Laminar swirling slender pipe flows Vinicius M. Sauer, Fernando F. Fachini Physics of Fluids, 2024 Swirling flows are extensively used to enhance mixing in chemical and physical processes. Although many fundamental studies involve decaying laminar swirls in circular ducts with constant area—for which several theoretical descriptions exist—converging and diverging pipe sections are often employed, demanding the extension of the analysis to swirling laminar flows in pipes with varying areas. This work analytically investigates axial swirl decay in laminar axisymmetric flows in converging and diverging pipes at moderate Reynolds numbers. The theoretical model extends the classical theory for laminar low swirling flows in straight pipes with impermeable walls to pipes with slowly varying areas. Inlet Reynolds number and converging/diverging angle effects are analyzed for incompressible axisymmetric laminar flows in slender pipes (lengths much greater than the radius). Results show that diverging pipes enhance the swirl decay rate, whereas converging systems have a weakening effect for flows with the same inlet Reynolds number. Conversely, increasing the inlet angle in converging flows decreases the decay rate, whereas larger diverging pipe inlet angles promote swirl decay. A simplified eigenvalue analysis shows that the relationship between the swirl decay lengths in diverging (ℓd,div), straight (ℓd,st), and converging (ℓd,conv) pipes is given by ℓd,div<ℓd,st<ℓd,conv for flows with similar inlet Reynolds numbers. Comparisons with numerical simulations show that the model predictions are almost exact for nondimensional pipe lengths up to 5×10−2 times the inlet Reynolds number. Approximating the axial velocity profile through a fully developed function representative of laminar flows with heat transfer through the walls shows that the narrower axial velocity profile in diverging flows increases viscous effects, enhancing the swirl decay rate. On the contrary, the flatter axial velocity profile in converging pipes further extends the decay length.
Dynamics of diffusion flames in a very low strain rate flow field: from transient one-dimensional to stationary two-dimensional regime Matheus P. Severino, Mariovane S. Donini, Fernando F. Fachini Combustion Theory and Modelling, 2021 The present work describes the transition of transient one-dimensional diffusion flame into a steady two-dimensional regime in a new flow field configuration. To that end, a cylindrical burner from which fuel is ejected radially and uniformly is positioned in the middle of two impinging flows. The chosen conditions are such that the strain rate is very low. The majority of the flame is located in a region of the flow field where spatial coordinates are scaled with the reciprocal of the square root of the strain rate, and the velocities are scaled with the square root of the strain rate. To simplify the model, a potential flow is assumed, with its results compared with those from a more detailed incompressible Navier–Stokes flow solution. The evolution of the flame is similar in both cases, which shows that the idealised potential flow describes well the flow field in such a geometry. Mixture fraction and excess enthalpy variables are employed to describe the infinitely fast chemical reaction, and therefore, fuel mass fraction, oxidiser mass fraction, and temperature fields. Results show that the initial flame displacement is controlled by the radial transport of fuel near the burner, where the impinging flows have a negligible influence. After that region, the flame is strongly influenced by the impinging flows where its acceleration is observed. Moreover, the proposed asymptotic solutions highlight the main transport mechanisms of reactants to the flame under different conditions and show the dependence of the flame on the chemical and flow field parameters. The stationary solution presents a diffusion flame with continuous geometric variation, from the counterflow to the coflow regime.
An Artificial Compressibility Based Approach to Simulate Inert and Reacting Flows Mariovane Donini, Fernando Fachini, Cesar Cristaldo, Pascal Bruel Journal of Fluid Flow Heat and Mass Transfer, 2021 An efficient methodology to simulate non-reactive and reactive flows is presented. Combining a finite-volume approach on fully staggered meshes along with the artificial compressibility method, the resulting code proves to be versatile enough to cope with flow configurations ranging from unsteady cylinder wakes, heated cylinder or steady and unsteady diffusion flames with excellent accuracy, in the limits of the underlying physical modelling.
