Michael Fairweather

Predictions of the Structure of Turbulent, Highly Underexpanded Jets

A mathematical model capable of predicting the shock and flow structure of turbulent, underexpanded jets is described. The model is based on solutions of the fluid flow equations obtained using a second-order accurate, finite-volume integration scheme together with an adaptive grid algorithm. Closure of these equations is achieved using a k-e turbulence model coupled to the compressible dissipation rate correction proposed by Sarkar et al. Extending earlier work which demonstrated the ability of this model to predict the structure of moderately underexpanded jets, the present paper compares model predictions and experimental data, reported in the literature, on a number of highly underexpanded releases. The results obtained demonstrate that the model yields reliable predictions of shock structure in the near field, inviscid region of such jets, while in the far field results derived using the compressibility corrected turbulence model are adequate for predicting meanflow properties, and are superior to those obtained using a standard k-e approach.

Stagnation Point Heat Transfer from Turbulent Methane-Air Flames

Abstract Mathematical models for the prediction of stagnation point heat flux in the chemical equilibrium region of turbulent flames are presented. These models include a numerical solution of the relevant boundary layer equations, and modified empirical correlations originally derived for the case of uniform, turbulent air flows. Experimental measurements of the stagnation point heat flux received by a hemisphere-cylinder probe placed in methane-air flames are included, and free stream temperatures, mean velocities and turbulence intensities were measured for comparisons between theory and experiment. Predictions of the mathematical models show that the influence of free stream turbulence on heat transfer from these names is relatively small for the geometry in question. Comparisons with experimental data confirm this finding. Good quantitative agreement occurs between numerical solutions and experimental data for flames which only entrain small amounts of atmospheric air. Conservative estimates of heat ...

Predictions of the Structure of Turbulent, Moderately Underexpanded Jets

A mathematical model capable of predicting the structure of turbulent, underexpanded jets is described. The model is based on solutions of the fluid flow equations obtained using a second-order accurate, finite-volume integration scheme coupled to an adaptive grid algorithm. Turbulence within these jets is modelled using a k-e approach coupled to the compressible dissipation rate model of Sarkar et al.

Predictions of Impacting Sonic and Supersonic Jets

A mathematical model of sonic and supersonic jets, validated previously by the present authors for the prediction of moderately and highly underexpanded free jets, is used to simulate the near field structure of jets which impact a flat surface orthogonally, and its accuracy assessed by comparing model predictions with experimental data available in the literature. For impacting, moderately underexpanded jets, results derived from the model are found to be in close agreement with data on the location of both free jet shocks, and the stand-off shock formed adjacent to the impacted surface. In addition, the model provides reasonable estimates of density within the free jet and stagnation regions of such flows, with the existence, or otherwise, of stagnation bubbles being successfully predicted. Measurements ofpressure occurring on the surface of the impacted plate, produced by the impingement of both sonic and supersonic jets, are also predicted with reasonable accuracy, although the decaying amplitude of spatially periodic pressure oscillations within the wall jet region of these flows is slightly overpredicted in some cases.

Inertial particle resuspension in a turbulent, square duct flow

Particle resuspension in a turbulent, square duct flow is studied using large eddy simulation combined with Lagrangian particle tracking under conditions of one-way coupling, with the particle equation of motion solved with the Stokes drag, lift, buoyancy, and gravitational force terms. Here, resuspension is taken to mean the movement of particles in close proximity to the duct walls back in to the mainstream of the flow. The flow considered has a bulk Re=250 k, with four particle sizes ranging from 5 to 500 μm examined. The results demonstrate that turbulence-driven secondary flows within the duct play an important role in the resuspension process. In the vertical direction, resuspension is promoted by the drag force arising from the secondary flows, which is balanced by the gravitational force, with this effect increasing with decreasing particle size. In the horizontal direction, particle resuspension is promoted by the particle’s inertial force, with this effect increasing with increasing particle siz...

An investigation of packed columns using a digital packing algorithm

This paper presents results concerning the validation of a recently developed packing algorithm. The basic ethos of this algorithm is to digitise particle shapes, and to use the digitised shapes to generate digital packing structures. A variety of simulations of packed columns, comprising mono, binary and ternary mixtures of spherical particles, have been undertaken and the results compared to existing experimental data with good agreement. The ultimate aim of this work is to develop the packing algorithm as a design tool for use in optimising the performance of packed bed systems and, as a first step, to enable the characterisation of any particle population and prediction of particle behaviour in packing, segregation and mixing.

NUMERICAL STUDY OF EMISSION CHARACTERISTICS OF A JET FLAME IN CROSS-FLOW

The authors numerically investigated the effect of changes in the fuel exit velocity and the cross-flow on the length, radiant fraction, and emission indices of pollutant species (NOx and CO), as well as the ratio NO2/NOx, of a high momentum jet flame in cross-flow. This flow configuration is of generic interest, and also practically relevant to flaring operations. The flow field is computed based on the Reynolds-Averaged Navier–Stokes equations incorporating the realizable k−ϵ turbulence closure. The combustion process is modeled using the unsteady Eulerian particle flamelet model based on the mixture fraction approach, and the heat loss by radiation is accounted for using the discrete ordinates method. Comparison of the predicted flame length and the trend of the emission indices with experimental measurements reveal good agreement for the range of jet-to-cross-flow momentum flux ratios investigated, namely 100–800.

