Assumption Of Incompressibility Research Articles

Задача нелинейной теории упругости о растяжении и кручении составного цилиндра с предварительно напряжённым включением, содержащим винтовую дислокацию

The problem of large torsional and tension-compression deformations of a composite circular cylinder of incompressible Bartenev-Khazanovich material is considered. The cylinder contains a central circular cylindrical inclusion in which a concentrated screw dislocation is formed. It is pre-twisted and stretched (or compressed) along the axis and bonded to an unstressed external hollow cylinder. A single reference configuration is used when solving a problem for a composite body. This configuration is natural (unstressed) for the outer hollow cylinder and prestressed for the inner solid cylinder. The large deformation superposition theory is used to write the determining ratios of the material of the inner cylinder. The nonlinear theory of torsion of elastic cylinders containing a screw dislocation is used to solve the problem of the prestressed state of the internal inclusion. This theory is physically correct not for any models of isotropic elastic materials, but only for those for which the screw dislocation in the cylinder has a finite linear energy and creates a longitudinal force of finite value. The Bartenev-Khazanovich model belongs to this class. The problem for a composite cylinder is solved by a semi-inverse method. Using this method, it is reduced to nonlinear ordinary differential equations. The assumption of isotropy and incompressibility of the material makes it possible to find an exact solution to the problem.

Analysis of open channel flow with various layered vegetation using CFD, considering different near-wall treatment methods

PurposeThe purpose of this paper is to investigate the impact of near-wall treatment approaches, which are crucial parameters in predicting the flow characteristics of open channels, and the influence of different vegetation covers in different layers.Design/methodology/approachAnsys Fluent, a computational fluid dynamics software, was used to calculate the flow and turbulence characteristics using a three-dimensional, turbulent (k-e realizable), incompressible and steady-flow assumption, along with various near-wall treatment approaches (standard, scalable, non-equilibrium and enhanced) in the vegetated channel. The numerical study was validated concerning an experimental study conducted in the existing literature.FindingsThe numerical model successfully predicted experimental results with relative error rates below 10%. It was determined that nonequilibrium wall functions exhibited the highest predictive success in experiment Run 1, standard wall functions in experiment Run 2 and enhanced wall treatments in experiment Run 3. This study has found that plant growth significantly alters open channel flow. In the contact zones, the velocities and the eddy viscosity are low, while in the free zones they are high. On the other hand, the turbulence kinetic energy and turbulence eddy dissipation are maximum at the solid–liquid interface, while they are minimum at free zones.Originality/valueThis is the first study, to the best of the author’s knowledge, concerning the performance of different near-wall treatment approaches on the prediction of vegetation-covered open channel flow characteristics. And this study provides valuable insights to improve the hydraulic performance of open-channel systems.

A computational fluid dynamic method for dense-phase carbon dioxide centrifugal pump

As an advanced approach for large-scale low-carbon utilization of fossil energy, the carbon capture, utilization and storage technology is a promising means to achieve the carbon-neutrality target by 2060. Among the most widely used approaches for carbon storage is the enhanced oil recovery technique, for which the centrifugal pump is used to inject high-pressure dense-phase carbon dioxide (CO2) into the stratum. This work focuses on real fluid effects and inter-stage matching deviation from the incompressibility assumption for a dense-phase CO2 centrifugal pump, of which the inlet condition is close to the fluid critical point. With a thermophysical-state table for CO2 based on the thermophysical-property database of the National Institute of Standards and Technology embedded into a computational fluid dynamics solver, a numerical simulation method for compressible dense-phase CO2 pumps is established. The developed method is validated in the 50kW main compressor for a supercritical CO2 cycle and then applied to the simulation of a multistage dense-phase CO2 pump designed for carbon storage. The stage with the most remarkable fluid compressibility is determined, which provides a priori basis for the follow-up design optimization of the pump. This work is of promising application prospect for design of advanced dense-phase fluid machinery.

Orbitally compact and loose vortex regions

The measure of orbital compactness of the motion of swirling material points inside a vortex is formulated without the assumption of incompressibility. Orbitally compact and loose vortex regions are distinguished. Their boundary is set very permissively and expressed through the introduced measure of orbital compactness. The present analysis is associated with the vortex-identification local trace criterion and explains its limited applicability. The comparison of compact and loose volumetric ratios for selected vortex-identification methods employs numerical data of four flow situations. The investigation shows that some vortex-identification criteria are too permissive, more or less ignoring the inherent vortex property of orbital compactness.

