Rigid Body Equations Of Motion Research Articles

Simulation of aircraft multi-axis acceleration in a four-axis Human Centrifuge System

High G-accelerations produced during Aircraft Combat Manoeuvres (ACMs) can adversely affect the physiological and psychological conditions of aircrew and deteriorate their performance. Human Centrifuge Systems (HCSs) provide an effective G-acceleration training tool to prepare and increase the G-tolerance of aircrew. Though highly capable HCSs are available, they are yet to be fully optimised to accurately and reliably recreate the G-vectors produced by ACMs. Optimisation steps to achieve this improvement involve the configurational structure, motion capability, and motion control of HCSs. To improve the motion capability and control of HCSs, the relationship between aircraft G-vectors and HCS G-vectors should be profoundly investigated. This work analyses the G-vectors of common ACMs and the corresponding G-vectors as well as kinematics of an active four Degree-of-Freedom (DoF) HCS. The mathematical models of an aircraft and HCS kinematics are developed using rigid body equations of motion through Newton-Euler method. The relationship between aircraft G-vectors and HCS G-vectors is established using inverse kinematics with an optimal solver. The outcomes of this study show that an active four-DoF HCS with gondola roll, pitch, and yaw rotation can replicate the G-vectors of common ACMs with small discrepancies. The largest error between the reference and achieved G-vectors occurred along the local z-axis of the HCS gondola during the transition of roll, pitch, and yaw motions of the gondola to the required angle replicating the G-vectors of the ACMs. The tracing errors are not significant; hence they can be mitigated with an optimal control technique. The presented outcomes will provide an essential step in identifying the optimal design and refined requirements for an HCS to efficiently replicate aircraft G-vectors. The applied methodology is easily adaptable to HCS with different structures and DoFs.

Multi-fidelity hydrodynamic analysis of an autonomous surface vehicle at surveying speed in deep water subject to variable payload

Autonomous surface vehicles (ASV) allow the investigation of coastal areas, ports, and harbors as well as harsh and dangerous environments such as the arctic regions. In the past decade, several studies addressed the shape optimization, control and stability, and seakeeping of ASVs. Nevertheless, the hydrodynamic analysis of ASV performance subject to variable operational parameters lacks a thorough investigation. In this context, this paper presents a multi-fidelity (MF) hydrodynamic analysis of a catamaran ASV, namely the shallow water autonomous multipurpose platform (SWAMP), at surveying speed in calm water and subject to variable payload and location of the center of mass, accounting for the variety of equipment that the vehicle can carry. The analysis is conducted in deep water, which is the condition mostly encountered by the ASV during surveys of coastal and harbor areas. The objective of the analysis is the investigation of the effects of the payload and its arrangement on the variations of the resistance, the vehicle attitude, and the wave generated in the region between the catamaran hulls. These are assessed using an unsteady Reynolds–averaged Navier–Stokes equation (URANSE) code and a linear potential flow (PF) solver. The latter also includes variable grid refinement and coupling between hydrodynamic loads and rigid body equations of motion. Furthermore, the limitation of a PF analysis in the current context is investigated. Finally, a multi-fidelity Gaussian process (MF-GP) model is obtained combining high- (URANSE) and low-fidelity (PF) solutions following an additive correction approach of the latter. The MF-GP model is iteratively refined using an active learning approach based on the maximum prediction uncertainty and the computational cost of the numerical simulations. Numerical results show that the MF-GP is effective in producing response surfaces of the SWAMP performance with a limited computational cost. It is highlighted how the SWAMP performance is significantly affected not only by the payload, but also by the location of the center of mass. The latter can be therefore properly calibrated to minimize the resistance and allow for longer-range operations.

Effect of degrees of structural freedom on the flow-induced vibrations of isolated and tandem cylindrical structures

This study aims to numerically investigate the influence of degrees of structural freedom on the flow-induced vibration characteristics of an isolated and tandem cylindrical structures at low Reynolds number. Both the single and tandem cylinders underwent transverse-only (1-DoF) and combined streamwise and transverse (2-DoF) vibrations which are characterized by the mass–spring system. A fluid–structure interaction scheme is formulated using the split-forcing lattice Boltzmann equation for the fluid domain in combination with an immersed boundary solver and equations of rigid body motion for the structural part. The dynamic response of an isolated and tandem structures computed for 1- and 2-DoF cases are similar regarding the lock-in phenomenon and hydrodynamic forces at a relatively large mass ratio. The comparison of vorticity field suggests that an additional degree of freedom has no significant effect on the vortex shedding pattern. Furthermore, in the presence of another identical structure placed in the upstream direction, the downstream structure oscillates with higher amplitudes.

