Aerodynamic Equations Research Articles

Structural design and dynamic characteristic analysis of adjustable badminton serving machine

System dynamics serves as a crucial foundation for evaluating the performance of mechanical auxiliary equipment. To enhance the stability and reliability of the badminton launch process, structural design and dynamic analysis were conducted on a mode-adjustable, precise control badminton serving mechanism. The combination of eccentric crank-slider mechanism, stretched springs, and electromagnets was used in mechanical structures, which could effectively effectively improve the smoothness of the badminton in the launching process. The virtual prototype of badminton serving machine was established and imported into ADAMS for dynamic simulation analysis, verifying the correctness of the serving and retrieving mechanisms. Using the aerodynamic equations, the trajectory of badminton movement under different working parameters was simulated and analyzed. The dynamic analysis results show that the design of the launching and catching mechanisms is scientific and effective. The launch angle and initial velocity are the key factors that determine the trajectory of the badminton.

АНАЛІЗ НАСЛІДКІВ ЕКСТРЕМАЛЬНИХ СИТУАЦІЙ НА БАЗІ ЧИСЕЛЬНИХ МОДЕЛЕЙ

The report considers some classes of numerical models that were built to predict the consequences of emergencies at industrial enterprises. The first class of models has been developed to predict chemical air pollution in case of accidental emissions of toxic substances. Modeling is carried out on the basis of the fundamental equations of aerodynamics and mass transfer. Difference splitting schemes are used for the numerical solution of the modeling equations. The second class of CFD models is designed to assess the risk of thermal damage to people in the event of thermal pollution of the air environment. The third class of models was developed to assess the risk of injury to people when a shock wave moves. To solve this problem Euler equations were used. Computer codes were developed on the base of proposed numerical models.

Dynamic response of multi-unit floating offshore wind turbines to wave, current, and wind loads

Motion of a multi-unit wind-tracing floating offshore wind turbine (FOWT) to combined wave–current and wind is obtained in the frequency-domain. The linear diffraction wave theory with a Green function for small current speeds and the blade-element momentum method are used for the hydrodynamic and aerodynamic analysis, respectively. A finite-element method is coupled with the hydrodynamic and aerodynamic equations to obtain the elastic responses of the FOWT to the environmental loads. The wind-tracing FOWT consists of three 5 MW wind turbines installed at the corners of an equilateral triangular platform. The platform is connected to the seabed through a turret-bearing mooring system, allowing the structure to rotate and face the dominant wind direction; hence, the multi-unit FOWT is called the wind-tracing FOWT. In this study, rigid-body responses of the wind-tracing FOWT to waves and wind are compared with those to combined wave, current, and wind loads for several current speeds and various wave heading angles. For a chosen current speed and wave heading angle, hydro- and aeroelastic responses of the wind-tracing FOWT to combined waves, current, and wind are obtained and compared with those of the rigid structure. Discussion is provided on the effect of the wave–current interaction on the motion and elastic responses of the wind-tracing FOWT. The numerical results show that under the rated wind speed, the motion of the wind-tracing FOWT is mainly governed by the wave-induced hydrodynamic forces and moments and the presence of current results in larger elastic motion of the FOWT to the environmental loads.

An axisymmetric characteristic model for enhancing prediction of centrifugal compressor characteristics

Rapid and accurate determination of compressor characteristic maps is essential for the initial design of centrifugal compressors in aircraft power systems. The accuracy of existing methodologies, which rely on combinations of loss models, varies significantly depending on the compressor’s geometry and operational range. This variance necessitates substantial experimental or Computational Fluid Dynamics (CFD) data for coefficient calibration. To address this challenge, this study presents an axisymmetric characteristic model for compressor performance assessment. This model incorporates the factors of blade angle, meridional passage area, and the radial deflection angle of meridional streamlines of the compressor. These factors are derived from fundamental aerodynamic equations encompassing mass, momentum, and energy conservation of the compressor. In contrast to conventional one-dimensional approaches, the proposed method reduces the number of loss coefficients and more effectively accounts for the impact of geometric alterations on centrifugal compressor properties. Furthermore, the model reduces dependence on experimental and CFD data. Efficacy of the model is validated using experimental data from four distinct types of centrifugal compressors. Correlation analysis reveals that the model’s coefficients can be expressed as functions of the ratio of the Reynolds number to the impeller tip speed. This ratio serves as a characteristic parameter for the design and optimization of centrifugal compressors. Consequently, the proposed method offers an efficient and accurate means for the quick computation of centrifugal compressor characteristics. This is of great significance for improving the efficiency of centrifugal compressors and reducing energy consumption.

