Fluid Dynamics Research

This work provides a multiscale model for accurate descriptions of the heat and mass transport during single microdroplet evaporation and single pulse spray cooling on a heated semi-infinite solid. The temperature drop from a high-pressure spray pulse is captured through thermocouples and an infrared camera for initial substrate temperatures ranging from negative to positive superheats. A representative average diameter is estimated using high-speed cameras and the droplet size distribution statistics. The model can correctly predict the wall heat flux and evaporation rates from room temperature to positive superheats up to 10 K. At superheats beyond 20 K the model breaks down due to presumably boiling and microlayer evaporation effects. The results highlight the validity of coupling lubrication theory with kinetically-limited and diffusion-limited evaporation over a wide range of temperatures, using the vapor temperature and vapor pressure as the key mediating properties for bridging the molecular-scale forces with continuum-scale thermal physics.

We derive the incompressible Navier–Stokes equations from the lattice Boltzmann equation using the Chapman–Enskog expansion and the Sone expansion and clarify the differences between the two approaches. In the Chapman–Enskog expansion, we first derive the compressible Navier–Stokes equations on the multiple time scales (the acoustic and diffusive time scales). Then the incompressible Navier–Stokes equations are derived under the conditions of low Mach number flows and small density variations on the diffusive time scale. If the acoustic time scale remains in the analysis of the derived macroscopic equations, the incompressible Navier–Stokes equations are recovered with only the first-order spatial accuracy. On the other hand, in the Sone expansion we can derive the incompressible Navier–Stokes equations under the condition of low Mach number flows on the diffusive time scale. Despite some differences between the two approaches, we obtain the same result that the flow velocity and the pressure satisfy the incompressible Navier–Stokes equations with the second-order spatial accuracy in low Mach number flows on the diffusive time scale. The accuracy is verified through simulating a generalized Taylor–Green problem.

A semi-analytical study of coupled translation and rotation of a composite spherical particle (a hard sphere core coated with a permeable porous layer) in a viscous fluid inside an eccentric spherical cavity normal to their common diameter is presented in the quasi-steady limit of low Reynolds number. To solve the Stokes and Brinkman equations for the flow fields outside and inside the porous layer, respectively, a general solution is constructed from the fundamental solutions in the two spherical coordinate systems based on both the composite particle and the cavity. The boundary conditions at the cavity wall and inner and outer surfaces of the porous layer are satisfied by a collocation method. Numerical results for the force and torque exerted on the particle by the fluid are obtained with good convergence for various values of the relevant parameters in practical applications. For the translation and rotation of a composite sphere inside a concentric cavity, our force and torque results agree well with the available solutions in the literature. The force and torque on a translating and rotating particle increase monotonically with increases in the ratios of particle radius to porous layer permeation length, core-to-particle radii, and particle-to-cavity radii. In general, they also increase with an increase in the relative distance between the particle and cavity centers. The boundary effect of the cavity on the translation of the particle is much more pronounced than that on the rotation. The coupling effect in the simultaneous translation and rotation inside an eccentric spherical cavity is complicated and not a monotonic function of the particle-to-cavity radius ratio.

D'Alembert's paradox is the contradictory observation that for incompressible and inviscid (potential) fluid flow, there is no drag force experienced by a body moving with constant velocity relative to the fluid. This paradox can be straightforwardly resolved by considering Navier's slip boundary condition. Potential flow around a cylinder then solves the Navier–Stokes equations using friction parameter $\beta = -2\nu$. This negative friction parameter can be interpreted physically as the fluid being accelerated by the cylinder wall. This explains the lack of drag. In this paper, we introduce the Navier slip boundary condition and show that choosing the friction parameter positive resolves d'Alembert's paradox. We then further examine the effect of the friction parameter β on the drag coefficient. In particular, we show that for large β the drag coefficient corresponds well with experimental values.

The generation of mean flows by trains of traveling, inviscid water waves is investigated. All ambiguities associated with the velocity potential are resolved by treating uniform wave trains as limits of wave packets, and appealing to the conservation of mass and momentum. This formulation leads to a systematic multiple-scales description of weakly nonlinear wave trains and the associated mean flows. The results are compared with the amplitude equation formulation of Davey and Stewartson and radiation stress formulation of Longuet-Higgins and Stewart which do not conserve mass. The momentum of the wave train can be uniquely specified only by an analysis of the wave generation mechanism. The present theory is sufficiently general that mean flows arising from different generation mechanisms can be included, and shows that a recently proposed singularity associated with mean flows is absent.

