Two identical tandem square prisms with rounded edges and hard marine fouling at incidence in cross-flow: effect of spacing and Reynolds number on unsteady fluid dynamics

Because of their long submerged columns, deep-draft semi-submersible floating structures are particularly susceptible to vortex-induced motions. This paper focuses on the steady and unsteady forces that act on such a column pair, as well as on the frequency and strength of the shed vortices behind the downstream column. Wind tunnel experiments were performed on two rounded and lightly rough square-section prisms in cross-flow for Reynolds numbers from 100,000 up to 7 million. They are arranged inline at centre-to-centre distances of S/D = 2.8, 4, and 5.6 and at 0° or 45° incidence angle. The trend of the drag curve for the upstream prism deviates at S/D = 2.8 and 4 sharply from that for a single prism. The drag force on the downstream prism strongly depends on both S/D and α. At S/D = 2.8, a thrust force occurs either in certain (α = 0°) or in all (α = 45°) flow states. Larger spacing values lead to an overall higher drag and a flattening of the Cd2 (ReD) curve. The highest fluctuating lift forces on the downstream prism are obtained at α = 45°. Regarding the vortex shedding frequency, differences between both incidence angles occur at S/D = 5.6 only

Clustering of vertically constrained passive particles in homogeneous, isotropic turbulence

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale, that maximizes the clustering of the particles

Evaluatie van de verzuringsdoelstellingen: kwantificering van de effecten van emissievarianten op half-natuurlijke terrestrische ecosystemen

In het kader van de evaluatie verzuringsdoelstellingen zijn depositiescenario's geëvalueerd met de dynamische modellen SMART2/MOVE. Het blijkt dat door naijleffecten overschrijdingen van normen kunnen optreden, terwijl kritische depositieniveaus niet meer overschreden worden. De vertraging is ongeveer tien jaar. Voor adequate bescherming van bossen en natuurgebieden is het van belang dat naast Nederlandse ook buitenlandse emissies gereduceerd worden

Scenario-ontwikkeling voor het natuurbeleid

De Natuurverkenning 2010-2040 is als scenariostudie uitgevoerd om te verkennen welke richtingen het natuurbeleid op termijn zou kunnen inslaan. Via de scenario-onderdelen worden beleidsmakers stap voor stap in het langetermijndenken meegenomen. Dit wordt versterkt doordat de onderdelen het karakter van kwalitatieve verhalen hebben gekregen, die bovendien toegankelijk zijn verbeeld en op onderdelen kwantitatief zijn uitgewerkt. Doordat beleidsmakers zelf in de verkenning hebben geparticipeerd is hun ontvankelijkheid ervoor vergroot. Over: natuurverkenning, scenariomethode, normatieve scenario's en stakeholderparticipati

On optimal interpolation schemes for particle tracking in turbulence

An important aspect in numerical simulations of particle-laden turbulent flows is the interpolation of the flow fleld needed for the computation of the Lagrangian trajectories. The accuracy of the interpolation method has direct consequences for the acceleration spectrum of the fluid particles and is therefore also important for the correct evaluation of the hydrodynamic forces for almost neutrally buoyant particles, common in many environmental applications. In order to systematically choose the optimal tradeoff between interpolation accuracy and computational cost we focuss on comparing errors: the interpolation error is compared with the discretisation error of the flow field. In this way one can prevent unnecessary computations and still retain the accuracy of the turbulent flow simulation. From the analysis a practical method is proposed that enables direct estimation of the interpolation and discretization error from the energy spectrum. The theory is validated by means of Direct Numerical Simulations (DNS) of homogeneous, isotropic turbulence using a spectral code, where the trajectories of fluid tracers are computed using several interpolation methods. We show that B-spline interpolation has the best accuracy given the computational cost. Finally, the optimal interpolation order for the different methods is shown as a function of the resolution of the DNS simulation

An efficient, second order method for the approximation of the Basset history force

The hydrodynamic forces exerted by a fluid on small isolated rigid spherical particles are usually well described by the Maxey-Riley (MR) equation. The most time-consuming contribution in the MR equation is the Basset history force which is a well-known problem for many-particle simulations in turbulence. In this paper a novel numerical approach is proposed for the computation of the Basset history force based on the use of exponential functions to approximate the tail of the Basset force kernel. Typically, this approach not only decreases the cpu time and memory requirements for the Basset force computation by more than an order of magnitude, but also increases the accuracy by an order of magnitude. The method has a temporal accuracy of O(Delta t^2) which is a substantial improvement compared to methods available in the literature. Furthermore, the method is partially implicit in order to increase stability of the computation. Traditional methods for the calculation of the Basset history force can influence statistical properties of the particles in isotropic turbulence, which is due to the error made by approximating the Basset force and the limited number of particles that can be tracked with classical methods. The new method turns out to provide more reliable statistical data.Comment: 21 pages, 9 figure

Clinopyroxene/melt trace element partitioning in sodic alkaline magmas

Clinopyroxene is a key fractionating phase in alkaline magmatic systems, but its impact on metal enrichment processes, and the formation of REE + HFSE mineralisation in particular, is not well understood. To constrain the control of clinopyroxene on REE + HFSE behaviour in sodic (per)alkaline magmas, a series of internally heated pressure vessel experiments was performed to determine clinopyroxene–melt element partitioning systematics. Synthetic tephriphonolite to phonolite compositions were run H2O-saturated at 200 MPa, 650–825°C with oxygen fugacity buffered to log f O2 ≈ ΔFMQ + 1 or log f O2 ≈ ΔFMQ +5. Clinopyroxene–glass pairs from basanitic to phonolitic fall deposits from Tenerife, Canary Islands, were also measured to complement our experimentally-derived data set. The REE partition coefficients are 0·3–53, typically 2–6, with minima for high-aegirine clinopyroxene. Diopside-rich clinopyroxene (Aeg5–25) prefer the MREE and have high REE partition coefficients (DEu up to 53, DSm up to 47). As clinopyroxene becomes more Na- and less Ca-rich (Aeg25–50), REE incorporation becomes less favourable, and both the VIM1 and VIIIM2 sites expand (to 0·79 Å and 1·12 Å), increasing DLREE/DMREE. Above Aeg50 both M sites shrink slightly and HREE (VIri ≤ 0·9 Å ≈ Y) partition strongly onto the VIM1 site, consistent with a reduced charge penalty for REE3+ ↔ Fe3+ substitution. Our data, complemented with an extensive literature database, constrain an empirical model that predicts trace element partition coefficients between clinopyroxene and silicate melt using only mineral major element compositions, temperature and pressure as input. The model is calibrated for use over a wide compositional range and can be used to interrogate clinopyroxene from a variety of natural systems to determine the trace element concentrations in their source melts, or to forward model the trace element evolution of tholeiitic mafic to evolved peralkaline magmatic systems