Blade Frequency Research Articles

Pressure Fluctuation Characteristics of High-Speed Centrifugal Pump with Enlarged Flow Design

The pressure fluctuations of high-speed centrifugal pumps are the hotspot in pump research. Pressure fluctuations is differ for different structural designs and flow structures. High-speed centrifugal pumps are usually designed to increase efficiency with an enlarged flow design at a low specific speed, which changes the structure of the pump. In order to analyze the pressure fluctuations of a high-speed centrifugal pump with an enlarged flow design, the pressure was measured, and the flow field of the pump was simulated with different flow rates. Through analysis, we found that pressure fluctuations varied periodically and was consistent with the blade frequency. The pressure fluctuations at the guide vane and the interference region were also closely related to the vortices at the impeller outlet, which changed differently at different flow rates. The results showed that the high-speed centrifugal pump with an enlarged design had better performance at a large flow rate. The results in this paper can provide reference for the design of a pump that should be designed with the enlarged flow method.

Icing condition prediction of wind turbine blade by using artificial neural network based on modal frequency

Wind turbines are increasingly installed in cold regions because of better wind resources. In these regions, high humidity and low temperature in winter increase the risk of ice accumulation on wind turbine blades. Different icing location and icing mass will lead to different natural frequency variation. In order to obtain an explicit relationship between the natural frequency of the iced blade and icing mass as well as icing location, the natural environment icing experiments and iced-blade modal experiments are carried out aiming at a 2 kW wind turbine respectively. In these experiments, the ice accumulates on the blade tip, blade middle, blade root or the whole blade respectively. The relationships between the first four-order natural frequencies of the iced blade and icing mass are constructed under four icing cases. Two artificial neural networks are used to predict the ice location and ice mass of the iced blade based on the established relationships in this paper. 335 data sets are generated to train the Back Propagation (BP) neural network and the Radial Basis Function (RBF) neural network. 12 groups of random mass samples are used to test the prediction ability of two neural networks. The prediction results show that the relative percentage error of local region (Elocal) icing is higher when a small amount of ice accretes on the blade. However, it decreases when more ice accretes on the blade. The mean relative percentage errors of the whole icing blade (Ewhole) predicted by BP and RBF neural network are all less than 7.5% when all three zones of blade are covered by ice. The mean Ewhole using the BP neural network is 2.83%, which is lower than that of the RBF neural network. The proposed method is also demonstrated on the 2 MW wind turbine blade data by using Finite Element Method (FEM), and the mean Ewhole using the BP neural network is 13.21%.

Numerical and experimental study in pressure pulsation and vibration of a two-stage centrifugal pump under cavitating condition

Instantaneous cavitating turbulent flow in a two-stage centrifugal pump with diffuser was simulated using a hybrid RANS/LES model and rotating corrected-based cavitation model in this paper. The predicted results of numerical simulation were in good agreement with the experimental results. The mechanism of pressure pulsation in the two-stage centrifugal pump was discussed. Some representative main frequencies of pressure pulsation such as main blade passing frequency, sub-blade passing frequency and intersection frequency of impeller blade and diffuser blade were analyzed systematically. Uncertainty estimation was used to ensure the accuracy of experimental results and it was also used to analyze the variation of pressure pulsation and vibration signals at different positions with the intensification of cavitation degree in the centrifugal pump. According to the results of uncertainty estimation, the center frequency of 1/3 octave band and the root mean square method were used to evaluate the energy change of the pressure pulsation signals and vibration signals at different frequency bands as the cavitation number decreases. The characteristics of pressure pulsation and vibration signals at different positions were analyzed in different frequency bands.

