Tangential Velocity Components Research Articles

Innovative eco-friendly design solutions for energy demands using swirl- induced burner by jets

Addressing the need for innovative burner designs to optimize combustion characteristics and meet energy efficiency goals, this study introduces a novel concept rooted in swirl-induced flames. The proposed burner employs a unique approach to generate air and fuel swirl using four opposing slots in two sets, each set at distinct angles. Incorporating of a channel within the outer casing allows for fine-tuning of entry angles, optimizing the double swirling process. The objective of this research is to enhance combustion characteristics through the implementation of the swirl principle, introducing a tangential velocity component to the airflow or fuel-air mixture upon entry into the burner. Systematic measurements at various entry angles (0°, 15°, 30°, 45°, and 60°) are conducted to identify optimal or near-optimal conditions. The research covers a comparison between flow fields generated by traditional swirled vanes and swirl-induced injection ports at identical inlet conditions, revealing enhanced flame stability and combustion efficiency in the latter configuration. The formation of recirculation zones around the burner, facilitated by increased outer air jet velocities, promotes better mixing and stability. This research contributes valuable insights into burner design and optimization, with implications for improved combustion efficiency and environmental sustainability.

Thermo-hydraulic Investigation of a Heat Exchanger Tube Equipped with 3D-Printed Swirl Flow Generators

AbstractHeat transfer capabilities of the heat exchangers require enhancements to save energy and decrease their size. For this purpose, the swirl generators have been widely preferred. However, the swirler inserts have not reached their optimum shape. Thus, this study experimentally and numerically investigates the impact of novel 3D-printed swirler inserts with varying twist angles in the range of 0°–450° on the thermo-hydraulic performance of solar absorber tube heat exchangers under laminar flow (Re = 513–2054) condition. Friction factor, Nusselt number, and performance evaluation criterion (PEC) were used to assess heat exchanger performance, and related correlations are provided. Tangential velocity components were also used to explore fluid flow characteristics in local analysis. Numerical investigation was done by using computational fluid dynamics adopting Finite Volume Method in ANSYS Fluent. Results show that 3D-printed swirlers considerably increase heat transfer compared to plain tube. The swirler with a twist angle of 450° led to the maximum enhancements of nearly 217% in average Nusselt number and around 1630% in friction factor at Reynolds number of 2054. Overall, increasing Reynolds number enhanced Nusselt number. The highest PEC of 1.15 was observed at a Reynolds number of 1031 using the swirler with 150° twist angle. Flow near the swirler has higher tangential velocities, hence contributing to local Nusselt number enhancement up to 453.8% compared to plain tube when swirler with twist angle of 450° utilized. It is anticipated that findings of this study can guide further related research and increase the usage of swirlers in heat exchangers.

Electrohydrodynamic flows inside a neutrally buoyant leaky dielectric drop

We present an experimental investigation of electrohydrodynamic (EHD) flows within a neutrally buoyant drop with a radius of 2.25 mm. Utilizing particle image velocimetry and high-speed shadowgraphy, we measure the internal circulation and reported velocity profiles in the bulk and at the interface of the drop. Two leaky dielectric liquids, silicone and castor oils, are employed as the drop and as the external phase, allowing the analysis of two shape configurations: oblate and prolate. The strength of the applied uniform electric field (from 0.125 to 1.75 kV/cm) enables the analysis covering both the small-deformation limit (CaE≪1) and drops with larger deformations. Our measurements show good agreement with the leaky dielectric model (LDM) for the small-deformation cases. The flows begin at the interface as a result of jump in the electric stresses, leading then to four counter-rotating vortices inside the drop. At a permanent regime, the analytical solutions adequately predict the radial and tangential velocity components within the drop. However, a nuanced behavior is noticed for larger deformations, where the LDM theory underpredicts the internal circulation. Moreover, due to the increased deformation, a non-uniform azimuthal profile is observed for the velocity at the interface, vθ. Transient measurements of this velocity component enlighten the dynamic response of the EHD flows of the drop. Following the available analytical solutions, the dynamic response is governed by the timescale of the deformation of the drop, τdef=μa/γ. We propose a critical value of CaE≈0.1 below which the LDM adequately describes the velocity field in both quasi steady-state and transitory regimes.

