Solid Wall Research Articles

Diffusion-weighted imaging-based radiomics model using automatic machine learning to differentiate cerebral cystic metastases from brain abscesses

ObjectivesTo develop a radiomics model based on diffusion-weighted imaging (DWI) utilizing automated machine learning method to differentiate cerebral cystic metastases from brain abscesses.Materials and methodsA total of 186 patients with cerebral cystic metastases (n = 98) and brain abscesses (n = 88) from two clinical institutions were retrospectively included. The datasets (129 from institution A) were randomly portioned into separate 75% training and 25% internal testing sets. Radiomics features were extracted from DWI images using two subregions of the lesion (cystic core and solid wall). A thorough image preprocessing method was applied to DWI images to ensure the robustness of radiomics features before feature extraction. Then the Tree-based Pipeline Optimization Tool (TPOT) was utilized to search for the best optimized machine learning pipeline, using a fivefold cross-validation in the training set. The external test set (57 from institution B) was used to evaluate the model’s performance.ResultsSeven distinct TPOT models were optimized to distinguish between cerebral cystic metastases and abscesses either based on different features combination or using wavelet transform. The optimal model demonstrated an AUC of 1.00, an accuracy of 0.97, sensitivity of 1.00, and specificity of 0.93 in the internal test set, based on the combination of cystic core and solid wall radiomics signature using wavelet transform. In the external test set, this model reached 1.00 AUC, 0.96 accuracy, 1.00 sensitivity, and 0.93 specificity.ConclusionThe DWI-based radiomics model established by TPOT exhibits a promising predictive capacity in distinguishing cerebral cystic metastases from abscesses.

Enhancing the sub-micrometer performance of a uniflow cyclone separator using a built-in stainless steel mesh filter

Although the uniflow cyclone separator has low pressure drop and high collection efficiency compared to other existing cyclone separators, it still has room to improve its collection efficiency of submicron particles. For this reason, we present a new uniflow cyclone separator with an installed mesh filter called the MFUC. The MFUC cyclone body is not made of a solid wall but a stainless steel mesh with porosity. Our research newly revealed that the pressure gradient in the radial direction at the front region of the mesh filter is reversed in the rear region, which can help to remove sub-micrometer particles which are difficult to collect using a basic cyclone separator. The measured MFUC performance showed the synergetic effect of filtration and inertial separation for the removal of fine particles. As the inlet flow rate increases, the inertial separation becomes more effective than filtration. In addition, the cut-off diameter of the MFUC was 0.83 μm at 500 lpm, which is 56.6 % smaller than that of the basic cyclone separator.

Shock wave induced by the collapse of a bubble cluster with each bubble distributed randomly

The phenomenon of bubble collapse is ubiquitous in both natural and industrial settings, often manifesting in the form of bubble clusters. Despite its prevalence, there has been limited research on the dynamics of bubble clusters. In order to gain a better understanding of shock wave emission, liquid jet propagation, and the resulting pressure loads during bubble cluster collapse, we have developed a high-fidelity numerical approach aimed at accurately capturing shock waves and phase interfaces. The interface compression technique is introduced into the compressible two-phase model to improve the sharpness of the phase interface. We solve the physical model using the BVD (Boundary Variation Diminishing) principle. Both the 5th order WENO (Weighted Essentially Non-Oscillatory) scheme and the interface capturing function THINC (Tangent of Hyperbola for INterface Capturing) are utilized to reconstruct primary variables at cell boundaries, effectively minimizing numerical dissipation. For further resolution improvement, we implement these numerical methods on the AMR (Adaptive Mesh Refinement) mesh. Our numerical results demonstrate that the distance between the wall and the bubble cluster, as well as the nearest bubble to the wall, significantly influence the wall peak pressure. However, they have a minimal impact on the overall evolution of the bubble cluster and the peak pressure induced in the flow field. Remarkably, the spatial distribution of bubbles and the total number of bubbles play a crucial role in shaping the dynamic behavior of the bubble cluster and the pressure loads exerted both on the solid wall and in the flow field. The crucial findings offer profound insights into a range of applications, including cavitation erosion, underwater explosions, and drug delivery.

