Equivalent Blade Research Articles

Novel method for determination the dynamic elastic modulus of composite wind turbine blades

A novel method, a non-destructive test, is developed to obtain the dynamic elasticity modulus of composite wind turbine blades. The proposed method is based on the free vibration theory of cantilever beams, the sectional analysis of laminated composites, the laminated composite theory, and the area contribution method. In response, the static elasticity modulus and the area properties of a hollow cross-section are obtained. On the other hand, by employing an equivalent beam that integrates all the cross-sections of a wind turbine blade. The method is tested with an equivalent blade, and all incidences of nonlinearity are avoided to obtain linear vibration modes; it is demonstrated that the free vibration test is applicable. Finally, it is observed that the first three natural frequencies were related to the dynamic elasticity modulus, where the third frequency shows an error of less than 1.2 %. This study revealed that the method for dynamics elasticity modulus has good potential to be used in the design of wind turbine blades as a quality control and non-destructive test.

Real time prediction and detection of drilling bit issues during drilling with the focus on bit status evaluation using along string measurement (ASM)

Real-time drilling optimization requires online knowledge about drilling bit status, and a novel bit–rock interaction model coupled with extensive drilling data lays the groundwork for bit evaluation. Furthermore, as part of the dynamic modeling of drill strings, forces at the bit must also be calculated. At present, the bit selection protocol is based on the post-drilling bit assessment, although some drilling penetration rate models that are calibrated for a specific field can also be used to estimate bit condition in some cases. This research presents a bit status simulator that overcomes the limitations of existing techniques by making use of a delicate and intelligent application of along-string measurement (ASM) data to predict issues related to drilling bits and mitigate them in real time. This research follows two main lines. The polycrystalline compact (PDC) bit is first reshaped into an equivalent blade bit that incorporates all the design criteria of the PDC bit. Each equivalent blade, however, is composed of some equivalent cutters. Utilizing the ASM data, a novel cutter–rock interaction model is used to estimate normal and contact forces on cutters. Cutter–rock interaction equations and the mechanical specific energy of the bit cutters are used to assess the condition of the bit in real time. Two bits are evaluated in a section of a well on the Norwegian continental shelf using the proposed algorithm. The drilling data, including weight and torque on the bit, are reformulated into normal and cutting forces utilizing a cutter–rock interaction model and recursive least squares method. Consequently, the final simulated values are well in line with the final dull grading reports.

Hovering Helicopter Rotors Modeling Using the Actuator Line Method

An implementation of the actuator line method (ALM) is applied to a hovering helicopter rotor. This method, which is widely used for wind turbine simulations, replaces the rotor blades by momentum source terms in the unsteady Reynolds-averaged Navier–Stokes equations. The removal of the blade mesh significantly reduces the computational mesh size, thus lowering the computational cost. The ALM is presented along with some improvements, notably the choice and treatment of the projection kernel. A parameter sweep is performed showcasing the importance of proper selection of the Gaussian smearing coefficient for accurate rotor performance predictions with a value of scaled around a quarter chord in size. With this value, a new set of simulations on a refined mesh is performed and analyzed covering global rotor performance coefficients, sectional blade loading, tip vortex characteristics in terms of positions, circulation, and core radius. The ALM is benchmarked against an equivalent blade resolved case on the well-known S-76 rotor. Results confirm the appropriateness of the ALM model for a hovering rotor for main flow features and performance metrics, although there was a small loss of accuracy on the tip blade loading in the presence of a blade–vortex interaction. Finally, computational performances indicate an elapsed-time speed-up between 3 and 4× in addition to a greater parallel efficiency in favor of the ALM.

Application of differential transformation method forfree vibration analysis of wind turbine

In recent years, there has been a tendency towards renewable energy sources considering the damages caused by non-renewable energy resources to nature and humans. One of the renewable energy sources is wind and energy is obtained with the help of wind turbines. To determine the behavior of wind turbines under earthquake loads, dynamic characteristics are required. In this study, the differential transformation method is proposed to determine the free vibration analysis of wind turbines with a variable cross-section. The wind turbine is modeled as an equivalent variable continuous flexural beam and blade weight is considered as a point mass at the top of the structures. The differential equation representing the free vibration of the wind turbine is transformed into an algebraic equation with the help of differential transformation method and the angular frequencies and the mode shapes of the wind turbine are obtained by the help of the differential transformation method. In the study, a sample taken from the literature was solved with the presented method and the suitability of the method was investigated. The same wind turbine example also modeled by finite element modelling software, ABAQUS. Results of the finite element model and differential transformation method are compared with each other and the results are in good agreement.

