Publisher’s Note: “A general nonlinear fluid model for reacting plasma-neutral mixtures [Phys. Plasmas 19, 072508 (2012)]

A method for leaks location in a pipeline, using sensors only at the extremes of the line is presented. The detection problem is solved, assuming a nonlinear fluid model of finite dimension with uncertainty in the leak position, and generating the residual with two minimal order nonlinear observers. Flow and pressure data at the beginning and at end of the line are considered as output and input of the system respectively. Since the proposed model satisfies (1) the condition to generate a residual, assuming at the most two leaks, and (2) the strong detectability fault property for each output component, two nonlinear robust filters with respect to a leak are designed to generate the residual. To simplify the residual evaluation and estimate the leak position, a static relationship between each component of the residual and the position error is derived. The main contribution of this paper is to take advantage of the residual equation with uncertainty to isolate a fault. The effectiveness of this approach is shown by a comparison with the practical method reported in [1] using results obtained from simulated and experimental data of a water pilot pipeline of 132 m long, with a diameter of 0.1 m and with a flow rate of 12 l/s.

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Statistical Response of a Simplified Nonlinear Fluid Model Under Random Parameters

Volume 1: 21st Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2007-34219 ◽

2007 ◽

Author(s):

T-P. Chang

Keyword(s):

Fluid Model ◽

Closed Form Solution ◽

Mean Value ◽

Form Solution ◽

Viscoelastic Materials ◽

Nonlinear Springs ◽

Constant Rate ◽

Viscoelastic Modeling ◽

Spring Constants ◽

Nonlinear Fluid

In this paper, a simplified spring-dashpot model is proposed to represent the complicated nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been adopted by many researchers to characterize some parts of human body in bioengineering. Among others, the following researchers have already contributed to the development of this field (Weiss et al., [1]; Guedes et al., [2]). Sometimes it is impossible to estimate the constant parameters in the model deterministically, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to characterize the random properties of the viscoelastic materials. The mean value of the displacement of the nonlinear model, subjected to constant rate displacement, can be solved analytically. Based on the closed-form solution, the proposed method produces the statistical responses of the simplified nonlinear fluid model, which is fairly useful in estimating the reliability of the nonlinear system.

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Stochastic Dynamic Response of a Simplified Nonlinear Fluid Model for Viscoelastic Materials

Journal of Mechanics ◽

10.1017/jmech.2012.41 ◽

2012 ◽

Vol 28 (2) ◽

pp. 365-372 ◽

Cited By ~ 1

Author(s):

T.-P. Chang

Keyword(s):

Dynamic Response ◽

Closed Form ◽

Fluid Model ◽

Closed Form Solution ◽

Mean Value ◽

Form Solution ◽

Stochastic Dynamic ◽

Viscoelastic Materials ◽

Viscoelastic Modeling ◽

Nonlinear Fluid

AbstractIn the present study, we propose a simplified nonlinear fluid model to characterize the complex nonlinear response of some viscoelastic materials. Recently, the viscoelastic modeling has been utilized by many researchers to simulate some parts of human body in bioengineering and to represent many material properties in mechanical engineering, electronic engineering and construction engineering. Occasionally it is almost impossible to evaluate the constant parameters in the model in the deterministic sense, therefore, the damping coefficient of the dashpot and the spring constants of the linear and nonlinear springs are considered as stochastic to model the stochastic properties of the viscoelastic materials. After some transformations, the closed-form solution can be obtained for the mean value of the displacement of the simplified nonlinear fluid model, subjected to constant rate of displacement. Based on the closed-form solution, the proposed method generates the stochastic dynamic response of the simplified nonlinear model, which plays an important role in performing the reliability analysis of the nonlinear system.

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A nonlinear fluid model for pulmonary blood circulation

Journal of Biomechanics ◽

10.1016/0021-9290(93)90029-e ◽

1993 ◽

Vol 26 (6) ◽

pp. 653-664 ◽

Cited By ~ 20

Author(s):

C.W. Li ◽

H.D. Cheng

Keyword(s):

Blood Circulation ◽

Fluid Model ◽

Nonlinear Fluid

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On an evolutionary nonlinear fluid model in the limiting case

Mathematica Bohemica ◽

10.21136/mb.2001.134014 ◽

2001 ◽

Vol 126 (2) ◽

pp. 421-428

Author(s):

Stephan Luckhaus ◽

Josef Málek

Keyword(s):

Fluid Model ◽

Limiting Case ◽

Nonlinear Fluid

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Nonlinear Fluid Models for Biofluid Flow in Constricted Blood Vessels under Body Accelerations: A Comparative Study

Journal of Applied Mathematics ◽

10.1155/2012/950323 ◽

2012 ◽

Vol 2012 ◽

pp. 1-27

Author(s):

D. S. Sankar ◽

Atulya K. Nagar

Keyword(s):

Flow Rate ◽

Fluid Model ◽

Plug Flow ◽

Casson Fluid ◽

Fluid Models ◽

Mean Flow ◽

Mean Velocity ◽

Casson Fluid Model ◽

The Mean ◽

Nonlinear Fluid

Pulsatile flow of blood in constricted narrow arteries under periodic body acceleration is analyzed, modeling blood as non-Newtonian fluid models with yield stress such as (i) Herschel-Bulkley fluid model and (ii) Casson fluid model. The expressions for various flow quantities obtained by Sankar and Ismail (2010) for Herschel-Bulkley fluid model and Nagarani and Sarojamma (2008), in an improved form, for Casson fluid model are used to compute the data for comparing these fluid models. It is found that the plug core radius and wall shear stress are lower for H-B fluid model than those of the Casson fluid model. It is also noted that the plug flow velocity and flow rate are considerably higher for H-B fluid than those of the Casson fluid model. The estimates of the mean velocity and mean flow rate are considerably higher for H-B fluid model than those of the Casson fluid model.

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