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Recent years have seen a renewed interest in rotary-wing aircraft, due to the emergence of urban air mobility. In the conceptual design of such aircraft, fast estimation of rotor performance is important. A challenge is that rotor performance models require a detailed description of the blade geometry, which is not always available at this stage. We have developed a new, robust method for rapidly computing optimal rotor designs, which is derived from blade element momentum theory. In this paper, we derive the rotor design method and prove its convergence for all reasonable model inputs. We verify the design method by comparing the optimal rotor designs it computes to those found by a nonlinear programming algorithm. Thousands of numerical experiments yield relative errors of less than 13 and 5% in terms of the chord and twist profiles, respectively, and less than 0.3% in terms of efficiency, thrust, torque, and power coefficients. In addition, the design method computes optimal designs 170 times faster compared to the nonlinear programming algorithm. Based on these findings, we expect this new rotor design method to be useful in the conceptual design of rotary-wing aircraft. [ABSTRACT FROM AUTHOR]

Ignition delays were systematically measured in a DI diesel engine under wide ranging and various engine operating conditions, including engine speeds, fuel injection pressures, intake gas temperatures, intake gas pressures, and intake oxygen concentrations changed with EGR. Empirical equations to predict the ignition delay based on the Arrhenius equation with and without the Livengood-Wu integral and multiple regression analysis of the experimental results. The simple equation assuming constant conditions during the ignition delay without the Livengood-Wu integral can accurately predict the ignition delay. However, the lack of generality has remained as the fuel injection pressure is directly included in the Arrhenius equation which should contain only the chemical parameters. To improve the generality of the equation, the ignition delay was separated into the initial physical process of the fuel spray breakup and the following chemical process. The start of the Livengood-Wu integral was set at the breakup time of liquid fuel jet assuming that the chemical reactions do not occur before the fuel spray breakup, and that the physical factors are directly involved in the physical processes and indirectly in the chemical processes. The fuel spray tip dynamics based on Wakuri's momentum theory was introduced to express the changes in the conditions in the fuel spray during the ignition delay. The ignition delay can be accurately predicted by the equation with the Livengood-Wu integral and six parameters, including the breakup time, the mass flow rates of air and fuel at the cross section of the spray tip, the oxygen partial pressure, the engine speed, and the averaged in-cylinder gas temperature. The empirical equation predicted longer ignition delays at high ignition pressure conditions, and the accuracy was improved by performing a multiple regression analysis separately at each fuel injection pressure, suggesting unknown factors varying with the fuel injection pressures. [ABSTRACT FROM AUTHOR]

In order to study the aerodynamic interaction of the airfoil and jet flow, the free streamline model and the panel method are combined to establish a calculation method for the aerodynamic characteristics of the airfoil in a two-dimensional inviscid jet flow. Using the assumption of constant total pressure difference and free streamline model to determine the vortex strength and position of the jet boundary, the aerodynamic force of the airfoil is solved by the vortex panel method, and the whole process is calculated by relaxation iteration. Firstly, the relevant theory in this paper is introduced, and the convergence and effectiveness of the present method are also tested. Next, the influence of the position and the ratio of jet height to airfoil chord on airfoil aerodynamics in the jet flow are studied. Finally, the momentum theory is used to analyze the aerodynamic characteristics of the airfoil in the jet flow. The results show that the aerodynamic characteristics of the airfoil in the jet flow is quite different from that in the freestream. When the jet flow is deflected, the airfoil will not only generate lift but also drag. The method in this paper can be used to study the aerodynamic characteristics of the airfoil immersed in the jet flow.

Small-scale rotorcraft, such as multi-rotor UAVs, is widely used for various purposes. In particular, aerial vehicles' inspections of infrastructures such as bridges or tunnels are highly demanded. During inspection activities, aerial vehicles must approach their walls. In those situations, walls affect the airflow around the rotor and the rotor's aerodynamic characteristics. This study aims to understand and model the wall effect that appears when the rotor approaches the wall and to develop a compensation method for the wall effect. We focused on the ceiling wall effect in this paper. A horizontal velocity of the air is induced upstream due to air intake from the surrounding region if the rotor approaches the ceiling wall. In this paper, model of the change in induced speed, thrust, and required power due to the ceiling wall effect was developed based on momentum theory, considering the airflow in the direction parallel to the ceiling wall induced near and upstream of the rotor disk surface. The effectiveness of the proposed method is demonstrated by comparing the experimental results of the thrust ratio at constant power and the thrust ratio at constant power. [ABSTRACT FROM AUTHOR]