Morphological analysis for thermodynamics of cavitation collapse near fractal solid wall

A fractal geometric boundary with natural wall features is introduced into a hybrid lattice-Boltzmann-method (LBM) multiphase model. The physical model of cavitation bubble collapse near the irregular geometric wall is established to study the thermodynamic characteristics of the bubble collapse. Due to the lack of periodicity, symmetry, spatial uniformity and obvious correlation in the LBM simulation of the bubble collapse near the fractal wall, the morphological analysis based on Minkowski functional is introduced into the thermodynamic investigation of cavitation bubble so as to analyze and obtain the effective information. The results show that the Minkowski functional method can employed to study the temperature information in complex physical fields hierarchically and quantitatively. The high/low temperature region of the cavitation flow is explored, and thermal effect between irregular and fractal geometric wall and cavitation bubble can be revealed. It illustrates that LBM and morphological analysis complement each other, and morphological analysis can also be used as an optional and potential tool in research field of complex multiphase flows.

Molecular dynamics investigation of the effect of nanostructured surfaces on flow boiling

As a prominent limiting factor in the performance of microelectronic devices, the improvement of heat dissipation is of utmost importance. The enhancement of heat and mass transfer during boiling by nanostructured surfaces has been demonstrated in many studies. In this study, a nanoscale flow-boiling model is developed by molecular dynamics method in order to deeply investigate the microscopic mechanism of nanostructure-enhanced heat transfer. Simple liquid argon is heated by grooved substrate to explore the effect of the depth of the cavities on the boiling heat transfer. The results indicate that the grooved surface improves heat transfer performance through two key mechanisms. Firstly, it induces bubble nucleation, and secondly, it delays the onset of film boiling. The presence of cavities allows the argon atoms within to absorb additional energy from the surrounding walls and be in closer proximity to the heating layer. This reduction in solid thermal resistance results in increased heat transfer efficiency, leading to earlier bubble nucleation and a greater propensity for nucleation within the cavities. The low horizontal velocity of argon atoms within the cavities suggests their ability to retain a significant number of atoms, thereby effectively mitigating the deterioration of heat transfer caused by the formation of a vapor film on the solid wall. The comprehensive performance is observed to improve with increasing depth of the cavities within the range investigated in this study.

Analysis of Thermomechanical Stress of High-Temperature Ignition Surface Caused by Drop–Wall Interaction at Engine Conditions

Abstract Drop–wall interaction is a complex phenomenon encountered in diverse industrial applications. An important example is fuel droplets impinging on a high-temperature ignition plug in a direct-injection compression-ignition engine. The ignition plug, comprised of heat-resistant materials, will experience thermal shock due to abrupt temperature changes. The ensuing temperature fluctuation in the solid wall induces thermal stress, and if this stress surpasses the material's strength in that mode, failure can occur. Therefore, it is imperative to analyze the temperature dynamics on the high-temperature surface to enhance material durability. This study focuses on drop–wall interactions in the engine environment. Utilizing the Smoothed Particle Hydrodynamics (SPH) method, this research simulates fuel droplet impingement on an ignition plug with various materials to characterize heat transfer, thermal penetration, and temperature distributions in the heated wall. The investigation also delves into the behavior of ceramic material, specifically silicon nitride, assessing its thermomechanical stress and durability based on the stress–number of cycles (S-N) curve. Thermal stress is computed by considering temperature gradients and material properties, while mechanical stress is evaluated based on the bending momentum and momentum flux induced by the spray. A parametric study explores diverse materials such as tungsten carbide, iron, stainless steel, carbon steel, and aluminum. Results indicate that thermal stress outweighs bending and spray-induced stress. Moreover, the analysis reveals that silicon nitride exhibits the lowest thermal stress distribution and superior durability, potentially capable of operating for infinite cycles under engine-relevant conditions.