Extension of the delayed equilibrium model to flashing flows of organic fluids in converging-diverging nozzles

Flashing flows of organic fluids find application in various energy systems, but the available modelling approaches rely on semi-empirical correlations calibrated for other fluids and operating conditions. This paper extends the state-of-the-art one-dimensional models developed for water to flashing of organic fluids, using R134a as a reference. First, the delayed equilibrium model combined with Grönnerud's friction correlation is identified as the most appropriate approach, reducing the error on mass flow rate with respect to experimental results from 48.3 %, obtained with the homogeneous equilibrium model, to 10.3 %. Then, the traditionally adopted incompressible flow assumption for the metastable liquid phase is replaced by a dedicated thermodynamic model, preventing the appearance of unphysical metastable phase temperatures. Moreover, the delayed equilibrium model is tailored to R134a by tuning the semi-empirical coefficients of the constitutive law. The proposed modifications to the state-of-the-art delayed equilibrium model result in an improvement in the prediction of the pressure profiles and the mass flow rate for flashing flows of R134a, with a decrease in the error on mass flow rate from 10.3 % to 6.1 % with respect to the original formulation.

A numerical study of gas focused non-Newtonian micro-jets

The present numerical study assesses the jet length, diameter and velocity of various non-Newtonian power-law fluids of a gas dynamic virtual nozzle. A related two-phase flow problem is formulated within the mixture framework and solved with the finite volume method and volume of fluid interface treatment in axisymmetry. The process parametric range allows the incompressible laminar flow assumption. A comprehensive jet characteristics analysis is carried out in a typical micro-nozzle configuration for a range of shear-thinning to shear-thickening fluids with power law indices 0.5 ≤ n < 1.5, gas mass flow rate of 10 mg/min and liquid volumetric flow rate of 43 µl/min, resulting in a gas Reynolds number of 130 with Reynolds and Weber numbers for a reference water jet being 90 and 10, respectively. It is observed that jets from shear-thinning fluids (0.5 ≤ n < 1.0) tend to be thicker, longer, and slower when compared with the shear-thickening fluids (1.0 < n ≤ 1.5). A dripping-jetting phase diagram of the nozzle is constructed by varying the power law index, gas and liquid flow rates in the range 0.9–1.1, 5–15 mg/min and 5–50 µl/min, respectively. It is observed that the area of stable jetting decreases with the increase of the power law index. The obtained novel information on the behaviour of non-Newtonian gas-focused micro-jets provides a possible new dimension for tailoring the serial crystallography sample delivery systems where the micro-jets carry dispersed crystals into an X-ray beam.

Physical mechanisms controlling a vapor bubble collapse and formation of a liquid jet during a laser-induced subcooled boiling near the end face of a thin waveguide

Laser-induced subcooled boiling near the tip of thin waveguide immersed in a liquid which temperature is less than the saturation temperature (subcooled liquid) can produce intensive liquid jets finding promising applications in medicine. Individual act of the boiling process consists of successive stages of the bubble inflation, bubble collapse and formation of the jet. In this paper we investigate the contribution of different physical mechanisms to the characteristics of these stages. Simplified mathematical model introducing evaporation and condensation processes in the fully controlled manner allows manipulation of these processes by varying model parameters. Depending on the evaporation intensity or disequilibrity of the bubble inflation stage three regimes of laser-induced subcooled boiling can be distinguished, that are the pressure driven regime, transition regime and condensation driven regime. Distinctive features of these regimes are discussed and ranges of evaporation intensity and disequilibrity index typical for each regime are determined. The validity of incompressible gas assumption for description of different regimes is estimated.

Investigation of strong isothermal stratification effects on multi-mode compressible Rayleigh–Taylor instability