Identification of the form of self-excited aerodynamic force of bridge deck based on machine learning

This paper introduces an intelligent identification method for self-excited aerodynamic equations. The method is based on advanced sparse recognition technology and equipped with a new sampling strategy designed for weak nonlinear dynamic systems with limit cycle characteristics. Considering the complexity of the experiment condition and the difficult a priori selection of hyperparameters, a method based on information criteria and ensemble learning is proposed to derive the global optimal aerodynamic self-excited model. The proposed method is first validated by simulated data obtained from some well-known equations and then applied to the identification of flutter aerodynamic equations based on wind tunnel experiments. Finally, reasons for the different sparse recognition results under different sizes of candidate function space are discussed from the perspective of matrix linear correlation and numerical calculation.

INVESTIGATION OF THE EFFECTIVENESS FOR PROTECTIVE SCREENS OF VARIOUS FORMS ON AIR POLLUTION REDUCTION

Problem statement. The task of evaluating the effectiveness of the use of protective screens of different geometric shapes to reduce the level of air pollution is considered. The data on the screen allow you to change the aerodynamics of the air flow and redirect the movement of polluted air away from the work areas in the other direction. The purpose of the article – study of the effectiveness of the use of protective screens of different geometric shapes to reduce the level of pollution, creation of a three-dimensional numerical model for the analysis of the effectiveness of the use of protective screens. Methodology. The method of physical experiment in laboratory conditions is used to analyze the effectiveness of screens of different geometric shapes. Three-dimensional equations of aerodynamics and mass transfer are used for mathematical modeling of impurity propagation in the presence of screens. The developed numerical model makes it possible to take into account the air flow velocity profile, atmospheric diffusion, the emission intensity of the impurity, the rate of gravitational sedimentation of the impurity in the air. For the numerical integration of the modeling equations of aerodynamics and mass transfer, finite-difference splitting schemes are used. Scientific novelty. Data on the effectiveness of the use of four protective screens, which differ in geometric shape, were obtained experimentally. Experimental data make it possible to carry out an initial assessment of the impact of various screens on reducing the level of pollution in working areas. A fast-calculating 3D numerical model was developed for solving problems of aerodynamics and mass transfer in relation to the problem of evaluating the effectiveness of the use of screens located in areas where atmospheric air pollution occurs. Practical significance. Experimental data make it possible to justify the choice of a protective screen near the highway or another area on the industrial site where the impurity emission takes place. A computer code was created on the basis of the developed mathematical model, which makes it possible to predict the intensity of air pollution in the presence of obstacles that change the aerodynamics and the direction of transport of impurities in the atmosphere. Conclusions. The results of the physical experiment allow us to imagine the regularities of the formation of areas of pollution near protective screens of different geometric shapes, the developed mathematical model allows us to estimate air pollution in areas where there are obstacles in the way of the movement of impurities. The results of physical and computational experiments are presented.

Математична модель розрахунку аеродинамічних сил, утворюваних роторним рушієм для пропульсивних крил