Analytical and numerical study on centrifugal stiffening effect for large rotating wind turbine blade based on NREL 5 MW and WindPACT 1.5 MW models

To pursue high efficiency for wind turbine and harness more energy from wind, the wind power generation system has been designed larger and larger. With length scale increasing, the natural frequency of blade will be lower and changing dramatically with rotational speed, which will threaten the stability of the blade and turbine. However, in the previous research, the parametric, analytical, and quantitative study of centrifugal stiffening effect is rare to see. As a result, the current research has comprehensively studied the centrifugal stiffening effect on the structural characteristics of large wind turbine blade. Specifically, the equivalent rotating wedge beam model has been proposed for composite wind turbine blade. Based on the proposed wedge beam model and Rayleigh-Ritz method, the natural frequency variation curve has been derived and verified by ANSYS 3D simulation results. The parameters, including blade length, stiffness-mass ratio, and aspect ratio, affecting the natural frequency curve have been uncovered and analysed. It was found that the centrifugal stiffening effect has a great impact on the fundamental frequency of blade, e.g. 10% for NREL 5 MW, while it has less impact on other modal frequencies. The variation curve of fundamental natural frequency can be approximated by parabola. The product of the parabola curvature and fundamental frequency is found to be approximately constant for both NREL 5 MW and WindPACT 1.5 MW turbine blades. This research will provide guidelines for the resonance avoidance design of large wind turbine blade in the future.

Analysis of Flow Field Characteristics and Pressure Pulsation in Horizontal Axis Double-Runner Francis Turbine

Horizontal axis double-runner Francis turbines have great advantages in the development of small hydropower plants, but the arrangement of double runners aggravates the complexity of the water flow between runners, and the mutual influence of the two runners cannot be ignored. In order to explore the relationship between the performance and the internal flow field and investigate the pressure pulsation characteristics of the double-runner Francis turbine, the steady and unsteady numerical analysis of the full flow channel of a prototype turbine was carried out based on the Realizable k-epsilon model and the polyhedral mesh method. The results show that the relationship between the average efficiency of the two runners and the flow difference between the runners is negatively correlated. As the flow rate difference between the runners on both sides increases, the average efficiency of the runners decreases. The draft tube flow of a horizontal-axis turbine has a profound effect on the flow field characteristics in the runner. When the working conditions change, the turning and converging timing of the mainstream at the outlet of the two runners will change. The movement of the mainstream promotes the change in location of the dead water zone. The existence of the vortex zone makes the pressure distribution at the outlet of the runner uneven, which is an important reason for the asymmetry of the flow in the runner. The analysis of pressure pulsation and its frequency spectrum shows that when the working conditions change, the low-frequency, strong pressure pulsation area on the surface of the guide vane will regularly migrate between the two runners, while the high-frequency pressure pulsation that occurs in the bladeless zone will dissipate in the runner. The doubling of the blade frequency on the pressure surface and back surface of the blades gradually attenuates with the increase of frequency. The pressure pulsation attenuation on the surface of the high-position blade conforms to the linear law, and the attenuation of the pressure pulsation on the surface of the low-position blade conforms to the exponential law. The research in this paper provides a certain reference value for revealing the flow field mechanism and pressure pulsation characteristics of the double-runner Francis turbine.

Simulations of 10MW wind turbine under seismic loadings

In this study, a shell-based finite element model based on Technical University of Denmark 10MW reference wind turbine (DTU 10 MW RWT) is used to study its dynamic responses under seismic loads. The natural vibration frequencies of blades and wind turbines from this study and the results from the literature Bak et al. (2013) are compared. The difference in natural vibration frequencies of the blades arises from simple assigned orientation in composites blades in Bak et al. (2013). The differences in natural vibration frequencies of the wind turbines are suggested to be due to shell elements used in this study whereas beam elements are used in Bak et al. (2013). The built shell-based finite element model of DTU 10MW reference Wind Turbine is then subject to artificially generated earthquake converted from codes of European union earthquake response spectrum. The simulation results show that the foundation has a significant impact on the responses of DTU 10 MW RWT. That is, the DTU 10 MW RWT suffers less stress in the flexible foundation than in the more rigid foundation . The results also show that neglecting the self-weight effect could significantly underestimate the dynamic responses of wind turbines under seismic loadings. This study suggests that shell-element based model should be used in company in the process for certification.