A novel approach to determine splitter vane length for an extremely high hub/tip ratio mixed-flow compressor impeller

This paper presents an approach to determine splitter vane length in radial compressor impellers based on a modified 1D performance prediction model, which considers the effects of splitter vane length and blade number on impeller internal losses. The splitter vane length corresponding to optimum blade number is investigated to achieve the maximum efficiency of a mixed-flow compressor impeller with an extremely high hub/tip ratio. An empirical formula for calculating splitter vane length is proposed. CFD results show that blade number and splitter vane length have a complex coupling interaction which makes it inappropriate to be described by equivalent solidity or effective blade number. 1D results and CFD verification indicate that optimum full-length blade number is 42 and corresponding splitter vane length is 20% of full-length blade length at design flow rate. The impeller peak efficiency mainly depends on minimum loss superposition of blade loading, skin friction and tip clearance. With the increase of splitter vane length and blade number, blade loading loss and clearance loss decline while skin friction loss increases.

Blade element momentum theory for a tidal turbine

A key hydrodynamic difference between tidal current and wind turbines is the volume-flux constrained flow field in which tidal turbines operate and the resulting streamwise static pressure difference that develops in the flow passage. Blade Element Momentum (BEM) theory is extended to account analytically for the effects of blockage and the development of the static pressure difference in the flow passage and shows agreement in thrust and power predictions to within ±3% of equivalent blade resolved simulations. The confined flow BEM model is employed to study two different power capping strategies: varying the rotational speed with fixed pitch blades; and pitching the blades to feather at constant rotational speed. Pitch-to-feather achieves reduced thrust above rated flow speed which leads to a greater extractable resource than achievable with overspeed control, due to the feedback between device thrust and available tidal resource. Flow confinement is shown to reduce the flow speed at which rated power occurs, and increases the rotor loads and power below rated conditions. It is also shown that root bending moments, which affect fatigue damage rates, increase with flow confinement.

Design Space Exploration of a Beam Flexible Hub Concept for an Inside-Out Ceramic Turbine Using a Simplified Rotordynamic Finite Element Model

This paper presents a new flexible hub design for the inside-out ceramic turbine (ICT) rotor configuration. This configuration is used in microturbines to integrate ceramic blades in order to increase turbine inlet temperature (TIT), which leads to higher cycle efficiency values. The ICT uses an outer composite rim to load the ceramic blades in compression by converting the centrifugal loads of the blades into hoop stresses in the composite rim. High stresses in the composite rim lead to high radial displacement of the blades. This displacement is compensated by using flexible hub in order to maintain the contact with the blades. However, hub flexibility can lead to rotordynamic problems as heavy hub deformation will induce high stresses in it. Thus, stresses in the hub are induced by both rotordynamics and centrifugation, requiring a multi-objective design process, which has yielded geometries that limited, until now, the blade tip speed to 358 m/s. In this paper, a simplified rotordynamics finite element model of a flexible hub is developed to allow quick design iterations. Using the model, a design space exploration of this hub concept is done while considering centrifugation and rotordynamics. Experimental validation is conducted on a simplified ICT prototype up to 129 krpm, i.e., an equivalent blade tip speed of 390 m/s. Finally, predictions from the experimentally calibrated model show that the tested prototype hub could reach a blade tip speed of 680 m/s.

Research into aero acoustic characteristics of two-row impellers of the axial compressor

We have conducted numerical simulation of current in the axial impellers with a single-row and a two-row geometrically equivalent blade crowns with a density of blade crowns over average radius of 1...2.5. The pressure characteristics of impellers obtained at q(λ)=0.45…0.8 show that using the two-row impellers can improve the pressure of a stage over the entire range of operation. Under the flow-around modes that correspond to the maximum pressure, the degree of pressure rise increases by 10.5 %. The research results showed that the two-row impellers demonstrate the higher level of losses compared with the level of losses in the equivalent single-row impellers. We have obtained results of research into aero acoustic characteristics of subsonic two-row impellers of the axial compressor. The research results showed that the use of two-row blade crowns in the impeller makes it possible to reduce the level of acoustic pressure in the range of operation q(λ)=0.45…0.8 by 0.5 dB to 3.2 dB at a density of blade crowns over average radius of 1...2.5. The replacement of a single-row blade crown in the impeller of a stage of the axial compressor with the equivalent two-row blade crown could ensure the enhancement of aerodynamic loading on the stage and reduce acoustic emission of the compressor.