The subject of the study is the modeling and obtaining of aerodynamic characteristics and determining the aerodynamic forces acting on an aircraft with a propulsive wing using a mathematical model. The research is based on mathematical methods and proposes a comprehensive model that accurately describes the interaction of airflow with wing and rotor propulsion. The aim of this study is to find solutions for faster calculations and approximate analysis of wings and aircraft that use them, compared to CFD methods. The task is to find methods that can perform calculations based only on geometric shapes and a minimal set of data that can be obtained by the researcher. The article begins with a review of previous research in the field of aerodynamics, demonstrating the need for the development of new models to better understand the aerodynamic forces generated by wing and rotor propulsion. A new mathematical model is considered, using methods based on Bernoulli's equation and taking into account parameters such as wing shape, angle of attack, airflow velocity, and rotor propulsion characteristics. This article describes the mathematical equations and approaches used to model aerodynamic forces. They include physical laws such as Newton's laws, the conservation of mass and momentum, and basic aerodynamic equations. Validation of the model was conducted by comparing the obtained results with experimental data. To verify the correctness of the presented claims, a series of computational experiments using numerical methods are performed to calculate the dynamic characteristics for different wing and rotor propulsion configurations, and the obtained data are compared. Through careful experiments and data analysis, the research results are expected to provide valuable insights into the practical implementation of an integrated tangential fan system in a wing by evaluating its efficiency, limitations, and potential advantages. This work can help engineers determine optimal wing and rotor propulsion configurations to achieve better aerodynamic efficiency and ensure the desired flight characteristics. This research can make an important contribution to the development of aviation technology and to the improvement of aircraft with rotor propulsion. Conclusions: the article proposes a new mathematical model for calculating the aerodynamic forces generated by wing and rotor propulsion and demonstrates its speed and efficiency by comparing it with experimental data. This research is just the first step in creating a mathematical framework. To improve calculation results and enable automation for greater variability in shape, the panel-vortex method with the consideration of flow acceleration over panel surfaces is more suitable. However, even at this stage, the research results can contribute to the development and optimization of aircraft structures with propulsive devices embedded in the wing design.

Energy-Efficient Fixed-Wing UAV Relay With Considerations of Airframe Shadowing

Owing to their high energy efficiency, fixed-wing unmanned aerial vehicles (UAVs) can operate as aerial relays to provide long periods of uninterrupted connectivity. In such systems, however, airframe shadowing may occur (i.e. the blockage of a UAV communication link by the UAV’s own airframe) and can significantly degrade the communications performance. In this work, we propose a novel approach to optimize the trajectory of a fixed-wing UAV operating as a relay between a ground user (GU) and a ground base station (BS) to maximize the relay efficiency (defined as the ratio of the amount of relayed data to the consumed energy). We use the aerodynamic equations of the fixed-wing UAV to derive a semi-deterministic airframe shadowing model for loitering trajectories. Analytical expressions and simulation results illustrate the dependence of the airframe shadowing on the UAV’s attitude and speed.

An Aerodynamic Equation of State—Part III: Applications to Fluid Statics and Dynamics

<div>The aerodynamic equation of state is introduced in Part I and applies to selected aerospace systems. Part II applies it to the flapping of hovering and forward-flying biological fliers. This last Part III expands the aerodynamic equation of state by adding the potential energy term, assumed up to this point to be zero as the system and its trajectory is placed coplanar with an arbitrary reference potential plane. Part III applies the expanded equation of state to familiar and well-trodden fluid-static and fluid-dynamic cases selected from fluid mechanic textbooks.</div>

An Aerodynamic Equation of State—Part I: Introduction and Aerospace Applications

<div>In subsonic aircraft design, the aerodynamic performance of aircraft is compared meaningfully <i>at a system level</i> by evaluating their range and endurance, but cannot do so at <i>an aerodynamic level</i> when using lift and drag coefficients, <i>C<sub>L</sub> </i> and <i>C<sub>D</sub> </i>, as these often result in misleading results for different wing reference areas. This Part I of the article (i) illustrates these shortcomings, (ii) introduces a dimensionless number quantifying the induced drag of aircraft, and (iii) proposes an <i>aerodynamic equation of state</i> for lift, drag, and induced drag and applies it to evaluate the aerodynamics of the canard aircraft, the dual rotors of the hovering <i>Ingenuity</i> Mars helicopter, and the composite lifting system (wing plus cylinders in Magnus effect) of a YOV-10 <i>Bronco</i>. Part II of this article applies this aerodynamic equation of state to the flapping flight of hovering and forward-flying insects. Part III applies the aerodynamic equation of state to some well-trodden cases in fluid mechanics found in fluid-mechanics textbooks.</div>

An Aerodynamic Equation of State—Part II: Applications to Flapping Flight

<div>Part I introduced the aerodynamic equation of state. This Part II introduces the aerodynamic equation of state for lift and induced drag of flapping wings and applies it to a hovering and forward-flying bumblebee and a mosquito. Two- and three-dimensional graphical representations of the state space are introduced and explored for engineered subsonic flyers, biological fliers, and sports balls.</div>

