Viscous Flow Theory Research Articles

Uniform solitary wave theory for viscous flow over topography

The flow of a density stratified fluid over obstacles has been intensively explored from a natural and scientific point of view. This flow has been successfully governed by using the forced Korteweg–de Vries-Burgers equation that generated solitons in a viscous flow. This is done by adding the viscous term beyond the Korteweg–de Vries approximation. It is based on the conservation laws of the Korteweg–de Vries-Burgers equation for mass and energy, and assumes that the upstream wavetrains are composed of solitary waves. Our results show that the influence of viscosity plays a key role in determining the upstream solitary wave amplitude of the bore. A good comparison is obtained between the numerical and analytical solutions.

Viscous correction to the potential flow analysis of Rayleigh–Taylor instability in a Rivlin–Ericksen viscoelastic fluid layer with heat and mass transfer

AbstractThe current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface.

Study of Activation Energy for Viscous Flow of Mixtures as a Measure of Dilution Efficiency for Heavy Oil-Diluent Systems

As the demand for crude oil continues to increase in response to the continued global needs for it, the development of unconventional crude oil reserves is the only way to sustain global supply. However, the excessively higher viscosity of heavy crude oil makes it less attractive for conventional pipeline transportation. Therefore, reducing the viscosity of heavy crude oil to meet crude oil transporting pipeline regulations is a necessity. This paper has assessed the dilution efficiency of well-known diluents in the petroleum industry, using different dilution ratios based on a thermodynamic approach involving activation energy and heat of vaporization determination. Based on selected dilution ratios, kinematic viscosities of binary and ternary systems of toluene and natural gas condensate as diluents, and Saudi Heavy crude oil as the base oil were measured, using anticipated field based temperatures reported in the literature, which facilitated the experimental approach. The study shows that although the ternary systems have the lowest activation energy for viscous flow and heat of vaporization in accordance with the thermal activation theory of viscous flow, natural gas condensate binary systems have the lowest cost of transportation per barrel of total fluid in the transporting pipeline. The study further shows that the binary systems for toluene and Saudi Heavy crude oil have higher activation energy for viscous flowed compared to the toluene systems.

Numerical Simulation of Ship-added Resistance Based on a Numerical Wave Tank

The wave resistance increase of a ship during its actual voyage can affect its speed and safety. To design ships with excellent sailing performance, it is necessary to accurately predict the wave resistance increase of a ship in waves, as well as the motion response and wave resistance prediction of ships in waves, which involves complex hydrodynamic problems. This paper first establishes a physical model of the KCS vessel, then utilizes the numerical wave tank platform independently developed by our university. Based on viscous flow theory, it calculates the resistance of the KCS under calm water conditions. Using three-dimensional potential flow methods and spectral analysis, it computes the wave-induced resistance values for the KCS under six-degree sea states, analyzes the wave-induced resistance performance of the KCS, and ultimately, based on the calculation results of calm water resistance and wave-induced resistance combined with propeller efficiency parameters, calculates the effective power of the engine.

Numerical simulation of the slamming effect of regular waves and freak waves on ultra heavy-lift amphibious connector

The Ultra Heavy-lift Amphibious Connector can be used for sea and land operations. When the amphibious connector opens the bow door, it will inevitably suffer from the combined action of wind, waves, currents, and other factors, resulting in the slamming of the wave on the hatch and various landing ship hull movements in the process. Due to the complexity of the actual UHAC model, in order to save computing resources, this paper selects the external load on the UAHC hatch when it is operated in water when the door is closed. The effects of crest height, draught, and focus position on UHAC slamming under the action of regular waves and freak waves were analyzed. Based on the viscous flow theory, the CFD commercial software FLUENT is used to simulate the interaction between the reduction of regular waves and floating structures. The simulation results are compared with the experimental results to verify the feasibility of the proposed method. Since the published UHAC data cannot be found in the network environment, this paper draws the UHAC based on the only data on the Internet and studies the slamming load of the wave on the UHAC on this basis.

Finger flow modeling in snow porous media based on lagrangian mechanics

Practical formulation for finger flow is lacking even though such a non-Darcy flow is commonly observed in homogeneous snow porous media. This study generalized physics for porous media flow based on the Lagrangian Mechanics; for instance, Darcy formula was theoretically derived minimizing the energy loss by solving the Euler-Lagrange Equation with Rayleigh dissipation function. This least energy loss (LEL) principle was then used to elucidate the finger flow formation in homogenous media. It was found that the inactive saturation (non-contributing void fraction) plays an important role in finger flow formation. This new theory also linked Darcy-Richards capillary flow and Newtonian viscous flow theories. Predicted flow area fractions by the LEL model were verified by the cold room laboratory experiment using well-controlled, homogeneous snow sample, as performed and documented by Katsushima et al. (2013).