Reactive collision-free motion generation in joint space via dynamical systems and sampling-based MPC

Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is constructed using continuously differentiable obstacle representations. However, state-of-the-art approaches may suffer from local minima induced by non-convex obstacles, thus failing to scale to complex, high-dimensional joint spaces. On the other hand, sampling-based Model Predictive Control (MPC) techniques provide feasible collision-free paths in joint-space, yet are limited to quasi-reactive scenarios due to computational complexity that grows cubically with space dimensionality and horizon length. To control the robot in the cluttered environment with moving obstacles, and to generate feasible and highly reactive collision-free motion in robots’ joint space, we present an approach for modulating joint-space DS using sampling-based MPC. Specifically, a nominal DS representing an unconstrained desired joint space motion to a target is locally deflected with obstacle-tangential velocity components navigating the robot around obstacles and avoiding local minima. Such tangential velocity components are constructed from receding horizon collision-free paths generated asynchronously by the sampling-based MPC. Notably, the MPC is not required to run constantly, but only activated when the local minima is detected. The approach is validated in simulation and real-world experiments on a 7-DoF robot demonstrating the capability of avoiding concave obstacles, while maintaining local attractor stability in both quasi-static and highly dynamic cluttered environments.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Theoretical approach for the equilibrium scour depth underneath a partially submerged bridge deck

The destructive implication of pressure-flow scour during flood events is a critical issue for researchers throughout the world. The current paper presents two models to estimate the pressure-flow scour depth underneath a partially submerged bridge deck in the equilibrium phase based on the jet flow theory. An estimate of the submergence distance of the jet flow under the bridge deck is the base point of the first model. The second model uses the phenomenological theory of turbulence where the tangential component of jet velocity is scaled to the velocity of the eddy formed under the bridge deck. This theory has already been used by researchers to estimate the scour depth of the jet flow. Dimensionless parameters are constructed in the theoretical framework of both models. The angle and velocity of the combined jet under the bridge deck and the effective depth underneath the bridge deck have been obtained using the relations presented in the previous research. The application of the presented models is limited to cases where the relative opening height of the bridge deck is greater than 0.25. The derived equations of the current study are calibrated based on the data with sufficient time durations. The results show that both models predict fairly well the maximum pressure-flow scour depth. The values of Nash–Sutcliffe efficiency and relative root mean square errors of the second model predictions are more appropriate, compared to the estimates of the first model and estimates obtained by equations presented in the previous studies.

CFD microscale modelling of flow behavior in different parts of a rotating packed bed

Process intensification (PI) is playing a key role in alleviating the challenge of reducing carbon footprint of many chemical processes and bringing down their development costs. Over the years, many PI technologies have been investigated with rotating packed bed (RPB) technology receiving much of the attention for its potential of significant intensification in terms of capital expenditure, operating costs, and hardware size. In this study, microscale CFD simulations of a rotating packed bed were conducted, and the results were validated with experimental data. The results show the strong relation between the reverse flow at the packing outer periphery and the gas maldistribution factor. The latter is mainly caused by the accelerating flow in the outer cavity. Inside the wire mesh packing, the gas flow is found to be almost fully uniform for nearly half of the total packing depth. Also, turbulent kinetic energy (TKE) levels at the packing outer edge are strongly linked to the slip tangential velocity component, while at its inner edge, they depend mainly on the radial packing velocity. The so-called gas end effect zone is detected by observing the TKE profiles near the packing outer edge. The latter accounts for less than 10% of the total packing depth. The validity of the widely used porous media model in RPBs’ packing for both radial and tangential directions is confirmed by the obtained results, but this excludes the packing inner and outer edges. In the inner cavity region, gas exhibits two distinctive behaviors and transits from free vortex flow to swirling flow as the flow becomes close to the vortex core. As a result of this transition, the increase in shear stress accelerates the decrease in the gas tangential velocity in the vortex core and help speed up the favorable pressure gradient and flow establishment beyond the vortex core.

