Xiao-Jun Gu

Modes of reaction front propagation from hot spots

The results of computations with detailed chemical kinetic schemes for the autoignition of stoichiometric H2-CO-air and H2-air mixtures at high pressure and high temperature are reported, with and without a single hot spot. Autoignition delay and excitation times first are computed in zero-dimensional, homogeneous mixture, simulations. Spherical hot spots of three different radii are then studied, for a range of temperature differences between the centre of the hot spot and the surrounding mixture. The effects of the resulting localised initial temperature gradients on the propagation modes of the ensuing reaction waves are examined, with particular regard to possible transitions to a developing detonation. Five modes of reaction front propagation are identified and demonstrated. One mode involves normal flame deflagration, the other four involve different types of hot spot autoignition. These modes depend upon the value of the initial hot spot temperature gradient normalised by the critical temperature gradient for a developing detonation. The latter is conveniently obtained from the homogeneous computations. Upper and lower limits of this normalised temperature gradient, ξ, are observed for a developing detonation. The bounds for this also depend upon the ratio of the hot spot acoustic time to the heat release rate excitation time. A tentative first attempt is described to quantify the bounds for all the modes, in terms of the two dimensionless groups.

A high-order moment approach for capturing non-equilibrium phenomena in the transition regime

The method of moments is employed to extend the validity of continuumhydrodynamic models into the transition-flow regime. An evaluation of the regularized 13 moment equations for two confined flow problems, planar Couette and Poiseuille flows, indicates some important limitations. For planar Couette flow at a Knudsen number of 0.25, they fail to reproduce the Knudsen-layer velocity profile observed using a direct simulation Monte Carlo approach, and the higher-order moments are not captured particularly well. Moreover, for Poiseuille flow, this system of equations creates a large slip velocity leading to significant overprediction of the mass flow rate for Knudsen numbers above 0.4. To overcome some of these difficulties, the theory of regularized moment equations is extended to 26 moment equations. This new set of equations highlights the importance of both gradient and non-gradient transport mechanisms and is shown to overcome many of the limitations observed in the regularized 13 moment equations. In particular, for planar Couette flow, they can successfully capture the observed Knudsen-layer velocity profile well into the transition regime. Moreover, this new set of equations can correctly predict the Knudsen layer, the velocity profile and the mass flow rate of pressure-driven Poiseuille flow for Knudsen numbers up to 1.0 and captures the bimodal temperature profile in forcedriven Poiseuille flow. Above this value, the 26 moment equations are not able to accurately capture the velocity profile in the centre of the channel. However, they are able to capture the basic trends and successfully predict a Knudsen minimum at the correct value of the Knudsen number.

Biomimetic design of microfluidic manifolds based on a generalised Murray's law

The relationship governing the optimum ratio between the diameters of the parent and daughter branches in vascular systems was first discovered by Murray using the principle of minimum work. This relationship is now known as Murrays law and states that the cube of the diameter of the parent vessel must equal the sum of the cubes of the daughter vessels. For symmetric bifurcations, an important consequence of this geometric rule is that the tangential shear stress at the wall remains constant throughout the vascular network. In the present paper, we extend this important hydrodynamic concept to arbitrary cross-sections and provide a framework for constructing a simple but elegant biomimetic design rule for hierarchical microfluidic networks. The paper focuses specifically on constant-depth rectangular and trapezoidal channels often employed in lab-on-a-chip systems. To validate our biomimetic design rule and demonstrate the application of Murrays law to microfluidic manifolds, a comprehensive series of computational fluid dynamics simulations have been performed. The numerical predictions are shown to be in very good agreement with the theoretical analysis, confirming that the generalised version of Murrays law can be successfully applied to the design of constant-depth microfluidic devices.

Investigation of Heat and Mass Transfer in a Lid-Driven Cavity Under Nonequilibrium Flow Conditions

Gaseous flow and heat transfer in a lid-driven cavity under nonequilibrium flow conditions is investigated using the direct simulation Monte Carlo method, from the slip to the free-molecular regime. The emphasis is on understanding thermal flow features. The impact of the lid velocity and various degrees of rarefaction on the shear stress and heat flux rates are analyzed. The role of expansion cooling and viscous dissipation on the heat transfer mechanism is investigated. Complex heat flow phenomena, such as counter-gradient heat transfer, are revealed by the simulations which the conventional Navier-Stokes-Fourier equations are not able to capture, even in the slip-flow regime.

Nonplanar oscillatory shear flow: From the continuum to the free-molecular regime

The case of oscillatory cylindrical Couette gas flow has been used to investigate the effects of curvature and rarefaction on the dynamic velocity and shear stress profiles. In addition, Stokes’ second problem for a curved surface has been extended to include the effects of slip. It is shown that curvature plays a more important role than slip in determining the penetration depth, but the effects of slip are enhanced if the surface is nonplanar. The current analysis for the oscillatory cylindrical Couette problem presents new analytical solutions in the slip-flow regime and the free-molecular regime. For both cases, direct simulation Monte Carlo data are in good agreement with the analytical solutions. To complete the study throughout the entire Knudsen regime, the direct simulation Monte Carlo method was used to predict the velocity and shear stress in the transition regime. There are marked differences between the solutions obtained for the inner and outer cylinders oscillating, especially at low freque...

