Fluid-filled Pipe Research Articles

Acoustics of fluid-filled pipes in fluid-filled bores

The acoustic transmission characteristics of fluid-filled elastic pipes inside fluid-filled bores in an infinite elastic solid are examined here. This model is of interest in exploratory drilling to study the propagation of drilling-related noises within the borehole and into the surrounding rock. The axially symmetric solutions in the four media (fluid inside the pipe, pipe, fluid in the annulus and the surrounding solid) are coupled through the boundary conditions. The resulting characteristic determinant is 9×9. The dispersion behaviors of the various modes are analyzed. The limiting behaviors at low and high frequencies are investigated. The cases of the surrounding solid being acoustically ‘‘fast’’ or ‘‘slow’’ compared to the fluid in the annulus are also examined.

Experiments on active control of wave propagation in fluid-filled elastic cylindrical shells

Experimental results of studies on active vibration control in fluid-filled piping systems are presented. Reductions of the total power flow, i.e., the power flow in the shell wall and the power flow in the fluid field, have been achieved by means of external radial forces applied to the structure. Axisymmetric wave propagation was first considered, using PVDF cables both as actuators and sensors. The shell radial displacement beyond the control discontinuity was reduced by 7 to 20 dB in a large frequency range. In addition, the internal pressure field was globally attenuated by the external forces. Considering a point force disturbance at low frequencies, attenuations of the shell motion associated with higher-order modes (n=1,2) have been achieved, by means of shaped PVDF films as error sensors and point forces as structural control inputs. [Work supported by ONR.]

Acoustic Properties Of Fluid-filled Elastic Pipes

The acoustic properties of an infinite, fluid-filled pipe have been investigated. The relation between radiated sound power and the system power distribution for a single mode is analyzed. Energy flow is examined. Coupling effects on acoustic properties are compared. Whether coupling with fluid will increase or decrease pipe response, and hence noise power, is largely dependent on the frequency range and on the method of excitation.

Separation devices based on forced coincidence response of fluid-filled pipes

A separation process based on the acoustic radiation force created in stationary fields produced by a forced coincidence excitation at ultrasonic frequencies of fluid-filled pipes has been developed. The efficacy of this method for the collection and manipulation of fine secondary phases in flowing suspensions will be compared to equivalent operations in stationary fields generated in acoustic interferometer chambers operated without coincidence effects. The basis for the axial translation of the phases concentrated at the pressure nodes to either end of the cell as a result of an applied periodic sweep in the driving frequency will be examined.

Vibroacoustical energy flow through straight pipes

At lower relative (i.e., non-dimensional) frequencies, four propagating waves exist in fluid-filled pipes. Each of these waves carries energy in the pipe wall, while three waves carry energy in the fluid as well. The otherwise fairly complex dispersion laws for waves in pipes simplify in the frequency region considered to simple rod- and beam-type laws. It is shown that these laws can be determined by approximate formulae fairly accurately, the accuracy decreasing with increase in frequency. Due to fluid-wall coupling, expressed again by simplifications, the energy flow in both the wall and the fluid can be evaluated in principle from knowledge of surface vibrations only. The portions of the flow in the solid and the fluid fluctuate along the pipe axis, and consequently spatial averaging has to be done in order to obtain useful results. In this way, the pipe becomes a homogeneous one-dimensional waveguide, suitable for measurements of energy flow by detection of surface vibrations only. Specific transducer patterns for this purpose are described. At higher frequencies however, where additional propagating waves take place, simplifications are no longer possible. The exact expression for the unit-length energy flow can be then employed in conjunction with averaging around the circumference to evaluate flow in the wall at a particular axial position.

A Method for Suppression of Pressure Pulse in Fluid-Filled Piping—Part II: Experimental Verification

A simple, nondestructive method to suppress pressure pulses in fluid-filled piping was proposed and theoretically analyzed in the previous companion paper. In this paper, the proposed method is verified experimentally. The results of experiments performed for the range of parameters of practical importance indicated that the attenuation of pressure pulses was sufficiently large for practical applications and in accordance with the theoretical predictions. This paper describes the experimental setup and the test models of the proposed pulse suppression devices and discusses the experimental results. In particular, the measured attenuation factors (transmitted pressure/incident pressure) are presented and compared with the theoretical predictions.

