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A numerical investigation on the film cooling performance of a symmetrical turbine blade is carried out for reverse injection (RH), forward injection (FH), and opposite injection (OH) which combines forward and reverse injection holes. Another objective of this work is to study the effect of the distances between the injection holes, and three different distances are considered. Five configurations are computed for five blowing ratios. A coolant flow is injected through holes inclined at 110 and 70o for reverse and forward jets, respectively. The laterally averaged film cooling effectiveness is obtained using commercial software ANSYS-CFX. In addition, several velocity vectors and contours are presented for analyzing the thermal behavior. The numerical model is based on the Navier–Stokes equations and the Reynolds stress turbulence model (SSG-RSM). The obtained results enable one to choose configurations with high film cooling effectiveness for different blowing ratios. [ABSTRACT FROM AUTHOR]

Fractured crystalline rocks have been chosen or are under consideration by several countries as host rock formations for deep geological repositories for spent nuclear fuel. In such geological formations, flow and solute transport are mostly controlled by a network of connected natural fractures, each of them being characterised by internal heterogeneity, also denoted as roughness. Fractures are, in turn, subject to variable load caused by various factors, such as the presence of thick ice sheets formed during glaciation periods. Understanding how coupled hydro-mechanical (HM) processes affect flow and transport at the scale of a single natural fracture is crucial for a robust parameterisation of large-scale discrete fracture network models, which are not only used for nuclear waste disposal applications but are also of interest to problems related to geothermics, oil and gas production or groundwater remediation. In this work, we analyse and model an HM experiment carried out in a single natural fracture and use the results of both, the experimental and the modelling work, to get insights into fundamental questions such as the applicability of local cubic law or the effect of normal load on channeling. The initial fracture aperture was obtained from laser scanning of the two fracture surfaces and an equivalent initial aperture was then defined by moving the two fracture surfaces together and comparing the results obtained using a Navier–Stokes based computational fluid dynamics (CFD) model with the experimental flowrate obtained for unloaded conditions. The mechanical effect of the different loading stages was simulated using a high-resolution contact model. The different computed fracture apertures were then used to run groundwater flow simulations using a modified Reynolds equation. The results show that, without correction, local cubic law largely overestimates flowrates. Instead, we show that by explicitly acknowledging the difference between the mechanical aperture and the hydraulic aperture and setting the latter equal to 1/5 of the former, cubic law provides a very reasonable approximation of the experimental flowrates over the entire loading cycle. A positive correlation between fluid flow channeling and normal load is also found. [ABSTRACT FROM AUTHOR]

The modeling of engineering systems considering fractional approach configures a tendency as due to the generalization of traditional models that use integer order and to the number of applications in different science fields that can benefit from this approach. The present contribution aims to analyze the physical parameters of a near-field acoustic levitation system, as described by the Reynolds equation, and to evaluate the influence of fractional orders on the obtained profiles. For this purpose, both time and space fractional derivatives found in the fractional differential model are approximated using Caputo and Grünwald–Letnikov formulas, respectively. The discretized nonlinear algebraic system is solved considering the Newton method. The proposed methodology was able to solve the time–space fractional near-field acoustic levitation model for both integer and fractional orders. The performed sensitivity analyses demonstrated the influence of the model parameters and the fractional orders on the pressure fields and levitation force. Physically, for a squeeze film levitation system, the increase of the squeeze number is necessary for levitation purposes. In addition, the maximum achievable levitation capacity of a squeeze film levitation system is determined by the excitation amplitude. As expected, the levitation domain is reduced as the mass increases and the reduction rate of the integer model is higher than the one of the fractional order. In this case, for mass bigger than 1.629 Kg, the levitation domain is larger for the fractional order model. It is worth mentioning that the proposed methodology can be used to solve other dynamic systems modeled by time–space fractional differential equations. [ABSTRACT FROM AUTHOR]

This paper presents the results of extensive testing of four recently proposed algebraic laminar-turbulent transition (LTT) models, which are significantly more computationally effective than differential models, while being potentially equally accurate. The models chosen for evaluation, namely, SST KD, SST kγ, SST alg-γ, and SA BCM, are implemented in the in-house code NTS and verified by comparing the obtained results with those published by the models' authors. The experimental database used for the evaluation of the models includes transitional boundary layers at different free-flow turbulence intensities with and without the pressure gradient, four airfoil flows with different LTT scenarios, and a tandem of two airfoils. It is found that at low levels of turbulence, the results of the SA BCM and SST kγ models may depend on the initial approximation, which does not allow them to be recommended for engineering applications. The best results, comparable in accuracy to those of differential models, are obtained using the SST alg-γ model. [ABSTRACT FROM AUTHOR]

In this work, a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks (PINNs) is proposed. The complementarity relationship between the pressure and the void fraction is used. There are several difficulties in problem solving, and the solutions are provided. Firstly, the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error. While the void fraction inequality constraint is considered by using the hard constraint with the max-min function. Secondly, to avoid the fluctuation of the boundary value problems, the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided. Lastly, for avoiding the trivial solution the limitation for the mean value of the void fraction is applied. The results are validated against existing data, and both the incompressible and compressible lubricant are considered. Good agreement can be found for both the domain and domain boundaries. [ABSTRACT FROM AUTHOR]

Polymer based additives with long chain of suspended particles in oil retain polarity effect in the presence of couple stresses. Further, at high speed of journal bearing, the oil film experiences substantial agitation due to pressure-viscosity interaction which evolve piezo-viscous dependency of the lubricant. The present article addresses the combined effects of piezo-viscous dependency and couple stresses of lubricant on the characteristics of multi-recessed hybrid journal bearing under misaligned operation. To govern the flow of piezo-viscous-polar lubricant in clearance space of the journal bearing, a piezo-polar function is used to obtain the modified form of Reynolds equation. Galerkin's technique is employed to obtain the finite element formulation in the form of algebraic equation, which is solved to determine the unknown pressure field in the bearing system. The present results reveal that the use of piezo-viscous-polar lubricant offers an enhancement in performance characteristics of bearing system, i.e., a significant hike of 13–36%, 27–30% and 7–10% in the values of S ¯ ij , C ¯ ij and ω ¯ th respectively vis-à-vis Newtonian lubricant. The numerically simulated non-dimensional results presented in the article may be useful to generate the bearing design data of the hybrid journal baring system functioning in realistic and stringent operating conditions. [ABSTRACT FROM AUTHOR]