Cleaning effects due to shape oscillation of bubbles over a rigid boundary

Recent experiments have revealed the interesting cleaning effects that take place due to the shape mode oscillation of bubbles over a rigid boundary. While a microbubble was undertaking shape oscillation moving over a bacterial biofilm, it removed the contaminants from the boundary and created a clean path through the biofilm. This demonstrated much higher cleaning efficiency than that associated with the volume oscillation of cavitation bubbles; however, the mechanism is unknown. Here, we study this phenomenon using the boundary integral method with the viscous effects modeled using the viscous potential flow theory and the compressible effects using the weakly compressible theory. The viscous stress at the rigid boundary is approximated using the boundary layer theory. We observed that the natural frequencies of shape mode oscillation decrease significantly due to the presence of the boundary. The shear stress at the boundary due to the shape oscillation of a nearby bubble is at least 20 times higher than that due to volume oscillation with the same energy and is significant only within the area directly beneath the bubble. This is explained by the notably faster decay for higher shape modes of the kinetic energy in the fluid as the distance to the center of the bubble r increases with the induced velocity of mode k decaying at a rate of O(r−(k+2)) away from the bubble. These results achieve excellent agreement with the intriguing cleaning effects first observed in the experiment and explain the mechanism behind this new highly efficient method of cleaning.

Navigational water resistance analysis and optimization of the gondola of unmanned boat retractable device

Combining the characteristics of the existing transfer slideway and double-point hanging type two retractable devices, this paper proposes a multiple-point hoisting, fast transfer, and retractable device. According to the viscous flow theory, one-way fluid-structure interaction simulation is used for the gondola structure of the unmanned boat retractable device. Considering the influencing factors of the width of the gondola, the void ratio, the shape and distribution of the void, and the deployment angle of the guardrail, the navigation water resistance of each model is compared and analyzed, and the optimal design of the gondola device is discussed. The results show that the increase of the top width and the decrease of the front-end void ratio will lead to an increase in the water resistance of the gondola; under the same porosity, the rectangular shape performs better than the circular shape, and the smaller interval between the rectangles is more conducive to reducing the water resistance of the gondola; the increase in the angle of the side door guardrail of the gondola will lead to an increase in the navigation water resistance; the final optimized design of the gondola device meets the strength requirements under extreme conditions of high sailing speed.

A viscosity equivalent reduced-order method and its application to ship roll prediction

The prediction of ship roll response in waves is still a major issue. The widely used potential flow theory can provide the results in a short time. However, its accuracy is highly dependent on the correction of fluid-viscosity. Viscous-flow theory can simulate the fluid viscosity directly, but it is accompanied by high computational costs. This study proposes a viscosity equivalent reduced-order method (VEROM) for predicting ship roll motion to achieve a balance between computational efficiency and prediction accuracy. To shorten the simulation time, the method neglects the fluid viscosity, solves the Euler equation, and uses large-size compatible meshes. To improve the prediction accuracy, the viscous effect is corrected in the time domain based on the principle of viscosity equivalence. A new type of forced roll motion with gradually increasing roll amplitude was introduced to obtain the nonlinear roll damping property for different KC numbers. The effectiveness of the VEROM model was examined by comparing the predicted roll responses with the experimental measurements. It was found that the maximum prediction error was less than 11%. Concerning the simulation time, the VEROM model is 20 times faster than the traditional viscous-flow model. The reduce-order method is effective for the seakeeping performance assessment.

Stability Characteristics of Planar Rivlin–Ericksen Fluid Interface With Mass and Heat Transfer

Abstract The interface of viscous-Rivlin-Ericksen fluids is analyzed through the linear theory of stability analysis when mass and heat is transferring across the interface. The Rivlin-Ericksen fluid lies in the upper region while the lower region of the interface contains viscous fluid. The gravitational acceleration destabilizes the top-heavy arrangement and interface instability is governed by Rayleigh–Taylor instability. The two-dimensional interface is considered, and the viscous potential flow theory is employed to establish the relationship between perturbation's growth and wave number. This relationship is analyzed, and the perturbation's growth is plotted for various flow parameters. A marginal stability condition is obtained, and it is given in terms of heat transport coefficient Λ and wave number. The marginal stability criterion is analyzed using the well-known Newton–Raphson method. The heat and mass transfer phenomenon drives the unstable interface toward stability. It is pointed out that the viscoelastic coefficient λo influences the interface to be stable while the thickness of the viscoelastic fluid makes the interface unstable. Atwood numbers and Weber numbers show destabilizing behavior.

