Fluid Dynamics Research

The mean wake of a three-dimensional surface-mounted rectangular flat plate was studied experimentally in a low-speed wind tunnel for four different aspect (height-to-width) ratios, AR = 3, 2, 1, and 0.5. The Reynolds number based on the plate width was Re = 3.8 × 10⁴ and the boundary layer thickness on the ground plane, relative to the plate width, was δ/W = 1.1. The incidence angle of the plate was varied from α = 0° (where the plate is normal to the flow) to α = 90° (where the plate is parallel to the flow). The mean velocity and vorticity fields in the wake were measured using a seven-hole pressure probe. At α = 0°, the length of the recirculation zone behind the plate becomes progressively shorter as the aspect ratio is lowered and follows the same tendency as that of a finite square prism. The wakes of the slenderer flat plates of AR = 3 and 2 are characterised by two pairs of streamwise vortices: a pair of tip vortices in the upper wake and a pair of ground-plane vortices on the lower edges of the wake. With increasing incidence angle, a single tip vortex comes to dominate the wake, secondary vorticity is induced at various locations, a 'traffic light' vortex pattern may form, and ultimately a familiar wing-tip (trailing) vortex develops. In contrast, flow downstream of the less slender flat plates of AR = 1 and 0.5 is characterised by a single pair of large streamwise vortices, which become asymmetric with increasing incidence. Close to the flat plate of AR = 0.5, and at small incidence angles only, a unique pair of small inner vorticity concentrations, of opposite sense of rotation to the main streamwise vortices, is found in the upper part of the wake.

We consider the general problem of matching rheological models to experiments. We introduce the concept of identifiability of models from a given set of experiments. To illustrate this in detail, we study two rheology models, the grade-two and Oldroyd 3-parameter models, and consider two hypothetical rheometers to see if the coefficients of the rheology models are identifiable from experimental measurements or not. For the Oldroyd models, we show that the coefficients can be estimated from experiments from the two rheometers. But for the grade-two model, it is not possible to distinguish the two nonNewtonian parameters, only their sum can be estimated, and thus the grade-two model is not identifiable by the two hypothetical rheometers. However, our results imply that a different rheometer may be able to do that.

We investigate the applicability of the data assimilation (DA) to large eddy simulations based on the lattice Boltzmann method (LBM). We carry out the observing system simulation experiment of a two-dimensional (2D) forced isotropic turbulence, and examine the DA accuracy of the nudging and the local ensemble transform Kalman filter (LETKF) with spatially sparse and noisy observation data of flow fields. The advantage of the LETKF is that it does not require computing spatial interpolation and/or an inverse problem between the macroscopic variables (the density and the pressure) and the velocity distribution function of the LBM, while the nudging introduces additional models for them. The numerical experiments with $256\times256$ grids and 10% observation noise in the velocity showed that the root mean square error of the velocity in the LETKF with $8\times 8$ observation points (${\sim} 0.1\%$ of the total grids) and 64 ensemble members becomes smaller than the observation noise, while the nudging requires an order of magnitude larger number of observation points to achieve the same accuracy. Another advantage of the LETKF is that it well keeps the amplitude of the energy spectrum, while only the phase error becomes larger with more sparse observation. We also see that a lack of observation data in the LETKF produces a spurious energy injection in high wavenumber regimes, leading to numerical instability. Such numerical instability is known as the catastrophic filter divergence problem, which can be suppressed by increasing the number of ensemble members. From these results, it was shown that the LETKF enables robust and accurate DA for the 2D LBM with sparse and noisy observation data.

The start-up creeping motion of a porous spherical particle, which models a permeable polymer coil or floc of nanoparticles, in an incompressible Newtonian fluid generated by the sudden application of a body force is investigated for the first time. The transient Stokes and Brinkman equations governing the fluid velocities outside and inside the porous sphere, respectively, are solved by using the Laplace transform. An analytical formula for the transient velocity of the particle as a function of relevant parameters is obtained. As expected, the particle velocity increases over time, and a particle with greater mass density lags behind a corresponding less dense particle in the growth of the particle velocity. In general, the transient velocity is an increasing function of the porosity of the particle. On the other hand, a porous particle with a higher fluid permeability will have a greater transient velocity than the same particle with a lower permeability, but may trail behind the less permeable particle in the percentage growth of the velocity. The acceleration of the porous particle is a monotonic decreasing function of the elapsed time and a monotonic increasing function of its fluid permeability. In particular, the transient behavior of creeping motions of porous particles may be much more important than that of impermeable particles.

