Time-averaged Equations Research Articles

Research on numerical prediction of hydrodynamic interference under coupling of pod propeller and hull

Abstract Taking the cable-laying ship and the pod propeller as the research objects, based on the Reynolds time-averaged RANS equation and sliding moving grid technology, the self-propulsion numerical calculation of the coupling of the pod propeller and the hull was completed. By comparing the resistance of the bare hull and the thrust of the pod propeller, the hydrodynamic interference under the coupling state of the pod propeller and the hull is analyzed. The results show that when Fr=0.295, the total resistance of the ship increases by 21.6%, the pressure difference resistance increases by 30.5%, the wake fraction is 0.011, and the thrust derating is 0.178. The research results provide theoretical and technical guidance on the interference problem between the hull and the pod propeller.

CFD modeling of orthogonal wave-current interactions in a rectangular numerical wave basin

Sea-crossing bridges are subject to long-term simultaneous wave and current loadings throughout thier life cycle. The wave-current interaction makes the hydrodynamic load calculation difficult and challenging, especially in simulating the noncollinear wave-current interactions between waves and currents due to potential disturbances such as wall reflections within the observational zone. Therefore, in this study, a numerical flume was built based on the Reynolds time-average (RANS) equation and k-ε turbulence model using the computational fluid dynamics (CFD) software Flow-3D to investigate noncollinear wave-current interaction numerical simulation methods. The collinear wave-current interactions were then numerically simulated using the inflow boundary and mass source wave generation method, and the developed numerical flume was validated with experimental results based on a large-scale wave-current flume. Furthermore, a three-dimensional numerical simulation of complex noncollinear wave-current interactions was developed. The developed rectangular numerical basin based on the collinear wave-current flume was validated with theoretical results regarding wavelength variations in a noncollinear wave-current interaction field. Finally, the effective observation zone of orthogonal wave-current interactions was explored. This study is important for advancing bridge hydrodynamic research into noncollinear wave-current interactions.

A time-averaged method to analyze slender rods moving in tubes

The motion of slender rods in narrow tubes involves the coupling of axial movements and transverse vibrations, in which the transverse vibration exhibits high frequency and chaotic characteristics. These characteristics render the computational cost of the time integration to the motions of rods and tubes expensive. To solve this problem, this paper proposes a novel time-averaged method, which contains two innovations: 1) By time averaging the traditional dynamic equations, the time-averaged dynamic equations describing the rod-tube system are established based on the time-averaged concept used in turbulence problems; 2) Two time-averaged contact models are developed, by fitting the time-averaged sample set using the polishing function and the machine learning, respectively, to construct the relationship between the time-averaged contact gaps and the time-averaged contact forces. The time-averaged method can use a large time step, which is far larger than that required for the time integration of traditional methods, thus reducing the computational cost. Inclined and rolling experiments of the rod-tube system, as well as numerical experiments of the control rod drop in a nuclear reactor, are conducted to validate the accuracy of the time-averaged method. Comparative analyses are carried out between the time-averaged method and six continuous contact models, demonstrating the high computational efficiency of the proposed method. Moreover, the experimental results can provide benchmark data for algorithm verification for scholars studying dynamic contact algorithms.

Integrated CFD and MBD methods for dynamic performance analysis of a high-speed train transitioning through varied windbreak corridor designs

With increasing train speeds, the wind environment along routes has become complex, variable, and extreme. Constructing windbreak facilities is an effective strategy to enhance train operational safety in windy zones. Various windbreak designs exhibit notable differences in improving train dynamic performance, and economic considerations are also crucial. Utilizing the non-constant compressible Reynolds time-averaged equation URANS (Unsteady Reynold-averaged Navier–Stokes) alongside the shear-stress transport (SST) k-ω turbulence model, this study simulates the non-constant aerodynamic characteristics of a 350 km/h high-speed train traversing through different forms of windbreak corridors in a 30 m/s wind zone. The train's dynamic response was captured using a combined CFD–MBD (Computational Fluid Dynamics and Multi-Body Dynamics) offline time-domain simulation, the accuracy of which was verified experimentally. Results indicate that vortices of various positions and shapes form in the flow field along the windbreak corridor depending on the size of the openings. Using the no-windbreak corridor (Case 1) and the fully enclosed corridor (Case 4) as control groups, it was observed that smaller openings lead to more stable airflow, enhancing peak damping and fluctuation effects, albeit with varying stages of aerodynamic load fluctuation. The 1/3-opening windbreak corridor (Case 3) effectively mitigated the sudden aerodynamic load changes at the wind zone transition of the 2/3-opening windbreak corridor (Case 2), with the primary fluctuation area in Case 3 being the wind section. Dynamic analyses revealed that Case 2 exhibited insufficient lateral aerodynamic performance, raising derailment concerns. In contrast, Case 3 ensured travel safety and comfort effectively, while Case 4 offered excessive protective capacity. This study's findings serve as a valuable reference for designing windbreak corridors and ensuring the safe operation of trains in windy regions.