Impact of gas bubbles on bacterial adhesion on super-hydrophobic aluminum surfaces

Super-hydrophobic surface (SHS), which traps micro/nano-scale gas bubbles on solid walls, has been reported to greatly reduce bacterial adhesion and biofouling. However, it is unclear whether and how the trapped gas bubbles reduce the bacterial adhesion. Here, we examine the role of the trapped gas on the bacterial adhesion by measuring the spatial distributions of attached bacteria on SHS using scanning electron microscopy (SEM). Two SHSs, one with regular micro-grooves, and the other with randomly roughed textures at micro/nano-scales, both created on aluminum substrates, were tested. We found that for a SHS where gas bubbles are trapped between roughness elements, bacteria only attach to the surface areas that are not covered by gas (e.g., top of roughness elements), while the areas covered by gas bubbles - gaps between roughness elements - are free of bacteria. In contrast, for a rough surface with the same texture geometry as that of SHS but no hydrophobic chemistry, bacteria are distributed evenly to the top and gap of roughness elements. Our results suggest that the SHS may reduce biofouling by providing a physical barrier of gas-liquid interface which separates bacteria from the solid walls. Furthermore, we showed that nano-scale roughness on SHS is insufficient to prevent bacterial adhesion. Our results should provide useful guidance for the future engineering design of efficient anti-biofouling materials.

How far can low emission retrofit of terraced housing in Northern Ireland go?

With both global and national targets to reduce greenhouse gas (GHG) emissions the improvement of existing buildings will be key to realising these ambitions. How this can be achieved, and the impact of whole-life emissions from retrofit remains a key question. This paper investigates the potential of retrofit to reduce and limit lifecycle GHG emissions resulting from an existing house, typical of one of the predominant housing typologies in Northern Ireland. Through the use of lifecycle assessment a range of retrofit scenarios are considered for an early 20th century, solid wall, terraced house, to understand the impacts of retrofit on lifecycle emissions. A range of retrofit scenarios were modelled and simulated, considering both embodied and operational emissions over the building’s lifetime, to understand how net emissions can be reduced. The results show that although fabric and some technological measures can reduce emissions by over 60% when applied in isolation, a holistic approach is required to achieve the greatest reductions. Although operation remains the largest single source of emissions, the results also show the importance of taking a holistic approach to the assessment of retrofit with varying lifecycle stages responsible for considerable emissions. It is seen that emissions reductions of up to 99% may be possible when taking a holistic approach to retrofit and its assessment, considering whole-life emissions. This study highlights the potential benefits of retrofit and how it could be effectively applied to the existing housing stock in Northern Ireland creating low-emission or net-zero emission buildings.

An experimental investigation on the ice-breaking phenomenon induced by the spark-generated bubble near a vertical plate

The present work experimentally studied the coupled interaction between the fracture of an ice plate floating on the water surface, induced by the pulsation of a high-pressure bubble, and the associated deformation of a vertically submerged aluminum plate. The dynamic behaviors of bubbles and fractured ice were concurrently recorded using two high-speed cameras, and the plastic deformation of the aluminum plate was measured by an ultra-depth three-dimensional microscope. The results indicated that the jet direction of the collapsed bubble is heavily influenced by the position to generate the bubble due to the competing Bjerknes forces caused by various boundaries. There is also a significant discrepancy in the phenomena of bubble collapse near thin vs thick ice plates, attributed to the sudden alteration in boundary conditions caused by ice fracturing. Three distinct ice-breaking mechanisms, namely, the hogging moment, jet impact, and the secondary shock wave, were identified based on the types of loads, leading to the initial ice fractures. In general, it was observed that the efficiency of ice breaking improved with a decrease in the bubble–ice distance (γf) and an increase in the bubble–plate distance (γm). It was found that the contacting jet from an upwardly collapsed bubble is the most effective in breaking the thickest ice plates for γm>1.9. While the shock wave from a bubble collapsing near solid wall corners could fracture thick ice plates, the aluminum plate risked damage from jet impacts when γm was less than 0.6.