Global Incremental Flight Control for Agile Maneuvering of a Tailsitter Flying Wing

This paper proposes a novel control law for accurate tracking of agile trajectories using a tailsitter flying wing unmanned aerial vehicle that transitions between vertical takeoff and landing and forward flight. The global control formulation enables maneuvering throughout the flight envelope, including uncoordinated flight with sideslip. Differential flatness of the nonlinear tailsitter dynamics with a simplified aerodynamics model is shown. Using the flatness transform, the proposed controller incorporates tracking of the position reference along with its derivatives velocity, acceleration, and jerk, as well as the yaw reference and yaw rate. The inclusion of jerk and yaw rate references through an angular velocity feedforward term improves tracking of trajectories with fast-changing accelerations. The controller does not depend on extensive aerodynamic modeling but instead uses incremental nonlinear dynamic inversion to compute control updates based on only a local input–output relation, resulting in robustness against discrepancies in the simplified aerodynamics equations. Exact inversion of the nonlinear input–output relation is achieved through the derived flatness transform. The resulting control algorithm is extensively evaluated in flight tests, where it demonstrates accurate trajectory tracking and challenging agile maneuvers, such as sideways flight and aggressive transitions while turning.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ РАВНОВЕСИЯ СТОЛБА СЖИМАЕМОЙ АТМОСФЕРЫ. ЧАСТЬ 1: СТАЦИОНАРНЫЕ РЕШЕНИЯ ДЛЯ ТЕМПЕРАТУРЫ

An analytical model of mathematical physics, which is implemented for an unbounded column of compressible atmosphere, is discussed. For the column, there are two equilibrium conditions, which are written in the form of a system of aerodynamic equations. The first condition is the classical condition of hydrostatic, which is derived from the equations of motion. The second one is derived from the continuity equation and arises due to temporal variations of air density. Two boundary conditions are selected near the solid surface: one is the magnitude of temperature and second condition is the magnitude of its vertical gradient. This allows us to consider the column without any restrictive conditions at some upper boundary. The analytical solution for adiabatic temperature can contain a sharp minimum at some height, above which the temperature rises with altitude. Herewith the temperature profile depends on the altitude linearly near the surface. The physical interpretation of the solutions based on the data of experimental measurements in the Earth's atmosphere is discussed. The analytical solution can be used to describe adiabatic atmospheric column, which is important for some applications. The research results improve understanding of processes in atmosphere and can be used for scientific and educational purposes.

Establishment of a crop evapotranspiration calculation model and its validation

AbstractIn order to contribute knowledge on the method used to calculate the actual crop evapotranspiration, soil, crop, atmosphere, and water spatial structure were integrated into a complete system. Based on the energy balance equation and aerodynamic equation, the meteorological data was reduced and the crop physiological parameter was increased, then the crop evapotranspiration calculation model under natural conditions was derived. The crop evapotranspiration calculation model was verified by the water balance formula using data generated from corn, potato, and flue‐cured tobacco grown under field conditions for three consecutive years from 2017 to 2019. The results showed that: from 2017 to 2019, the average root mean square error for measured and calculated evapotranspiration of corn, potato, and flue‐cured tobacco at different growth times were 0.5948, 0.4753, and 0.3326, respectively, the mean deviation, mean absolute error, and mean relative error were small, and the coefficient of determination and consistency index were both greater than 0.9100. The measured and calculated crop evapotranspiration of the selected crops increased at first and then decreased gradually as the crops matured, and finally decreased to harvest evapotranspiration, showing a parabolic trend. The crop evapotranspiration calculation model not only reflects the actual evapotranspiration of crops at different growth time but also reflects the change law of actual crop evapotranspiration. The model does not need the correction of soil moisture content, irrigation method, and crop coefficient and can directly calculate the actual crop evapotranspiration. It has the characteristics of consistency between the calculated value and the measured value, strong applicability, simple calculation process, and high accuracy and has the best effect on monitoring soil moisture and crop water shortage sensitivity. The model is significance in that it guides for monitoring soil moisture, determining actual crop evapotranspiration, crop water shortage index, and high yield and efficiency under water‐saving conditions.

