Charles Merkle

A Preconditioned Dual-Time, Diagonalized ADI Scheme for Unsteady Computations

The diagonalized ADI algorithm of Pulliam and Chaussee has been extended to include a timederivative preconditioning that permits efficient computation of flows over a wide range of Mach numbers. The algorithm has also been modified so that time-accurate analyses are possible through the use of dual-time stepping. The dual-time stepping has been incorporated in such a way that no additional factors are needed to handle the dual-time term in the left-hand-side inversion process. The preconditioning can accommodate general equations of state such as constant density (incompressible), perfect gas, or supercritical fluids. Unsteady vortex shedding from a circular cylinder is presented as an example of the capability of the algorithm.

Influence of Stagnation Regions on Preconditioned Solutions at Low Speeds

We have examined the effects of different preconditioning definitions on robustness in the vicinity of stagnation regions. Specifically, we have utilized a series of NACA0012 test cases and two different computer codes. Interestingly, the two codes—an in-house research code called GEMS and the wellknown NASA Ames research code ARC2D—are observed to show different degrees of sensitivity to the stagnation region. Based on the studies, we propose a modified definition referred to as local maximum preconditioning, which is shown to maintain robust performance over a range of parametric variations.

Convergence Assessment of General Fluid Equations on Unstructured Hybrid Grids

A general finite volume formulation for arbitrary fluids on generalized grids is presented and solved by implicit methods. Primary focus is on a line GaussSeidel method modified for unstructured grids, and a GMRES method. The effects of grid aspect ratio and control volume shape on convergence rates are addressed parametrically by means of simple problems. An effort is made to define an appropriate Courant number that allows various problems and various flow regimes to converge at near-optimum speeds for a single CFL value. Results show that both the LGS and GMRES methods give excellent aspect-ratio-independent convergence for rectangles, and good convergence for triangles. Results for hexahedrons are likewise good while for tetrahedrons or prisms much wider variations in convergence rates remain. Gauss-Seidel and LU methods are very effective for isotropic grids but slow dramatically as grid aspect ratios are increased. Representative applications of the modified LGS method to flows past airfoils on hybrid grids show excellent convergence for high and low Reynolds numbers and for subsonic and transonic Mach numbers.

COMPARISON OF COMPUTATIONAL CODES FOR MODELING HYDROGEN-OXYGEN INJECTORS

Computational solutions from three different groups are compared to ascertain current capabilities for using CFD techniques in the design of injector elements for gas-gas rocket engines. Results are compared for a single element injector configuration for which detailed local flowfield measurements are available. The results show that all computations are similar in quality, and that all provide reasonable predictions of the resulting flowfield. Specific issues of concern in the computations are summarized. Overall, capabilities for single element modeling are deemed to be acceptable as long as the solutions remain axisymmetric. Practical extension to three-dimensions appears to be feasible in the near future, while the prediction of configuration s that use liquid propellents requires additional physical model development.

Experimental and Computational Investiagtion of Combustor Acoustics and Instabilities, Part II: Transverse Modes

A combined experimental-computational study of transverse acoustic modes and combustion instabilities in a rectangular liquid rocket chamber is presented. Experimental results show that transverse modes can be spontaneously excited in the rectangular chamber. The amplitudes of the acoustic response are governed by the number and location of the injector elements. In general, stronger response of the 1W mode is observed when the injector element is positioned near a pressure anti-nodal location. Companion CFD solutions of the Euler and Navier-Stokes solutions are also performed and compared with the experimental measurements. Good qualitative agreement of the acoustic chamber response is obtained. Further, the computational studies are utilized to perform parametric studies of the eects of non-linear forcing and viscous eects due to the presence of side-wall boundary layers.

COMPUTATION OF COMPRESSIBLE MULTIPHASE FLOWS

A computational model capable of capturing fully compressible multiphase flow including energy conservation is presented. The model is a finite volume form based on the Reynolds Averaged Navier-Stokes Equations and is capable of considering fully general equations of state. The preconditioning matrix is presented and ensures a well conditioned eigensystem, essential for efficient and accurate multiphase computations. Solutions are given representing both the utility of the preconditioning method as well as the ability of the model to capture highly compressible multiphase flow fields. When considering compressible flows where thermal effects are significant and a general equation of state is necessary, energy conservation in a multiphase flow field is shown to be a requirement.

Computational fluid dynamic analysis of liquid rocket combustion instability

The paper presents a computational analysis of liquid rocket combustion instability. Consideration is given to both a fully nonlinear unsteady calculation as well as a new CFD-based linearized stability analysis. An analytical solution for the linear stability problem in a constant area combustion chamber with uniform mean flow is developed to verify the numerical analyses.

Fundamental Physics and Model Assumptions in Turbulent Combustion Models for Aerospace Propulsion

Abstract : The paper provides a fundamental overview of turbulence and turbulent combustion models for large eddy simulations of reacting flowfields. The focus is on examining model assumptions in the context of aerospace propulsion applications, which typically involve high-speed flows, high pressures, compressible phenomena such as shocks, ignition dynamics and acoustic instabilities. Models considered include the dynamic Smagorinsky model for turbulence, and laminar flamelets, transported-PDF and the linear eddy model (LEM) for turbulent combustion. Validation procedures are devised to determine modeling gaps and identify areas where model enhancements are needed.

The Effect of Swirl on Mixing Characteristics of Turbulent Shear Layers

Simulations utilizing a model based on the FavreAveraged Navier Stokes equations coupled with a k — e turbulence model have been carried out to investigate the impact of swirl on the mixing characteristics of reacting turbulent shear layers. A number of different coaxial injector configurations have been used in the study for both reacting and nonreacting flows. It has been attempted to incorporate the various attributes of swirling motions and gauge the impact that each of these variances would have on flame-dynamics and mixing characteristics. The various parameters studied include swirl intensity, initial swirl distribution, expansion ratio and splitter plate thickness.

Multi-dimensional analysis of combustion instabilities in liquid rocket motors

A three-dimensional analysis of combustion instabilities in liquid rocket engines is presented based on a mixed finite difference/spectral solution methodology for the gas phase and a discrete droplet tracking formulation for the liquid phase. Vaporization is treated by a simplified model based on an infinite thermal conductivitiy assumption for spherical liquid droplets of fuel in a convective environment undergoing transient heating. A simple two parameter phenomenological combustion response model is employed for validation of the results in the small amplitude regime. The computational procedure is demonstrated to capture the phenomena of wave propagation within the combustion chamber accurately. Results demonstrate excellent amplitude and phase agreement with analytical solutions for properly selected grid resolutions under both stable and unstable operating conditions. Computations utilizing the simplified droplet model demonstrate stable response to arbitrary pulsing. This is possibly due to the assumption of uniform droplet temperature which removes the thermal inertia time-lag response of the vaporization process. The mixed-character scheme is sufficiently efficient to allow solutions on workstations at a modest increase in computational time over that required for two-dimensional solutions.