Weak Compressibility Research Articles

Implicit Subgrid-Scale Modeling of a Mach 2.5 Spatially Developing Turbulent Boundary Layer.

We employ numerically implicit subgrid-scale modeling provided by the well-known streamlined upwind/Petrov–Galerkin stabilization for the finite element discretization of advection–diffusion problems in a Large Eddy Simulation (LES) approach. Whereas its original purpose was to provide sufficient algorithmic dissipation for a stable and convergent numerical method, more recently, it has been utilized as a subgrid-scale (SGS) model to account for the effect of small scales, unresolvable by the discretization. The freestream Mach number is 2.5, and direct comparison with a DNS database from our research group, as well as with experiments from the literature of adiabatic supersonic spatially turbulent boundary layers, is performed. Turbulent inflow conditions are generated via our dynamic rescaling–recycling approach, recently extended to high-speed flows. Focus is given to the assessment of the resolved Reynolds stresses. In addition, flow visualization is performed to obtain a much better insight into the physics of the flow. A weak compressibility effect is observed on thermal turbulent structures based on two-point correlations (IC vs. supersonic). The Reynolds analogy ( vs. ) approximately holds for the supersonic regime, but to a lesser extent than previously observed in incompressible (IC) turbulent boundary layers, where temperature was assumed as a passive scalar. A much longer power law behavior of the mean streamwise velocity is computed in the outer region when compared to the log law at Mach 2.5. Implicit LES has shown very good performance in Mach 2.5 adiabatic flat plates in terms of the mean flow (i.e., and ). iLES significantly overpredicts the peak values of , and consequently Reynolds shear stress peaks, in the buffer layer. However, excellent agreement between the turbulence intensities and Reynolds shear stresses is accomplished in the outer region by the present iLES with respect to the external DNS database at similar Reynolds numbers.

Application of a Numerical Simulation to the Estimation of Wind Loads on Photovoltaic Panels Installed Parallel to Sloped Roofs of Residential Houses

Many residential houses with sloped roofs are equipped with photovoltaic (PV) systems. In Japan, PV systems are generally designed based on JIS C 8955, which specifies wind force coefficients for designing PV panels. However, no specification is provided to the PV panels installed near the roof edges where high suctions are induced. When installing PV panels in such high-suction zones, we need to evaluate the wind loads on the PV panels appropriately, usually by performing a wind tunnel experiment. However, it is difficult to make wind tunnel models of PV panels with the same geometric scale as that for the building, e.g., 1/100, because the thickness of PV panels and the distance between PV panels and a roof are both several centimeters. Therefore, in the present paper a numerical simulation is applied to the estimation of pressures in the space between the lower surface of PV panels and the roof surface, called “layer pressures”, using the unsteady Bernoulli equation and the time histories of external pressure coefficients obtained from a wind tunnel experiment. An assumption of the weak compressibility of the air and an adiabatic condition is made for predicting the layer pressures from the flow speed through the gaps. The simulation method is validated by a wind tunnel experiment using a model of square-roof building.

Stability Analysis of Vaneless Space in High-Head Pump-Turbine under Turbine Mode: Computational Fluid Dynamics Simulation and Particle Imaging Velocimetry Measurement

When the Francis-type reversible pump-turbine runs under partial load, the pressure pulsation amplitude and frequency in vaneless space are high, posing a serious threat to the stability of unit operation. Water presents weak compressibility in a high-head pump-turbine, thereby affecting the amplitude–frequency characteristics of pressure pulsation. This study used numerical simulations in a model and prototype pump-turbine and particle image velocimetry (PIV) in a model pump-turbine to examine the internal flow field and pressure pulsation characteristics and determine the effect of the flow in the vaneless space on the amplitude–frequency characteristics of the pressure pulsation. The pressure pulsation amplitude–frequency characteristics were verified through prototype tests. The effects of the weak compressibility of the water on the propagation law of pressure pulsation throughout the flow passage of the prototype and model pump-turbine were roughly similar but exhibited certain differences. Considering the weak compressibility of water, the pressure pulsation fluctuations in each flow passage of the prototype and model pump-turbine exhibit varying degrees of improvement, which is more obvious at the prototype scale. Therefore, the pressure wave disturbance caused by the weak compressibility of the water has different effects on the prototype scale and model scale of the high-head Francis pump-turbine.