This paper explores the potential of a streamlined adaptive finite point method (FPM) in tackling two-dimensional coupled Burgers' equations, employing them as a testbed for further advancements. Firstly the coupled system is transformed into a two-dimensional heat equation through Cole–Hopf transformation and then this transformed equation is split into one-dimensional heat equations at intermediate temporal levels along X and Y directions and these one-dimensional equations are finally to be treated with the adaptive FPM. The distinctive feature of the adaptive FPM used here lies in employing an implicit 4-point stencil within each local cell to compute the solution at a higher temporal level through a linear combination of solutions from the preceding temporal level. The coefficients involved in this linear combination are derived via the local fundamental solutions within that cell, thereby imbuing the formulations with the intrinsic essence of the exact solution. Moreover, the separation constant utilized is tailored to consistently integrate the influence of the initial solution, independent of the temporal level. The method's theoretical underpinnings ensure its conditionally stable, consistent, and convergent behavior. The accuracy of the scheme is substantiated by its proficient handling of diverse examples, attesting to its superior cost-effectiveness and time efficiency.

The fluid dynamic phenomena of liquid drop impact are described and reviewed. These phenomena include bouncing, spreading and splashing on solid surfaces, and bouncing, coalescence and splashing on liquid surfaces. Further, cavitation and the entrainment of gas into an impacted liquid may be observed. In order to distinguish properly between the results of different experiments different impact scenarios are discussed. The specific conditions under which the above phenomena did occur in experiments are analyzed and the characteristics of drop impact phenomena are described in detail.

Thin liquid film flowing down the inner concave surface of a vertical cylindrical vessel is examined. At the top of the vessel, the water is injected horizontally at high speed circumferentially along the vessel wall and flows downwards due to the action of gravity. This turbulent film flow is modeled using the large eddy simulation (LES) and Reynolds averaged Navier–Stokes (RANS) approaches combined with the volume-of-fluid method. The results of both methods are validated with direct numerical simulation. The Favre-filtered two-phase LES, which is implemented and studied in this paper, can reasonably predict the film thickness similarly to that of the RANS approach using the elliptic blending Reynolds stress model, although it requires fine resolution in the wall region. The effect of volume flow rate on the film structure and thickness is investigated. The film thickness is shown to be nearly constant when the wall is partially wetted and changes as the cubic root of the volume flow rate when the spinning film encloses the entire circumference of the vessel.

Using methods of granular mechanics in the quasi-static limit, with inter-particle interactions derived from the lubrication limit, the intensity of velocity fluctuations in the slurry is associated with fluctuations in the local distribution of inter-particle distances. These are shown to consist of a vector intensity and a scalar intensity; the former couples to the first velocity gradient, the latter (which is associated with solidosity fluctuations) couples to the second velocity gradient. Rheologies for both are presented, as is the rheology that links the particle pressure to the intensity of the velocity fluctuations (also known as the 'granular temperature') to the dispersive pressure. The rheologies are informed by experimental results. The granular temperature profile, modified from previous work, is responsible for axial particle migration (Bagnold effect). Two broad categories are assessed: symmetrical vertical and non-symmetrical lateral flow. For the latter the roughness of the boundary walls and a non-zero density contrast are important; this case is studied for a system in which flow effects are confined to the immediate vicinity of the boundary. Sensitivity analysis reveals several key variables including the parameters that control a slipping boundary condition and the mean solidosity in the conduit. For lateral flow, a sedimentary deposit with a solidosity profile may develop near the upper or lower boundary. The theory predicts an approximate relation between the fluid-particle density contrast and sediment thickness as a function of the mean flow rate, conduit width, the mean particle diameter and fluid viscosity that has utility in a range of engineering and geological situations where particulate matter is transported in the laminar flow regime.

