Decay of Pressure and Energy Dissipation in Laminar Transient Flow
Marco Ferrante
Bruno Brunone2004, Journal of Fluids Engineering-transactions of The Asme
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
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 waterhammer calculations, is pointed out. Differences between accelerating and decelerating flows as well as between transients in metallic and plastic pipes are also highlighted.
Related papers
Improved Method for Simulating Frictional Losses in Laminar Transient Liquid Pipe Flow
This paper is devoted to the problem of energy dissipation and it concerns unsteady friction modeling of the liquid flow in hydraulic lines. One dimensional (1D) quasi-steady model of energy dissipation is in common use. It means that the loss of energy is estimated by the Darcy-Weisbach formulae. Such an approximation is close to reality only for slow changes of the velocity field in the pipe cross-section. In case of fast changes, like fast transients, e.g. water hammer, it fails. In this work the wall shear stress τ (defined as an effect of unsteady fluid friction) is presented as a sum of quasi-steady and unsteady components. The unsteady component of the wall shear stress is modeled as an convolution of the local fluid acceleration and a weighting function w(t). The weighting function, in general, makes an allowance for a relation of the historic velocity changes and the unsteady component of the wall shear stress. Primitive weighting functions have usually very complicated str...
Turbulence, friction, and energy dissipation in transient pipe flow
Vorticity and Turbulence Effects in Fluid Structure Interactions, 2006
The paper analyzes the energy dissipation in transient pipe flow focusing on friction and its relation with turbulence. Other important mechanisms of energy dissipation are also analyzed, in particular the viscoelastic behavior of polymeric pipes. Different models for the evaluation of friction forces and their limitations are examined by comparison with new experimental data.
Velocity profiles and unsteady pipe friction in transient flow
Journal of water …, 2000
Transient conditions in closed conduits have traditionally been modeled as 1D flows with the implicit assumption that velocity profile and friction losses can be accurately predicted using equivalent 1D velocities. Although more complex fluid models have been suggested, there has been little direct experimental basis for selecting one model over another. This paper briefly reviews the significance of the 1D assumption and the historical approaches proposed for improving the numerical modeling of transient events. To address the critical need for better data, an experimental apparatus is described, and preliminary measurements of velocity profiles during two transient events caused by valve operation are presented. The velocity profiles recorded during these transient events clearly show regions of flow recirculation, flow reversal, and an increased intensity of fluid turbulence. The experimental pressures are compared to a water hammer model using a conventional quasi-steady representation of head loss and one with an improved unsteady loss model, with the unsteady model demonstrating a superior ability to track the decay in pressure peak after the first cycle. However, a number of details of the experimental pressure response are still not accurately reproduced by the unsteady friction model.
Local and Integral Energy-Based Evaluation for the Unsteady Friction Relevance in Transient Pipe Flows
Journal of Hydraulic Engineering, 2017
Unsteady friction and its modeling have been widely studied in transient pipe flows for its influences and modification effect on pressure waves. Such a feature is of great importance particularly in pipe systems where the extreme pressure values are due to the overlapping of pressure waves generated in different sections. This paper investigates the relevance of unsteady friction term by considering different models available in the literature. In particular, attention is focused on the following two commonly used one-dimensional (1D) models: the weighting function-based (WFB) model and the instantaneous acceleration-based (IAB) model. The investigation is executed using laboratory experiments and field tests as well as 1D/2D numerical simulations in simple pipeline systems. Realistic ranges of both initial (pretransient) conditions and geometrical characteristics are considered. The data collected in experimental tests are first used to calibrate the unsteady friction models under investigation. The validated models are then applied to identify their respective domains of applicability and the limitations. The differences between models and data are measured using the local transient analysis (LTA) norm and the integral total energy (ITE) norm along the pipeline, and the reasons for such discrepancies are explored in the paper. The practical implications of the use and improvements of different unsteady friction models for transient pipe flow simulations are discussed in the paper.
A review of one-dimensional unsteady friction models for transient pipe flow
Cumhuriyet Science Journal, 2015
Abstract. This paper reviews a quasi-steady model and four unsteady friction models for transient pipe flow. One of the factors which may affect the accuracy of the one-dimensional models of transition flow is the friction coefficient. This coefficient can be estimated as steady, quasi-steady, and unsteady. In the steady approach, a constant value of the Darcy-Weisbach friction factor is used. In the quasi-steady approximation, friction losses are estimated by using formula derived for steady-state flow conditions. The fundamental assumption in this approximation is that the head loss during transient conditions is equal to the head loss obtained for steady uniform flow with an average velocity equal to the instantaneous transient velocity. During transient conditions the shear stress at the wall is not in phase with the mean velocity. In addition, the velocity profile can be completely different from a uniform flow profile. Therefore friction losses computed by using steady-state r...
