Navier-Stokes Approximation Research Articles

The impact of the Impeller's hub design on the performance and blood damage in a microaxial mechanical circulatory support device – A numerical study

This study uses CFD methods to investigate the effects of the impeller's geometry on the hemodynamic characteristics, pump performance, and blood damage parameters, in a percutaneous microaxial Mechanical Circulatory Support (MCS) device. The numerical simulations employ the steady state Reynolds-Averaged Navier-Stokes approximation using the SST k−ω turbulent model. Three different impeller models are examined with different hub conversion angles (α = 0○, 3○ and 5○). The analysis includes 23 cases for different pressure heads (Δp = 60–80 mmHg) and angular velocities (ω = 30–52 kRPM). The obtained flow rate is compared between the cases to assess the effect of the impeller's design and working conditions on the pump performance. The comparative risk of shear-induced platelet activation is estimated using the statistical median of the stress-accumulation values calculated along streamlines. The risk of hemolysis is estimated using the average exposure time to shear stress above a threshold (τ > 425 Pa). The results reveal that the shape of the impeller's hub has a great impact on the flow patterns, performance, and risk of blood damage, as well as the angular velocity. The highest flow rate (Q = 3.7 L/min) and efficiency (η = 11.3 %) were achieved using a straight hub (α = 0○). Similarly, for the same condition of flow and pressure, the straight hub impeller has the lowest blood damage risk parameters. This study shed light on the effect of pump design on the performance and risk of blood damage, indicating the roles of the hub shape and angular velocity as dominant parameters.

Acceleration waves and oscillating gas bubbles modelled by rational extended thermodynamics

The study of acceleration waves for a rarefied polyatomic gas is carried out in planar, cylindrical and spherical geometry referring to the rational extended thermodynamics theory with 14 moments. The case of a rarefied monatomic gas is determined as a limit case, and the role of geometry and molecular degrees of freedom is investigated. In addition, the behaviour of an acceleration wave travelling inside an oscillating gas bubble is modelled by the 14-moment PDE system under adiabatic condition. We show that dissipation combined with hyperbolicity tends to inhibit shock formation, and that the dynamic pressure cannot be zero inside the oscillating bubble. This fact can produce observable effects even in the Navier–Stokes approximation, if the gas exhibits high bulk viscosity.

On the efficiency of using the Navier-Stokes approximation in thermogasdynamic calculation of low-thrust liquid-propellant rocket engines at low Reynolds numbers

A numerical method for thermogasdynamic calculation of low-thrust liquid rocket engines is presented. These engines are used as end organs of the system of space attitude control for nanosatellites and small spacecraft. The method is based on the use of the TERRA software package for thermodynamic calculation and the Ansys CFX software package for gas-dynamic calculation using the Navier-Stokes equations. The results of the thermogasdynamic calculation, as well as the flow pattern of the working fluid in the chamber, are presented. The results of validating the described method are also presented. Its capabilities and limitations are analyzed. The validation procedure is based on the comparison with the results of experimental data on the Reynolds number and the momentum thickness.

Global Solutions of the Compressible Euler Equations with Large Initial Data of Spherical Symmetry and Positive Far-Field Density

We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density. The central feature of the solutions is the strengthening of waves as they move radially inward toward the origin. Various examples have shown that the spherically symmetric solutions of the Euler equations blow up near the origin at certain time. A fundamental unsolved problem is whether the density of the global solution would form concentration to become a measure near the origin for the case when the total initial-energy is unbounded and the wave propagation is not at a finite speed starting initially. In this paper, we establish a global existence theory for spherically symmetric solutions of the compressible Euler equations with large initial data of positive far-field density and relative finite-energy. This is achieved by developing a new approach via adapting a class of degenerate density-dependent viscosity terms, so that a rigorous proof of the vanishing viscosity limit of global weak solutions of the Navier-Stokes equations with the density-dependent viscosity terms to the corresponding global solution of the Euler equations with large initial data of spherical symmetry and positive far-field density can be obtained. One of our main observations is that the adapted class of degenerate density-dependent viscosity terms not only includes the viscosity terms for the Navier-Stokes equations for shallow water (Saint Venant) flows but also, more importantly, is suitable to achieve our key objective of this paper. These results indicate that concentration is not formed in the vanishing viscosity limit for the Navier-Stokes approximations constructed in this paper even when the total initial-energy is unbounded.

