A Comparison of Static and Rotordynamic Characteristics for Two Types of Liquid Annular Seals With Parallelly Grooved Stator/Rotor

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Leakage Flow ◽  
Frequency Range ◽  
Flow Rates ◽  
Pressure Drops ◽  
Force Coefficients ◽  
Operation Conditions ◽  
Annular Seal ◽  
Annular Seals

Abstract Liquid annular seals with parallelly grooved stator or rotor are used as replacements for smooth plain seals in centrifugal pumps to reduce leakage and break up contaminants within the working fluid. Parallelly grooved liquid annular seals have advantages of less leakage and smaller possibility of abrasion when the seal rotor–stator rubs in comparison to smooth plain seals. This paper deals with the static and rotordynamic characteristics of parallelly grooved liquid annular seals, which are limited in the literature. Numerical results of leakage flow rates, drag powers, and rotordynamic force coefficients were presented and compared for a grooved-stator/smooth-rotor (GS-SR) liquid annular seal and a smooth-stator/grooved-rotor (SS-GR) liquid annular seal, utilizing a modified transient computational fluid dynamics-based perturbation approach based on the multiple-frequency elliptical-orbit rotor whirling model. Both liquid annular seals have identical seal axial length, rotor diameter, sealing clearance, groove number, and geometry. The present transient computational fluid dynamics-based perturbation method was adequately validated based on the published experiment data of leakage flow rates and frequency-independent rotordynamic force coefficients for the GS-SR and SS-GR liquid annular seals at various pressure drops with differential inlet preswirl ratios. Simulations were performed at three pressure drops (4.14 bar, 6.21 bar, and 8.27 bar), three rotational speeds (2 krpm, 4 krpm, and 6 krpm) and three inlet preswirl ratios (0, 0.5, and 1.0), applying a wide rotor whirling frequency range up to 200 Hz, to analyze and compare the influences of operation conditions on the static and rotordynamic characteristics for both the GS-SR and SS-GR liquid annular seals. Results show that the present two liquid annular seals possess similar sealing capability, and the SS-GR seal produces a slightly larger (∼2–10%) drag power loss than the GS-SR seal. For small rotor whirling motion around a centered position, both seals have the identical direct force coefficients and the equal-magnitude opposite-sign cross-coupling force coefficients in the orthogonal directions x and y. For all operation conditions, both the GS-SR and SS-GR liquid annular seals possess negative direct stiffness K and positive direct damping C. The GS-SR seal produces purely positive Ceff throughout the whirling frequency range for all operation conditions, while Ceff for the SS-GR seal shows a significant decrease and transitions to negative value at the crossover frequency fco with increasing rotational speed and inlet preswirl. From a rotordynamic viewpoint, the GS-SR liquid annular seal is a better seal concept for pumps.

Numerical Comparison of Static and Rotordynamic Characteristics for a Grooved-Stator/Smooth-Rotor and a Smooth-Stator/Grooved-Rotor Liquid Annular Seals

2019 ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Working Fluid ◽  
Leakage Flow ◽  
Frequency Range ◽  
Flow Rates ◽  
Pressure Drops ◽  
Force Coefficients ◽  
Operation Conditions ◽  
Annular Seal ◽  
Positive Direct ◽  
Annular Seals

