Constricted Flow Research Articles

Bifurcate migration of neutrally buoyant particles in unilateral slippery channel flows

As an important technique for manipulating particles in fluid–solid channel flows, inertial focusing encourages the design of the channel geometry to enhance particle radial aggregation. Traditional methods typically use exquisite sheathes or elbows to create constricted flows, which ultimately increase flow resistance and lower fluid–solid separation efficiency. This paper presents a slippery wall modification technique that, by regulating the channel flows, is expected to induce nontrivial particle lateral migrations. More specifically, interface-resolved simulations are performed using the lattice Boltzmann method. A slip boundary condition is applied to the redesigned hydrophobic bottom wall. It is observed that the typical bifurcate migration, i.e., particles moving divergently toward the upper and lower equilibrium positions around a crucial location (CL), does not occur along the channel centerline. The CL is always below the centerline, and it decreases consistently with an increase in Kn or Re. By increasing Re, particles are prone to approach the channel centerline. With larger Kn, particles in the higher equilibrium position are affected in the same way, but their lower counterparts are drawn to the bottom wall.

Navigating Financial Constraints: Understanding Causes, Effects, and Strategic Solutions across Individual, Corporate and Governmental Sectors

Limitations in financial resources were a widespread obstacle in the interdependent global economy, impacting people, firms, and governments. These limitations were evident in the limited availability of financial resources, high levels of debt, and constricted cash flow, often resulting from an intricate interaction of internal and external elements. This paper offered an extensive investigation of the causes, consequences, and strategic remedies for financial limitations in these three areas. On an individual level, financial constraints were often caused by stagnating salaries, excessive living expenses, and insufficient financial knowledge, resulting in heightened susceptibility to financial shocks. Corporations, especially small and medium-sized firms (SMEs), have financial limitations caused by restricted capital access, increased operating expenses, and market instability, which may impede development and prevent innovation. As a result of fiscal mismanagement, increasing public debt, and economic recessions, governments, particularly in emerging countries, have financial limitations that might hinder their capacity to fund vital services and infrastructure. Financial limitations had extensive consequences, affecting economic stability, growth, and general living standards. Individuals with financial constraints encountered a decline in their quality of life and heightened levels of stress, while firms may endure declining profitability and competitiveness. Governments may be compelled to enforce austerity policies, resulting in enduring socio-economic repercussions. To tackle these difficulties, it was crucial to use customised approaches such as enhancing financial literacy, optimising corporate financial management, and advancing fiscal consolidation and structural changes at the governmental level. The objective of this research was to provide practical insights for improving financial resilience and fostering sustainable economic growth by adopting a comprehensive strategy that took into account the interdependence of financial limitations across different sectors. Keywords: Financial constraints, Global economy, Financial resources, Debt levels, Cash flow.

Viscoelastic flow instabilities for enhanced heat transfer in battery pack cooling

Effective thermal management plays a critical role in ensuring peak performance for heavy-duty electric vehicle battery packs and high-performance electronics. To address the need for effective heat dissipation, liquid coolants are employed, which exhibit higher heat transfer performance compared to traditional air-cooled systems. However, the associated increased viscosity of such liquid coolants and constricted flow path lead to reduced mixing, thereby deteriorating the thermal performance of the system. Here, we explore the potential of utilizing viscoelastic liquid coolants for enhancing heat transfer from the heated walls of a constricted flow path with obstacles, modeling features of battery coolant channels. At low-Reynolds number regime, viscoelastic fluids exhibit instabilities which can disrupt the thermal boundary layer and enhance fluid mixing in the domain, thereby facilitating wall heat transfer. We employed computational fluid dynamics simulations, validated with experimental observations, to explore the effect of the flow geometry, Weissenberg number, solvent viscosity ratio, polymer extensibility, and Reynolds number on thermal performance. Our study indicates that the heat transfer is enhanced with flow instabilities in viscoelastic fluids, which can be generated exclusively in the flow channel with obstacles by increasing the Weissenberg number, reducing the solvent viscosity ratio, increasing the polymer extensibility, and increasing the Reynolds number. The enhancement in the heat transfer can exclusively be attributed to the elastic properties of the fluid in contrast to the inelastic shear-thinning fluids exhibiting no instability. The insights from the study can play an important role in the development of advanced, high-efficiency battery cooling systems, combining surface engineering and synthesis of optimized heat transfer liquids.