The effect of fluctuating coagulation on particle distribution in multiphase turbulence of nanoparticles was studied based on the Reynolds averaged equation of turbulence flow and the general dynamic equation of particles. A one-order closed model was proposed to relate the fluctuating coagulation term to the average particle size distribution function for closing the particle equation. The proposed model and equations were applied to a turbulent jet flow using the k-ε turbulent model and the Taylor-series expansion moment method. The results showed that there is a difference in the values of particle number density M0, geometric average diameter dpg and geometric standard deviation σg of particle diameter with and without considering fluctuating coagulation. Larger Damkohler number leads to smaller M0, higher particle polydispersity M2, larger dpg and σg. Along the x direction of the flow, M0 decreases, while M2, dpg and σg increase. From the centerline to the outer edge of the jet, M0, M2 and dpg decrease, while σg increases first and then decreases. Finally, the further research that can be carried out has been proposed. [ABSTRACT FROM AUTHOR]

In this paper, the tribological characteristics of an oil-soluble magnetic fluid additive under mixed lubrication are studied by experiments and numerical simulation. [bmim][FeCl4] is dissolved in CF10W-40 lubricating oil as a magnetic liquid additive, and its friction coefficient is tested by a point contact friction tester at different temperatures, rotational speeds and magnetic field intensities. The transition condition of lubrication state is obtained through analyzing the Stribeck curves based on the experiments, and the strength model of boundary film is established accordingly. A mixed lubrication model is established by substituting the boundary film strength model and the surface roughness model into the hydrodynamic lubrication model based on Reynolds equation. The results show that the magnetic solution as an additive can obviously reduce friction and wear, and the effect is more obvious under the condition of magnetic field. The boundary film strength model can accurately reflect the transition characteristics of lubrication state in the presence of boundary film, and the mixed lubrication model based on boundary film strength model can more precisely reflect the tribological characteristics of friction pairs, so this study provides a new theoretical method for the related research on the influence of boundary film on lubrication characteristics. [ABSTRACT FROM AUTHOR]

In this paper, finite element method is used to calculate the static performance of gas journal bearing, in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed. The results indicate that the average gas film thicknesses corresponding to the maximum load capacity and stiffness, and the minimum attitude angle increase with the growth of orifice diameter. Load capacity and stiffness significantly improved with the increase of rotation speed, eccentricity ratio and supply pressure when the bearing has thin average gas film thickness. Attitude angle increases with the growth of rotation speed, while the growth rate slows down or even decreases at high speed. The most effective way of reducing attitude angle is to increase supply pressure. It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices, while other parameters have the same effect by changing gas pressure at orifice outlet. Article Highlights: Analyzing performances of gas journal bearings by solving Reynolds equation with FEM. Solving Reynolds equation with speed term using FEM. Investigating the effect of bearing parameters on attitude angle, stiffness, and load capacity. [ABSTRACT FROM AUTHOR]

Abstract—The results of numerical simulation of unsteady free convection developing near a suddenly heated plate, on which protrusions in the form of adiabatic cylinders of double height with respect to the diameter are arranged in a staggered order, are presented. The calculations were performed according to the Reynolds equations using a differential model of turbulent stresses. The range of variation of the Grashof number (plotted according to the thickness of the free convective flow), in which a significant intensification of heat transfer can be achieved, has been determined. It is shown that the best conditions for intensification are created if the longitudinal pitch in the array of protrusions is approximately twenty times the diameter of the latter. [ABSTRACT FROM AUTHOR]

The possible application of the results of numerical modeling in developing an approximate phenomenological mathematical aerodynamic model applicable in solving the problems of dynamics is studied with reference to the example of the unsteady flow past the NACA 0015 airfoil oscillating in the angle of attack at different frequencies, amplitudes, and mean angles of attack. For this purpose, the Reynolds equations are solved in both steady and unsteady formulations, together with the k–ω SST turbulence model. The results of the calculations are validated by means of comparing them with the experimental data. The model of the normal force and the longitudinal moment formulated within the framework of an approach introducing an internal dynamic variable is identified according to the data of calculations. The results of the modeling are compared with the numerical and experimental data. The comparison with the conventional approach to the modeling based on the linear unsteady model with the use of dynamic derivatives is also carried out. [ABSTRACT FROM AUTHOR]

Purpose: Thrust bearings play a critical role in high-speed rotating machinery, such as turbines, pumps, compressors, and turbogenerators, by transferring axial loads between the collar and the bearing pads. The lubricating fluid prevents contact, friction, and wear between solid parts and acts as a cooling medium. The purpose of this study is to evaluate the first- and second-order bearing coefficients of an inclined pad hydrodynamic thrust bearing, which have not been previously investigated, to improve the accuracy of modeling thrust bearings. Methods: In the analysis of thrust bearing systems, the lubricating fluid film is modeled as a massless spring-damper system. The finite perturbation method for the governing Reynolds equation is used to calculate the dynamic coefficients of the thrust bearing. This is done using the finite difference method (FDM) in polar coordinates. Results: This study investigates the influence of misalignment, rotating speed, and mesh size on the bearing coefficients of the thrust bearing. The results show that misalignment angle and film thickness have a clear effect on the dynamic coefficients, while changing the rotational speed has no effect on the damping coefficients. The study also investigates the axial force and moments and dynamic coefficients of an inclined pad thrust bearing. Conclusion: This study concludes that evaluating the first- and second-order bearing coefficients of the thrust bearing using the finite perturbation method can improve the accuracy of modeling thrust bearings. The study also highlights the significant influence of misalignment and film thickness on the dynamic coefficients of the thrust bearing. The results presented in this study provide valuable data that can be used as input for rotor dynamics analyses in high-speed rotating machinery. [ABSTRACT FROM AUTHOR]