Control Design for a Marine Hydrokinetic Cycloturbine Vehicle

Abstract Marine Hydrokinetic (MHK) cycloturbines generate sustainable power by exploiting tidal currents. By powering the turbines and using pitching foils for control, a vehicle comprised of MHK cycloturbines also has the ability to station keep and maneuver. The vehicle consists of four counter-rotating cycloturbines, with hydrofoils oriented perpendicular to the flow in a paddlewheel configuration. Lift and drag generated from these foils sum together to produce thrust. An experimentally tuned simulation model that solves the six-degrees-of-freedom rigid body equations of motion for the MHK vehicle subject to hydrodynamic, hydrostatic, and propulsive forces is used to aid the design of vehicle controllers. Global feedback controllers are initially designed by applying classical control methods to an approximate linear model of the system dynamics. A higher performing nonlinear controller is designed using the nonlinear dynamic inversion (NDI) method. NDI accounts for the nonlinearities of the MHK system and therefore is suitable for a wide range of operating conditions. The response of the classical and NDI controllers to speed, depth, roll, pitch, and yaw commands are evaluated and compared in simulation. The classical controller outperforms the NDI controller for small amplitude maneuvers, although the degradation with NDI is minor. However, in the nonlinear operating regime the NDI controller outperforms the classical controller and the classical controller exhibits instability.

Механический аналог движений неоднородной жидкости

The article considers the homogeneous vortex motion of an inhomogeneous fluid in a stationary ellipsoidal cavity arbitrarily oriented with respect to the direction of a uniform gravity field using the Lagrange variables. Uniform vortex motion of a fluid is a motion in which the rotor speed for all particles has the same value, and depends only on time. The article shows that the equations of homogeneous vortex motion of a heavy inhomogeneous fluid are possible in an ellipsoidal cavity with a linear density distribution and proposes a geometric interpretation of fluid motion. Using the Lagrange variables, the equations of motion of an inhomogeneous fluid are obtained, coinciding with the equations of a heavy rigid body motion around a fixed point, written in a fixed coordinate system arbitrarily located relative to the direction of a homogeneous gravity field.

Hydrodynamic analysis of ship manoeuvrability in shallow water using high-fidelity URANS computations

The manoeuvring performance of a ship in shallow water is substantially different from its performance in deep water, attributed to shallow water effects caused by the presence of a finite water depth. Without a doubt a ship will navigate in areas of shallow water at various times during its operational life (such as when approaching harbours or ports), which underscores the importance of understanding the shallow water effects on ship manoeuvrability. In the present paper, the manoeuvrability of the KRISO Container Ship (KCS) model in different shallow water conditions was comprehensively analysed by means of the unsteady Reynolds-Averaged Navier-Stokes (URANS) computations coupled with the equations of rigid body motion with full six degrees of freedom (6DOF). A dynamic overset grid approach was implemented to allow the ship hull to move in 6DOF in a computational domain and to enable the rudder to be deflected according to a rudder controller for free-running manoeuvres. A series of manoeuvring simulations were performed in shallow waters with water depth to draft ratios varying between 1.2 and 4.0, and partially validated with the available experimental data from a free running test. The numerical results revealed that the ship advance, transfer, and tactical diameter mainly increased with the decrease in the ratio of water depth to draft, closely associated with the complicated interactions between the hull wake, boundary layer, propeller, vortex, and sea floor.

Thermal-structural-optical integrated analysis method based on the complete equations of rigid body motion

Thermal-structural-optical integrated analysis method based on the complete equations of rigid body motion

A Simple Physical Model for Control of a Propellerless Aquatic Robot

Abstract This paper is concerned with the motion of an aquatic robot whose body has the form of a sharp-edged foil. The robot is propelled by rotating the internal rotor without shell deformation. The motion of the robot is described by a finite-dimensional mathematical model derived from physical considerations. This model takes into account the effect of added masses and viscous friction. The parameters of the model are calculated from comparison of experimental data and numerical solution to the equations of rigid body motion and the Navier–Stokes equations. The proposed mathematical model is used to define controls implementing straight-line motion, motion in a circle, and motion along a complex trajectory. Experiments for estimation of the efficiency of the model have been conducted.