Stroboscopic aliasing in long-range interacting quantum systems

We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades' rotation; the second is akin to the optical appearance of the helicopter blades moving in reverse direction. Analogously to other dynamically stabilized states in interacting quantum many-body systems, this stroboscopic aliasing is robust to detuning and excursions from a chosen set of driving parameters, and it offers a novel route for engineering dynamical n-tuplets in long-range quantum simulators, with potential applications to spin squeezing generation and entangled state preparation.

Empirical mode decomposition of ship hull pressure fluctuation induced by cavitating propeller

We report for the first time a cavitation-induced pressure fluctuation decomposition developed from empirical mode decomposition (EMD) [Huang et al., Proc. R. Soc. London, Ser. A 454, 903–995 (1998)]. The idea is to decompose the nonlinear and non-stationary time series data into a finite and usually small number of “intrinsic mode functions” based on the local properties of the signal, which admit a well-behaved Fourier transform. With this transform, we can obtain frequency characteristics that give sharp identifications of imbedded structures. The cavitation evolution and excited pressure fluctuation around a cavitating propeller in the nonuniform wake are investigated using high-speed imaging and pressure sensors. By the EMD method, we separate the pressure fluctuations induced by different types of cavitation. The high frequency components of the pressure fluctuations are mainly caused by the collapse of sheet cavitation, followed by the shrinking and growth of sheet cavitation. Furthermore, the tip vortex cavitation leads to higher frequency but contributes less to pressure fluctuations. The periodical motion of the propeller contributes to the first blade frequency, and the pressure fluctuations induced by cavitation are superimposed on it.

Influence of blade leaning on hydraulic excitation and structural response of a reversible pump turbine

Blade leaning is commonly seen in the runner design of reversible pump turbines which operate under varying conditions. However, there is no certain law in determine the leaning mode and level. Considering performance, hydraulic excitation and structural response, five runners with strong rotational (RL+), rotational (RL), strong counter-rotational (CL+), counter-rotational (CL) and without (NL) blade leaning are compared under high-efficiency condition in pump mode and turbine mode. The head, efficiency, internal flow pressure pulsation and runner stress are comparatively studied. Among the five runners, CL+ runner is found has the highest efficiency as pump when RL+ runner has the highest efficiency as turbine. Pressure pulsation results show that the rotor-stator interaction region is the strongest pulsation source especially for runner and blade frequencies. In pump mode, pressure pulsation intensity decreases when blade leaning mode gradually changes from rotational to counter-rotational. In turbine mode, the NL runner has the strongest pressure pulsation intensity in runner and guide vane. Both rotational and counter-rotational leaning will reduce pressure pulsation. Velocity contours indicate that blade leaning will affect the velocity uniformity especially along rotational direction and cause stronger or weaker local hydraulic excitation. Under hydraulic excitation, RL+ runner suffers the highest equivalent stress as pump while CL runner suffers the highest equivalent stress as turbine. From rotational to counter-rotational blade leaning, the maximum stress moves on the crown from low pressure side to high pressure side. Considering hydraulic excitation and structural response, the strong counter-rotational leaning blade is found better in reversible runner design.

Relative cyclic component mode synthesis: A reduced order modeling approach for mistuned bladed disks with friction interfaces

A new reduced order modeling technique for nonlinear dynamics of mistuned bladed disks with friction interfaces is presented. Although various models have been developed to characterize the dynamics of either mistuned or frictionally damped structures, predicting the vibratory response of mistuned bladed disks with frictional interfaces remains challenging due to the:large size of refined industrial models,nonsmooth friction nonlinearities and amplitude dependent dynamics, andlack of cyclic symmetry properties.The Relative Cyclic Component Mode Synthesis (RCCMS) approach benefits from the application of relative coordinates prior to performing a reduction. Based on the new method, the kinematics of contact surfaces are first described in terms of relative displacements between contact node pairs, afterwards the Craig-Bampton Component Mode Synthesis (CB-CMS) technique is employed to reduce the model size. Implementation of relative coordinates halves the number of nonlinear unknowns in the reduced space and enhances the CB-CMS reduction basis by incorporating system-level stick modeshapes.The proposed approach admits introduction of either blade or sector frequency mistuning into the final reduced order model. In this way, the reduction is performed only once, which makes it favorable for statistical analyses. In addition, the mistuned ROM can be developed with minimal computational effort by using the sector model only.The developed RCCMS-based ROM is demonstrated on a finite element model of a mistuned bladed disk with blade-root friction damping. Numerical simulations reveal the excellent accuracy in predicting the nonlinear forced response.