USE OF MATHEMATICAL MODELS IN THE PROBLEMS OF ASSESSING THE CONSEQUENCES OF EXTREME SITUATIONS ON INDUSTRIAL FACILITIES

The report considers some classes of numerical models that were built to predict the consequences of emergencies at industrial enterprises. The first class of models has been developed to predict chemical air pollution in case of accidental emissions of toxic substances. Modeling is carried out on the basis of the fundamental equations of aerodynamics and mass transfer. Difference splitting schemes are used for the numerical solution of the modeling equations. The second class of numerical models has been developed to assess the risk of chemical injury to people in industrial rooms. The third class of models was developed to assess the risk of injury to people when a shock wave moves. To solve this problem Euler equations were used. The fourth class of models was developed to predict river pollution in case of accident chemical pollution. The fifth class of models was developed to assess the influence of protection barriers to reduce air pollution Computer codes were developed on the base of proposed numerical models.

Flutter Prediction Using Reduced-Order Modeling with Error Estimation

This paper presents a methodology for dynamic aeroelastic analysis of aircraft based on model order reduction with error estimation. A projection-based model order reduction approach is used to create an aerodynamic reduced-order model (ROM), which is coupled to a structural model to create an aeroelastic ROM. The governing aerodynamic equations are the linearized semidiscrete Euler equations. Flutter analysis is conducted by analyzing the eigenvalues of the aeroelastic ROM. A dual-weighted residual-based error estimator is presented which approximates the error in the eigenvalues obtained from the reduced eigenproblem relative to the eigenvalues from the high-dimensional aeroelastic model. The error estimator thus allows for the construction of aeroelastic ROMs with select eigenvalues that satisfy a user-prescribed accuracy. The aerodynamic ROM is constructed using approximate high-dimensional aeroelastic eigenvectors computed using the two-sided Jacobi–Davidson algorithm. Dynamic aeroelastic analyses are presented for the NACA 64A010 Isogai case, the AGARD 445.6 wing model, and a NACA 0012 benchmark case. The error estimator is shown to have good agreement with the exact error. For the test cases presented in this work, the cost of computing the flutter point at a given Mach number is equivalent to the cost of approximately 5 to 12 steady nonlinear flow evaluations of the high-dimensional Euler equations.

Amplitude Control of Stall-Induced Nonlinear Aeroelastic System Based on Iterative Learning Control and Unified Pitch Motion

In this study, vibration control, a behavior which subordinates to stall-induced nonlinear vibration and amplitude control of a wind turbine’s blade section, based on unified pitch motion driven by slider-linkage mechanism, is investigated by using an iterative learning control (ILC) method. The nonlinear dynamical system is a nonlinear aeroelastic system. The aeroelastic system equations consist of three parts: the nonlinear structural equations derived by using Lagrange’s equations, the improved stall-induced nonlinear ONERA (ISNO) aerodynamic equations, and the pitch control equation. The ISNO model is not only suitable for the actual external pitch motion, but also suitable for the solution by using an ILC algorithm due to its fitted nonlinear aerodynamic coefficients. The ILC algorithm used here is an improved iterative learning algorithm (IILC) which considers the large-range, linearized, residual terms, and realizes gain adaptive tuning based on PID controller. On the one hand, it can control the amplitude of an unsteady flutter through trajectory tracking. On the other hand, when the preset value of the amplitude of the ideal trajectory is very small, it can make the system directly tend to convergence and stability of a nonlinear aeroelastic system. To simplify the extremely difficult iterative process, the pitch movement can track the elastic twist displacement in time, thus simplifying the aeroelastic equations and accelerating the IILC iteration process. Therefore, amplitude control for flap-wise/lead-lag displacements is realized by the unified pitch motion and the trajectory tracking controlled by using the IILC algorithm.

