Factorial Design Applied to CFD

2004 ◽  
Vol 126 (5) ◽  
pp. 791-798 ◽  
Author(s):  
Michel J. Cervantes ◽  
T. Fredrik Engstro¨m
Keyword(s):  
Boundary Conditions ◽  
Factorial Design ◽  
Draft Tube ◽  
Turbulence Models ◽  
Test Case ◽  
Unknown Boundary ◽  
Experimental Uncertainty ◽  
Complex Flow ◽  
Input Parameters ◽  
Unknown Boundary Conditions

Factorial design, a statistical method widely used for experiments, and its application to CFD are discussed. The aim is to propose a systematic, objective, and quantitative method for engineers to design a set of simulations in order to evaluate main and joint effects of input parameters on the numerical solution. The input parameters may be experimental uncertainty on boundary conditions, unknown boundary conditions, grid, differencing schemes, and turbulence models. The complex flow of the Turbine-99 test case, a hydropower draft tube flow, is used to illustrate the method, where four factors are chosen to perform a 24 factorial design. The radial velocity at the inlet (not measured) is shown to have an important influence on the pressure recovery (7%) and the energy loss factor (49%).

Large Eddy Simulation of the Heat Transfer Due to Swirling and Non-Swirling Jet Impingement

2008 ◽  
Author(s):  
Naseem Uddin ◽  
S. O. Neumann ◽  
B. Weigand
Keyword(s):  
Heat Transfer ◽  
Turbulence Models ◽  
Jet Impingement ◽  
Impinging Jet ◽  
Test Case ◽  
Complex Flow ◽  
Free Jet ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Target Wall

Turbulent impinging jet is a complex flow phenomenon involving free jet, impingement and subsequent wall jet development zones; this makes it a difficult test case for the evaluation of new turbulence models. The complexity of the jet impingement can be further amplified by the addition of the swirl. In this paper, results of Large Eddy Simulations (LES) of swirling and non-swirling impinging jet are presented. The Reynolds number of the jet based on bulk axial velocity is 23000 and target-to-wall distance (H/D) is two. The Swirl numbers (S) of the jet are 0,0.2, 0.47. In swirling jets, the heat transfer at the geometric stagnation zone deteriorates due to the formation of conical recirculation zone. It is found numerically that the addition of swirl does not give any improvement for the over all heat transfer at the target wall. The LES predictions are validated by available experimental data.

On the Use of the Squire-Long Equation to Estimate Radial Velocities in Swirling Flows

2006 ◽  
Vol 129 (2) ◽  
pp. 209-217 ◽  
Author(s):  
Michel J. Cervantes ◽  
L. Håkan Gustavsson
Keyword(s):  
Boundary Conditions ◽  
Radial Velocity ◽  
Swirling Flow ◽  
Draft Tube ◽  
Three Dimensional ◽  
Swirling Flows ◽  
Laser Doppler Velocimeter ◽  
Test Case ◽  
Swirl Number ◽  
Experimental Values

A method to estimate the radial velocity in swirling flows from experimental values of the axial and tangential velocities is presented. The study is motivated by the experimental difficulties to obtain this component in a draft tube model as evidenced in the Turbine-99 IAHR∕ERCOFTAC Workshop. The method uses a two-dimensional nonviscous description of the flow. Such a flow is described by the Squire-Long equation for the stream function, which depends on the boundary conditions. Experimental values of the axial velocities at the inlet and outlet of the domain are used to obtain the boundary conditions on the bounded domain. The method consists of obtaining the equation related to the domain with an iterative process. The radial velocity profile is then obtained. The method may be applied to flows with a swirl number up to about Sw=0.25. The critical value of the swirl number depends on the velocity profiles and the geometry of the domain. The applicability of the methodology is first performed on a swirling flow in a diffuser with a half angle of 3deg at various swirl numbers, where three-dimensional (3D) laser Doppler velocimeter (LDV) velocity measurements are available. The method is then applied to the Turbine-99 test case, which consists in a model draft tube flow where the radial inlet velocity was undetermined. The swirl number is equal to Sw=0.21. The stability and the convergence of the approach is investigated in this case. The results of the pressure recovery are then compared to the experiments for validation.