Shear stress tensor and specific shear viscosity of hot hadron gas in nuclear collisions

We extract the shear stress tensor of nuclear matter in the hadronic phase in high energy nuclear collisions. We use a blast-wave parametrization of the final state of nuclear collisions, including nonequilibrium deformations of particle distributions due to shear stress in the Navier-Stokes approximation. We fit spectra and elliptic flow of identified hadrons for a variety of collision energies and impact parameters at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The systems analyzed cover a temperature range from about 110 to 150 MeV and vary in their chemical potentials for stable hadrons. We then attempt to estimate the specific shear viscosity $\ensuremath{\eta}/s$ of nuclear matter for various temperatures and chemical potentials in the hadronic phase. We assign systematic uncertainties to our results. Using a recent systematic study of fluid dynamics pseudodata with the same blast-wave model [Z. Yang and R. J. Fries, arXiv:2007.11777], we apply a correction to the raw fit results which removes some biases typical for blast-wave fits. This work is complementary to efforts using viscous fluid dynamics to extract the specific shear viscosity of quark gluon plasma at higher temperatures. We put our work in context with existing theoretical calculations of the specific shear viscosity.

HYDRODYNAMIC CALCULATION OF CONTACTLESS SEALS WITH PLANE SLOTS IN DRIVES OF ELECTRIC POWER SYSTEMS

Non-contact seals with fl at slott ed gaps of drives of electric power systems used in switchgears of hydraulic units, as well as in pumps and hydraulic motors have been investigated. Calculation of seals based on average clearance results in an underestimation or overestimation of the leakage rate compared to the operational values. The regularity of the distribution of pressure and fl ow rate in the gap of a fl at conical slot is determined, and formulas for the fl ow rate (leakage) and friction forces acting on the walls of the conical slot are found. To solve the problem, the approximate Navier-Stokes and fl ow continuity equations are used. Several special cases of the fl ow of the working fl uid in diff erent gaps are considered: a plane-parallel gap with an oscillating wall and at a constant pressure gradient and a conical gap at diff erent ratios of the pressure drop and the frictional action of the moving channel wall. When the wall oscillates in a conical gap and constant pressure, the presence of an extremum is characteristic. In this case, an excess pressure appeared in the slott ed gap, creating a supporting force, and the pressure value became high enough. When the lower wall of the conical slot moves in the direction of the increasing gap, the pressure inside the slott ed channel, under certain conditions, can reach a complete vacuum, the value of which is limited by the bulk strength of the liquid and the pressure of saturated vapor at a given temperature. When the pressure drop and oscillations of the wall of the conical gap are additive, then at a suffi ciently high velocity of the wall movement, the pressure inside the slot can even increase and exceed the value of the supplied pressure.

Compressible Navier-Stokes approximation for the Boltzmann equation in bounded domains

It is well known that the full compressible Navier-Stokes equations can be deduced via the Chapman-Enskog expansion from the Boltzmann equation as the first-order correction to the Euler equations with viscosity and heat-conductivity coefficients of order of the Knudsen number $\epsilon>0$. In the paper, we carry out the rigorous mathematical analysis of the compressible Navier-Stokes approximation for the Boltzmann equation regarding the initial-boundary value problems in general bounded domains. The main goal is to measure the uniform-in-time deviation of the Boltzmann solution with diffusive reflection boundary condition from a local Maxwellian with its fluid quantities given by the solutions to the corresponding compressible Navier-Stokes equations with consistent non-slip boundary conditions whenever $\epsilon>0$ is small enough. Specifically, it is shown that for well chosen initial data around constant equilibrium states, the deviation weighted by a velocity function is $O(\epsilon^{1/2})$ in $L^\infty_{x,v}$ and $O(\epsilon^{3/2})$ in $L^2_{x,v}$ globally in time. The proof is based on the uniform estimates for the remainder in different functional spaces without any spatial regularity. One key step is to obtain the global-in-time existence as well as uniform-in-$\epsilon$ estimates for regular solutions to the full compressible Navier-Stokes equations in bounded domains when the parameter $\epsilon>0$ is involved in the analysis.