Investigation on responses and wave climbing of a ship in large waves using a fully nonlinear boundary element method

In this study, a fully nonlinear method, in the time domain, is used to simulate ship motion caused by large waves, and the problem of wave climbing along the freeboard in large waves is studied. The method is based on a three-dimensional potential flow theory. Further, the nonlinear free surface condition is adopted, the incident potential and disturbance potential are separated from each other, and the problem of determining the disturbance potential is established. In order to consider the nonlinearity of the body surface, the wetted surface area of the hull is continuously updated with time and extended along the tangential direction of the uppermost grid when the free liquid level exceeds the height of the hull deck. In addition, an artificial damping layer is provided to eliminate the reflection of waves at the outflow boundary. Under the fully nonlinear boundary conditions, the perturbation potential is solved by the Rankine source boundary element method. Introducing auxiliary functions solves the coupling problem between motion and load in the process of solving rigid body motion equations. After the solution is completed, it is updated to the next time step using the Runge-Kutta 4th order method. In this study, the convergence of the computational grid of the numerical model is firstly verified. Then, the motion and load responses of a zero-speed ship in the regular wave of unit wave amplitude using this method are examined and compared with the linear method. The latter verifies the accuracy of this method in the linear field. Afterwards, in order to investigate the superiority of the fully nonlinear method when the nonlinear phenomenon is strong, the motion and load of the ship in the large amplitute wave are simulated and the influence of the nonlinear phenomenon is analyzed. Finally, the phenomenon of wave climbing generated in high waves is analyzed, and the relationship between wave and water heights is evaluated.

Modeling of a Marine Hydrokinetic Cycloturbine Vehicle

A marine hydrokinetic (MHK) cycloturbine is a renewable electric power generation system used in rivers or tidal environments to address the need for electricity in remote regions. MHK cycloturbines have hydrofoils oriented perpendicular to the flow in a paddlewheel configuration, and use lift generated from these foils to produce power. Due to the high cost associated with its operation and maintenance, an MHK system with four stacked counter-rotating turbines that can self-deploy and with propulsion and control mechanisms similar to a cycloturbine aircraft has been designed. A detailed turbine simulation model is necessary to understand the vehicle dynamics and assist in the design of the vehicle controllers. The simulation model solves the six degree-of-freedom rigid body equations of motion for the maneuvering MHK system subject to the hydrodynamic lift and drag forces, hydrostatic forces, and the propulsive forces from the turbines. The turbine propulsive force model is matched to computational fluid dynamics analysis and experimental data. Experimental work includes investigation at 1/5.56 scale of a single turbine rapid prototype device and a subscale demonstrator in a reverberant tank.

Rigid-Body Dynamic Analysis of Multi-Stage Planetary Roller Screw Mechanism

Based on the structural characteristics of the multi-stage Planetary Roller Screw Mechanism (PRSM), the motion and force among the different stages are analyzed. In terms of the Newton's second law, the rigid-body motion equations of the multi-stage PRSM without considering the manufacturing and assembly errors are derived. Then, the method for solving the motion equations is given. The forces acting on the parts in the multi-stage PRSM and the motion of the mechanism can be obtained from the present rigid-body dynamic model. The influence of the friction coefficients among the different stages on the dynamic characteristics of the multi-stage PRSM is discussed. The results show that the forces acting on the first-stage PRSM are larger than that acting on the second-stage PRSM, although the nominal radius of the screw in the first-stage PRSM is smaller. The friction coefficient between the nut and the screw in the different stages has the great influence on the efficiency of multi-stages PRSM with small helix angles, while that among the screws in the different stages has the slight effect on the efficiency.

Numerical Simulation of Isolated Main Rotor and Full Helicopter Configuration in Vertical Autorotative Descent

This paper presents and discusses the results of the transient numerical simulation carried out for an isolated main rotor model and a helicopter in vertical descent autorotation by developing the 6-degree of freedom, rigid-body equations of helicopter motion. The Unsteady Reynolds Averaged Navier-Stokes model is used to simulate the unsteady flow field surrounding four-bladed BO-105 isolated main rotor and complete helicopter which includes the fuselage and the tail rotor. The principal autorotation characteristics for the helicopter such as induced velocity, rate of descent, main rotor angular speed, thrust and torque have been calculated. The simulation results show the creation of a spanwise flow on the upper surface of the blade, and moving fluid in the direction of the blade tip in a region downstream and beneath the leading edge vortex. The aerodynamic characteristics on the complete helicopter are similar to the ones attained for the isolated rotor simulation.

