Rochan Upadhyay

Evaluation of the 1-point quadrature approximation in QMOM for combined aerosol growth laws

This work examines the applicability of various assumptions in implementation of the quadrature method of moments (QMOM) for solving problems in aerosol science involving simultaneous nucleation, surface growth and coagulation. The problem of aerosol growth and coagulation in a box and the problem of vapor condensation in a nozzle are reworked using quadrature method of moments. QMOM uses Gaussian quadrature to evaluate integrals appearing in the moment equations and therefore does not require any assumptions on the form of the size distribution function, the growth laws and coagulation kernels. Results are compared with calculations which assume a lognormal size distribution. The conditions for which one, two and higher quadrature points can be used in the quadrature formula and the issues regarding the accuracy are considered for combined aerosol nucleation, growth and coagulation processes. Results show that for these problems, the simplest 1-point quadrature scheme gives accuracy comparable with the lognormal calculations while using two and higher point quadrature gives highly accurate results. Some difficulties associated with the QMOM are discussed and some insights are provided.

Loose-coupling algorithm for simulating hypersonic flows with radiation and ablation

Aprocedure has been developed to couple a hypersonic reacting flowmodel, a radiative heat transfermodel, and a surface ablation model to study the surface heat transfer and surface ablation rate of atmospheric reentry vehicles. The two-way loose-coupling algorithm is described for each of the models, as is the solution procedure to achieve convergence. Observations on the challenges of the loose-coupling strategy are given. Representative results are presented for two-dimensional benchmark examples and for three-dimensional flow at an angle of attack past a symmetric capsule based on the Crew Exploration Vehicle reentry vehicle. Effects due to the interaction with radiation and ablation are shown for two quantities of interest: the predicted peak surface heat flux and the ablation rate on the vehicle heat shield. Uncertain parameters are identified in each of the submodels, and a preliminary parameter sensitivity study is carried out by varying these values to examine their effects on the heat transfer and ablation rates in the coupled problem.

Effect of electromagnetic waves and higher harmonics in capacitively coupled plasma phenomena

High-resolution self-consistent numerical simulation of electromagnetic wave phenomena in an axisymmetric capacitively coupled plasma reactor is reported. A prominent centre-peaked plasma density profile is observed for driving frequencies of 60MHz and is consistent with observations in the literature and accompanying experimental studies. A power spectrum of the simulated wave electric field reveals the presence of well-resolved high frequency harmonic content up to the 20th harmonic of the excitation frequency; an observation that has also been reported in experiments. Importantly, the simulation results reveal that the occurrence of higher harmonics is strongly correlated with the occurrence of a centre-peaked plasma density profile.

Relationship between center-peaked plasma density profiles and harmonic electromagnetic waves in very high frequency capacitively coupled plasma reactors

An understanding of the factors that control radial plasma uniformity in very high frequency (VHF) capacitively coupled plasma (CCP) sources is important for many plasma processes in semiconductor device manufacturing. Here, we report experimental measurements and high-resolution self-consistent numerical simulations that illustrate the plasma density profile and the higher harmonic wave content in two types of VHF-CCP test-bench reactors. A distinct sharp center peak superimposed on a broad center peak in argon plasma was observed for driving frequencies of 60 and 106 MHz. Experimental measurements and numerical simulations of the electric field power spectrum reveal the presence of UHF waves when the electron density is over 5 × 1016 (#/m3). The presence of UHF waves closely correlates with the occurrence of a distinct and sharp-center-peaked electron density. The numerical simulations show that specific frequency bands in the UHF spectrum are amplified in the plasma and lead to the evolution of the sharp-center-peaked electron density.

Computational modeling of a single microdischarge and its interactions with high frequency electromagnetic waves

We discuss the computational modeling of a single microplasma and its interaction with high frequency electromagnetic waves in a microwave regime. The work is motivated by a strong recent interest in the area of reconfigurable plasma-based metamaterials (MM) and photonic crystals (PC) where the interaction of electromagnetic waves with plasma elements (e.g. microdischarges) forms the basis for the MM/PC operation. In this work the microplasma is assumed to be driven by a 1 GHz microwave source in a parallel plate electrode configuration. Its structure and properties are described using a fluid plasma model. The interaction of the microplasma with a 100 GHz transverse magnetic (TM) and transverse electric (TE) polarized microwave propagating in a rectangular waveguide is studied. Two operational regimes of the plasma discharge are considered. One in which the peak electron density is less than the critical density (under-dense) for the interacting wave and the other in which it is higher (over-dense). The under-dense plasma with positive less than unity dielectric constant has sufficient dielectric contrast from the surrounding medium that a slight perturbation of the incident wave and bending of wave path lines through the discharge is realized. The over-dense plasma interacts strongly with the TM polarized wave because of epsilon-zero resonance at the critical density locations and the wave path lines are observed to reverse their direction near the regions of critical plasma density. The transverse electric (TE) polarized wave does not exhibit epsilon-zero resonance and the interactions are weaker than the TM wave.

