An Aerodynamic Investigation of an Isolated Rotating Formula 1 Wheel Assembly

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
John Axerio-Cilies ◽  
Gianluca Iaccarino
Keyword(s):  
Large Scale ◽  
Cross Flow ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Turbulence Closures ◽  
Patch Boundary ◽  
The One

The flowfield around a 60% scale rotating Formula 1 tire in contact with the ground in a closed wind tunnel at a Reynolds number of 500,000 was examined computationally and experimentally. The goal of this study was to assess the accuracy of unsteady Reynolds-averaged Navier–Stokes (URANS) equations and confirm the existence of large scale vortical and flow recirculating features. A replica deformable F1 tire model that includes four tire treads and all brake components was used to determine the sensitivity of the wake to cross flow within the tire hub as well as the flow blockage caused by the brake assembly. Several turbulence closures were employed and the one that matched closest to the experimental PIV data was the Reynolds stress model. The variability between the six turbulence closures is shown by comparing velocity profiles, pressure distributions, and vortex eccentricity. The sensitivity of the wake to four different hub geometries, contact patch boundary conditions, multiple reference frame (MRF) rotor and spoke treatment, and time step size are also discussed.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions

2013 ◽  
Vol 13 (2) ◽  
pp. 386-410 ◽  
Author(s):  
Björn Sjögreen ◽  
Jeffrey W. Banks
Keyword(s):  
Stokes Equations ◽  
Normal Mode Analysis ◽  
Linear Equations ◽  
Mode Analysis ◽  
Navier Stokes ◽  
Computational Domain ◽  
Interface Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size

AbstractWe consider multi-physics computations where the Navier-Stokes equations of compressible fluid flow on some parts of the computational domain are coupled to the equations of elasticity on other parts of the computational domain. The different subdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping is very efficient. We address the issue of discrete interface conditions between the two domains of different physics that do not lead to instability, or to a significant reduction of the stable time step size. Finding such interface conditions is non-trivial.We discretize the problem with high order centered difference approximations with summation by parts boundary closure. We derive L2 stable interface conditions for the linearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate their stable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain the interface conditions derived through normal mode analysis by Banks and Sjögreen in [8] as a special case.

scholarly journals An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics

2013 ◽  
Vol 3 (3) ◽  
pp. 247-262 ◽  
Author(s):  
Wei-Fan Hu ◽  
Ming-Chih Lai
Keyword(s):  
Immersed Boundary Method ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Boundary Method ◽  
Stretching Factor ◽  
Vesicle Dynamics ◽  
Energy Stable

AbstractWe develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semi-implicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the projection method to solve the fluid equations, the pressure is decoupled and we have a symmetric positive definite system that can be solved efficiently. The method can be shown to be unconditionally stable, in the sense that the total energy is decreasing. A resulting modification benefits from this improved numerical stability, as the time step size can be significantly increased (the severe time step restriction in an explicit boundary forcing scheme is avoided). As an application, we use our scheme to simulate vesicle dynamics in Navier-Stokes flow.

The Dispersion in One- and Two-Dimensional Finite Element Solutions to the Heat Equation

2002 ◽  
Author(s):  
W. Dauksher ◽  
A. F. Emery
Keyword(s):  
Finite Element ◽  
Heat Equations ◽  
Two Dimensional ◽  
Step Size ◽  
Matrix Formulation ◽  
Time Step ◽  
Time Step Size ◽  
Time Stepping ◽  
Dimensional Finite Element ◽  
The One

The dispersive errors in the finite element solution to the one- and two-dimensional heat equations are examined as a function of element type and size, capacitance matrix formulation, time stepping scheme and time step size.

scholarly journals Numerical Gradient Schemes for Heat Equations Based on the Collocation Polynomial and Hermite Interpolation

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 93 ◽  
Author(s):  
Hou-Biao Li ◽  
Ming-Yan Song ◽  
Er-Jie Zhong ◽  
Xian-Ming Gu
Keyword(s):  
Hermite Interpolation ◽  
Mesh Size ◽  
Dirichlet Boundary Conditions ◽  
Maximum Norm ◽  
Heat Equations ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
The One ◽  
Delay Partial Differential Equations

As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is that it is unconditionally stable and convergent on the order O ( τ 2 + h 4 ) (where τ is the time step size and h is the mesh size), under the maximum norm for a class of nonlinear delay partial differential equations with initial and Dirichlet boundary conditions. In this article, a new numerical gradient scheme based on the collocation polynomial and Hermite interpolation is presented. The convergence order of this kind of method is also O ( τ 2 + h 4 ) under the discrete maximum norm when the spatial step size is twice the one of H-OCD, which accelerates the computational process. In addition, some corresponding analyses are made and the Richardson extrapolation technique is also considered in the time direction. The results of numerical experiments are consistent with the theoretical analysis.

