Corotational System Research Articles

Modeling of twin-turbine systems with vertical axis tidal current turbine: Part II—torque fluctuation

We recently showed the advantage of using a numerical system to extract energy from tidal currents by developing a new twin-turbine model ( Li and Calisal, 2010a). Encouraged by this result, we decided to use this model to study another important characteristic of the turbine system, torque fluctuation. This effort is summarized in this paper. The torque fluctuation is expected to reduce the fatigue life of tidal current turbines, though potentially it also may deteriorate the power quality of tidal current turbines. In this paper, after reviewing the twin-turbine model, we use it to predict the torque fluctuation of the system with the same configurations as we used to study the power output in Li and Calisal (2010a). Specifically, we investigate the torque fluctuation of twin-turbine systems with various turbine parameters (e.g., relative distance between two turbines and incoming flow angle) and operational condition (e.g., tip speed ratio). The results suggest that the torque of an optimally configured twin-turbine system fluctuates much less than that of the corresponding stand-alone turbine, under the same operating conditions. We then extensively compare the hydrodynamic interaction’s impact on the torque fluctuation and the power output of the system. We conclude that the hydrodynamic interactions pose more constructive impacts on the torque fluctuation than on the power output. The findings indicate that the optimally configured counter-rotating system should be a side-by-side system, and that the optimally configured co-rotating system should have the downstream turbine partially in the wake of the upstream turbine depending on the detailed configuration of the turbines. Furthermore, one must balance the optimal torque fluctuation against the optimal power output.

A mixed co-rotational curved quadrilateral shell element

This paper presents a 9-node isoparametric formulation of degenerated curved shell element, which is based on a co-rotational framework. Within this framework, the local reference axes are easily defined by the two diagonal vectors generated by the four corner nodes in the current deformed configuration. Furthermore, vectorial rotational variables are utilised, which consist of the two smaller components of each nodal orientation vector, enabling additive and commutative rotational operations. The element strain energy is evaluated in the local co-rotational system using the Green strain, where the Hellinger-Reissner functional is employed with assumed strain tensors for the membrane and shear strain fields to alleviate the membrane/shear locking phenomena. By defining the equilibrium conditions in terms of the out-of-balance between the work-conjugate internal and external forces, symmetric element tangent stiffness matrices are achieved in both the local and global systems, thus leading to considerable computational benefits. Finally, several examples of elastic shells subject to large displacements are considered, which demonstrate favourable performance of the proposed finite element formulation.

Modeling of twin-turbine systems with vertical axis tidal current turbines: Part I—Power output

Recent interest in the tidal current industry has driven development of the prototype from the stand-alone turbine to the twin-turbine system. In this paper, we develop a numerical model to systematically analyze the relationship between the power output and the configuration of a twin-turbine system. First, we present the design principle of the twin-turbine system. We then develop the numerical model for simulating the operation of the system, and validate the model by conducting towing tank experimental tests. We then use the model to predict the power output of the system. The results of this study show that the total power output of a twin-turbine system with optimal layout can be about 25% higher than two times that of a stand-alone turbine. We also discuss the hydrodynamic interaction between the two turbines under different configurations of the system. We conclude that the optimally configured counter-rotating system should be a side-by-side system, and that the optimally configured co-rotating system should have the downstream turbine partially in the wake of the upstream turbine, depending on the detailed configuration of the turbine.

Geometrically nonlinear analysis of laminate composite plates and shells using the eight-node hexahedral element with one-point integration

An eight-node hexahedral isoparametric element with one-point quadrature for the geometrically nonlinear static and dynamic analysis of plates and shells of laminate composite materials is formulated and implemented in this work. The element is free of volumetric and shear locking and spurious modes are not detected. Shear locking is avoided using a corotational system for strain and stress components, whereas volumetric locking is controlled using one-point quadrature for the dilatational (or spherical) part of the gradient matrix. The efficiency and potential of the three-dimensional element in the analysis of plates and shells of laminate composite materials undergoing large displacements and rotations are shown solving several numerical examples and comparing with results obtained by other authors using different plate and shells elements.

On the pressure drop and the velocity distribution in the cylindrical vortex chamber with two inlet pipes for the control of vortex flow

Vortex flow is applied to a cyclone dust collector, a vortex combustion chamber, and a vortex diode for vortex control. In order to apply the vortex flow to the industries, it is necessary to keep the stable flow condition and to estimate the response time of the transient flow process and also the intensity of the vortex flow. For control vortex flow, two types of vortex chamber with two inlet pipes were designed. One of them is to promote the vortex flow named as Co-Rotating Flow System and another one is to hinder the vortex flow named as Counter-Rotating Flow System. The pressure drops and the velocity distributions were measured for these vortex chambers. The estimation of the tangential velocity by the application of the angular momentum flux is compared with the measured velocity by a cylindrical Pitot-tube. The characteristics of the total pressure drop could be explained by introducing the circulation.