Analysis methods based on mode decomposition have been proposed to describe the characteristics of flow phenomena. Among them, proper orthogonal decomposition (POD), which decomposes modes into eigenvalues and basis vectors, has long been used. Many studies have shown that POD is a useful method for capturing the characteristics of unsteady flow. In particular, Snapshot POD has attracted much recent attention and has been used to solve unsteady flow problems. However, the basis vectors of the mode obtained by conventional POD is different for each condition. Therefore, whether the basis vectors of each mode are switching in the direction of parameters (e.g. different shapes or different Reynolds numbers) or whether they develop or decay is difficult to discuss. As a result, discussions on conventional POD tend to be qualitative. To address this issue, the present study uses Parametric Global POD, a method that perfectly matches basis vectors in results with different parameters (in this study, different Reynolds numbers). Parametric Global POD method was applied to the analysis of the flow field in a curved pipe and found to capture the development or decay of modes with major basis vectors in the direction of parameters, which is difficult to achieve with conventional POD methods.

In this article, is the concept of non-linear convective flow of an inclined porous square enclosure filled with titania–water (TiO₂–H₂O)/silver–water (Ag–H₂O)/copper–water (Cu–H₂O) nanoliquid is numerically investigated under the magnetic field effect. In the top and bottom horizontal walls there is cold and hot slits in the middle, remaining portions are kept adiabatic. The left and right walls are considered as hot and cold walls. The numerical computations are carried out using the finite difference method based Marker-and-Cell technique and the solution facilitates in understanding the heat and fluid flow variations within the cavity. In the momentum and energy equations, the impact of nonlinear Boussinesq approximation, internal heat absorption or generation, magnetic field, and porous medium are considered. Using the dimensionless variables, the governing partial differential equations are obtained in non-dimensional form. The significant effects of pertinent parameters on streamlines, isotherms, and the local heat transfer rate are graphically presented and the physical aspects are discussed. Further, the mean Nusselt number is examined using tables and the obtained results are consistent with the literature. The results clearly show a basic distinction between the linear and non-linear Boussinesq approximations. In average Nusselt number Ag–water nanofluid increases more heat transfer compared to other nanofluids.

D'Alembert's paradox is the contradictory observation that for incompressible and inviscid (potential) fluid flow, there is no drag force experienced by a body moving with constant velocity relative to the fluid. This paradox can be straightforwardly resolved by considering Navier's slip boundary condition. Potential flow around a cylinder then solves the Navier–Stokes equations using friction parameter $\beta = -2\nu$. This negative friction parameter can be interpreted physically as the fluid being accelerated by the cylinder wall. This explains the lack of drag. In this paper, we introduce the Navier slip boundary condition and show that choosing the friction parameter positive resolves d'Alembert's paradox. We then further examine the effect of the friction parameter β on the drag coefficient. In particular, we show that for large β the drag coefficient corresponds well with experimental values.

This work provides a multiscale model for accurate descriptions of the heat and mass transport during single microdroplet evaporation and single pulse spray cooling on a heated semi-infinite solid. The temperature drop from a high-pressure spray pulse is captured through thermocouples and an infrared camera for initial substrate temperatures ranging from negative to positive superheats. A representative average diameter is estimated using high-speed cameras and the droplet size distribution statistics. The model can correctly predict the wall heat flux and evaporation rates from room temperature to positive superheats up to 10 K. At superheats beyond 20 K the model breaks down due to presumably boiling and microlayer evaporation effects. The results highlight the validity of coupling lubrication theory with kinetically-limited and diffusion-limited evaporation over a wide range of temperatures, using the vapor temperature and vapor pressure as the key mediating properties for bridging the molecular-scale forces with continuum-scale thermal physics.

A semi-analytical study of coupled translation and rotation of a composite spherical particle (a hard sphere core coated with a permeable porous layer) in a viscous fluid inside an eccentric spherical cavity normal to their common diameter is presented in the quasi-steady limit of low Reynolds number. To solve the Stokes and Brinkman equations for the flow fields outside and inside the porous layer, respectively, a general solution is constructed from the fundamental solutions in the two spherical coordinate systems based on both the composite particle and the cavity. The boundary conditions at the cavity wall and inner and outer surfaces of the porous layer are satisfied by a collocation method. Numerical results for the force and torque exerted on the particle by the fluid are obtained with good convergence for various values of the relevant parameters in practical applications. For the translation and rotation of a composite sphere inside a concentric cavity, our force and torque results agree well with the available solutions in the literature. The force and torque on a translating and rotating particle increase monotonically with increases in the ratios of particle radius to porous layer permeation length, core-to-particle radii, and particle-to-cavity radii. In general, they also increase with an increase in the relative distance between the particle and cavity centers. The boundary effect of the cavity on the translation of the particle is much more pronounced than that on the rotation. The coupling effect in the simultaneous translation and rotation inside an eccentric spherical cavity is complicated and not a monotonic function of the particle-to-cavity radius ratio.

