Quasi-steady Model Research Articles

The nonlinear behavior of generic tail fins for small wind turbines

This paper describes analysis and measurements of the yaw response of tail fins for small wind turbines. It is based on an extension of unsteady slender body theory (USBT) to cover non-slender fins and high angles of incidence, both of which make the theory nonlinear. We provide three main additions to the substantial literature on linearized USBT for tail fins. First, USBT is extended to high angles by modeling the nonlinear vortex dynamics. Second, the restriction to slender bodies is removed by modeling the chordwise load variation. Third, we consider the effect of time-varying wind speed. The extended theory is compared to wind tunnel measurements of the yaw behavior of delta, elliptical, and rectangular tail fins without a rotor and nacelle. The fins were released from initial yaw angles of −40° and −80°; the latter is of sufficient magnitude to show the importance of the nonlinear yaw dynamics. Generally good agreement was found between the theory and measurements, and the theory was shown to be more accurate than a “polar” or quasi-steady model which uses only the lift and drag of a delta planform. Of the three planforms, the rectangular one showed the lowest accuracy in terms of frequency but the damping was accurately predicted. Overall, the results demonstrate the importance of nonlinearity in the response of a yawing tail fin, particularly for the higher aspect ratio fins at large yaw angles.

Two independent mechanisms with distinct laws for the generation of drag force on accelerating plates

Acceleration of objects in fluids widely exists in biological propulsions and contains rich unsteady fluid mechanisms. In this paper, the instantaneous drag force on accelerating normal flat plates (circular, elliptical, square, and rectangular plates) in a wide range of dimensionless acceleration (a*=16∼2) is measured, and the underlying mechanism for force generation is investigated. At first, we find that the drag force coefficient generally scales with the square root of a* when a*<1.0, coinciding with the scaling law given by Reijtenbagh et al. (PRL. 2023,130,174001). However, the drag force coefficient more linearly scales with a* rather than a* when a*>1.0, thereby indicating acceleration plays two distinct roles on the force generation depending on a*. Moreover, two scaling laws are built to quantitatively describe the two distinct roles of a* on the drag force generation. Based on fluid impulse, the drag force is largely contributed by the added mass of the accelerating plates (added mass force) and vorticity generation fed by the shear layer on the edge of the plates (vortex creation force). When a*<1.0, the vortex creation force scales with a* and almost contributes to the total drag force. When a*>1.0, the added mass force scaling with a* contributes to most of the drag force. Furthermore, the two force generation mechanisms associated with acceleration (a*) are independent, and a criterion based on the energy ratio is proposed to identify the transition of the two force generation mechanisms. The present results uncover the role of acceleration in force generation and explain the inconsistencies of using one quasi-steady model in describing the force on accelerating plates.

Accuracy and Computational Cost Comparison of Numerical Flight Dynamics Reduced-Order Models

This paper compares several approaches to model the unsteady and nonlinear longitudinal aerodynamics of a generic unmanned combat air vehicle configuration based on computational fluid dynamics (CFD). Three different reduced-order models (ROMs) are implemented through unsteady simulations to predict the evolution of forces and moments during prescribed trajectories carried out at M=0.15. The first model investigates a linear quasi-steady model based on a first-order Taylor series expansion of the aerodynamic coefficients. The second one picks up the mathematical formulation of the first model but adds a dynamic coefficient in order to take into account the unsteady effect of rotation rate variations. Finally, the third model is built on indicial functions computed from positive step changes in the angle of attack or pitch rate. The unknown parameters of the first two models and the unknown indicial functions of the third one are obtained, respectively, from the study of forced oscillations and step motions. These prescribed trajectories are performed using unsteady Reynolds-averaged Navier–Stokes simulations coupled with a grid displacement tool. Two different methods are tested and compared to carry out the CFD mesh motions: an overset method and a full moving grid (FMG) method. The indicial functions obtained using the FMG method give results equivalent to those found in the literature in half the time of the overset method. To reduce the computational costs to set up the ROMs, the FMG method is preferred to the overset method. ROMs are then applied, and their predictions are compared with CFD simulations for prescribed trajectories with different angular rates and angles of attack. A study of instantaneous and overall accuracy associated with the implementation cost of the ROMs has allowed to show their strengths and their weaknesses. Similar results are observed at low angles of attack for the ROMs studied, while a major modeling advantage of the indicial method has been identified for higher angles of attack in the nonlinear domain.

