Numerical simulations of a freely falling rigid sphere in bounded and unbounded water domains

Numerical studies were conducted on the hydrodynamics of a freely falling rigid sphere in bounded and unbounded water domains to investigate the drag coefficient, normalized velocity, pressure coefficient, and skin friction coefficient as a function of dimensionless time. The bounded domain was simulated by bringing the cylindrical water container's wall closer to the impacting rigid sphere and linking it to the blockage ratio (BR), defined as the ratio of the projection area of a freely falling sphere to that of the cross-section area of the cylindrical water container. Six cases of bounded domains (BR= 1%, 25%, 45%, 55%, 65%, and 75%) were studied. However, the unbounded domain was considered with a BR of 0.01%. In addition, the k–ω shear stress transport (SST) turbulence model was employed, and the computed results of the bounded domain were compared with those of other studies on unbounded domains. In the case of the bounded domain, which has a higher value of BR, a substantial reduction in normalized velocity and an increase in the drag coefficient were found. Moreover, the bounded domain yielded a significant increase in the pressure coefficient when the sphere was half-submerged; however, an insignificant effect was found on the skin friction coefficient. In the case of the unbounded domain, a significant reduction in the normalized velocity occurred with a decrease in the Reynold number (Re) whereas the drag coefficient increases with a decrease in Reynolds number.

Novel Analytical Solution and Type-Curves for Lost-Circulation Diagnostics of Drilling Mud in Fractured Formation

Loss of circulation is a major problem that often causes interruption to drilling operations, and reduction in efficiency. This problem often occurs when the drilled wellbore encounters a high permeable formation such as faults or fractures, leading to total or partial leakage of the drilling fluids. In this work, we present a novel semi-analytical solution and type-curves that offer a quick and accurate diagnostic tool to assess the lost-circulation of Herschel-Bulkley fluids in fractured media. Based on the pressure and mud loss trends, the tool can estimate the effective fracture conductivity, the cumulative mud-loss volume, and the leakage period. The behavior of lost-circulation into fractured formation can be assessed using analytical methods that can be deployed to perform flow diagnostics, such as the rate of fluid leakage and the associated fracture hydraulic properties. In this study, we develop a new semi-analytical method to quantify the leakage of drilling fluid flow into fractures. The developed model is applicable for non-Newtonian fluids with exhibiting yield-power-law, including shear thickening and thinning, and Bingham plastic fluids. We propose new dimensionless groups and generate novel dual type-curves, which circumvent the non-uniqueness issues in trend matching of type-curves. We use numerical simulations based on finite-elements to verify the accuracy of the proposed solution, and compare it with existing analytical solutions from the literature. Based on the proposed semi-analytical solution, we propose new dimensionless groups and generate type-curves to describe the dimensionless mud-loss volume versus the dimensionless time. To address the non-uniqueness matching issue, we propose, for the first time, complimentary derivative-based type-curves. Both type-curve sets are used in a dual trend matching, which significantly reduced the non-uniqueness issue that is typically encountered in type-curves. We use data for lost circulation from a field case to show the applicability of the proposed method. We apply the semi-analytical solver, combined with Monte-Carlo simulations, to perform a sensitivity study to assess the uncertainty of various fluid and subsurface parameters, including the hydraulic property of the fracture and the probabilistic prediction of the rate of mud leakage into the formation. The proposed approach is based on a novel semi-analytical solution and type-curves to model the flow behavior of Herschel-Bulkley fluids into fractured reservoirs, which can be used as a quick diagnostic tool to evaluate lost-circulation in drilling operations.