We derive the incompressible Navier–Stokes equations from the lattice Boltzmann equation using the Chapman–Enskog expansion and the Sone expansion and clarify the differences between the two approaches. In the Chapman–Enskog expansion, we first derive the compressible Navier–Stokes equations on the multiple time scales (the acoustic and diffusive time scales). Then the incompressible Navier–Stokes equations are derived under the conditions of low Mach number flows and small density variations on the diffusive time scale. If the acoustic time scale remains in the analysis of the derived macroscopic equations, the incompressible Navier–Stokes equations are recovered with only the first-order spatial accuracy. On the other hand, in the Sone expansion we can derive the incompressible Navier–Stokes equations under the condition of low Mach number flows on the diffusive time scale. Despite some differences between the two approaches, we obtain the same result that the flow velocity and the pressure satisfy the incompressible Navier–Stokes equations with the second-order spatial accuracy in low Mach number flows on the diffusive time scale. The accuracy is verified through simulating a generalized Taylor–Green problem.

In this paper, we present a review of featured works in the field of hydrodynamics with the main aim to clarify the ways of understanding the algorithms for solving the Navier–Stokes equations. Discussing the existing algorithms, approaches and analytical or semi-analytical methods, we especially note that important problems of stability for the exact solutions should be explored accordingly relate to this respect, e.g. exploring the case of non-stationary helical flows of the Navier–Stokes equations for incompressible fluids with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of the flow. Meanwhile, the system of Navier–Stokes equations (including continuity equation) has been successfully explored previously with respect to the existence of analytical way for presentation of non-stationary helical flows of the aforementioned type. Conditions for the stability criteria of the exact solution for such the type of flows are obtained herein in the current research, for which non-stationary helical flow with invariant Bernoulli-function is considered.

This paper reviews recent developments in the understanding of underwater bio-mimetic propulsion. Two impressive models of underwater propulsion are considered: cruise and fast-start. First, we introduce the progression of bio-mimetic propulsion, especially underwater propulsion, where some primary conceptions are touched upon. Second, the understanding of flapping foils, considered as one of the most efficient cruise styles of aquatic animals, is introduced, where the effect of kinematics and the shape and flexibility of foils on generating thrust are elucidated respectively. Fast-start propulsion is always exhibited when predator behaviour occurs, and we provide an explicit introduction of corresponding zoological experiments and numerical simulations. We also provide some predictions about underwater bio-mimetic propulsion.

Obtaining real flow information is important in various fields, but is a difficult issue because measurement data are usually limited in time and space, and computational results usually do not represent the exact state of real flows. Problems inherent in the realization of numerical simulation of real-world flows include the difficulty in representing exact initial and boundary conditions and the difficulty in representing unstable flow characteristics. This article reviews studies dealing with these problems. First, an overview of basic flow measurement methodologies and measurement data interpolation/approximation techniques is presented. Then, studies on methods of integrating numerical simulation and measurement, namely, four-dimensional variational data assimilation (4D-Var), Kalman filters (KFs), state observers, etc are discussed. The first problem is properly solved by these integration methodologies. The second problem can be partially solved with 4D-Var in which only initial and boundary conditions are control parameters. If an appropriate control parameter capable of modifying the dynamical structure of the model is included in the formulation of 4D-Var, unstable modes are properly suppressed and the second problem is solved. The state observer and KFs also solve the second problem by modifying mathematical models to stabilize the unstable modes of the original dynamical system by applying feedback signals. These integration methodologies are now applied in simulation of real-world flows in a wide variety of research fields. Examples are presented for basic fluid dynamics and applications in meteorology, aerospace, medicine, etc.

The extensive evaluation studies of the lattice Boltzmann method for micro-scale flows (μ-flow LBM) by the author's group are summarized. For the two-dimensional test cases, force-driven Poiseuille flows, Couette flows, a combined nanochannel flow, and flows in a nanochannel with a square- or triangular cylinder are discussed. The three-dimensional (3D) test cases are nano-mesh flows and a flow between 3D bumpy walls. The reference data for the complex test flow geometries are from the molecular dynamics simulations of the Lennard-Jones fluid by the author's group. The focused flows are mainly in the slip and a part of the transitional flow regimes at Kn < 1. The evaluated schemes of the μ-flow LBMs are the lattice Bhatnagar–Gross–Krook and the multiple-relaxation time LBMs with several boundary conditions and discrete velocity models. The effects of the discrete velocity models, the wall boundary conditions, the near-wall correction models of the molecular mean free path and the regularization process are discussed to confirm the applicability and the limitations of the μ-flow LBMs for complex flow geometries.