Interplay of roughness and wettability in microchannel fluid flows—Elucidating hydrodynamic details assisted by deep learning

Under microconfinement, the complex interaction between surface roughness and fluid slippage yields unexpected variations in friction factor and drag reduction. These variations arise from the combined effects of roughness and hydrophobic interactions of the surface with the hydrodynamic field. Our study investigates alterations in frictional characteristics within long microchannels, considering fluid slippage, hydraulic diameter, and roughness. This exploration holds promise for precise drag reduction control applications for lab-on-a-chip and small-scale devices. To address computational limitations in analyzing diverse hydrodynamic conditions, we employ an artificial neural network prediction model, validated with experimental and numerical results. Contrary to the macroscopic conclusions obtained from the Moody chart, our findings indicate that fluid slippage, apart from surface roughness, significantly influences the friction factor. The interdependencies of friction factor on the flow and fluid parameters are thoroughly studied toward the proposition of a new slip-modified constricted flow friction factor formula, predicting friction in microchannels with combined roughness and hydrophobicity effects. This combined numerical and machine-learning approach presents a noteworthy counterpart to the moody chart at microscales offering the potential for a unified continuum-based description to include interfacial effects.

Experimental investigation and application of soft computing models for predicting flow energy loss in arc-shaped constrictions

Abstract This investigation focuses on flow energy, a crucial parameter in the design of water structures such as channels. The research endeavors to explore the relative energy loss (ΔEAB/EA) in a constricted flow path of varying widths, employing Support Vector Machine (SVM), Artificial Neural Network (ANN), Gene Expression Programming (GEP), Multiple Adaptive Regression Splines (MARS), M5 and Random Forest (RF) models. Experiments span a Froude number range from 2.85 to 8.85. The experimental findings indicate that the ΔEAB/EA exceeds that observed in a classical hydraulic jump with constriction section. Within the SVM model, the linear kernel emerges as the best predictor of ΔEAB/EA, outperforming polynomial, radial basis function (RBF), and sigmoid kernels. In addition, in the ANN model, the MLP network was more accurate compared to the RBF network. The results indicate that the relationship proposed by the MARS model can play a significant role resulting in high accuracy compared to the non-linear regression relationship in predicting the target parameter. Upon comprehensive evaluation, the ANN method emerges as the most promising among the candidates, yielding superior performance compared to the other models. The testing phase results for the ANN-MLP are noteworthy, with R = 0.997, average RE% = 0.63%, RMSE = 0.0069, BIAS = −0.0004, DR = 0.999, SI = 0.0098 and KGE = 0.995.

Widespread wood placement and regrading drive lateral connectivity and reworking of the channel and floodplain in a valley bottom reset to Stage 0

Valley bottom process reset, or the excavation of high surfaces and fill of incised channels combined with large wood addition, is a new method for creating multi-channel river-wetland corridors (also referred to as Stage 0 valley bottoms). Valley bottom process reset seeks to increase lateral flow and sediment connectivity, retain water and sediment, and kickstart geomorphic processes that may sustain aquatic and riparian habitat. This study uses this anthropogenic intervention to examine relationships among wood-induced hydraulic roughness, valley bottom topography, and geomorphic processes such as overbank flow and sediment transport, avulsion, sediment retention, and pool scour. Here, I present a 6-year case study of a two-phase valley bottom process reset along Deer Creek, Oregon. Kickstarting the floodplain reshaping processes required a substantial increase in roughness and hydrologic connectivity. The first phase of construction enhanced hydrologic but not sediment connectivity, failing to kickstart avulsion and floodplain reworking even during a likely 2- to 5-year recurrence interval flood. A second, more intensive phase of construction substantially reduced the threshold discharge necessary for overbank flow and floodplain reworking, as evidenced by the occurrence of these processes after only a <2-year recurrence interval flood. During this flood, a spatially distributed wood lattice rearranged into discrete jams that scoured pools, retained sediment, and drove geomorphically effective overbank flows. While valley bottom regrading likely contributed to these geomorphic effects, the spatial correlation between newly incised floodplain channels and areas of wood aggregation indicates wood's important role in driving floodplain reworking. I derive from these findings a conceptual model that details how wood drove floodplain reworking via two mechanisms: In-channel wood jams backwatered and constricted flow into the floodplain, and small wood jams formed in the floodplain forest further constricted flow through nascent channels to facilitate channel incision.

Flow Structure and Transition to Local Turbulence Downstream of an Asymmetric Narrowing that Imitates Arterial Stenosis

The results of experimental studies and numerical simulation of the flow structure in the separation region downstream of an asymmetric narrowing of smooth canal that simulates 70% one-sided stenosis of the artery are presented. The Reynolds number was equal to 1800. The instantaneous flow velocity vector fields were measured using the SIV technique. The numerical solution was obtained by the large eddy simulation (LES) method. Setting the disturbances in numerical simulation close to the experimental conditions made it possible to obtain a satisfactory agreement between the calculated and experimental velocity fields and the components of the Reynolds stress tensor. The data on formation of the local flow turbulence region behind the constriction and subsequent downstream flow relaminarization are obtained. It is shown that a pair of secondary eddies localized within the region of flow separation is formed near the throat of the constriction.

