Adjoint algorithms for the Navier-Stokes equations in the low Mach number limit

This paper describes a derivation of the adjoint low Mach number equations and their implementation and validation within a global mode solver. The advantage of using the low Mach number equations and their adjoints is that they are appropriate for flows with variable density, such as flames, but do not require resolution of acoustic waves. Two versions of the adjoint are implemented and assessed: a discrete-adjoint and a continuous-adjoint. The most unstable global mode calculated with the discrete-adjoint has exactly the same eigenvalue as the corresponding direct global mode but contains numerical artifacts near the inlet. The most unstable global mode calculated with the continuous-adjoint has no numerical artifacts but a slightly different eigenvalue. The eigenvalues converge, however, as the timestep reduces. Apart from the numerical artifacts, the mode shapes are very similar, which supports the expectation that they are otherwise equivalent. The continuous-adjoint requires less resolution and usually converges more quickly than the discrete-adjoint but is more challenging to implement. Finally, the direct and adjoint global modes are combined in order to calculate the wavemaker region of a low density jet. © 2011 Elsevier Inc.

Effects of flow geometry and Damkohler number on turbulent premixed flame

DNS of planar turbulent flame and turbulent V-flame has been conducted to investigate turbulence-scalar interaction in relatively practical turbulent combustion. Several turbulence quantities are examined for the understandings of fundamental characteristics of flow field in V-flame. Due to the additional turbulence production by the hot-rod, turbulence does not simply decay in V-flame. Turbulence-scalar interaction, scalar alignments with the principal strain rate in other words, is then clarified. The competition of turbulence and dilatation can be found in the conditional PDF of flame normal alignment. The results suggests that the alignment characteristics in high Da flames are applicable to low Da flames in the region of intense heat release.

The geometry and the number of contacts of monodisperse sphere packs using X-ray tomography

The three-dimensional structure of very large samples of monodisperse bead packs is studied by means of X-Ray Computed Tomography. We retrieve the coordinatesofeach bead inthe pack and wecalculate the average coordination number by using the tomographic images to single out the neighbors in contact. The results are compared with the average coordination number obtained in Aste et al. (2005) by using a deconvolution technique. We show that the coordination number increases with the packing fraction, varying between 6.9 and 8.2 for packing fractions between 0.59 and 0.64. © 2005 Taylor & Francis Group.

A priori assessment of algebraic flame surface density models in the context of large eddy simulation for nonunity lewis number flames in the thin reaction zones regime

The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimension D and inner cut-off scale η i have been studied in detail. It has been found that D is strongly affected by Lewis number and increases significantly with decreasing Le. By contrast, η i remains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation of D is proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD. © 2012 Mohit Katragadda et al.

Effects of turbulent reynolds number on the performance of algebraic flame surface density models for large eddy simulation in the thin reaction zones regime: A direct numerical simulation analysis

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Ret has been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Ret and Ka before reaching an asymptotic value for large values of Ret and Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel'dovich flame thickness ηi/δz does not exhibit any significant dependence on Ret for the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width. © 2012 Mohit Katragadda et al.

The rise heights of low-and high-Froude-number turbulent axisymmetric fountains

We present the results of an experimental investigation across a broad range of source Froude numbers, 0. 4 ≤ Fr 0 ≤ 45, into the dynamics, morphology and rise heights of Boussinesq turbulent axisymmetric fountains in quiescent uniform environments. Typically, these fountains are thought to rise to an initial height, z i, before settling back and fluctuating about a lesser (quasi-) steady height, z ss. Our measurements show that this is not always the case and the ratio of the fountain's initial rise height to steady rise height, λ = z i/z ss, varies widely, 0. 5 ≈ λ ≈ 2, across the range of Fr 0 investigated. As a result of near-ideal start-up conditions provided by the experimental set-up we were consistently able to form a vortex at the fountain's front. This enabled new insights into two features of the initial rise of turbulent fountains. Firstly, for 1. 0 ≈ Fr 0 ≈ 1. 7 the initial rise height is less than the steady rise height. Secondly, for Fr 0 ≈ 5. 5, the vortex formed at the fountain's front pinches off, separates from the main body and rises high above the fountain; there is thus a third rise height to consider, namely, the maximum vortex rise height, z v. From our observations we propose classifying turbulent axisymmetric fountains into five regimes (as opposed to the current three regimes) and present detailed descriptions of the flow in each. Finally, based on an analysis of the rise height fluctuations and the width of fountains in (quasi-) steady state we provide further insight into the physical cause of height fluctuations. © 2011 Cambridge University Press.

