Search Results (86)

Hydraulic transients in pressurized pipe systems are significantly influenced by the presence of entrapped air, which alters wave propagation through increased compressibility and energy dissipation. Traditional discrete cavity models, such as the Discrete Gas Cavity Model (DGCM), often assume a constant wave celerity, which limits their accuracy under high gas content conditions. This study evaluated different approaches for representing the effects of gas cavities and unsteady friction in closed pipe transients. The work introduces the Adjustable-celerity Gas Cavity Model (AGCM), a formulation that explicitly couples local air volume and pressure to dynamically adjusted celerity values. Two variants are considered, a non-iterative (AGCM.v1) and an iterative approach (AGCM.v2), the latter ensuring consistency between pressure head and celerity at each time step. The models were evaluated through numerical simulations using both experimental datasets and a hypothetical test case with increasing air fractions. Results show that the AGCM was able to represent celerity magnitudes in unsteady flows with large fractions of air. Also, while constant-celerity models perform well under low-air conditions, variable-celerity formulations offer superior consistency in predicting wave amplitudes and celerity dynamics as gas content increases. These findings underscore the importance of dynamic celerity coupling in transient flow modeling and validate the AGCM as a useful approach for transient modeling in conditions with higher air phase fractions. Full article

This study introduces an efficient and accurate two-stage explicit computational scheme for solving partial differential equations (PDEs) containing first-order time derivatives. The suggested method is a modification of the classical Runge–Kutta scheme that introduces a new first-stage formulation. This minimizes numerical error with moderate step sizes while preserving the stability region of the classical method. Spatial discretization is performed using a sixth-order compact finite-difference scheme to obtain high-resolution solutions. The analysis of stability and convergence is strictly determined for both scalar and system forms of convection–diffusion-type equations. To illustrate the suitability of the method, a dimensionless mathematical model of the unsteady, incompressible, laminar flow of a Prandtl-type non-Newtonian nanofluid over a Riga plate is considered, accounting for viscous dissipation, thermophoresis, Brownian motion, and a magnetic field. Here, the Prandtl ternary nanofluid is defined as a non-Newtonian nanofluid that follows the Prandtl rheological model, and it exhibits three critical transport phenomena: heat conduction, viscous dissipation, and nanoparticle diffusion. Representative values of the Prandtl number $P_r=3$ and Reynolds number $R_e=5$ are used to perform the simulation, and other parameters, including but not limited to the Hartmann number $H_a$, Williamson number $W_e$, thermophoresis $N_t$ and Brownian motion $N_b$, are varied to evaluate the flow behavior. Moreover, an artificial neural network (ANN)-developed surrogate model is used to calculate the skin friction coefficient and the local Sherwood number, using five input parameters: the Reynolds number, Prandtl number, Schmidt number, Brownian motion parameter, and thermophoresis parameter. The governing partial differential equations yield high-fidelity numerical data used to train the surrogate model. The data is split into 80% for training, 10% for validation, and 10% for testing. The ANN is tested using regression analysis and error histograms, which demonstrate high accuracy and generalization capacity. Numerical simulation combined with AI-based prediction is a cost-efficient method for real-time estimation of complex non-Newtonian nanofluid systems. Full article

Laminar separation bubbles (LSBs) on low-Reynolds-number airfoils are sustained by intrinsic unsteadiness driven by Kelvin–Helmholtz (K-H) growth in the separated shear layer. Using incompressible 2D URANS with the SA-$\gamma$ transition model for a NACA 0012 airfoil at $Re=5.3\times {10}^4$, we reveal that numerical dissipation behaves as a critical bifurcation parameter. Validated against the recent Jardin (2025) experimental benchmark, the physical state correctly resolves the LSB-induced pressure plateau ($C_p$) and local negative skin friction ($C_f<0$). However, when numerical dissipation exceeds the K-H instability growth rate, the physical limit-cycle oscillation collapses into a spurious fixed-point attractor—a phenomenon defined as numerical quenching. This pseudo-convergence triggers a catastrophic ∼30% deficit in mean lift ($C_l$). Furthermore, at $\alpha =6^{\circ }$, a drag-mechanism inversion is identified: while the physical branch is dominated by LSB-induced pressure (form) drag, the quenched branch exhibits a non-physical drag surge that exceeds the fully turbulent baseline. Phase portraits and power spectral densities ($St\approx 0.2$) provide objective diagnostics, demonstrating that standard residual convergence is a deceptive indicator of physical fidelity in transitional separated aerodynamics. Full article

