This paper presents a complete derivation and design of a physics-informed neural network (PINN) applicable to solve initial- and boundary value problems described by linear ordinary differential equations. The objective not to develop a numerical solution procedure which is more accurate and efficient than standard finite element or finite difference based methods, but to give a fully explicit mathematical description of a PINN and to present an application example in the context of hydrodynamic lubrication. It is, however, worth noticing that the PINN developed herein, contrary to FEM and FDM, is a meshless method and that training does not require big data which is typical in machine learning.

Physics-informed neural networks are a promising method to yield surrogate models of flow fields. We present a metamodeling technique for variable geometries based on physics-informed neural networks. The method was applied to the DU99W350 airfoil at a Reynolds number of 1×10⁵. The model predicted the Reynolds-averaged velocity and pressure field around the airfoil for arbitrary angles of attack between 10.0° and 17.5°. The model was trained with data from CFD simulations for a limited set of angles of attack. Additionally, satisfaction of the a priori known boundary conditions as well as the Reynolds-averaged Navier-Stokes equations were trained. A sensitivity analysis concerning the Reynolds number, the amount and distribution of training data, and the turbulence model was conducted showing the superiority of the pseudo-Reynolds stress method and the demand of labeled training data in the domain. The trained network was capable of predicting the developing flow separation on the suction surface and exhibited excellent agreement with CFD results even in the proximity to the wall for interpolations as well as extrapolations from the labeled data set.

Unsupervised physics-informed deep learning can be used to solve computational physics problems by training neural networks to satisfy the underlying equations and boundary conditions without labeled data. Parameters such as network architecture and training method determine the training success. However, the best choice is unknown a priori as it is case specific. Here, we investigated network shapes, sizes, and types for unsupervised physics-informed deep learning of the two-dimensional Reynolds-averaged flow around cylinders. We trained mixed-variable networks and compared them to traditional models. Several network architectures with different shape factors and sizes were evaluated. The models were trained to solve the Reynolds-averaged Navier-Stokes equations incorporating Prandtl's mixing length turbulence model. No training data were deployed to train the models. The superiority of the mixed-variable approach was confirmed for the investigated high Reynolds number flow. The mixed-variable models were sensitive to the network shape. For the two cylinders, differently deep networks showed superior performance. The best fitting models were able to capture important flow phenomena such as stagnation regions, boundary layers, flow separation, and recirculation. We also encountered difficulties when predicting high Reynolds number flows without training data

In this paper, for the Reynolds-averaged Navier-Stokes equations, a self-closed turbulence model without any adjustable parameter is formulated and a simple model is proposed. The validation rule for self-closed turbulence model is rigorously derived from the Reynolds-averaged Navier-Stokes equation. The rule is not effected by turbulence modelling on the Reynolds stresses. As an application, two dimensional turbulent boundary layers, and plate turbulent boundary layers have been formulated.

Over the last few years there has been much effort put into the development and validation of stochastic models of the trajectories of swarming insects. These models typically assume that the positions and velocities of swarming insects can be represented by continuous jointly Markovian processes. These models are first-order autoregressive processes. In more sophisticated models, second-order autoregressive processes the positions, velocities and accelerations of swarming insects are collectively Markovian. Although it is mathematically conceivable that this hierarchy of stochastic models could be extended to higher orders, here I show that such a procedure would not be well-based biologically because some terms in these models represent processes that have the potential destabilize insect flight dynamics. This prediction is supported by an analysis of pre-existing data for laboratory swarms of the non-biting midge Chironomus riparius. I suggest that the Reynolds number is a finely tuned property of swarming, as swarms may disintegrate at both sufficiently low and sufficiently high Reynolds numbers.

This paper attempts to clarify an long-standing issue about the number of unknowns in the Reynolds-Averaged Navier-Stokes equations (RANS). This study shows that all perspectives regarding the numbers of unknowns in the RANS stem from the misinterpretation of the Reynolds stress tensor. The current literature consider that the Reynolds stress tensor has six unknown components; however, this study shows that the Reynolds stress tensor actually has only three unknown components, namely the three components of fluctuation velocity. This understanding might shed a light to understand the well-known closure problem of turbulence.

