M. Hanif Chaudhry

Leak detection in pipelines by frequency response method

A new technique for the detection of leaks in a pipeline is presented utilizing its frequency response. In the system frequency response, a leak increases the amplitude of pressure oscillations at the even harmonics. Such an increase in amplitude has an oscillatory pattern; the frequency and amplitude of this pattern may be utilized to predict the location and discharge of a leak. In this technique, the pressure transient history at one location is sufficient and the history of the transient in the pipe prior to leak is not needed; this makes it advantageous over a number of other existing techniques, in addition to being simpler to use. It is shown that the technique successfully detects the location of a leak in a number of simple systems with leak discharge as low as 0.2% of the steady discharge. The technique is verified by comparing the results with those computed by using the method of characteristics. Practical issues and limitations for field implementations are discussed.

Simulation of one-dimensional dam-break flows

Two new finite-difference schemes - Gabutti, and Beam and Warming - are introduced and compared for the analysis of unsteady free-surface flows resulting from the breaking of a dam. These schemes split the fluxvector into positive and negative parts, each of which corresponds to the direction of a characteristic, thereby allowing use of proper finite differences for the space derivatives. Central finite differences are used for subcritical flow and upwind differences are used for supercritical flow. The details of these schemes are presented and the computed results are compared with the analytical solution to demonstrate their validity. Because of their simplicity, these schemes are attractive for solving the dam-break problem, especially when supercritical flow is present.

Leak detection in pipes by frequency response method using a step excitation

This paper presents a new procedure utilizing transient state pressures to detect leakage in piping systems. Transient flow, produced by opening or closing a valve, is analyzed in the time domain by the method of characteristics and the results are transformed into the frequency domain by the fast Fourier transform. This method is used to develop a frequency response diagram at the valve end. The frequency response diagram of a system with leaks has additional resonant pressure amplitude peaks (herein called the secondary pressure amplitude peaks) that are lower than the resonant pressure amplitude peaks for the system if there were no leaks (herein called primary amplitude peaks). The location of a leak is determined from frequencies of the primary and secondary pressure amplitude peaks and the leak discharge is determined from the maximum and minimum discharge amplitudes. This method is applicable for practical values of the friction factor over the range 0.01 to 0.025 and can be used to detect leaks in real-life pipe systems conveying different types of fluids, such as water and petroleum. It can be used directly by comparing the frequency response diagram of a modeled system without leaks to the frequency response diagram developed by gradually opening or closing a valve at the downstream end of a pipe and taking measurements of pressure head and discharge at only one location.

Implicit methods for two-dimensional unsteady free-surface flows

Beam and Warming implicit Unite difference schemes are introduced to integrate the equations describing the two-dimensional unsteady free-surface flows. These schemes are second-order accurate in space and time, allow sharp discontinuous initial conditions, and do not require isolation of a bore. Subcritical and supercritical flows may be present indifferent parts of the channel or they may occur in sequence. Depending upon the Courant number used in the computations, sharp discontinuities may be slightly smeared since they are not isolated. Different procedures for incorporating the boundary conditions are discussed. The analysis of two-dimensional unsteady free-surface (lows resulting from the breaking of a dam are presented to illustrate the aplication of the methods.

Computation of flows in open-channel transitions

To analyze flows in channel expansions and contractions, two-dimensional, depth-averaged, unsteady flow equations in a transformed coordinate system are solved numerically by using the MacCormack scheme. The non-rectangular physical domain is converted into a rectangular computational domain. This transformation allows the use of an orthogonal grid and an easier inclusion of side wall boundaries. The unsteady flow model is used to obtain steady flow solutions by treating the time variable as an iteration parameter and letting the solution converge to the steady state. The results of the mathematical model are compared with experimental data. The comparison of the computed and measured results show satisfactory agreement in cases where the assumption of hydrostatic pressure distribution is valid. The capability of the model for handling mixed super- and sub-critical flows in a channel transition is demonstrated.

Analysis of transient pressures in bubbly, homogeneous, gas-liquid mixtures

Flow of a gas-liquid mixture in a piping system may be treated as a pseudo-fluid flow if the mixture is homogeneous and the void fraction is small. The governing equations for such flows are a set of nonlinear partial differential equations with pressure dependent coefficients. Shocks may be produced during transient state conditions. For numerical integration of these equations, two second-order explicit finite-difference shemes are introduced

A depth-averaged turbulence model for the computation of free-surface flow

A numerical model to compute the free-surface flow by solving the depth-averaged, two-dimensional, unsteady flow equations is presented. The turbulence stresses are closed by using a depth-averaged model. However, viscous stresses and momentum dispersion stresses are neglected. The governing equations are first transformed into a general curvilinear coordinate system and then solved by the Beam and Warming Alternating Direction Implicit (ADI) scheme. To verify the model and illustrate its applications in hydraulic engineering, it is used to analyze (i) the developed uniform flow in a straight rectangular channel, (ii) hydraulic jump in a diverging channel, (iii) supercritical flow in a diverging channel, and (iv) circular hydraulic jump. The computed results are compared with the available measured data. The comparison of results with and without effective stresses shows that in many cases the effective stresses do not significantly affect the solution. However, it was observed that the computation of sup...

Supercritical flow near an abrupt wall deflection

The supercritical flow near an abrupt wall deflection is investigated experimentally and by computer simulations. An extensive series of tests were conducted on a 500 mm wide flume with Froude number up to 8 and wall deflection angle up to 11.3°. A special inlet box was installed to provide smooth flow conditions at the flume entrance. By analyzing the experimental data, explicit expressions are derived for the height of the shock and the velocity ratio. Experimental results are presented in the form of universal plots of the shock surface and the two-dimensional velocity field. These may be utilized for engineering applications or for the verification of mathematical models. The flow field near a wall deflection was computed by using a two-dimensional flow model based on the numerical solution of steady, shallow-water equations by the MacCormack explicit finite-difference scheme. The computed and measured flow depths and flow velocities are compared and are found to be in satisfactory agreement where the...

Numerical and experimental investigation of transient pipe flow

Two mathematical formulations for the computation of transient flow in piping systems are compared with experimental data. The formulations are: a four-equations fluid structure interaction model (FSI) that includes Poisson coupling, and a two-equations model for the fluid. Both models are solved numericaly using the method of characteristics. A partial-closure of a valve located at an intermediate point in a pipeline is used to create transient flow. The two-equations model computed the maximum pressure peak satisfactorily but the FSI model gave an overall better simulation. An unsteady-friction model, added to the FSI model, did not influence the final results significantly. The experimental procedures followed to obtain the valve characteristics and the pressure history along the pipeline are explained in detail. Excellent numerical results at the valve are obtained when experimental data is used to simulate the time-dependent boundary condition.

Detection of Partial Blockages in a Branched Piping System by the Frequency Response Method

Steady oscillatory flow in a branched piping system with partial blockages is studied by using the frequency response method. The peak pressure frequency diagrams at the downstream end are developed with the partial blockage at different locations in the system by using the transfer matrix method. A systematic procedure is presented to estimate the size and the location of a single partial blockage in the system. For more than one partial blockage, it is observed that there is a definite relationship between the frequency responses of the individual and combined partial blockages.