Fluid–structure-interactive elasto- and thermo-hydrodynamics of electrokinetic binary fluid flows in compliant micro-confinements

We explore the intricate two-way fluid structure interaction arising due to the flow of a binary system of immiscible Newtonian fluids, composed of upper electrically conducting and lower electrically insulating fluids, flowing within a compliant microchannel, whose walls behave as linear elastic solids. The transport of the fluids along the domain occurs due to the collective impact of pressure gradient and applied electric field. We solve the closed-form system of equations and obtain semi-analytical expressions for the velocity fields and channel wall deformation from the coupled elasto-hydrodynamic problem. We then delineate the effect of four pivotal parameters: (a) Debye–Hückel parameter κ¯, (b) upper wall slip length, ls¯, (c) viscosity ratio, μr, and (d) elasticity ratio, Nr, on the morphological evolution of the wall deformation characteristics and the spatial distribution of the velocity profile of the fluids. Observations establish a positive co-relationship of wall deformation with fluid pressure, showcasing an increased collapsibility with augmented pressure gradients. Consequently, the channel walls show enhanced deformation with a decrease in κ¯, ls¯, μr and with an increase in Nr. We also demonstrate from our model that by properly tuning the applied pressure gradient and electric field, it is possible to achieve counterflow of the two fluids. We also consider the effect of heat generation in the fluids due to viscous dissipation and Joule heating, which dissipates to the surrounding by the mechanism of conjugate heat transfer. Accordingly, we provide semi-analytical expressions for the temperature profile distribution within the channel, and discuss their variation with three thermo-physical parameters: (a) Biot number of the top wall (Bi1), (b) Peclet number of the top fluid (Pe1), and (c) ratio of the thermal conductivities of the upper conducting fluid to that of the upper solid wall (kr2). We establish from our investigation that with the increase in Pe1 and with the decrease in Bi1 and kr2, the overall system temperature enhances. Finally, in order to design a thermally efficient system, we compute the global entropy generation rate in the system and evaluate optimum values of, Pe1, Bi1, and kr2 for which the system exhibits highest second law efficiency. We expect our findings to contribute toward the development of optimized microfluidic devices fabricated from deformable elastic materials.

Influence of Frictional Stress Models on Simulation Results of High-Pressure Dense-Phase Pneumatic Conveying in Horizontal Pipe

Based on the two-fluid model, a three-zone drag model was developed, and the kinetic theory of granular flows and the Schneiderbauer solids wall boundary model were modified to establish a new three-dimensional (3D) unsteady mathematical model for high-pressure dense-phase pneumatic conveying in horizontal pipe. With this mathematical model, the influence of the three frictional stress models, namely Dartevelle frictional stress model, Srivastava and Sundaresan frictional stress model, and the modified Berzi frictional stress model, on the simulation result was explored. The simulation results showed that the three frictional stress models accurately predicted the pressure drop and its variations with supplementary gas in the horizontal pipe, with relative errors ranging from −4.91% to +7.60%. Moreover, the predicted solids volume fraction distribution in the cross-section of the horizontal pipe using these frictional stress models exhibited good agreement with the electrical capacitance tomography (ECT) images. Notably, the influence of the three frictional stress models on the simulation results was predominantly observed in the transition region and deposited region. In the deposited region, stronger frictional stress resulting in lower solids volume fraction and a higher pressure drop in the horizontal pipe were observed. Among the three frictional stress models, the simulation results with the modified Berzi frictional stress model aligned better with the experimental data. Therefore, the modified Berzi frictional stress model is deemed more suitable for simulating high-pressure dense-phase pneumatic conveying in horizontal pipe.

