This study is on the development of numerical algorithms and models for simulation of a structure response in a fire. The flow field from the fire plume is modeled using the 2D Navier-Stokes equations supplemented with a transport equation for thermal energy and solved using a vorticity-streamfunction approach. Coupling of the fluid to the FEM based structure model is based on the use of a level set method describing the structure geometry in the fluid domain. The level set function allows for computation of normal gradients at the fluid-solid interface to enforce local boundary conditions of heat and mass transfer at prescribed fluid-structure coupling time increments. Numerical simulations of a two-dimensional composite cantilever beam subject to convection heat loading from a fire plume are presented requiring coupling of both the thermal and mass transfer processes at the fluid-structure interface. Results are presented showing the thermal response of a composite beam to a fire plume and the sensitivity of the heating to fire location.

1.
K.K. A. Hoffmann and S. T. Chiang, Computational Fluid Dynamics, Volume I, EES, Whichita, Kansas, fourth edition, (2000).
2.
Leonard
B. P.
,
A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation
,
Comput. Methods Appl. Mech. Eng.
,
19
,
59
98
(
1979
).
3.
Y. Colin, Numerical Simulation of Flow Around Bluff Bodies Using a Level Set Based Interface Capturing Method, MS thesis, University at Buffalo, the State University of New York, Buffalo, NY, (2004).
4.
Osher
S.
and
Fedkiw
R.
,
Level Set Methods: An Overview and Some Recent Results
,
J. of Comput. Phys.
,
169
,
463
502
, (
2000
).
5.
J. A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, Cambridge, UK (1999).
6.
D. Drysdale, An Introduction to Fire Dynamics, John Wiley and Sons, New York, NY, 2nd edition, (1998).
7.
F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, NY, third edition, (1990).
8.
Hirt
C. W.
and
Nichols
B. D.
,
Volume of Fluid Method for the Dynamics of Free Boundaries
,
J. of Comput. Phys.
,
29
,
201
225
, (
1981
).
9.
Rudman
M.
,
Volume-Tracking Methods for Interfacial Flow Calculations
,
Int. J. for Num. Methods in Fluids
,
24
,
671
691
, (
1997
).
10.
Udaykumar
H. S.
,
Kan
H.
,
Shyy
W.
and
Tran-Son-Tay
R.
,
Multiphase Dynamics in Arbitrary Geometries on Fixed Cartesian Grids
,
J. of Comput. Phys.
,
174
,
345
380
, (
1997
).
11.
Ingram
D. M.
,
Mingham
C. G.
and
Causon
D. M.
,
Developments in Cartesian Cut Cell Methods
,
Math. Comp.
,
61
,
561
572
, (
2003
).
12.
Russell
D.
and
Wang
Z. J.
,
A Cartesian Grid Method for Modeling Multiple Moving Objects in 2D Incompressible Viscous Flow
,
J. of Comput. Phys.
,
191
,
177
205
, (
2003
).
13.
Calhoun
D.
,
A Cartesian Grid Method for Solving the Two-Dimensional Streamfunction-Vorticity Equations in Irregular Regions
,
J. of Comput. Phys.
,
176
,
231
275
, (
2002
).
14.
A. Dadone and B. Grossman, An Immersed Body Methodology for Invisid Flows on Cartesian Grids, AIAA J., (2002)
15.
Esmaeeli
A.
and
Tryggvason
G.
,
A Front Tracking Method for Computations of Boiling in Complex Geometries
,
Int. J. of Multiphase Flows
,
30
,
1037
1050
, (
2004
).
16.
Li
Z.
and
Lai
M.
,
The Immersed Interface Method for the Navier-Stokes Equations with Singular Forces
,
J. of Comput. Phys.
,
171
,
822
842
, (
2001
).
17.
Udaykumar
H. S.
,
Mittal
R.
and
Shyy
W.
,
Computation of Solid-Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids
,
J. of Comput. Phys.
,
153
,
535
574
, (
1999
).
18.
Udaykumar
H. S.
,
Mittal
R.
,
Rampunggoon
P.
and
Khanna
A.
,
A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries
,
J. of Comput. Phys.
,
174
,
345
380
, (
2001
).
19.
Osher
S.
and
Sethian
J. A.
,
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
,
J. of Comput. Phys.
,
79
,
12
49
, (
1988
).
20.
Sethian
J. A.
,
Evolution, Implementation, and Application of Level Set and Fast Marching Methods for Advancing Fronts
,
J. of Comput. Phys.
,
169
,
503
555
, (
2001
).
21.
Chen
S.
,
Merriman
B.
,
Osher
S.
and
Smereka
P.
,
A Simple Level Set Method for Solving Stefan Problems
,
J. of Comput. Phys.
,
135
,
8
29
, (
1996
).
22.
T. Belytschko, W. K. Liu and B. Moran, Nonlinear Finite Elements for Continua and Structures, Wiley, (2003)
23.
S. R. Turns, An Introduction to Combustion, McGraw Hill, second edition, (2000)
24.
C. Luo and P. E. DesJardin, Thermo-mechanical Damage Modeling for a Glass-Fiber Phenolic-Resin Composite Material, 2005 International Mechanical Engineering Congress & Exposition, ASME paper IMECE2005-81719 (2005)
25.
Leveque
R. J.
and
Li
Zhilin
,
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
,
SIAM Journal on Numerical Analysis
,
31
(
4
),
1019
1044
, (
1994
)
26.
K. McGrattan, Fire Dynamics Simulator (Version 4) Technical Reference Guide, NIST Special Publication 1018
This content is only available via PDF.
You do not currently have access to this content.