Fully developed pipeline flow fast simulation model and application to a rod bundle subchannel

For the fully developed pipeline flow, if the radial time-averaged velocity and radial pressure gradient can be ignored, the time-averaged Navier-Stokes equations can be simplified into a diffusion equation. Based on this, the Fully Developed Model (FDM) was proposed. The adiabatic FDM was applied to the simulation of the flow field in a rod bundle subchannel and got results consistent with that from the commercial CFD code. The short time calculation of FDM makes its application in system analysis codes becoming possible.

Numerical Studies on Effects of Blade Number Variations on Performance of Sludge Pumps

The sedimentation of sludge in pangasius catfish ponds constitutes a notable challenge for the economic advancement of Vietnamese farmers. Sludge formation is the result of a composite process involving residual food, waste material, and algae, which undergo decomposition, thereby releasing hazardous gases such as hydrogen sulfide (H2S), ammonia (NH3), and nitrogen dioxide (NO2). These emissions subsequently diminish oxygen levels within the ponds, adversely affecting the growth of catfish. Removal of the accumulated sludge is deemed necessary every two months throughout the catfish cultivation cycle. A proficient sludge pump, designed to function effectively within the Vietnamese environmental context, becomes imperative to address this predicament. The primary objective of this research paper is to explore the influence of blade count on the performance metrics of a sludge pump. Given that pangasius ponds typically exhibit depths ranging from 2 to 4 meters, this study is predominantly centered on assessing pump performance within the specified head range of 2 to 4 meters. Employing the computational fluid dynamics (CFD) methodology, the research delves into the fluid dynamics of sludge pumps featuring impeller blades numbering 7, 8, 9, and 10. These pumps are modeled as semi-open impeller centrifugal pumps operating at a speed of 2200 revolutions per minute (rpm), with the k-e turbulence model and the time-averaged Navier-Stokes equation serving as the fundamental analytical framework.

Predicting the acoustic characteristics of seafloor sediments containing cold spring carbonate rocks

The acoustic and physical properties of two valuable marine cold spring carbonate rock samples gathered from the Chaoshan Depression in the South China Sea were measured. The Wyllie time-average equation was applied to analyze the measured sound speeds and their trend under different porosities, and the sound speeds of marine cold spring carbonate rocks were found to be consistent with those of terrestrial carbonate rocks. The Voigt model, Reuss model, and Voigt-Reuss-Hill model were used to predict the characteristics of the sound speed for four states of seafloor sediments containing cold spring carbonate mineral particles or rocks. For these four states of marine cold spring carbonate mineral particles existing on or in seafloor sediments, the sound speed and reflection coefficient of a mixture of seafloor surface sediments containing cold spring carbonate mineral particles or rocks decrease with an increase in the volume ratio of the seafloor sediment. This method for predicting the reflection coefficient provides evidence to explain the high and low reflection coefficients observed in Chirp sub-bottom profiles of cold spring seepage areas.