Numerical Simulation of Flow Around a Simplified Car Body

2003 ◽  
Author(s):  
Emmanuel Guilmineau
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Boundary Conditions ◽  
Turbulence Models ◽  
Test Case ◽  
Slant Angle ◽  
Acceptable Limit ◽  
Numerical Errors ◽  
Car Body ◽  
Ahmed Body

Simulations have been carried out for the generic car body (Ahmed body) for 25° and 35° slant angle. At a previous Workshop [1, 2], the results of different groups showed significant variations, even when the same turbulence models were used. This indicates that either the grids used in the investigation are too coarse to reduce the numerical errors below an acceptable limit, or that other factors, like boundary conditions, model implementation had a significant effect on the simulations. In any case, the results of the simulations were inconclusive, leading to a revaluation of this test case. In this study, we investigate numerically the flow around the Ahmed body for 25° and 35° slant angle. Results are compared with experimental data of Becker et al. [3].

An Inverse Method for Simultaneous Estimation of the Center and Surface Thermal Behavior of a Heated Cylinder Normal to a Turbulent Air Stream

2002 ◽  
Vol 124 (4) ◽  
pp. 601-608 ◽  
Author(s):  
Jiin-Hong Lin ◽  
Cha’o-Kuang Chen ◽  
Yue-Tzu Yang
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Measurement Errors ◽  
Boundary Behavior ◽  
Traditional Approach ◽  
Simultaneous Estimation ◽  
Unknown Boundary ◽  
Heated Cylinder ◽  
Air Stream ◽  
Unknown Boundary Conditions

A two-dimensional inverse analysis utilizes a different perspective to simultaneously estimate the center and surface thermal behavior of a heated cylinder normal to a turbulent air stream. A finite-difference method is used to discretize the governing equations and then a linear inverse model is constructed to identify the unknown boundary conditions. The present approach is to rearrange the matrix forms of the governing differential equations and estimate the unknown boundary conditions of the heated cylinder. Then, the linear least-squares-error method is adopted to find the solutions. The results show that only a few measuring points inside the cylinder are needed to estimate the unknown quantities of the thermal boundary behavior, even when measurement errors are considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown quantities, no initial guesses are required, no iterations in the calculating process are necessary, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can easily be identified.

scholarly journals Cable force estimation of cables with small sag considering inclination angle effect

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Wen-Yu He ◽  
Fan-Cheng Meng ◽  
Wei-Xin Ren
Keyword(s):  
Boundary Conditions ◽  
Inclination Angle ◽  
Estimation Methods ◽  
Unknown Boundary ◽  
Force Estimation ◽  
Numerical Examples ◽  
Cable Force ◽  
Angle Effect ◽  
Unknown Boundary Conditions ◽  
Cable Force Estimation

AbstractCable force estimation is essential for security assessment of cable-stayed bridges. Cable force estimation methods based on the relationship between cable force and frequency have been extensively studied and used during both construction phase and service phase. However, the effect induced by inclination angle of the cable is not included in the establishment of frequency-cable force relationship as horizontal cable model is normally employed. This study aims to investigate the influence of the inclination angle on vibration based cable force estimation and provide practical formulas accordingly. Firstly numerical examples of fixed-fixed and hinged-hinged cables are simulated to illustrate the necessity of considering the inclination angle effect on the modal parameters and cable force estimation for inclined cables with small sag. Then practical formulas considering the inclination angle effect to estimate the cable force of fixed-fixed and hinged-hinged cables via the fundamental frequency are established accordingly. For the inclined cables with unknown boundary conditions, the coefficients reflecting boundary condition are predicted via the practical formulas for fixed-fixed and hinged-hinged cables. And the cable force considering the influence of inclination angle and unknown boundary conditions is obtained by iteration method. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed method.

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