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Part I: Vortical flows over spinning cones at angles of incidenceThe aerodynamic performance of conically-shaped bodies are directly influenced by the flowsaround them. Flows over stationary cones develop symmetric trailing vortices near their leewardsurface, where any induced lateral forces are neutralized; however, a cone spinningabout its axis breaks the symmetry, resulting in unequal lateral forcing. To the author’sknowledge, there are no comprehensive experimental studies that characterize the asymmetricvortex systems behind spinning cones, a flow problem that has many implications on thetrajectory and stability of spin-stabilized bodies. Moreover, the laminar-turbulent transitionwithin the boundary layer has significant implications on skin friction and drag for incompressibleflows; over spinning cones, transitions form as circular and spiral waves resultingfrom cross-flow and centrifugal instabilities. To date, the effects of large angles of incidenceon the laminar-turbulent transition are not well-understood.Vortical flows over spinning cones with half-angles 10 (deg) ≤ θc ≤ 45 (deg) at angles of incidence, 0 ≤ α ≤ 36 (deg), are visualized using a smoke-wire technique, and measurements of the flows are made using a planar particle image velocimetry technique. The Reynolds numbers for all cones are O(10,000) and the range of rotational speed ratios is 1 ≤ |S| ≤ 3. Symmetric vortex triads composed of primary, secondary, and tertiary vortices are aligned parallel with the leeward surface of nonspinning cones at sufficient angles of incidence, α ≳ θc. The triads grow in size and strength as they are continuously fed by the adjacent shear layer. Asymmetries in vortex systems over spinning cones are characterized by anti-cyclonic vortices in the counter-rotating meridian and cyclonic vortices in the co-rotating meridian. Generally, the anti-cyclonic vortices grow as they embrace the surface of the cone and are pushed in the direction of rotation. At sufficient distances from the vertex of the cone, the anticyclonic vortices burst and initiate turbulent events downstream. Contrarily, cyclonic vortices readily detach from the leeward surface and cease to grow as they are cut off from the vorticity supply; an increase in SD or α expedites the detachment of cyclonic vortices.Distinct behaviours of the cyclonic and anti-cyclonic vortices arise for flows over the most slender cone, θc = 10 (deg). The distinction is attributed to vortex triads forming in closer vicinity to one another as the half-angle of the cone decreases. For θc = 10 (deg), cyclonic vortices are significantly influenced by the induced flows of the anti-cylonic vortices; they are pulled past the plane of symmetry into the counter-rotating meridian and smothered between the anti-cyclonic vortex triad and the surface of the cone, initiating detachment of anti-cyclonic vortices. Distinct flows are also observed over the largest half-angle cone corresponding to θc = 45 (deg). At nonzero angles of incidence, the stagnation point departs from the vertex of the cone and monotonically shifts along the windward surface. Low-speeds are measured near the vertex of the cone at zero incidence, resembling stagnation flows near the central axis of a disc. Regular vortex shedding events in the wake region are detected in the flow visualizations, a common characteristic of flows over discs and, more generally, bluff bodies.Boundary layer instabilities are detected and studied in the smoke streakline images. Regularly spaced wave patterns and small-scale wavy rolls consistently mark streaklines near the surfaces of the cones. The rolls form near the leeward surface of spinning cones and in streaklines ingested deep within the rotating boundary layer; hence, they are likely signatures of centrifugal spiral wave instability. The rolls leave small-scale waves on detached portions of trailing vortices that deteriorate their coherency. Contrarily, angled wave patterns form on streaklines over the entire surface of the cones in both nonspinning and spinning cases; hence, they indicate signatures of cross-flow instabilities. The flow visualizations of boundary layer instabilities primarily serve as motivation for future, more comprehensive studies.Part II: Vortical flows over a spinning disc at incidenceFlows normal to the surface of stationary discs exhibit periodic motions in their wakes attributed to vortex shedding events. The present study reveals and characterizes, for the first time, the origins of the shedding vortices near the upstream surface of a disc. Flows are studied over a disc at incidence angles between 0 and 36 (deg), both fixed and spinning with a rotational speed ratio of 2, and the Reynolds number of 27,000. A smoke-wire technique is used for flow visualization and planar particle image velocimetry for measurements near the plane of symmetry. Coherent vortical structures are observed near the upstream surface of the disc over the full range of the incidence angle. As the structures grow in size, they align themselves parallel to the surface of the disc and shed into the wake region. Two vortex shedding modes are observed. The first is dominant at low angles of incidence, up to ∼ 18 (deg). At the limiting case of normal flow, the vortical structures shed into the wake at the Strouhal number of about 0.2. At incidence beyond 18 (deg), a secondary mode becomes dominant that appears as a soliton on the vortical structures. It originates near the leading edge of the disc, traverses towards the trailing edge, and sheds into the wake region nearly twice as frequent as the first mode. The flows over spinning discs generally mimic the stationary disc flows; however, centrifugal forces affect the formation and decay of the vortical structures. Centrifugal effects leave cross-stream instability features on the vortical structures that are likely attributed to spiral wave instabilities within the boundary layer.