We analyze a 1 + 1-dimensional directed percolation system as a model for the spatio-temporal aspects of the turbulence transition in pipe flow and other shear flows. Space and time are discrete, and the model is characterized by two parameters: one describes the probability to remain turbulent in the next step and the other characterizes the spreading of turbulence to the neighboring cells. The transition to a persistent turbulence is evident in mean field arguments, but the actual critical values and exponents are considerably renormalized by fluctuations. Extensive numerical tests show that the model falls into the universality class of one-dimensional (1D) directed percolation. We also discuss the spreading of localized perturbations and an extension to 2D systems.

The study aims to enhance the aerodynamic performance of a NACA0012 profile by utilizing backward-facing steps inclined forward, inspired by shark denticles known for delaying boundary layer separation. The turbulent and steady-in-the-mean flow around the airfoil fitted with inclined backward-facing steps (IBFSs) is numerically investigated via Ansys Fluent. In this work, the effects of characteristic geometrical parameters of the IBFSs like the step height, the inclination angle and the layout of the steps along the airfoil suction surface on the lift and drag coefficients are brought to light. The results demonstrate a notable enhancement in aerodynamic finesse, showing an improvement of up to 4.53% compared to the standard NACA0012. This improvement is affected by the different geometrical parameters tested. Specifically, fitting IBFSs on 80% of the suction surface and decreasing the steps height and inclination angle contributed to increased performance. The impact of IBFSs is more noticeable at high angles of attack (AOA), where lift is significantly influenced compared to drag, while the opposite occurs at low AOA. These findings highlight the potential of the use of IBFSs for optimizing aerodynamic efficiency, particularly in scenarios characterized by high AOA.

Ultrasonic pretreatment and synchronous ultrasonic flotation can strengthen the bubble mineralization process and improve the separation of fine minerals, but the effect of ultrasonic on the flotation bubble dynamics is unclear. In this paper, the ultrasonic probe was embedded in the flotation column as ultrasonic field source, and a numerical model based on this test bed was constructed with the CFD method. Based on this, the bubble movement behavior under different ultrasonic fields was studied, combined with the analysis of internal flow field velocity and pressure, the mechanism of ultrasonic action on the dynamic behavior of bubbles was revealed. The results showed that the ultrasound field changed the velocity inside the flow field, significantly increasing the bubble's instantaneous displacement velocity at the turning point. Ultrasound changes the pressure field distribution, resulting in an alternating high and low-pressure distribution with uneven pressure gradients. Ultrasound ultimately causes bubbles to exhibit curved bubble motion trajectories and distributions, prolonging their motion trajectories and accompanying subtle bubble coalescence phenomena. These are beneficial for improving the contact probability between flotation bubbles and mineral particles.

D'Alembert's paradox is the contradictory observation that for incompressible and inviscid (potential) fluid flow, there is no drag force experienced by a body moving with constant velocity relative to the fluid. This paradox can be straightforwardly resolved by considering Navier's slip boundary condition. Potential flow around a cylinder then solves the Navier–Stokes equations using friction parameter $\beta = -2\nu$. This negative friction parameter can be interpreted physically as the fluid being accelerated by the cylinder wall. This explains the lack of drag. In this paper, we introduce the Navier slip boundary condition and show that choosing the friction parameter positive resolves d'Alembert's paradox. We then further examine the effect of the friction parameter β on the drag coefficient. In particular, we show that for large β the drag coefficient corresponds well with experimental values.

This work provides a multiscale model for accurate descriptions of the heat and mass transport during single microdroplet evaporation and single pulse spray cooling on a heated semi-infinite solid. The temperature drop from a high-pressure spray pulse is captured through thermocouples and an infrared camera for initial substrate temperatures ranging from negative to positive superheats. A representative average diameter is estimated using high-speed cameras and the droplet size distribution statistics. The model can correctly predict the wall heat flux and evaporation rates from room temperature to positive superheats up to 10 K. At superheats beyond 20 K the model breaks down due to presumably boiling and microlayer evaporation effects. The results highlight the validity of coupling lubrication theory with kinetically-limited and diffusion-limited evaporation over a wide range of temperatures, using the vapor temperature and vapor pressure as the key mediating properties for bridging the molecular-scale forces with continuum-scale thermal physics.