A Method for Suppression of Pressure Pulses in Fluid-Filled Piping—Part I: Theoretical Analysis

A simple, nondestructive method to suppress pressure pulses in fluid-filled piping is theoretically analyzed, and the result provides the basis needed for design and evaluation of a pressure-pulse suppression device based on the proposed theory. The method is based on forming of fluid jets in the event of a pressure surge, such that the pulse height and the energy of the pulse are reduced. The results for pressure pulses in the range of practical interest show that a substantial reduction in the pulse height can be attained, with accompanying reduction of the pulse remaining in the system. The analysis also reveals that a certain amount of trade-off exists in the design of the suppression device; a certain level of pulse energy remaining in the system must be accepted in order to keep the pulse height below a certain level, and vice versa.

Plastic deformation induced by pressure transients in fluid-filled pipes

Severe pressure transients, caused for example by pump breakdown, may induce plastic deformation of a pipe wall. The speed of propagation of waves inducing plastic deformation is of importance in the analysis and design of piping systems. A general expression for the speed of propagation is derived. This also accounts for the type of pipe support. The analysis presented in this paper suggests that there is no propagation at the point of plastic instability.

Wave Propagation and Attenuation in Piping Systems

Results of an investigation on wave propagation in two-dimensional fluid-filled piping systems is reported. This phenomenon is studied by first developing a model for the transmission of solid-borne and fluid-borne vibrations in fluid-filled piping system elements, such as bends and straight sections. The aforementioned model, which is represented by an element transmission matrix, is used to determine the transfer and point impedances between the motion and forces of both the pipe and the fluid at any point within the element. It allows for longitudinal vibrations in the fluid, and longitudinal and bending vibrations in the solid portion of the system. The effects of both shear strains and rotary inertia within the pipe are included, while the effects of fluid flow and radial or angular modes in the fluid are neglected. Computer results for two-dimensional piping systems with modes of vibration in the plane of the pipes are considered. This method which is exact, except for possible computational errors, can be easily extended to the three-dimensional case.

Dynamic Analysis of Fluid-Filled Piping Systems Using Finite Element Techniques

Two finite element procedures are described for predicting the dynamic response of general 3-D fluid-filled elastic piping systems. The first approach, a low-frequency procedure, models each straight pipe or elbow as a sequence of beams. The contained fluid is modeled as a separate coincident sequence of axial members (rods) which are tied to the pipe in the lateral direction. The model includes the pipe hoop strain correction to the fluid sound speed and the flexibility factor correction to the elbow flexibility. The second modeling approach, an intermediate frequency procedure, follows generally the original Zienkiewicz-Newton scheme for coupled fluid-structure problems except that the velocity potential is used as the fundamental fluid unknown to symmetrize the coefficient matrices. From comparisons of the beam model predictions to both experimental data and the 3-D model, the beam model is validated for frequencies up to about two-thirds of the lowest fluid-filled lobar pipe mode. Accurate elbow flexibility factors are seen to be important for effective beam modeling of piping systems.

Propagation of a soliton along a fluid-filled pipe

In [1, 2] a mathematical model of the motion of a fluid in a pipe whose axis is a curve in space was discussed and certain simplifications of the problem were studied. The propagation of linear and nonlinear waves in the framework of the model was studied. In the present paper we consider a simple wave flow in a pipe with elastic walls suing one of the models introduced in [1], which, unlike [2], takes into account axial displacements of the pipe. The basic equations describing the propagation of waves in the pipe are obtained.