Fluid mechanics simulation of steady state flow in complex geometries has many applications, from the micro-scale (cell membranes, filters, rocks) to macro-scale (groundwater, hydrocarbon reservoirs, and geothermal) and beyond. Direct simulation of steady state flow in such porous media requires significant computational resources to solve within reasonable timeframes. This study outlines an integrated method combining predictions of fluid flow (fast, limited accuracy) with direct flow simulation (slow, high accuracy) is outlined that reduces computation time by an order of magnitude without loss of accuracy. A convolutional neural network (CNNs) is trained with various configurations on simulations in 2D and 3D porous media to estimate steady state velocity fields. Permeability estimation (as an average of the field) is accurate, but the velocity fields themselves are error prone, unsuitable for further transport studies. This estimate can either be used as an indicative prediction, or as initial conditions in direct simulation to reach a fully accurate result in a fraction of the compute time. Using Deep Learning predictions (or potentially any other approximation method) to accelerate flow simulation to steady state in complex structures shows promise as a technique to push the boundaries fluid flow modelling.

Nonlinear fractional differential equations (NFDEs) offer an effective model of numerous phenomena in applied sciences such as ocean engineering, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics. Some studies in control theory, biology, economy, and electrodynamics, etc. demonstrate that NFDEs play the primary role in explaining various phenomena arising in real-life. Now-a-day NFDEs in various scientific fields in particular optical fibers, chemical physics, solid-state physics, and so forth have the most important subjects for study. Finding exact responses to these equations will help us to a better understanding of our environmental nonlinear physical phenomena. In this regard, in the present study, we have applied fractional reduced differential transform method (FRDTM) to obtain the solution of nonlinear time-fractional Hirota-Satsuma coupled KdV and MKdV equations. The novelty of the FRDTM is that it does not require any discretization, transformation, perturbation, or any restrictive conditions. Moreover, this method requires less computation compared to other methods. Computed results are compared with the existing results for the special cases of integer order. The present results are in good agreement with the existing solutions. Here, the fractional derivatives are considered in the Caputo sense. The presented method is a semi-analytical method based on the generalized Taylor series expansion and yields an analytical solution in the form of a polynomial.

Heart valve fluid–structure interaction (FSI) analysis is one of the computationally challenging cases in cardiovascular fluid mechanics. The challenges include unsteady flow through a complex geometry, solid surfaces with large motion, and contact between the valve leaflets. We introduce here an isogeometric sequentially-coupled FSI (SCFSI) method that can address the challenges with an outcome of high-fidelity flow solutions. The SCFSI analysis enables dealing with the fluid and structure parts individually at different steps of the solutions sequence, and also enables using different methods or different mesh resolution levels at different steps. In the isogeometric SCFSI analysis here, the first step is a previously computed (fully) coupled Immersogeometric Analysis FSI of the heart valve with a reasonable flow solution. With the valve leaflet and arterial surface motion coming from that, we perform a new, higher-fidelity fluid mechanics computation with the space–time topology change method and isogeometric discretization. Both the immersogeometric and space–time methods are variational multiscale methods. The computation presented for a bioprosthetic heart valve demonstrates the power of the method introduced.