A semi-analytical study of coupled translation and rotation of a composite spherical particle (a hard sphere core coated with a permeable porous layer) in a viscous fluid inside an eccentric spherical cavity normal to their common diameter is presented in the quasi-steady limit of low Reynolds number. To solve the Stokes and Brinkman equations for the flow fields outside and inside the porous layer, respectively, a general solution is constructed from the fundamental solutions in the two spherical coordinate systems based on both the composite particle and the cavity. The boundary conditions at the cavity wall and inner and outer surfaces of the porous layer are satisfied by a collocation method. Numerical results for the force and torque exerted on the particle by the fluid are obtained with good convergence for various values of the relevant parameters in practical applications. For the translation and rotation of a composite sphere inside a concentric cavity, our force and torque results agree well with the available solutions in the literature. The force and torque on a translating and rotating particle increase monotonically with increases in the ratios of particle radius to porous layer permeation length, core-to-particle radii, and particle-to-cavity radii. In general, they also increase with an increase in the relative distance between the particle and cavity centers. The boundary effect of the cavity on the translation of the particle is much more pronounced than that on the rotation. The coupling effect in the simultaneous translation and rotation inside an eccentric spherical cavity is complicated and not a monotonic function of the particle-to-cavity radius ratio.

We derive the incompressible Navier–Stokes equations from the lattice Boltzmann equation using the Chapman–Enskog expansion and the Sone expansion and clarify the differences between the two approaches. In the Chapman–Enskog expansion, we first derive the compressible Navier–Stokes equations on the multiple time scales (the acoustic and diffusive time scales). Then the incompressible Navier–Stokes equations are derived under the conditions of low Mach number flows and small density variations on the diffusive time scale. If the acoustic time scale remains in the analysis of the derived macroscopic equations, the incompressible Navier–Stokes equations are recovered with only the first-order spatial accuracy. On the other hand, in the Sone expansion we can derive the incompressible Navier–Stokes equations under the condition of low Mach number flows on the diffusive time scale. Despite some differences between the two approaches, we obtain the same result that the flow velocity and the pressure satisfy the incompressible Navier–Stokes equations with the second-order spatial accuracy in low Mach number flows on the diffusive time scale. The accuracy is verified through simulating a generalized Taylor–Green problem.

This paper explores the potential of a streamlined adaptive finite point method (FPM) in tackling two-dimensional coupled Burgers' equations, employing them as a testbed for further advancements. Firstly the coupled system is transformed into a two-dimensional heat equation through Cole–Hopf transformation and then this transformed equation is split into one-dimensional heat equations at intermediate temporal levels along X and Y directions and these one-dimensional equations are finally to be treated with the adaptive FPM. The distinctive feature of the adaptive FPM used here lies in employing an implicit 4-point stencil within each local cell to compute the solution at a higher temporal level through a linear combination of solutions from the preceding temporal level. The coefficients involved in this linear combination are derived via the local fundamental solutions within that cell, thereby imbuing the formulations with the intrinsic essence of the exact solution. Moreover, the separation constant utilized is tailored to consistently integrate the influence of the initial solution, independent of the temporal level. The method's theoretical underpinnings ensure its conditionally stable, consistent, and convergent behavior. The accuracy of the scheme is substantiated by its proficient handling of diverse examples, attesting to its superior cost-effectiveness and time efficiency.

Understanding the thermal conditions inside a burning cigarette is a top priority for controlling chemical emissions and cigarette design. Since experimental methods are difficult to observe in depth, this paper starts from the perspective of numerical simulation and models the structure of the tobacco distribution of the cigarette, integrating the end surface ignition model, puffing model, chemical reaction model, heat and mass transfer and diffusion model have established a three-dimensional comprehensive model that can represent the changes in combustion cone morphology during cigarette combustion. The model covers chemical reaction and mass transfer as well as generation, flow and reaction mechanism. The simulation results show that the model can better predict the temperature distribution, component distribution and combustion cone morphology changes during cigarette smoking and combustion. It provides an effective means for in-depth research on cigarette combustion.