Simulation of inertial fibre orientation in turbulent flow

The spatial and orientational behaviour of fibres within a suspension influences the rheological and mechanical properties of that suspension. An Eulerian-Lagrangian framework to simulate the behaviour of fibres in turbulent flows is presented. The framework is intended for use in simulations of non-spherical particles with high Reynolds numbers, beyond the Stokesian regime, and is a computationally efficient alternative to existing Stokesian models for fibre suspensions in turbulent flow. It is based on modifying available empirical drag correlations for the translation of non-spherical particles to be orientation dependent, accounting for the departure in shape from a sphere. The orientational dynamics of a particle is based on the framework of quaternions, while its rotational dynamics is obtained from the solution of the Euler equation of rotation subject to external torques on the particle. The fluid velocity and turbulence quantities are obtained using a very high-resolution large eddy simulation with dynamic calibration of the sub-grid scale energy containing fluid motions. The simulation matrix consists of four different fibre Stokes numbers (St = 1, 5, 25, and 125) and five different fibre aspect ratios (λ = 1.001, 3, 10, 30, and 50), with results considered at four distances from a channel wall (in the viscous sub-layer, buffer, and fully turbulent regions), which are taken as a measure of the flow velocity gradient, all at a constant fibre to fluid density ratio (ρp/ρ = 760) and shear Reynolds number Reτ = 150. The simulated fibre orientation, concentration, and streakiness confirm previous experimentally observed characteristics of fibre behaviour in turbulence, and that of direct numerical simulations of fibres in Stokesian, or creeping flow, regimes. The fibres exhibit translational motion similar to spheres, where they tend to accumulate in the near-wall (viscous sub-layer and buffer) region and preferentially concentrate in regions of low-speed streaks. The current results further demonstrate that the fibres’ translational dynamics, in terms of preferential concentration, is strongly dependent on their inertia and less so on their aspect ratio. However, the contrary is the case for the fibre alignment distribution as this is strongly dependent on the fibre aspect ratio and velocity gradient, and only moderately dependent on particle inertia. The fibre alignment with the flow direction is found to be mostly anisotropic where the velocity gradient is large (i.e., viscous sub-layer and buffer regions), but is virtually non-existent and isotropic where the turbulence is near-isotropic (i.e., channel centre). The present investigation highlights that the level of fibre alignment with the flow direction reduces as a fibre’s inertia decreases, and as the shape of the fibre approaches that of a sphere. Short fibres, and especially near-spherical λ = 1.001 particles, are found to exhibit isotropic orientation with respect to all directions, whilst sufficiently long fibres align themselves parallel to the flow direction, and orthogonal to the other two co-ordinate directions, and the vorticity and flow velocity gradient directions.

Modelling and simulation of particle re-suspension in a turbulent square duct flow

Abstract The ability of a Reynolds-averaged Navier–Stokes (RANS) approach, coupled with a Lagrangian particle tracking technique, to predict particle re-suspension rates in a high Reynolds number duct flow has been assessed for spherical particles over a range of sizes, with results compared with predictions based on large eddy simulation. In general, there is reasonable agreement between the two predictive techniques in regards to the locations where maximum re-suspension rates occur in the lower half of the duct, with both methods predicting the preferential re-suspension of smaller particles. The main difference between the approaches is in the magnitude of the re-suspension rate, with RANS predicting a greater variability across the duct. These differences are attributable to the method used to derive instantaneous fluid velocities, required by the Lagrangian particle tracking technique, from the RANS solutions, coupled with smaller inaccuracies due to the turbulence model employed as the basis of the RANS solutions.

Prediction of the ignition characteristics of flammable jets using intermittency-based turbulence models and a prescribed pdf approach

Abstract A mathematical model capable of predicting the ignition hazards presented by turbulent releases of flammable materials is presented. The model is based on solutions of the fluid flow equations, with closure of this equation set achieved using either a k – ɛ – γ turbulence model or an intermittency-based second moment closure. Solutions are coupled to a prescribed, three-part probability density function (pdf) to allow the prediction of the bimodal scalar distributions observed in intermittent free shear flows which can have a significant influence on ignition characteristics. Integration of this pdf over the flammable range of the release material then leads to the probability of ignition at any point in the flow. Predictions of the complete model are compared with data obtained in a number of jets, with comparisons for velocity and concentration fields, intermittency, concentration pdfs and ignition probabilities demonstrating that both turbulence modelling approaches are capable of reliably predicting ignition probabilities in the jet flows examined. Overall, results derived from the second-order modelling approach are superior to k – ɛ – γ turbulence model predictions.