The popular axial momentum theory relies on the steady, incompressible, axisymmetric, and inviscid flow through a so-called actuator disk. The most important result of this theory is the famous Betz-Joukowsky limit, stating that the maximum power coefficient achievable by an open disk is limited to 16/27. Generally, this value is obtained assuming a priori that the disk is radially uniformly-loaded and the flow is axially one-dimensional. This, however, does not prove that the uniform type is the optimal load, or else that it returns the maximum value of the extracted power. For this reason, this paper preliminary shows that 16/27 is the exact value of the maximum power coefficient of a uniformly loaded disk, even if the flow is not assumed as one-dimensional. Then, it proves, using a calculus of variation approach, that the radially uniform load is optimal. The proof refers to an approximate classical local form of the axial momentum equation. Finally, the paper points out that, since the proof of the Betz-Joukowsky limit relies on this simplifying assumption, the exact evaluation of the optimal radial distribution of the disk load, leading to the maximum value of the power coefficient, is still an open question. [ABSTRACT FROM AUTHOR]

The fuel injection in diesel engines have a significant effect on the engine performance. But there is little knowledge on the characteristics of dispersion of liquid phase concentration. The purpose of this study is to clarify the dispersion process of the liquid phase of diesel spray through quantitative analysis of the liquid phase concentration distribution in non-evaporating diesel spray. In this paper, a quantitative analysis method of the liquid phase concentration of diesel spray under non-evaporative conditions is developed. The cross-sectional mass flow of the fuel was obtained using the momentum theory from the measured concentration distribution of the liquid phase with the laser induced fluorescence method. The relationship between the fluorescence intensity and the liquid phase concentration was estimated. In addition, a scheme was developed to account for the attenuation of the laser light and fluorescence, which results in a quantitative spatial distribution of the liquid phase concentration. Using this method, the dispersion process of the liquid phase in diesel spray was evaluated.

Windmills were developed to a high degree between their initial European use in the twelfth century and the twentieth century when mathematical analysis was first applied to optimise the design of their sails. It led immediately to the concept of twisted sails in which the weather angle decreased with radius. Various theories were tested experimentally by Smeaton, who found twisted sails to be better than common sails but less good than the Dutch sails then normally used. A century passed before Rankine applied Newton's laws of motion to derive their power and efficiency (power coefficient). Annular windmills were developed in both Britain and the United States where they were extensively tested by Perry, who found them as efficient as Smeaton's sails. In the twentieth century, Lanchester, Betz, and Joukowski independently derived an upper limit for windmill power coefficient and this, combined with aerodynamic theory and streamlined aerofoils led to the development of the modern wind turbine. [ABSTRACT FROM AUTHOR]

A design and optimization procedure of simplified wind turbine rotors for small-scale applications is presented. The need for this research has arisen from the recent national initiative of the government of Sri Lanka titled 'Battle for Wind Energy' in promoting small scale grid connected wind plants for electricity customers under Net Metering scheme. The main objective of this research is to assist local developers to design optimum rotors for given electrical generators (as determined by customer requirements), suitable for wind characteristics at specific locations. Another objective is to enhance local manufacturing capabilities by providing a design option of a simplified rotor blade geometry. A study on the correlation between population density of electricity customers and wind energy potentials was carried out to categorize the demand centres based on wind energy potentials in proposing series of small-scale wind turbine designs. A unique and improved rotor design procedure is presented which attempts to match the point of maximum performance of a rotor (design tip speed ratio) with the design wind speed of a given location by considering generator performance. The new design procedure showed successful convergence on a unique blade diameter for each rotor configuration that allowed the design tip speed ratio to match the design wind speed. The performance evaluation of rotor designs showed that high solidity rotors work better on the low wind potential region while low solidity rotors dominate medium and high wind potential regions. The performance reductions of simplified rotor designs are not significant and therefore would be an effective way to enhance value addition through local manufacture. • Lack of a rotor design procedure that considers generator performance. • Lack of a rotor design procedure for blades with an optimum simplified geometry. • Geographical mismatch between high resource sites and location of electricity consumers in Sri Lanka. • Lack of optimized small-scale wind turbine designs for sites with different wind potentials in Sri Lanka. • Limited opportunities for local manufacture in Sri Lanka. • Identification of geographical locations most suitable for promoting small-scale wind turbines. • Creation of rotor design procedures for optimized and simplified blade geometries considering generator performance. • Creation of optimized and simplified wind turbine rotor designs for different wind potential regions in Sri Lanka. • Suitable geographical locations for promoting small-scale wind turbines in Sri Lanka • Improved rotor design procedure considering generator performance • Design procedure for rotors with simplified blade geometry. • Optimized rotor designs for different wind potential regions in Sri Lanka • Simplified rotor designs for different wind potential regions in Sri Lanka [ABSTRACT FROM AUTHOR]