Buoyant Tsuji diffusion flames: Global flame structure and flow field Mariovane S. Donini, Cesar F. Cristaldo, Fernando F. Fachini Journal of Fluid Mechanics, 2020 The present work analyses how buoyancy is impacting the topology of diffusion flames established around a horizontal cylindrical burner. The flow conditions are chosen such that the system is subjected to negative and positive buoyant forces. It is proposed in this study to investigate the effect of a modulation of the balance between these buoyant forces on the flame structure by varying the temperature of the ambient atmosphere. More specifically, conditions are sought for establishing a buoyant Tsuji diffusion flame characterized by a very low level of strain rate in its lower part (i.e. below the burner). To understand the fundamental mechanisms controlling the whole flame topology, a model is proposed which assumes steadiness and incompressibility of the flow while retaining buoyancy effects in the momentum balance. The results showed that an increase of the ambient temperature leads to the appearance of a counterflow zone below the burner where the flame is undergoing very low levels of strain rate. The overall flame proves to be shorter than its counterpart observed in the forced convection regime. In addition, it is shown that an order of magnitude analysis is able to recover the sensitivity of the flame behaviour to the Péclet and Froude numbers as well as to the combustion parameters. In a certain range of the ambient-atmosphere temperature, the flow field changes dramatically: for the same boundary conditions, there are two steady-state solutions which depend on the initial conditions, i.e. the system presents a hysteresis.
A microscopic approach to heating rate of ferrofluid droplets by a magnetic field E. C. Siqueira, L. R. N. Junior, A. R. Jurelo, J. F. H. L. Monteiro, P. A. Orellana, et al. Journal of Applied Physics, 2019 In this work, we study the heating process of colloidal ferrofluids by a magnetic field. The heating of the fluid occurs by the magnetic relaxation of the nanoparticles which provide thermal energy for the host liquid. In the limit of small volumes, the relaxation process occurs through the Neel mechanism since the magnetic nanoparticles present superparamagnetic behavior. Within this limit, we have used a microscopic model for the coupling to phonons and external magnetic field in order to model the relaxation mechanism and to obtain an expression for the heating rate of the fluid as a function of microscopic parameters. The analysis allows determining appropriate conditions for an optimal heating rate for ferrofluids based on superparamagnetic nanoparticles.In this work, we study the heating process of colloidal ferrofluids by a magnetic field. The heating of the fluid occurs by the magnetic relaxation of the nanoparticles which provide thermal energy for the host liquid. In the limit of small volumes, the relaxation process occurs through the Neel mechanism since the magnetic nanoparticles present superparamagnetic behavior. Within this limit, we have used a microscopic model for the coupling to phonons and external magnetic field in order to model the relaxation mechanism and to obtain an expression for the heating rate of the fluid as a function of microscopic parameters. The analysis allows determining appropriate conditions for an optimal heating rate for ferrofluids based on superparamagnetic nanoparticles.
Non-premixed swirl-type tubular flames burning liquid fuels Vinicius M. Sauer, Fernando F. Fachini, Derek Dunn-Rankin Journal of Fluid Mechanics, 2018 Tubular flames represent a canonical combustion configuration that can simplify reacting flow analysis and also be employed in practical power generation systems. In this paper, a theoretical model for non-premixed tubular flames, with delivery of liquid fuel through porous walls into a swirling flow field, is presented. Perturbation theory is used to analyse this new tubular flame configuration, which is the non-premixed equivalent to a premixed swirl-type tubular burner – following the original classification of premixed tubular systems into swirl and counterflow types. The incompressible viscous flow field is modelled with an axisymmetric similarity solution. Axial decay of the initial swirl velocity and surface mass transfer from the porous walls are considered through the superposition of laminar swirling flow on a Berman flow with uniform mass injection in a straight pipe. The flame structure is obtained assuming infinitely fast conversion of reactants into products and unity Lewis numbers, allowing the application of the Shvab–Zel’dovich coupling function approach.
Structure of nonpremixed swirl-type tubular flames burning condensed fuels with unity Lewis numbers 10th U S National Combustion Meeting, 2017
