Section: Application Domains

Fluid mechanics

Participants : Rémi Abgrall [Corresponding member] , Marc Duruflé, Mario Ricchiuto, Pietro Marco Congedo, Cécile Dobrzynzki, Héloïse Beaugendre, Sébastien Blaise.

The numerical simulation of steady and unsteady flows is still a challenge due to the large margin of improvement in efficiency and accuracy of the underlying numerical schemes, and of their computer implementation. The challenge is even greater when considering real applications involving complex geometries and large irregular unstructured grids. The numerical schemes developed in BACCHUS are implemented using Scotch , HIPS and PaStiX whenever the type of problems and the CPU requirements make this useful.

Steady transonic and supersonic flows

One of our application fields is the one of steady subsonic, transonic and supersonic flow problems when the equation of state is for example the one of air in standard conditions, or a more general one as in real gases and multiphase flows. This class of physical problems corresponds to “standard” aerodynamics and the models are those of the Euler equations and the Navier Stokes ones, possibly with turbulent effects. Here we consider residual distribution and SUPG schemes.

Unsteady transonic and supersonic flows

Another field of application is the one of unsteady problems for the same physical models. Depending on the applications, the physical models considered involve the Navier-Stokes equations, or the non-linear or linearized linearized Euler equations. The schemes we develop are the Residual distribution schemes 5.1 and Discontinuous Galerkin schemes 5.9 . Specific modifications, with respect to their steady counter parts, are done in order to reduce dramatically the computational time, while maintaining the desired accuracy.

Turbulent flows

Detached-Eddy Simulation (DES) is a hybrid technique proposed by Spalart et al. in 1997 as a numerically feasible and plausibly accurate approach for predicting massively separated flows. Traditionally, high Reynolds number separated flows have been predicted using Reynolds Averaged Navier-Stokes equations (RANS). Although RANS models are considered as the most practical turbulence handling technique for industrial problems these models are not adapted to massively separated flows widely encountered when dealing with iced bodies. Another growing approach, Large-Eddy Simulation (LES), offers the advantage to directly compute the dominant unsteady structures of the flow. Unfortunately the high computational cost of applying LES to complete configurations such as an airplane, a submarine, or a road vehicle remains prohibitive because of the resolution required in the boundary layers. The aim of Detached-Eddy Simulation (DES) is to combine the most favourable aspects of both techniques, i.e., application of RANS models for predicting the attached boundary layer and LES for time-dependent three-dimensional large eddies. The cost scaling of the method is then affordable since LES is not applied to solve the relatively smaller structures that populate the boundary layer. Simulations of performance degradations due to icing have increased the demand for numerically feasible and accurate approach for predicting massively separated flows around complex geometries. In this aspect flow field predictions obtained using DES are encouraging. To obtain the DES model formulation, the length scale of the S-A destruction term is modified to be the minimum of the distance to the closest wall and a length scale proportional to the local grid spacing. Concurrently with its encouraging results, weaknesses of DES were discovered. Starting from a valid RANS solution, gradually refining the grid alters the solution in obscure ways. The grid is ambiguous and the DES equations fail to recognize that pure RANS behaviour was intended. Resolving the issue of ambiguous grids is a priority but as proven to be a resilient difficulty. A better understanding of the coupling mechanisms between the models is needed.

Inflight icing and ice shedding

Inflight icing:

Every year, sudden aircraft performance degradation due to ice accretion causes several incidents and accidents. Icing is a serious and not yet totally mastered meteorological hazard due to supercooled water droplets that impact on aerodynamic surfaces. Icing results in performance degradations including substantial reduction of engine performance and stability, reduction in maximum lift and stall angle and an increase of drag. One of the most important challenges in understanding the performance degradation is the accurate prediction of complex and massively separated turbulent flows. Turbulent flows are currently modelled and computed using a variety of strategies. The majority of predictions around engineering geometries are obtained from solutions of the Reynolds Averaged Navier-Stokes (RANS) equations. These approaches are often acceptable in the thin shear layers where RANS methods have been calibrated. In other regimes, especially flows in which the turbulent eddies are not standard, i.e., not in the calibration range of the model, the performance of RANS models is, at best, uneven. This in turn motivates other strategies, one of them being Large-Eddy Simulation (LES). The application of LES to prediction of turbulent flows in practical configurations is increasing but the computational cost remains prohibitive. Within the past five years hybrid methods have emerged as a popular approach for predicting complex flows. Spalart et al. proposed DES as a cost-effective and plausibly accurate approach for predicting flows experiencing massive separation. Therefore, the overall objectives are the following:

1. Analysis of the DES approach;

2. Develop the DES model for the simulation of 3D turbulent flow;

3. Discuss the issues that impact the method, including the underlying RANS turbulence model and the simulation design for DES (grids and choice of time steps);

4. Use Airbus test cases to answer the following question: is it possible and advisable to use DES to quantify the performance degradation due to icing;

Potential benefits:

1. Help in the certification process;

2. Include the data in flight simulators to train pilots under icing operating conditions.

Ice shedding:

Actual concerns about greenhouse gases lead to changes in the design of aircraft with an increase use of composite materials. This in turns offers new possibilities for design of ice protection systems, thus renewing interest in de-icing simulation tools. To save fuel burn, aircraft manufacturers are investigating ice protection systems such as electro-thermal or electro-mechanical de-icing systems to replace anti-icing systems. By reducing the adhesive shear strength between ice and surface, de-icing systems remove ice formed on the protected surfaces following a periodic cycle. This cycle is defined such that inter cycle ice shapes remain acceptable from a performance point of view. One of the drawbacks of de-icing device is the ice pieces shed into the flow. The knowledge of ice shedding trajectories could allow assessing the risk of impact/ingestion on/in aircraft components located downstream. When the pieces leave the aircraft surface, they become projectiles that can hit and cause severe damage to aircraft surface or other components, such as aircraft horizontal and vertical tails, or aircraft engine. Aircraft certification authorities, such as FAA, have specific requirements for large ice fragment ingestion during engine certification. Control surfaces or wing flaps are also sensitive to ice shedding because they can be blocked by ice fragments. Aircraft manufacturers rely mainly on flight tests to evaluate the potential negative effects of ice shedding because of the lack of appropriate numerical tools. The random shape and size taken by ice shed particles together with their rotation as they move make it difficult for classical CFD tools to predict trajectories. The numerical simulation of a full unsteady viscous flow, with a set of moving bodies immersed within, shows several difficulties for grid based methods. Drawbacks income from the meshing procedure for complex geometries and the re-griding procedure in tracing the body motion. A new approach that take into account the effect of ice accretion on flow field is used to solve the ice trajectory problem. The approach is based on mesh adaptation, penalization method and level sets.

Geophysical flows

A challenging and important field of application is that of free surface flows for geophysical applications such as the propagation of tsunamis, and their interaction with complex coastal environments. A model often used to simulate these phenomena is the so-called shallow water model, describing the dynamics of depth and depth averaged velocity of the water. These model, while bearing many similarities with the equations of compressible gas-dynamics, present many peculiarities : the presence of source terms modeling the effects of bathymetry variations and of friction on the bottom and often controlling the dynamics of the flow, the fact that dry states occur normally (differently from vacuum in gas-dynamics), and that their dynamics when considering wave/coast interaction is one of the most important outputs of the simulation. Our work aims at borrowing tools developed in the context of industrial/aeronautics applications for these environmental applications. In particular, we have adapted to this model the residual schemes used for aeronautic applications 5.3 , showing a very important potential of this class of numerical schemes for these applications.

Real-gas flows in turbine cascade

An important field of application consists in the use of real-gas thermodynamic model for the simulation of turbulent flows in turbine cascade. The aim is to demonstrate the potentiality of BZT fluids for turbine applications. BZT fluids are characterized by negative values of the fundamental derivative of gasdynamics for a range of temperatures and pressures in the vapor phase, which leads to non- classical gasdynamic behaviors such as the disintegration of compression shocks. The non-classical phenomena typical of BZT fluids have several practical outcomes: prominent among them is an active research effort to reduce losses caused by wave drag and shock/boundary layer interactions in turbomachines and nozzles, with particular application to ORCs used to generate electric energy in low-power applications. The use of BZT fluids as ORC working fluids is potentially interesting because the shock formation and the consequent losses could be ideally avoided if turbine expansion could happen entirely within or very close to particular region called inversion zone where the fundamental derivative of gasdynamics is negative. In fact, as recently investigated, rarefaction shock waves are physically admissible in the inversion region. Within this project, several advancements with regards to the thermodynamic modeling of the fluids [8] , the numerical simulation of the fluid flow and the cross-validation of the numerical results [9] , and the robust optimization of some simple configuration [27] , [10] , [28] , have been performed. Here we consider more classical finite-volume scheme (HLL scheme with a second-order spatial accuracy ensured by means of a MUSCL-type reconstruction).