The impeller sealing ring in a pump is a critical component that plays an important role in reducing inner flow leakage. The nature of its design is closely related to the volumetric efficiency of the pump. This article provides details of a novel “J-shaped” impeller sealing ring design – in which the clearance length is extended through the use of a special bended structure – and explains its operating principles using fluid mechanics. In addition, a commercial double-suction split-case centrifugal pump is used to validate the new design scheme, and contractive computation results show that it offers a significant advantage in terms of volumetric efficiency, compared with conventional “L-shaped” structures. This work may provide a new, promising impeller sealing ring structure that has broad application in pumps. The first part of this article, which appears here, mainly describes background to the work, and the scheme and principles of the design. The second instalment will be published in the June 2021 issue of Sealing Technology.

According to recent trend of explosive growth of computation power and accumulated data, demand for the deep learning application in various research fields is increasing. As following this trend, remarkable achievements are presented in the experimental fluid mechanics field. One of the most outstanding research is Physics Informed Neural Networks (PINN) Raissi et al. (2020). Physical knowledge, which has been accumulated by humans, is imposed on the neural networks. PINN was used the automatic differentiation for implementing the governing equations as a physical constraint. By utilizing this concept, physical constraints make neural networks finding physical meaning of phenomena instead of simply fitting to the label data.

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. This manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

Under investigation in this paper is a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics. We derive the mixed lump-stripe waves, bright mixed rogue wave-stripe, dark mixed rogue wave-stripe and dark rogue waves solutions by virtue of the symbolic computation. We observe the fission and fusion phenomena between the lump and one-stripe wave through the mixed-stripe wave solutions. Then, we observe that the influence of l1, l2, l3, l4, l5, l6, l7 and l8 on the mixed lump-stripe waves, where l1 and l2 represent the dispersion and nonlinear effects, l3, l6, l7 and l8 are the perturbed effects, while l4 and l5 stand for the disturbed wave velocities along the transverse spatial coordinates y and z, respectively. We graphically present the interaction between a rogue wave and a pair of stripe waves through the mixed rogue wave-stripe solutions. We derive a dark mixed rogue wave-stripe when l1

The recently proposed targeted ENO (TENO) schemes (Fu et al. J Comput Phys 305:333–359, 2016) are demonstrated to feature the controllable low numerical dissipation and sharp shock-capturing property in compressible gas dynamic simulations. However, the application of low-dissipation TENO schemes to ideal magnetohydrodynamics (MHD) is not straightforward. The complex interaction between fluid mechanics and electromagnetism induces extra numerical challenges, including simultaneously preserving the ENO-property, maintaining good numerical robustness and low dissipation as well as controlling divergence errors. In this paper, based on an unstaggered constrained transport framework to control the divergence error, we extend a set of high-order low-dissipation TENO schemes ranging from 5-point to 8-point stencils to solving the ideal MHD equations. A unique set of built-in parameters for each TENO scheme is determined. Different from the TENO schemes in Fu et al. (2016), a modified scale-separation formula is developed. The new formula can achieve stronger scale separation, and it is simpler and more efficient than the previous version as the computation cost of high-order global smoothness measure $${\tau _K}$$ is avoided. The performances of tailored schemes are systematically studied by several benchmark simulations. Numerical experiments demonstrate that the TENO schemes in the constrained transport framework are promising to simulate more complex MHD flows.

In this study, a computational approach to the solution of an inverse modeling problem is developed to reconstruct unknown material properties of a Li-ion battery. In-situ MRI measurements performed on a layered graphite electrode during charging are used in comparison with Stefan-Maxwell concentrated electrolyte theory, Butler-Volmer reaction kinetics, and multiphase porous electrode theory to explore the overall accuracy of models for Li transport processes in the active material. In particular, the main research goal here is to determine if the original Cahn-Hilliard formulation for phase-separation can be improved upon through extension to a periodic bilayer model (two-layer Cahn-Hilliard). The original model contains a pair of two stable phases at low and high concentrations that produces the ``shrinking core'' behavior for lithiated graphite. The comparative advantage of the periodic bilayer model stems from the capturing of a third stable phase of intermediate concentration as the average between one concentrated layer and one dilute layer. Calibration is done simultaneously on concentration and cell voltage profiles through multi-objective optimization where the accuracy of a model is assessed based on the quantification of agreement with experimental data. The periodic bilayer model is found to improve upon the least-squares error for fitting of concentration profiles by roughly 20%, while the voltage fittings are too similar to be conclusive. Thesis Master of Science (MSc)

In an article published online in July 2018 it was stated that the algorithm proposed in the article is “enabling practical implementation of the space–time FEM for engineering applications.” In fact, space–time computations in practical engineering applications were already enabled in 1993. We summarize the computations that have taken place since then. These computations started with finite element discretization and are now also with isogeometric discretization. They were all in 3D space and were all carried out on parallel computers. For quarter of a century, these computations brought solution to many classes of complex problems ranging from Orion spacecraft parachutes to wind turbines, from patient-specific cerebral aneurysms to heart valves, from thermo-fluid analysis of ground vehicles and tires to turbocharger turbines and exhaust manifolds.

