Unsteady Friction Research Articles

Distortion of Compression Wave Propagating through Very Long Tunnel with Slab Tracks

Field measurement and numerical simulation were performed on the distortion of the compression wave generated by train entry and propagating through a slab track Shinkansen tunnel, which is the longest mountain tunnel in the world as of 2004. The compression wave was measured at twelve different locations. In the numerical simulation, the distortion of the compression waveform were calculated by one-dimensional compressible flow analysis, which takes account of steady and unsteady friction, combined with acoustic analysis on the effect of side branches in the tunnel. The results of numerical simulation are consistent with those of the field measurement. Furthermore, the results indicate that the compression wavefront steepens in the early stage and smoothes down in the later stage of propagation, and the maximum value of the pressure gradient of the compression wavefront reaches a peak under certain conditions of the initial compression wave and a tunnel length.

G506 バラスト軌道トンネルを伝播する圧縮波の現地測定と数値計算(2)(GS-5 数値シミュレーション,一般セッション)

The distortion process of the compression wave in a ballast-tracked tunnel was investigated by field measurement and numerical simulation. The field measurement was conducted in an actual Shinkansen ballast-tracked tunnel of about 4 km. The numerical simulation corresponding to the field measurement was carried out on the basis of a one-dimensional compressible flow analysis in which the effects of steady and unsteady friction were included and of an acoustic analysis on the effect of side branches. The results of the numerical simulation agreed well with those of the field measurement. It indicates that the ballast is effective for reducing pressure gradient of the compression wave generated by a high-speed exceeding 350km/h.

Frequency Domain Analysis for Detecting Pipeline Leaks

This paper introduces leak detection methods that involve the injection of a fluid transient into the pipeline, with the resultant transient trace analyzed in the frequency domain. Two methods of leak detection using the frequency response of the pipeline are proposed. The inverse resonance method involves matching the modeled frequency responses to those observed to determine the leak parameters. The peak-sequencing method determines the region in which the leak is located by comparing the relative sizes between peaks in the frequency response diagram. It was found that a unique pattern was induced on the peaks of the frequency response for each specific location of the leak within the pipeline. The leak location can be determined by matching the observed pattern to patterns generated numerically within a lookup table. The procedure for extracting the linear frequency response diagram, including the optimum measure- ment position, the effect of unsteady friction, and the way in which the technique can be extended into pipeline networks, are also discussed within the paper.

Extensive Development of Leak Detection Algorithm by Impulse Response Method

The oscillatory flows in pipeline systems due to excitation by valve operation are efficiently analyzed by the impulse response method. The impact of leakage is incorporated into the transfer functions of the complex head and discharge. Frequency-dependent friction is used to consider the impact of unsteady friction for laminar condition. Extensive development of the impulse response method was made by considering the sources of friction associated with the local and convective acceleration of velocity for turbulent flow. The genetic algorithm was integrated into the impulse response method to calibrate the location and the quantity of leakage. The calibration function for leakage detection can be made using the pressure-head response at the valve, or the pressure-head and flow response at the section upstream from the valve. The proposed leak detection algorithm shows the potentials for being applied to a simple pipeline system with a single leak or multiple leaks.

Modeling of long nonlinear waves on the interface in a horizontal two-layer viscous channel flow

The dynamics of two-dimensional waves of small but finite amplitude are theoretically studied for the case of a two-layer system bounded by a horizontal top and bottom. It is shown that for relatively large steady-state flow velocities and at certain fluid depth ratios the vertical velocity profile is nonlinear. An evolutionary equation governing the fluid interface disturbances and allowing for the long-wave contributions of the layer inertia and surface tension, the weak nonlinearity of the waves, and the unsteady friction on all the boundaries of the system is derived. Steady-state solutions of the cnoidal and solitary wave type for the disturbed flow are determined without regard for dissipation losses. It is found that the magnitude and the direction of the flow can alter not only the lengths of the waves but also their polarity.

Propagation of Compression Wave in a Long Tunnel with Slab Tracks

For prediction of the micro-pressure wave, which is one of the environmental problems in high-speed railways, it is necessary to clarify the distortion mechanism of the compression wave propagating through a tunnel. In this study, field measurement and numerical simulation were performed to investigate the distortion of the compression wave generated by a train entering a tunnel as it propagated through the tunnel. The field measurement was performed in a Shinkansen slab-tracked tunnel of 26 km in length with side branches, which was the longest mountain tunnel in the world as of 2004. The pressure of the compression wave was measured at 12 locations in the tunnel. In the numerical simulation, the distortion of the compression waveform was calculated by one-dimensional compressible flow analysis taking into account steady and unsteady friction on the tunnel wall and by acoustic analysis on the effect of side branches. The results of the numerical simulation agreed well with those from the field measurement and clarify the distortion process of the compression wave during its propagation in the tunnel with slab tracks.