This study compares the numerical results obtained with an axisymmetric quasi two-dimensional (Q2D) model with those from two different types of dimensional models for smooth–turbulent transient flows generated by an instantaneous valve closure. The first is a high-accuracy three-dimensional computational fluid dynamics (3D-CFD) model. The second type is the one-dimensional (1D) model, analysing results from five unsteady friction formulations, namely four convolution integral-based (CIB) formulations and one instantaneous acceleration-based (IAB) formulation. The Q2D and 1D models are also compared with experimental data collected under laboratory conditions for a fast but non-instantaneous valve closure. The differences between the 1D, Q2D and 3D-CFD modelling approaches are quantified and discussed, focusing on the ability of each model to reproduce the different features of the transient flow phenomenon and the associated computation–accuracy trade-offs. The 3D-CFD model exhibits a more pronounced front-wave rounding, as it more accurately represents the valve conditions, where its closure induces highly turbulent flow with a strongly heterogeneous velocity profile. The Q2D model provides an accurate estimation of unsteady energy dissipation, when fully developed flow conditions are ensured with the advantage of requiring less computational effort than the 3D-CFD. These conclusions also apply to full convolution-based 1D models, whereas approximate 1D formulations can significantly reduce accuracy and limit their range of applicability. The comparison with experimental data corroborates the excellent results of the Q2D model. The Q2D model demonstrates to be an efficient alternative in terms of accuracy and computational time to 3D-CFD and 1D full convolution models. Full article

The frictional resistance of impeller machinery blades such as aircraft engines, gas turbines, and wind turbines has a decisive impact on their efficiency and energy consumption. Inspired by the micro-tooth structure on the surface of shark skin, microstructural drag reduction technology has become a cutting-edge research direction for improving aerodynamic performance and a continuous focus of researchers over the past 20 years. However, the significant difficulty in fabricating microstructures on three-dimensional curved surfaces has led to the limited widespread application of this technology in engineering. Addressing the issue of drag reduction and efficiency improvement for small axial flow fans (local Reynolds number range: (36,327–40,330), this paper employs Design of Experiments (DOE) combined with high-precision numerical simulation to clarify the drag reduction law of bionic microgroove surfaces and determine the dimensions of bionic microstructures on fan blade surfaces. The steady-state calculation uses the standard k-ω model and simpleFoam solver, while the unsteady Large Eddy Simulation (LES) employs the pimpleFoam solver and WALE subgrid-scale model. The dimensionless height (h⁺) and width (s⁺) of microgrooves are in the range of 8.50–29.75, and the micro-grooved structure achieves effective drag reduction. The microstructured surface is fabricated on the suction surface of the blade via a spray coating process, and the dimensions of the microstructures are determined according to the drag reduction law of grooved flat plates. Aerodynamic performance tests indicate that the shaft power consumed by the bionic fan blades during the tests is significantly reduced. The maximum static pressure efficiency of the bionic fan with micro-dimples is increased by 2.33%, while that of the bionic fan with micro-grooves is increased by 3.46%. The fabrication method of the bionic microstructured surface proposed in this paper is expected to promote the engineering application of bionic drag reduction technology. Full article