This paper attempts to clarify an issue regarding the lasting unsolved problem of turbulence, namely the closure problem. This study shows that all perspectives regarding the numbers of un- known quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor. The current literatures have a consensus that the Reynolds stress tensor has six unknowns; however, this study shows that the Reynolds stress tensor actually has only three ones, namely the three components of fluctuation velocity. With this new understanding, the closed turbulence equations for incompressible flows are proposed.

This paper shown that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literatures have stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We shown the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. That is why we claim in this paper, that the Reynolds Navier-Stokes turbulence equations of incompressible flow are closed rather than unclosed. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

Physics-informed neural networks can be trained to serve as surrogate models by learning how spatial physical fields develop with change of parameters. This is an advantage over traditional numerical methods that can only be used to calculate a single solution field for a single discrete setting of a parameter. While many studies report accurate results of physics-informed deep learning of laminar flows, evaluations of surrogate modeling of high Reynolds number flows remain sparse. To contribute to this question, we here explore the capabilities and limits of physics-informed deep learning to solve the Reynolds-averaged Navier-Stokes equations for the flow around two airfoils under variable angles of attack. No labeled training data were provided and a single network was trained to simultaneously learn several solution fields in a single training run. The network captured essential flow features such as boundary layers and high and low pressure regions. Moreover, the qualitative correlations of lift and drag with the angle of attack and the higher drag of the thicker airfoil were captured. However, comparisons with reference simulations revealed an underestimation of the shear layer gradients as well as deviations of the fields' extrema. Thus, we also debate potential future improvements to increase the accuracy of the predicted flow. This work offers a prospect on the capabilities and current limitations of physics-informed neural networks for surrogate modeling of high Reynolds number flows. We argue that the method is promising and this work is aimed to encourage further research and development of the method when applied to Reynolds-averaged flows at high Reynolds numbers.

This paper presents a biologically inspired flocking-based aggregation behaviour of a swarm of mobile robots. Aggregation behaviour is essential to many swarm systems, such as swarm robotics systems, in order to accomplish complex tasks that are impossible for a single agent. We developed a robot controller using Reynolds’ flocking rules to coordinate the movements of multiple e-puck robots during the aggregation process. To improve aggregation behaviour among these robots and address the scalability issues in current flocking-based aggregation approaches, we used a K-means algorithm to identify clusters of agents. Using the developed controller, we simulated the aggregation behaviour among the swarm of robots. Five experiments were conducted using Webots simulation software. The performance of the developed system was evaluated under a variety of environments and conditions, such as various obstacles, agent failure, different numbers of robots and arena sizes. The results of the experiments demonstrated that the proposed algorithm is robust and scalable. Moreover, we compared our proposed algorithm with another implementation of the flocking-based self-organizing aggregation behaviour based on Reynolds’ rules in a swarm of e-puck robots. Our algorithms outperformed this method in terms of cohesion performance and aggregation completion time.

Acoustic emission (AE) is caused by the sudden release of energy by a material as a result of material degradation related to deformation, crack, or fault within a solid. The same situation also occurs in leaks caused by turbulence in the fluid around the leak. In this study, analytical modeling for AE due to leakage through a circular pinhole in a gas storage cylinder was performed. The displacement fields responsible for AE, excited by the concentrated force (CF) associated with the turbulent flow though the pinhole, were derived by solving the Navier-Lamé equation. The CF as an excitation source was formulated in terms of a fluctuating Reynolds stress (FRS) and spatial Green’s function. In particular, a series of experiments were conducted under different operating conditions to explore the characteristics of the AE signals due to leak in a gas cylinder. Finally, the simulation and experimental results were compared to verify the accuracy of the simulation results.

A century-old scientific conundrum is solved in this paper. The Prandtl mixing length modelled plane boundary turbulent flow is described by: $\frac{du^+}{d{y^+} }+\kappa^2{y^+} ^2\left( \frac{du^+}{d{y^+} }\right)^2=1$, together with boundary condition $ {y^+} =0:\, u^+=0$. Only an approximate solution to this nonlinear ordinary differential equation (ODE) has been sought so far, however, the exact solution to this ODE has not been obtained. By introducing a transformation, $2\kappa y^+=\sinh \xi$, I successfully find the exact solution of the ODE as follows: $u^+=\frac{1}{\kappa}\ln(2\kappa {y^+} +\sqrt{1+4\kappa^2{y^+} ^2})-\frac{2{y^+} }{1+\sqrt{1+4\kappa^2{y^+} ^2}}$.

