For a long time topological relationships between spatial objects have been a focus of research in a number of disciplines like artificial intelligence, cognitive science, linguistics, robotics, and spatial reasoning. Especially as predicates they support the design of suitable query languages for spatial data retrieval and analysis in spatial databases and geographical information systems (GIS). Unfortunately, they have so far only been defined for and applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions. With the introduction of complex spatial data types an issue arises regarding the design, definition, and number of topological relationships operating on these complex types. This article closes this gap and first introduces definitions of general and versatile spatial data types for complex points, complex lines, and complex regions. Based on the well known 9-intersection model, it then determines the complete sets of mutually exclusive topological relationships for all type combinations. Completeness and mutual exclusion are shown by a proof technique called proof-by-constraint-and-drawing. Due to the resulting large numbers of predicates and the difficulty of handling them, the user is provided with the concepts of topological cluster predicates and topological predicate groups, which permit one to reduce the number of predicates to be dealt with in a user-defined and/or application-specific manner.
With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatio-temporal databases. In this paper we consider the following problem: Given a set of moving object trajectories D and a query trajectory mq, find the k nearest neighbors to mq within D for any instant of time within the life time of mq. We assume D is indexed in a 3D-R-tree and employ a filter-and-refine strategy. The filter step traverses the index and creates a stream of so-called units (linear pieces of a trajectory) as a superset of the units required to build the result of the query. The refinement step processes an ordered stream of units and determines the pieces of units forming the precise result.To support the filter step, for each node p of the index, in preprocessing a time dependent coverage function C p (t) is computed which is the number of trajectories represented in p present at time t. Within the filter step, sophisticated data structures are used to keep track of the aggregated coverages of the nodes seen so far in the index traversal to enable pruning. Moreover, the R-tree index is built in a special way to obtain coverage functions that are effective for pruning. As a result, one obtains a highly efficient k-NN algorithm for moving data and query points that outperforms the two competing algorithms by a wide margin.Implementations of the new algorithms and of the competing techniques are made available as well. Algorithms can be used in a system context including, for example, visualization and animation of results. Experiments of the paper can be easily checked or repeated, and new experiments be performed.
In axial turbine the tip clearance flow occurring in rotor blade rows is responsible for about one third of the aerodynamic losses in the blade row and in many cases is the limiting factor for the blade lifetime. The tip leakage vortex forms when the leaking fluid crosses the gap between the rotor blade tip and the casing from pressure to suction side and rolls up into a vortex on the blade suction side. The flow through the tip gap is both of high velocity and high temperature, with the heat transfer to the blade from the hot fluid being very high in the blade tip area. In order to avoid blade tip burnout and a failure of the machine, blade tip cooling is commonly used. This paper presents the physical study and an improved design of a recessed blade tip for a highly loaded axial turbine rotor blade with application in high pressure axial turbines in aero engine or power generation. With use of three-dimensional Computational Fluid Dynamics (CFD), the flow field near the tip of the blade for different shapes of the recess cavities is investigated. Through better understanding and control of cavity vortical structures, an improved design is presented and the differences to the generic flat tip blade are highlighted. It is observed that by an appropriate profiling of the recess shape, the total tip heat transfer Nusselt Number was significantly reduced, being 15% lower than the flat tip and 7% lower than the baseline recess shape. Experimental results also showed an overall improvement of 0.2% in the one-and-1/2-stage turbine total efficiency with the improved recess design compared to the flat tip case. The CFD analysis conducted on single rotor row configurations predicted a 0.38% total efficiency increase for the rotor equipped with the new recess design compared to the flat tip rotor.
This paper presents an experimental investigation of a novel approach for controlling the rotor tip leakage and secondary flow by injecting cooling air from the stationary casing onto the rotor tip. It contains a detailed analysis of the unsteady flow interaction between the injected air and the flow in the rotor tip region and its impact on the rotor secondary flow structures. The experimental investigation has been conducted on a one-and-1/2-stage, unshrouded turbine, which has been especially designed and built for the current investigation. The turbine test case models a highly loaded, high pressure gas turbine stage. Measurements conducted with a two-sensor fast-response aerodynamic probe have provided data describing the time-resolved behavior of flow angles and pressures, as well as turbulence intensity in the exit plane of the rotor. Cooling air has been injected in the circumferential direction at a 30 deg angle from the casing tangent, opposing the rotor turning direction through a circumferential array of ten equidistant holes per rotor pitch. Different cooling air injection configurations have been tested. Injection parameters such as mass flow, axial position, and size of the holes have been varied to see the effect on the rotor tip secondary flows. The results of the current investigation show that with the injection, the size and the turbulence intensity of the rotor tip leakage vortex and the rotor tip passage vortex reduce. Both vortices move toward the tip suction side corner of the rotor passage. With an appropriate combination of injection mass flow rate and axial injection position, the isentropic efficiency of the stage was improved by 0.55 percentage points.
This paper presents an experimental study of the flow mechanisms of tip leakage across a blade of an unshrouded turbine rotor. It shows the design of a new one-and-1∕2-stage, unshrouded turbine configuration, which has been developed within the Turbomachinery Laboratory of ETH Zurich. This test case is a model of a high work (Δh∕u2=2.36) axial turbine. The experimental investigation comprises data from unsteady and steady probe measurements, which has been acquired around all the bladerows of the one-and-1∕2-stage, unshrouded turbine. A newly developed 2-sensor Fast Response Aerodynamic Probe (FRAP) technique has been used in the current measurement campaign. The paper contains a detailed analysis of the unsteady interaction between rotor and stator blade rows, with particular attention paid on the flow in the blade tip region. It has been found that the interaction of the rotor and the downstream stator has an influence on the development of the tip leakage vortex of the rotor. The vortex is modulated by the stator profiles and shows variation in size and relative position to the rotor trailing edge when it stretches around the stator leading edge. Thereby a deflection of the tip leakage vortex has been observed, which expresses in a varying circumferential distance between two neighboring vortices of ±20% of a rotor pitch. Furthermore, a significant influence of quasi-stationary secondary flow features of the upstream stator row on the secondary flow of the rotor has been detected. The geometry and flow field data of the one-and-1∕2-stage turbine will be available to the turbomachinery community for validation and improvement of numerical tools.
This paper presents an experimental study of the flow mechanisms of tip leakage across a blade of an unshrouded turbine rotor. It shows the design of a new one-and-1/2-stage, unshrouded turbine configuration, which has been developed within the Turbomachinery Laboratory of ETH Zurich. This test case is a model of a high work (Δh/u2 = 2.36) axial turbine. The experimental investigation comprises data from unsteady and steady probe measurements, which has been acquired around all the bladerows of the one-and-1/2-stage, unshrouded turbine. A newly developed 2-sensor Fast Response Aerodynamic Probe (FRAP) technique has been used in the current measurement campaign. The paper contains a detailed analysis of the unsteady interaction between rotor and stator blade rows, with particular attention paid on the flow in the blade tip region. It has been found that the pressure field of the second stator row has a influence on the development of the tip leakage vortex downstream of the rotor. The vortex is modulated by the stator profiles and shows variation in size and relative position to the rotor trailing edge when it stretches around the stator leading edge. Thereby a deflection of the tip leakage vortex has been observed, which expresses in a varying circumferential distance between two neighboring vortices of ±20% of a rotor pitch. Furthermore, a significant influence of quasi-stationary secondary flow features of the upstream stator row on the secondary flow of the rotor has been detected. The geometry data of the one-and-1/2-stage turbine will be available to the public domain for validation and improvement of numerical tools.
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