This paper assesses the effect of thermal stratification on the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large eddy simulation. The Reynolds number of the cavity flow, was 67 000. Thermal stratification was achieved through the heating or cooling of one or more of the walls within the cavity. When compared to an isothermal (neutral) case, unstable stratification from surface heating generally has a weak influence on the primary recirculating cavity vortex, except in the case where the windward wall is heated. For windward wall heating, a large secondary vortex appears at the corner of the windward wall and cavity floor. Unstable stratification has no significant influence on the removal of pollutant mass from the cavity. Stable stratification through surface cooling drastically alters the flow pattern within the cavity, pushing the cavity vortex towards the upper quadrant of the cavity. As a result, large regions of stagnant fluid are present within the cavity, reducing the effectiveness of the shear layer at removing pollutant concentration from the cavity. Some stable stratification configurations can increase the pollutant mass within the cavity by over a factor of five, when compared to the neutral case. Pollutant concentration flux maps show that, in stably stratified cases, the majority of pollutant transport from the cavity is the result of entrainment into the primary cavity vortex. The results show that pollutant concentrations in urban street canyon-type flows are substantially altered by diurnal heating and cooling, which may influence pedestrian management strategies in urban environments.

The effects of free-stream turbulence intensity and porosity on the drag on cylinders with porous outer layers in cross-flow was investigated experimentally. This work is motivated by the need to better model spotting—a forest fire propagation mechanism in which burning branches and other debris (termed firebrands) are transported away from the main fire by the prevailing wind and ignite new fires. Multiple levels of background turbulence were studied by using no grid, passive grids, and an active grid to generate turbulence intensities of 0.4%, 1.7%, 2.7% and 12.4%. The porous char-layer on the outer surface of firebrands was mimicked by wrapping wire meshes (of 10, 20 and 40 pores per cylinder diameter or PPD) around the cylinders, each to three different layer-thickness fractions (${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{16}}$, ${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{8}}$ and ${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{4}}$) of the cylinder's outer diameter. The drag on one smooth cylinder and nine cylinders with porous outer layers was measured for Reynolds numbers in the range 7000–17 000, at the aforementioned four turbulence intensities. The results showed that (i) the free-stream turbulence intensity and PPD of the wire meshes affect the Reynolds number dependence of the drag coefficient; (ii) the drag coefficient increases with free-stream turbulence intensity when it is relatively low (0.4%–2.7%), then decreases at high intensities (12.4%), and this decrease is more pronounced as the PPD increases; (iii) the drag coefficient increases with the thickness of the porous layer, and asymptotes to an effectively constant value after a critical thickness of about ${\scriptsize\raise2pt\hbox{1}\!/\!\lower.5pt\hbox{8}}$ of the cylinder's diameter; and iv) the drag coefficient exhibits a non-monotonic dependence on the PPD of the wire mesh. These results demonstrate the importance of accounting for free-stream turbulence intensity and the parameters that characterize the porous outer layers of cylinders when modeling the drag on firebrands, or in other applications in which there is cross flow over cylinders with porous outer surfaces.

This work presents a comparison between the PTT-X (extended Phan-Thien and Tanner (PTT)) and the generalised PTT (gPTT) viscoelastic models. The PTT-X model was derived based on a combination of reptation and network theories, allowing in this way a microstructural justification for the kernel function. The gPTT model is based on the network theory, with an empirical kernel function for the rate of destruction of junctions, that proved to be effective fitting experimental rheological data for polymer melts and solutions. A review on the background of both models is provided and the two models are then compared considering simple flows. This comparison allows one to attribute in some way a microstructural nature to the parameters involved in the gPTT model. Also, a new analytical solution is derived for the Poiseuille flow of the PTT-X model.

