  Projects: Pressure 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 component states.

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 as:

N n+1 = T (W n, A n, N n)
W n+1 = I (N n+1, W n)
A n+1 = Q (N n+1, A n)

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 n)
S n+1 = A (F n+1, S n)

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,