Balachandar, in collaboration with Short and Buckmaster, has analyzed non-axisymmetric fluid flow in solid rocket chambers. They have shown that modest deviations from symmetry, arising from cross-section perturbations, variations in burning rate, etc., lead to the generation of a strong axial vorticity field in the neighborhood of the axis. The magnitude of this vorticity is an increasing function of the flow Reynolds number. These results may have serious implications for the accurate calculation of the turbulent flow in the chamber when idealized symmetry is not achieved.
Aref and Pushkin explored analytical solutions representing vortex motion in compressible flows. There were at least two motivations for this. First, we were interested in the problem of the fluid exiting the rocket chamber. Since the fluid is turbulent, it will contain many vortex structures. However, in most work on rockets the effect of such vortex structures is ignored in the nozzle exit flow. A second motivation was the comparison with numerical simulations of compressible flow. It turns out that vortex structures in compressible flow have complex structure, such as shock waves, within them. In a numerical simulation this structure presumably needs to be resolved or at least modeled in an appropriate fashion. We hoped that by identifying analytical solutions we could use these for testing of computer codes and for order of magnitude assessment of various resolution issues that arise in numerical simulations. After a literature survey, Pushkin was able to derive a general formalism that captures the known cases studied in the literature. However, we were not able to find simple analytical forms for some of these solutions (as can be done in the incompressible case).
Alavilli and Tafti are developing ROCFLO, a new code for 2-D/3-D SRM core flow simulation and a component of the GEN1 system code. ROCFLO is a multi-block, compressible, inviscid (Euler) flow code for both steady and unsteady computations. Within a block, spatial discretization utilizes a structured, body-conforming mesh. The integral conservation laws are solved within control volumes using an explicit multistage Runge-Kutta time stepping scheme and a variety of spatial differencing schemes. Moving grid features are incorporated into the governing equations. These include flux corrections due to grid movement and source terms due to cell volume changes. A parallel (F90/MPI), time-explicit, multi-block implementation of ROCFLO has been completed. This figure shows the temperature in a cross section of a 3-D Space Shuttle Solid Rocket Booster.
Tafti has explored single processor and parallel optimization strategies for CFD codes and relevant linear system solvers on microprocessor based architectures including the SGI Origin2000. These findings will be used to optimize ROCFLO for ASCI systems.
The multiblock capabilities of ROCFLO will support the complex, regular geometries of an SRM (i.e., star grains, inhibitors, etc.). As burn proceeds, blocks will need to be redefined to maintain geometric regularity as well as computational efficiency. ROCFLO was implemented in F90 because of its support for dynamic creation, deletion and merging of computational blocks as the simulation progresses. F90 features are also invaluable in developing local adaptive mesh refinement strategies.
Liou and Balsara are developing an unstructured adaptive mesh fluid dynamics code for eventual integration into GEN2. The principal application of the unstructured mesh code will be fluid flow in cracks as they develop in failure scenarios. Additionally, an unstructured code may prove useful for meshing geometrically difficult portions of the flow or at receding boundaries. A 2-D code has been developed as a testbed to explore certain algorithmic features desirable in the final code, including monotonicity preservation at shock fronts, a multi-fluid Riemann solver for reactive flow, moving boundaries, and multigrid acceleration for convergence to steady state.
A variety of research projects, both analytical and numerical, have been initiated to better understand the micro- and macroscopic fluid dynamics of the multiphase core flow that is produced by the combustion of aluminized solid propellants. Many of these projects are done in collaboration with members of the Combustion and Energetic Materials Team. Findings from these projects will provide the physical basis for constructing the GEN2 core flow model.
Bagchi, Balachandar, and Ha, in collaboration with Stewart, Krier, and Brewster are constructing a subscale simulation of aluminum droplet combustion inside the rocket chamber. The objective is to obtain a comprehensive understanding of the combustion process, and develop models for burn rate, drag, etc., as a function of particle Reynolds number and surrounding flow environment. These models will be used in the GEN2 whole system simulation to account accurately for the volumetrically distributed exchange of mass, momentum and energy between the Al droplets and the surrounding core flow. Detailed 3-D micro-simulations of the combustion of aluminum droplets will be performed. Effects of droplet Reynolds number and critical parameters describing the surrounding medium such as temperature, species concentration and local flow gradient will be investigated. The Reynolds number of the flow inside the droplet is expected to be larger than that outside; as a result the coupled problem of flow both inside and outside the droplet will be considered. The effect of radiative heat transfer on droplet temperature distribution and hence combustion rate will also be eventually included in the analysis. In the past six months a comprehensive 3-D code has been under development. The code development, testing and parallelization efforts will require another six to nine months. Subsequent production runs will develop appropriate Al particulate combustion models.
Ferry and Balachandar are studying particle dispersion in the core flow. This project has two objectives. First, to determine the feasibility of an Eulerian (i.e., continuum) representation of the particles, which may be more efficient than the straightforward, Lagrangian approach. Second, to apply the optimal LES formalism, using it to test candidate subgrid-scale models. This involves calculating the requisite two-point correlations and also quantifying how the particle distributions differ when they are evolved using filtered velocity fields of varying coarseness. Work so far has consisted of porting a channel flow code to a parallel environment. Parallel optimization is currently underway.