Experimental Study of Local Scour around Tripod Foundation in Combined Collinear Waves-Current Conditions

A series of laboratory experiments were conducted in a wave-current flume to investigate the scour evolution and scour morphology around tripod in combined waves and current. The tripod model was made using the 3D printing technology, and it was installed in seabed with three installation angles α = 0°, 90°and 180° respectively. In the present study, the scour evolution and scour characteristic were first analyzed. Then, the equilibrium scour depth Seq was investigated. Furthermore, a parametric study was carried out to study the effects of Froude number Fr and Euler number Eu on equilibrium scour depth Seq respectively. Finally, the effects of tripod’s structural elements on Seq were discussed. The results indicate that the maximum scour hole appeared underneath the main column for installation angle α = 0°, 90° and 180°. The Seq for α = 90° was greater than the case of α = 0° and α = 180°, implying the tripod suffered from more severe scour for α = 90°. When KC was fixed, the dimensionless time scale T* for α = 90° was slightly larger than the case of α = 0° and α = 180° and the T* was linearly correlated with Ucw in the range of 0.347 < Ucw < 0.739. The higher Fr and Eu both resulted in the greater scour depth for tripod in combined waves and current. The logarithmic formula can depict the general trend of Seq and Fr (Eu) for tripod in combined waves and current.

Flow around a Rectangular Cylinder Placed in a Channel with a High Blockage Ratio under a Subcritical Reynolds Number

With the depletion of fossil energy sources, clean energy has become a growing concern for scholars. Vortex-Induced Vibration Aquatic Clean Energy (VIVACE), a device that uses water flow energy to generate electricity, has attracted much attention for its broad applicability and other advantages. Particle Image Velocimetry (PIV) experiments were conducted to improve the efficiency of the VIVACE device in low-velocity areas. The present study investigated the effects of the Blockage ratio (Br), Reynolds number (Re = ρU0D/μ), and Aspect ratio (Ar = B/D, width-to-height) of rectangular cylinders on flow characteristics. The influence of the Ar, Br, and Re on the flow field structure was systematically analyzed in terms of the time-averaged flow field, Reynolds shear stress, space–time correlation, vorticity field, and water pressure characteristics. The vorticity field was deconstructed by Proper Orthogonal Decomposition (POD). The results show that the first two orders of POD modal energy accounted for 75% of the total energy, indicating that the first two modes can be used to identify the large-scale vortex structure. The main water pressure frequency and vortex shedding frequency (f) had a high degree of consistency. Thus, vortex shedding was the main cause of wall water pressure fluctuations. Given the blockage effect, the shear layer’s development spanwise was restricted. Moreover, the blockage effect increased the local flow velocity and accelerated the vortex shedding. The dimensionless time-averaged flow velocity U/U0 increased to 1.5, and the frequency of vortex shedding increased by approximately 25% when the Br increased from 0.067 to 0.25. The frequency increased by 25% when the Ar decreased from 0.5 to 0.2. The experimental results also provide a new idea for optimizing the VIVACE device.

Power Law Kernel Analysis of MHD Maxwell Fluid with Ramped Boundary Conditions: Transport Phenomena Solutions Based on Special Functions

In this paper, a new approach to find exact solutions is carried out for a generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate, which is analyzed for ramped-wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters the effects of radiation. An innovative definition of the time-fractional operator in power-law-kernel form is implemented to hypothesize the constitutive mass, energy, and momentum equations. The Laplace integral transformation technique is applied on a dimensionless form of governing partial differential equations by introducing some non-dimensional suitable parameters to establish the exact expressions in terms of special functions for ramped velocity, temperature, and constant-concentration fields. In order to validate the problem, the absence of the mass Grashof parameter led to the investigated solutions obtaining good agreement in existing literature. Additionally, several system parameters were used, such as as magnetic value M, Prandtl value Pr, Maxwell parameter λ, dimensionless time τ, Schmidt number “Sc”, fractional parameter α, andMass and Thermal Grashof numbers Gm and Gr, respectively, to examine their impacts on velocity, wall temperature, and constant concentration. Results are also discussed in detail and demonstrated graphically via Mathcad-15 software. A comprehensive comparative study between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

Dynamics of quantum correlations in a qubit-qutrit spin system under random telegraph noise