Conjugate free convection in a non-uniform heating walled enclosure filled by ternary hybrid nanofluid under magnetic field

A study was conducted using numerical simulations to analyse the behaviour of heat transfer in a square enclosure filled with a ternary hybrid nanofluid in the occurrence of a magnetic field. The flow in the enclosure is characterised by steady and laminar conjugate-free convection. The enclosure has a vertical border with a finite thickness, while the other three borders are assumed to be very thin. The investigation aims to analyse the impact of several key factors on the average Nusselt number using the finite element method. These parameters include the volume fraction of ternary hybrid type nanoparticles (ranging from 0 to 0.03), Rayleigh number (varying from 103 to 106), solid wall thickness (changing from 0.1 to 0.3), Hartmann number (varying from 0 to 100), and the ratio of thermal conductivities (ranging from 0.1 to 10). A notable enhancement in heat transfer is found by employing a ternary hybrid nanofluid. This enhancement becomes more significant for small Rayleigh numbers, where heat conduction governs the primary means of heat transfer. Also, at low levels of Ra, the development of energy transfer strength becomes insignificant in the existence of a magnetic field. This magnetic field effect is primarily controlled by high values of Ra, which consequently leads to an enhancement in the strength of energy transmission.

Repair of the Wall Chest Using the Neocote Technique of a Huge Chondrosarcoma

Chondrosarcoma represents the most common malignant bone tumor, its prognosis is quite good provided that the surgical excision is wide because the evolution is loco-regional, metastases are only observed in tumors of high malignancy or during recurrences. A wide excision implies a significant parietal defect, a source of complications, justifying the need for reconstruction. The principle of the neocote technique is to attempt to reconstruct a solid wall, as anatomically as possible. The main advantages of this original technique are respect for the anatomy of the chest and the mobility of the wall, respiratory function is therefore better preserved. We report a case of a patient operated on for a huge rib chondrosarcoma and who benefited from repair using the neocote technique.

Qualitative Properties of the Solution of a Conjugate Problem of Thermal Convection

The joint convection of two viscous heat-conducting liquids in a three-dimensional layer bounded by flat solid walls was studied. The upper wall is thermally insulated, and the lower wall has a non-stationary temperature field. The liquids are immiscible and separated by a flat interface with complex conjugation conditions set on it. The evolution of this system in each liquid was described by the Oberbeck–Boussinesq equations. The solution of the problem was sought for velocities that are linear in two coordinates and temperature fields that are quadratic functions of the same coordinates. Thus, the problem was reduced to a system of 10 nonlinear integro-differential equations. Its conjugate and inverse nature is determined by the four functions of time. Integral redefinition conditions were set to find them. The physical meaning of the integral conditions is the closeness of the flow. The inverse initial-boundary value problem describes convection near the temperature extremum point on the lower solid wall in a two-layer system. For small Marangoni numbers, the problem was approximated linearly (the Marangoni number is analogous to the Reynolds number in the Navier–Stokes equations). Using the obtained a priori estimates, sufficient conditions were identified for the non-stationary solution to become a stationary one over time.

Wetting and Spreading Behavior of Axisymmetric Compound Droplets on Curved Solid Walls Using Conservative Phase Field Lattice Boltzmann Method.