Experimental investigation on the dynamics of buoyancy-induced vortices

Measurements were conducted within the flow field of a buoyancy-induced vortex at laboratory scale with a constant heat flux as input at the ground with swirl vanes set at 30° and 60° to the radial. Time-averaged velocity data were obtained using two-dimensional Particle Image Velocimetry (PIV). The velocity profiles in both cross-sectional and vertical planes were measured at heights of 0.3 m, 0.45 m, and 0.6 m above the ground level, and the time-averaged tangential, radial and vertical velocity components were derived. Two types of the vortex structures are identified based on the core swirl ratio, showing one-cell and two-cell type vortex structures with 30° and 60° swirl vane angles, respectively. Vortex wandering effects have also been investigated, including the centre distributions for different types of flow structures, and its impact on flow strength and vortex core sizes have also been quantified. Detailed turbulence statistics have been measured after removing the wandering effect, which show high level of turbulence intensities within the vortex core.

A Unified Transformation Framework for Studying Various Situations of Vertical/Oblique Drop Impact on Horizontal/Inclined Stationary/Moving Flat Surfaces

There are various situations of drop impact on solid surfaces widely occurred in natural phenomenon or used in different industrial applications. However, comparing and classifying these drop impact situations is not easy due to different states of the parameters affecting drop impact dynamics. In this article, a unified transformation framework is proposed to study various situations of vertical/oblique drop impact on horizontal/inclined stationary/moving flat surfaces with/without a crossflow. This simple framework consists of a coordinate with normal and tangential axes on a horizontal stationary surface. For each drop impact situation, the drop velocity, gravitational acceleration, possible induced flow due to the moving surface, and possible crossflow are transformed into the framework. Comparing the transformed versions of considered drop impact situations facilitates identification of their physical similarities/differences and determines which situations (and under what conditions) lead to identical results and can be used interchangeably. Although common situations of drop impact on moving surfaces (having tangential component of surface velocity) lead to asymmetric drop spreading, the possibility of symmetric drop spreading on moving surfaces is demonstrated and analyzed using the proposed transformation framework. This interesting possibility means that for related production lines or experimental setups, where symmetrical drop spreading is required, the surface does not need to be stationary. In such applications/setups, the use of moving surfaces (rather than stationary surfaces) can considerably accelerate the symmetric drop impact process. Our simulation results of several of the considered drop impact situations well confirm the facilities/predictions of the proposed transformation framework.

Understanding AP/HTPB composite propellant combustion from new perspectives

Combustion of the AP/HTPB composite propellant at the mesoscale is simulated by a partitioned numerical framework, in which the unsteady solid-phase conduction, gas-solid interface regression, and gaseous combustion are sequentially calculated on two sets of overlapped grids. The gas-solid interface is traced by the level-set method. The mass and species exchange conditions at the gas-solid interface are converted into source terms by the immersed-boundary method. Effectiveness of the entire framework is justified by applying the integrated solver to a Miller pack example. The predicted burning rates show good agreement with experimental data over a wide range of pressure conditions, and the gas-phase temperature field clearly depicts the final diffusion flame. The flame zone closely above the regressing interface can be identified by the fluctuation of the projected velocity components perpendicular to the main stream direction. Statistical results conditional on Lagrangian tracing of fluid parcels released from the AP and binder parts show distinction between the oxidizer-rich and fuel-rich flames in terms of the reaction intensity and the flame structure. Statement of SignificanceFrom the algorithm/simulation perspective: a partitioned numerical solution framework is built upon overlapped structured (for the gas phase) and unstructured (for the solid phase) meshes; the level-set approach is used on the unstructured mesh to identify solid-gas interface with complex geometry. From the analysis perspective: the flame front is newly defined in terms of the tangential velocity components; the fuel/oxidizer evolution pattern is analyzed from conditional statistics based on Lagrangian tracing; new insights in heterogeneous combustion include, for instance, effects of pressure on the tangential velocity fluctuation and flame properties conditional on different ingredients.