Hydrodynamic Model of Hydraulic Engineering Based on Trigonometric Function Relation Equation

Abstract In order to explore the application of fluid mechanics technology in water conservancy and hydropower stations, the author proposes the study of hydraulic engineering fluid mechanics model based on trigonometric function relationship equation. According to standard k- ε Double equation and Reynolds time average (N-S) equation, given the runner boundary conditions, establish the mathematical model of the internal flow of the hydraulic turbine. Through CFD simulation technology, the runner of hydraulic turbine is numerically simulated to obtain the velocity distribution and blade pressure distribution inside the runner, movable guide vane and fixed guide vane, the reliability of the design is improved, and the application of CFD technology in hydropower project is analyzed with an example. The results show that, when the diameter of guide vane distribution circle is 4760mm, the scheme is optimal, and the relative efficiency under the optimal working condition is 96.35%. The flow of the modified runner from the inlet of the volute to the outlet of the draft tube is very stable under the optimal working condition, and there is no obvious vortex, especially there is no obvious vortex belt and vortex at the outlet of the runner; There is no obvious vortex in the draft tube, the flow on both sides of the pier is very uniform, and the flow on one side is not significantly greater than that on the other side, which fully shows that the flow performance of the modified runner is good. After reconstruction, the runner outlet flow field is good, and the internal flow line of the draft tube is smooth. The application prospect of hydrodynamic algorithm for hydraulic engineering is relatively broad.

Interaction between Instabilities in Vertical-Axis Turbine Blades

This work investigates five different instability mechanisms that may occur and interact in straight-bladed H-rotor vertical-axis turbines. Specifically, it considers the static instabilities of divergence and centrifugal buckling as well as the dynamic instabilities of flutter, main resonance, and parametric resonance. This is done by applying Theodorsen’s model for unsteady aerodynamics with traditional finite element methods. The resulting model comprises bend-twist-coupled elements that inherently account for fluid and centrifugal effects. Comparisons with experimental results in the literature are used to assess the accuracy and limitations of the model. Eigenvalue analysis is used on time-averaged equations to predict divergence, flutter, and centrifugal buckling, as well as identify regions where main and parametric resonance may be excited. Time history analysis is used to provide further insight and show main and parametric resonance explicitly. Stability plots are constructed using both methods of analysis and presented in the forcing parameter space. Interaction between the different instability mechanisms is observed, including a region of parametric stabilization that is found to extend beyond the expected boundaries of both divergence and flutter.

Effect of High Solid Concentration on Friction in a Transitional and Turbulent Flow of Bioliquid Suspension

Some suspensions in nature have a complex structure and demonstrate a yield shear stress and a non-linear relationship between the shear rate and the shear stress. Kaolin clay suspension is such an example in engineering, whereas in nature it is blood. This study represents an innovative approach to simulate bioliquid flow, similar to that of blood when the solid concentration is high. The objective of this study is to examine the influence of high solid concentration of bioliquid, similar to blood, on energy losses and velocity profiles in turbulent and transitional flow in a narrow tube. Using the analogy between the suspension of kaolin clay and blood, the physical model and the mathematical model were formulated. The mathematical model comprises continuity and time-averaged momentum equations, a two-equation turbulence model for low Reynolds numbers, and a specially developed wall damping function, as such suspensions demonstrate the damping of turbulence. Experimental data on blood rheology for solid concentrations equal to 43% and 70% by volume, gathered from the literature, were used to establish a rheological model. The results of the simulations indicated that an increase of solid concentration in bioliquid suspension from 43% to 70% causes an increase in wall shear stress to approximately 10% and 6% for transitional and turbulent flow, respectively, and changes in velocity profiles. Such simulations are important if an inserted stent or a chemical additive to the bioliquid suspension is considered, as they can influence the shear stress. The results of the simulations are presented in graphs, discussed, and conclusions are formulated.

CONSTRUCTAL DESIGN APPLIED TO INVESTIGATE THE INFLUENCE OF GEOMETRY ON THE MASS FLOW RATE OF AN INCLINED PASSIVE WALL SOLAR CHIMNEY ATTACHED TO A ROOM