Rayleigh–Taylor instability, RTI, occurs at the interface separating two fluids subjected to acceleration when the density gradient and the acceleration are in opposite directions. Previous scientific research primarily considered RTI under the incompressible assumption, which may not be valid in many high-energy-density engineering applications and astrophysical phenomena. In this study, the compressibility effects of the background isothermal stratification strength on multi-mode two-dimensional RTI are explored using fully compressible multi-species direct numerical simulations. Cases under three different isothermal Mach numbers – Ma=0.15, 0.3, and 0.45 – are investigated to explore weakly, moderately, and strongly stratified compressible RTI, respectively, at an Atwood number of 0.04. Unlike incompressible RTI, an increase in the flow compressibility through the strength of the background stratification can suppress the RTI growth and can lead to a termination of the RTI mixing layer growth with a highly molecularly mixed state. Our findings suggest that even at the chosen relatively low Atwood number, the variable-density effects can be significantly enhanced due to an increase in the background stratification for the compressible RTI as different spatial profiles become noticeably asymmetric across the mixing layer for the strongly stratified case. In addition, this study compares the chaotic behavior of the cases by studying the transport of the turbulent kinetic energy as well as the vortex dynamics. The Reynolds number dependence of the results is also examined with three different Reynolds numbers, and the findings for the large-scale mixing and flow quantities of interest are shown to be universal in the range of the Reynolds numbers studied.

The effect of the triangular rib usage in the plate fin heat sinks on the pressure drop, base plate temperature, and entropy generation

Improving the thermal efficiency in plate fin heat sinks (PFHS) results in a reduction in the weight, volume and cost of the heat sink. This ensures long life and reliable operation of the cooled equipment. In this study, the performances of triangular ribbed PFHSs, which are formed by placing a staggered array of triangular ribs between plate fins, were numerically investigated. Pressure drop, base plate temperature and entropy generation are used for performance comparisons. Numerical heat transfer and flow analysis were performed in three-dimensional models with the help of Ansys Fluent program, which uses the finite volume method with incompressible, turbulent flow and conjugate heat transfer assumptions. The design parameters were determined as inlet velocity between 3 m/s and 9 m/s, number of plate fins 9, 12 and 15, plate fin heights 10 mm and 30 mm, triangular rib heights 0.1 mm and 0.3 mm. As a result, the heat sink base temperature decreases with the increase of velocity, fin height, number of plate fins and triangular rib height, lower pressure drop values were obtained in the case of Hrib=0.1 mm compared to the unribbed case. If the design with the least entropy production is desired as the optimum design, there is a %10.64 increase in the base temperature and a significant decrease in the pressure drop (220.88 Pa to 7.512 Pa). In this case, since the fin length is H=30 mm, the volume and weight of the heat sink also increase.

Design and optimization of an integrated novel desalination system based on the temperature difference between the sea and mountain

As the world’s population and increasing urbanization continue to grow, freshwater needs have risen dramatically. A desalination process based on a natural vacuum and pipeline desalination method that can produce freshwater and transfer it simultaneously is designed and modeled comprehensively in this research. It has been demonstrated that the effect of compressibility is negligible for pressure and temperature ranges of the system, indicating that the first system model using incompressible flow assumption is valid. Solar thermal energy was also utilized to improve the system’s efficiency. The results are investigated for three scenarios for Bandar-Abbas and the adjacent mountain, Genu. The first, second, and third scenarios are associated with the initial model based on pipeline desalination, the model utilizing solar cooling to reduce the temperature in the condensation section, and the model using solar energy to increase the temperature in the evaporation section, respectively. The results show that the highest freshwater production is estimated at 125,842,962 and 21,101,132 kg per year for a tube diameter of 2 and 1 m, respectively. Furthermore, the annual production rate of distilled water in scenarios #2 and #3 increased by 13.85% and 139.1% compared to scenario #1, with a tube diameter of 2 m.

Physics-Informed Deep-Learning For Elasticity: Forward, Inverse, and Mixed Problems.

Elastography is a medical imaging technique used to measure the elasticity of tissues by comparing ultrasound signals before and after a light compression. The lateral resolution of ultrasound is much inferior to the axial resolution. Current elastography methods generally require both axial and lateral displacement components, making them less effective for clinical applications. Additionally, these methods often rely on the assumption of material incompressibility, which can lead to inaccurate elasticity reconstruction as no materials are truly incompressible. To address these challenges, a new physics-informed deep-learning method for elastography is proposed. This new method integrates a displacement network and an elasticity network to reconstruct the Young's modulus field of a heterogeneous object based on only a measured axial displacement field. It also allows for the removal of the assumption of material incompressibility, enabling the reconstruction of both Young's modulus and Poisson's ratio fields simultaneously. The authors demonstrate that using multiple measurements can mitigate the potential error introduced by the "eggshell" effect, in which the presence of stiff material prevents the generation of strain in soft material. These improvements make this new method a valuable tool for a wide range of applications in medical imaging, materials characterization, and beyond.

