Viscous 3D Research Articles

On the vanishing viscosity limit for the viscous and resistive 3D magnetohydrodynamic system with axisymmetric data

The current paper aims to explore the three-dimensional axisymmetric viscous and resistive magnetohydrodynamic system. This article is concerned with two outcomes, in the first result we prove the global existence of a unique solution for this system under initial data lying in the Sobolev spaces Hs × Hs−2 with s>52, furthermore, we obtain uniform estimates with respect to the viscosity. The second outcome shows that the viscous and resistive solutions (vμ,bμ)μ>0 strongly converge to the non-viscous one (v, b). This convergence is performed in the space L∞(R+,Hs−2×Hs−2), also we obtain that the rate of convergence is (μt).

Fast Aero-Structural Model of a Leading-Edge Inflatable Kite

Soft-wing kites for airborne wind-energy harvesting function as flying tensile membrane structures, each of whose shape depends on the aerodynamic load distribution and vice versa. The strong two-way coupling between shape and loading poses a complex fluid-structure interaction problem. Since computational models for such problems do not yet meet the requirements of being accurate and at the same time fast, kite designers usually work on the basis of intuition and experience, combined with extensive iterative flight testing. This paper presents a fast aero-structural model of leading-edge inflatable kites for the design phase of airborne wind-energy systems. The fluid-structure interaction solver couples two fast and modular models: a particle system model to capture the deformation of the wing and bridle-line system and a 3D nonlinear vortex step method coupled with viscous 2D airfoil polars to describe the aerodynamics. The flow solver was validated with several wing geometries and proved to be accurate and computationally inexpensive for pre-stall angles of attack. The coupled aero-structural model was validated using experimental data, showing good agreement in the deformations and aerodynamic forces. Therefore, the speed and accuracy of this model make it an excellent foundation for a kite design tool.

On the dynamics of vortices in viscous 2D flows

We study the 2D Navier–Stokes solution starting from an initial vorticity mildly concentrated near N distinct points in the plane. We prove quantitative estimates on the propagation of concentration near a system of interacting point vortices introduced by Helmholtz and Kirchhoff. Our work extends the previous results in the literature in three ways: The initial vorticity is concentrated in a weak (Wasserstein) sense, it is merely Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} integrable for some p>2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p>2$$\\end{document}, and the estimates we derive are uniform with respect to the viscosity.

Global attractor for the three-dimensional Bardina tropical climate model

We prove the existence of global solutions and of a global attractor for a regularized viscous 3D tropical climate model. The regularization is carried out by means of the Helmholtz filter, in the spirit of what is done for some families of LES-turbulence models, thus obtaining (as α-model) the 3D Bardina tropical climate model for which we consider the associated dynamics.

S2 Stream Surface Approximation Approach for Quasi Three-Dimensional Turbine Time-Marching Design Method

A fast and reliable turbine design method is necessary in aeroengine development practice. As Q3D time-marching method iteration process can be time consuming and unstable, a novel S2 stream surface approximation approach coupled with flow tangential condition is proposed to reduce the computation requirement. The surface approximation uses a quadratic function of axial coordinate x to formulate distribution of circumferential coordinate θ . The flow tangential condition inherently represents inviscid blade force effect, and the formulation of inviscid blade force is not needed. A corresponding personal Q3D turbine computer code was developed, which was suitable for both design and analysis applications. The Q3D design method solves Euler’s equation through third-order Godunov’s scheme with TVD property in finite volume method. Semi-implicit Crank-Nicolson’s temporal scheme is implemented. Profile, secondary, and tip clearance energy loss models are added to predict viscous losses. Blade row exit swirl is required as the convergence target for Q3D design. A two-stage turbine and a single-stage high-pressure turbine were designed and analyzed by the Q3D method. Viscous 3D CFD was utilized to check design performances. The results showed that the Q3D method could finish a design case within 1 min. At design point, Q3D mass flow rate error was no more than 1.25%, expansion ratio error was no less than -0.022, and isentropic efficiency error was no more than 0.37 percentage points. The Q3D design method is fast and accurate. The stream surface approximation approach is suitable for Q3D design and analysis.

