An isoviscous, isothermal model investigating the influence of hydrostatic recesses on a spring-supported tilting pad thrust bearing

Tilting-pad hydrodynamic thrust bearings are used in hydroelectric power stations around the world, reliably supporting turbines weighing hundreds of tonnes, over decades of service. Newer designs incorporate hydrostatic recesses machined into the sector-shaped pads to enhance oil film thickness at low rotational speeds. External pressurisation practically eliminates wear and enhances service life and reliability. It follows that older generating plants, lacking such assistance, stand to benefit from being retrofitted with hydrostatic lubrication systems. The design process is not trivial however. The need to increase the groove size to permit spontaneous lifting of the turbine under hydrostatic pressure, conflicts with the need to preserve performance of the original plane pad design. A haphazardly designed recess can induce a significant rise in bearing temperature concomitant with reduced mechanical efficiency and risk of thermal damage. In this work, a numerical study of a sector-shaped pad is undertaken to demonstrate how recess size and shape can affect the performance of a typical bearing.

Dynamic effects of electrical pitting in steam-turbine tilting-pad thrust-bearings

This paper merges the analysis of a case history and the simplified theoretical model related to a rather singular phenomenon that may happen in rotating machinery. Starting from the first, a small industrial steam turbine experienced a very strange behavior during megawatt load. When the unit was approaching the maximum allowed power, the temperature of the babbitt metal of the pads of the thrust bearing showed constant increase with an unrecoverable drift. Bearing inspection showed that pad trailing edge had the typical aspect of electrical pitting. This kind of damage was not reparable and bearing pads had to replaced. This problem occurred several times in sequence and was solved only by adding further ground brushes to the shaft-line. Failure analysis indicated electrodischarge machining as the root fault. A specific model, able to take into consideration the effect of electrical pitting and loading capacity decreasing as a consequence of the damage of the babbitt metal, is proposed in the paper and shows that the phenomenon causes the irretrievable failure of the thrust bearing.

Antispin thrust allocation for marine vessels

In extreme weather conditions, thrusters on ships and rigs may be subject to severe thrust losses caused by ventilation and in-and-out-of-water events. When a thruster ventilates, air is sucked down from the surface and into the propeller. In more severe cases, parts of or even the whole propeller can be out of the water. These losses vary rapidly with time and cause increased wear and tear in addition to reduced thruster performance. In this paper, a thrust allocation strategy is proposed to reduce the effects of thrust losses and to reduce the possibility of multiple ventilation events. This thrust allocation strategy is named antispin thrust allocation, based on the analogous behavior of antispin wheel control of cars. The proposed thrust allocation strategy is important for improving the life span of the propulsion system and the accuracy of positioning for vessels conducting station keeping in terms of dynamic positioning or thruster-assisted position mooring. Application of this strategy can result in an increase of operational time and, thus, increased profitability. The performance of the proposed allocation strategy is demonstrated with experiments on a model ship.

Parameter estimation of thrust models of uninhabited airborne systems

This paper presents a method for the estimation of thrust model parameters of uninhabited airborne systems using specific flight tests. Particular tests are proposed to simplify the estimation. The proposed estimation method is based on three steps. The first step uses a regression model in which the thrust is assumed constant. This allows us to obtain biased initial estimates of the aerodynamic coeficients of the surge model. In the second step, a robust nonlinear state estimator is implemented using the initial parameter estimates, and the model is augmented by considering the thrust as random walk. In the third step, the estimate of the thrust obtained by the observer is used to fit a polynomial model in terms of the propeller advanced ratio. We consider a numerical example based on Monte-Carlo simulations to quantify the sampling properties of the proposed estimator given realistic flight conditions.

Benefits and risks of large hydrostatic recesses in hydroelectric turbine thrust bearings

Operators of hydroelectric power stations sometimes call upon engineers to modify existing hydroelectric turbines, usually several decades old, for improved maintainability and reliability. One common modification is the hybridisation of plain thrust pads to allow hydrostatic operation to reduce the risk of bearing wipe at low speed (virtually all new installations benefit from this feature). A modification such as this is not a difficult undertaking; however, there are numerous factors that need to be considered in order to maximize bearing performance. One factor that stands out above the others is whether the thrust bearing should be designed to lift the turbine immediately from the standing condition, which presents an interesting challenge: the recess has to have a sufficiently large area in order for the supply pressure to be able to overcome the dead weight of the turbine. If the combination of groove area and pressure is insufficient, then lifting is neither immediate nor guaranteed. This need not be a significant problem, as the bearings have exhibited adequate performance even in the absence of a hydrostatic lubricant supply. A case study is presented whereby relatively large hydrostatic recesses are added to the pads of thrust bearing. It is demonstrated with the aid of simple numerical modelling that the impact of the recess relative to the original pad is small under normal operating conditions. Most surprising, however, is that significant reductions in average oil film temperature and power dissipation are predicted.

Thrust allocation with linear constrained quadratic cost function

In this paper, a method of thrust allocation based on a linearly constrained quadratic cost function capable of handling rotating azimuths is presented. The problem formulation accounts for magnitude and rate constraints on both thruster forces and azimuth angles. The advantage of this formulation is that the solution can be found with a finite number of iterations for each time step. Experiments with a model ship are used to validate the thrust allocation system.

