Sean Davis

Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation

The effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. This is done with the express purpose of using metamodels to bridge scales between micro- and macro-scale models in a multi-scale multimaterial simulation. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver.

Dispersion of a cloud of particles by a moving shock: Effects of the shape, angle of rotation, and aspect ratio

This paper discusses the particle-laden flow development from a cloud of particles in an accelerated flow behind a normal moving shock. The effects of the aspect ratio of a rectangular and ellipsoidal cloud and the cloud’s angle of attack with respect to the carrier flow are studied. Computations are performed with an in-house high-order weighted essentially non-oscillatory (WENO-Z) finite-difference scheme-based Eulerian-Lagrangian solver that solves the conservation equations in the Eulerian frame, while particles are traced in the Lagrangian frame. Streamlined elliptically shaped clouds exhibit a lower dispersion than blunt rectangular clouds. The averaged and root-mean-square locations of the particle coordinates in the cloud show that the cloud’s streamwise convection velocity increases with decreasing aspect ratio. With increasing rotation angle, the cross-stream dispersion increases if the aspect ratio is larger than unity. The particle-laden flow development of an initially moderately rotated rectangle is qualitatively and quantitatively comparable to the dispersion of an initially triangular cloud.

SPARSE—A subgrid particle averaged Reynolds stress equivalent model: testing with a priori closure

A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian–Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles.

High-Fidelity Eulerian-Lagrangian Methods for Simulation of Three Dimensional, Unsteady, High-Speed, Two-Phase Flows in High-Speed Combustors

A preliminary study of a three-dimensional numerical model for determining the flow and particle developments through a shock tube containing 10 bronze particles is presented here. The numerical experiment is initialized as a hexahedral cloud of particles immediately adjacent to a right running normal shock. Flow characteristics are computed using a three-dimensional high-order Eulerian-Lagrangian method, which solves the Euler equations governing the gas dynamics with an improved high order weighted essentially non-oscillatory (WENO-Z) scheme, while individual particle trajectories are traced in the Lagrangian frame using high-order time integration schemes. Two way coupling between the carrier gas and the particles is modeled, using a high-order ENO interpolation, via the exchange of the momentum and energy at the particle positions through the use of an additional source term in the Euler equations. A high-order central weighing deposits the particle influence on the carrier phase. The preliminary solution as computed in the 3D model is then compared to similar experiments analyzed with 2D models.

Coupling of Micro-Scale and Macro-Scale Eulerian-Lagrangian Models for the Computation of Shocked Particle-Laden Flows

The accuracy and efficiency of several algorithms that couple output from full resolution micro-scale Direct Numerical Simulation computations to input for macro-scale Eulerian-Lagrangian (EL) methods for the computation of high-speed, particle-laden flow are assessed. A Stochastic Collocation method, a Gaussian Radial Basis Function (RBF) Artificial Neural Network (ANN), and an improved RBF-ANN are compared for the fitting of an analytical drag coefficient formula that depends on Mach number and Reynolds number. The improved RBF-ANN uses a clustering algorithm to enhance conditioning of interpolation matrices. The fitted drag coefficient mantle, used to trace point particles in macro-scale computations, is in excellent agreement with the analytical drag formula. The SC method requires fewer micro-scale realizations to obtain comparable accuracy of the drag coefficient. The Gaussian RBF does not converge monotonically, while the improved RBF-ANN converges algebraically and has the potential to provide error estimates.Copyright

The effect of non-uniform mass loading on the linear, temporal development of particle-laden shear layers

The effect of non-uniformity in bulk particle mass loading on the linear development of a particle-laden shear layer is analyzed by means of a stochastic Eulerian-Eulerian model. From the set of governing equations of the two-fluid model, a modified Rayleigh equation is derived that governs the linear growth of a spatially periodic disturbance. Eigenvalues for this Rayleigh equation are determined numerically using proper conditions at the co-flowing gas and particle interface locations. For the first time, it is shown that non-uniform loading of small-inertia particles (Stokes number (St) <0.2) may destabilize the inviscid mixing layer development as compared to the pure-gas flow. The destabilization is triggered by an energy transfer rate that globally flows from the particle phase to the gas phase. For intermediate St (1 < St < 10), a maximum stabilizing effect is computed, while at larger St, two unstable modes may coexist. The growth rate computations from linear stability analysis are verified numerically through simulations based on an Eulerian-Lagrangian (EL) model based on the inviscid Euler equations and a point particle model. The growth rates found in numerical experiments using the EL method are in very good agreement with growth rates from the linear stability analysis and validate the destabilizing effect induced by the presence of particles with low St.