Abstract Liquid annular seals with parallelly-grooved stator or rotor are used as replacements for smooth plain seals in centrifugal pumps to reduce leakage and break up contaminants within the working fluid. Parallelly-grooved liquid annular seals have advantages of less leakage and smaller possibility of abrasion when the seal rotor-stator rubs in comparison to smooth plain seals. This paper deals with the static and rotordynamic characteristics of parallelly-grooved liquid annular seals, which are limited in the literature. Numerical results of leakage flow rates, drag powers and rotordynamic force coefficients were presented and compared for a grooved-stator/smooth-rotor (GS-SR) liquid annular seal and a smooth-stator/grooved-rotor (SS-GR) liquid annular seal, utilizing a modified transient CFD-based perturbation approach based on the multiple-frequency elliptical-orbit rotor whirling model. Both liquid annular seals have identical seal axial length, rotor diameter, sealing clearance, groove number and geometry. The present transient CFD-based perturbation method was adequately validated based on the published experiment data of leakage flow rates and frequency-independent rotordynamic force coefficients for the GS-SR and SS-GR liquid annular seals at various pressure drops with differential inlet preswirl ratios. Simulations were performed at three pressure drops (4.14 bar, 6.21 bar, 8.27 bar), three rotational speeds (2 krpm, 4 krpm, 6 krpm) and three inlet preswirl ratios (0, 0.5, 1.0), applying a wide rotor whirling frequency range up to 200 Hz, to analyze and compare the influences of operation conditions on the static and rotordynamic characteristics for both the GS-SR and SS-GR liquid annular seals. Results show that the present two liquid annular seals possess similar sealing capability, and the SS-GR seal produces a slightly larger (∼ 2–10%) drag power loss than the GS-SR seal. For small rotor whirling motion around a centered position, both seals have the identical direct force coefficients and the equal-magnitude opposite-sign cross-coupling force coefficients in the orthogonal directions x and y. For all operation conditions, both the GS-SR and SS-GR liquid annular seals possess negative direct stiffness K and positive direct damping C. The GS-SR seal produces purely positive Ceff throughout the whirling frequency range for all operation conditions, while Ceff for the SS-GR seal shows a significant decrease and transitions to negative value at the crossover frequency fco with increasing rotational speed and inlet preswirl. From a rotordynamic viewpoint, the GS-SR liquid annular seal is a better seal concept for pumps.

Numerical Modeling of Static and Rotordynamic Characteristics for Three Types of Helically-Grooved Liquid Annular Seals

2019 ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Perturbation Method ◽  
Leakage Flow ◽  
Centrifugal Pumps ◽  
Flow Rates ◽  
Force Coefficients ◽  
Numerical Predictions ◽  
Multi Stage ◽  
Annular Seal ◽  
Helical Grooves ◽  
Annular Seals

Abstract This paper deals with numerical predictions of the leakage flow rates, drag power and rotordynamic force coefficients for three types of helically-grooved liquid annular seals, which include a liquid annular seal with helically-grooved stator (GS/SR seal), one with helically-grooved rotor (SS/GR seal), and one with helical grooves on stator and rotor (GS/GR seal). These seals are frequently used for multiple-stage centrifugal pumps as they have the advantage of low leakage (even to zero) due to the “pumping effect” of the helical grooves. However, the static and rotordynamic characteristics of helically-grooved liquid annular seals still are not fully understood, and even more pronounced is the lack of effective numerical models in the literature. A novel transient CFD-based perturbation method was proposed for the predictions of the leakage flow rates, drag power and rotordynamic force coefficients of helically-grooved liquid annular seals. This method is based on the unsteady Reynolds-Averaged Navier–Stokes (RANS) solution with the mesh deformation technique and the multiple reference frame theory. The time-varying fluid-induced forces acting on the rotor/stator surface were obtained as a response to the time-dependent perturbation of the seal stator surface with the periodic motion, based on the multiple-frequency elliptical-orbit stator whirling model. The frequency-independent rotordynamic force coefficients were determined using curve fit and Fast Fourier Transform (FFT) in the frequency domain. The CFD-based method was adequately validated by comparisons to the published experiment data of leakage flow rates and fluid response forces for three types of helically-grooved liquid annular seals. Based on the transient CFD-based perturbation method, numerical results of the leakage flow rates, drag powers and rotordynamic force coefficients were presented and compared for three types of helically-grooved liquid annular seals at five rotational speeds (n = 0.5 krpm, 1.0 krpm, 2.0 krpm, 3.0 krpm and 4.0 krpm), paying special attention to the effective stiffness coefficient and effective damping coefficient. Results show that the GS/GR seal has the best sealing capability, followed by the GS/SR seal and then the SS/GR seal. The leakage flow rate of all three helically-grooved seals monotonically decreases with the increasing rotational speed. The GS/SR seal possesses the best stiffness and damping capability, followed by the SS/GR seal and then the GS/GR seal. Rotordynamic instability problems are more likely caused by the GS/GR seal in multi-stage centrifugal pumps. From a rotordynamic viewpoint, the GS/SR helically-grooved liquid annular seal is a better seal concept for multi-stage centrifugal pumps.