The present work aims to analyze the turbulent flow in an inclined passive wall solar chimney attached to a room, evaluating the influence of its geometry on the thermal performance of the building (measured by the mass flow rate in the chimney exit) by means of Constructal Design. The flow is considered turbulent, incompressible, under natural convection heat transfer, transient and in a two-dimensional domain that simulates a solar chimney attached to a room. Time-averaged conservation equations of mass, momentum, and energy are numerically solved with the finite volume method using the commercial package FLUENT. For closure modeling of turbulence, it is employed the standard k – ε model. Chimney and room areas are the problem constraints. Moreover, the problem is subjected to three degrees of freedom: the ratio between the inlet opening size and chimney height (Hi/Ha) (which is maintained constant in the present investigations, Hi/Ha = 0.05); ratio between the width of inferior base of the chimney and its height (Wg/Ha); and the ratio between the exit air gap and the inferior base widths of the chimney (We/Wg). The latter two degrees of freedom are varied. Results showed that the degrees of freedom analyzed have a strong influence on the mass flow rate of the air in the building, confirming that the geometrical configuration of solar chimney can be important for the improvement of thermal conditions on the attached building.

Optimal Control of the Initial Condition in the Problem of Gas Lifting

A partially periodic control problem is considered, where the control parameter enters the initial condition. We study the formalization related to the calculus of variations. The necessary conditions are written out in the form of Euler–Lagrange equations, with the help of which an algorithm for finding the optimal program trajectories is developed. The results are illustrated by an example when the motion is described by a time-averaged hyperbolic equation at a sufficiently large well depth during a gas lift.

Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

Spatial patterns are a significant characteristic of lasers. The knowledge of spatial patterns of structured laser beams is rapidly expanding, along with the progress of studies on laser physics and technology. Particularly in the last decades, owing to the in-depth attention on structured light with multiple degrees of freedom, the research on spatial and spatiotemporal structures of laser beams has been promptly developed. Such beams have hatched various breakthroughs in many fields, including imaging, microscopy, metrology, communication, optical trapping, and quantum information processing. Here, we would like to provide an overview of the extensive research on several areas relevant to spatial patterns of structured laser beams, from spontaneous organization to multiple transformations. These include the early theory of beam pattern formation based on the Maxwell–Bloch equations, the recent eigenmodes superposition theory based on the time-averaged Helmholtz equations, the beam patterns extension of ultrafast lasers to the spatiotemporal beam structures, and the structural transformations in the nonlinear frequency conversion process of structured beams.

A turbulence modeling study of the precessing vortex core in a pipe flow

The phenomenon of precessing vortex core is observed experimentally when swirl is imparted on an axial flow in a pipe. It manifests as a coherent structure in the form of a helical vortex of regular wavelength whose axis is coincident with the pipe’s axis. The most striking consequence of this pattern of flow is the generation of periodic fluctuations in the streamwise distribution of the wall static pressure and skin friction. While the prediction of the precessing vortex has proved possible with large-eddy simulations, there is no record of this phenomenon being captured in great detail by Reynolds-averaged Navier-Stokes methods utilizing turbulence models to close the time-averaged equations. The purpose of the research reported here was to determine whether the precessing vortex core and its impact on conditions at the wall can be captured using this approach. The turbulence model used was of the Reynolds-stress transport type which involves the solution of a differential transport equation for each of the six non-zero components of the Reynolds stress tensor. Previous studies in which such models were used in the prediction of rotating and swirling flows have shown that their performance is largely determined by the way in which the difficult fluctuating pressure-strain correlations that appear in these equations are modeled. To this end, four very different alternative models for these correlations were assessed by comparisons with experimental data for a swirling pipe flow at relatively high swirl number. It was found that the models do indeed capture the precessing vortex revealing it to be in the form of an exceptionally well-defined double vortex. It was also found that the expected periodic fluctuations in static pressure and wall skin friction, not previously obtained in turbulence model studies, are captured by the present closures.

Investigation on the Influence of Flow Passage Structure on the Performance of Bionic Pumps