In vitro prediction of the lower/upper-critical biofluid flow choking index and in vivo demonstration of flow choking in the stenosis artery of the animal with air embolism

<i>In vitro</i> prediction of the lower/upper-critical biofluid flow choking index and <i>in vivo</i> demonstration of flow choking in the stenosis artery of the animal with air embolism

Effect of Pressure on Densification and Microstructure of W-Cr-Y-Zr Alloy during SPS Consolidated at 1000 °C

During the spark plasma sintering (SPS) consolidation process, the pressure affects the densification and microstructure evolution of the sintered body. In this paper, the W-Cr-Y-Zr alloy powder was heated to 1000 °C under different applied pressure conditions using spark plasma sintering process, and the effect of pressure on the densification process and microstructure was analyzed. Due to the low sintering temperature, the crystalline size of all the produced W-Cr-Y-Zr alloy is less than 10 nm, which is close to that of the original powders. Cr-rich phase can be detected in the sintered samples due to spinodal decomposition. It is found in this work that the external pressure will increase the contact area between the powder particles, resulting in a higher local pressure at the particle contact, which promotes densification by sliding between the particles under the condition of softening of the particle surface. Additionally, according to the viscous flow theory, the viscous flow activation energy decreases with the increase of pressure. This is because the pressure provides additional driving force to the powder viscous flow process and accelerates the powder shrinkage.

Calculation Methods of Added Resistance and Ship Motion Response Based on Potential Flow and Viscous Flow Theory

Calculation Methods of Added Resistance and Ship Motion Response Based on Potential Flow and Viscous Flow Theory

Energetic and Ecological Effects of the Slow Steaming Application and Gasification of Container Ships

One of the short-term operational measures for fuel savings and reducing CO2 emissions from ships at sea is sailing at reduced speed, i.e., slow steaming, while the gasification of the ship represents an important mid-term technical measure. In this study, the energetic and ecological benefits of slow steaming and gasification are studied for a container ship sailing between Shanghai and Hamburg. Resistance and propulsion characteristics in calm water are calculated using computational fluid dynamics based on the viscous flow theory for a full-scale ship, while the added resistance in waves is calculated by applying potential flow theory. The propeller operating point is determined for the design and slow steaming speeds at sea states with the highest probability of occurrence through the investigated sailing route. Thereafter, the fuel consumption and CO2 emissions are calculated for a selected dual fuel engine in fuel oil- and gas-supplying modes complying with IMO Tier II and Tier III requirements. The results demonstrate a significant reduction in fuel consumption and CO2 emissions for various slow steaming speeds compared to the design speed at different sea states, and for the gasification of a container ship. For realistic weather conditions through the investigated route, the potential reduction in CO2 emissions per year could be up to 11.66 kt/year for fuel oil mode and 8.53 kt/year for gas-operating mode. CO2 emission reduction per year due to gasification under realistic weather conditions could be up to 22 kt/year.

Temporal Instability of Liquid Jet in Swirling Gas with Axial Velocity Oscillation

In the present study, viscous potential flow theory is employed to investigate the temporal instability of a viscous liquid jet in swirling gas with axial velocity oscillation. The dispersion-relation equation is obtained between dimensionless growth rate and wave number. Because of the axial velocity oscillation of gas, there are more than one instability regions, including Kelvin–Helmholtz (K–H) instability region and parametric instability region. The results suggest that increasing gas swirling strength stabilizes the liquid jet in axisymmetric mode, while it enhances the instability in nonaxisymmetric modes. And the gas viscosity has a destabilizing effect. In addition, increasing the forcing frequency enhances instability in the K–H instability region. However, it has a stabilizing effect in the parametric instability region. Furthermore, increasing oscillation amplitude enhances instability in both the K–H instability region and the parametric instability region. Because of the competition between the parametric and K–H instabilities, the location of dominant wave number is uncertain.

Multi-fidelity Co-Kriging surrogate model for ship hull form optimization

For the simulation-based hull form optimization design, there are many methods to evaluate the hydrodynamic performance of the hull form. Although the high fidelity of the surrogate model can be guaranteed by evaluating a large number of new sample hulls based on viscous flow theory, the computational cost can be too high. Therefore, in order to release the burden of calculation, based on the traditional single-fidelity Kriging surrogate model, the multi-fidelity Co-Kriging surrogate model gives attention to both high accuracy and efficiency by combining the accuracy advantage of high-fidelity sample evaluation with the efficiency advantage of low-fidelity sample evaluation. This paper first introduces the construction process of the multi-fidelity Co-Kriging surrogate model, and then uses a series of numerical examples to illustrate the advantages of the multi-fidelity Co-Kriging surrogate model compared with the single-fidelity Kriging surrogate model in terms of fidelity and efficiency. Finally, a hull form optimization design for total drag of DTMB-5415 hull at the design speed is given in detail, where the viscous flow theory and potential flow theory are used for the hydrodynamic evaluations of the hull forms to obtain the high- and low-fidelity results respectively. Results show that the multi-fidelity Co-Kriging surrogate model can be established for hull form hydrodynamic performance optimization, which is superior to the single-fidelity Kriging surrogate model in accuracy, and the optimal hull obtained by Co-Kriging surrogate model has a better resistance optimization effect.

