Vessels | Fluid-Structure | Buckling | Filament WInding
Nonlinear Multiple-Discipline Solutions for Conjugate Heat Transfer and Fluid-Structure
Interaction Using a Staggered Approach
Research by: Mike Weaver
The analytical description of engineering systems often requires resort to nonlinear
governing equations from separate physical disciplines. Coupling of these discrete
physical mechanisms then naturally arises at component interfaces. One method for
approaching such a nonlinear multiple-discipline system is the partitioned
method, where each physical mechanism is formulated and discretized separately. A
special form of partitioning, called staggering uses separate modular solvers
for each set of discretized equations. Here, the solution modules are executed sequentially,
with interface information passed from module to module as required. For a steady-state
system solution, the process is iterated to convergence, with each module performing
a steady solution. Similarly, for an unsteady system solution, the process is marched
in time, with each module performing an unsteady solution.
Two examples where the staggered approach is applicable are conjugate heat transfer
in an arc-heater wind-tunnel nozzle, and fluid-structure interaction inside a segmented
solid rocket motor (SRM). Schematic representations are as follows:
Arc-heater wind tunnel nozzle
Segmented solid rocket motor
In general, a component solution is obtained by a nonlinear operator acting on
the current state of the system. The current system state will be a function of the
For the nozzle system, the components are the nozzle heat conduction N,
the water-coolant fluid dynamics W, and the air fluid dynamics A. The
nonlinear operators are a heat conduction solver T, a flow solver for
water I, and a flow solver for air Q. Now, with n
either the iteration number or time-step, the system solution algorithm can be represented
N n+1 = T (W n, A
n, N n)
W n+1 = I (N n+1,
A n+1 = Q (N n+1,
For the SRM system, the components are the internal fluid dynamics F, and
the structural mechanics S. The nonlinear operators are a flow solver P,
and a structural solver A. With n as before, the system solution
algorithm is then:
F n+1 = P (S n, F
S n+1 = A (F n+1,
This approach has been used to obtain an unsteady solution for the nozzle problem,
marched to steady-state convergence. The following figure shows water flow negotiating
the initial cooling passage turn. The confluence of constant-magnitude vectors shows
a stagnation point on the heated wall of the cooling passage.
This produces a "hot spot" on the nozzle wall, as illustrated by the
following temperature distributions for the nozzle water-side wall and air-side wall,
respectively. Maximum temperature for the water side is 1,261oR, and for
the air side is 1,974oR.
A linear analysis would have predicted maximum wall temperatures at the nozzle
throat. As seen in the above figures, the hot-spot temperatures are noticeably greater
than the throat temperatures.
Use of the partitioned method has also produced a steady-state solution for the
SRM problem by utilizing steady-state component solutions. The following figure shows
the deformation of an SRM inhibitor, with pressure contours indicating flow around
the structure (mean flow is from left to right). Deflections shown are not exaggerated,
thus geometric nonlinearity is present in the structure.
Such an analysis requires nonlinear modeling, and the strong coupling between
the structural state and the flow state dictates a multiple-discipline approach.
Projects: Pressure Vessels | Fluid-Structure | Buckling
| Filament WInding
© 1996 Mike Weaver, Georgia
Institute of Technology, All Rights Reserved.
© 1997 Kurt Gramoll, The University
of Oklahoma, All Rights Reserved.