Purpose: Elastic Ring Squeeze Film Damper (ERSFD) is normally incorporated into high-speed ball bearings to attenuate the vibration amplitude of the rotor system in aero-engines. At high rotor speeds, the bearing introduces considerable nonlinear excitation to the journal, causing it to exhibit distinct dynamic properties. As well, the deformation of the elastic ring in the ERSFD model significantly influences the hydrodynamic reaction force on the journal. This paper develops a high-speed ball-bearing excited ERSFD model with the deformation of the elastic ring analytically formulated. The effects of rotor operating speed and squirrel cage stiffness on the transient and steady-state dynamics of the journal were examined. Methods: The journal is modeled under the excitation of ball-outer raceway interaction rather than rotor unbalance force, emphasizing heavy thrust-applied load. Ball-outer raceway interaction is calculated using a modified quasi-static model. Elastic ring deformation is derived analytically through a thin-walled ring and the oil film pressure is governed by the generalized Reynolds equation. Runge–Kutta approach was used to numerically integrate the differential equations of motion, and the journal center orbit and vibration acceleration were experimentally measured. Results: The results show that as the squirrel cage stiffness increases by 1.23 times from 0.6855, the eccentricity and transmissibility for the ERSFD with bearings are increased by a factor of 1.8 and 3, respectively. Correspondingly, the values for the ERSFD without bearings are increased by a factor of 1.7 and 2.7. As the rotor operating speed increases by 1.75 times from 8000 r min−1, the eccentricity and transmissibility for the ERSFD with bearings are decreased by 28.6% and 54.6%, respectively; for the ERSFD without bearings, the eccentricity remains unchanged and the transmissibility is decreased by 26.2%. Conclusion: It was concluded that when the journal works at a steady state an increase in squirrel cage stiffness disadvantages attenuation in bearing excitation; adequately high rotor operating speeds benefit journal dynamics when bearing excitation is considered in ERSFD. At transient state, lower squirrel cage stiffness and higher rotor operating speed allow the journal to behave in stable periodic motion for the ERSFD with bearing excitation; however, for the ERSFD without bearing excitation, lower squirrel cage stiffness fails to make the journal whirl periodically, and the rotor operating speed has little effect on the transient dynamics of the journal. [ABSTRACT FROM AUTHOR]

In this Letter, it is shown how the determination of the effective coefficients involved in the macroscopic model for pressure driven and/or Couette flow in a rough fracture can be simplified by solving only one closure problem instead of two as originally reported in Prat et al. (Transp Porous Media 48(3):291–313, 2002. https://doi.org/10.1023/a:1015772525610). [ABSTRACT FROM AUTHOR]

A simplified mathematical model has been developed for understanding combined effects of surface roughness, viscosity variation and couple stresses on the squeeze film behaviour of a flat and a curved circular plate in the presence of transverse magnetic field. The Stokes (1966) couple stress fluid model is included to account for the couple stresses arising due to the presence of microstructure additives in the lubricant. In the context of Christensen's (1969) stochastic theory for the lubrication of rough surfaces, two types of one-dimensional roughness patterns (radial and azimuthal) are considered. The governing modified stochastic Reynolds type equations are derived for these roughness patterns. Expressions for the mean squeeze film characteristics are obtained. Numerical computations of the results show that the azimuthal roughness pattern on the curved circular and flat plate results in more pressure buildup whereas performance of the squeeze film suffers due to the radial roughness pattern. Further the Lorentz force characterized by the Hartmann number, couple stress parameter and viscosity variation parameter improve the performance of the squeeze film lubrication as compared to the classical case (Non-magnetic, Newtonian case and non-viscous case). [ABSTRACT FROM AUTHOR]

In order to study the influence of structural parameters of porous gas bearing and operating parameters of linear compressor on the static and dynamic performance of porous gas bearing, based on gas lubrication theory, Darcy's law and Reynolds equation, the mathematical model and simulation model of porous gas bearing of linear compressor are derived and established. The static and dynamic characteristics of the porous gas bearing of the linear compressor are studied by using Fluent software simulation. According to the simulation results, the effects of inlet pressure, porous material thickness and gas gap on the gas consumption and bearing capacity of the porous gas bearing under different eccentricities are analyzed. The results show that the higher the inlet pressure is, the larger the gas consumption and bearing capacity; the thicker the porous material is, the smaller the gas consumption and the larger the bearing capacity, the thicker the gas gap is, the larger the gas consumption and the smaller the bearing capacity. On the basis of simulation research, considering the difficulties of processing and assembly, multi-objective optimization of porous gas bearings is carried out based on response surface methodology. Taking the bearing capacity and gas consumption as the objective functions, the intake pressure is set between 0.3 and 0.5 MPa, the thickness of porous materials is set between 3 and 5 mm, and the thickness of gas gaps is set between 10 and 20 μm. While ensuring the stable operation of the linear compressor, the optimal combination of design parameters is provided for the optimal design of gas bearings used in linear compressors. [ABSTRACT FROM AUTHOR]

The results of numerical simulation of the formation and motion of turbulent vortex clouds (puffs) resulting from the blowing of pulsed jets with various initial velocities and durations are given. A model of axisymmetric turbulent flow described by the time-dependent Reynolds equations is adopted. It is shown that, regardless of the initial conditions, a puff which has the shape similar to a sphere develops after the same dimensionless time interval from the instant of jet outflow. In the rest of the space the vortex-induced flow is close to a potential flow. It is found that in the vortices the velocity profiles in the axial and transverse directions are close to self-similar profiles and similar each other for various conditions of outflow of pulsed jets. The time dependences of the geometric and kinematic characteristics of puffs, namely, the location of the cloud center (points with the maximum velocity) and the radius of a sphere equivalent in volume to the puff, as well as the maximum and mean velocities, are given and analyzed. For the jet outflow conditions considered, the characteristics of puffs turn out to be similar. [ABSTRACT FROM AUTHOR]