The open source CFD code OpenFOAM has emerged as one of the most popular alternative to commercial CFD solvers. The recent version of OpenFOAM supports overlapping grids, so called Overset mesh. In this type of mesh, one or more sub-collection of control volumes (or cells) are allowed to overlap with other set of cells. This allows for great flexibility in modelling Fluid Structure Interaction (FSI) problems. Fluid mesh can be standard structured mesh of a rectangular/cuboidal/or cylindrical domain. The structure mesh can be generated separately by creating multiple layers around a given body. The overset mesh functionality allows for overlapping or immersing this structured mesh inside the fluid mesh and a relevant FSI or moving dynamics problems can be solved. The idea of overset mesh has been around since eighties but its support in OpenFOAM is very recent. Most CFD codes which support overset mesh have either been in-house or commercial CFD codes. OpenFOAM's support for overset is the first major open source code resource available for CFD problems. The aim of this research is to solve a classical benchmark airfoil problem using OpenFOAM overset mesh and compare the numerical results with experimental result. We report here flow simulations results around NACA 0018. The result obtained from overset mesh compares convincingly well with experimental results. Computations have been carried out for Reynolds numbers in the range of 10⁵ with angle of attack ranging from α= 5 degree to α= 30 degree with an interval of 5 degree. Turbulence is incorporated using k - ε turbulence model. This study helps developing confidence in using OpenFOAM overset support for more complicated flows and moving dynamics. This report is complemented with a brief description of finite volume discretization using overset mesh.

This study presents head losses (hL) and loss coefficients (K) obtained experimentally for schedule 40 PVC pipe elbows, with 90o and 45o in small commercial diameters of ½ to 1½ inches that are commonly used in small networks. The investigation was conducted on a system constructed with short pipes and fittings necessary to measure, direct, and control flow, as well as to evaluate pressure head losses at elbows. Simple water flow was used with rates of 0.342 to 0.980 lps (Q), which generated moderate Reynolds numbers (Re) of 13337 to 80221. It was found that hL showed dependence on the velocity head in all elbows, as well as that hL are greater as the diameter increases for same velocity head. The K values in the elbows tended to be constant when Q > 0.75 lps, but for Q < 0.75 lps the K coefficient increased inversely proportional to Q, becoming larger as the diameter increased. Likewise, the K coefficient tended to increase as Re decreased, while K tended to be constant as Re increased. The results of the experimental coefficient were compared against K values reported in the literature, where significant similarities and discrepancies were found.

The amount of heat transfer in gas turbine blades depends on cooling techniques and various flow phenomena. The effect of eddies, passing shock waves and free flow turbulence has been noticed by many researchers since the beginning. The focus of the upcoming work is on the numerical investigation of the effects of turbulence intensity and Reynolds number on the amount of heat transfer from the blade surface with internal cooling. The SST model has been used to solve this problem, which has been compared with the experimental work to ensure the correctness of the numerical simulation. In this regard, by changing the free flow turbulence intensity with values of 1, 5, 7, and 10% and at three Reynolds numbers of 150,000, 350,000, and 750,000, the changes in heat transfer coefficients have been investigated. The results show that with the increase of the turbulence intensity at different Reynolds numbers, due to the positive effect of the flow turbulence on the suppression of separation and promotion of the boundary layer transition, the blade surface heat transferincreases and this increase is more evident at higher Reynolds numbers.

We study electrohydrodynamic (EHD) linear (in)stability of microfluidic channel flows, i.e. the stability of interface between two-shearing viscous (perfect) dielectrics exposed to an electric field in large aspect ratio microchannels. We then apply our results to particular microfluidic systems known as electroosmotic (EO) pumps. Our results are detailed analytical expressions for the growth rate of two-dimensional EHD modes in Couette-Poiseuille flows in the limit of small Reynolds number ($R$); the expansions to both zeroth- and first-order-$R$ are considered. The growth rates are complicated functions of viscosity-, height-, density- and dielectric-constant ratio, as well as of wavenumbers and voltages, and to our knowledge have not been presented before in literature. To make the results more useful, e.g., for voltage-control EO pump operations, we also derive equations for the impending voltages of the neutral stability curves that divide stable from unstable regions in voltage-wavenumber stability diagrams. The voltage equations and the stability diagrams are given for all wavenumbers. We finally outline the flow regimes in which our first-order-$R$ voltage corrections could potentially be experimentally measured. Our work gives the insight into the coupling mechanism between electric field and shear flow in parallel-planes channel flows, correcting an erroneous attempt from literature. Our general analysis enables us also to refine the renowned instability mechanism due to viscosity stratification, i.e., the case of pure shear instability, when the first-order-$R$ voltage correction equals zero.