In this paper, an exact expression for the drag coefficient of a streamwise-periodic steady incompressible laminar channel and pipe flow with micro- or macro-scale wall roughness is derived, whereby the drag coefficient is decomposed into contributions from different components of the velocity gradient tensor in the flow field. It is shown through our theoretical analysis that drag reduction cannot be achieved by adding micro- or macro-scale spanwise-periodic/-symmetry wall roughness structures to the smooth inner walls of streamwise-periodic steady incompressible laminar channel/pipe flows while maintaining the same volumetric flow rate. It is also shown that wall roughness produces a higher drag due to two factors: (a) wall roughness induces other non-zero velocity gradient terms apart from the wall-normal/radial gradient of streamwise velocity that exists in a smooth channel/pipe flow; (b) the profile of streamwise velocity in the wall-normal/radial direction deviates from the parabolic profile that produces the minimum kinetic energy loss for a given volumetric flow rate. Finally, numerical simulations of laminar channel flow with longitudinal and transverse bars are conducted, and the numerical results confirm the theoretical finding.

This paper assesses the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large Eddy simulation (LES). The flow Reynolds number was 67 000, based on the freestream velocity and cavity height. The flow upstream of the cavity was laminar, producing a cavity shear layer which underwent a transition to turbulence over the cavity. Three distinct meshes are used, with grid spacings of $H / 100$ (coarse), $H / 200$ (intermediate), and $H / 400$ (fine) respectively. The Smagorinsky, WALE, and Germano-Lilly subgrid-scale models are used on each grid to quantify the effects of subgrid-scale modelling on the simulated flow. Coarsening the grid led to small changes in the predicted velocity field, and to substantial over-prediction of the tracer gas concentration statistics. Quantitative metric analysis of the tracer gas statistics showed that the coarse grid simulations yielded results outside of acceptable tolerances, while the intermediate and fine grids produced acceptable output. Interrogation of the fluid dynamics present in each simulation showed that the evolution of the cavity shear layer is heavily influenced by the grid and subgrid scale model. On the coarse and intermediate grids the development of the shear layer is delayed, inhibiting the entrainment and mixing of the tracer gas into the shear layer, reducing the removal of the tracer gas from the cavity. On the fine grid, the shear layer developed more rapidly, resulting in enhanced removal of the tracer gas from the cavity. Concentration probability density functions showed that the fine grid simulations accurately predicted the range, and the most probable value, of the tracer gas concentration towards both walls of the cavity. The results presented in this paper show that the WALE and Germano-Lilly models may be advantageous over the standard Smagorinsky model for simulations of pollutant dispersion in the urban environment.

For both real fish and bionic fish, a rigid anterior portion is necessary for certain functions. How does the rigid anterior portion affect the locomotion of the flexible plate? Is it true that the rigid portion is redundant? It is lack of clear cognition on these questions. In this paper, the self-propulsion of the rigid-flexible composite plate is studied numerically. We suppose that the forces are exerted on the junction point to maintain a given pitch motion of the rigid portion, the deformation of the flexible portion is consequent. The ratio between the lengths of the flexible portion and the rigid portion is changed to model the composite plate, and the effect of the stiffness of the flexible plate is investigated. It is found that the propulsive velocity and the Froude efficiency actually decrease following the increasing proportion of the rigid plate. However, the conclusion is different as the elastic energy stored in the flexible plate is considered. We find that the case with larger flexible portion is efficient for the ultra-soft posterior plate, while the case with smaller flexible portion is efficient for the stiff posterior plate. It happens to coincide with the swimming behavior of live fish. The hydrodynamic force at the tail is hindering the propulsion of the plate, which means that the motion of the tail plays a decisive role on the force distribution on the plate, rather than the thrust only produced at the tail. We think that the short ultra-soft membrane at the tail of the real fish is an important feature to improve its swimming behavior. It is expected that the study in this paper will give a further insight into the mechanism of the locomotion of fish and give some implications for the design of the soft bionic fish.