Perturbation solutions of relativistic viscous hydrodynamics forlongitudinally expanding fireballs * * This work was in part Supported by the Ministry of Science and Technology of China (MSTC) under the "973" Project No. 2015CB856904(4), NSFC (11735007, 11890711), by the Sino-Hungarian bilateral Cooperation Program (Te'T 12CN-1-2012-0016). D. She is Supported by the China Scholarship Council (CSC) (201906770027)

The solutions of the relativistic viscous hydrodynamics for longitudinally expanding fireballs are investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and the Euler conservation equations for the viscous fluid are derived in Rindler coordinates, by assuming that the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the longitudinal expanding framework are presented. The specific temperature profile shows symmetric Gaussian shape in the Rindler coordinates. Further, we compare the results from the Israel-Stewart approximation with the results from the Bjorken and the Navier-Stokes approximations, in the presence of the longitudinal acceleration expansion effect. We found that the Israel-Stewart approximation gives a good description of the early stage evolutions than the Navier-Stokes theory.

Study on the non-equilibrium temperature behavior of normal shock waves and the bulk viscosity

The abnormality of small overshoot in the temperature profile of strong normal shock waves has been resolved, and the bulk viscosity of dilute monatomic gases cannot be ignored. By introducing the total energy conservation equation rather than the internal energy equation, an equation for the non-equilibrium temperature has been suggested. The postulated temperature equation gives a monotonically increasing profile of Monte Carlo data. The Navier–Stokes approximation derives shock equations in one differential equation and one algebraic equation and gives that the ratio of the bulk viscosity to the shear viscosity is equal to 1/15 for dilute monatomic gases.

Accuracy of boundary layer treatments at different Reynolds scales

Abstract Resistive forces associated to boundary layers (‘friction’) are usually out of scale in physical models of hydraulic structures, especially in the case of hydraulically smooth walls, generating distortions in the model results known as scale effects, that can be problematic in some relevant engineering problems. These scale effects can be quantified and corrected using suitable numerical models. In this paper the accuracy of using numerical simulation through the Reynolds Averaged Navier-Stokes (RANS) approximation in order to represent the head losses introduced by friction in hydraulically smooth walls is evaluated for a wide range of Reynolds scales. This is performed by comparing the numerical results for fully developed flow on circular pipes and between parallel plates against experimental results, using the most popular wall treatments. The associated numerical errors, mesh requirements and ranges of application are established for each treatment. It is shown that, when properly applied, RANS models are able to simulate the head losses produced by smooth wall friction accurately enough as to quantify the scale effects present in physical models. A methodology for upscaling physical model results to prototype scale, free of scale effects, is proposed.

Quantum hydrodynamic approximations to the finite temperature trapped Bose gases

For the quantum kinetic system modeling the Bose–Einstein Condensate that accounts for interactions between condensate and excited atoms, we use the Chapman–Enskog expansion to derive its hydrodynamic approximations, include both Euler and Navier–Stokes approximations. The hydrodynamic approximations describe not only the macroscopic behavior of the BEC but also its coupling with the non-condensates, which agrees with the Landau two-fluid theory.

Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle

Given an obstacle in $\mathbb{R}^3$ and a non-zero velocity with small amplitude at the infinity, we construct the unique steady Boltzmann solution flowing around such an obstacle with the prescribed velocity as $|x|\to \infty$, which approaches the corresponding Navier-Stokes steady flow, as the mean-free path goes to zero. Furthermore, we establish the error estimate between the Boltzmann solution and its Navier-Stokes approximation. Our method consists of new $L^6$ and $L^3$ estimates in the unbounded exterior domain, as well as an iterative scheme preserving the positivity of the distribution function.

Permeability of displaced fractures

Flow along fractures becomes increasingly important in the context of geo-engineering applications. Commonly, the permeability of fractures is approximated using the cubic law assumption. However, fracture flow is influenced by the surface roughness and the relative shear displacement. A numerical approach was used which calculates the flow pattern within a rough fracture. Therefore, fracture surfaces are generated using a power spectral density function and fracture flow is simulated under the incompressible Navier Stokes approximation. It is shown that the cubic law solution overestimates the permeability as modeled by the 3D numerical simulation of flow in fractures.

A Blast Wave Model With Viscous Corrections

Hadronic observables in the final stage of heavy ion collision can be described well by fluid dynamics or blast wave parameterizations. We improve existing blast wave models by adding shear viscous corrections to the particle distributions in the Navier-Stokes approximation. The specific shear viscosity η/s of a hadron gas at the freeze-out temperature is a new parameter in this model. We extract the blast wave parameters with viscous corrections from experimental data which leads to constraints on the specific shear viscosity at kinetic freeze-out. Preliminary results show η/s is rather small.