A Quasi-Steady Model for Estimating the Rate of Frost Heave When Subjected to Overburden Pressure

The soil beneath buildings constructed in cold regions is affected by frost heave, causing the walls to crack and even the buildings to incline and collapse. Therefore, predicting the frost heave when subjected to overburden pressure is crucial for engineering buildings in cold areas. Utilizing the conservation equation of mass, Darcy’s equation, and the assumption that the pore water pressure at the top of a frozen fringe, denoted as uw, during the quasi-steady state can be approximately estimated using the Clapeyron equation, a quasi-steady frost heave rate model considering the overburden pressure was proposed. This study considered the difference in pore water pressure within the frozen fringe, which causes water to move from the unfrozen zone to the ice lens, where it subsequently accumulates and freezes into ice. The pore water pressure at the bottom of the frozen fringe, denoted as uu, can be estimated using the soil water characteristic curve (SWCC). The thickness of the frozen fringe was determined using the freezing temperature, segregation temperature, and temperature gradient. The segregation temperature was determined using the two-point method. Additionally, the model suggested that, when uw = uu, the movement of water stopped, leading to the end of frost heave. To validate the proposed model, three existing frost-heaving experiments were analyzed. The findings demonstrated that the estimated rates of frost heave of the samples closely matched the experimental data. Additionally, external pressure delayed water migration. This study can offer theoretical support for building engineering in cold regions.

Data-driven aeroelastic analyses of structures in turbulent wind conditions using enhanced Gaussian Processes with aerodynamic priors

Recent advancements in data-driven aeroelasticity have been driven by the wealth of data available in the wind engineering practice, especially in modeling aerodynamic forces. Despite progress, challenges persist in addressing free-stream turbulence and incorporating physics knowledge into data-driven aerodynamic force models. This paper presents a hybrid Gaussian Process (GPs) methodology for non-linear modeling of aerodynamic forces induced by gusts and motion on bluff bodies. Building on a recently developed GP model of the motion-induced forces, we formulate a hybrid GP aerodynamic force model that incorporates both gust- and motion-induced angles of attack as exogenous inputs, alongside a semi-analytical quasi-steady (QS) model as a physics-based prior knowledge. In this manner, the GP model incorporates the absent physics of the QS model, and the non-dimensional hybrid formulation enhances its appeal from an aerodynamic perspective. We devise a training procedure that leverages simultaneous input signals of gust angles, based on random free-stream turbulence, and motion angles, based on random broadband signals. We verify the methodology through analytical linear aerodynamics of a flat plate and non-linear aerodynamics of a bridge deck using Computational Fluid Dynamics (CFD). The standout feature of the presented methodology is its applicability for aeroelastic buffeting analyses, showcasing robustness when handling broadband excitation. Importantly, the non-linear hybrid model preserves its capability to capture higher-order harmonics in the motion-induced forces and remains applicable for flutter analysis, while incorporating both motion and gust angles as input. Applications of the methodology are anticipated in the aeroelastic analysis and monitoring of slender line-like structures.