A weakly compressible, diffuse interface model of two-phase flows: Numerical development and validation

We present an approach to simulation of low speed, two-phase interfacial flows. It utilises the diffuse-interface method, based on the so-called conservative Allen–Cahn equation with some further modifications. The flow description allows for weak density variations (weak compressibility) as a computationally efficient treatment of incompressible flow regime. The proposed model conserves mass and momentum. The pressure field evolves according to the energy conservation law for inviscid fluids, expressed in primitive variables. The assumption of weak compressibility leads to some modelling and numerical issues related to the need of unique interface region identification required by the one-fluid formulation. We propose a successful and efficient remedy to this problem which, importantly, is independent of the Mach number. To numerically solve the governing equations we use the classical finite volume method and explicit time integration. This makes the presented strategy easy to implement in existing numerical codes and allows for efficient execution of the simulations using parallel computing devices. The spatial discretisation needs some special care to preserve the simplicity without impairing the fundamental physical consistency. We propose the values of tunable model parameters resulting in an universal approach, suitable for a wide variety of interfacial flows. The approach is validated both qualitatively and quantitatively for a selection of well known benchmark cases in two- and three-dimensional set-ups. High computational efficiency is obtained with simple programming techniques when the code is executed on multicore CPU.

Evolution mechanism of a prototype pump turbine after pump power-off

This study aimed to analyze the time–frequency characteristics of pressure fluctuations and reveal their underlying flow mechanisms during the unavoidable guide vane closing process after a pump power-off in a pumped-storage hydropower plant. In this study, the weak compressibility model, one- and three-dimensional (1D–3D) coupling simulation method, and dynamic mesh technology were adopted simultaneously to accurately simulate the transient flow in a prototype pump turbine during the guide vane closure process after the pump power-off. According to the analysis results of the short-time Fourier transformation for the pressure fluctuations, apart from the familiar runner blade passing frequency and its harmonics, this study found a new component that is five times the runner rotation frequency as well as components that are lower than 4.5 times the runner rotation frequency and correspond to severe fluctuations in the pressure. Internal flow analysis suggests that the former is induced by unstable vortices near the trailing edges of the runner blades, whereas the latter ones are induced by local backflow vortices near the runner inlet. Additionally, these severe pressure fluctuation components were significantly large closer to the maximum reverse discharge of the pump brake mode. This finding indicates that these severe unsteady pressure fluctuation components can be suppressed by optimizing the reduction in the maximum reverse discharge in the pump brake mode.

Study on the influence of elbow with different curvature radii on pipeline leak location

Experimental and numerical methods are used to locate the pipeline leakage in the present work. The weak compressibility of the fluid is taken into account when simulating the propagation of negative pressure wave (NPW) in the pipeline. The NPW attenuation coefficient is used to describe the influences of curvature radius on location accuracy. The results indicate that when the curvature radius is small, the location accuracy of pipeline leakage is low. When the radius of curvature increases or the inlet pressure increases, the accuracy of pipeline leak location is improved. Besides, with the change of inlet pressure, pressure, and velocity distributions in the elbow with different curvature radii are investigated. When the curvature radius of the elbow is three to four times of pipe diameter, the measurement accuracy of leakage location is the best. When the inlet pressure of the pipeline is 0.7 MPa, the sensitivity of the pipeline detection is the highest. The cavitation corrosion at the elbow is the most obvious. Therefore, the elbow is the area where pipeline leakage occurs most frequently.

On the mass exchange mode controlled by high-speed compressive mainstream/cavity interaction in a laboratory dual-mode scramjet combustor

