Modelling hydrodynamics and turbulence in a bubble column using the Euler-Lagrange procedure

Strong turbulence at a water–air free surface can lead to splashing and a disconnected surface as in a breaking wave. Averaging to obtain boundary conditions for such flows first requires equations of motion for the two-phase region. These are derived using an integral method, then averaged conservation equations for mass and momentum are obtained along with an equation for the turbulent kinetic energy in which extra work terms appear. These extra terms include both the mean pressure and the mean rate of strain and have similarities to those for a compressible fluid. Boundary conditions appropriate for use with averaged equations in the body of the water are obtained by integrating across the two-phase surface layer.A number of ‘new’ terms arise for which closure expressions must be found for practical use. Our knowledge of the properties of strong turbulence at a free surface is insufficient to make such closures. However, preliminary discussions are given for two simplified cases in order to stimulate further experimental and theoretical studies.Much of the turbulence in a spilling breaker originates from its foot where turbulent water meets undisturbed water. A discussion of averaging at the foot of a breaker gives parameters that may serve to measure the ‘strength’ of a breaker.

The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions

Study on the Eulerian dispersed phase equations in non-uniform turbulent two-phase flows: discussion and comparison with experiments

A gas turbine engine is an advanced apparatus for propulsion and power generation that has been developed over the last 60 years. The energy for this production
of propulsion and power in a gas turbine is generated by combustion.
It is feasible and relatively easy to solve the governing equations in combustion for one dimensional laminar hydrocarbon combustion with detailed chemistry. This has been done for several hydrocarbon fuels that are representative for liquid fuel combustion. The complex chemistry that is solved completely in a laminar flame is mostly modelled in simulations of turbulent combustion. Essential to this modelling is a correct understanding of the processes that govern the chemistry. Via the route of a numerical perturbation method, the CSP-method, this understanding can be developed. After analysis with CSP, the next step to a model describing turbulent combustion in gas turbines is taken using the CFI combustion model. This model comprises the definition of a reaction progress variable representing the reduced chemistry yielding from CSP, a mixture fraction variable and an enthalpy variable. The thesis presents a version of the CFI combustion model for application in evaporating fuel sprays.

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Combustion and noise phenomena in turbulent alkane flames

An “in-house” computational fluid dynamics code implementing a Euler-Lagrange approach is extended by incorporating the Euler-Euler (two-fluid model) approach, to improve prediction capabilities of flow and thermal characteristics of turbulent evaporating sprays. The performance of both approaches is assessed by comparing predictions with experimental data for a variety of evaporating-spray test cases. The applicability of the Euler-Lagrange and Euler-Euler approach is established in an isopropyl alcohol–air turbulent flow, in which characteristic droplet quantity predictions are in satisfactory overall agreement with measurements. The evaporating spray characteristics are then predicted under “stabilized cool flame” conditions and the computational results are compared to experimental data for a nonreactive case and a reactive case. In both cases, the velocity and thermal fields are successfully captured by both approaches. Overall, the article demonstrates an approach toward the development of performan...

Turbulent Sprays Evaporating Under “Stabilized Cool Flame” Conditions: Assessment of two CFD Approaches

A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2 PHF) formulations and modelling techniques is introduced. Basic theorems for the case of dispersed 2 PHF are presented. Phase interaction terms with a clear physical meaning enter the equations and this formalism provides some guidelines to avoid closure assumptions or to close those terms rationally. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations can be rigorously and systematically obtained with this methodology in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that the dispersed phase is well described by a "Boltzmann-type" equation and Eulerian "continuity", momentum and fluctuating kinetic energy equations for the dispersed phase are obtained. A k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy. Closure assumptions are proposed for the phase interaction terms. This model is then used to predict the behaviour of an axisymmetric turbulent jet of air laden with solid particles varying in sizes and concentrations. Numerical results compare reasonably well with available experimental data.

Ricardo Aliod

Papers

A Statistically Conditioned Averaging Formalism for Deriving Two-Phase Flow Equations†