Andrew Duggleby

Dynamical eigenfunction decomposition of turbulent pipe flow

The results of an analysis of turbulent pipe flow based on a Karhunen–Loeve decomposition are presented. The turbulent flow is generated by a direct numerical simulation of the Navier–Stokes equations using a spectral element algorithm at a Reynolds number Reτ = 150. This simulation yields a set of basis functions that captures 90% of the energy after 2763 modes. The eigenfunctions are categorized into two classes and six subclasses based on their wavenumber and coherent vorticity structure. Of the total energy, 81% is in the propagating class, characterized by constant phase speeds; the remaining energy is found in the non-propagating subclasses, the shear and roll modes. The four subclasses of the propagating modes are the wall, lift, asymmetric and ring modes. The wall modes display coherent vorticity structures near the wall, the lift modes display coherent vorticity structures that lift away from the wall, the asymmetric modes break the symmetry about the axis, and the ring modes display rings of coh...

Structure and dynamics of low Reynolds number turbulent pipe flow

Using large-scale numerical calculations, we explore the proper orthogonal decomposition of low Reynolds number turbulent pipe flow, using both the translational invariant (Fourier) method and the method of snapshots. Each method has benefits and drawbacks, making the ‘best’ choice dependent on the purpose of the analysis. Owing to its construction, the Fourier method includes all the flow fields that are translational invariants of the simulated flow fields. Thus, the Fourier method converges to an estimate of the dimension of the chaotic attractor in less total simulation time than the method of snapshots. The converse is that for a given simulation, the method of snapshots yields a basis set that is more optimal because it does not include all of the translational invariants that were not a part of the simulation. Using the Fourier method yields smooth structures with definable subclasses based upon Fourier wavenumber pairs, and results in a new dynamical systems insight into turbulent pipe flow. These subclasses include a set of modes that propagate with a nearly constant phase speed, act together as a wave packet and transfer energy from streamwise rolls. It is these interactions that are responsible for bursting events and Reynolds stress generation. These structures and dynamics are similar to those found in turbulent channel flow. A comparison of structures and dynamics in turbulent pipe and channel flows is reported to emphasize the similarities and differences.

The effect of spanwise wall oscillation on turbulent pipe flow structures resulting in drag reduction

The results of a comparative analysis based upon a Karhunen–Loeve expansion of turbulent pipe flow and drag reduced turbulent pipe flow by spanwise wall oscillation are presented. The turbulent flow is generated by a direct numerical simulation at a Reynolds number Reτ=150. The spanwise wall oscillation is imposed as a velocity boundary condition with an amplitude of A+=20 and a period of T+=50. The wall oscillation results in a 27% mean velocity increase when the flow is driven by a constant pressure gradient. The peaks of the Reynolds stress and root-mean-squared velocities shift away from the wall and the Karhunen–Loeve dimension of the turbulent attractor is reduced from 2763 to 1080. The coherent vorticity structures are pushed away from the wall into higher speed flow, causing an increase of their advection speed of 34% as determined by a normal speed locus. This increase in advection speed gives the propagating waves less time to interact with the roll modes. This leads to less energy transfer and ...

Evaluation of Massively-Parallel Spectral Element Algorithm for LES of Film-Cooling

A blind Large-Eddy Simulation (LES) of film-cooling heat transfer is performed on a canonical cylindrical cooling hole geometry using a massively-parallel, geometrically-flexible, open-source spectral element solver NEK5000. The simulation is for a blowing-ratio of 1.0, density-ratio of 1.5, and Reynolds-number Reθ = 4,300 based on boundary layer momentum thickness and ReD = 32,000 based on hole diameter. A low-Mach ideal gas formulation is used to match the density ratio. A spectral-damping LES subgrid model is used which does not restrict time-stepping, allowing CFL numbers of 5–10 through characteristics time-integration. The numerical mesh resolves the boundary layer and coarsens to acceptable LES sizing in the free stream, resulting in 88 million grid points (410,464 elements at 5th order polynomial). For this blowing ratio, the coolant hole Mach number is too large for the low-Mach formulation (> 0.3). This results in faster hole velocities as opposed to fluid compression, effectively changing the momentum ratio leading to coolant lift-off as compared to experiment. The film-cooling effectiveness along centerline and spanwise locations of x/D = 2 and 8 are lower than experiment. Ideal parallel scaling is shown up to 256 processors and estimated to continue at ideal scaling to 2048 processors.Copyright