In the presence of aquatic plants in streams, a variety of flow structures have been reported. Re-sults of earlier investigations indicated that the hydrodynamic features of flows in rivers, and streams are influenced by a wide range of submerged and non-submerged vegetation. In the pre-sent study, eight experiment runs were conducted in two artificial pools built in a laboratory flume to assess the flow structures across vegetation cover. The slopes for entrance and exit sec-tions of these two pools are of 5 and 10 degrees, respectively. A patch of artificial grass covered the entire pool area over the gravel bed. The effect of stream flow velocity was investigated by considering two aspect ratios of 2 and 2.7. Also, distributions of flow velocity, Reynolds normal and shear stresses, turbulence intensities, turbulent kinetic energy (TKE), and higher-order mo-ments of velocity fluctuations have been investigated. By means of quadrant analysis, it is found that the skewness coefficients of velocity profiles are significant parameters to evaluate. Based on skewness values for the bursting processes, along the pool entrance section with a smaller slope, the contribution of sweep motion occurs in a more restricted zone above the canopy, and this im-plies that the ejection motion occurs in a pool entrance section with a higher slope. Immediately above the vegetation canopy, the dominant process is the sweep motion of bursting events. Whereas, at the upstream boundary of the vegetation patch, an outward motion with slightly pos-itive value occurs; and around the downstream boundary of the vegetation patch, the isotropic turbulence appears at the boundary of the vegetation and gravel bed. Over the vegetation canopy in the pool, less mixing eddies result in lower Reynolds shear stress values, and thus the turbulent flow becomes weak with lower turbulent kinetic energy (TKE). Because of the shallow flow in an artificial channel with an aspect ratio less than five and the availability of vertical non-zero ve-locity components, secondary currents become stronger in the channel. Consequently, there is a divergence from a linear dispersion of Reynolds shear stress.

Calculation of the pressure field on and around solid bodies exposed to external flow is of paramount importance to a number of engineering applications. However, conventional pressure measurement techniques are inherently linked to problems principally caused by their point-wise and/or intrusive nature. In the present paper, we attempt to calculate the time-averaged two-dimensional pressure field by integrating PIV (Particle Image Velocimetry) velocity measurements into a CFD code and modifying them by the respective correction step of the SIMPLE algorithm. Boundary conditions are applied from the PIV data as a three-layer area of constant velocities, adjacent to the boundaries. A novel characteristic of the approach is the straightforward inclusion of the Reynolds Stresses into the source terms of the momentum equations, calculated directly from the PIV statistics. The methodology is applied to three regions of the symmetry plane parallel to the main boundary layer flow past a surface mounted cube. In spite of findings of deviations from the planar 2D flow assumption, the derived pressure fields and the adjusted velocity fields are found to be reliable, while the intrinsic turbulent nature of the flow is considered without modelling of the Reynolds stresses.

This study revisits the Reynolds-averaged Navier--Stokes equations (RANS) and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds' averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of on the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

The aim of this study is to introduce a novel method which can separate sand or gravel dominated bed load transport in rivers with mixed-size bed material. In engineering practice, the Shields-Parker diagram could be used for such purposes, however, the method has certain applicability limits, due to the fact that it is based on uniform bed material and provides information rather on river-scale, instead of reach or local scale. When dealing with large rivers with complex hydrodynamics and morphodynamics the bed load transport modes can also indicate strong variation even locally, which requires a more suitable approach to estimate the locally unique behavior of the sediment transport. Here, we suggest that the decision criteria utilizes the shear Reynolds number (Re*). The method was verified against field and laboratory measurement data, both performed at non-uniform bed material compositions. The comparative assessment of the results show that the shear Reynolds number based method operates more reliably than the Shields-Parker diagram and it is expected to predict the sand or gravel transport domination with a < 5% uncertainty. The introduced results can greatly contribute to the improvement of numerical sediment transport modeling as well as to the field implementation of bed load transport measurements.

