nonlinearity is potentially important when F differs from unity. For a three-bladed BG rotor with the tip speed ratio (λ) varying from 0 to 15, we show that the nonlinear angular momentum peaks at 12% of the blade element torque when λ is in the range 0.8≤λ≤1.5. As λ increases above 1.5, the nonlinear terms reduce in importance. Nonlinearities also arise in the axial momentum equation but are more difficult to analyze. An approximate treatment of them suggests similar behaviour to the nonlinear angular momentum terms, but those in the axial momentum equation arise purely from the trailing vortices.

Experimental research on wear of conical pick interacting with coal-rock

Abstract For severe wear of a conical pick on tunneling and mining equipment, the influence of pick cutting types, structure and working angle parameters on pick wear is studied using an experimental apparatus for cutting coal-rock. The influence of pick wear on cutting performance is analyzed, which provides an experimental basis for reducing pick wear. The results indicate that the pick wears on only one side under asymmetrical cutting types, which increases the pick's working life. The larger the height of carbide tip and cone angle of pick tip are, the easier it is to protect the head face of the pick-body from interference with coal-rock and avoid carbide tip loss due to wear of the pick-body. In the range of research, the suitable height of the carbide tip is found to be 20 mm ~ 24 mm, and the cone angle of the pick tip should be approximately 80°. The wear area on the pick-body increases with the head face diameter of the pick-body, and a suitable range for the head face diameter is found to be 20 mm–22 mm. Pick wear decreases with cutting angle, but the cutting angle should be maintained at 45°–50°, considering the pick cutting load and coal-rock caving effect. For picks with an inclined angle, pick wear increases with incline angle, however, wear differences on the two sides of the pick form and increase gradually, which improves the pick's self-rotatory ability. The mean peak of pick cutting torque increases with wear degree, and the largest increase percentage was found to be 30%. Furthermore, a worn pick is unfavorable for the caving of coal-rock and the coal-rock fragment size of

Numerical investigation of a HPT with different rotor tip configurations in terms of pressure ratio and efficiency

The choice of the most appropriate rotor tip configuration is important, because it helps to avoid high blade tip losses due to the leakage flow that are responsible for efficiency and pressure ratio drops, mainly in High Pressure Turbine (HPT). This subject has been investigated to improve the axial turbines performance. The HPT used in this work is the turbine designed during the Energy Efficient Engine Program (E3 Program). This HPT was evaluated with different rotor tip geometry configurations: without tip clearance (hypothetical condition), with standard tip clearance geometry (flat-tip), with squealer, with winglet and squealer with winglet. Results were obtained based on the three-dimensional turbulent flow calculations making the use of a commercial CFD RANS equation-based solver with the addition of a two-equation turbulence model, in which the numerical solutions were compared with data available in the open literature for a HPT design-point operation. It was determined that for the HPT studied in this work, the machine efficiency can be improved using the rotor tip geometry equipped with winglet tip configuration. However, the rotor tip geometry equipped with squealer–winglet tip configuration presented a better pressure ratio compromise.

Accurate load prediction by BEM with airfoil data from 3D RANS simulations

In this paper, two methods for the extraction of airfoil coefficients from 3D CFD simulations of a wind turbine rotor are investigated, and these coefficients are used to improve the load prediction of a BEM code. The coefficients are extracted from a number of steady RANS simulations, using either averaging of velocities in annular sections, or an inverse BEM approach for determination of the induction factors in the rotor plane. It is shown that these 3D rotor polars are able to capture the rotational augmentation at the inner part of the blade as well as the load reduction by 3D effects close to the blade tip. They are used as input to a simple BEM code and the results of this BEM with 3D rotor polars are compared to the predictions of BEM with 2D airfoil coefficients plus common empirical corrections for stall delay and tip loss. While BEM with 2D airfoil coefficients produces a very different radial distribution of loads than the RANS simulation, the BEM with 3D rotor polars manages to reproduce the loads from RANS very accurately for a variety of load cases, as long as the blade pitch angle is not too different from the cases from which the polars were extracted.