The effects of blade twist and nacelle shape on the performance of horizontal axis tidal current turbines

The paper presents the effects of blade twist and nacelle shape on the performance of horizontal axis tidal current turbines using both analytical and numerical methods. Firstly, in the hydrodynamic design procedure, the optimal profiles of untwisted and twisted blades and their predicted theoretical turbine performance are obtained using the genetic algorithm method. Although both blade profiles produce desired rated rotational speed, the twisted blade achieves higher power and thrust performance. Secondly, numerical simulation is performed using sliding mesh technique to mimic rotating turbine in ANSYS FLUENT to validate the analytical results. The Reynolds-Averaged Navier-Stokes (RANS) approximation of the turbulence parameters is applied to obtain the flow field around the turbine. It is found that power and axial thrust force from BEMT (Blade Element Momentum Theory) method are under-predicted by 2% and 8% respectively, compared with numerical results. Afterwards, the downstream wake field of the turbine is investigated with two different nacelle shapes. It is found that the rotor performance is not significantly affected by the different nacelle shapes. However, the structural turbulence caused by the conventional nacelle is stronger than that by the NACA-profiled shape, and the former can cause detrimental effect on the performance of the downstream turbines in tidal farms.

Global existence for the ellipsoidal BGK model with initial large oscillations

The ellipsoidal BGK model was introduced to fit the correct Prandtl number in the Navier-Stokes approximation of the classical BGK model. In this paper, we establish the global existence of mild solutions to the Cauchy problem on the model for a class of initial data allowed to have large oscillations. The proof is motivated by a recent study of the same topic on the Boltzmann equation.

A parabolic velocity-decomposition method for wind turbines

An economical parabolized Navier–Stokes approximation for steady incompressible flow is combined with a compatible wind turbine model to simulate wind turbine flows, both upstream of the turbine and in downstream wake regions. The inviscid parabolizing approximation is based on a Helmholtz decomposition of the secondary velocity vector and physical order-of-magnitude estimates, rather than an axial pressure gradient approximation. The wind turbine is modeled by distributed source-term forces incorporating time-averaged aerodynamic forces generated by a blade-element momentum turbine model. A solution algorithm is given whose dependent variables are streamwise velocity, streamwise vorticity, and pressure, with secondary velocity determined by two-dimensional scalar and vector potentials. In addition to laminar and turbulent boundary-layer test cases, solutions for a streamwise vortex-convection test problem are assessed by mesh refinement and comparison with Navier–Stokes solutions using the same grid. Computed results for a single turbine and a three-turbine array are presented using the NREL offshore 5-MW baseline wind turbine. These are also compared with an unsteady Reynolds-averaged Navier–Stokes solution computed with full rotor resolution. On balance, the agreement in turbine wake predictions for these test cases is very encouraging given the substantial differences in physical modeling fidelity and computer resources required.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Max-norm estimates for Stokes and Navier–Stokes approximations in convex polyhedra

We prove error estimates in the maximum norm, namely in $$W^{1,\infty }(\Omega )^3\times L^\infty (\Omega )$$W1,?(Ω)3×L?(Ω), for the Stokes and Navier---Stokes equations in convex, three-dimensional domains $$\Omega $$Ω with simplicial boundaries. We modify the weighted $$L^2$$L2 estimates for regularized Green functions used earlier by us, which impose restrictions on the domain beyond convexity. The new ingredient is a Holder regularity estimate proved recently by V. Maz'ya and J. Rossmann for the Stokes system on polyhedra. We also extend the error analysis to $$W^{1,r}(\Omega )^3\times L^r(\Omega )$$W1,r(Ω)3×Lr(Ω) for $$1

The gas dynamics equations of slow flows of polyatomic gas mixtures, non-uniform in temperature and concentrations

The formulation of the system of equations of the mechanics of a gas as a continuous medium is completed. This describes the non-stationary slow laminar flow of a mixture of gases (the Mach number being much less than unity), for a Reynolds number and relative drops in temperature and molar fractions of the order of unity. The distribution with respect to the internal energies of the molecules is close to Boltzmann (the case of rapid exchanges of translational and internal energies of the molecules). The difference from the similar system of equations in the Navier–Stokes approximation is the fact that in the equation of motion the Burnett stresses, expressed in terms of the second differential and paired products of the first derivatives with respect to the temperature and molar fractions (concentrations) are taken into account. A consequence of the action of these stresses is thermal-stress and concentration-stress convection. Special cases and possible extensions are considered.