Numerical Investigation on the Leakage and Rotordynamic Characteristics for Three Types of Annular Gas Seals in Wet Gas Conditions

2018 ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li
Keyword(s):  
Liquid Phase ◽  
Gas Phase ◽  
Labyrinth Seal ◽  
Leakage Flow ◽  
Flow Rates ◽  
Force Coefficients ◽  
Wet Gas ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Gas Seals

The modern compressor operation is challenged by the liquid presence in wet gas operating conditions. The liquid phase may affect the compressor stability by partially flooding the internal annular gas seals and inducing subsynchronous vibration. To improve the annular seal behavior and increase rotor stability, high-precision results of leakage flow rates and rotordynamic force coefficients are needed for annular gas seals in wet gas conditions. In order to better understand the leakage and rotordynamic characteristics of the annular gas seal in wet gas conditions, a 3D transient CFD-based perturbation method was proposed for computations of leakage flow rates and rotordynamic force coefficients of annular gas seals with liquid phase in main gas phase, based on inhomogeneous Eulerian-Eulerian multiphase flow model, mesh deformation technique and the multi-frequency rotor whirling orbit model. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for three types of non-contact annular gas seals, which include a smooth plain annular seal (SPAS), a labyrinth seal (LABY) and a fully-partitioned pocket damper seal (FPDS). These three seals were designed to have the identical rotor diameter, sealing clearance and axial length. The accuracy and availability of the present transient CFD numerical method were demonstrated with the experiment data of leakage flow rates and frequency-dependent rotordynamic force coefficients of the smooth plain seal with four inlet liquid volume fractions (LVF) of 0%, 2%, 5% and 8%. Steady and transient numerical simulations were conducted at inlet air pressure of 62.1 bar, pressure ratio of 0.5, rotational speed of 15 000 rpm and inlet preswirl ratio of 0.3 for four inlet LVFs varying from 0% to 8% and fourteen subsynchronous and synchronous whirling frequencies up to 280 Hz. The numerical results show that inlet liquid phase has a significant influence on the leakage and rotordynamic coefficients for all three types of annular gas seals. The mixture leakage flow rate increases with the increasing inlet LVF, combining the decreasing gas-phase and linearly increasing liquid-phase leakage flow rates. The smooth plain seal leaks the most gas phase and liquid phase, followed by the pocket damper seal and then the labyrinth seal. Increasing inlet LVF significantly decreases the direct stiffness and slightly increases the effective damping of the smooth plain seal. The labyrinth seal possesses evident negative direct stiffness and shows a noticeable decreasing effective damping with the increasing inlet LVF at the subsynchronous frequency range. Increasing inlet LVF obviously increases all the force coefficients of the pocket damper seal including the positive effective damping. From a rotordynamic viewpoint, the FPDS possesses a better liquid tolerant capability and so is a better sealing scheme for the balance piston seals and center seals of the centrifugal compressor in wet gas operating condition.

A Computational Fluid Dynamics Modified Bulk Flow Analysis for Circumferentially Shallow Grooved Liquid Seals

2017 ◽  
Author(s):  
Luis San Andrés ◽  
Tingcheng Wu ◽  
Hideaki Maeda ◽  
Ono Tomoki
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Friction Factor ◽  
Flow Model ◽  
Flow Analysis ◽  
Bulk Flow ◽  
Rotor Speed ◽  
Force Coefficients ◽  
Annular Seal ◽  
Direct Stiffness