Stabilized immersed isogeometric analysis for the Navier–Stokes–Cahn–Hilliard equations, with applications to binary-fluid flow through porous media

Binary-fluid flows can be modeled using the Navier–Stokes–Cahn–Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological changes of the binary-fluid interface. In this work, we propose an immersed isogeometric analysis framework to solve the Navier–Stokes–Cahn–Hilliard equations on domains with geometrically complex external binary-fluid boundaries. The use of optimal-regularity B-splines results in a computationally efficient higher-order method. The key features of the proposed framework are a generalized Navier-slip boundary condition for the tangential velocity components, Nitsche’s method for the convective impermeability boundary condition, and skeleton- and ghost-penalties to guarantee stability. A binary-fluid Taylor–Couette flow is considered for benchmarking. Porous medium simulations demonstrate the ability of the immersed isogeometric analysis framework to model complex binary-fluid flow phenomena such as break-up and coalescence in complex geometries.

Cross-Diffusion and Higher-Order Chemical Reaction Effects on Hydromagnetic Copper–Water Nanofluid Flow Over a Rotating Cone in a Porous Medium

Spin coating of engineering components with advanced functional nanomaterials which respond to magnetic fields is growing. Motivated by exploring the fluid dynamics of such processes, a mathematical model is developed for chemically reactive Cu–H2O magnetohydrodynamic (MHD) nanofluid swirl coating flow on a revolving vertical electrically insulated cone adjacent to a porous medium under a radial static magnetic field. Heat and mass transfer is included and Dufour and Soret cross-diffusion effects are also incorporated in the model. Thermal and solutal buoyancy forces are additionally included. To simulate chemical reaction of the diffusing species encountered in manufacturing processes, a higher-order chemical reaction formulation is also featured. Via suitable scaling transformations, the governing nonlinear coupled partial differential conservation equations and associated boundary conditions are reformulated as a nonlinear ordinary differential boundary value problem. MATLAB-based shooting quadrature with a Runge–Kutta method is deployed to solve the emerging system. Concentration, temperature and velocity variations for various nondimensional flow parameters have been visualized and analyzed. In addition, key wall characteristics, i.e., radial and circumferential skin friction, Nusselt number and Sherwood number, have also been computed. Validation with earlier studies is also included. The simulations indicate that when compared to a lower-order chemical reaction, a higher-order chemical reaction allows a greater rate of heat and mass transfer at the cone surface. Increasing Dufour (diffuso-thermal) and Soret numbers generally reduces radial and circumferential skin friction and also Nusselt number, whereas it elevates the Sherwood number. Both skin friction components are also suppressed with increasing Richardson number. Strong deceleration in the tangential and circumferential velocity components is induced with greater magnetic field.

Improved asymptotic expansion method for laminar fluid flow and heat transfer in conical gaps with disks rotating

PurposeThe purpose of this paper was to study laminar fluid flow and convective heat transfer in a conical gap at small conicity angles up to 4° for the case of disk rotation with a fixed cone.Design/methodology/approachIn this paper, the improved asymptotic expansion method developed by the author was applied to the self-similar Navier–Stokes equations. The characteristic Reynolds number ranged from 0.001 to 2.0, and the Prandtl numbers ranged from 0.71 to 10.FindingsCompared to previous approaches, the improved asymptotic expansion method has an accuracy like the self-similar solution in a significantly wider range of Reynolds and Prandtl numbers. Including radial thermal conductivity in the energy equation at small conicity angle leads to insignificant deviations of the Nusselt number (maximum 1.23%).Practical implicationsThis problem has applications in rheometry to experimentally determine viscosity of liquids, as well as in bioengineering and medicine, where cone-and-disk devices serve as an incubator for nurturing endothelial cells.Social implicationsThe study can help design more effective devices to nurture endothelial cells, which regulate exchanges between the bloodstream and the surrounding tissues.Originality/valueTo the best of the authors’ knowledge, for the first time, novel approximate analytical solutions were obtained for the radial, tangential and axial velocity components, flow swirl angle on the disk, tangential stresses on both surfaces, as well as static pressure, which varies not only with the Reynolds number but also across the gap. These solutions are in excellent agreement with the self-similar solution.