3D Printing of Stretchable, Adhesive and Conductive Ti3C2Tx-Polyacrylic Acid Hydrogels.

Stretchable, adhesive, and conductive hydrogels have been regarded as ideal interfacial materials for seamless and biocompatible integration with the human body. However, existing hydrogels can rarely achieve good mechanical, electrical, and adhesive properties simultaneously, as well as limited patterning/manufacturing techniques posing severe challenges to bioelectronic research and their practical applications. Herein, we develop a stretchable, adhesive, and conductive Ti3C2Tx-polyacrylic acid hydrogel by a simple pre-crosslinking method followed by successive direct ink writing 3D printing. Pre-polymerization of acrylic acid can be initiated by mechanical mixing with Ti3C2Tx nanosheet suspension, leading to the formation of viscous 3D printable ink. Secondary free radical polymerization of the ink patterns via 3D printing can achieve a stretchable, adhesive, and conductive Ti3C2Tx-polyacrylic acid hydrogel. The as-formed hydrogel exhibits remarkable stretchability (~622%), high electrical conductivity (5.13 S m−1), and good adhesion strength on varying substrates. We further demonstrate the capability of facilely printing such hydrogels into complex geometries like mesh and rhombus patterns with high resolution and robust integration.

Excitation and Damping of Slow Magnetosonic Waves in Flaring Hot Coronal Loops: Effects of Compressive Viscosity

Abstract Slow magnetosonic waves associated with flares were observed in coronal loops by Solar and Heliospheric Observatory/Solar Ultraviolet Measurements of Emitted Radiation, Solar Dynamics Observatory/Atmospheric Imaging Assembly in various EUV bandpasses, and other instruments. The excitation and damping of slow magnetosonic waves provides information on the magnetic, temperature, and density structure of the loops. Recently, it was found using 1.5D models that the thermal conduction is suppressed and compressive viscosity is enhanced in hot (T > 6 MK) flaring coronal loops. We model the excitation and dissipation of slow magnetosonic waves in hot coronal loops with realistic magnetic geometry, enhanced density, and temperature (compared to background corona) guided by EUV observations using a 3D magnetohydrodynamic (MHD) visco-resistive model. The effects of the compressive viscosity tensor component along the magnetic field are included with classical and enhanced viscosity coefficient values for the first time in a 3D MHD coronal loop model. The waves are excited by a velocity pulse at the footpoint of the loop at the coronal lower boundary. The modeling results demonstrate the excitation of the slow magnetosonic waves and nonlinear coupling to other wave modes, such as the kink and fast magnetosonic. We find significant leakage of the waves from the hot coronal loops with a small effect of viscous dissipation in cooler (6 MK) loops, and more significant effects of viscous dissipation in hotter (10.5 MK) coronal loops. Our results demonstrate that nonlinear 3D MHD models are required to fully account for the various wave couplings, damping, standing wave formation, and viscous dissipation in hot flaring coronal loops. Our viscous 3D MHD code provides a new tool for improved coronal seismology.

Experimental Validation and Evaluation of a Coupled Twist-Camber Morphing Wing Concept

A morphing wing concept allowing for coupled twist-camber shape adaptation is proposed. The design is based on an optimized thickness distribution both spanwise and chordwise to be able to morph the wing sections into targeted airfoil shapes. Simultaneously, the spanwise twist is affected by the actuation. The concept provides a higher degree of control on the lift distribution which can be used for roll control, drag minimization, and active load alleviation. Static deformation and flight tests have been performed to evaluate and quantify the performance of the proposed mechanism. The ground tests include mapped actuated wing shapes, and wing mass and actuation power requirements. Roll authority, load alleviation, and aerodynamic efficiency estimates for different configurations were calculated using a lifting line theory coupled with viscous 2D airfoil data. Roll authority was estimated to be low when compared to a general aviation aircraft while the load alleviation capability was found to be high. Differences between the lift to drag ratio between the reference and morphing wing configurations are considerable. Mass and actuation energy present challenges that can be mitigated. The flight tests were used to qualitatively assess the roll control capability of the prototype, which was found to be adequate.

