SCI Publications

The properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available high-quality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a predominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular significance is attached to the viscous/Reynolds-stress-gradient balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In particular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds number approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds number and have the same order of magnitude, there is additional theoretical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged momentum balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.

An analysis is given for fully developed thermal transport through a wall-bounded turbulent fluid flow with constant heat flux supplied at the boundary. The analysis proceeds from the averaged heat equation and utilizes, as principal tools, various scaling considerations. The paper first provides an accounting of the relative dominance of the three terms in that averaged equation, based on existing DNS data. The results show a clear decomposition of the turbulent layer into zones, each with its characteristic transport mechanisms. There follows a theoretical treatment based on the concept of a scaling patch that justifies and greatly extends these empirical results. The primary hypothesis in this development is the monotone and limiting Peclet number dependence (at fixed Reynolds number) of the difference between the specially scaled centerline and wall temperatures. This fact is well corroborated by DNS data. A fairly complete qualitative and order-of-magnitude quantitative picture emerges for a complete range in Peclet numbers. It agrees with known empirical information. In a manner similar to previous analyses of turbulent fluid flow in a channel, conditions for the existence or nonexistence of logarithmic-like mean temperature profiles are established. Throughout the paper, the classical arguments based on an assumed overlapping of regions where the inner and outer scalings are valid are avoided.

A known difficulty with using the Clauser chart method to determine the friction velocity in wall bounded flows is that it assumes, a priori, a logarithmic law for the mean velocity profile. Using both experimental and DNS data in the literature, this note explicitly shows how friction velocities obtained using the Clauser chart method can potentially mask subtle Reynolds-number-dependent behavior.

We present a review of the semi-Lagrangian method for advection–diffusion and incompressible Navier–Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable.

Keywords: Semi-Lagrangian method, spectral element method, incompressible flow

We present an \"equation-free\" multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast in the form of stochastic differential equations. A detailed fine-scale computation of such a problem requires discretization and solution of a large system of equations and can be prohibitively time consuming. To circumvent this difficulty, we propose an equation-free approach, where the fine-scale computation is conducted only for a (small) fraction of the overall time. The evolution of a set of appropriately defined coarse-grained variables (observables) is evaluated during the fine-scale computation, and \"projective integration\" is used to accelerate the integration. The choice of these coarse variables is an important part of the approach: they are the coefficients of pointwise polynomial expansions of the random solutions. Such a choice of coarse variables allows us to reconstruct representative ensembles of fine-scale solutions with \"correct\" correlation structures, which is a key to algorithm efficiency. Numerical examples demonstrating accuracy and efficiency of the approach are presented.

Keywords: multiscale problem, diffusion in random media, stochastic modeling, equation-free

Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic Galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations. On the other hand, the traditional sampling methods, e.g., Monte Carlo methods, are straightforward to implement, but they do not offer convergence as fast as stochastic Galerkin methods. In this paper, a high-order stochastic collocation approach is proposed. Similar to stochastic Galerkin methods, the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence. However, the numerical implementation of stochastic collocation is trivial, as it requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods. The computational cost of the collocation methods depends on the choice of the collocation points, and we present several feasible constructions. One particular choice, basedon sparse grids, depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs. Numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods.

Keywords: collocation methods, stochastic inputs, differential equations, uncertainty quantification

Keywords: Analytical models, Computational modeling, Context modeling, Microscopy, Nonlinear equations, Partial differential equations, Performance analysis, Sampling methods, Stochastic processes, Uncertainty

A theoretical method for predicting the smoke point of pure hydrocarbon liquids is presented. The method is based on a structural group contributions approach and does not require any experimental procedures or information of fuel properties, other than the molecular structure of the fuel molecules. The proposed correlation is presented in the form of a multivariable regression. The average deviation is only 1.3 TSI (threshold soot index) units for ∼70 compounds from low-sooting paraffins to highly sooting aromatics, and the average relative error is 9.08%. The results of three different sets of structural groups derived from the Quann and Joback group contribution methods are tested and compared. For a mixture with a defined composition, the estimation of smoke point is also discussed. The method is of potential value for the formulation of surrogate fuels of hydrocarbon mixtures, where matching the fuel's sooting tendency is important.

JP-8, a surrogate fuel, and several model compounds were used to produce soot aerosols in a drop-tube furnace with optical access. The soluble organic fractions (SOF) of soot aerosols were studied with GC, GC−MS, and ¹³C NMR. The residue of each aerosol sample was studied with Raman spectroscopy, ESR, and a recently developed technique used to determine the conductivity and extent of turbostratic structure formation in soot. The SOF values from different fuel sources exhibit variations in yield, and carbon aromaticity values, and the latter parameter correlates with the extent of turbostratic structure formation in the aerosol residues. Raman data of the soot residues indicate the presence of highly disordered graphitic structures, but the graphite factor measurements reveal differences among these disordered structures that are not apparent in the Raman data.