Over the past century, Blasius (Forschungsheft 131:1–41, 1913) gave empirical power law friction factors λ = 0.3164 Re - 1 / 4 for a turbulent pipe flow and later work published other empirical values of power law indexes. The present work deals with open Reynolds momentum equations by matched asymptotic expansions for large Reynolds number. In the overlap region, a rational dual solutions have power law and log law velocities and friction factor. If outer layer flow is neglected, the power-law friction factor becomes λ = m Re - n in a pipe flow, with power law index n (Re) and prefactor m (Re) . Further, tangent at a point on power law envelop gives log law at that point. Thus for each value of power index n with prefactor m, the power law theory holds at a point. As an engineering practice, power law at one point is often used in a limited domain of Reynolds number, which compares in that range with experimental and DNS data reported in the literature. The friction factor log law to higher order has been proposed and the second-order effect compares well for lower Reynolds numbers in an entire range of Reynolds numbers for a turbulent pipe flow. [ABSTRACT FROM AUTHOR]

The last decade has witnessed a surge of interest in artificial neural network in many different areas of scientific research. Despite the rapid expansion in the application of neural networks, few efforts have been carried out to introduce such a powerful tool into lubrication studies. Thus, this work aims to apply the physics-informed neural network (PINN) to the hydrodynamic lubrication analysis. The 2D Reynolds equation is solved. The PINN is a meshless method and does not require big data for network training compared with classical methods. Our results are consistent with those obtained by experiments and the finite element method. Hence, we envision that the PINN method will have great application potential in lubrication and bearing research. [ABSTRACT FROM AUTHOR]

In this paper, we study the linearized Navier–Stokes system around monotone shear flows in a finite channel with non-slip boundary condition. We prove that if the flow is linearly stable for the Euler equations, then it is also linearly stable for the Navier–Stokes equations at high Reynolds number. More importantly, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier–Stokes system, which may be crucial for nonlinear stability. One of the key ingredients is the resolvent estimates of the linearized operator. For this, we develop the compactness method and establish some sharper estimates for the boundary layer corrector. [ABSTRACT FROM AUTHOR]

The applicability of various mathematical models of turbulence for simulation of gas motion in reverse-flow cyclones was evaluated. Out of very numerous turbulence models, only those demonstrating the greatest efficiency in modeling complex flows were selected for the analysis. It is known that, among the models using the Reynolds equations supplemented with parameter equations expressing turbulent viscosity, the standard k–ε model does not provide an accurate description of the gas velocity field in reverse-flow cyclones. For this reason, the suitability of the shear stress transport (SST) turbulence model, as well as of the nonlinear k–ε model, which includes quadratic and cubic terms in the expression for the so-called Reynolds stresses and is advisable for swirling flow simulation, was examined. Also performed were calculations using Smagorinsky model representing a popular choice for large eddy simulations. The results of the calculations were compared with the published experimental data from measuring the gas velocity components inside the cyclone using a laser Doppler anemometer. It was shown that the best results were provided by the Smagorinsky model, which therefore may be usable for modeling gas cleaning processes in cyclones. Modeling will enable eliminating the need to perform time-consuming experiments for optimizing the geometric parameters of cyclones. Moreover, establishing a reliable method for calculating the aerodynamics of a cyclone allows using the calculations for optimizing the operating conditions of a cyclone under specified working parameters. [ABSTRACT FROM AUTHOR]

The article presents numerical simulation of turbulent flow in a rotating rectangular 90° bend channel using the WMLES method, and the effect of rotation on the flow structure is studied. The article also presents a study of the accuracy of various semi-empirical turbulence models for closing the Reynolds equations for flows of this type by comparison with the WMLES results for the cases with and without rotation. [ABSTRACT FROM AUTHOR]

As a smart material with controllable rheological properties, magnetorheological fluids (MRFs) have been increasingly used in various fields. The temperature of MRFs inevitably changes during operation, which markedly affects the rheological properties; thus, the modeling of temperature effects is critical for the control and design of magnetorheological devices. However, most studies only examine the temperature effects of MRFs in a narrow temperature range, which fails to effectively cover the operating temperature range of MRFs, and the viscosity-temperature models used have notable limitations. This paper proposes to use free volume theory, in the form of the universal Doolittle equation, to study the viscosity-temperature behavior of MRFs and their base oils over a wide temperature range. Compared with the existing Reynolds and Arrhenius equations, the Doolittle equation achieves an accuracy improvement of up to 17 times and eight times, respectively. It predicts the overall viscosity-temperature behavior of liquids based on four data points taken over a narrow temperature range, with a relative root-mean-square error (RMSE) of no more than 5%. Ignoring the limited effect of off-state yield stress, the Doolittle equation with strong expandability can be used to establish temperature-dependent MRF constitutive equations. It can even develop multiphysics models based on the highly similar viscosity-temperature characteristics between MRFs and their base oils, which will greatly facilitate the development and optimization of MRFs. [ABSTRACT FROM AUTHOR]

A two-dimensional coupled numerical model of creeping multiphase flow has been developed. The computational domain consists of two subdomains, namely, a relatively thick two-phase layer overlaid with a thin multilayered viscous sheet. At the interface between the subdomains, there is mass transfer between the light component of the two-phase layer and the bottom layer of the viscous sheet. The coupled system of governing equations consists of the compaction equations describing the flow in the two-phase layer and the Reynolds equations describing the flow in the sheet. The model takes into account the layered structure of the sheet (with any degree of detail) and the surface processes of erosion and sedimentation. An additional asymptotic boundary condition is used to couple the different-type hydrodynamic equations without any iterative improvement. As a result, the computational costs are reduced significantly in comparison with available coupled models. The evolution of the velocity field and the layer boundaries is numerically modeled. Numerical results reveal that the regimes of the evolution of the velocity field and the layer boundaries are different at short and long times. The evolution consists of at least two stages with typical time scales, namely, a fast stage at short times and a slowly varying (quasi-stationary) stage at long times. This kind of the flow evolution is determined by the geometric and physical parameters of the media, rather than by external causes. As a geophysical application, the accumulation of lightened mantle beneath the Earth's crust in the active ocean–continent transition zone is numerically calculated. [ABSTRACT FROM AUTHOR]

