Non-viscous Flow Research Articles

Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

In this paper, we propose an adaptive mesh refinement method for 2D multi-material compressible non-viscous flows in semi-Lagrangian coordinates.The mesh adaptation procedure is local and relies on a discrete metric field evaluation. The remapping method is second-order accurate and we prove its stability. We propose a multi-material treatment using two ingredients: the local remeshing is performed in a way that reduces as much as possible the creation of mixed cells and an interface reconstruction method that can be used to avoid the diffusion of the material interfaces.The obtained method is almost Lagrangian and can be implemented in a parallel framework. We provide some numerical tests which attest the validity of the method and its robustness.

Analytical Description of an Axisymmetric Supercavitation Bubble in a Viscous Flow

One of the basic elements which characterizes flow regimes, is viscosity. This element has typically been neglected in research on supercavitational flows, describing and predicting supercavitation bubbles geometry and formation using non-viscous potential flows. Arguing that the viscosity effect is much smaller than the inertial effect at high flow speeds, the viscosity has been ignored and the only parameter for modeling the flow has been the cavitation number. However, for some situations and conditions, the viscosity was found to be significant and crucial for the bubble geometry and formation, especially at the supercavitation bubble detachment point, hence some investigations based on numerical calculations have taken viscosity into account. This paper presents an analytical model of an axisymmetric supercavitation bubble in a viscous flow according to Serebryakov annular model for calculation of axisymmetric cavity flows. Viscosity effect on the bubble geometry is suggested, and an analysis for validation and examination is presented as well. The results show the change of the bubble formation from past models due to the viscosity, and offer a more accurate description of the bubble geometry close to the detachment point. Moreover, the slenderness parameter is calculated and presented for supercavitation bubbles in a viscous flow together with its dependency on Reynolds number and the cavitation number. The analysis reveals that the slenderness parameter increases with increasing both the cavitation number and Reynolds number, where the latter has a substantial effect.

Explicit Solutions to the 3D Incompressible Euler Equations in Lagrangian Formulation

We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the Lagrangian framework. Almost no exact Lagrangian solutions exist in the literature prior to this study. We search for solutions where the time component and the spatial component are separated, applying the same ideas we used previously in the two dimensional case. We show a general method to derive separate constraint equations for the spatial component and the time component. Using this provides us with a plenty of solution sets exhibiting several different types of fluid behaviour, but since they are computationally heavy to analyze, we have to restrict deeper analysis to the most interesting cases only. It is also possible and perhaps even probable that there exist more solutions of the separation of variables type beyond what we have found.

A fast unsmoothed aggregation algebraic multigrid framework for the large-scale simulation of incompressible flow

Multigrid methods are quite efficient for solving the pressure Poisson equation in simulations of incompressible flow. However, for viscous liquids, geometric multigrid turned out to be less efficient for solving the variational viscosity equation. In this contribution, we present an Unsmoothed Aggregation Algebraic MultiGrid (UAAMG) method with a multi-color Gauss-Seidel smoother, which consistently solves the variational viscosity equation in a few iterations for various material parameters. Moreover, we augment the OpenVDB data structure with Intel SIMD intrinsic functions to perform sparse matrix-vector multiplications efficiently on all multigrid levels. Our framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow. The code is available at http://computationalsciences.org/publications/shao-2022-multigrid.html.

On the origin of chains of cavities in the rotating flow between cylinders

Cavitation between rotating and immobile cylinders appears in the form of a regular chain of bubbles. The bubble sizes are practically equal, as well as the distances between the bubbles and their azimuthal locations. Though such a form of cavitation has been observed in numerous experiments (in particular, in the experiments with bearings), its nature was not clarified. The presented analysis shows that breakdown of the flow axial symmetry due to displacement of the axis of one of cylinders leads to the regular wave-similar three-dimensional flow perturbations. Their "wavelength" is predetermined by the minimal gap between cylinders. Though the flow between cylinders is not curl-free, these perturbations can be determined with the use of a velocity potential. Keywords: Cavitation, circular cylinders, misaligned cylinders, non-viscous flow.