Compound droplets have received increasing attention due to their applications in many several areas, including medicine and materials. Previous works mostly focused on compound droplets on planar surfaces and, as such, the effects of curved walls have not been studied thoroughly. In this paper, the influence of the properties of curved solid wall (including the shape, curvature, and contact angle) on the wetting behavior of compound droplets is explored. The axisymmetric lattice Boltzmann method, based on the conservative phase field formulation for ternary fluids, was used to numerically study the wetting and spreading of a compound droplet of the Janus type on various curved solid walls at large density ratios, focusing on whether the separation of compound droplets occurs. Several types of wall geometries were considered, including a planar wall, a concave wall with constant curvature, and a convex wall with fixed or variable curvature (specifically, a prolate or oblate spheroid). The effects of surface wettability, interfacial angles, and the density ratio (of droplet to ambient fluid) on the wetting process were also explored. In general, it was found that, under otherwise identical conditions, droplet separation tends to happen more likely on more hydrophilic walls, under larger interfacial angles (measured inside the droplet), and at larger density ratios. On convex walls, a larger radius of curvature of the surface near the droplet was found to be helpful to split the Janus droplet. On concave walls, as the radius of curvature increases from a small value, the possibility to observe droplet separation first increases and then decreases. Several phase diagrams on whether droplet separation occurs during the spreading process were produced for different kinds of walls to illustrate the influences of various factors.

Direct numerical simulations of turbulent channel flow with a rib-roughened porous wall

To describe the effects of porous roughness on turbulence, we have carried out direct numerical simulations using the lattice Boltzmann method. The simulated flows are fully developed turbulent flows in channels consisting of a solid smooth top wall and a porous bottom wall with transverse porous ribs whose heights are 10 % of the channel height. The considered ratios of the rib spacing to the rib height are $w/k\simeq 1$ and 9. The Kelvin-cell structure is applied to construct faithfully the porous media whose porosities are $\varphi \ge 0.79$ . Three kinds of porous media having different permeabilities are considered. The most permeable one has an approximately one order higher permeability than that of the least permeable one. The higher permeability case is designed to have a pore scale that is the same as the rib height so that it is the most permeable case for the rib roughness with the designed porosity. In the simulations, the bulk Reynolds number is set to $Re_b=5500$ , and the corresponding permeability Reynolds numbers are $Re_K=2.2\unicode{x2013}7.5$ . The simulated field data and the drag coefficient, which includes both the pressure drag by the ribs and the frictional drag over the porous wall, are analysed to understand the characteristics of the permeable roughness in terms of permeability. The decomposition of the drag coefficient into the integrated laminar, rib-drag, dispersion and turbulence parts elucidates the transition mechanism between the typical d-type to k-type roughness depending on $Re_K$ . By the double (time and space) averaged budget equations for the dispersion and Reynolds stresses, we explain how the energy generated by the roughness transfers to turbulence through dispersion resulting in the k-type characteristics. The nominal roughness sublayer thickness and the characteristic roughness height are introduced with the parameters obtained by fitting the velocity data to Best's and Nikuradse's logarithmic velocity formulae. Along with data in the literature, it is suggested that the ratio of the characteristic roughness height to the nominal roughness sublayer thickness becomes constant irrespective of the rib spacing in the full permeable-wall turbulence at $Re_K> 7$ .

The analytical solutions of long waves over geometries with linear and nonlinear variations in the form of power-law nonlinearities with solid vertical wall

In harbor engineering long waves cause some engineering challenges such as avoiding harbor resonance. Due to similar problems, it is necessary to comprehend and predict their dynamics. Whilst the literature has extensively researched their dynamics for a variety of geometries, the nonlinear geometries with power-law forms are not very well studied. The analytical solutions of the long-wave equation over nonlinear depth and breadth profiles with power-law forms are described by h(x)=c1xa and b(x)=c2xc, where the parameters c1, c2, a, and c are some real constants, are just recently derived by one of the authors of this paper Bayındır and Farazande, (2021). With this motivation, in this paper, we extend our work and obtain the exact analytical solutions of the long-wave equation over linear and nonlinear in the power-law form depth and breadth geometries where a solid vertical wall is present. We show that the long-wave equation admits solutions in terms of Bessel-Z functions and the Cauchy–Euler series for these particular power-law forms of depth and breadth profiles in the presence of the solid vertical wall. We present our results for the general type of the geometries considered with solid vertical walls. Additionally, six various cases for the aforementioned geometries where a solid vertical wall is present are discussed.