Low Pressure Turbine Relaminarization Bubble Characterization using Massively-Parallel Large Eddy Simulations

The separation and reattachment of suction surface boundary layer in a low pressure turbine is characterized using large-eddy simulation at Ress = 69000 based on inlet velocity and suction surface length. Favorable comparisons are drawn with experiments using a high pass filtered Smagorinsky model for sub-grid scales. The onset of time mean separation is at s/so = 0.61 and reattachment at s/so = 0.81, extending over 20% of the suction surface. The boundary layer is convectively unstable with a maximum reverse flow velocity of about 13% of freestream. The breakdown to turbulence occurs over a very short distance of suction surface and is followed by reattachment. Turbulence near the bubble is further characterized using anisotropy invariant mapping and time orthogonal decomposition diagnostics. Particularly the vortex shedding and shear layer flapping phenomena are addressed. On the suction side, dominant hairpin structures near the transitional and turbulent flow regime are observed. The hairpin vortices are carried by the freestream even downstream of the trailing edge of the blade with a possibility of reaching the next stage. Longitudinal streaks that evolve from the breakdown of hairpin vortices formed near the leading edge are observed on the pressure surface.

Identifying Inefficiencies in Unsteady Pin Fin Heat Transfer

Internal cooling of the trailing edge region in a gas turbine blade is typically achieved with an array of pin fins. In order to better understand the effectiveness of this configuration for heat transfer, an unsteady Reynolds-averaged Navier Stokes computation is performed on a single row of cylindrical pin fins with a spanwise distance to fin diameter ratio of 2 and height over fin diameter ratio of one. With a locally adapted mesh, the boundary layer is resolved throughout the domain. For validation purposes, the flow Reynolds number based on hydraulic channel diameter ReDH = 12,800 was set to match experiments available in the open literature. The resulting time-dependent flow field was analyzed using a variation of Proper Orthogonal Decomposition (POD), where the correlation matrices were built using the internal energy in addition to the three velocity components. This enables a flow decomposition with respect to the flow structure’s influence on surface heat transfer. The second and third most energetic modes showed a zero temperature eigenfunction, which means that a considerable amount of energy is contained in flow structures that don’t contribute to increasing endwall heat transfer. It was also found that the vortex shedding frequency changes over time and both lift coefficient and Strouhal number increase compared to experimental values for a single cylinder.Copyright

Mixing Analysis in a Lid-Driven Cavity Flow at Finite Reynolds Numbers

The influence of inertial effects on chaotic advection and mixing is investigated for a two-dimensional, time-dependent lid-driven cavity flow. Previous work shows that this flow exhibits exponential stretching and folding of material lines due to the presence of figure-eight stirring patterns in the creeping flow regime. The high sensitivity to initial conditions and the exponential growth of errors in chaotic flows necessitate an accurate solution of the flow in order to calculate metrics based on Lagrangian particle tracking. The streamfunction-vorticity formulation of the Navier-Stokes equations is solved using a Fourier-Chebyshev spectral method, providing the necessary exponential convergence and machine-precision accuracy. Poincare sections and mixing measures are used to analyze chaotic advection and quantify the mixing efficiency. The calculated mixing characteristics are almost identical for Re ≤ 1. For the time range investigated, the best mixing in this system is observed for Re = 10. Interestingly, increasing the Reynolds number to the range 10 < Re ≤ 100 results in an observed decrease in mixing efficacy.