For extracting oil and gas from low-permeability reservoirs, pulse hydraulic fracturing offers superior performance over conventional hydraulic fracturing. Pulse hydraulic fracturing employs variable-rate injection to create pressure waves, which significantly increases the recovery rate. However, current pulse hydraulic fracturing research primarily focuses on the wellbore. The theory describing how pressure waves propagate and attenuate within fractures is still immature, potentially hindering the achievement of optimal fracture propagation and diversion. A two-dimensional pressure-wave equation incorporating both steady and unsteady friction was established and numerically solved using a high-accuracy explicit compact finite-difference method and was validated. The propagation process and pressurization phenomenon of pressure waves were analyzed, and the effects of treatment frequency, amplitude, and waveform, as well as steady and unsteady friction coefficients, on the attenuation characteristics of pressure waves within fractures were analyzed. The model’s validity is based on the pad fluid stage of hydraulic fracturing, informing the rational selection of treatment parameters in engineering practice, thereby improving fracturing performance and having practical significance for enhancing the development efficiency of low-permeability reservoirs. Full article

Nowadays, the potential of hydrokinetic turbines as a sustainable alternative to complement traditional hydropower is widely recognized. This study presents a comprehensive numerical analysis of twin straight-bladed Darrieus hydrokinetic turbines, characterizing their hydrodynamic interactions and performance characteristics. The influence of turbine configuration spacing and flow parameters on efficiency and wake dynamics are investigated. The employed 3D computational approach combines the overset mesh technique, used to capture the unsteady flow around the turbines, with the URANS k-ω Shear Stress Transport (SST) turbulence model. Results show that turbine spacing improves power coefficients and overall efficiency, albeit at the cost of slower wake recovery. A noticeable performance increase is observed when the turbines are spaced between 1.5 and 2 diameters apart, which is predicted to reach up to 40% regarding the single turbine. Furthermore, the effect of flow interaction between the turbines is examined by analyzing the influence of turbine spacing on flow structures as well as pressure and skin friction coefficients on the blades. The performed analysis reveals that vortex detachment is delayed in the twin-turbine configuration compared to the isolated case, which partially explains the observed performance enhancement. The insights gained from this work are expected to contribute to the advancement of renewable hydrokinetic energy technologies. Full article

Dual-inlet tail escapes, combining an orifice and a weir, are key hydraulic structures that evacuate excess water from canal termini during maintenance and protect berms by discharging surplus irrigation flows. Conventional sizing methods typically depend on trial and error, which is time-consuming and may yield suboptimal design. This study introduces a graphical design approach and a MATLAB-based tool, TAILOPT, developed to streamline tail escape design. The tool incorporates both the Fanning and Darcy–Weisbach friction formulations for head loss estimation and can automatically generate an “.inp” file for EPA-SWMM, enabling direct unsteady-state hydraulic assessment. This integration reduces design effort and supports evaluation of alternative hydraulic and drainage scenarios within a single workflow. Two applications illustrate the framework. The first shows that overly steep drainage slopes (Sp > 2%) are impractical, while vertical drops may require larger pipe diameters. The second application applies TAILOPT to a distributary canal, determining the optimal pipe size and verifying its performance in EPA-SWMM under emergency surplus flow and routine dewatering conditions. The results demonstrate that the method yields economical, robust, and practitioner-friendly designs; however, modeling simplifications, such as assuming continuously submerged orifice flow, can introduce minor deviations in the predicted channel emptying times. Full article