The flapping hydrofoil bionic pump drives the hydrofoil to make simple harmonic motion and completes one-way water pumping in the flow passage. As a new pump device that can realize ultra-low head water delivery, the flapping hydrofoil device can effectively enrich the drainage methods of plain rivers and improve water delivery efficiency, and the passage structure is the key factor of ultra-low head devices. In this paper, the two-dimensional flow passage models are established, and the flapping of the airfoil is realized by using the dynamic grid technology. Based on the continuity equation, k-ε turbulence model, and Reynolds time-averaged equation, the flapping hydrofoil device is simulated by transient calculation. The hydraulic performance characteristics of various passages with different widths, such as square passages, micro-arc passages, and convergent–divergent passages, are calculated and simulated. The results show that, under the fixed motion parameters, the narrower the passage width, the higher the outlet velocity, lift, and efficiency of the device, the lower the flow rate. The contraction–expansion pipe can effectively improve the efficiency and flow rate of the device, and, before the wake is stable, the longer the contraction section the better the lifting effect. However, the micro-arc pipeline will affect the formation of a double-row anti-Karman vortex street, resulting in greater energy loss and in its hydraulic performance being inferior to that of the square passage.

Aerodynamic Analysis of Large Aspect Ratio Parafoil

Large aspect ratio parafoils are more attractive compared with moderate ones less than 3.5, since they either improves load-carrying capacity with the same aero-dynamical area or decreases taxing speed with the same load. Based on its original airfoil, one open-source elliptical parafoil with 4.7 AR is modified while scaling the canopy geometric parameters, then CFD simulations, solving the incompressible Reynolds time-averaged Navier-Stokes equation with the (SST) K-ω turbulence model in the finite volume method, are adopted to analyze its aerodynamics in forward taxing mode as well as steering mode with lateral wind. With the numerical simulation results of this canopy, lift and drag are analyzed according to their attack angle profiles for taxing. The steering mode with the deflection of one-side flap increases the drag coefficient significantly, even it raises its lift simultaneously, reduces the lift-drag ratio, and generate rolling and yaw moments; The rolling moment due to lateral wind during steering mode has two phases of rising linked by a short straight line when sideslip angle increases, while yaw moment increases to a peak value then reduces, finally followed by a relatively stable trend. Compared with the above two moments, the pitching moment changes moderately with the increase of the sideslip angle, although it has an overall decreasing trend; The simulation of the modified canopy provides a calculation basis for its following manufacture and dynamical modelling.

Geometrical investigation of cooling channels with two alternated isothermal blocks under forced convective turbulent flow

The present work performs a numerical analysis of the geometrical investigation of a two-dimensional channel with two alternated isothermal rectangular blocks subjected to turbulent forced convective flows. Constructal Design associated with Exhaustive Search is used to investigate the influence of the geometry of the isothermal blocks over the performance of the cooling convective flows in a multi-objective viewpoint, i.e., considering the pressure drop and heat transfer rate. The time-averaged equations of continuity, momentum, and energy conservation are solved with the finite volume method. The k–omega shear stress transport model is used for the closure of turbulence. The effect of the two proposed degrees of freedom, the height/length ratio of the two blocks (H_{1}/L_{1} and H_{2}/L_{2}), is analyzed in relation to the proposed objectives. Regarding the thermal purpose, the geometry with the highest insertion into the channel led to the best performance, while the opposite configuration led to the best fluid dynamic performance. This behavior was similar to that previously found in the literature for forced convective laminar flows. For a multi-objective perspective, the use of technique for order preference by similarity to ideal solution indicated that asymmetric blocks led to the best multi-objective performance when both performance indicators had the same weight.

Numerical Study for Flow Loss Characteristic of an Axial-Flow Pump as Turbine via Entropy Production Analysis

Low-head vertical axial-flow pump as turbine (PAT) devices play a vital part in the development of clean energy for hydropower in plain areas. The traditional method of evaluating the flow loss in hydraulic machinery is calculated by the pressure drop method, the limitation of which is that the location of the occurrence of large losses cannot be accurately determined. In this paper, entropy production theory is introduced to evaluate the irreversible losses in the axial-flow PAT from the perspective of the second law of thermodynamics. A three-dimensional model of the axial-flow PAT is established and solved numerically using the Reynolds time-averaged equation, and the turbulence model is adopted as Shear Stress Transport–Curvature Correction (SST-CC) model. The validity of the entropy production theory to evaluate the energy loss distribution of the axial-flow PAT is illustrated by comparing the flow loss calculated by the pressure drop and the entropy production theory, respectively. The entropy production by turbulent dissipative dominates the total entropy production in the whole flow conduit, and the turbulent dissipative entropy accounts for the smallest percentage of the whole conduit entropy production at the optimal working condition Qbep, which is 51%. The impeller and the dustpan-shaped conduit are the essential sources of hydraulic loss in the entire flow conduit of the axial-flow PAT, and most of the energy loss of the impeller occurs at the blade leading edge, the trailing edge, and the flow separation zone near the suction surface. The energy loss of the dustpan-shaped conduit results from the high-speed flow from the impeller outlet to dustpan-shaped conduit to form a vortex, backflow and other chaotic flow patterns. Flow impact, flow separation, vortex and backflow are the main causes of high entropy production and energy loss.