A study on the effect of blade inlet angle, attack angle and the diameter ratio on the efficiency of a Banki Mitchell turbine

In the present work, a theoretical investigation is presented on how the efficiency of a Banki Mitchell turbine is affected by its design parameters. With the help of general formulation of the control volume theory to the equation of the moment of momentum in the turbine’s runner and considering all assumption regarding the properties of the flow and the design geometry of the runner, a mathematical model has been developed. The water discharge through the turbine is considered incompressible, non-viscous, homogenous and steady flow; The loss due to shock on the inner and outer surface of the runner as well as leakage losses are neglected. As results of the present study, the behaviour of hydraulic efficiency was determined when varying the angle of attack, the blade entry angle as well as the runner diameter ratio, indicating their appropriate values in each different scenario. In this paper critical relationships between design parameters have been disclosed and therefore analysed and simulated using Simulink MATLAB. Furthermore, it was mentioned that for a better performance, the exit angle of the blade should be 90°. At length, an expression was given estimating the turbine’s efficiency at various operating conditions and for calculating the energy contribution per stage, respectively.

Simulation of Biological Wastewater Treatment in Aerotanks with Moving Biocenosis

Purpose. The main purpose of the article is to develop a numerical model for the analysis of the process of biological wastewater treatment in a reactor with a mobile biocenosis. Methodology. For mathematical modeling of the process of biological wastewater treatment in a reactor with a moving biocenosis, a hydrodynamic model of a non-viscous vortex-free flow is used. We calculated the boundary conditions for the modeling equation on the surfaces of the bioreactor, solid walls, and the upper surface; at the inlet boundary; at the outlet boundary from the building. To calculate the process of movement of activated sludge and substrate in the bioreactor, a mass transfer model is used, which takes into account the convective-diffusion movement of the substrate and activated sludge. The process of biological water purification in that part of the bioreactor where there are no mobile biocenosis carriers will be calculated based on the Monod model. The process of biological water purification in the part of the bioreactor where there are mobile carriers is calculated on the basis of an empirical model in three stages. The first stage is determined using the Harremoes model. At the second stage, the rate of substrate «consumption» in the biofilm is calculated. At the third stage, the change in the substrate concentration in the zone where the biocenosis carriers are located is determined due to convective movement, substrate diffusion in the flow and its destruction in the biofilm on the carriers. The chaotic motion of biocenosis carriers in the reactor is modeled based on the parabolic diffusion equation. Finite-difference schemes are used for numerical integration of modeling equations. Findings. The software implementation of the constructed numerical model is carried out. A computational experiment to determine the efficiency of biological wastewater treatment in different parts of the bioreactor was conducted. Originality. An effective multifactorial numerical model has been created, which allows quick analysis of the efficiency of biological wastewater treatment in an aeration tank with mobile biocenosis carriers. Practical value. The created two-dimensional numerical model can be used for serial calculations at the stage of designing biological wastewater treatment systems and analysis of the efficiency of bioreactors under different operating conditions.

A Bidirectional Knudsen Pump with a 3D-Printed Thermal Management Platform.