CFD analysis on blood flow inside a symmetric stenosed artery: Physiology of a coronary artery disease.

This research article interprets the computational fluid dynamics analysis on blood flow inside a symmetric stenosed artery. The current problem models the blood flow inside the left coronary artery as having a symmetric stenosis in the central region. A comprehensive physiological examination of coronary artery disease is numerically evaluated by using the computational fluid dynamics toolbox Open-Field Operation And Manipulation. There are no assumptions of mild stenosis taken into account since the considered stenosis has an exactly measured length, height and position, etc. The blood flow problem is modeled for the non-Newtonian Casson fluid with unsteady, laminar, and incompressible flow assumptions. The underlying problem is solved numerically in its dimensional form. A thorough graphical analysis is provided on the blood flow simulations, pressure profile, velocity line graphs, pressure line graphs, and streamlines for the left coronary artery having a symmetric stenosis formation. The considered artery is divided into three sections, i.e. pre-stenosis, post-stenosis, and stenosis region, and the velocity and pressure line graphs are plotted for these considered regions. The graphical illustrations provide a detailed analysis of how the blood flow is affected inside the left coronary artery due to coronary artery disease. These pre- and post-stenosis velocity line graphs reveal two intriguing results: In the pre-stenosis zone, the velocity increases with increasing axial coordinate length, whereas in the post-stenosis region, the velocity decreases with rising axial coordinate length. It is evident that as the flow moves toward the stenosis region, the flow profile rises; yet, after passing through the stenosis zone, the flow profile begins to fall as the flow moves away from the stenosis region.

A lumped parameter and CFD combined approach for the lubrication analysis of a helical gear transmission

This paper proposes a combined 1D-3D approach for the lubrication analysis of a standard transmission including two helical gears. A lumped parameter model of the entire lubrication system is developed to predict the flow distribution within the circuit and the localized pressure drops along the lines. This model considers the geometrical features of the real system, and it combines the experimental characteristic curves of the main hydraulic components. The steady-state condition is investigated, and the corresponding lubrication flow is provided as a boundary condition for a three-dimensional CFD model. The overset mesh method is employed to address the instantaneous position of the gears in the contact region and the Volume of Fluid (VOF) model assesses the multi-phase phenomenon. The turbulent behavior of the flow is described by the two-equation realizable k-ε model, and the incompressible assumption is made for both oil and air. The effect of different nozzles configurations on the lubrication efficiency is analyzed and the internal system fluid-dynamics is investigated to point out the oil path. The numerical results are discussed in terms of the volume fraction of oil on the gears teeth, the passive torques at the shafts and the associated power losses under specific operating conditions.

Biomechanical response of soft tissues during passage of synovial fluid in compression

The present study provides a novelty approach for the computational biological model based on continuum mixture theory in combination with power-law model for incorporating an accurate governing model for the synovial fluids. We investigated the biomechanical response of a soft tissue while passage of non-Newtonian fluid during act of loading at the rigid bony interface. A special kind of multiphasic deformation has been reported in these types of problems that justify nonlinear coupling between the fluid and solid. In modeling these types of problems, general assumption of mixture constituents incompressibility is often provoked. The mixture components are considered intrinsically incompressible; however, in the derivation of governing equations, viscoelastic behavior of the solid along with interstitial fluid was developed. The nonlinear interaction between the fluid–solid is modeled using strain-dependent permeability and is experimentally determined. This manipulation of linear model with nonlinear permeability required attention for the computational point of view. A system of nonlinear coupled partial differential equations is derived for the local fluid pressure along with an equation for solid deformation. The governing system of equations is solved numerically for the case of permeability dependent flow, whereas an exact solution is given for constant permeability case. Various interesting features, such as, pressure changes within the tissue, swelling behavior of the solid matrix, and effects of power law index on the tissue deformation have been presented graphically. A good qualitative agreement has been noticed between the exact and numerical solutions for constant permeability case.