The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II—model development, calibration and verification
Journal of Hydraulic Research, 2005
A state-of-the-art mathematical model has been developed to calculate hydraulic transients in pressurized polyethylene (PE) pipe systems. This hydraulic transient solver (HTS) incorporates additional terms to take into account unsteady friction and pipe-wall viscoelasticity. Numerical results obtained were compared with the classic waterhammer solution and with experimental data collected from a PE pipe-rig at Imperial College (London, UK). Unlike the classical model, the developed HTS is capable of accurately predicting transient pressure fluctuations in PE pipes, as well as circumferential strains in the pipe-wall. The major challenge was the distinction between frictional and mechanical dynamic effects. First, the HTS was calibrated and tested considering these two effects separately: if only unsteady friction was considered, a major disagreement between collected data and numerical results was observed; when only the viscoelastic effect was considered, despite the good agreement between data and numerical results, the calibrated creep function depended on the initial flow rate. In a second stage, the combination of these dynamic effects was analysed: creep was calibrated for laminar flow and used to test the solver for turbulent conditions, and a good agreement was observed. Finally, the HTS was tested using creep measured in a mechanical test, neglecting unsteady friction, and a good agreement was obtained. RÉSUMÉ Un nouveau modèle mathématique a été développé pour calculer les régimes transitoires hydrauliques des systèmes de conduites pressurisées en polyéthylène (PE). Ce modèle hydraulique (nommé HTS) intègre des termes additionnels pour simuler la friction pendant le régime transitoire et l'effet de la viscoélasticité de la conduite. Les résultats numériques obtenus ont été comparés avec la solution classique du coup de bélier et avec les résultats expérimentaux collectés à partir d'un système de conduites simples en PE construit au Imperial College (Londres, Royaume Unit). Contrairement au modèle classique, le modèle HTS est capable de prédire rigoureusement les fluctuations transitoires de pression dans la conduite de PE ainsi que l'extension de la circonférence des parois de la conduite. Le grand challenge de ce travaille est la distinction entre l'effet dynamique de la friction transitoire et l'effet mécanique de la déformation retardée de la conduite. Dans un premier temps, le modèle HTS a été calibré et testé en considérant les deux effets séparément. Lorsque la friction en régime transitoire est considérée seule, de grandes différences entre les résultats expérimentaux et numériques sont observées. Si l'effet viscoélastique de la conduite est considéré seul, même avec une bonne corrélation entre les résultats expérimentaux et numériques, les fonctions des fluage calibrées varient avec le flux initial. Dans un deuxième temps, la combinaison de ces deux effets a été analysée et une bonne correspondance entre les résultats expérimentaux et numériques a été observée. Enfin, le modèle HTS a été vérifié avec succès en utilisant la fonction de fluage mesurée lors d'un test mécanique négligeant la friction en régime transitoire.
Modeling of transient flow in plastic pipes
Contemporary Engineering Sciences, 2013
We present a numerical code for calculating transient flow in plastic pipes, especially in the polyethylene pipe, to analysis water hammer phenomena. The set partial differential equations to be solved is obtained using conservation laws and behavior for the fluid and the pipe wall, associated with constitutive equations of the two media, and relationships compatibility of interfaces on velocities and stresses. Coupling due to Poisson's ratio is also incorporated in this model. A global digital processing is achieved using the method of characteristics. The results obtained are in good agreement with those found in the literature.
Numerical Prediction Of Energy Losses Of NonNewtonian Laminar Flow Through An AbruptEnlargement
1970
A laminar flow of an incompressible pseudoplastic fluid through an abrupt enlargement is considered. The mathematical model has been solved numerically by a finite volume scheeme using a non uniform staggered grid. The purpose of this paper is to investigate the effects of different parameters on the energy losses due to this singularity. The results show that the coefficient of the energy loss tends to a limit with increasing generalized Reynolds number. By studing the evolution of the ratio of energy loss to wall shear stress, it is noted that it is practically linear function of Reynolds number. Therefore, it would be more efficient to use this ratio for prediction of the energy losses.
