Gianluca Iaccarino

Immersed boundary technique for turbulent flow simulations

The application of the Immersed Boundary ~IB! method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard Reynolds-Averaged Navier-Stokes models or the more sophisticated Large Eddy Simulation approach. The main features of the IB technique are described with emphasis on the treatment of boundary conditions at an immersed surface. Examples of flows around a cylinder, in a wavy channel, inside a stirred tank and a piston/cylinder assembly, and around a road vehicle are presented. Comparison with experimental data shows the accuracy of the present technique. This review article cites 70 references. @DOI: 10.1115/1.1563627# 1 CONTEXT The continuous growth of computer power strongly encourages engineers to rely on computational fluid dynamics ~CFD! for the design and testing of new technological solutions. Numerical simulations allow the analysis of complex phenomena without resorting to expensive prototypes and difficult experimental measurements. The basic procedure to perform numerical simulation of fluid flows requires a discretization step in which the continuous governing equations and the domain of interest are transformed into a discrete set of algebraic relations valid in a finite number of locations ~computational grid nodes! inside the domain. Afterwards, a numerical procedure is invoked to solve the obtained linear or nonlinear system to produce the local solution to the original equations. This process is simple and very accurate when the grid nodes are distributed uniformly ~Cartesian mesh! in the domain, but becomes computationally intensive for disordered ~unstructured! point distributions. For simple computational domains ~a box, for example! the generation of the computational grid is trivial; the simulation of a flow around a realistic configuration ~a road vehicle in a wind tunnel, for example!, on the other hand, is extremely complicated and time consuming since the shape of the domain must include the wetted surface of the geometry of interest. The first difficulty arises from the necessity to build a smooth surface mesh on the boundaries of the domain ~body conforming grid!. Usually industrially relevant geometries are defined in a CAD environment and must be translated and cleaned ~small details are usually eliminated, overlapping surface patches are trimmed, etc! before a surface grid can be generated. This mesh serves as a starting point to generate the volume grid in the computational domain. In addition, in many industrial applications, geometrical complexity is combined with moving boundaries and high Reynolds numbers. This requires regeneration or deformation of the grid during the simulation and turbulence modeling, leading to a considerable increase of the computational difficulties. As a result, engineering flow simulations have large computational overhead and low accuracy owing to a large number of operations per node and high storage requirements in combination with low order dissipative spatial discretization. Given the finite memory and speed of computers, these simulations are very expensive and time consuming with computational meshes that are generally limited to around one million nodes. In view of these difficulties, it is clear that an alternative numerical procedure that can handle the geometric complexity, but at the same time retains the accuracy and high efficiency of the simulations performed on regular grids, would represent a significant advance in the application of CFD to industrial flows.

Reynolds averaged simulation of unsteady separated flow

The accuracy of Reynolds averaged Navier–Stokes (RANS) turbulence models in predicting complex flows with separation is examined. The unsteady flow around square cylinder and over a wall-mounted cube are simulated and compared with experimental data. For the cube case, none of the previously published numerical predictions obtained by steady-state RANS produced a good match with experimental data. However, evidence exists that coherent vortex shedding occurs in this flow. Its presence demands unsteady RANS computation because the flow is not statistically stationary. The present study demonstrates that unsteady RANS does indeed predict periodic shedding, and leads to much better concurrence with available experimental data than has been achieved with steady computation.

Numerical simulation of the flow around a circular cylinder at high Reynolds numbers

The viability and accuracy of large-eddy simulation (LES) with wall modeling for high Reynolds number complex turbulent flows is investigated by considering the flow around a circular cylinder in the supercritical regime. A simple wall stress model is employed to provide approximate boundary conditions to the LES. The results are compared with those obtained from steady and unsteady Reynolds-averaged Navier–Stokes (RANS) solutions and the available experimental data. The LES solutions are shown to be considerably more accurate than the RANS results. They capture correctly the delayed boundary layer separation and reduced drag coefficients consistent with experimental measurements after the drag crisis. The mean pressure distribution is predicted reasonably well at ReD=5×105 and 106. However, the Reynolds number dependence is not captured, and the solution becomes less accurate at increased Reynolds numbers.