Numerical Simulation and Characterization of Swirl Fluid Motion through Cylindrical Chambers

Axisymmetric solution of radial, axial and tangential components of velocity of flow through a cylindrical chamber with an inflow containing swirl and outflowis investigated numerically using Finite Volume Method. An in-house developed computer code for solving the three components of velocity and pressure is developed and validated using experimental data available from literature on the problem of axial vortex breakdown of confined flow in a cylinder due to rotation of one of the end walls. The code uses a staggered approach and fractional step projection method for decoupling the velocity and pressure. The convection and diffusion terms are approximated using a second-order accurate central difference scheme. This paper discusses the characteristics features of flow such as mixing streams, streams of fluid flowing close to the solid walls (cooling streams), swirl motion and development of flow structures.

A numerical investigation of debris initialisation in tornado-like wind fields

The process of debris initialisation is examined for two tornado-like vortices with swirl ratios (S) of 0.3 and 0.7. The vortices were modelled using Large-eddy Simulation and the motion of spherical debris were calculated using Lagrangian-particle tracking. A total of 2700 individual debris particles, corresponding to three different groups (A, B and C) with different Tachikawa numbers (K=2.5, 1.2 and 0.6 respectively) were released. The vortex S=0.7 has greater magnitude of tangential velocity (∼12.7 m/s) compared to vortex S=0.3 (∼11.7 m/s). The corresponding maximum vertical velocities in the flow when S=0.3 were approximately twice those corresponding to S=0.7; this resulted in longer flight durations for debris group A, B and C, i.e., 65%, 73% and 58% longer respectively. An analysis of the spatial displacement of the vortex centre relative to the centre of the simulator shows that both vortices have a maximum displacement of less than 0.02 m. This suggests that the low wandering motions of the vortices have minimum effect on the debris initialisation. The vertical velocity component is shown to be key for the generation and sustaining of debris flight. For example, for S=0.3, approximately 22% (group A), 5% (group B) and 10% (group C) more particles were being initialised compared to S=0.7. The ensemble averaged flow fields associated with flight initiation show the greatest difference at low elevation (less than 0.11 m) compared to non-initialising conditions. It was also found that the tangential and radial velocity components have relatively little impact on flight initialisation. The findings presented in this research provide a fundamental insight into the physics which govern debris initialisation in tornado-like flow.

PROTECTING THE ENVIRONMENT AROUND POLISH QUARRIES FROM HARMFUL SEISMIC VIBRATIONS CAUSED BY ROCK BLASTING

The paper presents the legal and scientific conditions for Polish researchers to determine the vibration velocity and the radius of the safe zone of seismic vibrations generated during rock blasting. Until now, in Poland and worldwide, it has been assumed that seismic vibrations generated during rock blasting with explosives [BM] propagate circularly with equal energy in each direction. However, this is not always the case. A theoretical analysis of the variation of the tangential magnitude Vy of the vibration velocity as a function of the change of the direction angle was carried out for a circular distribution of the vibration velocity. It was shown that the value of the vibration velocity component at the same distance from the vibration source depends on the directional angle between the line of the blast holes and the line connecting the centre of the surface of the excavated BM block and the measuring point. New relationships have been given that take into account the directional angle in the calculation of the maximum values of vibration velocity necessary for the determination of the resulting damage in the building from the SWD. A dynamic impact scale [SWD] for the assessment of building damage as the vibration velocity acting on the building increases is given and discussed. Vibration velocity diagrams measured during the excavation of BM rock have been presented for circular distributions in accordance with theoretical predictions. A vibration velocity diagram for an elliptical distribution, inconsistent with a circular distribution, measured during the excavation of BM rock is presented. It is shown that the directionality of the horizontal tangential component of the vibration velocity exists for both circular and elliptical distribution of vibration velocity in rock excavation with explosive BM. The technical safety of the building in the area of seismic vibrations is determined by the vibration velocity included in zone II of the scale of dynamic influences [SWD] Fig.6A ,6B.