The effect of spanwise wing non-planarity, implemented in conjunction with a Gurney flap is presented. Testing was undertaken in a low speed wind tunnel using a rectangular wing with an aspect ratio of 3. The outer 1/3 of the wing was non-planar which took the form of dihedral or a circular arc. A 2% high Gurney flap was implemented such that it could extend over the entire span, or the planar inboard section. Loads were measured using a sting balance. The data shows that non-planarity increases the maximum lift coefficient and the wing’s lift curve slope. Gurney flap lift modulation was enhanced in the presence of non-planarity. The addition of Gurney flaps caused a greater minimum drag coefficient increment for the non-planar wings. The Gurney flaps reduced the lift dependent drag of the wings; however, the minimum drag coefficient was observed to increase. The Gurney flaps reduced the maximum lift to drag ratio (L/D) for the non-planar wings; however, the flat wing showed a small L/D increment with flap addition.

We present a mixing length based algebraic turbulence model calibrated to pipe flow; the main purpose of the model is to capture the increasing turbulence production-to-dissipation ratio observed in connection with the high Reynolds number transition region. The model includes the mixing length description by Gersten and Herwig which takes the observed variation of the von Kármán number with Reynolds number into account. Pipe wall roughness effects are included in the model. Results are presented for area-averaged (integral) quantities which can be used both as a self-contained model and as initial inlet boundary conditions for computational fluid dynamics simulations.

The common dandelion uses a bundle of drag-enhancing bristles (the pappus) that enables seed dispersal over formidable distances; however, the scaling laws of aerodynamic drag underpinning pappus-mediated flight remains unresolved. In this paper, we study the aerodynamic shape of dandelion, derive the scaling law of resistance, determine the Vogel exponent. In particular, we find that the total drag coefficient is proportional to the -2/3 power of the dandelion pappus Reynolds number, and obtain the terminal velocity of the dandelion seed under gravitation field.

The turbulent Poiseuille flow between two parallel plates is one of the simplest possible physical situations, and it has been studied intensively. In this paper, we propose a modified Prandtl-van Driest mixing length that satisfies both boundary conditions and wall damping effects. With our new formulations, we numerically solve the problem and, moreover, propose an approximate analytical solution of mean velocity. As applications of our solution, an approximate analytical friction coefficient of turbulent Poiseuille flow is proposed.

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

The aim of work is to derive an explicit expression for a function of vertical mixing induced by wind-waves. To this end, in the Navier-Stokes equations, a current is decomposed into four constituents: the mean flow, the wave-orbital motion, the wave-induced turbulent and the background turbulent currents. This decomposition allows separating the wave-induced Reynolds stress, Rw, from the background one, Rb. To make a statistical closure for Rw, the Prandtl approach for the background turbulent fluctuations is used that results in an implicit expression for the wave-induced vertical mixing function, Bv. Expression for Bv is specified based on the author’s results for the eddy viscosity found earlier in the frame of the three-layer concept for a wavy air–sea interface, used for modelling wind-drift currents [1]. Finally, the explicit parameterization for Bv(a, u*, z) is found as a linear function in both the wave amplitude at depth z, a(z), and the friction velocity in the air, u*. The linear dependence of function Bv(a) on the wave amplitude provides the enhanced vertical mixing induced by wind–waves in comparison with function Bv(a) having the cubic dependence found in [2], as far as the wind-wave amplitude a(z) decays exponentially with depth.

Based on author's previous work [Sun, B. The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed. Preprints 2018, 2018060461 (doi: 10.20944/preprints201806.0461.v1)], this paper proposed an explicit representation of velocity fluctuation and formulated the Reynolds stress tensor in terms of the mean velocity field. The proposed closed Reynolds Navier-Stokes turbulence formulations reveal that the mean vorticity is the key source of producing turbulence.

Uchino first initiated the study of generalized Reynolds operators on associative algebras. Recently, related research has become a hot topic. In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle. Then, we develop cohomology of generalized Reynolds operators on Hom-Lie triple systems with coefficients in a suitable representation. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable order $n$ deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying structure of generalized Reynolds operators on Hom-Lie triple systems.

