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The study of non-stationary vortex structures arising at the inlet of centrifugal pumps and at the outlet of turbines of the Kaplan and Francis type is the subject of the presented paper. Specific attention will be paid to spatial vortices, characterized by curvature and twist. Spiral vortices will also be monitored as sources of spatial vortex motion. Their core will be expressed by a mathematical model in curvilinear coordinates. Helicity, which indicates the degree of vorticity, will also be determined by computational simulation of turbulent motion. The swirling motion will be induced by a specially designed diffuser-shaped vortex generator, simulating the inlet to the turbine draft tube. A significant result of the study of vortex structures will be the dependence of the twist of the streamline in relation to the Hessian matrix, expressed as a function of the pressure function. This dependence will be significant for the optimization of the hydraulic machines.

The work presents four methods for assessing the stability of stationary vortex structures in multiple continuous regions. First one is based on linearized Navier - Stokes equations using modal analysis. The second method considers non-linear equations and is focused on the stability of the stationary flow at the inner point of the region. The third method is focused on the qualitative analysis of the dependence of an input power, performance and dissipation function. The fourth method is based on the analysis of the potential energy of the flowing liquid. Each of the mentioned methods will be described by a mathematical model, from which it will be possible to assess the influence of boundary conditions and the shape of the area on the mentioned stability.

A new knowledge of fluid flow on hydrophobic surface will be presented. The boundary condition will be refined considering the effects of air adhering to the rough, hydrophilic surface. Possibilities of turbulent viscosity effects as a result of liquid slippage on the hydrophobic surface will also be considered. These effects will be demonstrated on the basis of performed experiments. The experimental study will be focused on the determination of the pressure difference in the tube, whose surface is provided with an ultrahydrophobic coating with a contact angle higher than 140 °. Results will be reported based on Reynolds number. In addition to the results of the experiment, the thesis will also include a theoretical study aimed at refining the boundary condition, expressing the interaction of the liquid with the hydrophobic surface. In conclusion, the dissipation function will be derived, expressing the effects of liquid slippage on the hydrophobic surface and compared with its value taking into account the hydrophilic properties of the surface.

The report examined new scientific approaches to the creation of a combined cogeneration energy complex based on small or micro-hydropower. The most effective approaches to micro-hydropower facilities were considered to create a workable structural layout. A criterion has been developed that allows to evaluate the energy efficiency of hydroturbines at an early stage of design using the calculation method, including a predictive estimate of the hydraulic resistance function ξHT = f(Re) of a particular penstock geometry. The results of the theoretical task of creating a technologically advanced configuration of a blade system using Zhukovsky theory. By calculating and numerically (CFD) simulating the hydrodynamic lattices of flat profiles, the theoretical nomograms for determining the coefficients Cx and Cy are confirmed and supplemented. A series of comparative results of computational and experimental studies of the combined energy complex hydraulic part – microhydroturbines with experimental blade systems, including those modified by the principle of biomimetics (nature imitation technologies) is presented. Based on the calculated and experimental studies, the prospects of the chosen direction of development of small and microhydroenergy are shown, as well as the effectiveness of the approaches that were used in the design of the working bodies of microhydroturbines.

The research of liquids composed of two (or more) mutually immiscible components is a new emerging area. These liquids represent new materials, which can be utilized as lubricants, liquid seals or as fluid media in biomechanical devices. The investigation of the problem of immiscible liquids started some years ago and soon it was evident that it will have a great application potential. Recently, there has been an effort to use ferromagnetic or magnetorheological fluids in the construction of dumpers or journal bearings. Their advantage is a significant change in dynamic viscosity depending on magnetic induction. In combination with immiscible liquids, qualitatively new liquids can be developed for future technologies. In our case, immiscible fluids increase the dynamic properties of the journal hydrodynamic bearing. The article focuses on the stability of single-phase and subsequently multiphase flow of liquids in the gap between two concentric cylinders, one of which rotates. The aim of the analysis was to study the effect of viscosity and density on the stability/instability of the flow, which is manifested by Taylor vortices. Methods of experimental and mathematical analysis were used for the analysis in order to verify mathematical models of laminar and turbulent flow of immiscible liquids.