Numerical Analysis of a Surface Ship in Waves

Abstract Ship's resistance and engine power to sustain ship's speed in seaways are augmented due to complex non-linear interactions between the ship and the ambient sea (waves). Ship designers, in early design stage, use an ad hoc "sea margin" to account for the effects of seaways in selecting propeller and engine. A numerical tool capable of accurately predicting added resistance and power of a ship cruising in waves would greatly help select its powering (margin) requirement and determine the optimal operating point that can maximize the energy efficiency. For seakeeping analysis, strip theory-based methods have long been used. More recently, nonlinear time-domain three-dimensional (3D) panel methods have started being used widely. A more physics-based avenue to seakeeping analysis is offered by coupled solutions of two-phase unsteady Reynolds-Averaged Navier-Stokes equations and six degrees-of-freedom rigid-body motion (RBM) equations. The URANS approach also avails itself of including the effects of propulsors, either explicitly or approximately. By accounting for all the nonlinear effects in hydrodynamic forces and moments and the resulting ship motions, and the effects of fluid viscosity and turbulence, the coupled URANS-RBM method is believed not only able to predict added resistance and speed loss more accurately, but also to provide valuable insights into the physical mechanisms underlying added resistance and power. The objectives of this study are: (1) to validate a coupled URANS-RBM solver developed for high-fidelity prediction of added resistance, speed loss and added power on ships cruising in regular head sea and irregular waves, and (2) to conduct a detailed analysis of the interactions among ship hull, propeller and waves for a 1/49 scaled model of the ONR Tumblehome (ONRT) (Model 5613) in order to shed light on the physical mechanisms leading to added resistance, speed loss and added power. Figure 1 depicts the ONRT self-propellers with two 4-bladed propellers in regular waves. The main flow features such as the free surface, the hub vortices and blade-tip vortices from the propeller, as well as vortices generated by the sonar dome, shafts, shaft brackets and bilge keels are captured.

Simultaneous vortex- and wake-induced vibration suppression of tandem-arranged circular cylinders using active feedback control system

This paper deals with the active flow-induced vibration (FIV) suppression of two identical tandem-arranged circular cylinders at a low Reynolds number of Re=100. The adopted control system employs fuzzy PID controller in which the desired control force is computed based on the cylinder displacement amplitude, and applied transversely for effective attenuation of flow-induced instabilities in both transverse and streamwise directions. Moreover, the effect of FIV suppression of each cylinder on the response amplitude of other one, and the simultaneous vibration reduction of both cylinders are investigated based on fully-coupled fluid-structure interaction (FSI) simulations. The rigid body motion equations in streamwise and transverse directions are incorporated into the computational fluid dynamics solver to treat the coupling which exists between the fluid flow and cylinders movement. Next, in the utilized co-simulations, the active fuzzy PID controller implemented in Matlab/Simulink is coupled with the FSI oscillator model constructed in computational fluid dynamics solver package. It was shown that, the sudden suppression of the upstream cylinder vibration causes quick distortion in the flow field around the rear cylinder, and consequently, its steady-state response amplitude is destabilized and experiences transient fluctuations once again. On the contrary, the decrease in the transverse oscillation of the downstream cylinder leaves no sensible effect on the vibration of upstream cylinder. In particular, the active control system effectively reduces the transverse displacement amplitudes of upstream and downstream cylinders by as much as 99.9% and 98.7%, respectively, for Vr=5.5, while the corresponding values are 99.8% and 99.7% for Vr=7.5. This superb performance of active FIV control systems is mainly due to de-synchronization-type action in which the vortex shedding frequency is deviated from the oscillator natural frequency. Lastly, it is demonstrated that the vortex shedding patterns for uncontrolled cylinders, which primarily depend on reduced velocity, are turned very similar to that of the stationary cylinders after adopting the fully active control systems.