Energy Relations in Transient Closed-Conduit Flow
Journal of Hydraulic Engineering-asce, 1990
When the rate of flow in a closed conduit is changed, large-scale conversions of mechanical energy often occur, particularly if the pipeline is carrying water or some other slightly compressible liquid. Mathematical expressions describing these transient energy transformations are motivated from first principles and derived by mathematical manipulation of the governing continuity and momentum equations. The resulting expression accounts for the kinetic energy of the fluid, the internal energy associated with fluid compressibility and pipeline elasticity effects, the energy dissipated by friction, and the work done at the ends of the conduit. The energy approach provides an integrated view of transient conditions in the pipeline and is thus a simple, efficient, and logically consistent way of comparing the transient response of different systems and solution techniques. In particular, compressibility effects are shown to be negligible when the ratio of the change in internal energy to the change in kinetic energy is much less than one. This rule helps to distinguish the "rigid water column" model of unsteady flow from the more complex water-hammer theory. 1180 wnloaded 11 Jan
Energy losses of non-Newtonian fluids in sudden pipe contractions
Chemical Engineering Journal, 2008
There are very few experimental results available for flow of viscous fluids in sudden contractions. Furthermore, there are discrepancies between the few sets of experimental data published so far. The objective of this work is to provide a set of reliable experimental results that confirms and extends existing datasets for experimental and numerical validation and design purposes.
Related topics
Related papers
Fast and accurate modelling of frictional transient pipe flow
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2018
This paper is devoted to the one-dimensional (1D) modelling of hydraulic losses during transient flow of liquids in pressure lines. Unsteady pipe wall shear stress is present in the form of a convolution of liquid acceleration with a weighting function. The weighting function depends on the dimensionless time and the Reynolds number. In the original model of Zielke (1968), computation of the convolution integral had a complex and inefficient mathematical structure (featured power growth of computational time). Therefore, further work aimed at developing efficient models for estimation of unsteady hydraulic resistance (with nearly linear growth of computational time). In the present paper, a correction to the erratic recursive formula by Schohl (1993), being used to calculate the unsteady wall shear stresses during transient flow, is presented. The simulation results obtained with the corrected Schohl's recursive formula are consistent with the classic but computationally inefficient formula proposed recently by Vardy and Brown (2010). The accuracy of the efficient weighting function obtained in wall shear stress models is verified. The results of pressure pulsation obtained when taking into account cavitating flow, or not, are surprising in the sense that the weighting function does not need to be built by a lengthy sum of exponential terms to accurately simulate the transient event.
Structure of the transient wall-friction law in one-dimensional models of laminar pipe flows
Journal of Fluid Mechanics, 1981
The problem of describing an unsteady cylindrical pipe flow with one-dimensional equations is investigated, and an exact method for obtaining a closure relationship is proposed for the transient shear stress in a laminar flow submitted to an arbitrary transient pressure gradient. Extensive comparisons are given for a step or a harmonic pressure gradient between the approximate solution derived from this method, some results of the literature and exact solutions of the Navier-Stokes equations.
A numerical modeling of a profile velocity and Shear stress in transient flow applied in industrial technology
Periodicals of Engineering and Natural Sciences (PEN)
This research is devoted to theoretical and numerical models of transient shear stress in a transient laminar flow over the pipe wall. This work is an elementary method of the model Prado et al, which the base is on the expansion of velocity profiles ofthe flow in polynomial series of a radial space at acroass the right section of pipe. The set equations is derived from mass and momentum conservation laws. The system partial derivatives equations obtained is hyperbolique and suitable by the method of characteristics. This model is approved with the experimental results of Holmboe et al, and, Vardy et al. This digital code can be possible to join it in any tools, to simulateand to controle water hammer in pipe.
Transient flow characteristics through sudden expansion and contraction
International Journal of Innovative Research in Physics, 2020
The transient flow characteristics have significant applications in the engineering industry, especially in the domains of high energy fluid physics and compressible flow. The present research work provides an investigation of the laminar-to-turbulent transition fluid flow when air passes through successive contractions and expansions. The study has been performed through experimental runs in a fiberglass wind tunnel at different check points and then validated through simulation in the ANSYS workbench by keeping the input parameters constant. The simulation reveals the flow detachment due to turbulence and sudden increase in area. The research also plays a pivot roll to depicts that the velocity has been changing over the different sections of the flow conduit. The validation has resulted in an accuracy reach of almost 99% and has therefore, provided a lucid understanding of the velocity and pressure profiles of the flow through the conduit.
