# Numerical study of turbulent flow over an S-shaped hydrofoil

01 Sep 2008-Vol. 222, Iss: 9, pp 1717-1734

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TL;DR: In this article, a new duct is developed for a given turbine design, that reduces the variation in torque over a cycle by appropriately directing the flow upstream and downstream the turbine while increasing power conversion.

Abstract: Computational study is carried out to develop a new duct with the purpose of improving the performance of a straight-bladed Darrieus hydroturbine. Though Darrieus turbine is very simple to construct, it has some disadvantages when compared to axial turbines. These are a lower power coefficient and a variation in the torque produced within the cycle leading to periodic loading on the components of the turbine. The main objective of the present study is to retain the simple design and fabrication procedure of Darrieus turbine while reducing the disadvantages. In this study, a new duct is developed, for a given turbine design, that reduces the variation in torque over a cycle by appropriately directing the flow upstream and downstream the turbine while increasing power conversion. At the operating point, which is at a tip-speed ratio of 2, use of a duct reduces the torque ripple by a factor of 4.15 and the power coefficient( C p )is increased to 0.63 from 0.40. By choosing the position of the turbine in the duct appropriately, it is shown that the torque ripple may be reduced by a factor of 6.37, at the expense of the power coefficient. And, a maximum C p = 0.644 is observed when the turbine center coincided with the throat of the duct. Similarly, the effect of varying other parameters such as the convergence angle of the duct and its external shape on the performance of the turbine are studied through numerical simulation. It is seen that there exists an optimum value in each case. While varying the convergence angle of the duct it is observed that the maximum power coefficient and lowest torque ripple are obtained at the same value of duct half angle, equal to 27°. The dependence of the power coefficient and torque ripple on duct convergence angle is weak. The duct with straight external shape is observed to have best performance with a peak power coefficient of 0.72, while the convex external shape has a peak of only 0.51. The external shape is observed to have a negligible effect of the torque ripple factor. Significance of the emerging trends of parameters are discussed.

52 citations

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TL;DR: The efficiency of jet pump is poor and it usually has a sharp peak in the efficiency-discharge ratio curve as mentioned in this paper, which is undesirable for the purpose of transporting materials in the air.

Abstract: Jet pump plays a major role in transporting materials. The efficiency of jet pump is poor and it usually has a sharp peak in the efficiency–discharge ratio curve. These are undesirable. In the past...

15 citations

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14 citations

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TL;DR: In this paper, a numerical investigation of flow over a cascade of S-shaped hydrofoils is presented, and it is found from numerical simulations that the useful range of operation is restricted to 6° for turbine operation and −6° for pump operation.

Abstract: Hydrodynamic characteristics like lift and drag coefficients of a cascade of blades as well as comprehensive data of pressure loss and flow deflection are important for the design of a hydroturbomachine. In the present paper numerical investigation of flow over a cascade of S-shaped hydrofoils is presented. These S-shaped hydrofoils find potential application in the design of a fully reversible pump-turbine employed in tidal power generation. Influences of stagger angle, blade spacing and angle of incidence on the performance of S-blade cascade were investigated and these are reported here. Numerical results are validated with experimental data available in the literature and further simulations help to extend the knowledge of the flow field for such a complicated geometry. It is found from numerical simulations that the useful range of operation is restricted to +6° for turbine operation and −6° for pumping. A significant finding in this study is that the cascade pressure loss is significantly more for the pump cascade than the turbine cascade and this loss increases as the blade spacing is reduced.

5 citations

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TL;DR: In this article, the effects of convex wall curvature on turbulent boundary layer flow were studied using a numerical method using the non-linear k−e model often used in engineering applications.

Abstract: Effects of convex wall curvature on turbulent boundary layer flow are studied in this article using a numerical method. Since the non-linear k−e model often used in engineering applications...

4 citations

##### References

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TL;DR: In this paper, two new two-equation eddy-viscosity turbulence models are presented, which combine different elements of existing models that are considered superior to their alternatives.