Thin liquid film flowing down the inner concave surface of a vertical cylindrical vessel is examined. At the top of the vessel, the water is injected horizontally at high speed circumferentially along the vessel wall and flows downwards due to the action of gravity. This turbulent film flow is modeled using the large eddy simulation (LES) and Reynolds averaged Navier–Stokes (RANS) approaches combined with the volume-of-fluid method. The results of both methods are validated with direct numerical simulation. The Favre-filtered two-phase LES, which is implemented and studied in this paper, can reasonably predict the film thickness similarly to that of the RANS approach using the elliptic blending Reynolds stress model, although it requires fine resolution in the wall region. The effect of volume flow rate on the film structure and thickness is investigated. The film thickness is shown to be nearly constant when the wall is partially wetted and changes as the cubic root of the volume flow rate when the spinning film encloses the entire circumference of the vessel.

Using methods of granular mechanics in the quasi-static limit, with inter-particle interactions derived from the lubrication limit, the intensity of velocity fluctuations in the slurry is associated with fluctuations in the local distribution of inter-particle distances. These are shown to consist of a vector intensity and a scalar intensity; the former couples to the first velocity gradient, the latter (which is associated with solidosity fluctuations) couples to the second velocity gradient. Rheologies for both are presented, as is the rheology that links the particle pressure to the intensity of the velocity fluctuations (also known as the 'granular temperature') to the dispersive pressure. The rheologies are informed by experimental results. The granular temperature profile, modified from previous work, is responsible for axial particle migration (Bagnold effect). Two broad categories are assessed: symmetrical vertical and non-symmetrical lateral flow. For the latter the roughness of the boundary walls and a non-zero density contrast are important; this case is studied for a system in which flow effects are confined to the immediate vicinity of the boundary. Sensitivity analysis reveals several key variables including the parameters that control a slipping boundary condition and the mean solidosity in the conduit. For lateral flow, a sedimentary deposit with a solidosity profile may develop near the upper or lower boundary. The theory predicts an approximate relation between the fluid-particle density contrast and sediment thickness as a function of the mean flow rate, conduit width, the mean particle diameter and fluid viscosity that has utility in a range of engineering and geological situations where particulate matter is transported in the laminar flow regime.

Jets and wakes are fundamental fluid flows that arise in a wide range of environmental and aerospace applications. They are typically studied as open systems. Here we are interested in the implications of placing the jet or wake inside of another system, as well as the implications of compliant walls. In particular, the effect of asymmetry is considered on the absolute instability properties for this internal flow, when it is transversely confined by compliant walls. Two distinct cases are considered, namely the case of two compliant walls with non-identical wall parameters and the case of identical compliant walls asymmetrically located about the fluid center line. The absolute instability characteristics are identified by following special saddle points (pinch points) of the dispersion relation in the complex wavenumber plane, and the flow's stability properties are mapped out using parameter continuation techniques. The compliant walls introduce new modes which typically dominate the stability properties of the flow, in comparison to the case of pure shear layers. In the case of symmetrically located walls with non-identical wall parameters, it was found that the absolute stability properties are dominated by the modes linked to the more flexible of the two walls. In the case of identical walls asymmetrically confining the flow, it was found that these flows exhibit smaller regions of absolute instability in parameter space, when compared to the symmetric flow configuration.

Analysis methods based on mode decomposition have been proposed to describe the characteristics of flow phenomena. Among them, proper orthogonal decomposition (POD), which decomposes modes into eigenvalues and basis vectors, has long been used. Many studies have shown that POD is a useful method for capturing the characteristics of unsteady flow. In particular, Snapshot POD has attracted much recent attention and has been used to solve unsteady flow problems. However, the basis vectors of the mode obtained by conventional POD is different for each condition. Therefore, whether the basis vectors of each mode are switching in the direction of parameters (e.g. different shapes or different Reynolds numbers) or whether they develop or decay is difficult to discuss. As a result, discussions on conventional POD tend to be qualitative. To address this issue, the present study uses Parametric Global POD, a method that perfectly matches basis vectors in results with different parameters (in this study, different Reynolds numbers). Parametric Global POD method was applied to the analysis of the flow field in a curved pipe and found to capture the development or decay of modes with major basis vectors in the direction of parameters, which is difficult to achieve with conventional POD methods.