Based on finite element discretization and a recent variational multiscale-stabilized method, we propose a three-step defect-correction algorithm for solving the stationary incompressible Navier-Stokes equations with large Reynolds numbers, where nonlinear slip boundary conditions of friction type are considered. This proposed algorithm consists of solving one nonlinear Navier-Stokes type variational inequality problem on a coarse grid in a defect step, and solving two stabilized and linearized Navier-Stokes type variational inequality problems which have the same stiffness matrices with only different right-hand sides on a fine grid in correction steps. In the defect step, an artificial viscosity term is used as a stabilizing factor, making the nonlinear system easier to solve. Error bounds of the approximate solutions in L2 norms for the velocity gradient and pressure are estimated. Scalings of the algorithmic parameters are derived. Some numerical results are given to support the theoretical predictions and test the validity of the present algorithm. [ABSTRACT FROM AUTHOR]

The optimal texture shape considering surface roughness is determined by solving the average Reynolds equation, selecting Jakobsson–Floberg–Olsson boundary conditions, and using a genetic algorithm. The effects of surface roughness as indicated by the combined root-mean-square (RMS), surface pattern parameter, and operating parameters on the friction coefficient, area ratio, and depth of the optimal self-defined shape and optimal dimple were studied. Results show that the friction coefficient will be significantly reduced during the shape optimization considering the effect of surface roughness. The variation laws of the optimal dimple area ratio with the combined RMS, surface pattern parameter, minimum film thickness, sliding speed and the variation law of the optimal depth of the optimal self-defined shape with surface roughness and working parameters are obtained. Finally, this study concludes that the influence of roughness parameters on the optimal dimple shape is greater than that on the optimal self-defined shape under different sliding speeds. [ABSTRACT FROM AUTHOR]

In order to accurately predict the damping characteristics of a hydraulic shock absorber under piston inclination and eccentricity conditions, especially, considering effects of piston surface construction. In present work, taking account of piston slight inclination and eccentricity, a more detailed mathematical model was developed to estimate effects of piston texture on damping characteristics. Based on the mathematical models of reservoir and compression stroke coupled with Reynolds equation, a new damping force model was developed, which analyzed effects of piston structure on damping characteristics. The mathematical models of piston texture, piston slight inclination, piston eccentricity and combinations of three cases are developed to analyzed in detailed effects of piston texture at different work conditions on damping characteristics. The results shown that the friction force of piston increases parabolically with increasing depth ratio, and that of piston increases linearly with increasing area ratio. Piston textures have little effects on damping characteristics at specific structural parameters conditions when piston normal operation, however, textures of slight inclined and eccentric piston have great effects. As a result, piston textures might cause high damping force, destroyed comfort and safety. Therefore, it is necessary that effects of piston surface construction were precisely predicted on damping characteristics under different work conditions. The results might provide a new insight for the design of hydraulic shock absorber and investigation of vehicle system dynamics. [ABSTRACT FROM AUTHOR]

A fully conservative overset mesh method is proposed and applied to overcome the metric singularity at the symmetry line for blunt bodies, e.g., capsules and blunted cones, in general curvilinear coordinates. The overset mesh is placed automatically at the symmetry line by avoiding the collapse of the grid lines using a hexahedral structure in contrast to the prismatic structure of a body-orientated mesh. In addition, the grid points of the overset mesh coincide with those of the body-orientated mesh to avoid interpolation techniques to interchange the flow variables between the two meshes. This coincidence ensures the conservation of the flow variables and avoids uncertainties at the shock as the method is naturally conservative. The thin-layer Navier–Stokes equations for high Reynolds number flows are solved using an AUSM+ or an AUSMPW+ flux vector splitting in combination with a mesh adaption to capture the shock accurately. For verification purposes of the proposed method, a supersonic 2D-axisymmetric hemisphere cylinder is chosen and the results along the wall are verified. Furthermore, the conservative properties of the applied overset mesh method are shown and the results on the stagnation line are presented. In addition, a supersonic 3D calculation is investigated to show the applicability of the presented method for simulations with an angle of attack. [ABSTRACT FROM AUTHOR]

In actual operation, axial flow pump stations are often used for various special purposes to meet changing needs. However, because the hydrodynamic characteristics of axial flow pump systems are still unclear when used for special purposes, there are many risks when pump systems are used for special purposes. To explore the hydrodynamic characteristics of an axial flow pump system under special utilization conditions, a high-precision full-feature test bench for an axial flow pump system is established in this paper. For the first time, an energy characteristics experiment and a pressure fluctuation measurement for a pump are carried out for a large axial flow pump system model under zero head, reverse pump and reverse power generation conditions. Then, ANSYS CFX software is used to solve the continuous equation and Reynolds average Navier–Stokes equation, combined with the SST k–ω turbulence model, and the characteristic curve and internal flow field of the pump system under special conditions are obtained. Finally, the numerical simulation results are compared with the experimental results. The results show that the velocity gradient distribution in the pump is uniform under the near zero head condition (NZHC), and there is no obvious flow collision and reflux phenomenon in the pump. Compared with the designed condition (DC), the peak-to-peak value (PPV) of pressure pulsation at the inlet of the impeller decreased by 67.16%, and the PPV at the outlet of the impeller decreased by 8.14% at H = 0 m. The maximum value of the main frequency amplitude (MFA) in the impeller area appears at the impeller inlet. Under reverse pump conditions (RPC), the phenomenon of unstable flow in the pump system is obvious, and a large range of recirculation zones appears in the nonworking face of the blade. Compared with the DC, the PPV of the impeller inlet at the optimal point of RPC increased by 122.61%, and the impeller outlet PPV increased by 11.37%. The maximum value of MFA in the impeller area appears at the impeller inlet. Under the reverse power generation condition (RPGC), no obvious flow separation was found in the nonworking face of the impeller. Compared to the DC, the PPV of the impeller inlet at the optimal point of the RPGC increased by 65.34%, and the PPV of the impeller outlet increased by 206.40%. [ABSTRACT FROM AUTHOR]

This paper considers the problem of clarified turbulent flow over an erodible bed. A mathematical model of the problem is proposed which includes the Reynolds equations and transport equations for turbulent kinetic energy and turbulence dissipation. The bed surface evolution is described using the bed deformation equation and the original analytical model of bed-load sediment transport. An algorithm for solving the problem based on the control volume method is proposed. Numerical solution of the problem shows that when the bed is eroded by clarified flow, a wave packet of low-steepness bed waves is formed. The velocity of bed waves obtained from the numerical solution is in good agreement with the velocity of bed waves calculated by an asymptotic analytical formula. [ABSTRACT FROM AUTHOR]

