A Simplified Hydroplaning Simulation for a Straight-Grooved Tire by Using FDM, FEM and an Asymptotic Method

2007 ◽  
Author(s):  
Changwon Oh ◽  
Taewung Kim ◽  
Kwonshik Park ◽  
Hyun-Yong Jeong
Keyword(s):  
Iterative Method ◽  
Pressure Distribution ◽  
Asymptotic Method ◽  
Simulation Method ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Simulation Methodology ◽  
Continuity Equations ◽  
Different Types ◽  
Long Time

Much research has been conducted to simulate the hydroplaning phenomenon of tires using commercial explicit FEM (finite element method) codes such as MSC.Dytran and LS-DYNA. However, it takes a long time to finish such a simulation because its model has a great number of Lagrangian and Eulerian elements and a contact should be defined between the two different types of elements, and the simulation results of the lift force and the contact force are oscillatory. Thus, in this study a new methodology was proposed for the hydroplaning simulation using two separate mathematical models; an FDM (finite difference method) code was developed to solve Navier-Stokes and continuity equations and consequently to obtain the pressure distribution around a tire with the inertia and the viscous effects of water taken into account, and an FE tire model was used to obtain the deformed shape of the tire due to the vertical load and the pressure distribution. The two models were iteratively used until a converged pressure distribution was obtained. Since the converged pressure distribution could not be obtained near or at the contact zone due to very shallow water, an asymptotic method was also proposed to estimate the pressure distribution. This new simulation methodology was applied to a straight-grooved tire, and its hydroplaning speed was determined for the water depth of 5 mm, 10 mm, 15 mm and 20 mm. In addition, a simplified simulation method was proposed instead of the fully iterative method. Only one iteration was conducted at each speed to reduce the total number of iterations, still resulting in a similar hydroplaning speed. Moreover, a new simulation methodology of using LS-DYNA was proposed, and its results were compared with those from the iterative method in terms of accuracy and efficiency.

A Cartesian Explicit Solver for Complex Hydrodynamic Applications

2014 ◽  
Author(s):  
P. Bigay ◽  
A. Bardin ◽  
G. Oger ◽  
D. Le Touzé
Keyword(s):  
Level Set ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Flow Past A Cylinder ◽  
Explicit Solver

In order to efficiently address complex problems in hydrodynamics, the advances in the development of a new method are presented here. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with a ghost-cell method for geometry handling and a Level-set method for the treatment of biphase-flows. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used. The treatment of arbitrary geometries is addressed in the hyperbolic and viscous framework. Viscous effects are computed via a finite difference computation of viscous fluxes and turbulent effects are addressed via a Large-Eddy Simulation method (LES). The Level-Set solver used to handle biphase flows is also presented. The solver is validated on 2-D test cases (flow past a cylinder, 2-D dam break) and future improvements are discussed.

scholarly journals Numerical determination of aerodynamic characteristics of an airfoil in a ground effect

2021 ◽  
pp. 44-50
Author(s):  
М.А. Ливеринова ◽  
Н.В. Тряскин
Keyword(s):  
Pressure Coefficient ◽  
Independent Solution ◽  
Ground Effect ◽  
Simulation Method ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Method Of Images ◽  
Reverse Motion ◽  
Continuity Equations ◽  
The Difference

В работе изучается движение профиля над экраном на различных относительных высотах. Рассмотрены следующие методы его моделирования: условие неподвижного экрана и метод зеркального отображения для моделирования обращённого движения и условие экрана, движущегося со скоростью профиля, что моделирует прямое движение. Целью работы является выбор метода моделирования экрана, при котором обтекание профиля соответствует действительности и оценка разницы между рассмотренными методами. Задача решена в открытом пакете OpenFOAM методом контрольного объёма, где совместно решены уравнения Навье-Стокса и неразрывности, осреднённые по Рейнольдсу. Произведена верификация и валидация математической модели и найдено сеточно-независимое решение. Выбраны два профиля в плане: сегментный и симметричный. Рассмотрены несколько относительных высот. В работе построены эпюры скоростей под профилем, представлены картины обтекания профилей, исследованы их основные эксплуатационные характеристики: коэффициент подъёмной силы и коэффициент сопротивления в зависимости от относительной высоты. Построено распределение коэффициента давления по поверхности рассматриваемых профилей в зависимости от граничных условий и относительных высот. В результате анализа показано различие происходящих физических процессов при обтекании профилей в прямом и обращённом движении. Данная работа позволяет сделать вывод о том, каким образом проводить физический эксперимент для различных профилей, показывает преимущество использования метода зеркальных отображений или подвижного экрана при проведении эксперимента. In this article the movement of the profile above the screen at different relative heights is reviewed. The following methods of its modeling are considered: the condition of a stationary screen and the method of images for simulating reverse motion and the condition of a screen moving with the profile speed that simulate forward motion are considered. The aim of the work is to select a screen simulation method for a physical experiment. An open-source packet OpenFOAM based on finite-volume method is used to solve the Navier-Stokes and continuity equations averaged by Reynolds method. The mathematical model is verified and validated, and a grid-independent solution is found. Two profiles are selected: segmental and symmetrical. Several relative heights are considered. The velocitiy profiles under the airfoil are constructed, the patterns of the flow around the airfoils are presented. The dependences of coefficients on the studied parameters and the distribution of the pressure coefficient over the profile are studied and analyzed. As a result of the analysis, the difference between the physical processes when flowing around the airfoils is in forward and reverse motion is shown. This work allows us to make a conclusion about how to conduct a model experiment for various profiles, shows the advantage of using the method of images or a movable screen in the experiment.