Numerical Study and Geometric Investigation of the Influence of Rectangular Baffles over the Mixture of Turbulent Flows into Stirred Tanks

The present work aims to define strategies for numerical simulation of the mixture of turbulent flows in a stirred tank with a low computational effort, and to investigate the influence of the geometry of four rectangular baffles on the problem of performance. Two computational models based on momentum source and sliding mesh are validated by comparison with experimental results from the literature. For both models, the time-averaged conservation equations of mass, momentum and transport of the mixture are solved using the finite volume method (FVM) (FLUENT® v.14.5). The standard k–ε model is used for closure of turbulence. Concerning the geometrical investigation, constructal design is employed to define the search space, degrees of freedom and performance indicators of the problem. More precisely, seven configurations with different width/length (L/B) ratios for the rectangular baffles are studied and compared with an unbaffled case. The momentum source model leads to valid results and significantly reduces the computational effort in comparison with the sliding mesh model. Concerning the design, the results indicate that the case without baffles creates the highest magnitude of turbulence kinetic energy, but poorly distributes it along the domain. The best configuration, (L/B)o = 1.0, leads to a mixture performance nearly two times superior than the case without baffles.

Aerodynamic study of low Reynolds number airfoil and mini-unmanned aerial vehicle in simulated rain environment

PurposeRainfall is one of the main atmospheric conditions that significantly affect the aerodynamic performance of the low Reynolds number flights. In this paper, the adverse effects of rain on the aerodynamic performance of a two-dimensional (2D) airfoil with a chord-based low Reynolds number of 2 × 105 and the mini-unmanned aerial vehicle (UAV) for various flight conditions, i.e. 0°–40° at Mach number 0.04 were studied numerically. The purpose of this study is to explore the aerodynamic penalties that affect the liquid water content (LWC = 5.33) of the airfoil and UAV performance in rain under different flying conditions.Design/methodology/approachThe Eulerian–Lagrangian two-phase flow method is adopted to simulate the rain environment over an airfoil and mini-UAV aerodynamic performances. The Reynolds Averaged Navier–Stokes equations are considered to solve the time-averaged equations of motion for fluid flow.FindingsThe effect of rainfall on the airfoil and mini-UAV is studied numerically and validated experimentally. For 2D airfoil, the lift and drag coefficients for both numerical and experimental results show a very good correlation at Reynolds number 2 × 105. For three-dimensional (3D) mini-UAV, the lift and drag coefficients for both numerical and experimental results show a very good correlation at Mach number 0.04. The raindrops distribution around the airfoil, premature trailing edge separation, boundary-layer velocity profiles at five different chord positions (i.e. LE, 0.25c, 0.5c, 0.75c and 0.98c) on the upper surface of the airfoil, water film height and the location of rivulet formation on the upper surface of the airfoil are also presented.Originality/valueFor 2D airfoil, the recorded maximum variation of the coefficient of lift and lift-to-drag (L/D) ratio is observed to be 5.33% at an 8° and 10.53% at a 4° angle of attack (AOA) between numerical and experimental results under the influence of rainfall effect for LWC = 5.33. The L/D ratio percentage degradation is seen to be 61.9% at an AOA of 0°–2° for the rain environment. For 3D mini-UAV, the recorded maximum variation of the coefficient of lift and L/D ratio are observed to be 2.84% and 4.60% at a 30° stall AOA under the influence of rainfall effect for LWC = 5.33. The numerical results are impressively in agreement with the experimental results. UAV designers will benefit from the findings presented in this paper. This will be also helpful for training the pilots to control the airplanes in a rain environment.