Turbulence Impact on Wind Turbines: Experimental Investigations on a Wind Turbine Model

Experimental investigations have been conducted by exposing an efficient wind turbine model to different turbulence levels in a wind tunnel. Nearly isotropic turbulence is generated by using two static squared grids: fine and coarse one. In addition, the distance between the wind-turbine and the grid is adjusted. Hence, as the turbulence decays in the flow direction, the wind-turbine is exposed to turbulence with various energy and length scale content. The developments of turbulence scales in the flow direction at various Reynolds numbers and the grid mesh size are measured. Those measurements are conducted with hot-wire anemometry in the absence of the wind-turbine. Detailed measurements and analysis of the upstream and downstream velocities, turbulence intensity and spectrum distributions are done. Performance measurements are conducted with and without turbulence grids and the results are compared. Performance measurements are conducted with an experimental setup that allow measuring of torque, rotational speed from the electrical parameters. The study shows the higher the turbulence level, the higher the power coefficient. This is due to many reasons. First, is the interaction of turbulence scales with the blade surface boundary layer, which in turn delay the stall. Thus, suppressing the boundary layer and preventing it from separation and hence enhancing the aerodynamics characteristics of the blade. In addition, higher turbulence helps in damping the tip vortices. Thus, reduces the tip losses. Adding winglets to the blade tip will reduce the tip vortex. Further investigations of the near and far wake-surrounding intersection are performed to understand the energy exchange and the free stream entrainment that help in retrieving the velocity.

An enhanced disk averaged CFD model for the simulation of horizontal axis tidal turbines

Simulating fully resolved Horizontal Axis Tidal Turbine (HATT) geometry for a time period great enough to resolve a fully developed wake, and accurately predict power and thrust characteristics, is computationally very expensive. The BEM-CFD method is an enhanced actuator disk and is able to reduce the computational cost by simulating a time averaged downstream velocity field. Current implementations fall short of accurately determining tip losses, which are a function of the hydrofoil geometry. This work proposes a method of addressing this shortfall by modifying the angle of attack to conform to the constraints outlined in Prandtl's lifting line theory, i.e. the zero lift angle of attack at the hydrofoil tip. The revised model is compared to existing BEM-CFD methods and validated against experimental data. The revised BEM-CFD method presented in this work shows a significant improvement over previous BEM-CFD methods when predicting power and thrust. The coefficient of power is reduced from 0.57 (approx. 30% above experiment) to 0.44 (approx. 3% above experiment). An increase in turbulence intensity in the rotor region, in particular at the wake boundary, improves the recovery of the wake without the addition of empirical turbulence source terms. Good correlation with experimental results for power, thrust and wake prediction, is observed. The model may also be applied to wind turbines.

Performance analysis of wind turbines at low tip-speed ratio using the Betz-Goldstein model

Analyzing wind turbine performance at low tip-speed ratio is challenging due to the relatively high level of swirl in the wake. This work presents a new approach to wind turbine analysis including swirl for any tip-speed ratio. The methodology uses the induced velocity field from vortex theory in the general momentum theory, in the form of the turbine thrust and torque equations. Using the constant bound circulation model of Joukowsky, the swirl velocity becomes infinite on the wake centreline even at high tip-speed ratio. Rankine, Vatistas and Delery vortices were used to regularize the Joukowsky model near the centreline. The new formulation prevents the power coefficient from exceeding the Betz-Joukowsky limit. An alternative calculation, based on the varying circulation for Betz-Goldstein optimized rotors is shown to have the best general behavior. Prandtl’s approximation for the tip loss and a recent alternative were employed to account for the effects of a finite number of blades. The Betz-Goldstein model appears to be the only one resistant to vortex breakdown immediately behind the rotor for an infinite number of blades. Furthermore, the dependence of the induced velocity on radius in the Betz-Goldstein model allows the power coefficient to remain below Betz-Joukowsky limit which does not occur for the Joukowsky model at low tip-speed ratio.

Blade Element Momentum Modeling of Low-Reynolds Electric Propulsion Systems

A model for the propulsion system of a small-scale electric unmanned aerial system is presented. This model is based on a blade element momentum (BEM) model of the propeller, with corrections for tip losses, Mach effects, three-dimensional flow components, and Reynolds scaling. Particular focus is placed on the estimation of scale effects not commonly encountered in the full-scale application of the BEM modeling method. Performance predictions are presented for geometries representative of several commercially available propellers. These predictions are then compared with experimental wind tunnel measurements of the propellers’ performance. The experimental data support the predictions of the proposed BEM model and point to the importance of scale effects on prediction of the overall system performance.