Flow and Heat Transfer in a Co-Rotating Cavity with Tubes: A Coupled Prediction Model

In previous studies, researchers established mathematical models for predicting the pressure coefficient in simple cavities and tubed vortex reducers based on the assumptions of incompressibility and adiabatic reversibility. However, these mathematical models are not suitable for engineering design and cannot predict the internal pressure and temperature. In this study, we first derived mathematical equations for predicting the pressure drop and temperature change in a tubed vortex reducer, by considering the irreversible loss at the tube inlet. To compensate for the shortcomings of the incompressibility assumption, we developed an iterative alternating calculation method that revises the density. Subsequently, we established a coupled prediction model based on the aforementioned equations and methods. The verified Reynolds stress model results proved that the coupled prediction model and the single prediction model, which represents the incompressible case, yield similar results in predicting pressure under low-rotating-speed conditions. However, as the rotating speed was increased, the error of the single prediction model gradually increased, whereas the coupled prediction model still had good prediction accuracy. With an increase in the length and number of tubes, the pressure drop showed a decreasing trend, whereas the temperature change did not fluctuate significantly.

Comparison of haemodynamics in carotid endarterectomy: primary closure versus patch angioplasty

We investigated differences in haemodynamic forces between carotid arteries that underwent primary closure (PC) or patch angioplasty (PA) using computational fluid dynamics (CFD). A total of 30 subjects were enrolled in this study, consisting of 10 subjects who underwent PC, 10 who underwent PA and 10 healthy subjects. Three-dimensional models of carotid arteries were reconstructed using patient-specific computed tomography angiography images. The conventional Navier-Stokes, continuity equation and constitutive stress-strain law with a stabilized Petrov-Galerkin scheme were solved with Newtonian and incompressible assumptions. The boundary conditions employed patient-specific velocity profiles as the inflow and lumped parameters of the three-element Windkessel model as the outflow with a rigid wall assumption. Thus, the CFD results exhibited good agreement with measurements from the subjects (r = .78). The carotid arteries of the PC group were exposed to abnormal haemodynamic forces related to building atherosclerosis in a smaller (p .05) to healthy arteries. The morphological characteristics of the carotid artery were significantly associated with the area exposed to abnormal haemodynamic forces. We identified that abnormal haemodynamic forces could be avoided by selecting appropriate surgical techniques that produce less bifurcation expansion.

Analysis of Thickness Distributions Calculated from Surface Strains Obtained through Digital Image Correlation for Incremental Sheet Forming

This paper discusses the thickness distributions calculated from surface strain measurements using stereo Digital Image Correlations (DIC) for parts produced with Single Point Incremental Forming (SPIF). The research is carried out on six benchmark cones and pyramids with each convex, straight and concave walls. The accuracy of the thickness calculations, under the assumption of material incompressibility and using the formula for the Green-Lagrange strains, is compared to the thickness distributions measured with a fringe projection scanner. The thickness estimations based on the measured strains proved to be representative for the measured thickness distributions with a mean error of 0.0182 mm, which corresponds to a relative error of 1.47 % of the mean measured thickness. However, errors of up to 0.1688 mm were found in areas of high wall angles and curvatures, corresponding to a relative maximal error of 13.69 % of the mean measured thickness. Hence, the DIC measurements are well suited for characterizing the thickness. Using the thicknesses calculated from the DIC measurements to find the minimal thickness as an indicator of part failure, is possible with relative errors that have an average overestimation of 2.87% of the minimal measured thickness.

No Pure Capillary Solitary Waves Exist in 2D Finite Depth

We prove that the 2D finite depth capillary water wave equations admit no solitary wave solutions. This closes the existence/non-existence problem for solitary water waves in 2D, under the classical assumptions of incompressibility and irrotationality, and with the physical parameters being gravity, surface tension and the fluid depth.

Analysis of Entropy Generation in Micropolar Magneto-Nanoliquid Material with Activation Energy and Nonlinear Radiation

This study investigates entropy production analysis in the flow of micropolar nanoliquid due to its application in thermal engineering systems for the identification of the factors which causes the destruction in the available energy and consequently affects overall performance of the thermal devices. The model is built on a two-dimensional porous stretching sheet with an incompressible fluid assumption and steady with the influence of variable thermal conductivity, nonlinear thermal radiation, haphazard motion and thermo-migration tiny particles. A prescribed surface temperature is adopted as the thermal heating condition while the impact of the reaction order and activation energy are incorporated into the concentration field. The model equations are restructured to ordinary derivative system, which is computationally solved by Fehlberg Runge-Kutta technique. The results agree well with previous outcomes for limiting situations while the effects of the embedded terms are presented graphs. The analysis reveals that a rise in variable thermal conductivity, the material term and viscous dissipation leads to a rise in the irreversibility process.

Linearization of elasticity models for incompressible materials

We obtain linear elasticity as Gamma -limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.