The dynamic interactions among the internal components of aero-engine main shaft bearings under unsteady-state conditions are intricate, involving clearance collisions, contact, friction, and lubrication. The dynamic characteristics of bearings significantly influence the performance and stability of mechanical systems. This study establishes a rigid–flexible coupling dynamic model for angular contact ball bearings with two-piece inner rings based on Hertz contact theory and lubrication theory. It systematically analyzes the dynamic characteristics of bearings under the coupling effects of acceleration, deceleration, and impact load. This study explores the influence of various loads, bearing speeds, and groove curvature radius coefficients on the dynamic characteristics of bearings. The findings indicate that the uniform speed phase of a bearing is highly responsive to impact load, followed by the deceleration phase, while the acceleration phase shows lower sensitivity to impact load. The groove curvature radius coefficient significantly affects the contact stress between the ball and its corresponding raceway, with contact stress increasing as the groove curvature radius coefficient rises. As the axial load decreases and the radial load, bearing speed, and groove curvature radius coefficient increase, there is a rise in pocket force, guiding force, and maximum equivalent stress of the flexible cage. Impact load leads to short-term intense fluctuations in the thickness of the bearing oil film, which can be alleviated by an increase in axial load. The oil film thickness firstly increases and then decreases with respect to the groove curvature radius coefficient. Furthermore, variations in bearing speed notably influence the thickness of the bearing oil film. This study analyzes the dynamic characteristics of bearings under the coupling effects of acceleration, deceleration, and impact load, offering insights for the design and optimization of angular contact ball bearings with two-piece inner rings. Full article

A high-speed valve (HSV) is used to control the friction plate accurately and flexibly in the shifting stages of an automatic transmission. In the past, the transient modeling and dynamic improvement of HSVs neglected fluid–solid coupling and motion-induced fluid force (MIFF), which made it difficult to improve the response performance and kinetic energy efficiency of HSVs. In order to fully represent the MIFF and internal flow field features, a novel general approximate model for HSVs with a more accurate fidelity unsteady computational fluid dynamics (CFD) analysis is built in this paper. In addition, the experimental data of HSVs when the sphere is moving in oil-free or oil-immersed media are collected to verify the proposed model. In order to validate the model, the mechanism law of buffer groove towards the MIFF is tracked at length. The motion-induced added mass with buffer groove is reduced by 43.9%. The experimental results show that under the working pressure of 1 MPa (rated pressure), the opening time is shortened to 0.90 ms, which is 11.8% shorter than the original structure. The closing time is shortened from 1.5 ms to 1.34 ms, which represents a decrease of 10.7%. The buffer groove improves the kinetic energy efficiency from 41.91% to 46.70% in the start-up phase and from 41.98% to 56.75% in the close-up phase. This study provides a new perspective for improving the dynamic performance and energy efficiency of the system in terms of the MIFF. Full article

The transport of deformable particles (TDPs) through porous media has been of considerable interest due to the multiple applications found in industrial and medical processes. The adequate design of these applications has been mainly achieved through experimental efforts, since TDPs through porous media are challenging to model because of the mechanical blockage of the pore throat due to size exclusion, deformation in order to pass through the pore throat under the driven pressure, and breakage under strong extrusion. In this work, based on the diffusivity equation and considering the TDP as a complex fluid whose viscosity and density depend on the local pressure, a simple but accurate theoretical model is proposed to describe the pressure behavior under steady- and unsteady-state flow conditions. Assuming a linear pressure dependence of the viscosity and density of the TDPs, valid for moderate pressure changes, the solution of the mathematical model yields a quantitative correlation between the pressure evolution and the parameters compressibility, viscosity coefficient, elastic modulus, particle size, and friction factor. The predictions of the model agree with experiments and allow the understanding of transport of deformable particles through a porous media. Full article

The current paper focuses on the assessment of radial mesh influence on the description of the transient event obtained by an axisymmetric model. The objective is to reduce computational effort while accurately calculating hydraulic transients in smooth–turbulent pressurized pipes. The analyzed pipe system has a reservoir–pipe–valve configuration with an inner diameter of 0.02 m and a total length of 14.96 m, with the initial discharge being equal to 120 × 10⁻³ L/s (Re = 7638). An extensive study is carried out with 80 geometric sequence meshes by varying the total number of cylinders, the geometric common ratio, and the pipe axial discretization. The benefit of increasing the geometric common ratio is highlighted. A detailed comparison between two meshes is presented, in which the best mesh (i.e., the one with the lowest computational effort) has a three-fold higher value of the geometric common ratio. The two meshes show small differences for the instantaneous valve closure, limited to a time interval immediately after the arrival of the pressure surge and only during the first pressure wave. The dynamic characterization of the transient phenomenon demonstrates the in-depth consistency between the model results and the hydraulic transients’ phenomenon in terms of the piezometric head, the wall shear stress, and the mean velocity time-history, in comparison to the results obtained with the shear stress, lateral velocity, and axial velocity profiles. Full article