Effects of blade rotation on axial turbine tip leakage vortex breakdown and loss

The tip leakage vortex breakdown occurs under a few conditions in modern turbines, which leads to extra vortex breakdown losses, but the mechanisms of vortex breakdown and its influencing factors still remain unclear. This paper is a continuation of the previous effort and focuses on the effect of blade rotation on the leakage vortex dynamics in an unshrouded turbine. The analyses on leakage vortex breakdown characteristics are first shown, and then the isolating effects of relative casing motion and Coriolis and centrifugal forces on leakage vortex breakdown and loss are investigated. Based on these, the overall effects of blade rotation on leakage vortex breakdown characteristics are examined. Results indicate that the scraping effects of the casing endwall have a great influence on the blade tip leakage vortex breakdown and loss. However, the effect of Coriolis and centrifugal forces is relatively small. Although the mismatch of both velocity components of the leakage flow and the main flow becomes slightly small with the casing motion, the blade tip mixing loss per unit leakage flow increases due to the fact that the leakage vortex breaks down in advance.

Prediction of Aerodynamic Loads for NREL Phase VI Wind Turbine Blade in Yawed Condition

Aerodynamic loads for a horizontal axis wind turbine of the National Renewable Energy Laboratory (NREL) Phase VI rotor in yawed condition were predicted by using the blade element momentum theorem. The classical blade element momentum theorem was complemented by several aerodynamic corrections and models including the Pitt and Peters' yaw correction, Buhl's wake correction, Prandtl's tip loss model, Du and Selig's three-dimensional (3-D) stall delay model, etc. Changes of the aerodynamic loads according to the azimuth angle acting on the span-wise location of the NREL Phase VI blade were compared with the experimental data with various yaw angles and inflow speeds. The computational flow chart for the classical blade element momentum theorem was adequately modified to accurately calculate the combined functions of additional corrections and models stated above. A successive under-relaxation technique was developed and applied to prevent possible failure during the iteration process. Changes of the angle of attack according to the azimuth angle at the specified radial location of the blade were also obtained. The proposed numerical procedure was verified, and the predicted data of aerodynamic loads for the NREL Phase VI rotor bears an extremely close resemblance to those of the experimental data.

Loss and Deviation in Windmilling Fans

For an unpowered turbofan in flight, the airflow through the engine causes the fan to freewheel. This paper considers the flow field through a fan operating in this mode, with emphasis on the effects of blade row losses and deviation. A control volume analysis is used to show that windmilling fans operate at a fixed flow coefficient which depends on the blade metal and deviation angles, while the blade row losses are shown to determine the fan mass flow rate. Experimental and numerical results are used to understand how the loss and deviation differ from the design condition due to the flow physics encountered at windmill. Results are presented from an experimental study of a windmilling low-speed rig fan, including detailed area traverses downstream of the rotor and stator. Three-dimensional computational fluid dynamics (CFD) calculations of the fan rig and a representative transonic fan windmilling at a cruise flight condition have also been completed. The rig test results confirm that in the windmilling condition, the flow through the fan stator separates from the pressure surface over most of the span. This generates high loss, and the resulting blockage changes the rotor work profile leading to modified rotational speed. In the engine fan rotor, a vortex forms at the pressure surface near the tip and further loss results from a hub separation caused by blockage from the downstream core and splitter.

Direct calculation of wind turbine tip loss

The usual method to account for a finite number of blades in blade element calculations of wind turbine performance is through a tip loss factor. Most analyses use the tip loss approximation due to Prandtl which is easily and cheaply calculated but is known to be inaccurate at low tip speed ratio. We develop three methods for the direct calculation of the tip loss. The first is the computationally expensive calculation of the velocities induced by the helicoidal wake which requires the evaluation of infinite sums of products of Bessel functions. The second uses the asymptotic evaluation of those sums by Kawada. The third uses the approximation due to Okulov which avoids the sums altogether. These methods are compared to the tip loss determined independently and exactly for an ideal three-bladed rotor at tip speed ratios between zero and 15. Kawada's asymptotic approximation and Okulov's equations are preferable to the Prandtl factor at all tip speed ratios, with the Okulov equations being generally more accurate. In particular the tip loss factor exceeds unity near the axis of rotation by a large amount at all tip speed ratios, which Prandtl's factor cannot reproduce. Neither the Kawada nor the Okulov equations impose a large computational burden on a blade element program.