SUBSTANTIATION OF MAGNETOELECTRIC VERTICAL-AXIAL GENERATOR FOR WIND TURBINE POWER SUPPLY OF ROAD INFRASTRUCTURE

The article is devoted to research on the creation of electromagnetic systems of electricity generation using wind flows of road infrastructure. The aerodynamic model of the air flow of a moving vehicle is evaluated on the basis of known models made on the basis of the equations of aerodynamics. For the construction of the electromagnetic system of the electric generator of a vertical-axial wind turbine intended for the energy supply of road infrastructure, it is necessary to take into account special requirements for the efficiency of the use of multidirectional air flows from moving vehicles and wind activity from any direction. Experimental studies of the speed of wind flows generated by traffic on highways were conducted and confirmed the possibility of using their energy by wind turbines with a vertical axis. An analysis of scientific sources of generator development for compatible use with vertical-axis turbines was carried out. Several types of existing generators are considered and the structural similarity with the proposed prototype is described in detail, as well as a number of fundamental shortcomings.The result of the development was the creation of a system with increased vertical force of the magnetic suspension with its mechanical transmission to the wind turbine, minimizing the pulsations of the vertical forces of the magnetic suspension and reducing scattering fluxes and simplifying the manufacture and repair of windings.

SIMULATION OF A WATER CURTAIN APPLICATION TO PROTECT WORKERS FROM THERMAL INJURIES

Problem statement. The problem of evaluating the effectiveness of using the water curtain to reduce the risk of thermal injury to people in a fire is considered. The problem is to determine the temperature fields when supplying water for air cooling. The purpose of the article. Development of a numerical model for calculating the process of propagation of water droplets in the air, their evaporation to reduce the temperature of heated air due to fire. Methodology. For mathematical modeling of the process of propagation of water droplets in air, thermal air pollution, the convective-diffusion equation of mass transfer, the energy equation and the equation describing the motion of an ideal liquid (potential flow model) are used. The potential flow model allows you to quickly determine the field of air flow velocity in areas with a complex geometric shape. Implicit difference splitting schemes are used for numerical integration of the convective-diffusion mass transfer equation and the energy equation. Physical splitting of basic equations is used to construct a difference analogue of modeling equations. The Richardson method and the conditional approximation scheme are used to solve the aerodynamics problem of determining the velocity potential field and the components of the air velocity vector. An engineering method for calculating the process of evaporation of a drop of water based on Sreznevsky's law has been developed. Scientific novelty. An effective numerical model has been developed that allows the method of computational experiment to determine the efficiency of using the water curtain to reduce the level of thermal pollution of atmospheric air due to fire. The numerical model is based on the integration of the fundamental equations of aerodynamics, heat and mass transfer. The model takes into account the most significant physical factors that affect the process under study: the movement of heated air, the movement of water droplets in the air, evaporation of the droplet, and so on. Practical significance. Based on the built model, a computer code has been created that allows you to quickly determine the temperature fields in the air when using a water curtain. The numerical model will be useful when conducting computational experiments for the purpose of scientifically sound choice of the location of the water curtain in case of fire. Conclusions. A computer code has been created that allows a computational experiment to investigate the effectiveness of using a water curtain in a fire. The developed computer program can be implemented on low and medium power computers. The results of a computational experiment are presented.

The Impact of Icing on the Airfoil on the Lift-Drag Characteristics and Maneuverability Characteristics

Icing has now become an important factor endangering flight safety. This paper takes the icing data of the NACA 23012 airfoil as an example, establishes an icing influence model for real-time simulation based on icing time and aircraft angle of attack, and analyzes the influence of different icing geometry on aircraft characteristics. The two-dimensional interpolation method is used to improve the model of the aircraft’s stall area, which is mainly divided into the correction of the lift-drag coefficient linear area and the stall area and the correction of the aircraft stability derivative and the control derivative. The aerodynamic equation of the airplane after icing is established, and the modal analysis of the airplane under different icing conditions is completed through the linearization of the flight equation. The closed-loop simulation system of the altitude holding mode and roll attitude holding mode is used to calculate and analyze the flight quality changes of the aircraft after the wing surface is frozen. The analysis results show that, under icing conditions, in the range of small angles of attack, icing has no obvious influence on the aircraft mode. As the degree of icing increases, the throttle skewness and the negative deflection angle of the airplane’s level flight requirements continue to increase. The case of icing flight in altitude hold and roll hold modes shows that flying in the autopilot mode under severe icing conditions is very dangerous and is prone to cause the aircraft to stall.