The effects of free-stream turbulence intensity and porosity on the drag on cylinders with porous outer layers in cross-flow was investigated experimentally. This work is motivated by the need to better model spotting—a forest fire propagation mechanism in which burning branches and other debris (termed firebrands) are transported away from the main fire by the prevailing wind and ignite new fires. Multiple levels of background turbulence were studied by using no grid, passive grids, and an active grid to generate turbulence intensities of 0.4%, 1.7%, 2.7% and 12.4%. The porous char-layer on the outer surface of firebrands was mimicked by wrapping wire meshes (of 10, 20 and 40 pores per cylinder diameter or PPD) around the cylinders, each to three different layer-thickness fractions (${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{16}}$, ${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{8}}$ and ${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{4}}$) of the cylinder's outer diameter. The drag on one smooth cylinder and nine cylinders with porous outer layers was measured for Reynolds numbers in the range 7000–17 000, at the aforementioned four turbulence intensities. The results showed that (i) the free-stream turbulence intensity and PPD of the wire meshes affect the Reynolds number dependence of the drag coefficient; (ii) the drag coefficient increases with free-stream turbulence intensity when it is relatively low (0.4%–2.7%), then decreases at high intensities (12.4%), and this decrease is more pronounced as the PPD increases; (iii) the drag coefficient increases with the thickness of the porous layer, and asymptotes to an effectively constant value after a critical thickness of about ${\scriptsize\raise2pt\hbox{1}\!/\!\lower.5pt\hbox{8}}$ of the cylinder's diameter; and iv) the drag coefficient exhibits a non-monotonic dependence on the PPD of the wire mesh. These results demonstrate the importance of accounting for free-stream turbulence intensity and the parameters that characterize the porous outer layers of cylinders when modeling the drag on firebrands, or in other applications in which there is cross flow over cylinders with porous outer surfaces.

It is of certain importance for noise reduction to investigate the relationship between the aeroacoustic characteristics of blade and root boundary conditions when considering the fluid-structure interaction (FSI) effect. In this study, a set of precise dynamic models and two-way FSI calculation methods are developed to predict the dynamic load and response of blades more accurately. The natural frequency inaccuracy of the blade model is kept within 5% by comparing the results of the modal test using the ploy-reference time domain method and adopting the sensitivity analysis method with the blade beam stiffness as the modification parameter. Besides, based on the numerical results from the computational fluid dynamics method considering the FSI effect, the aeroacoustic characteristics of blades with different root boundary conditions are analyzed by adopting the Ffowcs Williams-Hawkings equations. The aeroacoustic characteristics of the NACA blade in hover are thoroughly discussed, with emphasis on the impact of different root boundary conditions on rotation noise. The result demonstrates that, the sound pressure level (SPL) difference of loading noise can reach 1.4 dB between blades with various root boundary conditions, while the SPL difference of thickness is only 0.4 dB.

Turbulent boundary layer (TBL) flows over various spanwise-heterogeneous rough walls exhibit spanwise variations in turbulence statistics, implying modifications of the turbulent/non-turbulent interface (T/NTI). In this work, based on the datasets of TBL flows over a spanwise-alternating converging/diverging riblets wall, we investigate behavior of T/NTI, properties of 'bubble' and 'drop' that are associated with T/NTI, as well as connections between T/NTI and large-scale structures within the boundary layer. The flow datasets were obtained through stereoscopic particle image velocimetry measurements on the cross-stream plane of the TBL flow at a Reynolds number $R{e_\theta }$ = 1.3 × 10⁴. The T/NTI and associated 'bubble' and 'drop' are identified using a kinetic energy criterion, while the large-scale structures by a streak detection algorithm. It is observed that the T/NTI height and the occurrence of 'bubble' and 'drop' display a spanwise-heterogeneous feature, with lower T/NTI height and higher occurrence probability of 'bubble' over the diverging section of riblets than over the converging section of riblets. Results of conditional average show that the 'bubble' is associated with positive streamwise fluctuations, common-down flow and a pair of counter-rotating streamwise vortices, while the 'drop' with negative streamwise fluctuation, common-up flow and a pair of counter-rotating streamwise vortices. Probability density functions of the 'bubble' size and fractal dimensions of the T/NTI are found similar for both the riblets and smooth wall flows. Furthermore, it is observed that the large-scale low-speed structures occurring preferentially over the converging section of riblets play a role in elevating T/NTI while the large-scale high-speed ones over the diverging section of riblets lowering down T/NTI.

The response of two incompressible and immiscible liquids of comparable densities at different depth ratios in a rectangular container subject to parametric sinusoidal forcing, similar to Faraday waves, has been considered in the present study. The effect of various depth ratios on the instability threshold and the flow field are investigated for (0, 2) and (0, 4) modes. Numerical simulation has been performed using OpenFOAM to solve Navier-Stokes equations. A source term is added in the interFoam module of OpenFOAM to take the effect of the oscillating container without using any dynamic mesh function. The threshold amplitude and wavenumbers are validated following the linear Floquet analysis of Kumar and Tuckerman (1994 J. Fluid Mech.279 49–68). The Floquet analysis showed a substantial shift in natural frequency (reduction) and an increase in threshold amplitude when the interface is in close proximity to the wall. The response amplitude follows a square law with the forcing amplitude for all the depth ratios considered in the present study. The wave amplitude response above the threshold curve is found to be an exponential function of liquid depths and forcing parameters.