Calculation of sound power level of tandem axial fan

A numerical simulation of the flow in axial fans with single and tandem geometrically equivalent blade rows was carried out. During the research, the sound power level of the fans was calculated. The acoustic characteristics of the single fan obtained in the numerical experiment were compared with the results of the physical experiment. The divergence between the results of the physical and numerical experiments on the sound power level for the first harmonic is 0.08 %, for the second harmonic – 0.35 %. In order to reduce the acoustic emission, a 3D model of the axial fan with the geometrically equivalent tandem row was constructed. The results showed that at the fan rotation frequency of 900 rpm, the sound power level on the first two harmonics is reduced by more than 7 dB. Also, the change in the total sound power level for axial single and tandem fans in the rotation frequency range of 900 to 1,500 rpm was investigated. The fan with the geometrically equivalent tandem blade row has the total sound power level by 6.9...7.4 dB lower than the single fan. The use of the tandem axial fan allows improving acoustic characteristics

Influence of geometrical modeling on the results of numerical prediction for the centrifugal compressor with shrouded impeller

The overall perfomance of a centrifugal compressor prototype stage with shrouded impeller has been measured. Some factors influencing the numerical prediction accuracy and choke mass flow rate have been investigated numerically using different computational models generated by the component superposition method. A structure correction method using the equivalent blade thickness to replace the impeller fillet was proposed and verified. The main goal of this research was to find out a reasonable simulation strategy for the centrifugal compressor with shrouded impeller through assessing the influence of various fine structures and omitted treatments on the overall performance. A peak isentropic efficiency of 80.28% for the compressor stage was obtained experimently while the numerical model with the equivalent blade thickness correction achieved a peak efficiency of 82.02%. The results indicate that the shroud gap and seal, the impeller fillet as well as the blade machining error are the main geometric structure factors to influence the shrouded centrifugal compressor performance. The shroud gap leakage flow decreases the effective throat area of the shrouded impeller, which leads to the decrease of the choke mass flow rate, the acceleration of the fluid in the impeller passage and the reduce of the impeller diffusion ability. At a given exit pressure, the choke mass flow rate decreases with the increase of the impeller blade relative thickness. Using the equivalent blade thickness to replace the impeller fillet can make the compressor maintain an unchanged performance in the small mass flow conditions , but improve the numerical simulation accuracy in the large mass flow conditions.

A 3D analytical model for orthogonal blade-vortex interaction noise

A 3D analytical model of an Orthogonal Blade-Vortex Interaction (OBVI) for Counter-Rotating Open Rotor (CROR) tonal noise is investigated. The specific influence of two parameters taking into account the three-dimensionality of both the vortex velocity and the convection velocity within the rotor-rotor volume is addressed. The first step is to extract the vortex parameters from a recent unsteady Reynolds-Averaged Navier-Stokes computation and validate different vortex models. Lamb-Oseen and Scully vortices reproduce the behavior of the tip-vortex tangential velocity fairly well. Regarding the vortex axial velocity modeling, a Gaussian profile fits well with numerical results. On the one hand, the impact of the stream-tube contraction unbalances the lobes of the unsteady pressure with opposite phases produced by the OBVI event. This effect is larger than that of an equivalent blade sweep. On the other hand, adding the axial velocity deficit to the tangential one also unbalances the pressure lobes. Finally, from an acoustic point of view using Curle's acoustic analogy, both the stream-tube contraction and the axial velocity deficit have the same effect: they turn an acoustically-low efficient quadrupole into a strong dipole making these parameters fundamental for future CROR OBVI investigations.

Convective cooling model for aero-thermal coupled through-flow method

The aero-thermal coupled phenomenon is significant in the modern cooled turbine, and it is necessary to consider the cooling effect and predict the coolant requirement in the through-flow design. A new cooling model was developed for the aero-thermal coupled through-flow method in this paper to predict the temperatures of both the pressure and suction surfaces of the blade. Based on the given blade temperature limitation rather than the mean blade surface temperature in the formal cooling model, the coolant requirement prediction can be more accurate. The equivalent blade thickness and heat exchange area estimation methods were further developed for blades with different cooling structures, and the estimations were carried out for each calculation station instead of the whole blade. The cooled blade was divided into a few calculation stations, and the heat transfer was studied for each station. Three operating conditions for the NASA-Mark II vane were selected for the verification. The predicted temperatures of both the pressure and suction surfaces agree with the experimental data, and the calculation results for the subsonic conditions are more accurate than the one for the transonic conditions.

