Sanjeeb Bose

Using singular values to build a subgrid-scale model for large eddy simulations

An eddy-viscosity based, subgrid-scale model for large eddy simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor. The proposed σ-model has, by construction, the property to automatically vanish as soon as the resolved field is either two-dimensional or two-component, including the pure shear and solid rotation cases. In addition, the model generates no subgrid-scale viscosity when the resolved scales are in pure axisymmetric or isotropic contraction/expansion. At last, it is shown analytically that it has the appropriate cubic behavior in the vicinity of solid boundaries without requiring any ad-hoc treatment. Results for two classical test cases (decaying isotropic turbulence and periodic channel flow) obtained from three different solvers with a variety of numerics (finite elements, finite differences, or spectral methods) are presented to illustrate the potential of this model. The results obtained with the proposed model are systematically equivalent...

Grid-independent large-eddy simulation using explicit filtering

The governing equations for large-eddy simulation are derived from the application of a low-pass filter to the Navier–Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter, causing results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operation, and hence the resolved turbulence, from the underlying mesh distribution alleviating some of the grid sensitivities. We investigate the use of explicit filtering in large-eddy simulation in order to obtain numerical solutions that are grid independent. The convergence of simulations using a fixed filter width with varying mesh resolutions to a true large-eddy simulation solution is analyzed for a turbulent channel flow at Reτ=180, 395, and 640. By using explicit filtering, turbulent statistics and energy spectra are shown to be independent of the mesh resolution used.

An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements

We describe and characterize a method for estimating the pressure field corresponding to velocity field measurements such as those obtained by using particle image velocimetry. The pressure gradient is estimated from a time series of velocity fields for unsteady calculations or from a single velocity field for quasi-steady calculations. The corresponding pressure field is determined based on median polling of several integration paths through the pressure gradient field in order to reduce the effect of measurement errors that accumulate along individual integration paths. Integration paths are restricted to the nodes of the measured velocity field, thereby eliminating the need for measurement interpolation during this step and significantly reducing the computational cost of the algorithm relative to previous approaches. The method is validated by using numerically simulated flow past a stationary, two-dimensional bluff body and a computational model of a three-dimensional, self-propelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio and out-of-plane effects. Particle image velocimetry measurements of a freely swimming jellyfish medusa and a freely swimming lamprey are analyzed using the method to demonstrate the efficacy of the approach when applied to empirical data.

A dynamic slip boundary condition for wall-modeled large-eddy simulation

Wall models for large-eddy simulation (LES) are a necessity to remove the prohibitive resolution requirements of near-wall turbulence in high Reynolds turbulent flows. Traditional wall models often rely on assumptions about the local state of the boundary layer (e.g., logarithmic velocity profiles) and require a priori prescription of tunable model coefficients. In the present study, a slip velocity boundary condition for the filtered velocity field is obtained from the derivation of the LES equations using a differential filter. A dynamic procedure for the local slip length is additionally formulated making the slip velocity wall model free of any a priori specified coefficients. The accuracy of the dynamic slip velocity wall model is tested in a series of turbulent channel flows at varying Reynolds numbers and in the LES of a National Advisory Committee for Aeronautics (NACA) 4412 airfoil at near-stall conditions. The wall-modeled simulations are able to accurately predict mean flow characteristics, inc...

Direct Numerical Simulation and Large Eddy Simulation of Laminar Separation Bubbles at Moderate Reynolds Numbers

Flows over airfoils and blades in rotating machinery for unmanned and microaerial vehicles, wind turbines, and propellers consist of different flow regimes. A laminar boundary layer near the leading edge is often followed by a laminar separation bubble with a shear layer on top of it that experiences transition to turbulence. The separated turbulent flow then reattaches and evolves downstream from a nonequilibrium turbulent boundary layer to an equilibrium one. Typical Reynolds-averaged Navier–Stokes (RANS) turbulence modeling methods were shown to be inadequate for such laminar separation bubble flows (Spalart and Strelets, 2000, “Mechanisms of Transition and Heat Transfer in a Separation Bubble,” J. Fluid Mech., 403, pp. 329–349). Direct numerical simulation (DNS) is the most reliable but is also the most computationally expensive alternative. This work assesses the capability of large eddy simulations (LES) to reduce the resolution requirements for such flows. Flow over a flat plate with suitable velocity boundary conditions away from the plate to produce a separation bubble is considered. Benchmark DNS data for this configuration are generated with the resolution of 59 × 106 mesh points; also used is a different DNS database with 15 × 106 points (Spalart and Strelets, 2000, “Mechanisms of Transition and Heat Transfer in a Separation Bubble,” J. Fluid Mech., 403, pp. 329–349). Results confirm that accurate LES are possible using O(1%) of the DNS resolution.