Experimental investigation and quasi-steady modeling of nucleate boiling in mini-channel thermosyphons

This study explores the understanding of two-phase cooling in thermosyphons using a quasi-steady state methodology during the boiling process. A thermosyphon is built as a passive loop to dissipate heat with an evaporator and a condenser. The evaporator is made of multiple mini channels (hydraulic diameter of 1.54 mm, length of 260 mm with 7 × 2 internal ports for a Confinement number of 0.55) with HFO-1336mzz(E) as the working fluid. Different heat loads (500 – 4000 W) are generated directly on the external contact surface of the evaporator to create all the different stages of boiling, from monophasic regime to steady nucleate boiling with the Onset of Nucleate Boiling transition. The temperature evolution inside the evaporator is measured at different heights and compared with a theoretical assumption of a quasi-steady state. A characteristic time depending on critical factors such as thermal mass is determined to model the temperature during a generated heat load. A good agreement between experimental measurements and the quasi-steady model is shown. Thus, this study emphasizes tracking the temperature evolution over time within the system. This dynamic perspective offers a nuanced understanding of the system’s response to varying heat inputs, transient phases, and the onset of boiling. This characterized local behavior provides an original insight into the boiling appearing inside mini-channels. It is shown that boiling is initiated by nucleation at a few specific sites and then propagates up to a critical length due to high vapor generation, introducing a thermal lag during the boiling incipience.

Extraction of amplitude-domain characteristics from dynamic electric signals that cause large errors in electricity metering

Abstract Recent studies have shown that the power and current of high-power dynamic loads exhibit dynamic behaviors that cause large errors in electrical energy meters. Aimed at fast variations and large fluctuations in dynamic electric signals, this study examines a characteristic extraction method for small-time granularity and the impact of these characteristics on electrical energy meters. First, we constructed quasi-steady and dynamic model parameters for the dual-modal modulation models of current and power signals. Second, based on the two sets of signals sampled from the electrified railway traction substation and steelmaking arc furnace substation, we extracted quasi-steady and dynamic signal model parameters from fundamental active power signals. Third, we proposed three novel characteristic parameters by mapping the model parameter method, and extracted the four important characteristics. Finally, we designed a set of on-off-keying test signal experiments to determine the impact of the proposed characteristic parameters on the electric energy meter. The experimental results show that the electrical energy meter errors are sensitive to the proposed characteristic parameters, wherein the maximum impulse coefficient is the most sensitive characteristic of the EEM, which causes an error as large as −81.28%. The proposed characteristic parameters can be used as the input characteristic information of dynamic test signals for type testing and updating the test standards for electrical energy meters.

A general framework for the design of efficient passive pitch systems

Mitigating the impact of variable inflow conditions is critical for a wide range of engineering systems such as drones or wind and tidal turbines. Passive control systems are of increasing interest for their inherent reliability, but a mathematical framework to aid the design of such systems is currently lacking. To this end, in this paper a two-dimensional rigid foil that passively pitches in response to changes in the flow velocity is considered. Both an analytical quasi-steady model and a dynamic low-order model are developed to investigate the pivot point position that maximizes unsteady load mitigation. The paper focuses on streamwise gusts, but the proposed methodology would apply equally to any change in the inflow velocity (speed and/or direction). The quasi-steady model shows that the force component in any arbitrary direction can be kept constant if the pivot lies on a particular line, and that the line coordinates depend on the gust and the foil characteristics. The dynamic model reveals that the optimum distance of the pivot location from the foil increases with decreasing inertia. For a foil at small angles of incidence, the optimum pivot point is along the extended chord line. This knowledge provides a methodology to design optimum passively pitching systems for a plethora of applications, including flying and swimming robotic vehicles, and provides new insights into the underlying physics of gust mitigation.

Sensitivity analysis of parameters impacting the performance of an energy ship using airborne wind energy

This study assesses the impact of different model parameters on the power performance of energy ship systems using point-mass models, focusing on two operational modes. The first mode involves a kite operating in a pumping mode with adjustable tether lengths, aided by additional propellers for ship propulsion. It utilizes a quasi-steady kite model coupled with ship motion’s drag force and velocity triangles. The second mode features a kite pulling the ship, while underwater hydraulic turbines harness energy from ship velocity. Derived from a sail-based model, calculations deploy the force balance equation in line with ship motion, considering the drag forces of the ship and hydraulic turbines, alongside the propulsive force resulting from the kite’s interaction with the ship. The investigated parameters influencing the power performance include kite surface, ship length, wind speed, the angle between the ship’s motion direction and wind direction, and, for the pumping mode, ship speed. The power production of the propulsion mode is generally lower, with differences of at least 72%, depending on the combination of considered parameters.

