Unsteady Motion Research Articles

The dynamics of a laden skip of the shaft pneumatic winding plant during acceleration

Introduction. Ratios for calculating the laden skip acceleration and speed at the motion start are required to calculate skip pneumatic winding plant cycle components. The ratios are the solution to the skip dynamics equation which takes into account the relationship between the flow generated by a power unit and air pressure. Research methodology. The dynamics equation including the dependence of the pressure on the flow rate (aerodynamic characteristic) in a general form is compiled. In a special case of the unit’s physical model, a discharge unit with a linear aerodynamic characteristic is used. Research result. For a particular case, equations are obtained that allow to theoretically describe the kinematic parameters of a skip in the period of unsteady motion. It is established that the skip acceleration, velocity and displacement are asymptotic functions. The obtained expressions for kinematic parameters make it possible to theoretically determine the duration of the acceleration period and the path that the ISSN 0536-1028 «Известия вузов. Горный журнал», № 1, 2021 121 skip takes during this period. A method for calculating skip dynamics during acceleration is proposed, which contains approximating formula conclusion for the power unit aerodynamic characteristics, its substitution into the dynamics equation, and obtaining skip kinematic parameters by solving the dynamics equation. Conclusion. The obtained relations allow to calculate skip dynamics during acceleration taking into account power unit aerodynamic characteristics, which is necessary to determine the working cycle time of the pneumatic winding plant.

Eulerian derivation of the conservation equation for energy in a non-inertial frame of reference in arbitrary motion

The standard inertial Navier–Stokes equations consisting of the conservation equations for mass, momentum and energy are often used to investigate the motion of a compressible fluid around an object that is in arbitrary motion. The non-inertial form of the Navier–Stokes equations can be used to accurately capture the acceleration effects that arise from the unsteady motion. The acceleration source terms that arise in the conservation equation for momentum have been extensively documented. In this paper, an Eulerian approach for deriving the apparent forces is presented to transform the governing conservation equation for energy into a non-inertial reference frame that is in arbitrary motion. The Eulerian approach is based on successive Galilean transformations between an inertial frame, an orientation-preserving non-inertial frame and a rotating non-inertial frame. The paper demonstrates that for an object in arbitrary motion, the rate of work done due to fictitious forces affects the rate of change of the total energy. The fictitious work arises in the kinetic energy equation while the internal energy and enthalpy equations remain invariant in the non-inertial frame. The present derivation is a step towards quantifying the contribution of the fictitious work terms to the heat transfer of a body that is accelerating/decelerating.

Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Multistability for nonlinear acoustic-gravity waves in a rotating atmosphere.

The multistable states of low-frequency, short-wavelength nonlinear acoustic-gravity waves propagating in a small slope with respect to the vertical ones are explored in a rotating atmosphere. The bifurcation patterns en route to irregular behaviors and the long-term dynamics of the low-order nonlinear model system are studied for varying air Prandtl number σ between 0.5 and 1. In contrast to non-rotation, the transition to the unsteady motion occurs both catastrophically and non-catastrophically due to the Earth's rotation. The connections between the Prandtl number and the slope parameter on the stabilities of the system are highlighted. The model system exhibits hysteresis-induced multistability with coexisting finite multi-periodic, periodic-chaotic attractors in certain parameter spaces depending on the initial conditions. Studies revealed that the rotation parameter instigates these heterogeneous coexisting attractors, resulting in the unpredictable dynamics. However, the relevance of this study is strongly restricted to a very small vertical wavelength, a small slope, and a weakly stratified atmosphere.

Asymptotic Behavior of Small Perturbations for Unsteady Motion an Ideal Fluid Jet

The stability problem of unsteady rotating circular jet motion of an ideal fluid is reduced to solving an initial-boundary value problem for Poincare–Sobolev type equation with an evolutionary condition on the jet free initial boundary. The solution of this problem is constructed by the method of variables separation. The asymptotic amplitudes behavior perturbations of the free jet boundary at t → ∞ is found. The results obtained are compared with the known results on the stability of the potential jet motion

Reflected shock/turbulent boundary layer interaction structure analysis based on large eddy simulation

In order to understand the physical phenomenon of the reflected shock/turbulent boundary layer interaction, the Large Eddy Simulation (LES) is conducted to investigate shock wave and turbulent boundary layer interaction in a 12° compression ramp with inlet high Mach number of 2.9. Rescaling/recycling method is used as inflow turbulence generation technique and validated on a supersonic flat plate turbulent boundary layer. The flow field of recycling plane in the plate computation domain is obtained to give the inlet boundary condition for the LES computation. This paper focuses on the reflected shock/turbulent boundary layer interaction region, where the fine flow structure and instantaneous flow field are analyzed in detail. It is found that the unsteady motion of the shock wave leads to the increase of wall pressure fluctuation.

Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall

Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the plates which is moving in its plane and the obtained solutions satisfy all imposed initial and boundary conditions. The starting solutions corresponding to the oscillatory motion are presented as sum of their steady-state and transient components. They can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for the incompressible Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. The influence of physical parameters on the fluid motion is graphically shown and discussed. It is found that the Maxwell fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state.

Added Masses of an Elliptical Cylinder with Unsteady Motion or in Unsteady Flow

Added Masses of an Elliptical Cylinder with Unsteady Motion or in Unsteady Flow

Hydro-Vortex Classification of Composite Microparticles

The use of nanomaterials for the implementation of a new set of functional properties has no alternative when creating refractory composite materials. Fine-dispersed Al2O3 is a necessary component of special high-quality cements, heat-resistant inert refractories and abrasive materials. Equations are obtained for the average values of the Euler and Reynolds criteria, the relaxation time of liquid droplets with integrated nanoparticles depending on their median size in the process of hydro-vortex classification. The tests carried out confirmed that under the conditions of self-similar hydro-vortex coagulation in the process of hydro-vortex classification, the inertial forces acting on the unsteady hydro-vortex motion of the dispersed system a drop of liquid — a microparticle of material, significantly affect the trajectory of its motion in comparison with the forces acting in the direction of motion of the fluidized bed of dispersed material. In this case, the control action provides a constant relaxation time, which significantly increases the efficiency of the influence of the angular velocity of droplet rotation on the classification process. Thus, inertial hydro-vortex classification in the self-similarity mode makes it possible to control the trajectories of motion of microparticles. At the same time, the energy of the translational motion of liquid droplets, determined by the characteristics of the hydro-vortex nozzles of the aerator, ensures the constancy of the time of the inlet manifold of the receiving hopper for relaxation, allowing the median diameter range of 0.5 × 10–6 – 5 × 10–6 m to be provided with a dispersion of no more than 20 % on their median diameter with a larger width of the inlet header of the receiving hopper.

Aeroacoustic modal analysis of underexpanded pipe jets with and without an upstream cavity

The investigation of the aeroacoustics of an underexpanded pipe-cavity jet is carried out experimentally. Two different aspect ratios of the cavity are tested for a wide range of nozzle pressure ratios. Both internal and externally radiated pipe-cavity acoustics are studied. Linear and higher-order spectral analyses are implemented on the unsteady cavity pressure to comprehend the nature of the cavity acoustics and nonlinear interactions of different acoustic modes of the pipe–cavity system. Results show that an increase in depth leads to an enhancement in the nonlinear interactions. Furthermore, the power spectral and overall sound pressure level analyses of pipe and pipe-cavity jet noise radiation are carried out. High-speed schlieren imaging techniques are used to understand jet dynamics. Highly unsteady motion of the jet initial shear layer is observed due to an upstream disturbance of the cavity. In addition, proper orthogonal and dynamic mode decomposition methods are used to extract the spatial and dynamic modes of the jet structure. These methods are used to segregate the cavity associated jet dynamics and screech dynamics.

Modeling internal waves in a two-layer fluid flow

This study presents mathematical model of the internal waves and examines wave propagation in a two-layer fluid flow. Elements of the functional-analytical approach are used to develop the model. A flat unsteady motion of a two-layer liquid under a cover over a flat bottom is considered. The fluid is assumed to be ideal and incompressible. Internal waves are caused by external pressure application to the interface between the layers, oscillation of the flat bottom and disturbances in the flow. The power of the wave source is characterized by dimensionless parameter ε. The problem is formulated, and its solution is based on asymptotic analysis for 0<ε<1.

Расчет нагрузки на штанговую подвеску при неустановившемся колебательном движении штанг скважинной насосной установки

The efficiency of a rod pumping unit is determined by the straightness of its rod string, which is impacted by the load when the rod string is in motion. Determining the dependence of the load impacting the rod suspension on the dynamic forces is one of the major issues in ensuring its straightness. In order to provide equal distribution of the stresses along the entire length of the polished rod under dynamic loading, it is necessary to determine the load on its surface, which is impossible without the equation of unsteady motion of the rod string. To this end, the article examines the issues related to the equation of unstable motion of well pumping unit rods. Formulae for calculating the loads acting on the rod suspension point are derived, and the equation of the rod string motion and load on the polished rod after the initial deformation is obtained.