Unstructured Large Eddy Simulations for Nozzle Interior Flow Modeling and Jet Noise Predictions

Large eddy simulations are performed for a heated over-expanded supersonic jet issued from twin converging-diverging nozzles. As the focus of the study is on nozzle interior flow modeling and its potential impact on flow and noise predictions in the jet plume, the Y-duct, S-ducts and angle adapters upstream of the nozzles are explicitly included the computational domain, using unstructured body-fitted grids. The present modeling approach consists in adaptive mesh refinement of the internal boundary layers, application of inlet synthetic turbulence, and wall-stress modeling on the interior surfaces. The main effects of the additional modeling inside the exhaust system are twofold: first it appears to prevent reverse flow observed in the baseline simulations without modeling near the start of the converging part of the nozzle; second, it tends to promote thin perturbed boundary layers inside the nozzle that rapidly transition to turbulent (rather than laminar) shear layer in the jet plume, with higher spreading rate than in the baseline cases. Overall, the farfield noise predictions show good agreement with experimental measurements from NASA Glenn Research Center. In particular, the azimuthal variations in radiated sound and the shielding effects reducing noise in the plane of the jets are well captured in the simulations. The numerical results exhibit however an unusual over-prediction of the mixing noise at peak angles, of up to +3dB. The current hypothesis is that the installation effects present in the experiment and not in the simulations would be the likely cause of these discrepancies.

Large-eddy simulation of turbulent channel flow using explicit filtering and dynamic mixed models

Large-eddy simulations of turbulent channel flow at Reτ = 395 are performed using explicit filtering. Two different subfilter-scale models, the dynamic Smagorinsky mixed model and the dynamic global-coefficient mixed model, are formulated in accordance with the explicitly filtered governing equations. The use of explicit filtering separates the filtering operation from discretization, thereby producing a grid-independent solution. In explicit-filter large-eddy simulations, both the dynamic Smagorinsky mixed and the dynamic global-coefficient mixed subfilter-scale models are found to produce solutions close to the non-filtered direct numerical simulation data when explicit-filter widths in the streamwise and spanwise directions and at the center of the channel in the wall normal direction are about four times the grid spacings for direct numerical simulation. Solutions obtained using explicit-filter large-eddy simulation are compared with solutions obtained using implicit-filter large-eddy simulation in a ...

Aerodynamic Heating in Wall-Modeled Large-Eddy Simulation of High-Speed Flows

Aerospace vehicles flying at supersonic and hypersonic speeds are subject to increased wall heating rates caused by viscous friction with the gas environment. This extra heat is commonly referred t...

Large Eddy Simulations for blood dynamics in realistic stenotic carotids

In this paper, we consider large eddy simulations (LES) for human stenotic carotids in presence of atheromasic plaque, a pathological condition where transitional effects to turbulence may occur, with relevant clinical implications such as plaque rupture. We provide a reference numerical solution obtained at high resolution without any subgrid scale model, to be used to assess the accuracy of LES simulations. In the context we are considering, ie, hemodynamics, we cannot refer to a statistically homogeneous, isotropic, and stationary turbulent regime; hence, the classical Kolmogorov theory cannot be used. For this reason, a mesh size and a time step are deemed fine enough if they allow to capture all the features of the velocity field in the shear layers developed after the bifurcation. To assess these requirements, we consider a simplified model of the evolution of a 2D shear layer, a relevant process in the formation of transitional effects in our case. Then, we compare the results of LES σ model (both static and dynamic) and mixed LES models (where also a similarity contribution is considered). In particular, we consider a realistic scenario of a human carotid, and we use the reference solution as gold standard. The results highlight the accuracy of the LES σ models, especially for the static model.

Wall-Modeling in Complex Turbulent Flows

Resolution of wall layer turbulent structures in large eddy simulation of high Reynolds number flows of aeronautical interest requires inordinate computational resources. LES with wall models is therefore employed in engineering applications. We report on recent advances at the Center for Turbulence Research (CTR) in the development of wall boundary conditions for complex turbulent flows computed on unstructured grids. We begin by describing a novel application of wall modeled LES to a high lift airfoil system. This flow field is very complex involving boundary layers, free shear flows, separation and laminar/turbulence transition. We then describe a non-equilibrium model that requires the solution of the full 3D RANS equations in the near wall region. This model is successfully applied to a spatially evolving transitional and a high Reynolds number flat plate boundary layer. Finally we describe a new approach to LES using differential filters. An important byproduct of this approach is the derivation of slip velocity boundary conditions for wall modeled LES. This methodology is successfully applied to flow over NACA4412 airfoil at near stall conditions.