In this work, a modified Particle Method in fluid mechanics involving irregular distribution and discontinuity issues is proposed. Due to the approximation accuracy, momentum conservation and governing equation feasibility, traditional Particle Method, Moving Particle Semi-implicit (MPS) method in this paper, cannot guarantee the accuracy and stability of computation, and the divergence calculation in Navier–Stokes equation may cause numerical error in computation domain with discontinuity. To enhance the computation accuracy of Particle Method, we modify the gradient operator with a corrected tensor emanating from minimizing the local error of the first-order Taylor Expansion approximation. Besides, inspired by Peridynamic which is mostly used in solid mechanics, a new governing equation in an integral form which maintains the momentum conservation is obtained. Combining the modified gradient and new governing equation, we obtain a new particle-based method. The numerical results verify its feasibility and illustrate a good computational performance of proposed Method in the fluid dynamics involving non-uniform particle distribution.

This paper investigates water hammer flows using two- and three-dimensional (2D and 3D) numerical simulations. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations in conjunction with the...

Impedance cardiography is a non-invasive methodology for measuring cardiodynamic parameters, such as stroke volume and heart rate, as well as cardiac output. For the measurement, the electric conductivity of blood is important. The conductivity of blood depends on various parameters, such as the haematocrit value as well as the red blood cells’ (RBC) shape and orientation. In models, the response is usually affected by uncertainty, which may lead to inaccurate medical diagnosis. Therefore, a ranking of the influence of the model’s input factors may be necessary. Also, physically and physiologically correct assumptions are fundamental for the accuracy of the model. The basis for predicting the conductivity of blood in this study is the Maxwell–Fricke theory, which allows computing the electrical bulk conductivity of quiescent blood. For flowing blood, fluid mechanics has to be coupled in the modelling phase. Nevertheless, some assumptions may lead to invalid or inaccurate results. Based on a global sensitivity analysis, this work shows which fluid mechanical assumptions are incorrect and should be avoided. Moreover, positive effects based on accurate rheological modelling of the fluid properties are shown, and the factors with a decisive influence on the computed conductivity change of flowing blood are illustrated.

The present work describes and supports the methodology for the improvement of the wall model developed in AINA and its specific application to the Japanese DEMO Water Cooled Pebbled Bed. The set-up and application of this approach aims to obtain robust models by estimating the behavior of the studied systems as accurately as possible. These systems are represented in a simplified way. This requires the computation of a 3D radiation transport which has been carried out by means of MCNP6.1, ADVANTG and thermal-hydraulic calculations using ANSYS ® Fluent ® . Several CFD mesh typologies and discretizations have also been employed to test the Richardson theorem. In addition, 1D simplified models have also been created and optimized for their usage in AINA code. The temperature distribution also shows good agreement (within 7%). In some cases the simplified models have not behaved in a conservative manner compared with the outcomes obtained for the 3D models. This observed absence of conservatism is intrinsic to the 1D approach. To cope with these effects, scaling functions have been determined as a ratio between the most conservative radial temperature distribution – computed by fully detailed 3D CFD – and the 1D simplified model. The scaling functions will be applied to the AINA computed wall temperature distribution. To conclude, the determination and coherence of the result obtained using independent tools and approaches, ANSYS ® Fluent ® vs AINA thermal-hydraulic routines, lead us to recommend the proposed methodology.