Aerodynamic Analysis of Hovering Flapping Wing Using Multi-Plane Method and Quasi-Steady Blade Element Theory

In the design of flapping-wing micro-size air vehicles capable of hovering, wings serve as the primary source of hovering power, making the analysis of aerodynamics and aerodynamic efficiency crucial. Traditional quasi-steady models treat the wings as single rigid plane, neglecting the deformable characteristics of flexible wings. This paper proposes a multi-plane method that, in conjunction with various design parameters of flexible wings in a two-dimensional plane, analyzes their deformation characteristics under the assumption of multiple planes in three-dimensional space, and describes the deformation of wings during flapping. By combining the quasi-steady aerodynamic model, aerodynamic analysis of the deformed wings can be conducted. The relationship between the slack angle, wing flapping position, and wing deformation are analyzed, along with their effects on aerodynamics and aerodynamic efficiency. Experiments validate the deformation patterns of wings during flapping and compare the simulated aerodynamic forces with measured ones. The results indicate that wing deformation can be accurately described by adjusting the parameters in the multi-plane method and that the aerodynamic analysis using this method closely approximates the average lift results. Additionally, the multi-plane method establishes a connection between wing morphology and aerodynamic forces and efficiency, providing valuable insights for aerodynamic analysis.

Modeling Climate Characteristics of Qinghai Lake Ice in 1979–2017 by a Quasi-Steady Model

Lakes on the Qinghai Tibet Plateau (QTP) are widely distributed spatially, and they are mostly seasonally frozen. Due to global warming, the thickness and phenology of the lake ice has been changing, which profoundly affects the regional climate evolution. There are a few studies about lake ice in alpine regions, but the understanding of climatological characteristics of lake ice on the QTP is still limited. Based on a field experiment in the winter of 2022, the thermal conductivity of Qinghai Lake ice was determined as 1.64 W·m−1·°C−1. Airborne radar ice thickness data, meteorological observations, and remote sensing images were used to evaluate a quasi-steady ice model (Leppäranta model) performance of the lake. This is an analytic model of lake ice thickness and phenology. The long-term (1979–2017) ice history of the lake was simulated. The results showed that the modeled mean ice thickness was 0.35 m with a trend of −0.002 m·a−1, and the average freeze-up start (FUS) and break-up end (BUE) were 30 December and 5 April, respectively, which are close to the field and satellite observations. The simulated trend of the maximum ice thickness from 1979 to 2017 (0.004 m·a−1) was slightly higher than the observed result (0.003 m·a−1). The simulated trend was 0.20 d·a−1 for the FUS, −0.34 d·a−1 for the BUE, and −0.54 d·a−1 for the ice duration (ID). Correlation and detrending analysis were adopted for the contribution of meteorological factors. In the winters of 1979–2017, downward longwave radiation and air temperature were the two main factors that had the best correlation with lake ice thickness. In a detrending analysis, air temperature, downward longwave radiation, and solar radiation contributed the most to the average thickness variability, with contributions of 42%, 49%, and −48%, respectively, and to the maximum thickness variability, with contributions of 41%, 45%, and −48%, respectively. If the six meteorological factors (air temperature, downward longwave radiation, solar radiation, wind speed, pressure, and specific humidity) are detrending, ice thickness variability will increase 83% on average and 87% at maximum. Specific humidity, wind, and air pressure had a poor correlation with ice thickness. The findings in this study give insights into the long-term evolutionary trajectory of Qinghai Lake ice cover and serve as a point of reference for investigating other lakes in the QTP during cold seasons.