Blade Load Unsteadiness and Turbulence Statistics in an Actuator-Line Computed Turbine–Turbine Interaction Problem

The objective of this study is to investigate how different volumetric projection techniques used in actuator-line modeling affect the unsteady blade loads and wake turbulence statistics. The two techniques for the body-force projection radius are based on either (i) the grid spacing or (ii) the combination of grid spacing and an equivalent elliptic blade planform. An array of two National Renewable Energy Laboratory 5-MW turbines separated by seven rotor diameters is simulated for 2000 s (about rotor 300 revolutions) within a large-eddy simulation (LES) solver of the neutral and moderately convective atmospheric boundary layer (ABL). The statistics of sectional angle of attack (AOA), blade loads, and turbine power histories are quantified. Moreover, the degree of unsteadiness of sectional blade loads in response to atmospheric and wake turbulence is computed via a reduced frequency based on the rate-of-change in sectional AOA. The goal of this work is to make the wind energy community aware of the uncertainties associated with actuator-line modeling approaches.

Bit/rock interface laws in directional drilling

This paper deals with the formulation of global relationships between the forces and moments acting on a PDC drag bit and the kinematic variables describing the penetration of the tool into the rock. It considers the general situation where the bit penetration is characterized not only by an axial but also by lateral and angular components, as it is the case when drilling a deviated well with a bit tilted on the borehole axis. These interface laws serve as boundary conditions for the drillstring treated as a rod when modeling the propagation of the borehole. While the relationships between forces and penetrations assume the bit to be reduced to a point, determination of the parameters of the interface laws requires information about the bit geometry and the cutter characteristics, as well as knowledge about the local cutter/rock interaction. We show that it is actually possible to construct the interface laws by using the device of an equivalent blade, which embodies the properties and geometry of the bit. The use of this device eliminates the need to consider the interaction of each individual cutter with the rock during one revolution of the bit. The approach is illustrated for a cylindrical bit. In this case, the interface parameters and their dependence on the bit tilt can be determined in closed form.

Aerodynamic study of a 'humpy' propeller

A detailed aerodynamic study of a ‘humpy’ high-speed propeller is presented. This propeller is the result of a bi-disciplinary optimisation procedure and features blade segments of wider chord bordered by narrow segments. The aerodynamic consequences of these regions are investigated and correlated to the aeroacoustic properties by comparison to an equivalent blade without hump.

Composite blade damaging under impact

Composites materials are now being used in primary aircraft structures, and other domains because of numerous advantages. A part of a continuous in-flight operating costs, gas turbine engine manufacturers are always looking for ways to decrease engine weight. This is the case of compressor blades which have to satisfy, for example, the standard bird strike or debris in order to measure the crashworthiness. Bird strike impacts are actually among the most challenging loads that composite blades must accommodate. Thus for the further development of composite structures, it becomes important to have available predictive tools for simulating the response of composite structures under crash or impact loads, which will allow to evaluate damage state in the structure in function of time. A composites damage model, without mesh dependency, is presented, and allows to obtain agreement with impact experiment. Examples of finite element simulations for the impact response of blade based on this materials model are developped. These numerical results correspond to a bird strike on an equivalent composites blade, and insists on damage evolution in structure.

Analysis and Testing of Powered Tillage Blades

ABSTRACT FUNDAMENTAL design considerations for powered rotary tillage blades are presented and discussed. The relationship between blade angular velocity and the geometric dimensions of cutting edges is specified for tillage blades rotating counter to the direction of travel and assuming a typical forward speed for tillage. Analyses showed that a powered blade rotated op-posite to the direction of travel can be operated at relatively lower angular velocities than can one rotated in the direction of travel to achieve equivalent blade velocity and acceleration relative to the soil. Furthermore, a blade rotated opposite to the direction of travel requires relatively lower power to achieve equivalent blade velocities relative to the soil. Experiments revealed that, in order to minimize power requirements, the ratio of the tangential velocity of cutting edges on a blade divided by the ground speed should be as low as possible as long as a proper tillage action is obtained.