Through a series of experiments in a wind tunnel, we study the near-surface profiles of the mean streamwise velocity in thermally stratified boundary layers. The surface is horizontal and is smooth or roughened by rods. We heat or chill this surface to achieve that stratification. Temperature-compensated hot-film anemometry is used to measure the mean streamwise velocity. Within the transition sublayer, lying in between the surface and the constant-flux sublayer, we find that the velocity profile is always a power-law function of the height from the surface. Its exponent ranges from 0.01 to 0.2 and increases with the surface roughness and the surface temperature. We summarize these findings in a formula and discuss its applications to the atmospheric boundary layer via the so-called Reynolds number similarity.

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 effects of free-stream turbulence intensity and porosity on the drag on cylinders with porous outer layers in cross-flow was investigated experimentally. This work is motivated by the need to better model spotting—a forest fire propagation mechanism in which burning branches and other debris (termed firebrands) are transported away from the main fire by the prevailing wind and ignite new fires. Multiple levels of background turbulence were studied by using no grid, passive grids, and an active grid to generate turbulence intensities of 0.4%, 1.7%, 2.7% and 12.4%. The porous char-layer on the outer surface of firebrands was mimicked by wrapping wire meshes (of 10, 20 and 40 pores per cylinder diameter or PPD) around the cylinders, each to three different layer-thickness fractions (${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{16}}$, ${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{8}}$ and ${\scriptsize \raise2pt\hbox{1}\!/\!\lower.5pt\hbox{4}}$) of the cylinder's outer diameter. The drag on one smooth cylinder and nine cylinders with porous outer layers was measured for Reynolds numbers in the range 7000–17 000, at the aforementioned four turbulence intensities. The results showed that (i) the free-stream turbulence intensity and PPD of the wire meshes affect the Reynolds number dependence of the drag coefficient; (ii) the drag coefficient increases with free-stream turbulence intensity when it is relatively low (0.4%–2.7%), then decreases at high intensities (12.4%), and this decrease is more pronounced as the PPD increases; (iii) the drag coefficient increases with the thickness of the porous layer, and asymptotes to an effectively constant value after a critical thickness of about ${\scriptsize\raise2pt\hbox{1}\!/\!\lower.5pt\hbox{8}}$ of the cylinder's diameter; and iv) the drag coefficient exhibits a non-monotonic dependence on the PPD of the wire mesh. These results demonstrate the importance of accounting for free-stream turbulence intensity and the parameters that characterize the porous outer layers of cylinders when modeling the drag on firebrands, or in other applications in which there is cross flow over cylinders with porous outer surfaces.

The start-up creeping motion of a porous spherical particle, which models a permeable polymer coil or floc of nanoparticles, in an incompressible Newtonian fluid generated by the sudden application of a body force is investigated for the first time. The transient Stokes and Brinkman equations governing the fluid velocities outside and inside the porous sphere, respectively, are solved by using the Laplace transform. An analytical formula for the transient velocity of the particle as a function of relevant parameters is obtained. As expected, the particle velocity increases over time, and a particle with greater mass density lags behind a corresponding less dense particle in the growth of the particle velocity. In general, the transient velocity is an increasing function of the porosity of the particle. On the other hand, a porous particle with a higher fluid permeability will have a greater transient velocity than the same particle with a lower permeability, but may trail behind the less permeable particle in the percentage growth of the velocity. The acceleration of the porous particle is a monotonic decreasing function of the elapsed time and a monotonic increasing function of its fluid permeability. In particular, the transient behavior of creeping motions of porous particles may be much more important than that of impermeable particles.