Unsteady three-dimensional rotational flamelets

A new unsteady flamelet model is developed to be used for sub-grid modeling and coupling with a resolved flow description for turbulent combustion. Difficulties with prior unsteady flamelet models are identified. The model extends the quasi-steady rotational flamelet model, which differs from prior models in several critical ways: (i) the effects of shear strain and vorticity are determined, in addition to normal-strain-rate impacts; (ii) the strain rates and vorticity are determined from the conditions of the environment surrounding the flamelet without a contrived progress variable; (iii) the flamelet model is physically three-dimensional but reduced to a one-dimensional, unsteady formulation using similarity; (iv) variable density is fully addressed in the flamelet model; and (v) non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. For both quasi-steady and unsteady cases, vorticity creates a centrifugal force on the flamelet counterflow that modifies the transport rates and burning rate. In the unsteady scenario, new unsteady boundary conditions must be formulated to be consistent with the unsteady equations for the rotating counterflow. Eight boundary values on inflowing scalar and velocity properties and vorticity will satisfy four specific relations and, therefore, cannot all be arbitrarily specified. The temporal variation of vorticity is connected to the variation of applied normal strain rate through the conservation principle for angular momentum. Limitations on the model concerning fluctuation of the interfacial plane are identified and conditions under which interfacial plane fluctuation is negligible are explained. An example of a rotating flamelet counterflow with oscillatory behavior is examined with linearization of the fluctuating variables.

A semi-analytical time-domain model with explicit fluid force expressions for fluidelastic vibration of a tube array in crossflow

It is widely acknowledged that fluidelastic instability (FEI), among other mechanisms, is of the greatest concern in the flow-induced vibration (FIV) of tube bundles in steam generators and heat exchangers. A range of theoretical models have been developed for FEI analysis, and, in addition to the earliest semi-empirical Connors' model, the unsteady model, the quasi-steady model and the semi-analytical model are believed to be three advanced models predominant in the literature. The unsteady and the quasi-static models share the merits of having explicit fluid force expressions and ease of being implemented but require more experimental inputs, whereas the semi-analytical model requires fewer parameters due to its analytical nature but is hard, if not prohibitive, to derive explicit fluid force expressions. Since the fluid force formulations set in the core of development of FEI models, the understanding and in particular the implementation of the semi-analytical model has been impaired by the nonexistence of explicit fluid force expression. This issue becomes more profound in time-domain analysis whereby the simple harmonic assumption is discarded. Here we report a new semi-analytical time-domain (SATD) FEI model with explicit fluid force expressions. The new model allows a consistent frequency-domain stability analysis and more importantly a truly time-domain response analysis. The theory was validated by calculating linear stability thresholds of two typical tube array patterns and comparing against reported experimental data. We then present a nonlinear time-domain analysis of a single loosely-supported tube with piece-wise linear stiffness. The nonlinear and nonsmooth dynamics was probed in details by utilizing various techniques, playing an emphasis on characterizing and distinguishing the chaotic vibration. We found that the system follows a quasi-periodic route to chaos. Such an in-depth study of the nonlinear dynamics of tubes in crossflow has never been reported in the context of SATD model. Our results enrich the theory and provide a different approach for linear and nonlinear dynamics of tube bundles, which are essential for the subsequent fretting wear analysis.

One-degree-of-freedom galloping instability of a 3D bluff body pendulum at high Reynolds number

The cross-flow swinging dynamics of a cube pendulum is studied experimentally in a flow at high Reynolds numbers (Re∼105) with a low free-stream turbulence intensity. A galloping instability is observed and results in the exponential growth of the swinging motion. The onset of galloping is found to be very sensitive to the static yaw angle of the cube. Despite the 3D geometry of the cube, flow mechanisms similar to the case of a square cylinder appear to govern the onset of the instability. A quasi-steady linear model of the motion is assessed to predict the stability of the pendulum.For the lowest reduced velocity investigated (U∗=18.5), unsteady phenomena arise during the saturation phase of the pendulum oscillations. From the analysis of the unsteady loads and the pressure distribution on the faces of the cube, an unsteady phase delay between the wake and the pendulum dynamics is identified. It produces an energy loss in the pendulum motion which favors its saturation.