When water pipelines undergo scenarios such as valve closure or leakage, they often operate in a gas-liquid two-phase flow state, which can easily cause abnormal pressure fluctuations, exacerbating the destructiveness of water hammer and affecting the safe operation of the pipeline. To study the problem of abnormal fluctuations in complex water pipelines, this paper establishes a transient flow model for gas-containing pipelines, considering unsteady friction, and solves it using the discrete gas cavity model (DGCM). It also studies the influence of factors such as valve closing time, initial flow rate, gas content rate, leakage location, and leakage amount on the end-of-valve pressure. Furthermore, it locates the leakage position using a genetic algorithm-backpropagation neural network (GA-BP neural network). The results show that increasing the valve closing time, increasing the gas content rate, decreasing the initial flow rate, and increasing the leakage amount all reduce the pressure peak inside the pipeline. The model constructed using the GA-BP neural network effectively predicts the leakage location with a mean absolute percentage error (MAPE) of 9.26%. The research results provide a reference for studies related to the safety protection of water conveyance projects. Full article

This paper presents the results of laboratory tests of water hammer phenomenon induced in two series-connected copper pipes with different diameters (a diameter ratio of 1:1.25) by a quick-closing valve installed at the end of the simple upstream tank–pipeline–valve system. Test results were compared with calculations made with the use of various friction loss models incorporated in a one-dimensional model based on a method of characteristics. The calculation takes into consideration quasi-steady and unsteady friction models as well as a special discretization procedure of the solution domain that ensures the elimination of numerical diffusion in the numerical scheme. The main attention was paid to determining the value of the pressure wave speed in the pipes, which has a significant influence on the compliance between the calculations and the experimental results of the pressure amplitudes and wave frequencies. Two methods of determining the wave speed were proposed and evaluated based on the measurements. The results presented in this article indicate that the use of the proposed procedure instead of the classic formulas for determining the pressure wave speed gives the desired correspondence between the frequencies of the measured and calculated waves. Calculation examples made with the use of different friction models showed that application of the developed procedure for discretization of the solution domain and the method used for determining the wave speed opened the possibility of reliable verification of these models, free of numerical errors and frequency discrepancies between the computational and measured wave. Full article

Hydraulic fracturing, especially pulse hydraulic fracturing, is an important method for extracting oil and gas from low-permeability reservoirs, improving recovery rates significantly. Pulse hydraulic fracturing, which involves varying injection rates to create pressure waves, outperforms traditional constant-flow fracturing methods significantly. However, during pulse hydraulic fracturing operations, the flow properties of the fluid in the column change from moment to moment. Furthermore, current research on pulse hydraulic fracturing primarily focuses on vertical wells, while horizontal wells have become a common operational strategy. Therefore, a transient flow model of fluid within a horizontal well, considering variable-flow injection and unsteady friction conditions, is established in this paper. The model is solved using both the characteristic line method and the finite difference method. The hydrodynamic properties of the fracturing fluid were analyzed, and the propagation mechanisms of pressure waves within horizontal wells under various fluid injection schemes and well depths are analyzed to provide a reference for selecting appropriate fluid injection schemes in engineering practice. The study highlights the impact of fluid viscosity and injection flow amplitude on bottomhole pressure fluctuations, advancing the efficient development of low-permeability oilfields. Full article