A rigid protruding surface, agitator and vortex generator often dissipate more energy than to produce a satisfied turbulence production. In contrast, a passively-oscillating flexible protruding surface has the ability in generating greater turbulence level. In the current study, a circular finite cylinder (cantilever) was used as the geometry of the rigid and protruding surface. They were varied through the aspect ratio (AR) and materials. Also, a local Reynolds number within the subcritical flow range (102<ReD<105) was considered. The results from the rigid protruding surface (finite cylinder) is served as a validation to the published results and benchmark to the improve-ment of the turbulence generated by the flexible protruding surface. It was mentioned in the pre-vious work that the increment of turbulence production by the flexible cylinder is speculated to be oscillation, this work investigates the validity of the speculation through manipulating the struc-tural stiffness of the flexible cylinder by employing different materials. The results have further demonstrated that the flexible cylinder is capable of generating a greater turbulence through the examination of turbulence intensity, turbulence production term and Reynolds stress. All the flex-ible cylinders that oscillate show increment in turbulence production but at a different percentage. The cylinders studied in this work ranged from the least structural stiffness (EVA), moderate (al-uminium) to the highest structural stiffness (carbon steel). Through studying the normalized am-plitude responses graph of the flexible cylinder, it is identified that the oscillating motion does in-deed contribute to increment. A further investigation into the results, it is found that the factor which governs the increment is the structural velocity instead of just oscillating motion alone.

Micro-technology has played a substantial role in bioscience, biomedical and biotechnological research due to its core advantages in modern science and engineering. It has created unique development in various sectors of bio-research and upsurges the efficacy of research at the molecular level in recent years. Microfluidic technology makes it possible to manipulate sample volumes at the micro- and nano-level (called nanofluidics) with terrific control outside in vivo cellular microenvironment, enabling the reduction of discrepancies between in vivo and in vitro environments as well as reducing reaction time and cost. In this review, we discuss various effective integrations of microfluidic technologies into biotechnology and its paradigmatic significance in bio-research, supporting mechanical and chemical in vitro cellular micro-environment. Specific innovations relating to the application of microfluidics to advance microbial life, solitary and co-cultures along with a multiple-type cell culturing, cellular communications, cellular interactions and population dynamics are discussed.

Heat exchangers play a vital role in numerous sectors like power generation and automotive manufacturing. Enhancing the energy efficiency of these exchangers stands as a significant hurdle. Utilizing nanofluids emerges as an optimal solution to augment heat transfer rates, leveraging their superior thermal conductivity while addressing economic constraints linked with traditional heat exchanger technologies. The motivation for this study is to consider the comprehensive synergistic features of MWCNTs, SiO₂, and hybrid MWCNTs–SiO₂ EG-based nanofluids in plate heat exchangers. This was achieved by simulating a plate heat exchanger using CFD (Fluent and Gambit softwares) considering the comparison of two SiO₂, MWCNTs, and their hybrid forms at different mass concentrations. The Reynolds-Averaged Navier-Stokes (RANS) method was employed to model turbulent flows, and the nanoparticles were compared in both single-phase and two-phase states, with their properties derived from experimental studies. Moreover, Nusselt number, convective heat transfer coefficient, and pressure drop variations were computed at different Reynolds numbers. The findings indicated an increase in the Nusselt number with the incorporation of the hybrid nanofluid, achieving a maximum enhancement of 11.19% in comparison to EG at a Reynolds number of 240 and a concentration of 0.86 wt.%. Noticeably, the pressure drop remained negligible at lower Reynolds numbers, exhibiting marginal variations up to 0.3% at higher Reynolds numbers. At a concentration of 0.86 wt.% and a Reynolds number of 480, the introduction of MWCNTs, hybrid, and SiO₂ nano-additives resulted in respective increases in the heat transfer coefficient by 21.02%, 10.76%, and 2.16% and corresponding alterations in pressure drop of 0.11%, 0.04%, and 0.02%.

The exact similarity solutions (also called as special exact solutions) of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, no similarity solutions for two dimensional turbulent boundary layers have been reported in the literature. With the help of dimensional analysis and invariance principle, Prandtl mixing length $\ell=\kappa y$ for one dimensional turbulent boundary layer is extended to $\ell(x,y)=\kappa y (1-\frac{y}{\delta})\sqrt{\frac{\nu}{U\delta}} $ for the two dimensional turbulent boundary layers, furthermore, with a similarity transformation, we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation $f'''+ ff''+\beta(1-f'^2)+\kappa^2[\eta^2(1-\eta)^2f''|f''|]'=0$. As an application, similarity solutions of the two dimensional turbulent boundary layer on a flat plate at zero incidence have been studied in detail. To solve the ordinary differential equation numerically, a complete Maple code is provided.