CIBSE TM54 energy projections I: A case study using quasi-steady state modelling

CIBSE TM54 was recently revised and covers best practice methods to evaluate the operational energy use of buildings. TM54 is a guidance document that can be used for performance evaluation at every stage of the design and construction process, and during the occupied stage, to ensure that long-term operational performance aligns with the design intent. The main performance evaluation principles in TM54 are a step-by-step modelling approach and scenario testing, to improve the robustness of the design proposal calculations. The latest edition of this technical memorandum brings an updated perspective to the modelling approaches, including detailed Heating, Ventilation and Air Conditioning (HVAC) modelling and simulation. It also incorporates more detailed guidance around risks, target setting, scenario testing and sensitivity analysis. A case study approach is used to explore and demonstrate some important aspects described in TM54. TM54 recommends three modelling approaches (aka implementation routes) that a project can follow depending on its scale and complexity: using quasi-steady state tools; dynamic simulation with a template HVAC system; and dynamic simulation with detailed HVAC system modelling. As part of a series of three, this case study provides an application of the first implementation route: modelling using quasi-steady state tools. Practical Application This case study provides detailed guidance on undertaking CIBSE TM54 modelling and projecting design stage building performance. The study covers the interpretation and clarifications of how TM54 can be applied, through the quasi-steady-state modelling tools.

A simplified dynamic tool for building heating and cooling energy requirements estimation on a daily time scale

A persistent dilemma in building energy modeling consists of finding the proper trade-off between accurate results, data availability and limited modelling effort. In fact, quasi-steady state models require a limited number of inputs, however providing often rough results; dynamic tools are instead usually very accurate but involve a huge effort to obtain all the needed information and implementing it into the tool. In this context, we propose a simplified dynamic model for building heating and cooling demand estimation on a daily basis, according to the assessment of all the involved heat transfer mechanisms of the thermal zone. The required inputs are limited and comparable to those needed for other quasi-steady state models, but three tuning coefficients allow the simulation to be performed at the daily time scale. The proposed tool is here successfully tested on a wide set of test cases, differing for building structure, external climate, and occupants’ profile. In addition, reliable results are provided also in case of multi-year application and availability of a little amount of data for calibration, with average errors typically below 10% in daily cooling and heating energy requirement estimation, compared to benchmark demands. Finally, an example of application explores the application field of the tool.

Modeling of a liquid nitrogen droplet evaporating inside an immiscible liquid pool

Evaporation of liquid nitrogen in another immiscible liquid occurs in many industrial applications. Existing oversimplified one-dimensional (1D) quasi-steady models, although can quantitatively predict the evaporation rate by introducing an empirical fitting parameter, rely on configurations inconsistent with experimental observation so more rigorous models are required to get in-depth physical insights and improve modeling capability. This study proposes a 2D quasi-steady-state theoretical model, free of fitting parameters, that predicts the bubble growth rate and estimates the heat transfer rate for a liquid nitrogen droplet evaporating inside a liquid pool within the spherical bubble regime. The droplet's shape and position within a spherical bubble are determined by the equilibrium between the gravitational force and the upward pressure force resulting from the vapor flow between the droplet and the pool. The vapor layer thickness is calculated to be on the order of 10 microns. Notably, the primary contribution to heat transfer arises from the lower portion of the droplet, leading to local heat flux values up to approximately six times higher at the bottom compared to the top. The predicted bubble growth is quantitatively consistent with experimental data within the capillary spherical bubble regime. Furthermore, the overall heat transfer rate Q exhibits a distinct scaling relationship with the volume ratio between the bubble and droplet, yielding Q∼(Vb/Vd)−0.1.

