LDG Method with P-Adaptivity Applied to LES of Blade-Vortex Interaction

In the present work the Local Discontinuous Galerkin (LDG) method with polynomial adaptivity is applied to the Large Eddy Simulation (LES) of the parallel blade-vortex interaction (BVI). The BVI phenomenon occurs on helicopter and drone rotors in manoeuvring conditions and it produces impulsive changes in the pressure distributions, vibrations and noise. To deeply understand the mechanism of load generation related to the pressure field and three dimensional perturbations growth, to focus on the interaction between the vortex and the three dimensional structures in boundary layer and wake, accurate 3D unsteady numerical simulations of turbulent flows are necessary. For this reason, it is very important the use of a numerical code based on high order schemes such as LDG. Moreover, in the LDG approach, the numerical resolution can be varied on each element and in time, adapting to the requirement of the simulated flow and saving a large amount of computing resources. In the used numerical code the criterion for variation of the polynomial order is based on a refinement indicator especially suited for LES and based on the structure function. The local polynomial representation directly provides a means to separate large from small scale modes, thus providing the starting point for the definition of the subgrid scale models. In the present simulations, the subgrid scales contribution is represented with a sophisticated dynamic anisotropic subgrid model, suitable and well tested for wall resolved LES and complex separated turbulent flows. The BVI is simulated highlighting the effect of the vortex on the pressure distributions, on the boundary layer separation and on the resulting forces

Dynamical p-adaptivity for LES of compressible flows in a high order DG framework

We investigate the possibility of reducing the computational burden of LES models by employing locally and dynamically adaptive polynomial degrees in the framework of a high order DG method. A degree adaptation technique especially featured to be effective for LES applications, that was previously developed by the authors and tested in the statically adaptive case, is applied here in a dynamically adaptive fashion. Two significant benchmarks are considered, comparing the results of adaptive and non adaptive simulations. The proposed dynamically adaptive approach allows for a significant reduction of the computational cost of representative LES computation, while allowing to maintain the level of accuracy guaranteed by LES carried out with constant, maximum polynomial degree values

Pressure and kinetic energy transport across the cavity mouth in resonating cavities

Basic properties of the incompressible fluid motion in a rectangular cavity located along one wall of a plane channel are considered. For Mach numbers of the order of 1 × 10−3 and using the incompressible formulation, we look for observable properties that can be associated with acoustic emission, which is normally observed in this kind of flow beyond a critical value of Reynolds number. The focus is put on the energy dynamics, in particular on the accumulation of energy in the cavity which takes place in the form of pressure and kinetic energy. By increasing the external forcing, we observe that the pressure flow into the cavity increases very rapidly, then peaks. However, the flow of kinetic energy, which is many orders of magnitude lower than that of the pressure, slowly but continuously grows. This leads to the pressure-kinetic energy flows ratio reaching an asymptotic state around the value 1000 for the channel bulk speed Reynolds number. It is interesting to note that beyond this threshold when the channel flow is highly unsteady—a sort of coarse turbulent flow—a sequence of high and low pressure spots is seen to depart from the downward cavity step in the statistically averaged field. The set of spots forms a steady spatial structure, a sort of damped standing wave stretching along the spanwise direction. The line joining the centers of the spots has an inclination similar to the normal to the fronts of density or pressure waves, which are observed to propagate from the downstream cavity edge in compressible cavity flows (at Mach numbers of 1 × 102 to 1 × 103, larger than those considered here). The wavelength of the standing wave is of the order of 1/8 the cavity depth and observed at the channel bulk Reynolds number, Re ∼ 2900. In this condition, the measure of the maximum pressure differences in the cavity field shows values of the order of 1 × 10−1 Pa.We interpret the presence of this sort of wave as the fingerprint of the noise emission spots which could be observed in simulations where the full compressible formulation is used. The flow is studied by means of a sequence of direct numerical simulations in the Reynolds number range 25-2900. This allows the study to span across the steady laminar regime up to a first coarse turbulent regime. These results are confirmed by the good agreement with a set of laboratory results obtained at a Reynolds number one order of magnitude larger in a different cavity geometry [M. Gharib and A. Roshko, J. Fluid Mech. 177, 501 (1987)]. This leaves room for a certain degree of qualitative universality to be associated with the present findings. DOI: 10.1103/PhysRevE.87.01301

A 3D Shape Optimization Problem in Heat Transfer: Analysis and Approximation via BEM

In this paper an optimal shape control problem dealing with heat transfer in enclosures is studied. We have considered an enclosure heated by a flame surface (taking into account radiation, conduction and convection effects), and we look for an optimal flame shape which minimizes a cost functional defined on the temperature field. This kind of problem arises in industrial furnaces optimization, as temperature uniformity is one of the most important aspects in industrial plant analysis and design. Analytical results (smoothness of the control-to-state mapping, existence of an optimal shape in a certain admissible class) as well as numerical optimization results by the boundary element method have been obtained; we have employed the gradient method to optimize the flame shape, exploiting the adjoint equation associated with our state equation and cost functional

Potential of Maritime Transport for Ocean Liming and Atmospheric CO₂ Removal

Proposals to increase ocean alkalinity may make an important contribution to meeting climate change net emission targets, while also helping to ameliorate the effects of ocean acidification. However, the practical feasibility of spreading large amounts of alkaline materials in the seawater is poorly understood. In this study, the potential of discharging calcium hydroxide (slaked lime, SL) using existing maritime transport is evaluated, at the global scale and for the Mediterranean Sea. The potential discharge of SL from existing vessels depends on many factors, mainly their number and load capacity, the distance traveled along the route, the frequency of reloading, and the discharge rate. The latter may be constrained by the localized pH increase in the wake of the ship, which could be detrimental for marine ecosystems. Based on maritime traffic data from the International Maritime Organization for bulk carriers and container ships, and assuming low discharge rates and 15% of the deadweight capacity dedicated for SL transport, the maximum SL potential discharge from all active vessels worldwide is estimated to be between 1.7 and 4.0 Gt/year. For the Mediterranean Sea, based on detailed maritime traffic data, a potential discharge of about 186 Mt/year is estimated. The discharge using a fleet of 1,000 new dedicated ships has also been discussed, with a potential distribution of 1.3 Gt/year. Using average literature values of CO2 removal per unit of SL added to the sea, the global potential of CO2 removal from SL discharge by existing or new ships is estimated at several Gt/year, depending on the discharge rate. Since the potential impacts of SL discharge on the marine environment in the ships' wake limits the rate at which SL can be applied, an overview of methodologies for the assessment of SL concentration in the wake of the ships is presented. A first assessment performed with a three-dimensional non-reactive and a one-dimensional reactive fluid dynamic model simulating the shrinking of particle radii, shows that low discharge rates of a SL slurry lead to pH variations of about 1 unit for a duration of just a few minutes