An isothermal compressible single-phase fluid flow through a non-homogeneous granular body composed of densely packed overlapping spheres imitating rock under high pressure was numerically studied using two different approaches. The first approach called the full 3D CFD model used the finite volume method (FVM) to solve the Reynolds-averaged Navier–Stokes equations using Reynolds stress model (BSL) in the continuous domain between the granulates. The model was verified, based on experimental and numerical results from the literature. The second approach was a simplified coupled DEM-CFD model based on a fluid flow network. The main aim of the work was to develop a validation procedure for simplified coupled DEM-CFD models due to the lack of experimental data for fluid flow characteristics in densely packed granules under extremely high-pressure conditions. First, a series of numerical simulations were performed for the fluid domain with the full 3D CFD model. The results of those simulations were next used to validate the 2D numerical results of the simplified coupled DEM-CFD model with respect to velocities, pressures, densities and flow rates. Almost the same pressure and density distributions and mass flow rates were obtained in both approaches. However, the fluid velocity was different due to the different fluid volumes in both fluid domains. The current simulation results constitute a reliable benchmark for validating other coupled 2D/3D DEM-CFD models that use a fluid flow network approach. [ABSTRACT FROM AUTHOR]

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Compression shear failure of rock is a common failure mode in engineering, and there are often complicated seepage phenomena in its shear crack. Due to the anisotropic and irregular rough cross-section on both sides of the natural crack, the experimental study of rock seepage is difficult to operate. In order to study the microscopic seepage characteristics of rock cracks, granite crack specimens were prepared through shear experiments. The data was obtained by scanning the section with laser and imported into MATLAB software to reconstruct the three-dimensional section and crack opening model. In view of the difficulty of observing the microscopic characteristics of rock seepage flow, in this paper, the Reynolds equation of rock fracture flow considering the dynamic effect of boundary is derived, and under the condition of the definition of Reynolds equation theory, based on the advantage of fractal geometry for irregular cross-section, the relationship between flow velocity, permeability and simulation scale is studied by using COMSOL simulation software. The results show that the granite cross-section has a good statistical self-similarity feature, and the fractal matrix mesh covering the fracture surface can well express the feature of the fracture surface; The roughness of the fracture surface has a positive correlation with the fractal dimension. The larger the fractal dimension, the greater the roughness of the fracture surface, which verifies the reliability of the fractal dimension to describe the roughness of the section. There is a positive correlation between the scale-up of the simulation and the velocity of the micro-research points, and the permeability of the model; The feasibility of the fractal percolation model is investigated and the general suggestions for simulating scale are given. Some of the results of this study can be used for reference in the analysis of seepage characteristics of fractures in rough rock mass. [ABSTRACT FROM AUTHOR]

Background: Gas Foil Bearings (GFBs) have fulfilled most of the requirements of novel oil-free turbomachinery. It has been considered as an alternative to traditional bearings in turbopumps, turbocompressors and turbochargers. However, they are prone to instabilities due to its low damping characteristics. Therefore, a hybrid bearing combining the GFBs and Active Magnetic Bearings (AMBs) has been in rigorous study due to its obvious advantages. Purpose: The main aim of this paper is to provide a coupled time domain numerical model of the rotor supported on hybrid GFBs. The developed non-dimensional model has been used to investigate the capability of hybrid GFBs to mitigate the effect of unbalance force and in turn instability. Further, the ability of the hybrid GFB to withstand unbalance at an arbitrary time has also been investigated. Methods: The magnetic force generated is calculated using reluctance network method while fluid film forces are obtained by solving the governing Reynolds equation. The magnetic force of the AMB is non-dimensionalized in line with the fluid film forces of the conventional GFB. The non-dimensionalized fluid film forces from the GFBs and the electromagnetic forces from the EMAs are integrated into the equations of motion of the rotor. The response is then recorded for different operating parameters of the rotor. Results: The sub-synchronous frequency which is the dominating frequency in case of the conventional GFB is eliminated due to the implementation of hybrid GFB. It has been demonstrated that the hybrid GFB has higher capability to withstand unbalance compared to conventional GFB. It has been observed that higher control current is required for higher unbalance eccentricity. Moreover, the hybrid GFB is also capable of adapting to the unbalance occurring at an arbitrary time. [ABSTRACT FROM AUTHOR]

The one-equation turbulence models by Spalart and Allmaras (SA) and Sekundov et al. (Nut-92) are tested against two compressible two-dimensional flows, namely, the turbulent flat-plate boundary layer at zero pressure gradient and the mixing layer. The boundary layer (BL) approximation is applied to the system of Reynolds equations (RANS). The BL results obtained are compared with the available RANS results and the results of direct numerical simulation (DNS). The modified Nut-92m model proposed predicts the characteristics of the turbulent flat-plate boundary layer at zero pressure gradient more accurately than the Nut-92 and SA models. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of rotor coaxiality error on spindle accuracy under different operating conditions in the precision hydrostatic spindle with a mid-thrust bearing structure. Firstly, a linearized model of rotor dynamics equation with five degrees-of-freedom is established based on Newton's law of motion and angular momentum principle. Then, by solving the Reynolds equation and the flow continuity equation using the mathematical perturbation method, the steady and transient pressure distribution functions of the hydrostatic bearings are obtained; subsequently, the stiffness and damping coefficient matrices of the spindle are determined. Furthermore, the linearized stiffness and damping coefficients are substituted into the rotor dynamics equation to obtain the instantaneous acceleration of the rotor, and the motion trajectory of the rotor is solved iteratively by the Euler method. Finally, the paper studies the influences of different rotor coaxiality, rotating speed, cutting load, oil supply pressure, and oil film clearance on dynamic characteristics, amplitude amplification factor, and radial runout of the spindle by computer simulation. The simulation results show that the spindle runout is more sensitive to rotor coaxiality error and oil film clearance. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of micropolar fluid flows in a thin domain of thickness η ε with a periodic oscillating boundary with wavelength ε . We consider the limit when ε tends to zero and, depending on the limit of the ratio of η ε / ε , we prove the existence of three different regimes. In each regime, we derive a generalized Reynolds equation taking into account the microstructure of the roughness. [ABSTRACT FROM AUTHOR]