This work is focused on calculating the force effects of an incompressible homogeneous liquid on a surface of a rigid or a flexible tube. An unsteady flow induced by differential pressure at the beginning and at the end of the tube is assumed. The pressure difference for the unsteady flow is determined experimentally. The mathematical model is based on modified Navier-Stokes equations. The unsteady term is modified in order to be able to use the Gauss-Ostrogradsky theorem to calculate the force. This method of solution will allow the calculation of the force by integration of the Navier-Stokes equations, which will help to refine and simplify the calculations. In the article, both methods of force calculation will be presented and compared both through the ANSYS FEA and CFD ANSYS Fluent solvers and by the integration of the Navier-Stokes equation. The calculation will not only respect the compliance of the tube but also its movement status.

The article is focused on calculating the force effects of a heterogeneous liquid on pipe walls. The solution is based on the concentration of solid particles. The base fluid is assumed to be incompressible. The solution will apply Euler-Lagrange's solution principle. Two tasks will be solved; with a rigid and a flexible tube wall. The solution will be carried out with non-stationary boundary conditions that were determined experimentally. Interaction of a heterogeneous fluid with a flexible wall assumes its deformation. The force effects will be solved by two methods; FSI simulation using ANSYS FEA solvers and CFD solvers ANSYS Fluent and using Navier-Stokes equations by direct integration through liquid volume. In this case, the unsteady term of the Navier-Stokes equations will be modified so that the Gauss Ostrogradsky theorem can be used to calculate the force. At the end, the force effects on the rigid and compliant wall will be compared with the unsteady turbulent flow of the heterogeneous liquid.

Solution of both laminar and turbulent flow with consideration of hydrophobic surface is based on the original Navier assumption that the shear stress on the hydrophobic surface is directly proportional to the slipping velocity. In the previous work a laminar flow analysis with different boundary conditions was performed. The shear stress value on the tube walls directly depends on the pressure gradient. In the solution of the turbulent flow by the k-ε model, the occurrence of the fluctuation components of velocity on the hydrophobic surface is considered. The fluctuation components of the velocity affect the size of the adhesive forces. We assume that the boundary condition for ε depending on the velocity gradients will not need to be changed. When the liquid slips over the surface, non-zero fluctuation velocity components occur in the turbulent flow. These determine the non-zero value of the turbulent kinetic energy K. In addition, the fluctuation velocity components also influence the value of the adhesive forces, so it is necessary to include these in the formulation of new boundary conditions for turbulent flow on the hydrophobic surface.

Additional effect of fluid on the solid body is often ignored phenomenon. Although it is possible to do an analytic derivation of equations describing additional effects for many various conditions, it can be difficult to solve them. The paper shows pressure pulsations in the pipe with piston solved by transfer matrix and harmonic analysis with ANSYS Acoustics, where effect of second viscosity is included.

Technological solution, frequently used to suppress vibrations in rotating machines, consists in adding damping devices between the rotor and its frame. This is enabled by dampers working on the principle of a squeezing thin classical or magnetorheological fluid film. The Navier-Stokes equations, Reynolds equation, and modified Navier-Stokes equations are used to determine the pressure distribution in the thin fluid film. The damping and stiffness coefficients are computed by the developed procedure presented in this paper. The proposed computational approach is based on the perturbation of the synchronous circular whirling motion. The carried-out computational simulations show that the investigated mathematical models of the squeeze film damper and magnetorheological squeeze film damper allowed computation of the damping and stiffness coefficients. It has been found that the stiffness coefficients computed by the proposed mathematical models may be different.

The production and use of manufactured chemicals have risen significantly in the last few decades. With interest in preserving and improving the state of the environment, there is also growing interested in new technologies for water purification and wastewater treatment. One frequently discussed technological group is advanced oxidation processes (AOPs). AOPs using sulphur-based radicals appear to reduce the volume of organic contaminants in wastewater significantly. The use of persulfate has excellent potential to successfully eliminate the number of emerging contaminants released into the environment. The main disadvantage of sulphur-based AOPs is the need for activation. We investigated an economically and environmentally friendly solution based on hydrodynamic cavitation, which does not require heating or additional activation of chemical substances. The method was evaluated for emerging contaminant removal research, specifically for the group of steroid estrogens. The mixture of estrone (E1), 17β-estradiol (E2), estriol (E3), and 17α-ethinylestradiol (EE2) was effectively eliminated and completely removed during a treatment that lasted just a few seconds. This novel method can be used in a broad spectrum of water treatment processes or as the intensification of reactions in chemical engineering technologies. [ABSTRACT FROM AUTHOR]