Radial and Axial Variations in Transient Pressure Waves Transmitted Through Liquid Transmission Lines

1985 ◽  
Vol 107 (1) ◽  
pp. 105-111 ◽  
Author(s):  
A. K. Mitra ◽  
W. T. Rouleau
Keyword(s):  
Transmission Lines ◽  
Pressure Pulse ◽  
Plane Waves ◽  
Factorization Method ◽  
Navier Stokes ◽  
Transient Pressure ◽  
Initial Pulse ◽  
Viscous Effects ◽  
Thin Boundary Layer ◽  
Continuity Equations

An implicit factorization method has been developed for solving numerically the complete two-dimensional Navier-Stokes and continuity equations for pressure transients in a slightly compressible viscous liquid contained in a rigid pipe. Two problems have been analyzed: (1) The stopping of a steady Poiseuille flow by closure of a valve, and (2), the initiation of a nearly rectangular pressure pulse at the end of the pipe. In problem (1), radial as well as axial pressure variations were found; nearly periodic damped waves exist at the centerline and at the wall, and are approximately 180 deg out of phase. Essentially plane waves are found for problem (2), regardless of whether the fluid is flowing or not, provided that the initial pulse magnitude is not too large; the results show that the viscous effects are concentrated in a thin boundary layer.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Obtaining Expressions for Time-Dependent Functions That Describe the Unsteady Properties of Swirling Jets of Viscous Fluid

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1860
Author(s):  
Eugene Talygin ◽  
Alexander Gorodkov
Keyword(s):  
Blood Flow ◽  
Viscous Fluid ◽  
Swirling Flow ◽  
Fluid Flows ◽  
Theoretical Method ◽  
Flow Channel ◽  
Navier Stokes ◽  
Swirling Jets ◽  
Continuity Equations ◽  
Dynamic Velocity

Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity equations for the class of centripetal swirling viscous fluid flows. In this paper, analytical expressions were obtained. They describe the functions C0t and Г0t, included in the solutions, for the velocity components of such a flow. These expressions make it possible to relate the values of these functions to dynamic changes in the geometry of the flow channel in which the swirling flow evolves. The obtained expressions allow the reconstruction of the dynamic velocity field of an unsteady potential swirling flow in a flow channel of arbitrary geometry. The proposed approach can be used as a theoretical method for correct numerical modeling of the blood flow in the heart chambers and large arteries, as well as for developing a mathematical model of blood circulation, considering the swirling structure of the blood flow.

Influences of Recess Geometry and Restrictor Dimension on Flow Patterns and Pressure Distribution of Hydrostatic Bearings

2007 ◽  
Author(s):  
Cheng-Hsien Chen ◽  
Yuan Kang ◽  
Yeon-Pun Chang ◽  
De-Xing Peng ◽  
Ding-Wen Yang
Keyword(s):  
Pressure Distribution ◽  
Stokes Equations ◽  
Flow Patterns ◽  
Lubricant Film ◽  
Navier Stokes ◽  
Width Ratio ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Lubricant Flow ◽  
Land Width

This paper studies the influences of recess geometry and restrictor dimensions on the flow patterns and pressure distribution of lubricant film, which are coupled effects of hybrid characteristics of a hydrostatic bearing. The lubricant flow is described by using the Navier-Stokes equations. The Galerkin weighted residual finite element method is applied to determine the lubricant velocities and pressure in the bearing clearance. The numerical simulations will evaluate the effects of the land-width ratio and restriction parameter as well as the influence of modified Reynolds number and the jet-strength coefficient on the flow patterns in the recess and pressure distribution in lubricant film. On the basis of the simulation drawn from this study, the simulated results are expected to help engineers make better use of the design of hydrostatic bearing and its restrictors.