Numerical Simulations on Unsteady Nonlinear Transonic Airfoil Flow

Large-amplitude excitations need to be considered for gust load analyses of transport aircraft in cruise flight conditions. Nonlinear amplitude effects in transonic flow are, however, only marginally taken into account. The present work aims at closing this gap by means of systematic unsteady Reynolds-averaged Navier-Stokes simulations. The RAE2822 airfoil is analyzed for a variety of sinusoidal gust excitations at different transonic Mach numbers. Responses are evaluated with respect to lift and moment coefficients, their derivatives and the unsteady shock motion. A strong dependency on inflow Mach number and excitation frequency is observed. Generally, amplitude effects decrease with lower Mach numbers or higher excitation frequencies. The unsteady nonlinear simulations predict lower maximum lift values and lower lift and moment derivatives compared to their linear counterparts for lower frequencies in combination with large-amplitude excitations. For the mid-frequency range, trends are not as clear. Additionally, it is shown that the variables of harmonic distortion and maximum shock motion might not be reasonable indicators to predict a nonlinear response.

An efficient grid assembling method in unsteady dynamic motion simulation using overset grid

The overset grid method may be a competitive choice of structured grid to discretize the progressively complicated aerodynamic shapes. Grid assembling process is a unique process for the overset grid method, which should be done repeatedly followed by any occurrence of grid motion in unsteady dynamic motion simulation. In this work, a simplified grid assembling method for the unsteady dynamic overset grid method is devised and validated. The grid motion information, generally including the position or the speed of the solid body, could be viewed as an additional information. The difference of the grid position indicates the change of the relative position of the grid points. The relative position of a grid point is very critical in the corresponding grid assembling process. The traditional grid assembling method usually omits the additional grid motion information. The proposed method utilizes the difference value of the grid position and the specially designed grid system to simplify the traditional grid assembling method. Three test cases including a 2D airfoil with different motion types and a 3D commercial airplane with pitching motion are implemented to demonstrate the high efficiency of the proposed method while the accuracy is kept. According to the results, the proposed method saves more than 85% of the computational time spent on the grid assembling process. This method is potentially a better candidate for the unsteady motion simulation using overset grid.

Визначення кута між осьовими лініями задньої секції шарнірно-зчленованого трактора та причіпної машини під час повороту

Goal of the study is to analyze the change in time of the angle between tractor sections with lateral wheel slip and with different modes of movement of the unit in a turn. To achieve this goal, you must: – analyze the kinematics of turning an articulated tractor with a trailer or a trailed machine and determine the presence of stable and unsteady motion; – to conduct an analytical study of the formation of the values of the angle between the sections of the articulated tractor in time. Research methods. The methodological basis of the work is the generalization and analysis of well-known scientific results on the kinematics of turning a wheeled tractor with an articulated frame, a rational combination of theoretical and experimental research and the use of a systematic approach. The results of the study. The kinematics and traction dynamics of an articulated tractor are considered taking into account the axle wheel slip angles. One of the factors influencing the side slip of the tractor wheels is the pulling force on the hook. The direction of this force when turning is determined by the kinematics of the trailed unit and other parameters. The position of the towed implement depends on the angle between it and the center line of the rear section of the articulated tractor. In the process of studying the angle between the axial lines of the rear section of the articulated tractor and the trailed unit at the turn, three periods were distinguished: the period of entering the turn can be divided into two phases; the period of steady turn, when the tractor and the attached implement move around the center of the turn; and the period of exit from the turn, which is divided into two phases. Conclusions. When carrying out theoretical studies, the dependences of the angle of rotation of the tractor (the angle between the rear section of the tractor and the trailed machine or trailer) were established. The obtained dependences make it possible to determine the direction of the traction force on the hook when turning, which is very important when taking into account the influence of the lateral slip angles of the tractor wheels on the kinematics and traction dynamics.