An enhanced co-rotational approach for large displacement analysis of plates

This paper presents a new co-rotational approach for the large displacement analysis of plates employing 4-noded quadrilateral flat shell elements. The proposed approach benefits from (i) a simple local co-rotational system invariant to the element nodal ordering, (ii) the choice of the two smallest components of the nodal normal vector as global rotational degrees of freedom, and (iii) the use of hierarchic freedoms, that are unaffected by the co-rotational transformations, for higher-order accuracy. Important additional benefits that arise from the aforementioned features include symmetry of the tangent stiffness matrix and complete insensitivity of the large displacement transformations to the size of the incremental step. The applicability of the new approach to moderately thick as well as thin plates is illustrated by considering two alternative local formulations based on the Reissner–Mindlin and discrete Kirchhoff hypotheses. Several examples are finally presented which demonstrate the accuracy, step-insensitivity and computational benefits of the proposed co-rotational approach for large displacement analysis of plate structures. Copyright © 2005 John Wiley & Sons, Ltd.

Dynamics of multiple swirling burner flows

Numerical predictions of four counter and co-rotating swirling flows issuing from small-scale low NOx burners have been performed and compared to laser Doppler anemometry (LDA) measurements. The results demonstrate that the near-burner features, such as the central reverse flow zones and the mixing of the burner jets, are resolved correctly by the computational model. Predicted tangential velocity components are in good agreement with the LDA measurements, and show the correct swirl velocity profiles and rate of decay. The anti-gearing phenomenon associated with the entrainment pattern of the counter and co-rotating burner arrays, where flow is entrained into the centre of the array against the direction of swirl, is captured by the LDA measurements and is predicted by the CFD model. Predicted rates of entrainment of surrounding air by the counter and co-rotating burners intimate that a counter-rotating burner array entrains at a greater rate than a single burner. A co-rotating system, however, entrains at a lower rate. The ability to control levels of entrainment may provide the means of further controlling air staging in real furnaces. The research demonstrates that multi-burner systems may be characterised in terms of the number of burners, their rotational direction, the burner pitch and the degree of entrainment.

Finite element analysis of three-dimensional contact and impact in large deformation problems

An algorithm that models three-dimensional contact with friction, including cases where large deformations occur is proposed. The algorithm is an extension to three-dimensions of an algorithm for contact previously proposed by Ponthot and Hogge [1]. The present algorithm can be used in implicit or explicit codes, when contact between a rigid and a deformable body or among deformable bodies (multibody contact) is to be determined. The penalty method is used as the contact–friction formulation. Constitutive relations for contact–friction and integration of these relations in a corotational reference system are detailed. In order to provide a good convergence rate, the contact–friction stiffness matrices used are consistent with the time integration process. A simple and fully explicit form was obtained for these matrices. For contact problems involving rigid and deformable bodies, interpenetrations are detected using an iterative procedure. For frictionless multibody contact, a new element that simplifies the gap calculation, eliminating iterative procedures, is proposed. Comparison with benchmark results and the solution of practical examples demonstrate the effectiveness of the algorithm.

On the Pao Theory for Non-Newtonian Viscosity

An improved version of the Pao theory (J. Polym. Sci., 61, 413 (1962)) is given. The theory is based on a linear tensorial relation between the stress σ and the recoverable strain r-1 on a corotational system rigidly rotating with the material element. We discard Pao's assumption that the ij-element of stress is independent of kl-element of recoverable strain (k≠i or l≠j) on the fixed orthonormal system. Instead we assume that the recoverable shear strain in steady shear flow is given by half the ratio of the principal normal stress to the shear stress. The steady shear viscosity thus obtained is very close to that of the Cox-Merz empirical law, which is applicable to many polymeric systems

On the Torques Due to Tidal Friction of the Oceans and Adjacent Seas

The torques of the frictional forces on the bottoms of the seas are calculated in an approximate inertial system and not in the corotating system used hitherto. In this way, the loss of rotational energy of the Earth – corresponding to the mean torque – can be compared with the value obtained from astronomical observations. The calculations are based on velocities which are computed by numerical integrations of the hydrodynamical equations. Initial results are presented for the North Sea, the Bering Sea and rough models of theworld ocean.

Shimmy of a Nose Gear With Dual Co-Rotating Wheels

In the attempt to reduce weight and complexity, many nose gears have been designed with dual co-rotating wheels to prevent shimmy. In some cases these designs have not resulted in shimmy-free landing gears. In this paper equations are developed which describe the behavior of a dual-wheeled landing gear with co-rotating wheels. These equations show that the role of the tire in determining the shimmy characteristics is more important in the dual-wheeled co-rotating system than in more conventional designs. The method is useful for analysis both of conventional landing gears and of landing gears with dual co-rotational wheels.