Numerical Thermomechanical Viscous 2D Material Rheology Modelling Enhanced by Marker-in-Cell (MIC) Technique

The rheology of a material especially related to mechanical behaviour is an important characteristic. Rheology has wide applications for example in nanomaterials, engineering design, biology, and in a large scale case in geodynamics study. Rheology relies on several physical equations such as continuity equation, momentum equation, gravity potential, state equation, heat transfer, and advection equation. The equations seem to be simple, however, the application of those equations to a real case is not easy and causes many numerical problems. Marker-in-Cell (MIC) is a technique to solve a numerical rheology modelling problem especially diffusion of sharp gradients during the advection process. The technique successfully simulates the advection process for thermomechanical viscous material for a 2-dimensional case study. The model was initially set up two parts with laterally contrast difference of material characteristics. The lateral density difference of material induced gravitational force and generated circular movement of material. After the simulation was run for the 20-time step, the whole material moved more clockwise circulation. The model started to be stable when all denser material at the lower layer and lower density material at the upper part. The model was fully stable and become at a stationary state at a time more than 100-time steps. The final simulation result showed that the MIC algorithm successfully simulated the conversion process involving the thermomechanical mechanism with diffusion error control and without breaking the contrast density of the material.

Aerodynamic performance of chevron geometry trailing edge for a transonic axial compressor impeller

Several studies present how serrated rotor blades mix wakes in order to attenuate noise levels. The current paper analyses how this geometry, applied on the trailing edge, affects the global parameters of a transonic axial compressor impeller. Innovative solutions tackling the rotor-stator interaction mechanism in an axial compressor for noise reduction include serrated trailing edges. Inspired by chevron nozzles, serrations can be transferred to the open-rotor concept in order to reduce tonal noise. Throughout the study we will be focusing on aerodynamic loss estimation while being mindful of the mechanisms which lead to rotor-stator interaction noise, without assessing its per-se effectiveness for noise mitigation. Owing to its qualitative experimental data availability, NASA’s Rotor 37 was chosen as a baseline. A set of fully viscous 3D simulations, using the SST k omega turbulence model and RANS, was carried out to this effect. Spatial discretization was made using a fully structured pre-mesh in order to optimize resolution and accelerate convergence. Full-factorial samples were generated for the geometric variations in order to capture the aerodynamic implications of this concept. Overall, the analysed case provides promising perspectives, pending optimization studies and experimental tests thereof.

Determining the effect of nozzle groove on the fluid flow through viscous 2D planar fluid

The study aims to determine the effect of the nozzle groove on fluid flow through the viscous 2D planar fluid. To fulfil the study's aim, a numerical method was adopted to introduce grooves of different dimensions from the nozzle exit. The study adopts SolidWorks software that was used to design nozzles and introduce groove shaped nozzles, each consisting of six different designs. The nozzle base model used in this study was similar to the one used in a previous study. The procedure was performed with different pressures (8, 10, and 12 bar) at a similar firefighting nozzle. The velocities contours were predicted based on the choice of nozzle section during the numerical stimulation. The present study results demonstrated a new approach that can be used for the increasing velocity at various types of modified nozzles through grooves at different pressures and locations. For grooves, dimensions 1×1 (mm) and location 15 mm at 8 bar, 10 bar and 12 bars showed no effect on velocity as it reduces velocity by increasing surface area. The velocity increases with increasing pressure in the proportion relationship. It clearly explains that the groove does not affect velocity as it rises due to increase in pressure. It is because the groove reduces the velocity by increasing surface area. The study concludes that the use of groove increases the velocity of water that further improves nozzles operation.

