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Moser, Robert D.

Publications and source records attributed to Moser, Robert D..

At least 19 records

Characterization of uncertainties in electron-argon collision cross sections

Abstract The predictive capability of a plasma discharge model depends on accurate representations of electron-impact collision cross sections, which determine the corresponding reaction rates and electron transport properties. The values of cross sections can be known only approximately either through experiments or simulations and are thus subject to uncertainties. Quantifying the uncertainties in plasma simulations allows us to assess the reliability of simulations and to provide a basis for interpreting discrepancies between simulations and experiments. For such uncertainty quantification of plasma simulations, it is essential to quantify the uncertainties of the underlying cross sections. Although much effort has been committed to calibrate the cross section values, their uncertainties are not well investigated. We characterize uncertainties in electron-argon atom collision cross sections using a Bayesian framework. Six collision processes—elastic momentum transfer, ionization, and four excitations—are characterized with semi-empirical models, which effectively capture the features important to the macroscopic properties of the plasma. A probability model for the uncertain parameters of these semi-empirical models is developed. Specifically, a Gaussian-process likelihood model is proposed to capture discrepancies among data sets, as well as the model-form inadequacies of the semi-empirical models. Two other likelihood models are compared with the proposed Gaussian-process model, to illustrate the importance of the choice of the likelihood model. The cross section models are calibrated using the electron-beam experiments and ab-inito quantum simulations. The resulting calibrated uncertainties capture well the scattering among the data sets. The calibrated cross section models are further validated against swarm-parameter experiments and zero-dimensional Boltzmann equation simulations of widely used cross section datasets.

Chung, Seung Whan (ORCID:0000000302501549)

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

A novel algorithm for explicit temporal discretization of the variable-density, low-Mach Navier-Stokes equations is presented here in this study. Recognizing there is a redundancy between the mass conservation equation, the equation of state, and the transport equation(s) for the scalar(s) which characterize the thermochemical state, and that it destabilizes explicit methods, we demonstrate how to analytically eliminate the redundancy and propose an iterative scheme to solve the resulting transformed scalar equations. The method obtains second-order accuracy in time regardless of the number of iterations, so one can terminate this subproblem once stability is achieved. Hence, flows with larger density ratios can be simulated while still retaining the efficiency, low cost, and parallelizability of an explicit scheme. The temporal discretization algorithm is used within a pseudospectral direct numerical simulation which extends the method of Kim, Moin, and Moser for incompressible flow to the variable-density, low-Mach setting, where we demonstrate stability for density ratios up to ~25.7.

97 MATHEMATICS AND COMPUTING

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Loulou, Patrick

Two-dimensional mesh embedding for Galerkin B-spline methods

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Shariff, Karim

Direct simulation of a self-similar plane wake

Direct simulations of two time-developing turbulent wakes have been performed. Initial conditions for the simulations were obtained from two realizations of a direct simulation of a turbulent boundary layer at momentum thickness Reynolds number 670. In addition, extra two-dimensional disturbances were added in one of the cases to mimic two-dimensional forcing. The unforced wake is allowed to evolve long enough to attain self-similarity. The mass-flux Reynolds number (equivalent to the momentum thickness Reynolds number in spatially developing wakes) is 2000, which is high enough for a short kappa(exp -5/3) range to be evident in the streamwise one-dimensional velocity spectrum. Several turbulence statistics have been computed by averaging in space and over the self-similar period in time. The growth rate in the unforced flow is low compared to experiments, but when this growth-rate difference is accounted for, the statistics of the unforced case are in reasonable agreement with experiments. However, the forced case is significantly different. The growth rate, turbulence Reynolds number, and turbulence intensities are as much as ten times larger in the forced case. In addition, the forced flow exhibits large-scale structures similar to those observed in transitional wakes, while the unforced flow does not.

Moser, Robert D.