Mine aerology of dust aerosols under conditions of hydro-vortex coagulation

Dust suppression is the most popular method for depositing dust from the air to blast isolation. Improving the isolation system for probable coal dust explosions is an integral part of the problem of dust explosion protection of mining enterprises, the solution of which is one of the most important tasks in the field of occupational safety and health. Purpose: study of physics of the process and the construction of a mathematical model of the movement of aerosols in mine workings in a wide range of changes in the inertial kinematic parameters of the air flow. Research methods. Based on the Boussinesq equation, the Fourier rule and the similarity theorem of complex systems, the analogy of vorticity dispersion and kinematic viscosity, a mathematical model of the movement of dust aerosols under hydro-vortex coagulation conditions is constructed. Some similarity criteria are obtained that ensure the identity of experimental studies and real aerological processes in mines, as well as criterion equations for calculating the coefficient of aerodynamic drag and the time of unsteady inertial motion. Results. Equations are obtained that make it possible to identify aerodynamic processes of aerosol motion under hydro-cyclonic dust suppression through the criteria of Reynolds, Euler and Archimedes, corresponding to the overStokes and Stokes flow regimes. The possibility of reducing the aerodynamic resistance to 20% during hydro-vortex coagulation has been confirmed, which makes it possible to increase the energy efficiency of dust suppression by up to 15% and to increase the turbulization coefficient by at least 20%, thereby reducing the likelihood of a hazardous concentration of dust aerosols. Application. The use of the proposed mathematical model will make it possible to better calculate local aerological processes in mine workings and, as a consequence, to increase the efficiency of turbulization and dust suppression process control at mining enterprises.

A revisit of the tonal noise of small rotors.

In this study, asymptotic analysis of the frequency-domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi-rotor powered drones is conducted. Simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number, flow speed, rotation speed, unsteady motion, thrust and observer angle on the tonal noise. The rate of noise increment with thrust (or rotational speed) is determined by orders of blade passing frequency harmonics and the unsteady motion. The axial mean flow influence can be approximated by quadratic functions. At given thrust, the sound decreases rapidly with the radius and blade number as the surface pressure becomes less intensive. The higher tonal harmonics are significantly increased if unsteady motions, although of small-amplitude, are existed, as indicated by the defined sensitivity function, emphasizing that the unsteady motions should be avoided for quiet rotor designs. The scaling laws are examined by comparing with the full computations of the rotor noise using the frequency-domain method, the implementation of which has been validated by comparing with experiments. Good data collapse is obtained when the proposed scaling laws, which highlights the dominant influence of the design parameters, are incorporated.

A linearized reduced-order model approach for sloshing to be used for aerospace design

This paper proposes Reduced-Order Models (ROMs) based on data provided by Computational Fluid Dynamics (CFD) simulations for generally flexible tanks to be embedded in a larger aerospace structure. A commercial off-the-shelf CFD code addressed to sloshing analyses is employed to generate data set to be used for the synthesis of the sloshing system ROM. The developed sloshing ROM, based on a Linearized Frequency Domain (LFD) approach, makes use of an Input/Output system identification technique from CFD transient simulations to construct an unsteady Generalized Sloshing Force (GSF) transfer function (or frequency response function) matrix. This is done in analogy with the Generalized Aerodynamic Force (GAF) matrix used to model the aircraft unsteady aerodynamics for linearized aeroelastic analyses. The obtained GSF frequency response function data are suitably fitted via a rational polynomial form in the frequency domain so achieving a state-space representation for the sloshing system. Although the formulation is applicable for any 3D tanks of arbitrary shape, a parallelepiped tank is used as benchmark in order to compare the obtained GSF frequency response matrix with that available in the literature for simple tank geometries. The prediction capability of such method is also assessed by comparing the sloshing forces provided by the ROM and those obtained via direct CFD simulations even using unsteady boundary motions different than those used for ROM identification. The obtained linearized ROM of flexible tank with sloshing fluid seems suitable for aerospace applications for perspective integrated stability and response analyses and design of the aircraft/spacecraft structures.

Friction behavior of Radial Shaft Sealing Ring subjected to unsteady motion

A friction model for evaluating friction force of a Radial Shaft Sealing Ring (RSSR) in contact with the rotating shaft subjected to unsteady motion is presented. The model takes both the magnitude and the acceleration sign-changes from positive to negative into account and removes the shortcoming of the existing friction models in the sliding domain. It is shown that acceleration has a pronounced influence on the hydrodynamic regime. The results signify that hysteresis behavior exists in the boundary, mixed lubrication and hydrodynamic regimes as well as the pre-sliding domain, making the conventional Stribeck friction model unsuitable for characterization of friction behavior. To account for the hysteresis effect in the hydrodynamic regime, the model incorporates the solution of the unsteady Navier-Stokes equation that accommodates the magnitude as well as the sign change in the acceleration (and, hence, the viscous friction). In addition to the hysteresis, the results show a frictional lag when the motion starts from stick to slip. Test results are presented at low speed, and unknown parameters of the friction model are determined using an experimental test rig.

Solubility of unsteady equations of the three-dimensional motion of two-component viscous compressible heat-conducting fluids

We consider equations for the three-dimensional unsteady motion of mixtures of viscous compressible heat-conducting fluids in the multi-velocity approach. We prove the existence, globally in time and the input data, of a generalized (dissipative) solution of the initial-boundary value problem corresponding to flows in a bounded domain.