A velocity-vorticity method for highly viscous 3D flows with application to digital rock physics

In this article, we present a numerical iterative method for the solution of internal viscous and incompressible flows in real porous three-dimensional bodies at their pore scale. We use the penalized formulation of the problem involving velocity and vorticity: an operator splitting allows to split apart the diffusion (inherited from Stokes equation) and the penalization phenomena (which takes into account the solid matrix). By means of the numerical analysis of the splitting, we exhibit the penalization coefficient which is actually effective. This method allows to deal only with fast-evaluation operators, that is to say scaling at most as O(nlog⁡n) where n is the number of underlying grid points, such as straightforward computations of finite differences schemes or FFT solver. The numerical analysis and implementation solutions are presented, and validated on various digital rock physics geometries acquired by micro-tomography, using numerical and physical diagnostics. To enforce this validation, we also present permeability estimations of several porous samples. The simulation of transport of passive and active scalars is finally investigated in order to perform the practical upscaling to 1D models of transport and diffusion at the Darcy scale.

Aerodynamic development of a high-pressure ratio compressor for an advanced microturbine powerplant

Microturbine engines are increasing in popularity both for small poly-generation power plants and unmanned aerial vehicle; however, their overall efficiency is severely limited by their thermodynamic cycle and component efficiency. This compressor allows the real cycle of the engine to operate with lower specific fuel consumption, extending the rage of the vehicle and lowering pollutant emissions. Optimization methods were implemented in the compressor design, in order to increase the aerodynamic efficiency. A 4.5:1 pressure ratio was selected in order to keep the exhaust jet subsonic. Linear models were used to optimize the speed and gross geometry while the TEIS and later fully viscous 3D models were used successively to optimize the end walls and blade shapes. For all numerical simulations, the Menter SST turbulence model was used. In order to minimize modelling errors, the rotor-stator interface was placed as far as possible downstream of the impeller.

Global uniform boundedness of solutions to viscous 3D primitive equations with physical boundary conditions

Global uniform boundedness of solutions to 3D viscous Primitive equations in a bounded cylindrical domain with physical boundary condition is proved in space $H^m$ for any $m\geqslant2$. A bounded absorbing set for the solutions in $H^m$ is obtained. These results seem rather difficult for the methods recently developed in [8] and [10]. A completely different approach based on hydrostatic helmholtz decomposition is presented, which can also be applied to cases with other different boundary conditions. Several important results about hydrostatic Leray projector are obtained and utilized. These results are expected to be of general interest and will be helpful as well for solving some other problems for 3D viscous Primitive equations which appeared hard previously for the cases with non-periodic boundary conditions (see e.g. [9]).

Derivation of a viscous KP equation including surface tension, and related equations

The aim of this article is to derive surface wave models in the presence of surface tension and viscosity. Using the Navier-Stokes equations with a free surface, flat bottom and surface tension, we derive the viscous 2D Boussinesq system with a weak transverse variation. The assumed transverse variation is on a larger scale than along the main propagation direction. This Boussinesq system is proved to be consistent with the Navier-Stokes equations. This system is only an intermediate result that enables us to derive the Kadomtsev-Petviashvili (KP) equation which is a 2D generalization of the KdV equation. In addition, we get the 1D KdV equation, and lastly the Boussinesq equation. All these equations are derived for non-vanishing initial conditions.

CENTRIFUGAL COMPRESSOR EFFICIENCY CALCULATION WITH HEAT TRANSFER

In this paper we present a case study of apparent performance variation ofan optimized centrifugal compressor design when its metal parts are cold - before the conjugated heat transfer between the fluid and parts reaches an energetic equilibrium. The methods used are numerical, using full viscous 3D computational fluid dynamics with heat transfer. Three cases were considered, an adiabatic wall baseline, an all-blade cooling at 293 K and a more realistic stator row cooling at 293 K. Results indicate an apparent yet erroneous isentropic efficiency reading increase beyond 100% - which was to be expected due to the fluid cooling. However the isentropic and polytropic efficiencies could be estimated and were used to more accurately assess the performance of the compressor. Power consumption decreased to approximately 97% of the original load while the pressure ratio was marginally increased. This alone does not, however, explain the non-physical efficiency readings, which are mainly due to the assumptionsand manner under which the efficiency itself is calculated. The paper presents a more robust approach to measuring efficiency, regardless of the heat transfer within the turbomachinery itself. Possible applications of the study may range from cold-start regime simulation to the optimization of inter-cooling setup or even flow angle control without mechanically actuated OGV