Massively-Parallel DNS and LES of Turbine Vane Endwall Horseshoe Vortex Dynamics and Heat Transfer

Higher turbine inlet temperatures enable increased gas turbine efficiency but significantly reduce component lifetimes through melting of the blade and endwall surfaces. This melting is exacerbated by the horseshoe vortex that forms as the boundary layer stagnates in front of the blade, driving hot gasses to the surface. Furthermore, this vortex exhibits significant dynamical motions that increase the surface heat transfer above that of a stationary vortex. To further understand this heat transfer augmentation, the dynamics of the horseshoe vortex must be characterized in a 3D time-resolved fashion which is difficult to obtain experimentally. In this paper, a 1st stage high pressure stator passage is examined using a spectral element direct numerical simulation at a Reynolds number Re = U∞ C/v = 10,000 . Although the Re is lower than engine conditions, the vortex already exhibits similar strong aperiodic motions and any uncertainty due to sub-grid scale modeling is avoided. The vortex dynamics are analyzed and their impact on the surface heat transfer is characterized. Results from a baseline case with a smooth endwall are also compared to a passage with film cooling holes. Higher Reynolds number simulations require a Large Eddy Simulation turbulent viscosity model that can handle the high accelerations around the blade. A high-pass-filter sub-grid scale model is tested at the same low Reynolds number to test its effectiveness by direct comparisons to the DNS. This resulted in a significant drop in turbulence intensity due to the high strain rate in the freestream, resulting in different dynamics of the vortex than observed in the DNS. Appropriate upstream engine conditions of high freestream turbulence and large integral length scales for all cases are generated via a novel inflow turbulence development domain using a periodic solution of Taylor vortices that are convected over a square grid. The size of the vortices and grid spacing is used to control the integral length scale, and the intensity of the vortices and upstream distance is used to control the turbulence intensity. The baseline DNS exhibits a bi-modal horseshoe vortex, and the presence of cooling-holes qualitatively increases the number of vortex cores resulting in more complex interactions.Copyright

Massively Parallel Computational Fluid Dynamics With Large Eddy Simulation in Complex Geometries

To perform complex geometry large eddy simulations in an industrially relevant timeframe, one must reduce the total time to half a day (overnight simulation). Total time includes the time of developing the mesh from the computer-aided design (CAD) model and simulation time. For reducing CAD-to-mesh time, automatic meshing algorithms can generate valid but often non-efficient meshes with often up to an order of magnitude more grid points than a custom-based mesh. These algorithms are acceptable only if paired with high-performance computing (HPC) platforms comprising thousands to millions of cores to significantly reduce computational time. Efficient use of these tools calls for codes that can scale to high processor counts and that can efficiently transport resolved scales over the long distances and times made feasible by HPC. The rapid convergence of high-order discretizations makes them particularly attractive in this context. In this paper we test the combination of automatic hexahedral meshing with a spectral element code for incompressible and low-Mach-number flows, called Nek5000, that has scaled to P >262,000 cores and sustains >70% parallel efficiency with only ≈7000 points/core. For our tests, a simple pipe geometry is used as a basis for comparing with previous fully resolved direct numerical simulations.Copyright

Massively-Parallel Compressible Discontinuous Galerkin Spectral Element LES of Film Cooling

There are many gas turbine flows that are subsonic but still at speeds where gas compresses and the assumptions made in a low-Mach formulation are inadequate. In particular, a low-Mach spectral element solver, NEK5000, was used to perform a LES study of a film cooling hole at a blowing ratio and density ratio of 1.0 and 1.5, respectively. Due to a lack of real compressibility effects in the formulation, the simulation over-predicted the velocity in the hole, leading to large coolant lift-off and poorer film cooling performance than expected. Recently, the capabilities of NEK5000 have been extended to solve the compressible Navier-Stokes equations using the discontinuous Galerkin spectral element method (DGSEM). In this paper, details of the new algorithm are given, and results of the new simulation show vast improvements over the low-Mach code and compare well to previous experimental results.Copyright