Distortion of the Compression Wave Propagating Through a Very Long Tunnel with Slab Tracks

Field measurement and numerical simulation were performed on the distortion of the compression wave generated by train entry and propagating through a slab track Shinkansen tunnel, which is the longest mountain tunnel in the world at present. The pressure of the compression wave measured at 12 locations. In the numerical simulation, the distortion of the compression waveform was calculated by one-dimensional compressible flow analysis which takes account of steady and unsteady friction combined with acoustic analysis on the effect of side branches. The results of numerical simulation agree well with those of the field measurement. Furthermore, the results show that the compression wavefront steepens in the early stage and smoothes down in the later stage of propagation.

Pressure transients in a Canadian sewage force main

Severe water hammer following pump shutdown was suspected to be the cause of pipe displacement at a pump station in Saguenay, Quebec, because it appeared that insufficient surge protection was installed on the force main. To confirm this assertion and prevent further pipe displacement, data logging of a field test of the sewage pump station undergoing power failure was conducted in combination with the development of a water-hammer computer model for the design of additional surge protection measures. This paper describes the results of field testing, both before and after the installation of additional surge protection, and the calibration of a method of characteristics water-hammer model that accounts for vaporous cavitation and unsteady friction effects within the force main. Good agreement is shown between measured and computed pressure head histories at the pump station and at a vacuum relief valve following loss of power to a pump. To the authors' knowledge, this paper presents one of the first applications of the unsteady friction model referenced in this paper to a real system.Key words: sewage, force main, pump, water hammer, unsteady friction, data logging.

Decay of Pressure and Energy Dissipation in Laminar Transient Flow

In the present paper, some peculiar characteristics of transient laminar flow are discussed. After presenting a review of the existing literature, attention is focused on transient energy dissipation phenomena. Specifically, results of both laboratory and numerical experiments are reported, the latter by considering one-dimensional (1D) along with two-dimensional (2D) models. The need of modifying a criterion for simulating unsteady friction proposed some years ago by one of the writers, and extensively used for water-hammer calculations, is pointed out. Differences between accelerating and decelerating flows as well as between transients in metallic and plastic pipes are also highlighted.

Efficient Approximation of Unsteady Friction Weighting Functions

A simple method is presented for evaluating wall shear stresses from known flow histories in unsteady pipe flows. The method builds on previous work by Trikha, but has two important differences. One of these enables the method to be used with much larger integration time steps than are acceptable with Trikha’s method. The other, a general procedure for determining approximations to weighting functions, enables it to be used at indefinitely small times (high frequencies). The method is applicable to both laminar and turbulent flows.

Surge damping analysis in pipe systems: modelling and experiments

The current study focuses on the analysis of pressure surge damping in single pipeline systems generated by a fast change of flow conditions. A dimensionless form of pressurised transient flow equations was developed, presenting the main advantage of being independent of the system characteristics. In lack of flow velocity profiles, the unsteady friction in turbulent regimes is analysed based on two new empirical corrective- coefficients associated with local and convective acceleration terms. A new surge damping approach is also presented taking into account the pressure peak time variation. The observed attenuation effect in the pressure wave for high deformable pipe materials can be described by a combination of the non-elastic behaviour of the pipe-wall with steady and unsteady friction effects. Several simulations and experimental tests have been carried out, in order to analyse the dynamic response of single pipelines with different characteristics, such as pipe materials, diameters, thickness, lengths and transient conditions.

Surge damping analysis in pipe systems: modelling and experiments

The current study focuses on the analysis of pressure surge damping in single pipeline systems generated by a fast change of flow conditions. A dimensionless form of pressurised transient flow equations was developed, presenting the main advantage of being independent of the system characteristics. In lack of flow velocity profiles, the unsteady friction in turbulent regimes is analysed based on two new empirical corrective-coefficients associated with local and convective acceleration terms. A new surge damping approach is also presented taking into account the pressure peak time variation. The observed attenuation effect in the pressure wave for high deformable pipe materials can be described by a combination of the non-elastic behaviour of the pipe-wall with steady and unsteady friction effects. Several simulations and experimental tests have been carried out, in order to analyse the dynamic response of single pipelines with different characteristics, such as pipe materials, diameters, thickness, lengt...

Transient turbulent friction in fully rough pipe flows

A weighting-function model of unsteady skin friction in fully rough-walled flows in one-dimensional ducts is derived using an idealized radial viscosity distribution. The model complements previous work by the authors for smooth-walled flows. It is assumed that, for sufficiently short-lived transients, the viscosity distribution in the cross-section may be regarded as constant and equal to that in a pre-existing steady flow. The eddy viscosity in an outer annulus is assumed to vary linearly from a minimum at the wall to a maximum at the edge of a central core of uniform viscosity. The resulting weighting-function model for short-lived transients is used to develop a simple formula predicting values of unsteady skin friction coefficients suitable for an instantaneous-acceleration model of unsteady skin friction in fully rough pipe flows.