This work is focused on reduction of swirling in cases from hydraulic machinery and, thus, mitigation of instabilities associated with swirling flow. We study this problem analytically using the torque integral equation, numerically using computational fluid dynamics (CFD) simulations, and experimentally using a swirl generator that generates swirling flow approximating that in a draft tube of a hydro turbine operating at a part load, featuring an unsteady spiral vortex—the vortex rope. The analytical description elucidates the effect of different installations on the circumferential velocity. Unconventional conical perforated installations targeting at increasing the dissipation were proposed and tested. The rather unsatisfactory results led to proposing fins placed unconventionally away from the wall, closer to the diffuser axis, which were subsequently shown to be able to reliably suppress the unsteady vortex rope. Their effect is documented by an analysis of CFD results including the proper orthogonal decomposition as well as experimental observations and measurements. [ABSTRACT FROM AUTHOR]

The work is divided into theoretical and experimental parts. In the theoretical part the viscous forces performance for both laminar as well as turbulent flow of compressible fluids are defined. It is split into the viscous forces useful power and the power corresponding to mechanical losses. This part is expressed by the dissipation function. It is shown that the dissipation function considering hydrophobic surfaces cannot be determined from the pressure difference. It is necessary to take into account the slip of the liquid over the hydrophobic surface which depends on the value of surface energy. The values of surface energy for different types of hydrophobic surfaces, obtained by experiment, are shown within this work. The new definition of the dissipation function for hydrophobic surfaces is presented depending on the adhesion coefficient, also determined by an experiment. The theoretical part of the work is complemented by experiment. The experiment is aimed at the differential pressure measurement in a circular cross section pipe. The results are processed for both laminar and turbulent stationary flow in relation to the flow. Both hydrophilic and hydrophobic surfaces and their mutual correlation are taken into consideration. On the basis of the new mathematical model for hydrophobic surfaces the value of dissipation function is determined depending on the slip velocity of the liquid along the hydrophobic surface.

Hydrodynamic cavitation in single and multihole orifices was experimentally investigated to assess their hydraulic characteristics: loss coefficients, inception cavitation number, cavitation number for transition to supercavitation. Significant difference for singlehole and multihole orifices was observed in terms of the measured loss coefficient. It is significantly more effective to use multihole orifices, where energy dissipation is much lower.It was found that using scaling factor given by ratio of orifice thickness suggests linear behaviour of both loss coefficient and inception cavitation number. Orifices seem to be convenient choice as flow constriction devices inducing cavitation due to their simplicity.

The results of research on viscous liquid flow upon a superhydrophobic surface are presented in the paper. In the introduction, the degrees of surface hydrophobicity in correlation with an adhesion coefficient are defined. The usage of the adhesion coefficient for the definition of a new boundary condition is employed for expressing the slip of the liquid over the superhydrophobic surface. The slip of the liquid was identified on a special experimental device. The essence of the device consists of a tunnel of rectangular cross section whose one wall is treated with a superhydrophobic layer. The other walls are made of transparent organic glass whose surface is hydrophilic. Velocity profiles are measured by PIV. The methodology is drawn so that it allows the speed determination at the closest point to the wall. The measurements were performed for different Reynolds numbers for both laminar and turbulent flow. Based on the measured velocity profiles, marginal terms of use have been verified, expressing slippage of the liquid on the wall. New forms of velocity profiles considering superhydrophobic surfaces are shown within the work.

The article deals with a side channel turbine, which can be used as a suitable substitute for a pressure reducing valve. Reducing valves are a source of hydraulic losses. The aim is to replace them by a side channel turbine. With that in mind, hydraulic losses can be replaced by a production of electrical energy at comparable characteristics of the valve and the turbine. The basis for the design is the loss characteristics of the valve. Thereby creating a kind of turbine valve with speed-controlled flow in dependence of runner revolution.

Contribution is focused on discussion of different design modifications of the volute, impeller and rotor-stator cavity in case of very low specific speed pump with recirculation channels. Amount of the liquid flowing through the recirculation channels has significant effect on delivery height, stability of the head curve and hydraulic efficiency. Analysis of these effects is based on the evaluation of the dissipated power in different internal parts of the pump and for different flow rates. It has already been proved in our previous research that volute has substantial impact on stability of the head curve. It is apparent that similar effect can also be attributed to distribution and shape of the recirculation channels. This fact is connected with the inflow into the channels and with magnitude of the flow rate through the recirculation channels. Influence of mentioned parameters on recirculation is discussed in present paper.