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no similarity solutions (special exact solutions) have ever been found. In the light of Blasius' pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. By author's Maple code, we numerically solve the ordinary differential equation and produce some useful quantities.

Based on the insight gained from single jet analysis performed earlier [1], CFD analysis on turbulent jets impinging on one another at an angle was performed. Multiple impingement angles were considered for this study to gain better understanding of the parameters affecting resultant jet growth and velocity distribution. From the study of single jet, it was concluded that the SST k-ω turbulence model was the ideal turbulence model capable of accurately predicting the flow physics of the jets exiting a fully developed pipe at low Reynolds number. Hence, for the study of impinging jets, SST k-ω turbulence model was used to study the velocity and jet growth characteristics. It became evident that the mesh alignment with the velocity vector at exit of the pipe domain plays a crucial role in the accuracy of the results. The parameter used to evaluate this condition was identified as False Diffusion and was observed to affect the TKE parameter significantly. Methods to reduce false diffusion are also discussed in this article. Based on the mesh obtained from the grid sensitivity study, jets impinging at 30, 45 and 60 degrees at Reynolds number of 7500 were numerically analyzed. It was observed that the profile of the resultant jet closely matched with the prediction of elliptical profile predicted by past researchers, [2] and [3]. Also, it was seen that higher jet growth was predicted in case of jets impinging at a higher impingement angle.

The time-resolved flowfield of a spatially oscillating jet emitted by a Sweeping Jet (SWJ) actuator is investigated numerically using three-dimensional Reynolds-averaged Navier-Stokes (3D-URANS) equations. Numerical simulations are performed for a practical range of mass flow rates providing flow conditions ranging from incompressible to subsonic compressible flows. A linear relationship between the mass flow rate and the jet oscillation frequency is found. The results of the numerical model are compared with the experimental data in the literature, and good agreement is found. Additionally, it is observed that the SWJ actuator frequency response switches from one linear mode to another linear mode when the compressibility effects become important.

In this study, the field measurement-based validation of a novel sediment transport calculation method is presented. River sections with complex bed topography and inhomogeneous bed material composition highlight the need for an improved sediment transport calculation method. The complexity of the morphodynamic features can result in the simultaneous appearance of the gravel and finer sand dominated sediment transport (e.g. parallel bed armoring and siltation) at different regions within a shorter river reach. For the improvement purpose of sediment transport calculation in such complex river beds, a novel sediment transport method was elaborated. The base concept of it is the combined use of two already existing empirical sediment transport models. The method was already validated against laboratory measurements. The major goal of this study is the verification of the novel method with a real river case study. The combining of the two sediment transport models is based on the implementation of a recently presented classification method of the locally dominant sediment transport nature (gravel or sand transport dominates). The results are compared with measured bed change maps. The verification clearly refers to the meaningful improvement in the sediment transport calculation by the novel manner in case of spatially varying bed content.

Transient conjugate heat transfer measurements under varying temperature and velocity inlet boundary conditions at incompressible flow conditions were performed for flat plate and ribbed channel geometries. Therefrom local adiabatic wall temperatures and heat transfer coefficients are determined. Those data are analyzed using typical heat transfer correlations, e.g. Nu=CRe^mPr^n determining the local distribution of C and m. It is shown that they are closely linked. A relationship lnC=A−mB is observed with A and B as modeling parameters. They could be related to parameters in log law or power law representations for turbulent boundary layer flows. The parameter m is shown to have a close link to local pressure gradients and therewith near wall streamlines as well as friction factor distributions. A normalization of the C parameter allows to derive a Reynolds analogy factor and therefrom local wall shear stresses.

Gaining insight into tribological systems is crucial for optimizing efficiency and prolonging operational lifespans in technical systems. Experimental investigations are time-consuming and costly, especially for reciprocating seals in fluid power systems. Elastohydrodynamic lubrication (EHL) simulations offer an alternative but demand significant computational resources. Physics-informed neural networks (PINNs) provide a promising solution using physics-based approaches to solve partial differential equations. While PINNs have successfully modeled hydrodynamics with stationary cavitation, they have yet to address transient cavitation with dynamic geometry changes. This contribution applies a PINN framework to predict pressure build-up and transient cavitation in sealing contacts with dynamic geometry changes. The results demonstrate the potential of PINNs for modeling tribological systems and highlight their significance in enhancing computational efficiency.