Large-Eddy Simulation of Reacting Turbulent Flows in Complex Geometries

Large-eddy simulation (LES) has traditionally been restricted to fairly simple geometries. This paper discusses LES of reacting flows in geometries as complex as commercial gas turbine engine combustors. The incompressible algorithm developed by Mahesh et al. (J. Comput. Phys., 2004, 197, 215-240) is extended to the zero Mach number equations with heat release. Chemical reactions are modeled using the flamelet/progress variable approach of Pierce and Moin (J. Fluid Mech., 2004, 504, 73-97). The simulations are validated against experiment for methane-air combustion in a coaxial geometry, and jet-A surrogate/air combustion in a gas-turbine combustor geometry.

An immersed boundary method for compressible flows using local grid refinement

This paper combines a state-of-the-art method for solving the three-dimensional preconditioned Navier-Stokes equations for compressible flows with an immersed boundary approach, to provide a Cartesian-grid method for computing complex flows over a wide range of the Mach number. Moreover, a flexible local grid refinement technique is employed to achieve high resolution near the immersed body and in other high-flow-gradient regions at a fraction of the cost required by a uniformly fine grid. The method is validated versus well documented steady and unsteady test problems, for a wide range of both Reynolds and Mach numbers. Finally, and most importantly, for the case of the laminar compressible steady flow past an NACA-0012 airfoil, a thorough mesh-refinement study shows that the method is second-order accurate.

A least-squares approximation of partial differential equations with high-dimensional random inputs

Uncertainty quantification schemes based on stochastic Galerkin projections, with global or local basis functions, and also stochastic collocation methods in their conventional form, suffer from the so called curse of dimensionality: the associated computational cost grows exponentially as a function of the number of random variables defining the underlying probability space of the problem. In this paper, to overcome the curse of dimensionality, a low-rank separated approximation of the solution of a stochastic partial differential (SPDE) with high-dimensional random input data is obtained using an alternating least-squares (ALS) scheme. It will be shown that, in theory, the computational cost of the proposed algorithm grows linearly with respect to the dimension of the underlying probability space of the system. For the case of an elliptic SPDE, an a priori error analysis of the algorithm is derived. Finally, different aspects of the proposed methodology are explored through its application to some numerical experiments.

Analysis of flow conditions in freejet experiments for studying airfoil self-noise

A new set of mean wall pressure data has been collected on a controlled diffusion airfoil at a chord Reynolds number of 1.2 £ £105 in a freejet anechoic wind tunnel. Comparisons of the experimental data with Reynoldsaveraged Navier‐ Stokes (RANS) simulationsin freeairshow signie cant e owe eld and pressure loading differences, indicatingsubstantialjetinterferenceeffects.Toanalyzetheseeffects,asystematicRANS-basedcomputationale uid dynamicsstudyoftheexperimentale owconditionshasbeencarriedout,whichquantie esthestrongine uenceofthe e nite jet (nozzle) width on the aerodynamic loading and e ow characteristics. When the jet width is not sufe ciently large compared to the frontal wetted area of the airfoil, the airfoil pressure distribution is found to be closer to the distribution on a cascade than that of an isolated proe le. The airfoil lift is signie cantly reduced. Accounting for the actual wind-tunnel setup recovers the wall pressure distribution on the airfoil without further empirical angle-of-attack corrections. These jet interference effects could be responsible for the discrepancies among some earlier experimental and computational studies of airfoil self-noise. They should be accounted for in future noise computations to ensure that the experimental e ow conditions are simulated accurately.