Experimental Investigation of Bladed Disk Dynamics at Design Speed Under Synchronous Vibration

This work presents an experimental and computational investigation of a rotating bladed disk excited with air jets. The bladed disk is accelerated through critical speeds corresponding to specific engine orders of interest while air jets apply a constant forcing. These conditions induce synchronous vibrations in the blades. The experimental results were used to compute mistuning and damping values of the system, which were used in the computational analyses. This work uses a parametric reduced order model (PROM) that can adjust the system stiffness based on the rotational speed within the reduced space. Component mode mistuning was coupled with the PROM to create a mistuned model capable of capturing the mistuned system dynamics. Computational values for the blade frequency, amplitude, and damping were compared with experimental results to show how the computational model presented in this work can be used to characterize a rotating bladed disk.

Key Action Mechanisms of Intentional Mistuning

Intentional mistuning is a common procedure to decrease the uncontrolled vibration amplification effects of the (unavoidable) random mistuning, and to reduce the sensitivity to it. The idea is to introduce an intentional mistuning pattern that is small, but much larger than the existing random mistuning. The frequency of adjacent blades is moved apart by the intentional mistuning, reducing the blade-to-blade coupling and, thus, the effect of the random mistuning. In order to clearly show the action mechanisms of intentional mistuning, we focus in this work in a quite simple configuration: forced response of a blade dominated modal family in a mistuned rotor with linear material damping. The problem is analysed using the asymptotic mistuning model methodology. A more reduced order model is derived that allows us to understand the relevant parameters behind the effect of intentional mistuning, and gives a simple expression for the estimation of its beneficial effect. The results from the reduced model are checked against detailed FEM simulations of two mistuned rotors.

Modal analysis of Kaplan turbine in Haditha hydropower plant using ANSYS and SolidWorks

In this study, numerical analysis is conducted to investigate the failure modes in Kaplan turbine. All necessary steps for Kaplan turbine failure analysis are presented in this work using the modal analysis computational approach. The modal behaver analysis is carried out on a model of an existing Kaplan turbine blade, which is based on the existing turbine used in Haditha hydropower plant in Iraq. This work investigates the modal behavior of the blade of interest, which aid in predicting structural damage initiation. The Kaplan turbine blade is designed using the commercial software ANSYS and SolidWorks. To simulate the blade in operation, the blade is fixed from one end, and all degrees of freedom are measured. Moreover, the turbine blade is moved and rotated to simulate multiple operational conditions. Both mode shapes and natural frequencies are predicted and analyzed using the two aforementioned commercial software and the numerical formula involving the arrest Lanczos method. It is clear from the results that the natural frequency of the specified mode shape does not match with the natural frequency of the runner blade. Hence, there is no failure due to resonance phenomenon in this specific Kaplan turbine. The future work must investigate other aspect of the failure modes in such turbine, such as unbalance dynamic loading. The Results obtained from this study will help study the different possibilities for detecting the failure of the Kaplan blade by examining the modal behavior of the blade.

Experimental study on pressure fluctuation characteristics of model pump in Huangjinxia hydro-junction

In this study, the pressure pulsation characteristics of different position in the model pump unit are studied by experiments in combination with the Huangjinxia hydro-junction. The pressure pulsation of the inlet pipe, the volute outlet and the area between impeller and guide vane under different operating conditions were measured and analyzed. The results show that the maximum pressure pulsation amplitude of the pump is less than the guaranteed values by comparing the test results with the value requirement of the pump, which ensures the safe and stable operation of the pump. FFT transform is used to analyze the main frequency and amplitude of pressure pulsation. The main frequency and secondary frequency at the impeller inlet are respectively 15.29 and 7.65 times of the rotating frequency, which are 2 and 1 times of the blade frequency. The amplitude of main frequency at each monitoring point increases with the increase of head. The test results of pressure pulsation value meet the requirements of the contract in the whole pump operation rang.