Stable and efficient mass exchange is crucial to the combustion stability of a dual-mode scramjet. In subsonic mode, the progression of mass exchange between the cavity fluid and the mainstream, which is controlled by the cavity shear layer, is different from the scramjet mode due to the weak compressibility effects. However, mass exchange mode studies in the subsonic mode are rare. In this study, experimental research has been conducted to obtain the flow structure of Mach 0.3 and 0.5 inflow over a rectangular cavity and reveal the properties of mass exchange using particle image velocimetry technology. The results reveal the weak compressibility effects and geometry effects on the mass exchange by analyzing the growth rate and turbulence characteristics of the cavity shear layer. The mass exchange between the cavity fluid and mainstream is determined based on the vertical velocity along the cavity lip line. When the flow Mach number increased from 0.3 to 0.5, the growth rate of the cavity shear layer decreases due to the weak compressibility effects. Also, the growth rate of the cavity shear layer is smaller than that of the compressible free shear layer due to the effects of recirculation within the cavity. For length-to-depth (L/D) ratios ranging from 0.8 to 1.2, the cavity shear-layer growth rate decreases with increasing L/D. However, at an L/D of 1.5, the shear-layer growth rate increases, which changes the mass exchange mode. Finally, the effects of increasing the Mach number (Mach = 0.3 versus 0.5) show that the L/D ratio at the “crossover” point of the mass exchange mode transition is reduced (L/D = 1.5 versus 1.2) due to the weak compressibility at a higher Mach number.

Stress-strain state of elastomeric vibroseismic insulators

A method for solving problems of viscoelastic deformation of structures made of weakly-compressible elastomers, based on the application of the hereditary Boltzmann-Volterra theory, is considered. To consider the weak compressibility and eliminate the “false shift” effect, the moment scheme of the finite element is used.

Measurements of Fast Transitions at a Reversible Pump Turbine Model in Closed Loop Test Rig

It is common practice to experimentally investigate the performance characteristics of hydraulic fluid machinery in power plants with steady-state operating points by scaled homologous model machines in closed-loop test rigs. In this case, the piping of the main water conduit from the power plant and the test rig plays a minor role. However, for studies of operating transient, e.g. load rejection, the influence of the weak compressibility of water in the pipes is considered by 1-D water hammer analyses. Due to differences in the main water conduit between the power plant and the test rig, the test rig is specifically controlled by new procedures to replicate the relevant conditions at the fluid machine in the test rig under similarity conditions.The results of this newly developed method for specific control of the test rig for operating transients are presented and successfully validated on a closed-loop experimental system. In future, suitable instrumented model machines then allow the measurement of dynamic pressures or even strains in and on machine components in order to elaborate, as a goal, the influence of different operating transients on the service life of machine components. Furthermore, these experimental data can also be used to validate Computational Fluid Dynamics (CFD) and Finite Element Analyses (FEA) simulations.

ВИБРОСЕЙСМО ЗАЩИТА ЗДАНИЙ И СООРУЖЕНИЙ ОТ ДИНАМИЧЕСКОГО ВОЗДЕЙСТВИЯ ПРИРОДНОГО И ТЕХНОГЕННОГО ХАРАКТЕРА

In this article, the authors analyze results of their long-term researches on protection of buildings and structures against dynamic loads caused by the nature and/or human activities. They also give the grounds for necessity to provide vibration insulation of buildings, and show how to choose and calculate proper parameters for rubber vibroseismic insulators. Specifics of finite element method applied for static calculating the vibroseismic insulators is also described. In order to take into account weak compressibility of rubber, a moment finite element scheme was used, which assumes a triple approximation of the displacement vector components consisting of strain tensor and volume change function. Stress-strain state of the shock absorbers was determined for different standard sizes and diameters. The authors also describe two variants of calculation depending on the method of fixing the insulator’s ends. In the first case, the ends are vulcanized to the metal plates. In the second variant, the ends are free and can move in a horizontal plane. Influence of ratio of the shock absorber height and radius to the strain state of a structure was also analyzed. In order to determine factual levels of the soil and pile vibration (in two horizontal and one vertical directions), vibrodynamic studies were carried out. The obtained vibration signals were registered by the one-component vibration transducers 731A (vibration sensors) produced by the Wilcoxon Research company (the USA). Then, the vibration records were processed by the specialized program “Seismic Monitoring”. Based on the results of these studies, numerical calculations were performed in order to determine whether the predicted levels of the residential building vibrations are in compliance with the existing sanitary standards when exposed to real technogeneous loads. Vibrodynamic tests on vibration acceleration levels of the vibration-insulated reinforced concrete slabs and floors in residential building confirmed high effectiveness of the used vibroseismic insulation system with the rubber elements: the registered vibration acceleration levels in the residential building on all floors did not exceed acceptable levels set by the sanitary standards, and ensured comfortable living conditions under different dynamic impacts. The results of this work make it possible to design buildings with anti-seismic protection by using the designed rubber elements in accordance with the local conditions of the city of Almaty.