In straight-through centrifugal pumps, a grooved seal acts as a balance piston to equilibrate the full pressure rise across the pump. As the groove pattern breaks the development of fluid swirl, this seal type offers lesser leakage and lower cross-coupled stiffnesses than a similar size and clearance annular seal. Bulk-flow models predict expediently the static and dynamic force characteristics of annular seals; however they lack accuracy for grooved seals. Computational fluid dynamics (CFD) methods give more accurate results, but are not computationally efficient. This paper presents a modified bulk-flow model to predict the rotordynamic force coefficients of shallow depth circumferentially grooved liquid seals with an accuracy comparable to a CFD solution but with a simulation time of bulk-flow analyses. The procedure utilizes the results of CFD to evaluate the bulk flow velocity field and the friction factors for a 73 grooves annular seal (depth/clearance dg/ Cr = 0.98 and length/diameter L/D = 0.9) operating under various sets of axial pressure drop and rotor speed. In a groove, the flow divides into a jet through the film land and a strong recirculation zone. The penetration angle (α), specifying the streamline separation in the groove cavity, is a function of the operating conditions; an increase in rotor speed or a lower pressure difference increases α. This angle plays a prominent role to evaluate the stator friction factor and has a marked influence on the seal direct stiffness. In the bulk-flow code the friction factor model (f = nRem) is modified with the CFD extracted penetration angle (α) to account for the flow separation in the groove cavity. The flow rate predicted by the modified bulk-flow code shows good agreement with a measured result (6% difference). A perturbation of the flow field is performed on the bulk-flow equations to evaluate the reaction forces on the rotor surface. Compared to the rotordynamic force coefficients derived from the CFD results, the modified bulk-flow code predicts rotordynamic force coefficients within 10%, except that the cross-coupled damping coefficient is over-predicted up to 14%. An example test seal with a few grooves (L/D = 0.5, dg/Cr = 2.5) serves to further validate the predictions of the modified bulk-flow model. Compared to the original bulk-flow analysis, the current method shows a significant improvement in the predicted rotordynamic force coefficients, the direct stiffness and damping coefficients in particular.

Numerical Investigation on the Leakage and Rotordynamic Characteristics for Three Types of Annular Gas Seals in Wet Gas Conditions

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li
Keyword(s):  
Liquid Phase ◽  
Gas Phase ◽  
Labyrinth Seal ◽  
Leakage Flow ◽  
Flow Rates ◽  
Force Coefficients ◽  
Wet Gas ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Gas Seals

The modern compressor operation is challenged by the liquid presence in wet gas operating conditions. The liquid phase may affect the compressor stability by partially flooding the internal annular gas seals and inducing subsynchronous vibration (SSV). To improve the annular seal behavior and increase the rotor stability, high-precision results of leakage flow rates and rotordynamic force coefficients are needed for annular gas seals in wet gas conditions. In order to better understand the leakage and rotordynamic characteristics of the annular gas seal in wet gas conditions, a 3D transient CFD-based perturbation method was proposed for computations of leakage flow rates and rotordynamic force coefficients of annular gas seals with liquid phase in main gas phase, based on inhomogeneous Eulerian-Eulerian multiphase flow model, mesh deformation technique, and the multifrequency rotor whirling orbit model. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for three types of noncontact annular gas seals, which include a smooth plain annular seal (SPAS), a labyrinth (LABY) seal, and a fully partitioned pocket damper seal (FPDS). These three seals were designed to have the identical rotor diameter, sealing clearance, and axial length. The accuracy and the availability of the present transient CFD numerical method were demonstrated with the experiment data of leakage flow rates and frequency-dependent rotordynamic force coefficients of the smooth plain seal with four inlet liquid volume fractions (LVFs) of 0%, 2%, 5%, and 8%. Steady and transient numerical simulations were conducted at inlet air pressure of 62.1 bar, pressure ratio of 0.5, rotational speed of 15,000 rpm, and inlet preswirl ratio of 0.3 for four inlet LVFs varying from 0% to 8% and 14 subsynchronous and synchronous whirling frequencies up to 280 Hz. The numerical results show that the inlet liquid phase has a significant influence on the leakage and rotordynamic coefficients for all three types of annular gas seals. The mixture leakage flow rate increases with the increasing inlet LVF, combining the decreasing gas-phase and linearly increasing liquid-phase leakage flow rates. The smooth plain seal leaks the most gas phase and liquid phase, followed by the pocket damper seal (PDS) and then the labyrinth seal. Increasing inlet LVF significantly decreases the direct stiffness and slightly increases the effective damping of the smooth plain seal. The labyrinth seal possesses evident negative direct stiffness and shows a noticeable decreasing effective damping with the increasing inlet LVF at the subsynchronous frequency range. Increasing inlet LVF obviously increases all the force coefficients of the pocket damper seal including the positive effective damping. From a rotordynamic viewpoint, the FPDS possesses a better liquid tolerant capability and so is a better sealing scheme for the balance piston seals and center seals of the centrifugal compressor in wet gas operating condition.