A prototype of a new physics-based wind resource assessment method is presented, which allows the prediction of upper limits to the performance of large wind farms (including the power loss due to wind farm blockage) in a site-specific and time-dependent manner. The new method combines the two-scale momentum theory with a numerical weather prediction (NWP) model to assess the “extractability” of wind, i.e., how high the wind speed at a given site can be maintained as we increase the number of turbines installed. The new method is applied to an offshore wind farm site in the North Sea to demonstrate that: (1) Only a pair of NWP simulations (one without wind farm and the other with wind farm with an arbitrary level of flow resistance) are required to predict the extractability. (2) The extractability varies significantly from time to time, which may cause more than 30% of change in the upper limit of the performance of medium-to-high-density offshore wind farms. These results suggest the importance of considering not only the natural wind speed but also its extractability in the prediction of (both long- and short-term) power production of large wind farms.

To simulate the motion of a rotor while accelerating during slow descent, a simulation model that corrects errors in data obtained experimentally is developed in this paper. The effect caused by acceleration is expressed as errors in induced velocity and external thrust force, and defined by two correction factors. Best-fit correction factors that provide good approximations for experimental flight data of a bamboo dragonfly are searched and the effectiveness of the method proposed is shown. [ABSTRACT FROM AUTHOR]

A new theoretical method is presented for future multi-scale aerodynamic optimization of very large wind farms. The new method combines a recent two-scale coupled momentum analysis of ideal wind turbine arrays with the classical blade-element-momentum (BEM) theory for turbine rotor design, making it possible to explore some potentially important relationships between the design of rotors and their performance in a very large wind farm. The details of the original two-scale momentum model are described first, followed by the new coupling procedure with the classical BEM theory and some example solutions. The example solutions, obtained using a simplified but still realistic NREL S809 aerofoil performance curve, illustrate how the aerodynamically optimal rotor design may change depending on the farm density. It is also shown that the peak power of the rotors designed optimally for a given farm (i.e. 'tuned' rotors) could be noticeably higher than that of the rotors designed for a different farm (i.e. 'untuned' rotors) even if the blade pitch angle is allowed to be adjusted optimally during the operation. The results presented are for ideal very large wind farms and a possible future extension of the present work for real large wind farms is also discussed briefly. [ABSTRACT FROM AUTHOR]

Abstract The paper presents a free-wake actuator disk model as applied to uniformly loaded propellers without slipstream rotation. The wake vorticity, originating from the disk edge, is represented by the superposition of a ring vortex sheet and a semi-infinite cylindrical vortex tube modelling the far wake. The shape and the density strength of the sheet are iteratively evaluated using two conditions. Firstly, the vortex sheet stability condition is strongly enforced, that is the static pressures just above and beneath the sheet are required to be equal. Secondly, the vortex sheet is constrained to align with the overall induced flow field, namely it is compelled to be a streamsurface. By doing so, the contraction of the wake is naturally accounted for in the model and no assumptions on its shape are made. The first part of this work deals with the theoretical foundations of the model and with the description of its discrete counterpart. The characteristics of the flow singularities used to model the flow induced by the wake are also presented. [ABSTRACT FROM AUTHOR]

Abstract The paper investigates the flow through a uniformly-loaded propeller by means of a free-wake ring-vortex actuator disk without wake rotation. In particular, the model represents the near wake by the superposition of N ring vortices, while the far wake is modelled by a semi-infinite vortex cylinder with uniform radius. This second part presents the iterative solution procedure of the method illustrated in the companion paper as well as the implementation of the wake boundary conditions. Then, the power coefficient, the ideal propulsive efficiency and the wake contraction ratio are presented as a function of the propeller thrust coefficient, thus revealing the relevance of the wake convergence effects. Finally, the method is used to investigate the main characteristics of the local flow field induced by such an actuator disk. [ABSTRACT FROM AUTHOR]

Entrainment process of surrounding fluid for a diesel spray is investigated based on the momentum theory and 1-D simple spray model developed by Musculus et. al. Entrained fluid distribution along the spray axis is theoretically estimated. The results show that the absolute value of entrainment velocity depends on axis location and is inversely proportional to the distance from the nozzle. Therefore, the large amount of entrained fluid comes from the upstream region near field of nozzle. 1-D simple spray model is performed for the same target and the effect of the injection rate on entraining process is clarified.