An Explicit Guidance Scheme For A Low-Thrust Terminal Rendezvous

An explicit near-optimal guidance scheme is developed for a terminal rendezvous of a spacecraft with a passive target in circular orbit around the earth. The thrust angle versus time profile for the continuous-thrust, constant-acceleration maneuver is derived, based on the assumption that the components of inertial acceleration due to relative position and velocity are negligible on account of the close proximity between the two spacecraft. The control law is obtained as a ''bilinear tangent law'' and an analytic solution to the state differential equations is obtained by expanding a portion of the integrand as an infinite series in time. A differential corrector method is proposed, to obtain real-time updates to the guidance parameters at regular time intervals. Simulation of the guidance scheme is carried out using the Clohessy-Wiltshire equations of relative motion as well as the inverse-square two-body equations of motion. Results for typical examples are presented.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

Boundary-layer effects on internal flow choking in dual-thrust solid rocket motors

Theoretical studies have been carried out to examine internal flow choking in the inert simulators of a dual-thrust motor. Using a two-dimensional k-omega turbulence model, detailed parametric studies have been carried out to examine aerodynamic choking and the existence of a fluid throat at the transition region during the startup transient of dual-thrust motors. This code solves standard k-omega turbulence equations with shear flow corrections using a coupled second-order-implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-averaged, Navier-Stokes equations is employed. It was observed that, at the subsonic inflow conditions, there is a possibility of the occurrence of internal flow choking in dual-thrust motors due to the formation of a fluid throat at the beginning of the transition region induced by area blockage caused by boundary-layer-displacement thickness. It has been observed that a 55% increase in the upstream port area of the dual-thrust motor contributes to a 25% reduction in blockage factor at the transition region, which could negate the internal How choking and supplement with an early choking of the dual-thrust motor nozzle. If the height of the upstream port relative to the motor length is too small, the developing boundary layers from either side of the port can interact, leading to a choked,flow. On the other hand, if the developing boundary layers are far enough apart, then choking does not occur. The blockage factor is greater in magnitude for the choked case than for the unchoked case. More tangible explanations are presented in this paper for the boundary-layer blockage and the internal flow choking in dual-thrust motors, which hitherto has been unexplored.

Hall thruster sequencer using Intel-8051 microcontroller for ion thrust measurement

Hall thrusters, such as Stationary Plasma Thruster (SPT), have been widely used on board modern satellites placed in geo-synchronows orbits for reasons such as orbit maintenance, repositioning and attitude control. In order to study the performance of the stationary plasma thruster, the thrust produced by it has been measured, using a thrust balance with strain gauge sensors under vacuum conditions, by activating the thruster. This activation of thruster has been carried out by switching ON and switching OFF of the necessary power supplies and control of other feed system such as the propellant flow in a particular sequence. Hitherto, these operations were done manually in the required sequence. This paper reports the attempt made to automate the sequential operation of the power supplies and the necessary control valves of the feed system using Intel 8051 microcontroller. This automation has made thrust measurements easier and more sophisticated.

Analysis of performance of a hot gas injection thrust vector control system

The complex three-dimensional flowfield produced by secondary injection of hot gases in a rocket nozzle for thrust vector control is analyzed by solving unsteady three-dimensional Euler equations with appropriate boundary conditions. Various system performance parameters like secondary jet amplification factor and axial thrust augmentation are deduced by integrating the nozzle wall pressure distributions obtained as part of the flowfield solution and compared with measurements taken in actual static tests. The agreement is good within the practical range of secondary injectant flow rates for thrust vector control applications.

A unified view of energetic efficiency in active drag reduction, thrust generation and self-propulsion through a loss coefficient with some applications

An analysis of the energy budget for the general case of a body translating in a stationary fluid under the action of an external force is used to define a power loss coefficient. This universal definition of power loss coefficient gives a measure of the energy lost in the wake of the translating body and, in general, is applicable to a variety of flow configurations including active drag reduction, self-propulsion and thrust generation. The utility of the power loss coefficient is demonstrated on a model bluff body flow problem concerning a two-dimensional elliptical cylinder in a uniform cross-flow. The upper and lower boundaries of the elliptic cylinder undergo continuous motion due to a prescribed reflectionally symmetric constant tangential surface velocity. It is shown that a decrease in drag resulting from an increase in the strength of tangential surface velocity leads to an initial reduction and eventual rise in the power loss coefficient. A maximum in energetic efficiency is attained for a drag reducing tangential surface velocity which minimizes the power loss coefficient. The effect of the tangential surface velocity on drag reduction and self-propulsion of both bluff and streamlined bodies is explored through a variation in the thickness ratio (ratio of the minor and major axes) of the elliptical cylinders.

Medieval pulse of great earthquakes in the central Himalaya: Viewing past activities on the frontal thrust

The Himalaya has experienced three great earthquakes during the last century1934 Nepal-Bihar, 1950 Upper Assam, and arguably the 1905 Kangra. Focus here is on the central Himalayan segment between the 1905 and the 1934 ruptures, where previous studies have identified a great earthquake between thirteenth and sixteenth centuries. Historical data suggest damaging earthquakes in A.D. 1255, 1344, 1505, 1803, and 1833, although their sources and magnitudes remain debated. We present new evidence for a great earthquake from a trench across the base of a 13m high scarp near Ramnagar at the Himalayan Frontal Thrust. The section exposed four south verging fault strands and a backthrust offsetting a broad spectrum of lithounits, including colluvial deposits. Age data suggest that the last great earthquake in the central Himalaya most likely occurred between A.D. 1259 and 1433. While evidence for this rupture is unmistakable, the stratigraphic clues imply an earlier event, which can most tentatively be placed between A.D. 1050 and 1250. The postulated existence of this earlier event, however, requires further validation. If the two-earthquake scenario is realistic, then the successive ruptures may have occurred in close intervals and were sourced on adjacent segments that overlapped at the trench site. Rupture(s) identified in the trench closely correlate with two damaging earthquakes of 1255 and 1344 reported from Nepal. The present study suggests that the frontal thrust in central Himalaya may have remained seismically inactive during the last similar to 700years. Considering this long elapsed time, a great earthquake may be due in the region.

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.