A Computational Fluid Dynamics Modified Bulk Flow Analysis for Circumferentially Shallow Grooved Liquid Seals

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Luis San Andrés ◽  
Tingcheng Wu ◽  
Hideaki Maeda ◽  
Ono Tomoki
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Friction Factor ◽  
Flow Analysis ◽  
Operating Conditions ◽  
Bulk Flow ◽  
Rotor Speed ◽  
Force Coefficients ◽  
Annular Seal ◽  
Direct Stiffness

In straight-through centrifugal pumps, a grooved seal acts as a balance piston to equilibrate the full pressure rise across the pump. As the groove pattern breaks the development of fluid swirl, this seal type offers lesser leakage and lower cross-coupled stiffnesses than a similar size and clearance annular seal. Bulk-flow models (BFMs) predict expediently the static and dynamic force characteristics of annular seals; however they lack accuracy for grooved seals. Computational fluid dynamics (CFD) methods give more accurate results, but are not computationally efficient. This paper presents a modified BFM to predict the rotordynamic force coefficients of shallow depth, circumferentially grooved liquid seals with an accuracy comparable to a CFD solution but with a simulation time of bulk-flow analyses. The procedure utilizes the results of CFD to evaluate the bulk flow velocity field and the friction factors for a 73 grooves annular seal (depth/clearance dg/Cr = 0.98 and length/diameter L/D = 0.9) operating under various sets of axial pressure drop and rotor speed. In a groove, the flow divides into a jet through the film land and a strong recirculation zone. The penetration angle (α), specifying the streamline separation in the groove cavity, is a function of the operating conditions; an increase in rotor speed or a lower pressure difference increases α. This angle plays a prominent role to evaluate the stator friction factor and has a marked influence on the seal direct stiffness. In the bulk-flow code, the friction factor model (f = nRem) is modified with the CFD extracted penetration angle (α) to account for the flow separation in the groove cavity. The flow rate predicted by the modified bulk-flow code shows good agreement with the measured result (6% difference). A perturbation of the flow field is performed on the bulk-flow equations to evaluate the reaction forces on the rotor surface. Compared to the rotordynamic force coefficients derived from the CFD results, the modified bulk-flow code predicts rotordynamic force coefficients within 10%, except that the cross-coupled damping coefficient is over-predicted up to 14%. An example test seal with a few grooves (L/D = 0.5, dg/Cr = 2.5) serves to further validate the predictions of the modified BFM. Compared to the original bulk-flow analysis, the current method shows a significant improvement in the predicted rotordynamic force coefficients, the direct stiffness and damping coefficients, in particular.

Prediction of Rotordynamic Performance of Smooth Stator-Grooved Rotor Liquid Annular Seals Utilizing Computational Fluid Dynamics

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Farzam Mortazavi ◽  
Alan Palazzolo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Excitation Frequency ◽  
Computationally Efficient ◽  
Operational Conditions ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Liquid Seal ◽  
Frequency Ratios ◽  
Annular Seals