Contribution is focused on modification of low-specific speed pump impellers with respect to stability of their Y-Q curves (i.e. head curves). The design modifications are driven by analysis of the dissipated power. First, dissipated power is evaluated by CFD software in individual working parts of the pump and then its dependence on flow rate is investigated. Pressure fields within the pump are also carefully examined. Special attention is paid to impellers and configuration of the blade channels and recirculating channels. Results point to significant influence of the proper inflow to recirculating channels and also to role of the volute, which is more pronounced than in conventional impellers. All integral characteristics from CFD simulations are verified experimentally.

Deficit of air in water causes complications with cyanobacteria mainly in the summer months. Cyanobacteria is a bacteria that produces poison called cyanotoxin. When the concentration of cyanobacteria increases, the phenomena „algal bloom“ appears, which is very toxic and may kill all the organisms. This article describes new equipment for aeration of water in dams, ponds and reservoirs with small depth. This equipment is mobile and it is able to work without any human factor because its control is provided by a GPS module. The main part of this equipment consists of a floating pump which pumps water from the surface. Another important part of this equipment is an aerator where water and air are blended. Final aeration process runs in the nozzles which provide movement of all this equipment and aeration of the water. Simulations of the flow are solved by multiphase flow with diffusion in open source program called OpenFOAM. Results will be verified by an experiment.

This contribution is focused on analysis of pressure losses in spiral case of centrifugal pump with thick trailing edges and with recirculation channels. Recirculation channels have different geometrical configuration and influence the size of available specific energy as well as hydraulic efficiency. Subsequently, the contribution analyses the flow in spiral case itself with respect to its function and its filling with liquid. Studied phenomena affect the research of pumps with low specific speed, the stability of specific energy characteristic curves and also the configuration of recirculation channels.

The article contains mathematical models of Reynolds equation with the effects of hydrophobicity of surface and magnetic field. The first section provides a new mathematical model of the solution of the generalized Reynolds equation and its application for a hydrophilic surface. It also derives a new boundary condition for the contact of a flowing liquid with a hydrophobic surface. This wettability condition is defined in dependence on the adhesion coefficient k. The second part presents mathematical models of Reynolds equation including the effect of hydrophobia and magnetic field. For all problems, the solutions are shown and the definitions of the stiffness and damping matrices of the liquid layer are outlined. From the results, it can be deduced that hydrophobic surface significantly affects the velocity profile of the liquid. It leads to a higher effect of the Lorentz force and thus of the magnetic field in comparison with a hydrophilic surface of the bearing lining. [ABSTRACT FROM AUTHOR]

A new model for calculation of the velocity field in a pump meridian is presented in this paper. It is a parameterized rotational flow model providing the pump designer with an option to simulate various flow conditions at the blade leading edge using a single parameter, which leads to different blade designs. Despite being rotational, this flow model does not allow for creation of helical swirl structures, a feature that is usually sought to be suppressed in a pump impeller. A condition for a flow pattern suitable for a pump hydraulic design is derived using curvilinear coordinates. The variation of the meridional velocity for different choices of the parameter is demonstrated, and the meridional flow field is compared against the turbulent flow. The resulting velocity field is easy to obtain and provides a unified approach to determine the distribution of the blade inlet angles along the leading edge for a range of design requirements. [ABSTRACT FROM AUTHOR]

The work is focused on the study of bulk viscosity of liquids. The methodology is based on non-equilibrium thermodynamics. Using its laws the irreversible stress tensor is derived and two viscosities depending on the strain rate tensor deviator and spherical strain rate tensor are defined. By analysis of pressure wave distribution, the bulk viscosity of water is determined. [ABSTRACT FROM AUTHOR]

The convolute equation of the gel structure as a rheology material is presented in the paper. The convolute equation is expressed in the memory dependence as a linear model in the first case. This model is compound of reversible and irreversible parts that characterize the stress tensor. The dependence is formulated by the convolution integral. Next model considers the nonlinearity between certain characteristic stress and the strain rate. Another part of the paper is the methodology concept of the gel memory determination and the volumetric compressibility modulus definition. The gels usage is assumed as well in the biomedical engineering as in the engineering industry, for example for the noise and shocks elimination and the special sleeve bearings design. [ABSTRACT FROM AUTHOR]