Reynolds number effects on scalar dissipation rate transport and its modeling in turbulent premixed combustion

The effects of turbulent Reynolds number, Ret, on the transport of scalar dissipation rate of reaction progress variable in the context of Reynolds averaged Navier-Stokes simulations have been analyzed using three-dimensional simplified chemistry-based direct numerical simulation (DNS) data of freely propagating turbulent premixed flames with different values of Ret. Scaling arguments have been used to explain the effects of Ret on the turbulent transport, scalar-turbulence interaction, and the combined reaction and molecular dissipation terms. Suitable modifications to the models for these terms have been proposed to account for Ret effects, and the model parameters include explicit Ret dependence. These expressions approach expected asymptotic limits for large values of Ret. However, turbulent Reynolds number Ret does not seem to have any major effects on the modeling of the term arising from density variation. Copyright © Taylor and Francis Group, LLC.

Experimental studies of an accelerating, pitching, flat plate at low Reynolds number

The understanding of low Reynolds number aerodynamics is becoming increasingly prevalent with the recent surge in interest in advanced Micro-Air Vehicle (MAV) technology. Research in this area has been primarily stimulated by a military need for smaller, more versatile, autonomous, surveillance aircraft. The mechanism for providing the high lift coefficient required forMAV applications is thought to be largely influenced by the formation of a Leading Edge Vortex (LEV). This paper analyses experimentally, the influence of the LEV effect for a flat plate wing (AR = 4) under fast and slow pitch-up motions at Re =10,000 using a combination of dye flow visualisation and PIV measurements. It is found that a fast pitch over 1c shows a flow topology dominant LEV, while for a slow pitch case over 6c, the flow is largely separated. The development of the suction surface flow and the LEV was strongly correlated with the kinematics of the leading edge, suggesting that the effective local angle of incidence at the Leading Edge (LE) is of considerable significance in unsteady pitching motions. © 2013 by P.R.R.J Stevens.

Updated correlation between aircraft smoke number and black carbon concentration

Aircraft emissions of black carbon (BC) contribute to anthropogenic climate forcing and degrade air quality. The smoke number (SN) is the current regulatory measure of aircraft particulate matter emissions and quantifies exhaust plume visibility. Several correlations between SN and the exhaust mass concentration of BC (CBC) have been developed, based on measurements relevant to older aircraft engines. These form the basis of the current standard method used to estimate aircraft BC emissions (First Order Approximation version 3 [FOA3]) for the purposes of environmental impact analyses. In this study, BC with a geometric mean diameter (GMD) of 20, 30, and 60 nm and filter diameters of 19 and 35 mm are used to investigate the effect of particle size and sampling variability on SN measurements. For BC with 20 and 30 nm GMD, corresponding to BC emitted by modern aircraft engines, a smaller SN results from a given CBC than is the case for BC with 60 nm GMD, which is more typical of older engines. An updated correlation between CBC and SNthat accounts for typical size of BC emitted by modern aircraft is proposed. An uncertainty of ±25% accounts for variation in GMD in the range 20-30 nm and for the range of filter diameters. The SN-CBC correlation currently used in FOA3 underestimates by a factor of 2.5-3 for SN <15, implying that current estimates of aircraft BC emissions derived from SN are underestimated by the same factor. Copyright © American Association for Aerosol Research.

Diameter and wall number control of carbon nanotubes by chemical vapor deposition

We analyze the relationship between the average wall number (N) and the diameter (d) for carbon nanotubes (CNTs) grown by chemical vapour deposition. It is found that N depends linearly on d for diameters in the range of 2.5-10 nm, while single wall nanotubes predominate for diameters under about 2.1 nm. The linear relationship is found to depend somewhat on the growth conditions. It is also verified that the mean diameter depends on the diameter of the originating catalyst nanoparticle, and thus on the initial catalyst thickness where a thin film catalyst is used. This simplifies the characterisation of CNTs by electron microscopy. We also find a linear relationship between nanotube diameter and initial catalyst film thickness. © 2013 AIP Publishing LLC.