RANS simulations have been broadly used to investigate turbulence in the oceans and atmosphere. Within these environments there are a multitude of tracers undergoing reactions (eg. phytoplankton growth, chemical reactions). The distribution of these reactive tracers is strongly influenced by turbulent mixing. With a 50 member ensemble of two dimensional Rayleigh-Taylor induced turbulent mixing, we show that the dynamics of a reactive tracer growing according to Fisher’s equation are poorly captured by the mean. A fluctuation-dependent sink introduced by Reynolds averaging Fisher’s equation transfers concentration from the mean to the fluctuations. We compare the dynamics of the reactive tracer with those of a passive tracer. The reaction causes the concentration of reactive tracer to increase thereby increasing Fickian diffusion and allowing the reactive tracer to diffuse into turbulent structures that the passive tracer cannot reach. A positive feedback between turbulent mixing and fluctuation growth is identified. We show that eddy viscosity and diffusivity parameterizations fail to capture the bulk trends of the system and identify a need for negative eddy diffusivities. One must therefore be cautious when interpreting RANS results for reactive tracers.

This review is a first attempt at bringing together various concepts from research on wall- and magnetically-bounded turbulent flows. Brief reviews of both fields are provided: The main similarities identified are coherent (turbulent) structures, flow generation and transport barriers. Examples are provided and discussed.

This paper attempts to develop a Dynamic Mode Decomposition (DMD) based Reduced Order Model (ROMs) which can quickly but accurately predict the forces and moments experienced by a road vehicle such that they be used by an on-board controller to determine the vehicle's trajectory. DMD can linearize a large dataset of high-dimensional measurements by decomposing them into low-dimensional coherent structures and associated time-dynamics. This ROM then also can be applied to predict the future state of the fluid flow. Existing literature on DMD is limited to low Reynolds number applications. This paper presents DMD analyses of the flow around an idealized road vehicle, called the Ahmed body, at a Reynolds number of 2.7E6. The high dimensional dataset used in this paper was collected from a computational fluid dynamics (CFD) simulation performed using Menter's shear stress transport (SST) turbulence model within the context of Improved Delayed Detached Eddy Simulations (IDDES). The DMD algorithm, as available in literature, was found to suffer nonphysical dampening of the medium-to-high frequency modes. Enhancements to the existing algorithm were explored, and a modified DMD approach is presented in this paper which includes: (a) a requirement of higher sampling rate to obtain higher resolution of data, and (b) a custom filtration process to remove spurious modes. The modified DMD algorithm thus developed was applied to the high Reynolds number, separation dominated flow past the idealized ground vehicle. The effectiveness of the modified algorithm was tested by comparing future predictions of force and moment coefficients as predicted by the DMD-based ROM to the reference CFD simulation data, and found to offer significant improvement.

The aim of the studies was to test the hydraulic pressure losses along the length, local pressure losses, absolute and relative roughness values of the pipeline walls made of modern polymer material. The article presents the results of the experimental studies of hydraulic resistance of pipelines from modern polymer materials, the method of theoretical determination of resistance coefficients in the VALTEC ISO 21003 metal polymer pipeline, the classification and method of determining the values of local hydraulic resistance coefficients of T-Junctions are given, the dependence for determining the Darcy λ hydraulic friction coefficient associated with the value of the equivalent hydraulic roughness coefficient of the inner surface of pipes and the Reynolds number. The experimental data of the hydraulic coefficient of friction Darcy λ was compared with the known theoretical relationships of A.D. Altschul, Colbrooke for smooth pipes, Colbrooke and White, an alternative to the Colbrooke-White, Offengenden equation for low-shear pipes and pipes from polymer materials with Reynolds numbers Re>10^4. Dependence of hydraulic coefficient of friction on relative equivalent roughness of pipeline walls and Reynolds number, specific energy loss per one linear meter on total flow rate in system of hydraulically short pipeline is obtained. The empirical dependence of values of coefficients of local resistance ζ=f(Q2/Q3) from a ratio of the divided expenses of Q2/Q3 of the equal-pass T-Junction α=90 the pipeline to a branch up, on pass in the direct T-Junction and division of streams at various internal pipeline diameters of VALTEC.