Hydrodynamic collective effects of active proteins in biological membranes.

Lipid bilayers forming biological membranes are known to behave as viscous two-dimensional fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it was shown [A. S. Mikhailov and R. Kapral, Proc. Natl. Acad. Sci. USA 112, E3639 (2015)PNASA60027-842410.1073/pnas.1506825112] that such active proteins should induce nonthermal fluctuating lipid flows leading to diffusion enhancement and chemotaxislike drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid rafts. We demonstrate that passive particles tend to become attracted by active rafts and are accumulated inside them.

Dynamic behaviour of high- bypass- ratio turbofan carbon fiber-reinforced plastic blade ubder unsteady airloads

The dynamic behavior of vibrating blades of an advanced high- bypass- ratio turbojet engine wide-chord fan under unsteady air loads has been researched. Unsteady air loads occur because of the flow around the impeller situated in the air inlet in the case of strong crosswind. These loads affect the blade dynamic behavior and could lead to increasing of the blade vibration amplitude and the stress in the blades. Blade dynamic behavior is investigated on the basis of 3D high-level gas-dynamic and finite-element models. The gas-dynamic model takes into account unsteady viscous 3D air flows. The strength model takes into account geometrical non-linearity and anisotropy of the composite material. The Cobra software package developed at CIAM and based on Godunov’s method is used for aerodynamic research and obtaining unsteady aerodynamic loads. The ANSYS package of finite-element analysis is used to solve the mechanical problem. The paper deals with both forced vibrations of a blade under given cyclic aerodynamic loads and vibrations with account for the fluid-structure interaction (FSI) of the structure and the flow of titanium and carbon-fiber-reinforced blades. The results of investigations have been compared. The differences between the results of solving the task of forced vibrations and vibrations with FSI, as well as the differences between the results obtained for blades of the same configuration but made of different materials are presented.

Dynamic behaviour of high- bypass- ratio turbofan carbon fiber-reinforced plastic blade ubder unsteady airloads

The dynamic behavior of vibrating blades of an advanced high- bypass- ratio turbojet engine wide-chord fan under unsteady air loads has been researched. Unsteady air loads occur because of the flow around the impeller situated in the air inlet in the case of strong crosswind. These loads affect the blade dynamic behavior and could lead to increasing of the blade vibration amplitude and the stress in the blades. Blade dynamic behavior is investigated on the basis of 3D high-level gas-dynamic and finite-element models. The gas-dynamic model takes into account unsteady viscous 3D air flows. The strength model takes into account geometrical non-linearity and anisotropy of the composite material. The Cobra software package developed at CIAM and based on Godunov’s method is used for aerodynamic research and obtaining unsteady aerodynamic loads. The ANSYS package of finite-element analysis is used to solve the mechanical problem. The paper deals with both forced vibrations of a blade under given cyclic aerodynamic loads and vibrations with account for the fluid-structure interaction (FSI) of the structure and the flow of titanium and carbon-fiber-reinforced blades. The results of investigations have been compared. The differences between the results of solving the task of forced vibrations and vibrations with FSI, as well as the differences between the results obtained for blades of the same configuration but made of different materials are presented.

Local and Global Well-Posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity

In this paper, we consider the initial-boundary value problem of the viscous 3D primitive equations for oceanic and atmospheric dynamics with only vertical diffusion in the temperature equation. Local and global well-posedness of strong solutions are established for this system with H 2 initial data.