This paper reports on a bidirectional Knudsen pump (KP) with a 3D-printed thermal management platform; the pump is intended principally for microscale gas chromatography applications. Knudsen pumps utilize thermal transpiration, where non-viscous flow is created against a temperature gradient; no moving parts are necessary. Here, a specialized design leverages 3D direct metal laser sintering and provides thermal management that minimizes loss from a joule heater located on the outlet side of KP, while maintaining convective cooling on the inlet side. The 3D-KP design is integrative and compact, and is specifically intended to simplify assembly. The 3D-KP pumping area is ≈1.1 cm2; with the integrated heat sink, the structure has a footprint of 64.2 × 64.2 mm2. Using mixed cellulose ester (MCE) membranes with a 25 nm average pore diameter and 525 μm total membrane thickness as the pumping media, the 3D-KP achieves a maximum flow rate of 0.39 sccm and blocking pressure of 818.2 Pa at 2 W input power. The operating temperature is 72.2 °C at ambient room temperature. In addition to MCE membranes, anodic aluminum oxide (AAO) membranes are evaluated as the pumping media; these AAO membranes can accommodate higher operating temperatures than MCE membranes. The 3D-KP with AAO membranes with 0.2 μm average pore diameter and 531 μm total membrane thickness achieves a maximum flow rate of 0.75 sccm and blocking pressure of 496.1 Pa at 9.8 W at an operating temperature of 191.2 °C.

On the determination of the number of positive and negative polynomial zeros and their isolation

Abstract A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real coefficients and degree n can be restricted with significantly better determinacy than that provided by the Descartes rule of signs. The method also allows the isolation of the zeros of the polynomial quite successfully, and the determined root bounds are significantly narrower than the Cauchy and the Lagrange bounds. The method relies on solving equations of degree smaller than that of the given polynomial. One can determine analytically the exact number of positive and negative zeros of a polynomial of degree up to and including five and also fully isolate the zeros of the polynomial analytically, and with one of the variations of the method, one can analytically approach polynomials of degree up to and including nine by solving equations of degree not more than four. For polynomials of higher degree, either of the two variations of the method should be applied recursively. Numerous examples are given. Presented is the full classification of the roots of the cubic equation, together with their isolation intervals – especially important for various scientific models for which the coefficients of the equation might be functions of the model parameters. An application of the method to a quartic equation with variable coefficients (resulting from the study of wave–current interactions in the physically realistic model of azimuthal two-dimensional non-viscous flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface) has been demonstrated. A step-by-step algorithm for each version of the method has also been presented.

Modeling of a long sand-pack for heavy crude oil through depletion tests utilizing methane gas

With the enormous increase in the demand for crude oil, and decrease in the resources of conventional oil reservoirs, there is a great need to understand heavy or foamy oil-gas drive mechanism to maximize the oil and gas production. To analyze the real movement of non-viscous heavy oil flow, the characteristic features of the oil-gas mixture has to be estimated to forecast the future potential supply from a heavy oil reservoir. An important question in heavy oil flow under solution gas drive is whether the behaviour of depletion tests can be simulated to model the heavy oil flow behaviour. The main objective of this research is to develop a reliable numerical model for modelling heavy oil flow calibrated with controlled solution gas drive experiments, and that makes a novelty in this manuscript. In this paper, CMG-STARS model which is capable of simulating solution gas drive tests that matched the research experiments. This heavy oil recovery model can determine the relative permeability curves for oil and gas in the dual-phase system using Corey’s relations. At a depletion rate of 0.0418 psi/min, the maximum cumulative oil and gas production was observed to be 13,000 cm 3 and 8500 cm 3 , respectively. The results from the bottom hole pressure and the block pressure simulation runs indicate that the fluid properties such as surface tension plays a significant role in the gas bubble formation. These results are promising, and helps to understand the complex behaviour of heavy oil reservoirs and thus can improve heavy oil recovery.

On Hypothesis of the Existence of Superfine Fluid that Producing Electromagnetic Field

Based on previous work of reformulation of equation for compressible fluid flow by analogy with Maxwell equation, further effort is successfully done to show similarity between governing equations for continuum, incompressible, non-viscous fluid flow and Maxwell equation for homogeneous medium without electric charge and without magnetic pole. From mathematical analysis of both system of equations, impulse vector in fluid field is equivalent with electric field in electromagnetic field, vorticity in fluid field is equivalent with magnetic fields in electromagnetic field, and speed of sound in fluid field is equivalent with speed of light in electromagnetic field. The success of finding the similarity leads to a hypothesis about the existence of a “superfine fluid” that forming background field in universe that having a characteristic similar with fluid field which is continuum, incompressible and inviscid

Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity

We introduce a numerical method for the approximation of linear poroelasticity equations, representing the interaction between the non-viscous filtration flow of a fluid and the linear mechanical response of a porous medium. In the proposed formulation, the primary variables in the system are the solid displacement, the fluid pressure, the fluid flux, and the total pressure. A discontinuous finite volume method is designed for the approximation of solid displacement using a dual mesh, whereas a mixed approach is employed to approximate fluid flux and the two pressures. We focus on the stationary case and the resulting discrete problem exhibits a double saddle-point structure. Its solvability and stability are established in terms of bounds (and of norms) that do not depend on the modulus of dilation of the solid. We derive optimal error estimates in suitable norms, for all field variables; and we exemplify the convergence and locking-free properties of this scheme through a series of numerical tests.

Magnetic helicity and prospects for its observation in the interstellar medium

Magnetic helicity is one of the integrals of nonviscous flows in magnetohydrodynamics that determines the number of linkages of magnetic field lines in a medium. It is among a number of helicities that characterize the degree of mirror asymmetry of velocity and magnetic fields. The helicities play a crucial role in driving the generation of large-scale magnetic fields in stars and spiral galaxies. Until recently, measurements of various helicities were based on astronomical observations of the Sun’s active regions, but not in the Sun’s deep layers where the solar dynamo is operative. Galaxies are transparent to some extent and are therefore very attractive in this sense for observing the helicity of its magnetic field. Theoretical advances and the first successful attempts at such observations are reviewed.

A modified Taylor Galerkin scheme for turbulent compressible flow simulation

As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The Characteristic Based Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows).&nbsp

Построение туннельных осесимметричных сверхзвуковых воздухозаборников

Актуальность работы. Эффективность преобразования химической энергии топлива в механическое движение сверхзвукового летательного аппарата определяется потерями механической энергии на сопротивление летательного аппарата и потерями полного давления при торможении потока в воздухозаборнике воздушно-реактивного двигателя. Поэтому при прочих равных условиях более энергоэффективным будет тот летательный аппарат, у которого эти потери меньше. Существенное повышение энергоэффективности ожидается от применения осесимметричных изоэнтропических туннельных воздухозаборников. В рамках модели невязкого течения предлагается численная методика построения указанных воздухозаборников с профилированным центральным телом и цилиндрической обечайкой. Цель работы. В настоящее время отсутствуют способы профилирования осесимметричных изоэнтропических туннельных воздухозаборников, не имеющих элементов, выступающих за цилиндрический корпус летательного аппарата. Поэтому целью исследования является разработка методики построения таких воздухозаборников. Методы исследования. Используется численная реализация метода характеристик при условии изоэнтропичности течения. Предлагаемая методика состоит из двух задач. В первой задаче от угловой точки строится контур центрального тела с заданной ординатой точки фокусировки характеристик. Во второй задаче производится построение оставшейся части контура до другой угловой точки, при этом используется обращенное течение в кольцевом сопле с цилиндрической обечайкой. Одновременно с решением второй задачи определяется положение обечайки. Центральное тело может содержать на краях по угловой точке. При использовании промежуточной линии тока центральное тело будет гладким. Результаты. Создана методика для расчета семейства контуров осесимметричных туннельных сверхзвуковых воздухозаборников, геометрические характеристики которых однозначно описываются исходными данными.

Combined demonstration of non-viscous and viscous flow

A simple lecture demonstration has been developed which demonstrates how viscosity dramatically changes fluid flow in a pipe. Water in an open reservoir is first allowed to escape through circular apertures near the bottom of the reservoir, which shows volume flow rates proportional to the area of the aperture for a low viscosity fluid. Then, a viscous 60% glycerol–40% water solution escapes from the same open container but through long horizontal tubes, with the flow rate proportional to the square of the area. This is direct visual confirmation of the Hagen–Poiseuille prediction that volume flow rates scale as the fourth power of the tube radius for laminar flow. Overcoming experimental complications involving vena contracta and entry length issues is discussed, along with detailed measurements and fits to theory.