Numerical solution of the Jeffery–Hamel flow through the wavelet technique

AbstractThe theory of viscous fluid flow through convergent and divergent channels has many applications in chemical, aerospace, civil, biomechanical, mechanical, and environmental engineering. It also plays a role in sympathetic rivers and canals and in human anatomy, in how capillaries and arteries are linked. In this study, we developed a new operational matrix of integration with the Hermite wavelet. We proposed a new method called the Hermite wavelet method (HWM) to solve the highly nonlinear Jeffery–Hamel flow problem. The proposed technique is beneficial and appropriate for solving nonlinear differential equations. Furthermore, the outcomes are compared with other techniques such as differential transformation method, homotopy perturbation method, variational iteration method, and Runge–Kutta method in the literature, revealing that the current method's solution is better than those of other methods. The obtained results show that HWM is more satisfactory and precise than the other known techniques in the literature. Also, the property of Reynolds number, convergent, and divergent replica of the channel on applications of the Jeffery–Hamel flow is discussed.

The effect of side-hull position on the seakeeping performance of a trimaran at various headings

As a kind of high-performance ship, compared with traditional mono-hull, the side-hull position of a trimaran plays an essential role in the hydrodynamics and motion characteristics, which is more significant for the seakeeping performance of a trimaran in waves of different headings. In this paper, the moving forward of trimaran in waves of various headings was simulated by a hybrid numerical method, which combines the fully nonlinear potential flow theory and viscous flow theory. The numerical method was validated firstly. Then, the trimaran model with two different layouts was obtained by increasing the hull separation and moving the side hulls forward. Finally, the motion of the trimaran with different layouts in waves of various headings was simulated, and the effect of layout on the motion response and added resistance were investigated.

Platform Motions and Mooring System Coupled Solver for a Moored Floating Platform in a Wave

In advance of building moored floating offshore platforms, in recent years, there has been a greater demand for two-way coupled simulations between a motion solver based on the viscous flow theory and a mooring line model, including cable dynamics. This paper introduces open-source libraries such as MoorDyn (the lumped-mass mooring line model) and OpenFOAM (the computational fluid dynamics libraries). It describes the methods by which they can be coupled bi-directionally. In each time step, the platform motions calculated by OpenFOAM are transferred to MoorDyn as the boundary conditions for the mooring system analysis. In contrast, MoorDyn calculates the restoring force and moment due to the mooring system and transfers them to OpenFOAM. The restoring force and moment act on the platform as the external force and moment for the platform motions in the next time step. The static tension and profile of the mooring system, dynamic tension of the mooring system, and free decay motions of the floating buoy in the still water were simulated to check the accuracy of OpenFOAM and MoorDyn. The coupled solver was used to produce simulations of the moored decay motions of the floating buoy in the still water and the moored motions with the Stokes 5th order wave. All simulation results were compared and showed good agreement with the numerical solution and experiment results. In addition, the characteristics of each solver were investigated.

The impact of slow steaming on reducing CO2 emissions in the Mediterranean Sea

One of the short-term operational measures for reducing CO2 emissions from ships at sea is sailing at reduced speed, i.e. slow steaming. In this study, the benefits of slow steaming are studied using the example of a container ship on a typical sailing route passing through the Mediterranean Sea. Thus, the reduction of fuel consumption and CO2 emissions is assessed in calm water and in waves for the design speed and slow steaming speed. Resistance and propulsion characteristics in calm water are determined by means of computational fluid dynamics based on the viscous flow theory for a full-scale ship. The added resistance in waves is calculated by the potential flow theory. The propeller operating point is determined for the design speed and slow steaming speed and for sea states with the highest probability of occurrence in the Mediterranean Sea. The fuel consumption and CO2 emissions are then calculated for an engine powered by both low sulphur marine gas oil and liquefied natural gas. For the investigated route, the potential reduction in CO2 emissions could be up to 286 t for an engine fuelled by low sulphur marine gas oil and up to 448 t for an engine fuelled by liquefied natural gas.