libMoM : a library for stochastic simulations in engineering using statistical moments

Stochastic simulations are becoming increasingly important in numerous engineering applications. The solution to the governing equations are complicated due to the high-dimensional spaces and the presence of randomness. In this paper we present libMoM (http://libmom.sourceforge.net), a software library to solve various types of Stochastic Differential Equations (SDE) as well as estimate statistical distributions from the moments. The library provides a suite of tools to solve various SDEs using the method of moments (MoM) as well as estimate statistical distributions from the moments using moment matching algorithms. For a large class of problems, MoM provide efficient solutions compared with other stochastic simulation techniques such as Monte Carlo (MC). In the physical sciences, the moments of the distribution are usually the primary quantities of interest. The library enables the solution of moment equations derived from a variety of SDEs, with closure using non-standard Gaussian quadrature. In engineering risk assessment and decision making, statistical distributions are required. The library implements tools for fitting the Generalized Lambda Distribution (GLD) with the given moments. The objectives of this paper are (1) to briefly outline the theory behind moment methods for solving SDEs/estimation of statistical distributions; (2) describe the organization of the software and user interfaces; (3) discuss use of standard software engineering tools for regression testing, aid collaboration, distribution and further development. A number of representative examples of the use of libMoM in various engineering applications are presented and future areas of research are discussed.

RANS models for scalar transport in ablating compressible boundary layers

DNS of a high temperature flow over a modeled ablator surface is used to investigate models for turbulent scalar flux and chemical source term closures. Two different Mach numbers of 0.6 and 1.2 are considered. The ablating surface is described using a 1-D quasisteady model. Results show that the simple gradient diffusion scalar flux model, which uses an isotropic coefficient for the components of the flux, provides a poor match for the DNS scalar flux. Allowing anisotropy in the flux coefficient, as in the generalized gradient diffusion model, provides a much better match. Further, the simple laminar closure for the chemical source term introduces significant errors. The large fluctuations of temperature close to the ablator cause significant fluctuations in the chemical source term.

Bayesian Model Comparison and Selection for Quantifying Uncertainty in Active Graphite Nitridation

In this paper, two stochastic model classes corresponding to di erent choices of (modeling and measurement) error structure are considered and compared using Bayesian framework. A single deterministic physical model of active graphite nitridation is embedded within these stochastic model classes, where estimation of surface reaction e ciency of graphite with atomic nitrogen is of primary interest. These model classes di er in the covariance matrix structure that is used in the uncertainty model to represent uncertainties associated with the physical model and experimental measurements. First model class (M1) is based on independent normal distributions assuming error to be uncorrelated between di erent data points whereas the second class (M2) uses -exponential covariance function to correlate error in the same data quantity among di erent data points. For each model class, Bayesian inference is used to estimate the posterior probabilities of the physical model parameters, stochastic model parameters as well as of the candidate stochastic models. Model comparison and selection is then applied based on two measures including Bayesian evidence and Bayesian information criterion (BIC), and deviance information criterion (DIC). Both measures suggest the second stochastic model class (M2) to be selected indicating that there is a correlation between errors in the same data quantity among di erent data points. However, with the second model class the range of uncertainty in surface reaction e ciency is estimated to be higher, which is consistent with the large scatter seen in the reported values.

Use of a Quasi-Steady Ablation Model for Design Sensitivity With Uncertainty Propagation

Sensitivity analysis and design calculations are often best performed using low-order models. This work details work done on adding complementary pieces to a low-order, quasi-steady-state ablation model to facilitate uncertainty propagation. The quasi-steady-state ablation model is a one-dimensional, quasi-steady-state, algebraic ablation model that uses finite-rate surface chemistry and equilibrium pyrolysis-gas-production submodels to predict surface recession rate. The material response model is coupled to a film-transfer boundary layer model to enable the computation of heat and mass transfer from an ablating surface. For comparison to arc jet data, a simple shock heated gas model is coupled. A coupled model consisting of submodels for the shock heated gases, film heat and mass transfer, and material response is exercised against recession rate data for surface and in-depth ablators. Comparisons are made between the quasi-state-state ablation model and the unsteady ablation code, Chaleur, as well as to other computations for a graphite ablator in arcjet facilities. The simple models are found to compare reasonably well to both the experimental results and the other calculations. Uncertainty propagation using a moment based method is presented. The results of this study are discussed, and conclusions about the utility of the method as well as the properties of the ablation code are drawn.Copyright