Multi‐fidelity digital twin structural model for a sub‐scale downwind wind turbine rotor blade

AbstractThis paper presents the development of a multi‐fidelity digital twin structural model (virtual model) of an as‐built wind turbine blade. The goal is to develop and demonstrate an approach to produce an accurate and detailed model of the as‐built blade for use in verifying the performance of the operating two‐bladed, downwind rotor. The digital twin model development methodology, presented herein, involves a novel calibration process to integrate a wide range of information including design specifications, manufacturing information, and structural testing data (modal and static) to produce a multi‐fidelity digital twin structural model: a detailed high‐fidelity model (i.e., 3D finite element analysis [FEA]) and consistent beam‐type models for aeroelastic simulation. A key element is that the multi‐fidelity structural digital twin method follows the rotor from the stages of design, to manufacturing, then to the ground testing and field operation. The result of this comprehensive approach is an accurate multi‐fidelity digital twin structural model for the geometric, structural, and structural dynamic properties of the as‐built blade within a 1% match in mass properties, 3.2% in blade frequencies, and 6% in deflection. The different stages of processing this information within the methodology are discussed. The rotor examined is the SUMR‐Demonstrator (SUMR‐D), which was installed on the Controls Advanced Research Testbed (CART‐2) wind turbine at the National Wind Technology Center. The digital twin model developed here was utilized to design controllers to safely operate SUMR‐D in field tests, which are providing additional data for further evaluation and development of the multi‐fidelity digital twin structural model.

Numerical method for the vibration analysis of pre-swirl stator

ABSTRACT Marine transportation is continuously oriented to the reduction of fuel consumption and nowadays this is even more pronounced due to stringent rules and regulations leading to the reduced ship environmental footprint. For this purpose, there are different technical solutions and operational strategies at disposal. Typical technical solution that reduces ship total power needs (particularly for the propulsion) is the Energy Saving Device (ESD), i.e. special hydrodynamically designed appendage installed on the ship aft body. There are different types of ESDs such as ducts, flow control fins (FCFs), pre swirl stators (PSSs), propeller boss cap fins, Costa bulbs, rudder fins and so on, and their design procedures differ from each one to another. If PSS is considered, from a structural point of view, beside its yielding and buckling capacities relevant dynamic properties should be ensured in order to reduce fatigue risks and probable damage accumulation. Proper design from the vibration viewpoint includes natural vibration analysis of PSS fins and comparisons with relevant loadings in order to avoid frequency overlapping, i.e. resonant behaviour. In this work, the procedure is illustrated on the pre-swirl stator of a tanker. Several approaches to determine PSS fin natural frequencies were examined ranging from approximate procedures to sophisticated FEM approaches combined with different options to account for the effect of added mass. The obtained responses are compared with Vortex Induced Vibration (VIV) frequencies and propeller blade frequencies. Special attention is paid to VIV frequency determination where approximate expressions are validated against computational fluid dynamics (CFD) approach.

Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning

Abstract The last-stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes, unfavorable flow conditions may occur, which can lead to flow separation in some circumstances. Consequently, there is the risk of flutter in principle, particularly at nominal speed under part load conditions. For this reason, intentional mistuning is employed by the manufacturer with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits since only two different blade designs are allowed. In this sense, two different series of blades have been made. However, it is well known that small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional but unwanted deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference in this particular case. Focusing on the first flap mode, it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Again, only two different blade designs are admitted. Finally, mistuning patterns could be identified causing a tremendous increase of aerodynamic damping ratios. The robustness of the solutions found could be proved by superimposing additional random mistuning.