This article is focused on the derivation of constitutive equations for magnetic liquids. The results can be used for both ferromagnetic and magnetorheological fluids after the introduced simplifications. The formulation of constitutive equations is based on two approaches. The intuitive approach is based on experimental experience of non-Newtonian fluids, which exhibit a generally non-linear dependence of mechanical stress on shear rate; this is consistent with experimental experience with magnetic liquids. In these general equations, it is necessary to determine the viscosity of a liquid as a function of magnetic induction; however, these equations only apply to the symmetric stress tensor and can only be used for an incompressible fluid. As a result of this limitation, in the next part of the work, this approach is extended by the asymmetry of the stress tensor, depending on the angular velocity tensor. All constitutive equations are formulated in Cartesian coordinates in 3D space. The second approach to determining constitutive equations is more general: it takes the basis of non-equilibrium thermodynamics and is based on the physical approach, using the definition of density of the entropy production. The production of entropy is expressed by irreversible thermodynamic flows, which are caused by the effect of generalized thermodynamic forces after disturbance of the thermodynamic equilibrium. The dependence between fluxes and forces determines the constitutive equations between stress tensors, depending on the strain rate tensor and the magnetization vector, which depends on the intensity of the magnetic field. Their interdependencies are described in this article on the basis of the Curie principle and on the Onsager conditions of symmetry. [ABSTRACT FROM AUTHOR]

This paper deals with a mathematical modeling of flow stability of Newtonian and non-Newtonian fluids in the gap between two concentric cylinders, one of which rotates. A typical feature of the flow is the formation of a vortex flow, so-called Taylor vortices. Vortex structures are affected by the speed of the rotating cylinder and the physical properties of the fluids, i.e., viscosity and density. Analogy in terms of viscosity is assumed for non-Newtonian and magnetorheological fluids. Mathematical models of laminar, transient and turbulent flow with constant viscosity and viscosity as a function of the deformation gradient were formulated and numerically solved to analyze the stability of single-phase flow. To verify them, a physical experiment was performed for Newtonian fluids using visualizations of vortex structures—Taylor vortices. Based on the agreement of selected numerical and physical results, the experience was used for numerical simulations of non-Newtonian magnetorheological fluid flow. [ABSTRACT FROM AUTHOR]

In this paper, new forms of Maxwell's equations in vector and scalar variants are presented. The new forms are based on the use of Gauss's theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms. [ABSTRACT FROM AUTHOR]

Cyanobacterial water blooms represent toxicological, ecological and technological problems around the globe. When present in raw water used for drinking water production, one of the best strategies is to remove the cyanobacterial biomass gently before treatment, avoiding cell destruction and cyanotoxins release. This paper presents a new method for the removal of cyanobacterial biomass during drinking water pre-treatment that combines hydrodynamic cavitation with cold plasma discharge. Cavitation produces press stress that causes Microcystis gas vesicles to collapse. The cyanobacteria then sink, allowing for removal by sedimentation. The cyanobacteria showed no signs of revitalisation, even after seven days under optimal conditions with nutrient enrichment, as photosynthetic activity is negatively affected by hydrogen peroxide produced by plasma burnt in the cavitation cloud. Using this method, cyanobacteria can be removed in a single treatment, with no increase in microcystin concentration. This novel technology appears to be highly promising for continual treatment of raw water inflow in drinking water treatment plants and will also be of interest to those wishing to treat surface waters without the use of algaecides. [ABSTRACT FROM AUTHOR]

The present paper investigated the potential of hydrodynamic cavitation (HC) as an effective tool for activating sodium percarbonate (SPC). The method's efficiency was demonstrated by effectively removing estrogens, which are pollutants that have adverse impacts on aquatic ecosystems. The effects of the SPC concentration, temperature of solution, and cavitation time were evaluated. After SPC/HC treatment, the removal of estrogens was monitored by liquid chromatography-tandem mass spectrometry (LC -MS/MS). Already after 4 s of treatment and 24 h of reaction time, more than 97% of estrogens (initial concentration of 300 ng/L) were removed. The effect of post-treatment time is not considered in several papers, even though it seems to be crucial and is discussed here. The results were supported by the values of degradation rate constants, which fit the pseudo-first-order kinetic model. We also verified that HC alone was not effective for estrogen removal under the selected conditions. The sustainability of the SPC/HC system was evaluated based on electric energy per order calculation. The combination of SPC and HC is a promising approach for rapidly degrading micropollutants such as estrogenic compounds without the need for additional technological steps, such as pH or temperature adjustment.