Direct simulation of a self-similar plane wake

Direct simulations of two time-developing turbulent wakes have been performed. Initial conditions for the simulations were obtained from two realizations of a direct simulation of a turbulent boundary layer at momentum thickness Reynolds number 670. In addition, extra two dimensional disturbances were added in one of the cases to mimic two dimensional forcing. The unforced wake is allowed to evolve long enough to attain self similarity. The mass-flux Reynolds number (equivalent to the momentum thickness Reynolds number in spatially developing wakes) is 2000, which is high enough for a short k(exp -5/3) range to be evident in the streamwise one dimensional velocity spectrum. Several turbulence statistics have been computed by averaging in space and over the self-similar period in time. The growth rate in the unforced flow is low compared to experiments, but when this growth-rate difference is accounted for, the statistics of the unforced case are in reasonable agreement with experiments. However, the forced case is significantly different. The growth rate, turbulence Reynolds number, and turbulence intensities are as much as ten times larger in the forced case. In addition, the forced flow exhibits large-scale structures similar to those observed in transitional wakes, while the unforced flow does not.

Moser, Robert D.

Direct Simulation of a Self-Similar Turbulent Mixing Layer

Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.

Rogers, Michael M.

The Roles of Large- and Small-Scale Structures in Turbulent Free Shear Layers

The occurrence of large-scale coherent structures in turbulent free shear flows (especially the planar mixing layer) has been recognized for some time. Indeed, the observation of such structures in mixing layers did much to promote interest in the study of coherent structures in turbulence. It has been widely assumed that the large-scale structures in these flows are responsible for the entrainment of free-stream fluid and the overall growth of the layer, while the small-scale structures provide mixing and dissipation. A model of scalar mixing based on these ideas was proposed for these flows. However, recent experimental and computational evidence suggests that the dominance of the large-scale structures in turbulent mixing layers is not universal. In addition, there is a substantial variation among experiments in several statistical measures of self-similar mixing layers, for example growth rate and velocity variances. To investigate the importance of large-scale structures, several free shear flows (mixing layers and wakes) have been simulated via direct numerical simulation. The simulations are designed to mimic experimental mixing layers in which the splitter plate boundary layers are turbulent. Different levels of two-dimensional forcing are included resulting in large-scale structures of differing strength and importance. These simulations are used to investigate the role of large-scale coherent structures in free shear layers and the effect of these structures on relevant turbulence statistics and scalar mixing. It is found that the statistics and structures in several experiments involving turbulent mixing layers are in better agreement with simulations that do not exhibit dominant large-scale structures than those in which the common mixing layer structures do dominate. It is also found that the level of forcing can have a profound effect on the qualitative and quantitative features of these shear layer, even when they are nominally self-similar.

Moser, Robert D.

The three-dimensional evolution of a plane mixing layer - Pairing and transition to turbulence

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Moser, Robert D.

Spanwise scale selection in plane mixing layers

Direct numerical simulations of temporally evolving plane mixing layers undergoing as many as three pairings have been examined for evidence of spanwise scale change. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. The amplitude of the initial three-dimensional disturbances varied from infinitesimal to large enough to trigger a rapid transition to turbulence. The time required for a change of characteristic spanwise scale with infinitesimal three-dimensional disturbances was found to be very long, requiring three or more pairings to complete a doubling of the spanwise scale. Stronger three-dimensionality can produce more rapid scale changes, but it is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one spanwise scale to a similar array at a larger spanwise scale.

Rogers, Michael M.

The three-dimensional evolution of a plane mixing layer. Part 2: Pairing and transition to turbulence

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings was simulated numerically. Initial conditions for all simulations consisted of a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found both to inhibit the growth of infinitesimal three-dimensional disturbances and to trigger the transition to turbulence in highly three dimensional flows. The mechanisms responsible for the growth of three-dimensionality as well as the initial phases of the transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of span wise vorticity, which undergo a secondary roll up. Transition also produces an increase in the degree of scalar mixing, in agreement with experimental observations of mixing transition. Simulations were also conducted to investigate changes in span wise length scale that may occur in response to the change in stream wise length scale during a pairing. The linear mechanism for this process was found to be very slow, requiring roughly three pairings to complete a doubling of the span wise scale. Stronger three-dimensionality can produce more rapid scale changes but is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one span wise scale to a similar array at a larger span wise scale.