Abstract: Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

12,746 citations

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TL;DR: In this paper, the authors examined the modeling of the pressure-strain correlation of turbulent flows from a basic theoretical standpoint with a view toward developing improved second-order closure models and proved that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor.

Abstract: The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

1,438 citations

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TL;DR: In this article, the k-e-v2 model is used to predict the time-averaged properties of bluff body flow, which is necessary to resolve the coherent vortex shedding.

Abstract: Tlirbulent separated flows over a backstep, in a plane diffuser and around a triangular cylinder, are computed with the k-e-v2 model. These provide examples of massive separation, of smooth separation, and of unsteady vortex shedding. It is shown that to accurately predict the time-averaged properties of bluff body flow, it is necessary to resolve the coherent vortex shedding. The near-wall treatment of the v2-/22 system of equations is able to cope with both the massive and smooth separations. Good agreement between experiment and prediction is found in all

571 citations

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TL;DR: In this paper, a two-dimensional, separating turbulent boundary layer for an airfoil-type flow in which the flow was accelerated and then decelerated until separation is presented.

Abstract: The problem of turbulent-boundary-layer separation due to an adverse pressure gradient is an old but still important problem in many fluid flow devices. Until recent years little quantitative experimental information was available on the flow structure downstream of separation because of the lack of proper instrumentation. The directionally sensitive laser anemometer provides the ability to measure the instantaneous flow direction and magnitude accurately. The experimental results described here are concerned with a nominally two-dimensional, separating turbulent boundary layer for an airfoil-type flow in which the flow was accelerated and then decelerated until separation. Upstream of separation single and cross-wire hot-wire anemometer measurements are also presented. Measurements in the separated zone with a directionally sensitive laser-anemometer system were obtained for U, V , $\overline{u^2}, \overline{v^2}, - \overline{uv}$ , the fraction of time that the flow moves downstream, and the fraction of time that the flow moves away from the wall. In addition to confirming the earlier conclusions of Simpson, Strickland & Barr (1977) regarding a separating airfoil-type turbulent boundary layer, much new information about the separated region has been gathered. (1) The backflow mean velocity profile scales on the maximum negative mean velocity U N and its distance from the wall N . A U + vs. y + law-of-the-wall velocity profile is not consistent with this result. (2) The turbulent velocities are comparable with the mean velocity in the backflow, although low turbulent shearing stresses are present. (3) Mixing length and eddy viscosity models are physically meaningless in the backflow and have reduced values in the outer region of the separated flow. Downstream of fully developed separation, the mean backflow appears to be divided into three layers: a viscous layer nearest the wall that is dominated by the turbulent flow unsteadiness but with little Reynolds shearing stress effects; a rather flat intermediate layer that seems to act as an overlap region between the viscous wall and outer regions; and the outer backflow region that is really part of the large-scaled outer region flow. The Reynolds shearing stress must be modelled by relating it to the turbulence structure and not to local mean velocity gradients. The mean velocities in the backflow are the results of time averaging the large turbulent fluctuations and are not related to the source of the turbulence.

267 citations

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TL;DR: In this paper, direct numerical simulations of turbulent flows seeded with millions of passive inertial particles are presented, where the maximum Reynolds number is Re λ∼ 200 and the acceleration fluctuations as a function of the Stokes number in the range St ∈ [0.16:3].

Abstract: We present the results of direct numerical simulations (DNS) of turbulent flows seeded with millions of passive inertial particles. The maximum Reynolds number is Re λ∼ 200. We consider particles much heavier than the carrier flow in the limit when the Stokes drag force dominates their dynamical evolution. We discuss both the transient and the stationary regimes. In the transient regime, we study the growth of inhomogeneities in the particle spatial distribution driven by the preferential concentration out of intense vortex filaments. In the stationary regime, we study the acceleration fluctuations as a function of the Stokes number in the range St ∈ [0.16:3.3]. We also compare our results with those of pure fluid tracers (St = 0) and we find a critical behavior of inertia for small Stokes values. Starting from the pure monodisperse statistics we also characterize polydisperse suspensions with a given mean Stokes, .

207 citations

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