Parameter Identification Applied to Analytic Hingeless Rotor Modeling

It is known that dynamic rotor inflow has a substantial effect on rotor dynamic loads. Despite the complexity of the unsteady flow problem, simple analytical models can be made useful by identifying their parameters from transient response tests without performing flow measurements. Two analytical inflow models are studied: the first is based on an equivalent blade Lock number, the second is based on a time delayed unsteady momentum inflow. In preparation for the experimental data analysis, identifications from simulated test data and an eigenvalue analysis are performed. The experimental results show that the first analytical inflow model is accurate for rotor advance ratios of 0.4 and above. For lower advance ratios, the second inflow model provides better accuracy. Prediction studies with experimental data not used for the identification are performed to determine the accuracy of the mathematical models.

Diamond Drilling Model Verified in Field and Laboratory Tests

A simple, theoretical blade-type approach to the mechanical aspects of how a diamond bit drills has been developed. The technique is incorporated into a mathematical model that yields a bit-design philosophy essential to the understanding of diamond-bit mechanical philosophy essential to the understanding of diamond-bit mechanical design variables. Introduction For more than 25 years, most diamond bits have been used in the oil field without the purchaser understanding how they drilled or the significance of the design variables. In many cases, it appears that the industry has learned what bit type drilled best by a trial-and-error procedure. To gain an understanding of the effect of the procedure. To gain an understanding of the effect of the mechanical design variables, a simplified model was developed and verified by laboratory and field tests. Through proper application of the model, bit penetration rate can be improved up to 25 percent while penetration rate can be improved up to 25 percent while lowering the bit cost and over-all drilling cost per foot. The Model The model describes the mechanical aspects of any diamond bit. Because of the complexity of the hydraulic component of diamond drilling, no attempt was made to use equations to describe the cleaning effects. The equations developed assume "perfect cleaning;" however, that condition is not necessary to apply the model. In developing a universal model for understanding the mechanical aspects of bit design, all equations are based on a flat-bottom bit with round, surface-so diamonds. The bit is modeled to be a combination of several "equivalent blades," where each makes a series of cuts in a stair-step fashion as the bit rotates. Fig. 1 shows the bottom of a bit with enough stones in each quadrant for their combined cutting action to make a uniform depth of cut from the center of the hole to the gauge section, forming an equivalent blade. The lower section of Fig. 1 shows an expanded cross-section of the gauge of the hole with the position of the four blades at various times during one rotation. For the four-blade bit, there are four diamonds that pass over the same point in each revolution. Therefore, the bit advance per revolution is four times the depth of cut of each blade. After traveling 90 degrees at a given depth of penetration, the diamonds reach the section removed by the preceding blade and then repeat the process by advancing into the formation. From a practical standpoint, however, the actual advance of each diamond is better represented by a spiral. Similarly, the diamonds on a particular blade would be laid out on a helix rather than being located within a given quadrant. The diamonds can penetrate the formation if the load applied to each diamond divided by the projected surface area of the diamond in contact with the formation exceeds the formation resistance. Fig. 2 shows a diamond drilling, while Fig. 3 shows the projected area in contact with the formation. When drilling. only Side 1 is in contact with the formation; however, both Sides 1 and 2 are in contact initially. Adjacent-blade diamonds work together to make a uniform depth of cut, as illustrated in Fig. 4 for the case of maximum diamond penetration. The number of diamonds working together at each radius provides redundancy that is equal to the number of equivalent blades in the bit. JPT P. 213

System Mode Shapes in the Flutter of Compressor Blade Rows

The problems associated with the prohibitive number of possible system modes for a fluttering compressor or turbine blade row are eliminated by the development that comprises the present report. The existence and uniqueness of extremely simple system flutter modes are proved for blade rows consisting of identical blades equally spaced about a common rotor. These simple system modes, if properly interpreted, have the effect of reducing by a factor of n the number of degrees of freedom necessary to analyze an w-bladed configuration. Stated differently, the system of n blades may be considered, with no loss of generality whatsoever, in terms of a single equivalent blade. The proof holds under any type of flow and any and all types of interblade coupling, so long as a linear analysis is permissible. Moreover, since it is the flutter-inception point that is of interest in predicting critical velocity or rotational speed, it may well be that the conclusions developed apply even to the onset of stall flutter. Practical application of the method to stall-flutter calculations would, of course, require the availability of aerodynamic stallflutter coefficients. The development is carried out first under the assumption of infinite rotor inertia or, in other words, constant rotor velocity. This restriction is then relaxed, and the treatment is expanded to permit torsional oscillations of the rotor itself. I t is proved that under certain conditions the assumption of infinite rotor inertia introduces no error whatsoever.