Moser, Robert D.

Coherent structures in a simulated turbulent mixing layer

A direct numerical simulation of a plane turbulent mixing layer has been performed. The simulation was initialized using two turbulent velocity fields obtained from direct numerical simulation of a turbulent boundary layer at momentum thickness Reynolds number 300 (Spalart, 1988). The mixing layer is allowed to evolve long enough for self-similar linear growth to occur, with the visual thickness Reynolds number reaching 14,000. The simulated flow is examined for evidence of the coherent structures expected in a mixing layer (rollers and rib vortices). Before the onset of self-similar growth, such structures are present with properties similar to the corresponding laminar or transitional structures. In the self-similar growth regime, however, only the rollers are present with no indication of rib vortices and no indication of conventional pairing. This results in a reduction of mixing and layer growth.

Moser, Robert D.

The three-dimensional evolution of a plane mixing layer - The Kelvin-Helmholtz rollup

The hydrodynamic evolution of an incompressible plane mixing layer is addressed to elucidate scalar mixing in free shear flows. A detailed description of the onset of three-dimensionality in a mixing layer before or in the absence of pairing is presented. Various simulations were performed to investigate the sensitivity of these results to variations in initial conditions. These variations included changes in amplitude, wavelength, functional form, and relative phasing of the initial low-wavenumber disturbances. Pierrehumber and Widnall's (1982) translative instability eigenfunctions are found to include rib vortices in the braid region and oppositely signed streamwise vorticity in the roller core. The translative instability is an instability of the late-time oversaturated flow. Three-dimensional perturbation growth similar to that of the translative instability can occur whenever spanwise vorticity is present in the braid region. The nonlinear effects that occur when the initial rib circulation is sufficiently high are discussed.

Rogers, Michael M.

Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow

The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.

Vastano, John A.

Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions

The time-dependent, 3D incompressible Navier-Stokes equations in (1) boundary layers, the semiinfinite domain, and (2) mixing layers or wakes, the fully infinite domain, are respectively solved by two numerical methods which employ rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions. These functions are then combined with one, for method (1), and two, for method (2), slowly decaying 'extra functions' for each wave vector. Each extra function can exactly represent the solution's irrotational component at large distances. The two methods have been applied to extensive direct-numerical simulation of transition and turbulence.

Spalart, Philippe R.

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.

Rogers, Michael M.

Characteristic eddy decomposition of turbulence in a channel

The proper orthogonal decomposition technique (Lumley's decomposition) is applied to the turbulent flow in a channel to extract coherent structures by decomposing the velocity field into characteristic eddies with random coefficients. In the homogeneous spatial directions, a generaliztion of the shot-noise expansion is used to determine the characteristic eddies. In this expansion, the Fourier coefficients of the characteristic eddy cannot be obtained from the second-order statistics. Three different techniques are used to determine the phases of these coefficients. They are based on: (1) the bispectrum, (2) a spatial compactness requirement, and (3) a functional continuity argument. Results from these three techniques are found to be similar in most respects. The implications of these techniques and the shot-noise expansion are discussed. The dominant eddy is found to contribute as much as 76 percent to the turbulent kinetic energy. In both 2D and 3D, the characteristic eddies consist of an ejection region straddled by streamwise vortices that leave the wall in the very short streamwise distance of about 100 wall units.

Moin, Parviz

Statistical analysis of near-wall structures in turbulent channel flow

The two-point correlation tensor is used to analyze near-wall structures in turbulent channel flow. Simulation results have been utilized to obtain the correlation tensor with sufficient spatial resolution to permit accurate differentiation for computing the vorticity correlation, and the resolution of sharp features such as the shear layer and its corresponding region of spanwise vorticity. Proper orthogonal decomposition and stochastic estimation were observed to yield similar results when appropriate conditions were employed for the estimation. Resulting structures were such that they would be detected by standard conditional sampling methods. The results of decomposing the vorticity field and the velocity field were significantly different, indicating that if a coherent structure is found that dominates the velocity fields, the curl of that velocity structure will not dominate the vorticity field.

Moser, Robert D.