Generation of PDFS for flame curvature and for flame stretch rate in premixed turbulent combustion

Abstract Experimentally derived pdfs of turbulent, premixed, flame curvatures from a variety of sources, for a wide range of conditions are surveyed and a suitable expression sought to generalize these. This proves to be one based on the Damkohler number, Da. This is tantamount to normalizing the curvature by multiplying it by the Taylor scale of turbulence. It enables the distribution of flame curvature when normalized by the laminar flame thickness, to be expressed in terms of the Karlovitz stretch factor, K, and the turbulent Reynolds number, R l . The value of the pdf at zero curvature is linearly related to Da 1/2 . The pdf expressions of Yeung et al. [3] obtained from numerical simulations are used for the strain rate distribution and, on the assumption that these and that for flame curvature are statistically independent, values of flame stretch rate pdfs are generated numerically. It is necessary to define an appropriate surface to define the burning velocity, flame stretch rate, and appropriate Markstein numbers. Two surfaces are considered and employed in the computations, one located at the start of the preheat zone, the other at the start of the reaction zone. The latter seems more rational and gives the better generalisation of the pdfs of flame stretch rate. An assumed linearity of laminar burning velocity with flame stretch rate, extending over both positive and negative stretch rates, enables flame stretch rate pdfs to be generated. It is concluded that negative values of burning velocity are unlikely and that burning velocities should tend to zero rather than attain negative values. This modifies the derivation of flame stretch rate pdfs. These depend on the Markstein number, Karlovitz stretch factor and turbulent Reynolds number. Computations suggest that, for values of K above 0.1 and of R l above 100, the pdf of stretch rate is similar to that of strain rate. At very low values of K and negative values of Markstein number, pronounced flamelet instability might be anticipated.

Mathematical modeling of turbulent non-premixed piloted-jet flames with local extinctions

Flamelet modeling of highly stretched jet flames is combined with the use of conditional moment closuresecond-order closure procedures to evaluate a pdf, p ˜ ( θ | η ) , of the reaction progress variable, θ, that is conditioned upon a value of the mixture fraction η. Through the use of a probability of burning function. P h , the model expresses the effects of strain rate and localized flame quenching. The product of this function and another term embodying the relevant laminar flamelet source term from a flamelet library, together with p ˜ ( θ | η ) , yields the required mean turbulent source term. Both heat release rate and the formation rate of species are dealt with in this way. It was found appropriate and convenient to use the k-ω model, with a kinematic eddy viscosity, for the flow turbulence. The overall model is applied to those experimental piloted-jet methane/air flames of Barlow and Frank, in which there are pronounced extinctions and reignitions. Velocity vectors and spatial contours of mean mixture fraction, mean volumetric heat release rate, and mean strain rate clearly show the essential structures of the flames. As the flow rate increases, so does the extent of the penetration of the region of high strain rates into that of flammable mixtures. This creates localized regions of reduced mean heat release rate in which localized extinctions might be anticipated, due to the strain rate being high and the mixture being less reactive. These locations are confirmed by experiments, as is the predicted extent of the flames. There is generally good agreement between predicted and measured mean temperatures, mean mixture fractions, and mass fractions of CH 4 , O 2 , and H 2 O. Agreement is less satisfactory for transient species. Possible limitations of the model are discussed.

Modelling thermal flow in the transition regime using a lattice Boltzmann approach

Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58.

Recent advances in computational fluid dynamics relevant to the modelling of pesticide flow on leaf surfaces

Increasing societal and governmental concern about the worldwide use of chemical pesticides is now providing strong drivers towards maximising the efficiency of pesticide utilisation and the development of alternative control techniques. There is growing recognition that the ultimate goal of achieving efficient and sustainable pesticide usage will require greater understanding of the fluid mechanical mechanisms governing the delivery to, and spreading of, pesticide droplets on target surfaces such as leaves. This has led to increasing use of computational fluid dynamics (CFD) as an important component of efficient process design with regard to pesticide delivery to the leaf surface. This perspective highlights recent advances in CFD methods for droplet spreading and film flows, which have the potential to provide accurate, predictive models for pesticide flow on leaf surfaces, and which can take account of each of the key influences of surface topography and chemistry, initial spray deposition conditions, evaporation and multiple droplet spreading interactions. The mathematical framework of these CFD methods is described briefly, and a series of new flow simulation results relevant to pesticide flows over foliage is provided. The potential benefits of employing CFD for practical process design are also discussed briefly.

NUMERICAL INVESTIGATIONS OF CAVITATION AROUND A HIGH SPEED SUBMARINE USING OPENFOAM WITH LES

Under water cavitation occurs when the liquid changes the phase into its vapor due to the local pressure is lower than the water saturation pressure. If a body is moving very fast under water, the local pressure around it at a certain flow regime will be lower than the water saturation pressure. The cavitation around the body will occur. Following the increase of the intensity of the cavitation, a cloud cavitation will occur. Under the cloud cavitation occurrence, the cavitation is unsteady and periodic, which involves formation, detachment and collapse of sheet cavities. In this paper, large Eddy simulation (LES) is employed together with a mixture assumption and a finite rate mass transfer modeling into OpenFOAM to study the cavitation phenomena. The validation comparisons of numerical simulations with experiments of a sphere under water are performed. After the validation, a full submarine model with sail and appendages under water is studied. The submarine is under water around 450 m deep with a moving speed at 60 m/s. It is found that the cavitation changes under the different cavitation numbers (from 1.0 to 0.1). Small cavitation numbers induce a large area cavitation, whereas large ones reduce this phenomenon. A supercavitation, which can be described as a large bubble, is found around the high speed submarine at cavitation number equals to 0.1.