Unsteady mixed convection due to time-dependent free stream velocity

An analysis has been presented to study the unsteady combined convection from a horizontal circular cylinder to a transverse flow. A perturbation method is used to transform the governing set of partial differential equations, representing the constitutive laws, into a system of ordinary differential equations. For the case of sinusoidal variation of the free stream velocity, the boundary layer response is estimated due to both low frequency as well as high frequency oscillation. Numerical solutions are presented for the distribution of unsteady Nusselt number and friction factor.

TRANSIENT TURBULENT FRICTION IN SMOOTH PIPE FLOWS

A weighting function model of unsteady skin friction in smooth-walled, one-dimensional ducts is derived using an idealized form of the radial viscosity distribution. The model is an enhancement of earlier work by the authors in which additional simplifying assumptions were made. Important improvements include (1) replacing the assumption of uniform (solid) behaviour in an extensive core region by an assumption of uniform turbulent viscosity and (2) relating the wall shear stress to the mean flow velocity instead of to the maximum velocity. The resulting model can be used directly in numerical analyses of transient flows in pipes. It can also be used to deduce numerical values of an empirical coefficient in a popular alternative model of skin friction in which the unsteady contribution is assumed to be proportional to the instantaneous mean acceleration.

Discussion of “Velocity Profiles and Unsteady Pipe Friction in Transient Flow,” by Bruno Brunone, Bryan W. Karney, Michele Mecarelli, and Marco Ferrante

Discussion of “Velocity Profiles and Unsteady Pipe Friction in Transient Flow,” by Bruno Brunone, Bryan W. Karney, Michele Mecarelli, and Marco Ferrante

Closure to “Velocity Profiles and Unsteady Pipe Friction in Transient Flow,” by Bruno Brunone, Bryan W. Karney, Michele Mecarelli, and Marco Ferrante July/August 2000, Vol. 126, No. 4, pp. 236–244

Closure to “Velocity Profiles and Unsteady Pipe Friction in Transient Flow,” by Bruno Brunone, Bryan W. Karney, Michele Mecarelli, and Marco Ferrante July/August 2000, Vol. 126, No. 4, pp. 236–244

Efficient Treatment of the Vardy–Brown Unsteady Shear in Pipe Transients

An accurate, simple and efficient approximation to the Vardy-Brown unsteady friction equation is derived and shown to be easily implemented within a one-dimensional characteristics solution for unsteady pipe flow. For comparison, the exact Vardy-Brown unsteady friction equation is used to model shear stresses in transient turbulent pipe flows and the resulting waterhammer equations are solved by the method of characteristics. The approximate Vardy-Brown model is more computationally efficient (i.e., requires one-sixth the execution time and much less memory storage) than the exact Vardy-Brown model. Both models are compared with measured data from different research groups and with numerical data produced by a two-dimensional turbulence waterhammer model. The results show that the exact Vardy-Brown model and the approximate Vardy-Brown model are in good agreement with both laboratory and numerical experiments over a wide range of Reynolds number and wave frequencies. The proposed approximate model only requires the storage of flow variables from a single time step while the exact Vardy-Brown model requires the storage of flow variables at all previous time steps and the two-dimensional model requires the storage of flow variables at all radial nodes.

Unsteady Friction in Rough Pipes

An energy dissipation model is presented for the computation of unsteady friction losses adapted to smooth-to-rough transition and fully rough pipes. The eddy viscosity model used to compute the Reynolds stresses in turbulent flow is modified to include the effect of roughness, which is considered in the computation of the velocity profiles. The model is tested by comparing the computed transient pressures with measured data from a laboratory test facility and a prototype test. Details of the experimental setup, pressure-head measurements, and valve characteristics during transient flow conditions are presented. The quasi-steady approximation gives an inaccurate prediction of the pressure head history; however, significantly better results are obtained if the unsteady friction effects are included.

Developments in unsteady pipe flow friction modelling

This paper reviews a number of unsteady friction models for transient pipe flow. Two distinct unsteady friction models, the Zielke and the Brunone models, are investigated in detail. The Zielke model, originally developed for transient laminar flow, has been selected to verify its effectiveness for "low Reynolds number" transient turbulent flow. The Brunone model combines local inertia and wall friction unsteadiness. This model is verified using the Vardy's analytically deduced shear decay coefficient C * to predict the Brunone's friction coefficient k rather than use the traditional trial and error method for estimating k. The two unsteady friction models have been incorporated into the method of characteristics water hammer algorithm. Numerical results from the quasi-steady friction model and the Zielke and the Brunone unsteady friction models are compared with results of laboratory measurements for water hammer cases with laminar and low Reynolds number turbulent flows. Conclusions about the range of validity for the three friction models are drawn. In addition, the convergence and stability of these models are addressed.