The current paper discusses the optimum parameter setting of asymmetric high-static low-dynamic stiffness (HSLDS) suspensions to reduce vibrations of a high-speed symmetric rotary system, excited by an unbalance force. The rotating system consists of a shaft that is supported by tilting pad journal bearings on the asymmetric HSLDS suspensions. The Reynolds equation is solved numerically to obtain the oil pressure distribution for each pad of bearing. With the aim of calculating the hydrodynamic forces applied to each pad, an analytical approach is presented. Its results are validated using a numerical integration approach. Given the considerable difference between the shaft mass and pads moment of inertia, the mathematical equations governing the motions of disk, journal, bearing and pads are solved implementing a routine specified for stiff ordinary differential equations in MATLAB. The optimum parameters of HSLDS suspensions are obtained, using a multi-objective genetic algorithm. Design objectives are considered to minimize the vibrations of rotor, journal, and bearing and bearing force transmission to the external supports. The efficiency of optimum HSLDS suspensions in reducing the vibrations of journal, bearing and rotor within the operating speed range is shown. The high performance of the designed suspensions in decreasing the bearings force transmission is proved as well. In addition, the design robustness to uncertainties in HSLDS suspensions parameters is studied. [ABSTRACT FROM AUTHOR]

Purpose: A close form solution was developed in this paper to find the nonlinear tuning parameters of symmetric/asymmetric rotor—Squeeze film damper system. Methods: Initially, close form solution was developed to find the optimum tuning criteria using linear models. Later, it has been extended to nonlinear unbalanced rotor damper system using circular centre orbit condition. Analytical modeling of Squeeze film damper forces is carried out considering viscous, inertial and temporal contributions under laminar and turbulent conditions. Modified Reynolds equation with short damper approximation is used to derive the SFD forces for 2π-film. The solution of the system of equations helped to predict optimum tuning parameters, such as cross-over frequency and maximum possible amplitudes. Contributions of various governing parameters are discussed. Conclusion: Mass ratio of damper-to-rotor mass and nonlinear radial/tangential damper forces play an important role in finding the tuning parameters of symmetric system. Additional shaft parameter, fp, plays an important role in getting the optimum tuning parameters of asymmetric system as compared to symmetric system. [ABSTRACT FROM AUTHOR]

This paper presents a novel fixed and free abrasive combined wire sawing which uses the diamond wire with surface abrasive-groups interval distribution and combines with free SiC abrasives slurry to obtain sliced surface that can be textured by acid etching. During the sawing process, the ability that the free abrasives lapping the sawn surface has a positive correlation with the elasto-hydrodynamic (EHD) pressure, and the appropriate size of the free abrasives is related to the minimum film thickness of the cutting coolant. In this paper, the EHD action during the FFACWS is analyzed, and the film thickness equation and Reynolds equation of the sawing area are deduced. The influences of feed speed, wire speed, wire tensioning force, cutting coolant viscosity, core wire diameter, and surface structure parameters on EHD pressure and film thickness are analyzed, which provides theoretical reference for selection of the free abrasives diameter and analysis of their lapping effect on the slice surface. The research results show that the EHD pressure changes periodically in the direction of the wire axis in the entire sawing area. The change period is the same as a structural change period of the abrasive area (AA) and the bare wire area (BWA) on the wire surface. In one period, there are two EHD pressure peaks. The size range of free abrasives should be greater than the protruding height of the fixed abrasives on the diamond wire and less than the minimum film thickness in BWA, so that the free abrasives can be constrained in BWA to lap the slice surface. [ABSTRACT FROM AUTHOR]

The stiffness and dampness parameters of journal bearings are required in rectangular coordinates for analyzing the stability boundary and threshold speed of oil film bearings. On solving the Reynolds equation, the oil film force is always obtained in polar coordinates; thus, the stiffness and dampness parameters can be easily obtained in polar coordinates. Therefore, the transformation between the polar and rectangular coordinates of journal bearing stiffness and dampness parameters is discussed in this study. [ABSTRACT FROM AUTHOR]

In order to investigate the influence of adjustable inlet guide vanes on the hydraulic performance of axial-flow pump and impeller, the axial-flow pump with different inlet guide vane adjustable angles was simulated based on the RNG k-ε turbulent model and Reynolds time-averaged equations. The multivariate non-linear regression prediction model was established about the effect of adjustable inlet guide vane on the hydraulic performance of axial-flow pump based on the numerical simulation. The performance curves of axial-flow pump with different inlet guide vane adjustable angles were obtained by calculation, showing that the performance curve shifts towards larger flow volume in case the guide vanes are turned from positive to negative angle. With the increase of inlet guide vane positive angle, the optimum operating of pump is closer to smaller operating condition, but the hydraulic efficiency of pump is lower. The larger the flow is, the larger the decreasing amplitude of pump efficiency is. With the decreases of inlet guide vane negative angle, the higher hydraulic efficiency of pump increases first then decreases. The inlet guide vane angle affects the axial velocity distribution of the blade trailing edge. [ABSTRACT FROM AUTHOR]

The objective of current research is to study the adiabatic solutions of a plain journal bearing operating with bio-based lubricants containing nanoparticles. Estimation of pressure and temperature fields has been accomplished by simultaneous numerical solutions of the modified Reynolds equation and the adiabatic energy equation. These equations have been solved by adopting the finite difference method with suitable iterative scheme. The analysis has been carried out taking into account the heating effects and non-Newtonian rheology of bio-based nanolubricant following the power law model. The results have been investigated for temperature and pressure fields and the static performance parameters for a broad range of eccentricity ratio ε and different power law index values. The calculated results present that the involvement of nanoparticles in bio-based lubricant significantly enhances the pressure, load carrying capacity and friction force. Moreover, the influence of thermal effects on performance parameters is seen to be maximum at higher values of power law index. [ABSTRACT FROM AUTHOR]