We study the dimensionless time evolution of the logarithmic negativity and geometric quantum discord of a qubit-qutrit XXX spin model under the both Markovian and non-Markovian noise channels. We find that at a special temperature interval the quantum entanglement based on the logarithmic negativity reveals entanglement sudden deaths together with revivals. The revival phenomenon is due to the non-Markovianity resulting from the feedback effect of the environment. At high temperatures, the scenario of death and revival disappears. The geometric quantum discord evolves alternatively versus time elapsing with damped amplitudes until the system reaches steady state. It is demonstrated that the dynamics of entanglement negativity undergoes substantial changes by varying temperature, and it is much more fragile against the temperature rather than the geometric quantum discord. The real complex heterodinuclear [Ni(dpt (H2O)Cu(pba)]·2H2O [with pba =1,3-propylenebis(oxamato) and dpt = bis-(3-aminopropyl)amine] is an experimental representative of our considered bipartite qubit-qutrit system that may show remarkable entanglement deaths and revivals at relatively high temperatures and high magnetic field that is comparable with the strength of the exchange interaction J between Cu+2 and Ni+2 ions, i.e., kBT ≈ J and μBB ≈ J.

Special functions-based solutions of unsteady convective flow of a MHD Maxwell fluid for ramped wall temperature and velocity with concentration

In this paper a new approach is taken to find the exact solutions for generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate and is analyzed for ramped wall temperature and velocity with constant concentration. The vertical plate is suspended in a porous medium and encounters radiation effects. Solutions based on special functions are obtained using an integral transform for an unsteady MHD Maxwell fluid in the presence of ramped velocity, temperature and constant concentration. The relations for Nusselt number and skin-friction coefficient are efficiently computed to precisely estimate the rate of heat transfer at the boundary and the shear stress. Results are also discussed in detail and demonstrated graphically using software to comprehensively analyze the dynamics of the proposed problem, and the physical impact of several system parameters, such as magnetic field M, Prandtl number Pr, the relaxation time λ, dimensionless time τ, Schmidt number Sc, Mass and Thermal Grashof numbers Gm and Gr, respectively, is studied. Furthermore, solutions for some recently published work are compared with the current study that endorses the authenticity of our derived results and proves that those investigations are limiting or special cases of the current problem.

Time-averaging axion-like interacting scalar fields models

In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $$\phi _1$$ ϕ 1 and $$\phi _2$$ ϕ 2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems approach, where expansion normalized dynamical variables are usually adopted, are due to the oscillations entering the nonlinear system through the Klein–Gordon (KG) equations. This motivates the analysis of the oscillations using methods from the theory of averaging nonlinear dynamical systems. We prove that time-dependent systems, and their corresponding time-averaged versions, have the same late-time dynamics. Then, we study the time-averaged system using standard techniques of dynamical systems. We present numerical simulations as evidence of such behavior.

Progress in Analytical Modeling of Water Hammer

In this paper analytical formulas of water hammer known from the literature are simplified to the shortest possible mathematical form based on dimensionless parameters: dimensionless time, water hammer number, etc. Novel formulas are determined, for example for the flow velocity and wall shear stress in the Muto and Takahashi solution. A complete solution in the Laplace domain is presented and the problem of its inverse transformation is discussed. A series of comparative studies of analytical solutions with numerical solutions and the results of experimental research were carried out. The compared analytical solutions, taking into account the frequency-dependent nature of the hydraulic resistances, show very good agreement with the experimental results in a wide range of water hammer numbers, in particular when Wh ≤ 0.1. On the other hand, it turned out that the analytical model based on the quasi-steady friction in great detail simulates dynamic pressure response in systems characterized by a high value of the water hammer number Wh ≥ 0.5.

New Tool Wear Estimation Method of the Milling Process Based on Multisensor Blind Source Separation

Timely and effective identification and monitoring of tool wear is important for the milling process. However, traditional methods of tool wear estimation have run into difficulties due to under small samples with less prior knowledge. This article addresses this issue by employing a multisensor tool wear estimation method based on blind source separation technology. Stationary subspace analysis (SSA) technology is applied to transform multisensor signals to stationary and nonstationary sources without prior information of signals. Ten dimensionless time-frequency indices of the nonstationary signal are extracted to train least squares support vector regression (LS-SVR) to obtain a tool wear estimation model for small samples. The analysis and comparison of one benchmark tool wear dataset and tool wear experiments verify the feasibility and effectiveness of the proposed method and outperform other two current methods.