Energy Conversion between Ions and Electrons through Ion Cyclotron Waves and Embedded Ion-scale Rotational Discontinuity in Collisionless Space Plasmas

Abstract Wave–particle interaction is a fundamental process in collisionless plasma, which results in the redistribution of energy between plasma waves and particle species. The analysis of high-resolution Magnetospheric Multiscale plasma and magnetic field data directly reveals the energy exchange between electromagnetic energy, particle bulk kinetic energy, and thermal kinetic energy in magnetosheath turbulence. This work focuses on the energy transfer associated with ion cyclotron waves (ICWs) and embedded rotational discontinuity (RD). We find that (1) the particle kinetic energy of ions is converted into electromagnetic energy; (2) the electrons are gaining energy from electromagnetic fields, having significant electron heating in the parallel direction around the RD; (3) the ICWs and RD connect and redistribute energy between ions and electrons in the postshock downstream sheath region; and (4) the interactions between pressure tensor and strain tensor redistribute the ion and electron bulk and thermal kinetic energies, but less significantly than direct field–particle interaction by one order of magnitude in the ICW turbulence with weak compressibility, in the sense that , .

Measuring compressibility in the optima AUC™ analytical ultracentrifuge

A method is described to accurately measure the compressibility of liquids using an analytical ultracentrifuge. The method makes use of very large pressure gradients, which can be generated in the analytical ultracentrifuge at high speeds to induce a maximum compression signal. Taking advantage of the new Optima AUC, which offers 10 micron radial resolution, a novel calibration centerpiece for measuring rotor stretch, and a speed-ramping procedure, even the weak compressibility of liquids like water, typically considered to be incompressible, could be detected. A model using the standard expression for the secant-average bulk modulus describing the relative compression of a liquid in the analytical ultracentrifuge is derived. The model is a function of the loading volume and the hydrostatic pressure generated in the analytical ultracentrifuge, as well as the secant-average bulk modulus. The compressibility of water and toluene were measured and the linear secant-average bulk modulus and meniscus positions were fitted. In addition to the measurement of the compressibility of liquids, applications for this method include an improved prediction of boundary conditions for multi-speed analytical ultracentrifugation experiments to better describe highly heterogeneous systems with analytical speed-ramping procedures, and the prediction of radius-dependent density variations.

Thermoelasticity of elastomeric constructions with initial stresses

The article presents an algorithm for solving linked problems of thermoelasticity of elastomeric structural elements on the basis of a moment scheme of finite elements. To model the processes of thermoelastic deformation of structures with initial stresses the incremental theory of a deformed solid is used. At each step of deformation, the stiffness matrix is adjusted using an incremental geometric stiffness matrix. The use of triple approximation of displacements, deformations and volume change function allows to consider the weak compressibility of elastomers. The components of the stress tensor are calculated according to the Duhamel-Neumann law. To solve the problem of thermal conductivity, a thermal conductivity matrix considering the boundary conditions on the surface of a finite element is constructed. A sequential approximation algorithm is used to solve the thermoelasticity problem. At each stage of the solution, the characteristics of the thermal stress state are calculated. Based on the obtained components of stress and strain tensors, the intensity of internal heat sources is calculated as the dissipative energy averaged over the load cycle. To calculate the dissipative characteristics of the viscoelastic elastomer the parameters of the Rabotnov’s relaxation nucleus are used. Solving the problem of thermal conductivity considering the function of internal heat sources allows you to specify the heating temperature of the body. At each cycle of the algorithm, the values of the physical and mechanical characteristics of the thermosensitive material are refined. This approach to solving thermoelastic problems is implemented in the computing complex "MIRELA+". Based on the considered approach, the solutions of a number of problems are obtained. The results obtained satisfactorily coincide with the solutions of other authors. Considering the effect of preload and the dependence of physical and mechanical properties of the material on temperature leads to significant adjustments to the calculated values.