Circumferentially grooved, annular liquid seals typically exhibit good whirl frequency ratios (WFRs) and leakage reduction, yet their low effective damping can lead to instability. The current study investigates the rotordynamic behavior of a 15-step groove-on-rotor annular liquid seal by means of computational fluid dynamics (CFD), in contrast to the previous studies which focused on a groove-on-stator geometry. The seal dimensions and working conditions have been selected based on experiments of Moreland and Childs (2016, “Influence of Pre-Swirl and Eccentricity in Smooth Stator/Grooved Rotor Liquid Annular Seals, Measured Static and Rotordynamic Characteristics,” M.Sc. thesis, Texas A&M University, College Station, TX). The frequency ratios as high as four have been studied. Implementation of pressure-pressure inlet and outlet conditions make the need for loss coefficients at the entrance and exit of the seal redundant. A computationally efficient quasi-steady approach is used to obtain impedance curves as functions of the excitation frequency. The effectiveness of steady-state CFD approach is validated by comparison with the experimental results of Moreland and Childs. Results show good agreement in terms of leakage, preswirl ratio (PSR), and rotordynamic coefficients. It was found that PSR will be about 0.3–0.4 at the entrance of the seal in the case of radial injection, and outlet swirl ratio (OSR) always converges to values near 0.5 for current seal and operational conditions. The negative value of direct stiffness coefficients, large cross-coupled stiffness coefficients, and small direct damping coefficients explains the destabilizing nature of these seals. Finally, the influence of surface roughness on leakage, PSR, OSR, and stiffness coefficients is discussed.

scholarly journals Theoretical Analysis of Brush Seals Leakage Using Local Computational Fluid Dynamics Estimated Permeability Laws

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Lilas Deville ◽  
Mihai Arghir
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Reynolds Number ◽  
Principal Direction ◽  
Experimental Results ◽  
Leakage Flow ◽  
Cfd Analysis ◽  
Brush Seal ◽  
Brush Seals ◽  
Local Reynolds Number

Brush seals are a mature technology that has generated extensive experimental and theoretical work. Theoretical models range from simple correlations with experimental results to advanced numerical approaches coupling the bristles deformation with the flow in the brush. The present work follows this latter path. The bristles of the brush are deformed by the pressure applied by the flow, by the interference with the rotor and with the back plate. The bristles are modeled as linear beams but a nonlinear numerical algorithm deals with the interferences. The brush with its deformed bristles is then considered as an anisotropic porous medium for the leakage flow. Taking into account, the variation of the permeability with the local geometric and flow conditions represents the originality of the present work. The permeability following the principal directions of the bristles is estimated from computational fluid dynamics (CFD) calculations. A representative number of bristles are selected for each principal direction and the CFD analysis domain is delimited by periodicity and symmetry boundary conditions. The parameters of the CFD analysis are the local Reynolds number and the local porosity estimated from the distance between the bristles. The variations of the permeability are thus deduced for each principal direction and for Reynolds numbers and porosities characteristic for brush seal. The leakage flow rates predicted by the present approach are compared with experimental results from the literature. The results depict also the variations of the pressures, of the local Reynolds number, of the permeability, and of the porosity through the entire brush seal.

scholarly journals Effect of hydraulic and geometric factors upon leakage flow rate in pressurized pipes

RBRH ◽  
2021 ◽  
Vol 26 ◽  
Author(s):  
Mayara Francisca da Silva ◽  
Fábio Veríssimo Gonçalves ◽  
Johannes Gérson Janzen
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Flow Rate ◽  
Leakage Flow ◽  
Cfd Simulations ◽  
Mean Velocity ◽  
Leakage Flow Rate ◽  
Geometric Factors ◽  
Leakage Area ◽  
Computational Fluid Dynamics Cfd

ABSTRACT Computational Fluid Dynamics (CFD) simulations of a leakage in a pressurized pipe were undertaken to determine the empirical effects of hydraulic and geometric factors on the leakage flow rate. The results showed that pressure, leakage area and leakage form, influenced the leakage flow rate significantly, while pipe thickness and mean velocity did not influence the leakage flow rate. With relation to the interactions, the effect of pressure upon leakage flow rate depends on leakage area, being stronger for great leakage areas; the effects of leakage area and pressure on leakage flow rate is more pronounced for longitudinal leakages than for circular leakages. Finally, our results suggest that the equations that predict leakage flow rate in pressurized pipes may need a revision.

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