Tandem Spheres: Motivation and Case Specification
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1 Tandem Spheres: Motivation and Case Specification Stephen L. Wood 1 Ryan Glasby 1 Kevin Holst 2 1 :JICS, UT-K, Oak Ridge, TN 2 :UT-SI, Tullahoma, TN January 7, 2018
2 Outline Motivation BANC-I Tandem Cylinders Approach Participants Prerequisite S. L. Wood (JICS) Case Specification Mandatory Computations and Results Bibliography Tandem Spheres January 7, / 11
3 Motivation Goal A case that features: Accessible geometry Spacing large enough to asses wake growth and interaction Tractable run times Minimal far-field boundary interactions Prediction Why? Look beyond Figures of Merit on bodies Impactful and interesting flow physics in off-body regions Wake propagation is central to many control and design problems down stream control surfaces minimum interval takeoff / landing swarms wind and solar arrays pedestrian safety and comfort S. L. Wood (JICS) Tandem Spheres January 7, / 11
4 Motivation BANC-I Tandem Cylinders BANC-I Tandem Cylinders Benchmark problems for Airframe Noise Computations-I Workshop: Tandem Cylinders [1 3] Accessible geometry Spacing large enough to asses wake growth and interaction 3.7 D separation [1] Important spanwise variation occurs over many cylinder diameters [1 3] Tractable run times Resolution challenges: Small-scale, Kelvin-Helmholtz instabilities grow in the shear layers... the wake must be propagated to the downstream cylinder without excessive diffusion [1] Grid points needed can easily be in the hundreds of millions [1 3] Requires a sufficiently long sample to compute the statistics [1 3] Minimal far-field boundary interactions Periodic boundary conditions employed in nearly all the simulations undoubtedly have some nonphysical effect on the flow [1] Prediction Experimental data sets were available to the 15 participants [1 3] S. L. Wood (JICS) Tandem Spheres January 7, / 11
5 Motivation Approach Approach A case that features: Accessible geometry Spacing large enough to asses wake growth and interaction Tractable run times Minimal far-field boundary interactions Prediction Tandem Spheres Analytic or geometric 10 D separation Geometry does not require extended domain No periodic boundaries Is there an experiment? C D = 0.39 for a single sphere [4]. S. L. Wood (JICS) Tandem Spheres January 7, / 11
6 Participants Participants ZJ Wang, Kansas Univ. Johan Jansson, KTH/BCAM Marian Zastawny, Siemens Philip Johnson (WS1), Univ. of Michigan Kevin Holst, Univ. Tennessee - Space Institute Grids Hexahedral and tetrahedral girds were provided by Steve Karman of Pointwise and Samuel James of GridPro in CGNS and gmsh file formats [5]. S. L. Wood (JICS) Tandem Spheres January 7, / 11
7 Prerequisite Prerequisite Why focus on wake physics? To quantify Energy dissipation rate Kinetic energy spectrum Vorticity transport and distribution Agreement between transient / steady state Difference between up stream / down stream bodies HOW5: WS1 Taylor-Green Vortex [6] Energy dissipation rate Enstrophy Kinetic energy spectrum Vorticity traces Code verification and order assessment S. L. Wood (JICS) Tandem Spheres January 7, / 11
8 Case Specification Case Specification Prediction of complex unsteady multi-scale flow under low Mach and low Reynolds number conditions [5]. Two spheres of diameter D whose centers are separated by 10D along the stream wise centerline Far field boundaries: characteristic Sphere surface boundaries: adiabatic wall Mach number (M = 0.1) Temperature is (T = 300 K) Density (ρ = kg/m 3 ) Reynolds number based on single sphere diameter, D, (Re D = 3900) Prandlt number (Pr = 0.72) Characteristic time scale (t = t U D ) Compare quantities of interest during t [100, 200] S. L. Wood (JICS) Tandem Spheres January 7, / 11
9 Mandatory Computations and Results Figures of Merit Converged average drag coefficient (C D ) and Strouhal Number (St) based on lift for the down stream sphere during t [100, 200] Integral quantities for both spheres: 1 Mean values: lift coefficient C L, drag coefficient C D 2 Root-means-squared values: C L, C D Surface quantities on x y, x z, and y z planes passing through the center of each sphere: 1 Mean values: pressure coefficient C P, skin friction coefficient C f 2 Root-means-squared values: C P, C f S. L. Wood (JICS) Tandem Spheres January 7, / 11
10 Mandatory Computations and Results Flow Quantities Quantities 1 Mean values on stream wise and transverse transects: 1 u, v, and w velocity components (non-dimensionalized by U ) 2 Reynolds stresses (u u, u v, v v ) (non-dimensionalized by U 2 ) 2 Root-means-squared values on stream wise and transverse transects: 1 u, v, and w velocity components (non-dimensionalized by U ) 2 Reynolds stresses (u u, u v, v v ) (non-dimensionalized by U 2 ) 3 Frequency spectra at points: 1 Total velocity 2 Pressure coefficient C P 3 Turbulent kinetic energy Locations 1 Three Stream wise sample lines 2 Six y Transverse samples lines 3 Six z Transverse samples lines 4 Three Points Provide details of the computational resources utilized in terms of DOF, work units, and time marching scheme. Provide details of the computational hardware and parallelization strategy utilized. S. L. Wood (JICS) Tandem Spheres January 7, / 11
11 Bibliography Presentation References I [1] Lockard, D. P., Summary of the tandem cylinder solutions from the benchmark problems for airframe noise computations-i workshop, AIAA paper, Vol. 353, 2011, p [2] Palau-Salvador, G., Stoesser, T., and Rodi, W., LES of the flow around two cylinders in tandem, Journal of Fluids and Structures, Vol. 24, No. 8, 2008, pp [3] Brès, G. A., Freed, D., Wessels, M., Noelting, S., and Pérot, F., Flow and noise predictions for the tandem cylinder aeroacoustic benchmark a, Physics of Fluids, Vol. 24, No. 3, 2012, p [4] Constantinescu, G., and Squires, K., Numerical investigations of flow over a sphere in the subcritical and supercritical regimes, Physics of fluids, Vol. 16, No. 5, 2004, pp [5] CS1 - Tandem Spheres Re=3900,, URL [6] WS1 DNS of the Taylor-Green vortex at Re=1600,, URL https: //how5.cenaero.be/content/ws1-dns-taylor-green-vortex-re1600. S. L. Wood (JICS) Tandem Spheres January 7, / 11
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