A numerical method was developed to study the effects of the micropolar (MP) lubricants at pure squeeze action in an isothermal elastohydrodynamic lubrication point contact with surface roughness under constant load condition, but without asperities contact. The modified transient stochastic Reynolds equation was derived in polar coordinates by means of the Christensen's stochastic theory and the Eringen's MP fluid theory. The Gauss–Seidel method and the finite difference method were both used to solve simultaneously the modified transient stochastic Reynolds, the load balance, the lubricant rheology and the elasticity deformation equations. The simulation results revealed that the effect of the MP lubricant was equivalent to enhancing the lubricant viscosity. Therefore, the central pressure and film thickness for MP lubricants were larger than those of Newtonian fluids under the same load in the elastic deformation stage. The maximum central pressure of the radial type roughness (RN) was greater than that of the circular type RN. The film thickness of the radial type RN was smaller than that of the circular type RN. [ABSTRACT FROM AUTHOR]

A new approach of coupling multibody dynamics and fluid dynamics is developed to model hydrodynamic lubrication of spherical clearance joints with thin fluid film and relative multidirectional motion. The model accounts for dynamics motion of articulating components as well as both squeeze- and wedge-film actions of the synovial fluid. Multibody dynamics methodology is employed to derive the motion equations and Reynolds equation governs the fluid dynamics. The finite difference method is utilized to discretize the governing equation of lubricant and the multi-grid method augments computational efficiency to acquire outcomes employing a Gauss–Seidel relaxation scheme. Fluid–structure interaction is incorporated into the methodology using a partitioned formulation embedded in a high-order Runge–Kutta time integrators for integrating the nonlinear equations of the coupled system over time of interest. A demonstrative example of total hip arthroplasty is considered and the developed model is assessed against outcomes available in the literature. The effect of initial conditions on the pressure, film thickness and dynamics of the lubricated spherical joint is analyzed and discussed. It is illustrated that maximum fluid pressure is undergone by the hip implant at the first walking cycle of movement due to an unstable state, which is strongly dependent upon the initial condition. Finally, the approach presented in this research work is a robust dynamic model to study hydrodynamic lubrication of spherical joints. [ABSTRACT FROM AUTHOR]

Large propeller lateral loads during ship turning maneuver may cause serious damage on after stern tube bearing. Failure of after stern tube bearing frequently occurs, especially when environmentally acceptable lubricants are used in the ship's stern tube. Therefore, a new design rule for after stern bearing is urgently needed. This paper presents a numerical investigation on the oil film performance of the after stern tube bearing of a super handy-max bulk carrier in turning maneuver. Computational fluid dynamics is adopted to estimate the propeller lateral forces and moments, which are introduced into the shafting alignment calculation. In shafting alignment analysis, the after stern tube bearing is divided into several bearing segments, and the midpoint of journal segments is used to characterize the deflection of the journal centerline. The accurate deflection of the journal center of the after stern tube bearing is obtained through the iteration of the shafting alignment program and Reynolds equation. Moreover, the distribution of oil film pressure and the minimum oil film thickness are recorded. Finally, the criterion for oil film is discussed. [ABSTRACT FROM AUTHOR]

The interaction of a laminar boundary layer with a shock wave at a Mach number M = 1.43 is studied by numerical simulation. The results obtained by direct numerical simulation are compared with the results of calculations using the Reynolds-averaged Navier–Stokes (RANS) equations supplemented with different turbulence models describing laminar–turbulent transition. The possibility of determining the position of the flow turbulence zone based on linear stability theory and the e N -method is estimated. Comparison of the numerical simulation with experimental data shows that engineering RANS methods can be used to study supersonic flows in which transition to turbulence occurs in regions of shock wave–boundary layer interaction. [ABSTRACT FROM AUTHOR]

Transient flow structures and surface heat flux distribution of the interfered flow field induced by a backswept fin were obtained by Nano-tracer-based Planar Laser Scattering and temperature sensitive paints under M = 6. Meanwhile, the Reynolds-averaged Navier–Stokes equations with k-ω Shear-Stress Transport turbulence model were solved to simulate the flow field. The numerical results were compared and analyzed with the experimental results. Typical flow structures in interference areas of the swept fin were observed in experiment, including the detached bow shock wave, separation zone, thin boundary layer around the fin and horseshoe vortex, etc. The numerical results were in good agreement with flow visualization images. For heat flux distribution, the experiment observed the high heat flux region near the side of the fin leading edge caused by separated flow and the region with heat flux increase caused by bow shock. The numerical results of the heat flux caused by bow shock were pretty good, but the results of the high heat flux region near leading edge due to reattachment had much difference with the experimental results, which still need further improvement. [ABSTRACT FROM AUTHOR]

Unsteady flows of a gas with solid particles in a system of two plane "rotor–stator" cascades are investigated. The carrier-gas flow is modeled using the Navier–Stokes equations (pseudo DNS approach) and, for comparison, the Reynolds equations (URANS approach) with the Menter SST k–ω model of turbulence. In both cases, the equations are solved using a second-order finite- volume method. In the absence of particle collisions, the admixture motion is modeled using a Lagrangian approach and the colliding particles are modeled by the Monte Carlo method. The feedback effect of the particles on the carrier gas flow is taken into account. The influence of different factors of random nature (particle distribution over sizes, particle scattering after collisions with the blades, particle–particle collisions) on the admixture flow pattern and particle concentration profiles at the outlet of the stator cascade is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, a square textured parallel slider is considered for a study to improve the hydrodynamic performance of moving parts. The numerical method is employed for the analysis of a square texture with different bottom profiles: flat, triangle T1, triangle T2, and curved. The governing Reynolds equation is solved using a finite difference numerical discretization technique with the Gauss—Seidel iterative scheme. To obtain optimized process parameters, the response surface methodology-based central composite design along with grey relational analysis multi-objective optimization is used. The multi-objective responses are the load capacity and friction coefficient. The triangle T2 bottom profile yields the highest load capacity and the lowest friction coefficient compared to flat, triangle T1, and curved bottom profiles, of which the triangle T1 bottom profile yields the worst results. For the triangle T2 bottom profile, the flow speed is found to be the most significant process parameter, followed by the aspect ratio. Texture density is found to be the least significant parameter based on increasing the load capacity and decreasing the friction coefficient. [ABSTRACT FROM AUTHOR]