Investigation of non-Newtonian fluid effects during transient flows in a pipeline
Strojniški vestnik – Journal of Mechanical Engineering, 2015
A sudden change in the flow rate brings about significant pressure oscillations in the piping system, known as water hammer (fluid hammer). Unsteady flow of a non-Newtonian fluid due to instantaneous valve closure is studied. Power law and Cross models are used to simulate non-Newtonian effects. Firstly, the appropriate governing equations are derived and then, they are solved by a numerical approach. A fourth-order Runge-Kutta scheme is used for the time integration, and the central difference scheme is employed for the spatial derivatives discretization. To verify the proposed mathematical model and numerical solution, a comparison with corresponding experimental results from the literature are made. The results reveal a remarkable deviation in pressure history and velocity profile with respect to the water hammer in Newtonian fluids. The significance of the non-Newtonian fluid behaviour is manifested in terms of the drag reduction and line packing effect observed in the pressure history results. A detailed discussion regarding the fluid viscosity and its shear-stress diagrams are also included. Keywords: transient pipe flow, generalized Newtonian fluid, shear thinning fluids Highlights • Unsteady flow equations developed for non-Newtonian fluids. • The numerical method employed for non-Newtonian transient fluid flow equations. • Flow characteristics in a pipe section have been considered in detailed. • Significant changes observed in drag reduction and line packing effect.
Energy dissipation and pressure decay during transients in viscoelastic pipes with an in-line valve
Journal of Fluids and Structures, 2014
In this paper, the effect of a partially closed in-line valve, viscoelasticity, and unsteady friction on the transient behavior of a pressurized pipe is examined. Such an analysis is executed by considering global energy quantities evaluated by means of a onedimensional numerical model calibrated on the basis of a huge amount of laboratory tests. In the numerical experiments, the effect of the initial conditions and in-line valve characteristics has been analyzed by considering different values of the initial Reynolds number, N 0 , in-line valve head loss coefficient, χ, and location, δ. By introducing dimensionless quantities, exponential laws are shown to interpolate the time-history of maxima of both pressure and global energy quantities reliably with the related coefficients being a function of N 0 , χ, and δ. Thus, the links between the decay of pressure peaks at single sections and the dissipation of the global kinetic and internal energy are established. Moreover, it is shown that a given decay of pressure peaks may derive from very different transients. This result has crucial implications to inverse transient analysis based on the evaluation of the pressure decay at a given section with particular attention to the uniqueness of the solution.
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.
A polynomial expansion of axial velocity profiles to solve transient laminar flow in elastic pipe
Applied mathematical sciences, 2015
This study provides a theoretical and numerical modelling of shear stress due to the friction of transient laminar flow on pipe wall. This work is a simplified model of Prado et al. [1]. It is based on the expansion of the instantaneous velocity profiles of the flow in polynomial series in time and radial variable across the section of pipe. The set partial derivatives equations obtained from the conservation of mass and the theorem of momentum is then solved by the method of characteristics. The results obtained are in good agreement with those of Holmboe and Rouleau [2], in steady state Newtonian laminar flow. 448 H. Samri et al.
Effect of Length to Diameter Ratio on Transient Flow Characteristics
2020
Hydraulic transient analysis is vital in the design of water pipeline systems for the selection of appropriate pipe materials and pressure classes as it leads to large fluctuations in pressure, known as water hammer. The different parameters that influence the water hammer characteristics are closure time, length of pipe, the diameter of pipe and pipe wall thickness. A clear understanding of the situations leading to water hammer is required to avoid system malfunction or breakdown. This paper numerically analyses how the length to diameter ratio of pipe affects the water hammer effect. Numerical modelling and analysis are carried out in ANSYS FLUENT solving the Navier-Stokes Equations. This study simulates the flow in elastic and viscoelastic pipes with varying length to diameter ratio. Change in L/D ratio affects the water hammer pressure based on the 2L/c criteria for closure time. If the closure condition changes from sudden to gradual, the water hammer pressure reduces signific...
Friction relaxation model for fast transient flows application to water hammer in two-phase flow – The WAHA code
International Journal of Multiphase Flow, 2008
The paper deals with the problem of the wall shear stress during rapid transient 1D flows in a piping system caused by water hammers in two-phase flow induced by a fast valve closure. The evolution of the transient wall shear stress is interpreted in terms of two steps. The first step is a sudden and dramatic change of the wall shear stress due to the passage of the pressure wave. The second step is a relaxation process of the shear stress which is modeled from the Extended Irreversible Thermodynamics theory. The friction relaxation model (FRM) presented in the first part of this paper describes both steps of the evolution of the wall shear stress during water hammers. The second part of the paper deals with the application of the FRM model as a closure law in the WAHA code. The main purpose of the WAHA code is to predict various situations relative to single-and two-phase water hammer transients in piping systems. The last part of the paper deals with the simulation of several cases from the UMSICHT databank using the adapted WAHA computer code with the FRM model. The results of these simulations are systematically compared with the experimental data. It is concluded that the new FRM model has a clear effect on water hammer pressure wave damping and on the pressure wave propagation velocity.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.