Rotational and Quasiviscous Cold Flow Models for Axisymmetric Hybrid Propellant Chambers

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Joseph Majdalani ◽  
Michel Akiki
Keyword(s):  
Rocket Engine ◽  
Navier Stokes ◽  
Mathematical Treatment ◽  
Hybrid Rocket ◽  
Mean Flow ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Flow Models ◽  
Hybrid Rocket Engine ◽  
Wall Injection

In this work, we present two simple mean flow solutions that mimic the bulk gas motion inside a full-length, cylindrical hybrid rocket engine. Two distinct methods are used. The first is based on steady, axisymmetric, rotational, and incompressible flow conditions. It leads to an Eulerian solution that observes the normal sidewall mass injection condition while assuming a sinusoidal injection profile at the head end wall. The second approach constitutes a slight improvement over the first in its inclusion of viscous effects. At the outset, a first order viscous approximation is constructed using regular perturbations in the reciprocal of the wall injection Reynolds number. The asymptotic approximation is derived from a general similarity reduced Navier–Stokes equation for a viscous tube with regressing porous walls. It is then compared and shown to agree remarkably well with two existing solutions. The resulting formulations enable us to model the streamtubes observed in conventional hybrid engines in which the parallel motion of gaseous oxidizer is coupled with the cross-streamwise (i.e., sidewall) addition of solid fuel. Furthermore, estimates for pressure, velocity, and vorticity distributions in the simulated engine are provided in closed form. Our idealized hybrid engine is modeled as a porous circular-port chamber with head end injection. The mathematical treatment is based on a standard similarity approach that is tailored to permit sinusoidal injection at the head end.

On computing the long-time solution of the two-dimensional Navier-Stokes equations

1995 ◽  
Vol 7 (4) ◽  
pp. 261-278 ◽  
Author(s):  
M. S. Jolly ◽  
C. Xiong
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Time Solution ◽  
Long Time

scholarly journals Computational Analysis to Factor Wind into the Design of an Architectural Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Hassam Nasarullah Chaudhry ◽  
John Kaiser Calautit ◽  
Ben Richard Hughes
Keyword(s):  
Fluid Dynamics ◽  
Power Generation ◽  
Computational Fluid Dynamics ◽  
Three Dimensional ◽  
Numerical Data ◽  
Navier Stokes ◽  
Windward Side ◽  
Average Value ◽  
Continuity Equations ◽  
Prevailing Wind Direction

The effect of wind distribution on the architectural domain of the Bahrain Trade Centre was numerically analysed using computational fluid dynamics (CFD). Using the numerical data, the power generation potential of the building-integrated wind turbines was determined in response to the prevailing wind direction. The three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations along with the momentum and continuity equations were solved for obtaining the velocity and pressure field. Simulating a reference wind speed of 6 m/s, the findings from the study quantified an estimate power generation of 6.4 kW indicating a capacity factor of 2.9% for the benchmark model. At the windward side of the building, it was observed that the layers of turbulence intensified in inverse proportion to the height of the building with an average value of 0.45 J/kg. The air velocity was found to gradually increase in direct proportion to the elevation with the turbine located at higher altitude receiving maximum exposure to incoming wind. This work highlighted the potential of using advanced computational fluid dynamics in order to factor wind into the design of any architectural environment.

Dynamics of Interstitial Fluid Pressure in Extracellular Matrix Hydrogels in Microfluidic Devices

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Joe Tien ◽  
Le Li ◽  
Ozgur Ozsun ◽  
Kamil L. Ekinci
Keyword(s):  
Extracellular Matrix ◽  
Pressure Distribution ◽  
Interstitial Fluid ◽  
Scaling Laws ◽  
Fluid Pressure ◽  
Interstitial Fluid Pressure ◽  
External Loading ◽  
Interstitial Pressure ◽  
Time Resolved ◽  
Long Time

In order to understand how interstitial fluid pressure and flow affect cell behavior, many studies use microfluidic approaches to apply externally controlled pressures to the boundary of a cell-containing gel. It is generally assumed that the resulting interstitial pressure distribution quickly reaches a steady-state, but this assumption has not been rigorously tested. Here, we demonstrate experimentally and computationally that the interstitial fluid pressure within an extracellular matrix gel in a microfluidic device can, in some cases, react with a long time delay to external loading. Remarkably, the source of this delay is the slight (∼100 nm in the cases examined here) distension of the walls of the device under pressure. Finite-element models show that the dynamics of interstitial pressure can be described as an instantaneous jump, followed by axial and transverse diffusion, until the steady pressure distribution is reached. The dynamics follow scaling laws that enable estimation of a gel's poroelastic constants from time-resolved measurements of interstitial fluid pressure.

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