A Direct-Forcing Immersed Boundary Method with Dynamic Velocity Interpolation Randall J. McDermott Engineering Laboratory, Fire Research Division National Institute of Standards and Technology APS/DFD, Long Beach, CA, November 22, 2010 Support: U.S. Nuclear Regulatory Commission, U.S. Forest Service Special thanks to: Glenn Forney (NIST), J.-I. Choi (NC State, KAIST)
Overview of the Fire Dynamics Simulator (FDS)
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Low Mach LES Cartesian, staggered Generally second-order, energy-conserving, explicit numerics Semi-implicit (Poisson equation for pressure) TVD scalar transport (CHARM, Superbee) Dynamic Smagorinsky SGS stress closure Historically, zeroth-order treatment of immersed boundaries
GOAL: To provide reliable engineering predictions of drag for curved surfaces at high Reynolds number with coarse grids.
tunnel fires
http://www.protectowire.com
wildland-urban interface fires
4 km GIS terrain data (10 m resolution)
Courtesy Coeur d‘Alene tribe GIS
Previous Work
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Charles Peskin (2D heart model), Boyce Griffith (3D, AMR), NYU
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E. A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof. Combined Immersed-Boundary FiniteDifference Methods for Three-Dimensional Complex Flow Simulations, J. Comp. Phys., 161:3560, 2000.
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E. Balaras. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations. Computers and Fluids, 33:375-404, 2004.
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J. Emblemsvåg, R. Suzuki, and G. Candler. A Cartesian Grid Method for Moderate-Reynolds Number Flows around Complex and Moving Solid Objects, AIAA Journal, 43(1):76-86, 2005.
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J.-I. Choi, R. C. Oberoi, J. R. Edwards, and J. A. Rosati. An immersed boundary method for incompressible flows. J. Comp. Phys., 224:757-784, 2007.
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M. J. B. M. Pourquie. Accuracy Close to the Wall for Large-Eddy Simulations of Flow Around Obstacles Using Immersed Boundary Methods, In Quality and Reliability of Large-Eddy Simulations, J. Meyers, B. Geurts, and P. Sagaut, Eds., Springer, 2008.
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F. Roman, V. Armenio, and J. Frohlich. A simple wall-layer model for large-eddy simulation with immersed boundary method. Phys. Fluids, 21:101701, 2009.
Cutcell Methods vs. Immersed Boundary Methods
Interpolation Methods
DVI Part 1: Defining the local streamwise coordinate system
DVI Part 2: Solving the boundary layer equations
Discretization:
ODE solution method
from wall model
Finally, transform back to grid system:
rho = 1.2; mu = 0.001; dn = 0.1; u0 = 1; u_wall = 0; v = .5; duds = -.1; dudn = 1; dpds = -1; tau = -.2; SF = -100;
Masked Cells and Boundary Layer Weighting
“p mask”
“u mask”
DVI Drag Coefficient Results
Munson,Young, Okiishi. Fundamentals of Fluid Mechanics. Wiley (1990).
Contours and particle streaks colored by velocity magnitude.
Drag (Exp. 1.34 +/- 0.01)
Lift (Exp. +/- 0.3)
Cylinder , Re=100, D/dx=10. Tracer particles colored by velocity magnitude. Strouhal = 0.18 (Exp. 0.16)
Drag and lift coefficients computed using method of Balaras.
Conclusions, Outstanding Issues, and Future Work
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Work in progress… A 3D version of DVI has been implemented and tested for coarse grids Issues with cylinder case at low Re Grid resolution study for high Re cases Requires nonuniform mesh, mpi Domain boundaries sufficient? BL to bulk flow smoothing function? Many more simple test cases to try: moving boundaries, etc. Simple variable-density test cases 2-way coupling to flow solver Heat and mass transfer to solid