We investigate the applicability of the data assimilation (DA) to large eddy simulations based on the lattice Boltzmann method (LBM). We carry out the observing system simulation experiment of a two-dimensional (2D) forced isotropic turbulence, and examine the DA accuracy of the nudging and the local ensemble transform Kalman filter (LETKF) with spatially sparse and noisy observation data of flow fields. The advantage of the LETKF is that it does not require computing spatial interpolation and/or an inverse problem between the macroscopic variables (the density and the pressure) and the velocity distribution function of the LBM, while the nudging introduces additional models for them. The numerical experiments with $256\times256$ grids and 10% observation noise in the velocity showed that the root mean square error of the velocity in the LETKF with $8\times 8$ observation points (${\sim} 0.1\%$ of the total grids) and 64 ensemble members becomes smaller than the observation noise, while the nudging requires an order of magnitude larger number of observation points to achieve the same accuracy. Another advantage of the LETKF is that it well keeps the amplitude of the energy spectrum, while only the phase error becomes larger with more sparse observation. We also see that a lack of observation data in the LETKF produces a spurious energy injection in high wavenumber regimes, leading to numerical instability. Such numerical instability is known as the catastrophic filter divergence problem, which can be suppressed by increasing the number of ensemble members. From these results, it was shown that the LETKF enables robust and accurate DA for the 2D LBM with sparse and noisy observation data.

This paper assesses the effect of thermal stratification on the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large eddy simulation. The Reynolds number of the cavity flow, was 67 000. Thermal stratification was achieved through the heating or cooling of one or more of the walls within the cavity. When compared to an isothermal (neutral) case, unstable stratification from surface heating generally has a weak influence on the primary recirculating cavity vortex, except in the case where the windward wall is heated. For windward wall heating, a large secondary vortex appears at the corner of the windward wall and cavity floor. Unstable stratification has no significant influence on the removal of pollutant mass from the cavity. Stable stratification through surface cooling drastically alters the flow pattern within the cavity, pushing the cavity vortex towards the upper quadrant of the cavity. As a result, large regions of stagnant fluid are present within the cavity, reducing the effectiveness of the shear layer at removing pollutant concentration from the cavity. Some stable stratification configurations can increase the pollutant mass within the cavity by over a factor of five, when compared to the neutral case. Pollutant concentration flux maps show that, in stably stratified cases, the majority of pollutant transport from the cavity is the result of entrainment into the primary cavity vortex. The results show that pollutant concentrations in urban street canyon-type flows are substantially altered by diurnal heating and cooling, which may influence pedestrian management strategies in urban environments.

This work presents a comparison between the PTT-X (extended Phan-Thien and Tanner (PTT)) and the generalised PTT (gPTT) viscoelastic models. The PTT-X model was derived based on a combination of reptation and network theories, allowing in this way a microstructural justification for the kernel function. The gPTT model is based on the network theory, with an empirical kernel function for the rate of destruction of junctions, that proved to be effective fitting experimental rheological data for polymer melts and solutions. A review on the background of both models is provided and the two models are then compared considering simple flows. This comparison allows one to attribute in some way a microstructural nature to the parameters involved in the gPTT model. Also, a new analytical solution is derived for the Poiseuille flow of the PTT-X model.

We consider the general problem of matching rheological models to experiments. We introduce the concept of identifiability of models from a given set of experiments. To illustrate this in detail, we study two rheology models, the grade-two and Oldroyd 3-parameter models, and consider two hypothetical rheometers to see if the coefficients of the rheology models are identifiable from experimental measurements or not. For the Oldroyd models, we show that the coefficients can be estimated from experiments from the two rheometers. But for the grade-two model, it is not possible to distinguish the two nonNewtonian parameters, only their sum can be estimated, and thus the grade-two model is not identifiable by the two hypothetical rheometers. However, our results imply that a different rheometer may be able to do that.