An Analysis of Complication Risk Factors in 641 Nipple Reconstructions

Nipple-areola reconstruction represents the completion of the breast restorative process and is associated with significant positive psychological implications. While factors such as medical comorbidities, smoking status, and radiation therapy have been shown to be associated with an increase in complications following breast reconstruction, their impact on nipple reconstruction remains largely unaddressed in the literature. An IRB-approved, retrospective review of 472 patients who underwent nipple reconstruction at Wake Forest University over a 15-year period was completed. Demographic and surgical characteristics were assessed including age, body mass index, medical comorbidities, smoking status, need for radiation, breast reconstruction type, and nipple flap used. Four hundred and seventy-two patients with 641 nipple reconstructions were included with an average follow-up of 56.5months. Radiation prior to nipple reconstruction was required in 146 breasts (22.8%). Overall, postoperative nipple projection problems occurred in 7.6% of reconstructions with a 4.1% rate of other complications, including nipple necrosis, tip loss, wound infection and wound breakdown. Implant-based reconstruction and radiation were associated with significantly more nipple projection problems (p=0.009 and 0.05, respectively). Higher rates of complications and nipple projection problems were seen with skate flap reconstruction compared to a star flap (p=0.046 and 0.001, respectively). Implant-based breast reconstruction and radiotherapy are associated with higher rates of nipple reconstruction problems. Identification of patient and surgical variables associated with increased risk of poor outcomes preoperatively could help in patient counseling and selection of the most appropriate method of breast and nipple reconstruction.

Assessment of blockage effects on the wake characteristics and power of wind turbines

Large Eddy Simulations (LES) are performed in order to study the wake and power characteristics of a horizontal-axis wind turbine in a wind tunnel. Using an actuator line technique, the effect of wind tunnel blockage ratio (defined as the ratio of the rotor swept area to the tunnel cross-sectional area) is investigated for a wide range of tip speed ratios from 1 to 12, and for four blockage ratios (0.2, 0.09, 0.05 and 0.02). The results demonstrate how the blockage effect increases with the tip speed ratio. When the tip speed ratio is close to or above the optimal design value, blockage ratios of larger than 0.05 affect both tangential and normal forces on the blades and therefore on the power and thrust coefficients. At the highest blockage ratio of 0.2, the mean velocity of the wake is also affected significantly, although the effect on the wake mixing rate is less pronounced. Further, the effect of the Reynolds number on the wake development is illustrated and the impact of numerics and subgrid-scale models are investigated by comparing two different LES codes. Finally, the importance of tip loss correction in actuator-line modeling of wind turbines is illustrated using comparative computations.

Tenckhoff tunneled peritoneal catheter placement in the palliative treatment of malignant ascites: technical results and overall clinical outcome.

BackgroundTo assess the technical and clinical outcome of percutaneous insertion of tunneled peritoneal catheters in the palliative treatment of refractory malignant ascites and to determine the safety and feasibility of intraperitoneal administration of cytotoxic drugs through the tunneled catheter.Materials and methodsConsecutive patients palliatively treated with a tunneled peritoneal catheter to drain the malignant ascites were identified. Patients’ medical history, procedural and clinical follow-up data, including complications and estimated survival, were reviewed. Additionally, a sub analysis of the patients with widespread ovarian cancer and refractory ascites treated with or without intraperitoneal administration of cytotoxic drugs was made.ResultsIn all 94 patients it was technically feasible to insert the peritoneal drainage catheter and to drain a median of 3260 cc (range 100 cc – 8500 cc) of malignant ascitic fluid. Post procedural complications included catheter infection (n = 2; 2%), fluid leakage around the entry site (n = 4; 4%), catheter occlusion (n = 2; 2%), sleeve formation around the catheter tip (n = 1; 1%) and accidental loss of the catheter (n = 1; 1%). There was no increase in catheter infection rate in patients treated with or without intraperitoneal administration of cytotoxic drugs. Median overall survival after catheter insertion is 1.7 months.ConclusionsPercutaneous insertion of a tunneled Tenckhoff catheter for the palliative drainage of malignant ascites and intraperitoneal infusion of cytotoxic drugs is feasible and associated with a very low complication rate, including catheter infection. These tunneled peritoneal lines are beneficial for symptomatic palliative treatment of refractory ascites and allow safe intraperitoneal chemotherapy.