Entropy generation in a partially heated hybrid nanofluid saturated wavy porous cavity

PurposeA porous cavity flow field generates entropy owing to energy and momentum exchange within the fluid and at solid barriers. The heat transport and viscosity effects on fluid and solid walls irreversibly generate entropy. This numerical study aims to investigate convective heat transfer together with entropy generation in a partially heated wavy porous cavity filled with a hybrid nanofluid.Design/methodology/approachThe governing equations are nondimensionalized and the domain is transformed into a unit square. A second-order finite difference method is used to have numerical solutions to nondimensional unknowns such as stream function and temperature. This numerical computation is conducted to explore a wide range of regulating parameters, e.g. hybrid nano-particle volume fraction (σ = 0.1%, 0.33%, 0.75%, 1%, 2%), Rayleigh–Darcy number (Ra = 10, 102, 103), dimensionless length of the heat source (ϵ = 0.25, 0.50,1.0) and amplitude of the wave (a = 0.05, 0.10, 0.15) for a number of undulations (N = 1, 3) per unit length.FindingsA thorough analysis is conducted to analyze the effect of multiple factors such as thermal convective forces, heat source, surface corrugation factors, nanofluid volume fraction and other parameters on entropy generation. The flow and temperature fields are studied through streamlines and isotherms. The average Bejan number suggested that entropy generation is entirely dominated by irreversibility due to heat transport at Ra = 10, and the irreversibility due to the viscosity effect is severe at Ra = 103, but the increment in s augments irreversibility due to the viscosity effect over the heat transport at Ra = 102.Originality/valueTo the best of the authors’ knowledge, this numerical study, for the first time, analyzes the influence of surface corrugation on the entropy generation related to the cooling of a partial heat source by the convection of a hybrid nanofluid.

Classical and local similarity in problems of turbulent convection: Extension of Prandtl semi-empirical theory for horizontal layers of water and air mediums

A variant of the local similarity theory is considered, assuming a priori specification of two basic dimensional parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. Such selection of basic parameters lets us interpret the algebraic formulas of Prandtl's semiempirical turbulence theory for the coefficients of turbulent heat transfer and kinetic energy dissipation as relationships of the local similarity theory. A priori approximations of the basic parameters are based on known relationships and consider the upper boundary of the convective layer as a solid wall. Within the framework of local similarity theory, approximations for the turbulent moments of buoyancy and vertical velocity of arbitrary order are also proposed. The correspondence of these approximations to experimental data has been established in both air and water mediums, as well as in the results of numerical modeling. Such correspondence allows us to conclude that a wide class of vertical profiles of turbulent moments in a windless convective layer depends only on two basic parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. The obtained result indicates the universal nature of the theory of local similarity and is a significant addition to the semiempirical Prandtl theory.

Grad's 13 moments-based gas kinetic flux solver with triangle unstructured meshes for simulating continuum and rarefied fluid flows

A numerical framework based on the gas kinetic flux solver (GKFS) with unstructured meshes of triangle cells has been proposed and assessed in this work. Like conventional GKFS, the present scheme only updates the cell-average macroscopic conservative variables in time, thereby saving computational costs. At each cell interface, the numerical normal flux is computed with the GKFS scheme proposed by Liu et al. [J. Comput. Phys. 415, 109548 (2020)], in which the distribution functions at the surrounding points are reconstructed with the Grad's 13 moments (G13). Additionally, a solid wall boundary condition treatment has been proposed in the present G13-GKFS framework, which allows one to model from purely specular to perfectly thermalized solid walls. The present framework has been validated with the steady cylindrical Couette flow, the lid-driven cavity flow, the unsteady Rayleigh flow, and the rarefied flow around the NACA0012 airfoil test-cases, where good agreements are found with references for a quite wide range of flow regimes, from continuum to transitional flow regimes.