scholarly journals Feasibility Study of Rans in Predicting Propeller Cavitation in Behind-Hull Conditions

2020 ◽  
Vol 27 (4) ◽  
pp. 26-35
Author(s):  
Yuxin Zhang ◽  
Xiao-ping Wu ◽  
Ming-yan Lai ◽  
Guo-ping Zhou ◽  
Jie Zhang
Keyword(s):  
Model Test ◽  
Turbulence Models ◽  
Tip Vortex ◽  
Navier Stokes ◽  
Design Stage ◽  
Step Size ◽  
Time Step ◽  
Tip Vortex Cavitation ◽  
Time Step Size ◽  
Sheet Cavitation

AbstractThe propeller cavitation not only affects the propulsive efficiency of a ship but also can cause vibration and noise. Accurate predictions of propeller cavitation are crucial at the design stage. This paper investigates the feasibility of the Reynolds-averaged Navier–Stokes (RANS) method in predicting propeller cavitation in behind-hull conditions, focusing on four aspects: (i) grid sensitivity; (ii) the time step effect; (iii) the turbulence model effect; and (iv) ability to rank two slightly different propellers. The Schnerr-Sauer model is adopted as the cavitation model. A model test is conducted to validate the numerical results. Good agreement on the cavitation pattern is obtained between the model test and computational fluid dynamics. Two propellers are computed, which have similar geometry but slightly different pitch ratios. The results show that RANS is capable of correctly differentiating the cavitation patterns between the two propellers in terms of the occurrence of face cavitation and the extent of sheet cavitation; moreover, time step size is found to slightly affect sheet cavitation and has a significant impact on the survival of the tip vortex cavitation. It is also observed that grid refinement is crucial for capturing tip vortex cavitation and the two-equation turbulence models used – realizable k-ε and shear stress transport (SST) k-ω – yield similar cavitation results.

Unsteady Simulation of Film Cooling Flow From an Inclined Cylindrical Jet

2007 ◽  
Author(s):  
Sung In Kim ◽  
Ibrahim G. Hassan ◽  
Xuezhi Zhang
Keyword(s):  
Film Cooling ◽  
Thermal Environment ◽  
Density Ratio ◽  
Navier Stokes ◽  
Step Size ◽  
Time Step ◽  
Film Cooling Effectiveness ◽  
Time Step Size ◽  
Cooling Flow ◽  
Jet In Crossflow

Film cooling is extensively used to provide protection against the severe thermal environment in gas turbine engines. Most of the computational studies on film cooling flow have been done using steady Reynolds-Averaged Navier-Stokes (RANS) calculation procedures. However, the turbulent stress field is highly anisotropic in the wake region of the coolant jet, and the inherent unsteadiness of the coolant jet-crossflow interactions may have important implications in the cooling performance. In this paper, a computational investigation about the unsteady behavior of jet-in-crossflow applications is performed using DES. Detailed computation of a single row of 35 degree round holes on a flat plate has been obtained for a blowing ratio of 1.0 and a density ratio of 2.0. Firstly, time step size, grid resolution tests have been conducted. Comparison of the time-averaged DES prediction with the measured film cooling effectiveness shows that DES prediction is reasonable. From present simulations, the typical coherent vortical structures of the jet-in-crossflows can be seen. The unsteady physics of jet-in-crossflow interactions and a jet liftoff in film cooling flows have been explored.

Efficient Time-Stepping/Spectral Methods for the Navier-Stokes-Nernst-Planck-Poisson Equations

2017 ◽  
Vol 21 (5) ◽  
pp. 1408-1428 ◽  
Author(s):  
Xiaoling Liu ◽  
Chuanju Xu
Keyword(s):  
Stability Condition ◽  
Time Discretization ◽  
Equation System ◽  
Second Order ◽  
Navier Stokes ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
First Order ◽  
Time Stepping

AbstractThis paper is concerned with numerical methods for the Navier-Stokes-Nernst-Planck-Poisson equation system. The main goal is to construct and analyze some stable time stepping schemes for the time discretization and use a spectral method for the spatial discretization. The main contribution of the paper includes: 1) an useful stability inequality for the weak solution is derived; 2) a first order time stepping scheme is constructed, and the non-negativity of the concentration components of the discrete solution is proved. This is an important property since the exact solution shares the same property. Moreover, the stability of the scheme is established, together with a stability condition on the time step size; 3) a modified first order scheme is proposed in order to decouple the calculation of the velocity and pressure in the fluid field. This new scheme equally preserves the non-negativity of the discrete concentration solution, and is stable under a similar stability condition; 4) a stabilization technique is introduced to make the above mentioned schemes stable without restriction condition on the time step size; 5) finally we construct a second order finite difference scheme in time and spectral discretization in space. The numerical tests carried out in the paper show that all the proposed schemes possess some desirable properties, such as conditionally/unconditionally stability, first/second order convergence, non-negativity of the discrete concentrations, and so on.

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