Assessment of weak compressibility in actuator line simulations of wind turbine wakes

The trend of increasing rotor diameters and tip-speeds has brought about concerns of non-negligible compressibility effects in wind turbine aerodynamics. The investigation of such effects on wakes is particularly difficult when using actuator line models (ALM). This is because crucial regions of the flow, i.e. the direct vicinity of the blade, are not simulated but represented by body forces. To separately assess the impact of compressibility on the wake and the ALM itself, we conduct large-eddy simulations (LES) where the forces of the ALM are prescribed and based on the local sampled velocity (standard procedure), respectively. The LES are based on the weakly-compressible Lattice Boltzmann Method (LBM). Further to the comparison of (near-)incompressible to compressible simulations we investigate cases with artificially increased compressibility. This is commonly done in weakly-compressible approaches to reduce the computational demand. The investigation with prescribed forces shows that compressibility effects in the wake flow are negligible. Small differences in the wake velocity (of max. 1%) are found to be related to local compressibility effects in the direct vicinity of the ALM. Most significantly, compressibility is found to affect the sampled velocity and thereby accuracy of the ALM.

Numerical simulation of the transient flow in a pump-turbine during load rejection process with special emphasis on hydraulic acoustic effect

In this study, a load rejection process of a pump-turbine was simulated using the large eddy simulation method with and without considering the hydraulic acoustic effect. In the simulation, the hydraulic acoustic effect was considered via a revised density function which is called weak water compressibility model. Analysis showed that numerical results considering water compressibility and without the consideration both agree well with the experimental data except some local regions. Compared with the experiments, the simulation deviations of the rotational speed were less than 5%, and the local maximum deviations of the fluctuating pressure were no more than 30% during the whole load rejection process. However, the simulation considering the water compressibility has a better behavior than that without the consideration in the predictions of pressure fluctuation. And the performance characteristics with the consideration are systematically lower than those without the consideration. In some operating conditions, the performance characteristics with the consideration are even 30%–50% lower than those obtained without the consideration. Additionally, it is noted that the fluctuation of the axial hydraulic thrust on the runner with consideration is more severe than that without the consideration. Hence, the water compressibility has an obvious influence on the simulation of the load rejection of pump-turbines.

Theoretical estimation of sonochemical yield in bubble cluster in acoustic field**Project supported by the National Natural Science Foundation of China (Grant No. 11674207).

In order to learn more about the physical phenomena occurring in cloud cavitation, the nonlinear dynamics of a spherical cluster of cavitation bubbles and cavitation bubbles in cluster in an acoustic field excited by a square pressure wave are numerically investigated by considering viscosity, surface tension, and the weak compressibility of the liquid. The theoretical prediction of the yield of oxidants produced inside bubbles during the strong collapse stage of cavitation bubbles is also investigated. The effects of acoustic frequency, acoustic pressure amplitude, and the number of bubbles in cluster on bubble temperature and the quantity of oxidants produced inside bubbles are analyzed. The results show that the change of acoustic frequency, acoustic pressure amplitude, and the number of bubbles in cluster have an effect not only on temperature and the quantity of oxidants inside the bubble, but also on the degradation types of pollutants, which provides a guidance in improving the sonochemical degradation of organic pollutants.

Validation of the MRT-LBM for three-dimensional free-surface flows: an investigation of the weak compressibility in dam-break benchmarks

ABSTRACTFree-surface flow problems occur in numerous disaster simulations, such as tsunami inland penetration in urban areas. Simulation models for these problems must be non-hydrostatic, three-dimensional and highly resolved because of the strong non-linearity and higher-order physical phenomena. However, three-dimensional large-scale tsunami simulations based on conventional computational fluid dynamics (CFD) solving the Navier-Stokes equations are challenging due to the pressure Poisson equation in incompressible Navier-Stokes fluid modeling. The lattice Boltzmann method (LBM) is an alternative simulation tool that is attracting attention as a fully explicit and efficient approach. The LBM does not have to iteratively solve the pressure Poisson equation and is therefore considered to have an advantage over other methods when executing high-performance three-dimensional tsunami simulations. In the current study, we developed a fully explicit free-surface model using the LBM in which the more advanced multiple-relaxation-time (MRT) collision model is used, along with the piecewise linear interface calculation (PLIC) approach. Through classic dam-break problems, we validated the appropriate parameter settings, including the weak compressibility, for tsunami simulations. The benchmark tests showed that our model accurately simulates the three-dimensional dam-break flows and controls the compressibility drop in the second-order value of the Mach number.