Wind turbine rotors in surge motion: new insights into unsteady aerodynamics of floating offshore wind turbines (FOWTs) from experiments and simulations

Abstract. An accurate prediction of the unsteady loads acting on floating offshore wind turbines (FOWTs) under consideration of wave excitation is crucial for a resource-efficient turbine design. Despite a considerable number of simulation studies in this area, it is still not fully understood which unsteady aerodynamic phenomena have a notable influence on the loads acting on a wind turbine rotor in motion. In the present study, investigations are carried out to evaluate the most relevant unsteady aerodynamic phenomena for a wind turbine rotor in surge motion. As a result, inflow conditions are determined for which a significant influence of these phenomena on the rotor loads can be expected. The experimental and numerical investigations are conducted on a two-bladed wind turbine rotor subjected to a tower-top surge motion. A specialised wind tunnel test rig has been developed to measure the aerodynamic torque response of the rotor subjected to surge motions with moderate frequencies. The torque measurements are compared to two free-vortex-wake (FVW) methods, namely a panel method and a lifting-line method. Unsteady contributions that cannot be captured using quasi-steady modelling have not been detected in either the measurements or the simulations in the covered region of motions ranging from a rotor reduced frequency of 0.55 to 1.09 and with motion velocity amplitudes of up to 9 % of the wind speed. The surge motion frequencies were limited to a moderate range (5 to 10 Hz) due to vibrations occurring in the experiments. Therefore, a numerical study with an extended range of motion frequencies using the panel and the lifting-line method was performed. The results from both FVW methods reveal significant unsteady contributions of the surge motions to the torque and thrust response that have not been reported in the recent literature. Furthermore, the results show the presence of the returning wake effect, which is known from helicopter aerodynamics. Additional simulations of the UNAFLOW scale model and the IEA 15 MW rotor demonstrate that the occurrence of the returning wake effect is independent from the turbine but determined by the ratio of 3P and surge motion frequency. In the case of the IEA 15 MW rotor, a notable impact of the returning wake effect was found at surge motion frequencies in the range of typical wave periods. Finally, a comparison with OpenFAST simulations reveals notable differences in the modelling of the unsteady aerodynamic behaviour in comparison to the FVW methods.

Using the petiole of the miriti palm for the core of a small wind turbine blade

In many small wind turbine blades, the interior space between laminate skins is filled by a material core. The mechanical properties of the core are much less important than its density, which must be low to reduce the moment of inertia as high inertia increases both the starting time of the turbine and the gyroscopic loads on the blades. In this paper, we use, for the first time, the petiole of the miriti palm (PMP) as the core of four small blades, in order to analyze its effect on turbine starting performance. PMP is abundant in the Amazon region and harvesting it does not destroy the palm because the petiole regrows; therefore, harvesting is fully sustainable and may well have a major role in increasing the sustainability on wind turbine manufacturing. We consider the benefits of using the easily worked petiole for the core in terms of manufacturing, as demonstrated by the construction of a 0.598 m blade. PMP is less dense on average than alternative materials, such as expanded polystyrene and balsa wood. The starting performance is an important issue for small wind turbines. It is evaluated using a quasi-steady model, in which blade element momentum theory is coupled to Newton's Second Law. The low density of the small blade made using petiole of the miriti reduces the starting time by 10% when compared with expanded polystyrene and 42% when compared to balsa wood.

Influence of fluidelastic vibration frequency on predicting damping controlled instability using a quasi-steady model in a normal triangular tube array

Researchers have applied theoretical and CFD models for years to analyze the fluidelastic instability (FEI) of tube arrays in steam generators and other heat exchangers. The accuracy of each approach has typically been evaluated using the discrepancy between the experimental critical flow velocity and the predicted value. In the best cases, the predicted critical flow velocity was within an order of magnitude comparable to the measured one. This paper revisits the quasi-steady approach for damping controlled FEI in a normal triangular array with a pitch ratio of P/d=1.375. The method addresses the fluidelastic frequency at the stability threshold as an input parameter for the approach. The excellent agreement between the estimated stability thresholds and the equivalent experimental results suggests that the fluidelastic frequency must be included in the quasi-steady analysis, which requires minimal computing time and experimental data. In addition, the model allows a simple time delay analysis regarding flow convective and viscous effects.