Global Stability Analysis of the Interaction Between a Longitudinal Vortex and an Oblique Shock Wave

AbstractIn this study, the interaction of a longitudinal vortex with an oblique shock was studied numerically. A global stability approach was used to investigate the onset of unsteadiness due to vortex breakdown. For this purpose, steady and unsteady laminar flow simulations were performed. A longitudinal vortex with an exponentially decaying tangential velocity profile, a so‐called Erlebacher vortex, was introduced into the flow field by a modification of the inflow boundary, while the oblique shock was created by a ramp in supersonic flow. Parametric studies concerning the influence of the axial velocity deficit and the tangential velocity component on the stability of the vortex were performed. Several amplified global eigenmodes could be identified and it could be shown that the frequencies predicted by the global stability analysis were in reasonable agreement with dominant frequencies observed in the unsteady simulations.

ВЗАИМОДЕЙСТВИЕ И ДИНАМИКА ТОПОЛОГИЧЕСКИХ ДЕФЕКТОВ В ДОМЕННОЙ СТРУКТУРЕ ЗАКРУЧЕННОГО НЕМАТИКА

The dynamics and interaction of topological defects in the domain structure of π/2 twisted nematic liquid crystal are studied. A feature of Williams domains in twisted nematics is that hydrodynamic flows in them, along with the tangential velocity component, also have an axial component, the direction of which is opposite in neighboring domains. The axial velocity component arises as a result of the strong coupling between the initial twisted director orientation n and the hydrodynamic flow velocity. In domain structures of π/2 twisted nematics, as well as in planar oriented ones, edge dislocations with topological charges S =±1 arise. With increasing applied voltage density of dislocations grows. Dislocations move both along the Williams domains ( climb ) and perpendicular to them ( glide ). At a certain rate of the increasing applied voltage U > U c, distortions of the domain structure begin to propagate on both sides of the defect core. This leads to the formation of a special topological defects - dislocations with a “diffused” core, or linear defects, which are oriented perpendicular to the Williams domains and move mainly along them. The arising linear defect has the same topological charge as the initial dislocation. It is shown that their interaction is qualitatively well described by the perturbed sine-Gordon equation.

Technical safety of buildings around polish quarries against harmful seismic vibrations caused by rock blasting

This paper presents the results of measurements of the elliptical distribution of seismic vibrations generated during rock blasting.The technical safety of a building in the area of seismic vibrations is determined by the vibration velocity that does not exceed the line B included in zone II of the scale of dynamic influences [SWD]. The hypothesis proved in the paper is that for both elliptical and circular distributions of the vibration velocity in rock mining with blasting material [BM] there is a directionality of the horizontal radial component Vx and the tangential component Vy of the vibration velocity.The magnitude of the components Vx and Vy of the vibration velocity at the same distance from the vibration source depends on the directional angle "α" between the line of the blast holes and the line connecting the centre of the surface of the rock block being mined with [BM] and the place of measurement. The elliptical shapes of the graphs Vx and Vy obtained during the mining of the BM of the basalt deposit, which depend on the value of the directional angle, were compared with the shape of the circular velocity graphs Vx and Vy. New correlations are given that take into account the directional angle when calculating the maximum vibration velocity values needed to determine the damage caused to a bulding by the SWD.A dynamic impact scale [SWD] for the assessment of building damage as the vibration velocity acting on the building increases is given and discussed. Vibration velocity diagrams measured during the excavation of BM rock are presented for circular distributions in accordance with theoretical predictions. A vibration velocity diagram for an elliptical distribution, inconsistent with a circular distribution, measured during the excavation of BM rock is presented. It is shown that the directionality of the horizontal radial and tangential components of vibration velocity exists for both circular and elliptical distribution of vibration velocity in rock excavation with BM. In the conclusions, for the elliptical velocity field of the vibrations, the conditions to be observed in order to be able to direct the smallest vibrations towards the built up area are given.

A nonsmooth optimization approach for time-dependent hemivariational inequalities

This paper is devoted to the study of time-dependent hemivariational inequality. We prove the existence and uniqueness of its solution, provide a fully discrete scheme, and reformulate this scheme as a series of nonsmooth optimization problems. The introduced theory is later applied to a sample quasistatic contact problem that describes a viscoelastic body in frictional contact with a foundation. This contact is governed by a nonmonotone friction law with dependence on the normal component of displacement and the tangential component of velocity. Finally, computational simulations are performed to illustrate the obtained results.