A Two-Dimensional Axisymmetric Finite Element Analysis of Coupled Inertial-Viscous-Frictional-Elastic Transients in Magnetorheological Dampers Using the Compressible Herschel-Bulkley Fluid Model

It has been challenging to accurately predict the unique characteristics of magnetorheological (MR) dampers, due to their inherent nonlinear nature. Multidimensional flow simulation has received increasing attentions because it serves as a general methodology for modelling arbitrary MR devices. However, the compressibility of MR fluid which greatly affects the hysteretic behavior of an MR damper is neglected in previous multidimensional flow studies. This paper presents a two-dimensional (2D) axisymmetric flow of the compressible Herschel-Bulkley fluid in MR dampers. We simulated the fully coupled inertial-viscous-frictional-elastic transients in MR dampers under low-, medium- and high frequency excitations. An arbitrary Lagrangian-Eulerian kinematical description is adopted, with the piston movements represented by the moving boundaries. The viscoplasticity and compressibility of MR fluid are respectively modeled by the modified Herschel-Bulkley model and the Tait equation. The streamline-upwind Petrov–Galerkin finite element method is used to solve the model equations including the conservation laws and mesh motion equation. We tested the performances of an MR damper under different electric currents and different frequency displacement excitations, and the model predictions agree well with the experimental data. Results showed that the coupled transients of an MR damper are frequency dependent. The weak compressibility of MR fluid, which mainly happens in the chamber rather than in the working gap, is crucial for accurate predictions. A damper’s transition from the pre-yield to the post-yield is essentially a step-response of a second order mass-spring-viscous system, and we give such step-response a detailed explanation in terms of mass flow rate.

On the role of (weak) compressibility for fluid‐structure interaction solvers

SummaryIn the present study, a weakly compressible formulation of the Navier‐Stokes equations is developed and examined for the solution of fluid‐structure interaction (FSI) problems. Newtonian viscous fluids under isothermal conditions are considered, and the Murnaghan‐Tait equation of state is employed for the evaluation of mass density changes with pressure. A pressure‐based approach is adopted to handle the low Mach number regime, ie, the pressure is chosen as primary variable, and the divergence‐free condition of the velocity field for incompressible flows is replaced by the continuity equation for compressible flows. The approach is then embedded into a partitioned FSI solver based on a Dirichlet‐Neumann coupling scheme. It is analytically demonstrated how this formulation alleviates the constraints of the instability condition of the artificial added mass effect, due to the reduction of the maximal eigenvalue of the so‐called added mass operator. The numerical performance is examined on a selection of benchmark problems. In comparison to a fully incompressible solver, a significant reduction of the coupling iterations and the computational time and a notable increase in the relaxation parameter evaluated according to Aitken's Δ2 method are observed.

A new liquid transport model considering complex influencing factors for nano- to micro-sized circular tubes and porous media

A new liquid transport model in wetted nano- to microsized circular tubes is proposed using basic dynamical analyses that comprehensively consider the Lifshitz–van der Waals force (LWF), the electroviscous force, the weak liquid compressibility, and the Bingham-plastic behavior. The model predicts that the average velocity is initially zero and increases nonlinearly with a concave shape before increasing linearly with the pressure gradient (ΔP/L) and is validated using the experimental data. The threshold pressure gradient (TPG) and the lower limit of the movable-fluid radius (Rm) are calculated based on the proposed model, which are mainly determined by the yield stresses from the Bingham plastic behavior and are also affected by the compressibility and LWF. Considering the microstructural complexity of real porous media, the average velocity model is also applicable for tight porous media with a capillary equivalent radius from the permeability. The calculated average velocity is non-Darcy with TPG. The TPG decreases as the permeability increases, and the Rm decreases with the pressure gradient in the low range and remains constant at the higher ranges, which is primarily between 10 and 30 nm. All these results for porous media are compared with the experimental data of core seepage and show good agreement in general. The proposed model has a clear parametric representation compared with previous nonlinear models. It explains the underlying reasons for the nonlinear, low-velocity flow mechanism in nano- to microsized tubes and pores and provides theoretical guidance for liquid transport in porous media and oil recovery from tight oil reservoirs.