Reynolds averaged simulation of flow and heat transfer in ribbed ducts

The accuracy of modern eddy-viscosity type turbulence models in predicting turbulent flows and heat transfer in complex passages is investigated. The particular geometries of interest here are those related to turbine blade cooling systems. This paper presents numerical data from the calculation of the turbulent flow field and heat transfer in two-dimensional (2D) cavities and threedimensional (3D) ribbed ducts. It is found that heat transfer predictions obtained using the v 2 –f turbulence model for the 2D cavity are in good agreement with experimental data. However, there is only fair agreement with experimental data for the 3D ribbed duct. On the wall of the duct where ribs exist, predicted heat transfer agrees well with experimental data for all configurations (different streamwise rib spacing and the cavity depth) considered in this paper. But heat transfer predictions on the smooth-side wall do not concur with the experimental data. Evidence is provided that this is mainly due to the presence of strong secondary flow structures which might not be properly simulated with turbulence models based on eddy viscosity. 2002 Elsevier Science Inc. All rights reserved. Accurate evaluation of heat loads in the components of a gas-turbine engine is a key factor in the development of new, efficient engines. Common design techniques utilize experimental data correlations to quickly estimate the heat transfer coefficients (Webb et al., 1971). These methods do not reveal the underlying mechanism of turbulence and heat transfer for the device in question. They often are inaccurate. Owing to advances in available computer resources, elaborate numerical techniques, based on the solution of the full 3D Reynolds averaged Navier–Stokes (RANS) equations, are now being used to shed light on the flow phenomena and to provide guidelines to improve design methodology. In the RANS approach, the Navier– Stokes equations are averaged and the Reynolds stresses are computed with a turbulence model. The choice of turbulence model is crucial, as it directly affects the computational requirements and the accuracy of the

Reynolds-Averaged Navier-Stokes Simulations of the HyShot II Scramjet

The internal flow in the HyShot II scramjet is investigated through numerical simulations. A computational infrastructure to solve the compressible Reynolds-averaged Navier–Stokes equations on unstructured meshes is introduced. A combustion model based on tabulated chemistry is considered to incorporate detailed chemical– kinetics mechanics while retaining a low computational cost. Both nonreactive and reactive simulations have been performed, and results are compared with ground test measurements obtained at DLR, German Aerospace Center. Different turbulence models were tested, and the dependence on the mesh is assessed through grid refinement. The comparison with experimental data shows good agreement, although the computed heat fluxes at the wall are higher thanmeasurements for the reactive case. A sensitivity analysis on the turbulent Schmidt and Prandtl numbers shows that the choice of these parameters has a strong influence on the results. In particular, variations of the turbulent Prandtl number lead to large changes in the heat flux at the walls. Finally, the inception of thermal choking is investigated by increasing the equivalence ratio, whereby a normal shock is created locally and moves upstream, leading to a large increase in the maximum pressure. Nevertheless, a large portion of the flow is still supersonic.

LES prediction of wall-pressure fluctuations and noise of a low-speed airfoil

This paper discusses the prediction of wall-pressure fluctuations and noise of a low-speed flow past a thin cambered airfoil using large-eddy simulation (LES). The results are compared with experimental measurements made in an open-jet anechoic wind-tunnel at Ecole Centrale de Lyon. To account for the effect of the jet on airfoil loading, a Reynolds-averaged Navier-Stokes calculation is first conducted in the full wind-tunnel configuration, and the mean velocities from this calculation are used to define the boundary conditions for the LES in a smaller domain within the potential core of the jet. The LES flow field is characterized by an attached laminar boundary layer on the pressure side of the airfoil and a transitional and turbulent boundary layer on the suction side, in agreement with experimental observations. An analysis of the unsteady surface pressure field shows reasonable agreement with the experiment in terms of frequency spectra and spanwise coherence in the trailing-edge region. In the nose region, characterized by unsteady separation and transition to turbulence, the wall-pressure fluctuations are highly sensitive to small perturbations and thus diffcult to predict or measure with certainty. The LES, in combination with the Ffowcs Williams and Hall solution to the Lighthill equation, also predicts well the radiated trailing-edge noise. A finite-chord correction is derived and applied to the noise prediction, which is shown to improve the overall agreement with the experimental sound spectrum.