Influence of different types of volutes on centrifugal aviation fuel pump

High efficiency and low vibration are two hot topics in the field of fluid mechanics. In this paper, different spiral volutes are designed for centrifugal aviation fuel pump based on Velocity Coefficient Method. Physical fields under different operating conditions are simulated by computational fluid dynamics (CFD) software that solved the Navier–Stokes equations for three-dimensional flow (3D-RANS). And theoretical and simulation values of radial and axial forces are analyzed. The unsteady pressure fluctuation based on the steady results at the monitoring point is solved and Fast Fourier Transform (FFT) is used to obtain the influence of different volutes on pressure pulsation. The influence of three volutes on is analyzed and compared with the simulation. The results show that the double volutes improve significantly the large flow efficiency of the aviation fuel pump, 20%–30% higher than that of the single volute. The doubles volute can also optimize the radial force under the off-design condition. The radial force of the single volute fuel pump is 100 N. The radial force of the two types of double volute fuel pump is between 10 and 20 N. The three types of volute have no obvious influence on the axial force. Two types of double volutes provide excellent suppression of fuel pump pulsation spikes over the full frequency range. The peak value of single volute is mainly concentrated in the low frequency area below 2000 Hz. The blade frequency (170 Hz) and frequency multiplication are the main frequencies of the pulsation and the pulsation decreases rapidly in the high frequency area. The research results provide theoretical support for the design of aviation fuel pump with low pressure pulsation.

Mistuning Identification Technique Based on Blisk Detuning

The structural dynamics of turbomachinery bladed disks is of paramount importance to ensure safety and reliability. Due to their sensitivity to mistuning (that is, any deviation from nominal properties), bladed disk vibrations encountered in practical applications can be significantly amplified. Thus, it is important to identify mistuning of as-manufactured blisks so that computational models can be updated to include mistuning and used to accurately characterize the behavior of blisks in operating conditions. Several mistuning identification techniques based on bench tests have been developed. This paper focuses on the techniques based on blade isolation through mass detuning and modal testing: methods that require a simple experimental setup. The typical shortcoming of these methods is that they rely on measured blade frequencies as a proxy for blade mistuning. However, as presented in this study, it is often impossible to completely isolate a blade from the neighboring ones using mass detuning; as a result, the measured frequencies do not represent the cantilevered blade frequencies that many reduced-order models use to model mistuning. This is especially true for blisks in which the blade-to-disk stiffness ratio is not negligible: a scenario that could become more and more prevalent as the trend to design thinner disks to reduce blisk mass continues. A technique based on modal testing that is able to accurately identify mistuning by appropriately capturing the effect of residual blade-to-blade and blade-to-disk coupling is introduced in this paper. A validation is carried out using an academic blisk model and surrogate data, and the results demonstrate that the proposed method outperforms the direct use of blade frequencies as proxies for mistuning.

Effects of the hydrofoil blade on the pressure pulsation and jet‐wake flow in a centrifugal pump

AbstractA hydrofoil blade design (HBD) is proposed to suppress the unsteady pressure pulsations in a centrifugal pump. Numerical simulation is carried out using the SST k‐ω model to obtain the unsteady flow field in the pump both with HBD and the conventional blade design (CBD). The pressure pulsations with the two types of blade profiles are compared at the nominal flow rate, whereas the jet‐wake flow patterns and vortex structures are analyzed to clarify the effect of the HBD on the flow field. The pressure pulsation amplitudes at the blade frequency (fBPF) are significantly reduced with the HBD, especially near the volute tongue, with a reduction of 72%. It is evident that HBD can effectively suppress the pressure pulsation. It is for these reasons that the relative velocities in the jet region at the impeller outlet are reduced, and the velocity gradients between the pressure and suction side are decreased, which contributes to improving the flow uniformity at the impeller outlet. Besides, the vorticities at the impeller outlet are reduced, and the high energy vortices shedding from the blade trailing edge are restrained. The combined effects of the uniform flow field and low vorticities contribute to the reduction of pressure amplitude with the HBD. The findings would serve as a reference for the pump designs with low noise and vibration.