Aeroelasticity Analysis of Unsteady Rotor Blade Forces and Displacements in LP Last Stage Steam Turbine with Various Pressure Distributions the Stage Exit

Several high vibration amplitude problems have been reported regarding the slender last stage blading of commercial LP steam turbines. This paper analyses rotor blade unsteady forces and displacements in the last stage of a low pressure steam turbine with symmetrical and non-symmetrical (exhaust hood induced) pressure distributions behind the rotor blades. The FSI partially integrated method was used for the 3D ideal gas flow. 3D unsteady non-viscous flow was analysed using the Godunov-Kolgan method. Non-symmetrical pressure distributions in the stage exit were taken from 3D viscous CFX ANSYS calculations, using a CFD mesh of all the stator blades, all the rotor blades (rotating and not vibrating) and the exhaust hood. The non-uniform and uniform pressure distributions cause rotor blades to vibrate in different bending-torsion modes. Introducing blade vibration into the flow model causes the appearance of unsteady force and blade displacement harmonics that are not multiples of the rotation frequency. The unsteady rotor blade forces and blade displacements analysis shows the importance of including an exhaust hood in the CFD mesh.

A cut finite element method for the solution of the full-potential equation with an embedded wake

Potential flow solvers represent an appealing alternative for the simulation of non-viscous subsonic flows. In order to deliver accurate results, such techniques require prescribing explicitly the so called Kutta condition, as well as adding a special treatment on the “wake” of the body. The wake is traditionally modelled by introducing a gap in the CFD mesh, which requires an often laborious meshing work. The novelty of the proposed work is to embed the wake within the CFD domain. The approach has obvious advantages in the context of aeroelastic optimization, where the position of the wake may change due to evolutionary steps of the geometry. This work presents a simple, yet effective, method for the imposition of the embedded wake boundary condition. The presented method preserves the possibility of employing iterative techniques in the solution of the linear problems which stem out of the discretization. Validation and verification of the solver are performed for a NACA 0012 airfoil.

Fast and accurate SPH modelling of 3D complex wall boundaries in viscous and non viscous flows

The treatment of wall boundary conditions is a difficult issue in the SPH method and still represents a challenging topic in the scientific community. After a review of state of the art wall treatment methods, an SPH method for modelling viscous and non-viscous flows in the presence of 3D complex wall boundaries is presented. New developments embedded in the proposed method include the addition of a Laplacian operator adapted to the adopted formalism, as well as a cutface process for calculating the particle/wall interactions on any type of geometry. Validations are proposed on a 2D Poiseuille flow, a flow around a 2D cylinder, a 3D hydrostatic tank, and a 3D dambreak. Comparisons are performed with results from the literature. Finally, an industrial automotive application is presented as illustration of the method ability to deal with arbitrarily complex geometries.

Aeroelastic Behaviour of a 3.5-Stage Aircraft Compressor Rotor Blades Following a Bird Strike

This paper analyses unsteady forces acting on rotor blades in a 3.5 stage compressor following a bird strike. The strike was modelled by partially blocking the engine inlet. An in-house code was used to calculate 3D unsteady non-viscous flow of ideal gas through a 3.5 stage compressor. The numerical analysis included blade vibrations. This paper has shown that partial admission causes low-frequency harmonics to affect not only the 1st and 2nd rotor blade stages, but also the 3rd stage, with only slightly smaller amplitude values. Partial admission at the inlet strongly influenced unsteady forces in all three stages, with the dominance of low frequency unsteady force components. In the case of full admission, only high frequency components appeared, due to the number of stator blades.