In the design of wind energy farms, the loss of power should be seriously considered for the second wind turbine located inside the wake region of the first one. The rotation of the first wind-front rotor generates a high-vorticity wake with turbulence, and a suitable model is required in computational fluid dynamics (CFD) to predict the deficit of energy of the second turbine for the given configuration. A simplified numerical model based on the classical momentum theory is proposed in this study for multiple wind turbines, which is proposed with a couple of tuning parameters applied to Reynolds-averaged Navier-Stokes (RANS) analysis, resulting in a remarkable reduction of computational load compared with advanced methods, such as large eddy simulation (LES) where two parameters reflect on axial and rotational wake motion, simply tuned with the wind-tunnel test and its corresponding LES result. As a lumped parameter for the figure of merit, we regard the normalized efficiency on the kinetic power output of computational domain, which should be directed to maximize for the optimization of wind farms. The parameter surface is plotted in a dimensionless form versus intervals between turbines, and a simple correlation is obtained for a given hub height of 70% diameter and a fixed rotational speed tuned from the experimental data in a wide range.

A new unsteady three-dimensional aerodynamic performance prediction approach is established to achieve fast and accurate prediction of the unsteady aerodynamics of cycloidal propellers. This model is developed by the coupling of momentum theory, lifting-line method, free wake model, and the Leishman--Beddoes semi-empirical dynamic stall model. The overall calculation process includes two parts. Firstly, to reduce the computational time and improve the computational convergence, the momentum theory is coupled with the Leishman--Beddoes semi-empirical dynamic stall model to predict a uniform inflow velocity through the cycloidal propeller disc, which is set as the initial induced velocity for iterations in the subsequent process. Then, the blade aerodynamic model, which couples the unsteady lifting-line method with the Leishman--Beddoes dynamic stall model, is used to calculate the unsteady aerodynamic response of blades. The wake of cycloidal propeller is represented by a serious of finite-length shed and trailing vortex elements, and the free wake model is utilized to model the dynamics of cycloidal propeller wake. Predictions from the present model are shown to be agreed reasonably well with the overall experimental data and the computational fluid dynamics results, both in terms of the aerodynamic performance prediction of cycloidal propeller and instantaneous blade force variations. [ABSTRACT FROM AUTHOR]

Wind tunnel experiments are performed to investigate the aerodynamic characteristics of a quadrotor helicopter in a uniform flow. At first, the thrust and drag coefficients of a single rotor under low-Reynolds number conditions are measured to deduce the basic design parameters of the rotor. Second, the aerodynamic interference between two rotors in a tandem configuration is investigated. It is experimentally found that the thrust coefficient of the rear rotor is a maximum of 11% lower than that of the front rotor during forward flight. Moreover, it is found that the interference effect of the front rotor on the rear rotor can be predicted qualitatively using a theoretical formula on the basis of the Biot-Savart Law. Finally, it is shown that the theoretical predictions of the thrust coefficient and drag coefficient agree well with the experimental results of a quadrotor helicopter model within limited ranges of the inflow ratio and advance ratio. [ABSTRACT FROM AUTHOR]

The paper provides a verification of the well-known momentum theories by comparing their results with those of a semi-analytical method based on the exact solution of the flow through an actuator disk. In fact, many error sources are disseminated in these theories. Specifically, the axial momentum balance is diffusely applied in an approximate differential form, and several linearization are customarily introduced in the equations of the motion. In the present study, an analytical formulation of these two kinds of errors is provided and a set of data generated with controlled accuracy is used to quantify them both in terms of global (power coefficient) and local (axial velocity at the disk plane) quantities. The overall errors increase by increasing the thrust coefficient and decreasing the tip speed ratio. Although the errors can be generally considered small in terms of global performance coefficients, the differences between the two methods are significant when looking at local quantities. In particular, for the cases presented herein, the momentum theory is shown to overestimate the axial velocity at the tip and at the disk centre regions and to underestimate this velocity elsewhere. For low values of the tip speed ratio, an underestimation also occurs in the zone near to the disk centre. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]