Vanka and Mukhopadhyay have developed a 3-D incompressible CFD code that will be used to simulate turbulent pipe flow with particles. The code employs a finite volume formulation of the Navier-Stokes equation with staggered locations for velocity components and pressure. Temporal integration uses an Adams-Bashforth scheme. The elliptic pressure equation is solved using FFTs in the axial and angular coordinates and line inversion in the radial direction. Various LES prescriptions from the literature as well as those developed by R. Moser’s group will be employed. The project has two thrusts: in one effort, LES simulations of flow in a pipe with realistic L/D will be carried out, including transverse injection of fluid. Results have been obtained for a series of simulations with injection Reynolds numbers of 10, 20, 40, 45.55, 80, 120 and 160. These simulations show that at these low Reynolds numbers the 3-D flow remains axisymmetric. In the second effort, DNS and LES simulations of particle-laden flows will be carried out to study the effect of particles on turbulence.
Under separate ASCI funding, Norman and Hayes are exploring the performance and parallel scalability of numerical algorithms for 3-D radiation hydrodynamics simulations on ASCI Tflop architectures. This effort will provide the basis for the radiation transport solver needed for the GEN2 core flow code. The ZEUS-MP code has been developed as a testbed implementing both explicit and implicit algorithms to solve the radiation diffusion equation, which is then coupled to the Euler equations of hydrodynamics. The efficacy of multigrid and preconditioned conjugate gradient methods are compared for solving the system of linear equations resulting from the implicit scheme. Preliminary time-to-solution studies indicate the implicit algorithm may be preferable to the explicit algorithm for optically thin, strongly coupled media. However this may change as problem sizes are increased. Near ideal scaling of both algorithms is found to 128 processors on a SGI/CRAY T3E supercomputer—the largest configuration attempted to date. On the SGI/CRAY Origin2000, speedup is sublinear indicating network bottlenecks. The single node performance of the Origin2000 processor is roughly 2x the speed of the T3E. Scaling studies to >1000 processors of the ASCI Red machine have recently been performed. See this project's final report.
Moser, Bagchi and others have been pursuing the development of LES models applicable to the solid rocket core and nozzle flow. A new technique for developing formulations is being applied, in which the LES formulation is determined through a formal optimization. The result is a LES model that best represents large-scale turbulence dynamics and assures that the large-scale statistics match those of real turbulence. The technique has been applied to isotropic turbulence with the surprising result that only the scale-dependent dissipation can be modeled correctly, and that this is enough to generate an accurate LES. This provides a theoretical explanation for previously observed properties of LES models.
Application of these techniques in strongly inhomogeneous flows requires development of appropriate inhomogeneous formulations. This is being pursued using data for a turbulent channel flow. By careful application of inhomogeneous filters and using the optimization procedure discussed above, it was found that the filter inhomogeneities caused the magnitude of the model term to be orders of magnitude larger than in the isotropic case. It was also found that this large model term was essentially unpredictable, making a LES with such filter a questionable undertaking. These results suggest the importance of filter definitions in these highly inhomogeneous flows. For the later the DNS data being obtained by Najjar will be particularly valuable.
Najjar and Balachandar are also working on the development of optimal LES models for complex flows. The optimal LES formalism has so far been developed and tested in only simple flows, such as isotropic turbulence and turbulent channel flow. The application of optimal LES formalism to the rocket flow is likely to be far more complex, owing to directional inhomogeneity, geometric complexity, strong wall transpiration, two-phase nature of the flow, etc. The development of near optimal LES models requires information on unconditional statistics in the form of two-point correlations. Lack of homogeneous directions in the actual rocket flow will place severe restrictions on the size of two-point correlation and on the number of data samples available for model development and testing. New approaches (different from those taken in the simpler problems) are required to cope up with these restrictions. Here we have developed a new approach for the application of optimal LES formalism to complex problems with multiple directions of inhomogeneity. This approach relies upon projection and filtering in the eigenspace along the inhomogeneous directions. It has been tested in a problem with two inhomogeneous directions. The efficacies of optimal linear and quadratic eddy viscosity and Smagorinsky type models have been tested.
Adrian and Tomkins are concentrating on two areas relevant to CSAR: the design of laboratory experiments to investigate turbulent flows within a solid rocket engine, and the analysis of structures in wall turbulence. The experiments will produce data over a range of Reynolds numbers; this will allow for comparison with direct and large eddy simulations, while providing results at higher speeds closer to actual operating conditions. Experiments are planned in both channel and pipe configurations. For the former we have designed modifications of an existing wind tunnel to create a 2-D channel flow with one end sealed and blowing through one rough wall. For the latter we have designed and are ordering a pipe flow apparatus with blowing through a porous section, as shown in the figure below.
This device allows for two operating scenarios: purely injection-driven flow in the test section of the rocket core with the upstream inlet sealed, as in the actual engine, and fully developed turbulent pipe flow entering the test section where it encounters wall injection.