Purpose The purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of nonlinear boundary value problems (NBVPs). Design/methodology/approach A major problem with the previously modified HAM, namely, predictor homotopy analysis method, which is used to predict multiplicity of solutions of NBVPs, is a time-consuming computation of high-order HAM-approximate solutions due to a symbolic variable namely “prescribed parameter”. The proposed new technique which is based on traditional shooting method, and the HAM cuts the dependency on the prescribed parameter. Findings To demonstrate the computational efficiency, the mentioned method is implemented on three important nonlinear exactly solvable differential equations, namely, the nonlinear MHD Jeffery–Hamel flow problem, the nonlinear boundary value problem arising in heat transfer and the strongly nonlinear Bratu problem. Originality/value The more high-order approximate solutions are computable, multiple solutions are easily searched and discovered and the more accurate solutions can be obtained depending on how nonhomogeneous boundary conditions are transcribed to the homogeneous boundary conditions.

In this paper, numerical investigation of three-dimensional, developing turbulent flow, subjected to a moderate adverse pressure gradient, has been investigated using various turbulence models, namely: the lowRe k  , the SST k , the 2 v f  and a variant of Reynolds stress model. The results are compared with the detailed velocity and pressure measurements. Since the inlet condition is uncertain, a study was first performed to investigate the sensitivity of the results to the inlet boundary condition. The results showed the importance of including the contraction effects. It is seen that the developing flow inside the straight duct, is highly sensitive to the inlet boundary condition. The comparisons indicate that all turbulence models are able to predict a correct trend for the centerline velocity and pressure recovery inside the straight duct and diffuser but the low-Re k  and RSM turbulence models yield more realistic results. The SST k  model largely overpredicts the centerline velocity and boundary layer thickness in the straight duct. The comparisons of the numerical results also revealed that the RSM model, due to its anisotropic formulation, is able to reproduce the secondary flows. As expected, the RSM model demonstrates the best performance in prediction of the flow field and pressure recovery in the asymmetric diffuser. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

CFD (Computational Fluids Dynamic) is an important branch of fluid dynamics. It applies various kinds of discrete mathematical method to analyze and simulate problems in fluid mechanics with the use of computer. During the computation, huge computational tasks on a single CPU often makes it very inefficient to get the result, so there is an increasing number of application of parallel computation in CFD. With more powerful computing capability and lower price, GPU (Graphic Processing Unit) has become a better solution for parallel computing than CPU in some cases in recent years. In this paper, we implemented the HSMAC and SIMPLE algorithms on GPU. For the simulation of 2D lid-driven cavity flow, the GPU version could get a speedup up to 58x and 21x respectively with double precision, and 78x and 32x with single precision, compared to the sequential CPU version. It demonstrates a good prospects of GPU acceleration of CFD algorithms.

In the computation of fluid mechanics problems with moving boundaries, including fluid-structure interaction, fluid mesh deformation is a common problem to be solved. An automatic mesh deformation technique for large deformations of the fluid mesh is presented on the basis of a pseudo-solid method in which the fluid mesh motion is governed by the equations of elasticity. A two-dimensional mathematical model of a linear elastic body is built by using the finite element method. The numerical result shows that the proposed method has a better performance in moving the fluid mesh without producing distorted elements than that of the classic one-step methods.

We present a method for structural and fluid mechanics computations of ram-air parachutes. A ram-air parachute is a parafoil inflated by the airflow through the inlets at the leading edge. It has better control and gliding capability than round parachutes. Reliable analysis of ram-air parachutes requires accurate representation of the parafoil geometry, fabric porosity and the complex, multiscale flow behavior involved in this class of problems. The key components of the method are (i) the Space–Time Variational Multiscale (ST-VMS) method, (ii) the version of the ST Slip Interface (ST-SI) method where the SI is between a thin porous structure and the fluid on its two sides, (iii) the ST Isogeometric Analysis (ST-IGA), and (iv) special-purpose NURBS mesh generation techniques for the parachute structure and the flow field inside and outside the parafoil. The ST-VMS method is a stabilized formulation that also serves as a turbulence model and can deal effectively with the complex, multiscale flow behavior. With the ST-SI version for porosity modeling, we deal with the fabric porosity in a fashion consistent with how we deal with the standard SIs and how we enforce the Dirichlet boundary conditions weakly. The ST-IGA, with NURBS basis functions in space, gives us, with relatively few number of unknowns, accurate representation of the parafoil geometry and increased accuracy in the flow solution. The special-purpose mesh generation techniques enable NURBS representation of the structure and fluid domains with significant geometric complexity. The test computations we present are for building a starting parachute shape and a starting flow field associated with that parachute shape, which are the first two key steps in fluid–structure interaction analysis. The computations demonstrate the effectiveness of the method in this class of problems.