Water hammer and propagation of perturbations in elastic fluid-filled pipes

A Korteweg—de Vries (KV) approximation is constructed in this paper for the perturbations being propagated in elastic pipes filled with fluid. On the basis of the approximation constructed and the equation obtained for the perturbations of a finite-amplitude velocity, the water-hammer phenomenon is analyzed in the Zhukovskii formulation, and the water hammer in systems with preliminary longitudinal tension is considered separately. Special attention in the study of the perturbations is paid to the signal structure and evolution in the hydraulic line. Taking account of the inertial properties of the pipe in the approximation mentioned permitted the indication of new effects, in principle, which are essential for applied problems of the propagation of perturbations in elastic hydraulic lines. In particular, it is shown that the initial signal can be doubled in such lines by redistributing its intensity over the frequencies. It is established that the origination of an oscillating forerunner is possible in hydraulic lines with preliminary tension. Starting with [1], the water-hammer phenomenon was investigated in many papers, in [2], for example. The main attention in these papers was paid to the propagation velocity of the water hammer and its intensity. After simplification, the initial system of Zhukovskii equations contains no mechanism hindering the twisting of the wave profile, and, therefore, there is no possibility of stationary shock formation within the framework of this theory. Moreover, the Zhukovskii theory of the water hammer and of propagation of perturbations in elastic pipes results in the conclusion that the wave structure, velocity, and amplitude depend essentially on the characteristics of the initial perturbation and can differ significantly from the water hammer predicted by theories for powerful signals in sufficiently long pipes.

Energy Transmission in Piping Systems and Its Relation to Noise Control

The piping in a process plant acts as a distribution and radiation system throughout the plant for many significant sources of noise and vibration such as compressors, pumps, valves and other flow discontinuities, and the like. The acoustical and vibrational energy carried by the piping can result in the establishment of undesirable acoustic fields. This paper looks at those factors which are important to the proper description of the energy interaction and propagation in the fluid-filled piping system and discusses their significance in achieving noise control.

Acoustic performance tests and parameters for fluid piping system components: A critical evaluation of the state of the art: Part 2

This paper, which has been published in two parts, presents a critical evaluation of the state of the art relating to the measurement and characterisation of the acoustic performance of fluid system components, in particular of pumps and acoustic filters for liquid piping systems. The first part reviewed, in non-mathematical terms, the analysis techniques which can be used for acoustic circuits, and pointed out that the effect of any component (such as a filter) cannot be predicted accurately without making a complete circuit analysis. Various performance measurements and analytical parameters for acoustic filters were described, the theoretical relationships between ‘measured attenuation’ and ‘transmission loss’ were demonstrated, and causes for discrepancies between theoretical and measured filter performance discussed. Approaches toward acoustic characterisation of pumps and other noise sources were examined, and this lead to the conclusion that the difficulties therein have only begun to be recognised, and are far from solved. Some new suggestions for experimental approaches were presented. This second part deals more directly with practical considerations in the design of acoustic test loops for liquid piping system components. After a review of the general requirements, more detailed consideration is given to the measurement of standing waves, to entrained and entrapped air problems, to the design of practicable acoustic ‘terminations’, and to the advantages and disadvantages of plastic pipes for loop piping and filter models. Slightly more mathematical appendices deal with the acoustic impedance and acoustic velocity in fluid-filled elastic pipes, and the measurement of acoustic power flow.

Acoustic performance tests and parameters for fluid piping system components: A critical evaluation of the state of the art: Part 1

This paper, to be published in two parts, presents a critical evaluation of the state of the art relating to the measurement and characterisation of the acoustic performance of fluid system components, in particular of pumps and acoustic filters for liquid piping systems.The first part reviews, in non-mathematical terms, the analysis techniques which can be used for acoustic circuits, and points out that the effect of any component (such as a filter) cannot be predicted accurately without making a complete circuit analysis. Various performance measurements and analytical parameters for acoustic filters are described, the theoretical relationships between ‘measured attenuation’ and ‘transmission loss’ are demonstrated, and causes for discrepancies between theoretical and measured filter performance are discussed. Approaches toward acoustic characterisation of pumps and other noise sources are examined, and this leads to the conclusion that the difficulties therein have only begun to be recognised, and are far from solved. Some new suggestions for experimental approaches are presented.The second part will deal more directly with practical considerations in the design of acoustic test loops for liquid piping system components. After a review of the general requirements, more detailed consideration will be given to the measurement of standing waves, to entrained and entrapped air problems, to the design of practicable acoustic ‘terminations’, and to the advantages and disadvantages of plastic pipes for loop piping and filter models.Slightly more mathematical appendices will deal with the acoustic impedance and acoustic velocity in fluid-filled elastic pipes, and the measurement of acoustic power flow.