Parallel algorithms for moving boundary problems by local remeshing

Purpose The purpose of this paper is to develop parallel algorithms for moving boundary simulations by local remeshing and compose them to a fully parallel simulation cycle for the solution of problems with engineering interests. Design/methodology/approach The moving boundary problems are solved by unsteady flow computations coupled with six-degrees-of-freedom equations of rigid body motion. Parallel algorithms are developed for both computational fluid dynamics (CFD) solution and grid deformation steps. Meanwhile, a novel approach is developed for the parallelization of the local remeshing step. It inputs a distributed mesh after deformation, then marks low-quality elements to be deleted on the respective processors. After that, a parallel domain decomposition approach is used to repartition the hole mesh and then to redistribute the resulting sub-meshes onto all available processors. Then remesh individual sub-holes in parallel. Finally, the element redistribution is rebalanced. Findings If the CFD solver is parallelized while the remaining steps are executed in sequential, the performance bottleneck of such a simulation cycle is observed when the simulation of large-scale problem is executed. The developed parallel simulation cycle, in which all of time-consuming steps have been efficiently parallelized, could overcome these bottlenecks, in terms of both memory consumption and computing efficiency. Originality/value A fully parallel approach for moving boundary simulations by local remeshing is developed to solve large-scale problems. In the algorithm level, a novel parallel local remeshing algorithm is present. It repartitions distributed hole elements evenly onto all available processors and ensures the generation of a well-shaped inter-hole boundary always. Therefore, the subsequent remeshing step can fix the inter-hole boundary involves no communications.

A massively-parallel, unstructured overset method to simulate moving bodies in turbulent flows

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O(105)) moving bodies, utilizing many computational cores (O(105)), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries.

Numerical investigations on the oblique water entry of high-speed projectiles

In this paper, we investigate the main characteristics of oblique water entry of high-speed cylindrical projectiles, which involves multiphase flows due to cavitation. Numerical simulations are performed by solving Reynolds-averaged Navier–Stokes (RANS) equations coupled with 6-degree of freedom (DOF) rigid-body motion equations. The model is validated firstly by comparing with previous results. Then the studies of different entry conditions are performed, and we find that the velocity attenuation during the entry process is mainly affected by the projectile geometric parameters such as its head shape and length, rather than the entry angles and velocities. The drag coefficient is also dominated by the head shape. Furthermore, the time of surface closure of cavity is linear with the entry velocity of the projectile.

Features of the mathematical model for the control forces calculation of the four-wheeled robot

The article discusses the issue of determining program forces in drives of a four-wheel robotic platform - the issue of opening the uncertainty of the equations system. The motion laws are synthesized on the basis of application of the calculus of variations. The method of determining the program forces is based on the compilation of equations of the dynamics of a rigid body motion and additional equations - “zero-functions” (displacements) of the points of the application of redundant reactions.

Design of a supervisory fuzzy logic controller for monitoring the inflow and purging of gas through lift bags for a safe and viable salvaging operation

This paper presents a mathematical model and numerical time-domain approach to simulate the dynamics of a sunken ship/vessel being raised from seafloor by buoyancy (gas-inflating) systems in a form which is suitable for integrating control techniques to ensure hydrodynamic stability for a safe and viable salvaging operation. According to the two-degree-of-freedom equations of rigid-body vessel motion in diving plane, a conventional sliding mode controller is designed as the primary controller to regulate flow rate of filling gas inside the lift bags and a PID controller is designed as the secondary controller for regulating the purging of gas through the valves fitted on lift bags. Then a supervisory fuzzy logic controller is designed to monitor or switch between the primary and secondary controllers based on the buoyancy requirement. From the simulation studies, it is found that the supervisory fuzzy logic controller is capable to maintain hydrodynamic stability by suitably defining the linguistic fuzzy rules, which is created based on the author's experience in conducting numerical simulation using primary and secondary controllers.

Rankine source time domain method for nonlinear ship motions in steep oblique waves

ABSTRACTThis article presents a weakly nonlinear time domain Rankine source boundary element method to calculate wave-induced ship motions. Radiation forces were calculated using convolution integrals, whereas Froude–Krylov and hydrostatic forces were obtained from ship positions relative to the instantaneously wetted surface. The nonlinear rigid body motion equations were coupled with the flow equations to enable reliable predictions also in finite amplitude (steep) waves. A system of soft springs prevented excessive low-frequency motions of the ship, but allowed it to move in six degrees of freedom. Numerical results of a 14,000TEU container ship at two different forward speeds in oblique waves of different steepness were validated against comparable ship motions obtained from available experimental towing tank measurements and a frequency domain method. The influence of wave steepness and wave heading on ship motions was of particular interest.