An efficient and thorough strategy to introduce undergraduate students to a numerical approach of calculating flow is outlined. First, the basic steps, especially discretization, involved when solving Navier-Stokes equations using a finite-volume method for incompressible steady-state flow are developed with the main aim being for the students to follow through from the mathematical description of a given problem to the final solution of the governing equations in a transparent way. The well-known &lsquo, driven-cavity&rsquo, problem is used as the problem for testing coding written by the students, and the Navier-Stokes equations are initially cast in the vorticity-streamfunction form. This is followed by moving on to a solution method using the primitive variables and discussion of details such as, closure of the Navier-Stokes equations using turbulence modelling, appropriate meshing within the computation domain, various boundary conditions, properties of fluids, and the important methods for determining that a convergence solution has been reached. Such a course is found to be an efficient and transparent approach for introducing students to computational fluid dynamics.

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached, however, general algorithms&mdash, allowing a robust and accurate simulation for any process&mdash, are still missing. Either a very high computational cost is necessary for a direct numerical solution (DNS) or some limiting procedure is used by adding artificial dissipation to the system. These stabilization methods are useful, however, they are often applied relative to the element size such that a local monotonous convergence is challenging to acquire. We need a computational strategy for solving viscous fluid flow using solely the balance equations. In this work, we present a general procedure solving fluid mechanics problems without use of any stabilization or splitting schemes. Hence, its generalization to multiphysics applications is straightforward. We discuss emerging numerical problems and present the methodology rigorously. Implementation is achieved by using open-source packages and the accuracy as well as the robustness is demonstrated by comparing results to the closed-form solutions and also by solving well-known benchmarking problems.

Real-time infrared simulation technology can provide a large number of infrared images under different conditions to support the design, test and evaluation of a system having infrared imaging equipment with very low costs. By synthesizing heat transfer, infrared physics, fluid mechanics and computer graphics, a real-time infrared simulation method is proposed based on the method of characteristics to predict the infrared feature of aircraft plumes, which tries to obtain a good balance between simulation precision and computation efficiency. The temperature and pressure distribution in the under-expansion status can be rapidly solved with dynamically changing flight statuses and engine working states. And a modified C–G (Curtis–Godson) spectral band model that combines the plume streamlines with the conventional C–G spectral band model was implemented to calculate the non-uniformly distributed radiation parameters inside a plume field. The simulation result was analyzed and compared with the CFD++, which validates the credibility and efficiency of the proposed simulation method.

We present a new method for the computation of hydraulic axial thrust of Francis hydro-turbine. This approach combines the computation of axial thrust on the crown, band and blade by using the numerical simulation and calculation of the pressure distribution outside the crown and band based on the theory of fluid mechanics. The axial thrusts are calculated for different flow conditions with various suction head and flow rate. The calculated results are consistent with that of experimental test on the prototype hydro-turbine, and this combination is proven to be an effective way to assess the magnitude of hydraulic axial thrust for hydro-turbine. Also, the suction head of the turbine is shown to have significant influence on the hydraulic axial thrust.

A numerical study is conducted using a standard numerical model for a porous medium consisting of a staggered arrangement of square cylinders. Fully developed macroscopic turbulent kinetic energy a ...

The Korteweg-de Vries (KdV)-type equations have been seen in fluid mechanics, plasma physics and lattice dynamics, etc. This paper will address the bilinearization problem for some higher-order KdV equations. Based on the relationship between the bilinear method and Bell-polynomial scheme, with introducing an auxiliary independent variable, we will present the general bilinear forms. By virtue of the symbolic computation, one- and two-soliton solutions are derived.

Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite there being a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, and there are still open questions regarding the underlying physics of fluid flow, especially with respect to the continuum hypothesis and thermodynamic local equilibrium. The aim of this Special Issue is to reference recent advances in the field of fluid mechanics both in terms of developing sophisticated mathematical methods for finding solutions of the equations of motion, on the one hand, and on novel approaches to the physical modelling beyond the continuum hypothesis and thermodynamic local equilibrium, on the other.