The mean wake of a three-dimensional surface-mounted rectangular flat plate was studied experimentally in a low-speed wind tunnel for four different aspect (height-to-width) ratios, AR = 3, 2, 1, and 0.5. The Reynolds number based on the plate width was Re = 3.8 × 10⁴ and the boundary layer thickness on the ground plane, relative to the plate width, was δ/W = 1.1. The incidence angle of the plate was varied from α = 0° (where the plate is normal to the flow) to α = 90° (where the plate is parallel to the flow). The mean velocity and vorticity fields in the wake were measured using a seven-hole pressure probe. At α = 0°, the length of the recirculation zone behind the plate becomes progressively shorter as the aspect ratio is lowered and follows the same tendency as that of a finite square prism. The wakes of the slenderer flat plates of AR = 3 and 2 are characterised by two pairs of streamwise vortices: a pair of tip vortices in the upper wake and a pair of ground-plane vortices on the lower edges of the wake. With increasing incidence angle, a single tip vortex comes to dominate the wake, secondary vorticity is induced at various locations, a 'traffic light' vortex pattern may form, and ultimately a familiar wing-tip (trailing) vortex develops. In contrast, flow downstream of the less slender flat plates of AR = 1 and 0.5 is characterised by a single pair of large streamwise vortices, which become asymmetric with increasing incidence. Close to the flat plate of AR = 0.5, and at small incidence angles only, a unique pair of small inner vorticity concentrations, of opposite sense of rotation to the main streamwise vortices, is found in the upper part of the wake.

In this paper, an exact expression for the drag coefficient of a streamwise-periodic steady incompressible laminar channel and pipe flow with micro- or macro-scale wall roughness is derived, whereby the drag coefficient is decomposed into contributions from different components of the velocity gradient tensor in the flow field. It is shown through our theoretical analysis that drag reduction cannot be achieved by adding micro- or macro-scale spanwise-periodic/-symmetry wall roughness structures to the smooth inner walls of streamwise-periodic steady incompressible laminar channel/pipe flows while maintaining the same volumetric flow rate. It is also shown that wall roughness produces a higher drag due to two factors: (a) wall roughness induces other non-zero velocity gradient terms apart from the wall-normal/radial gradient of streamwise velocity that exists in a smooth channel/pipe flow; (b) the profile of streamwise velocity in the wall-normal/radial direction deviates from the parabolic profile that produces the minimum kinetic energy loss for a given volumetric flow rate. Finally, numerical simulations of laminar channel flow with longitudinal and transverse bars are conducted, and the numerical results confirm the theoretical finding.

This paper presents an investigation of the stability of a vortex with azimuthal velocity profile $\bar{V} = \left[1 - \left(1 - \varepsilon r^2 \right) e^{- r^2}\right]/r$. When ε = 0, the Lamb–Oseen vortex model is recovered. Although the Lamb–Oseen vortex supports propagating waves known as Kelvin waves, the flow is stable according to Rayleigh's circulation criterion. In this paper, on the other hand, the modified vortex profile admits linearly unstable disturbances for ε > 0 and we investigate their characteristics. These may be either axisymmetric or non-axisymmetric, but we find that the axisymmetric perturbations have the largest growth rates. When their growth rates are small, it becomes very difficult to solve the linear equation governing the axisymmetric perturbations because the eigenfunctions have a rapid exponential growth as one moves outward radially from the vortex center. To deal with such cases, a modified Riccati transformation was employed and found to be effective in solving the associated eigenvalue problem.

This paper assesses the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large Eddy simulation (LES). The flow Reynolds number was 67 000, based on the freestream velocity and cavity height. The flow upstream of the cavity was laminar, producing a cavity shear layer which underwent a transition to turbulence over the cavity. Three distinct meshes are used, with grid spacings of $H / 100$ (coarse), $H / 200$ (intermediate), and $H / 400$ (fine) respectively. The Smagorinsky, WALE, and Germano-Lilly subgrid-scale models are used on each grid to quantify the effects of subgrid-scale modelling on the simulated flow. Coarsening the grid led to small changes in the predicted velocity field, and to substantial over-prediction of the tracer gas concentration statistics. Quantitative metric analysis of the tracer gas statistics showed that the coarse grid simulations yielded results outside of acceptable tolerances, while the intermediate and fine grids produced acceptable output. Interrogation of the fluid dynamics present in each simulation showed that the evolution of the cavity shear layer is heavily influenced by the grid and subgrid scale model. On the coarse and intermediate grids the development of the shear layer is delayed, inhibiting the entrainment and mixing of the tracer gas into the shear layer, reducing the removal of the tracer gas from the cavity. On the fine grid, the shear layer developed more rapidly, resulting in enhanced removal of the tracer gas from the cavity. Concentration probability density functions showed that the fine grid simulations accurately predicted the range, and the most probable value, of the tracer gas concentration towards both walls of the cavity. The results presented in this paper show that the WALE and Germano-Lilly models may be advantageous over the standard Smagorinsky model for simulations of pollutant dispersion in the urban environment.