Flow Structure and Transition to Local Turbulence Downstream of an Asymmetric Narrowing that Imitates Arterial Stenosis

The results of experimental studies and numerical simulation of the flow structure in the separation region downstream of an asymmetric narrowing of smooth canal that simulates 70% onesided stenosis of the artery are presented. The Reynolds number was equal to 1800. The instantaneous flow velocity vector fields were measured using the SIV technique. The numerical solution was obtained by the large eddy simulation (LES) method. Setting the disturbances in numerical simulation close to the experimental conditions made it possible to obtain a satisfactory agreement between the calculated and experimental velocity fields and the components of the Reynolds stress tensor. The data on formation of the local flow turbulence region behind the constriction and subsequent downstream flow relaminarization are obtained. It is shown that a pair of secondary eddies localized within the region of flow separation is formed near the throat of the constriction.

Computational fluid dynamics model of laryngotracheal stenosis and correlation to pulmonary function measures

3D models of airway lumens were created from CT scans of 19 patients with laryngotracheal stenosis. Computational fluid dynamics (CFD) simulations were completed for each, and results were compared to measured peak inspiratory flow rate, grade of lumen constriction, and measures of airway geometry. Results demonstrate flow resistance and shear stress correlate with degree of lumen constriction and absolute cross-sectional area as well as flow rate. Flow recirculation depends on airway constriction but does not vary with flow rate. Resistance and wall shear stress did not correlate well with functional measures. Flow recirculation did differ between subjects with higher functional measures and subjects with lower functional measures. This analysis provides mathematical models to predict airway resistance, wall shear stress, and flow reversal according lumen constriction and inspiratory flow rate. It suggests aerodynamic factors such as flow recirculation play a role in differences in functional performance between patients with similar airway measures.

Locating block caused by stuck PIGs in multi product pipeline using combination of radioisotope techniques

Blockages in pipelines inhibit the normal use of the pipeline due to constricted flow of fluid through the pipeline. Locating blockages in pipelines is a challenge and there is an increasing demand for sensitive inspection methods to locate blockages in pipelines, caused either due to presence of foreign undesired material during commissioning or maintenance of the pipeline or due to accumulation of product remanent during the prolonged use of the pipelines. A block was caused in a multiproduct pipeline due to a stuck pig (pipe inspection gauge). Radiotracer techniques viz. gamma scanning and radiography were employed to pinpoint the block location.

Diffusion tensor imaging of anisotropic inhomogeneous turbulent flow.

Inhomogeneous anisotropic turbulent flow is difficult to measure, and yet it commonly occurs in nature and in many engineering applications. This work aims to introduce a technique based on magnetic resonance imaging which can spatially map the degree of turbulence as well as the degree of anisotropy. Our interpretation relies on the eddy diffusion model of turbulence, and combines this with the technique of diffusion tensor imaging. The result is an eddy diffusion tensor, which is represented by a symmetric three-by-three matrix. This tensor contains a wealth of information about the magnitude and directions of the turbulent fluctuations; however, the correlation time must be considered before interpreting this information. In the constricted pipe flow used in this study, the turbulence is greatest in magnitude in the space surrounding the core of the turbulent jet, and the turbulence is highly anisotropic.

Heat Transfer and Pressure Drop in Single-Phase Flows in Tapered Microchannels

Abstract This paper presents a comparison of heat transfer and pressure drop during single-phase flows inside diverging, converging, and uniform microgaps using distilled water as the working fluid. The microgaps were created with a plain 10 mm × 10 mm heated copper surface and a polysulfone cover that was either uniform or tapered with an angle of 3.4 deg, and average gap heights of 400 and 800 μm. Experiments were conducted with single-phase water flow with an inlet temperature of 30 °C for flow rates varying from 57 to 498 mL/min and heat flux from 27 to 153 W/cm2 depending on the flowrate and microgap configuration. The uniform configuration resulted in the lowest pressure drop due to the less constricted flow. A slight decrease of pressure drop with heat flux was observed due to temperature dependent properties. The best heat transfer performance was obtained with the converging configuration, which was especially significant at low flow rates and shorter average gap. This behavior could be explained by an increase in the heat transfer coefficient due to flow acceleration in the converging gaps, which compensates for the decrease in temperature difference between the fluid and the surface along the flow length. Overall, the converging microgaps have better performance than uniform or diverging ones for single-phase flows, and this effect is more pronounced at lower flow rates, where the fluid experiences higher temperature changes.

A case study on dynamic capabilities developed by a product start-up to grow at the time of pandemic

ABSTRACT Business operations became challenging when the COVID-19 pandemic struck, and governments applied significant lockdown measures to stop the spread. Start-ups and small-medium businesses started facing hardships due to the changes in the business environment and the resulting constricted cash flow. This case describes challenges faced by a high-tech product start-up company and the way they tackled these hardships. The company had adopted an agile programming methodology for product development which faced a major challenge because of the sudden introduction of “work from remote” (WFR). WFR had disrupted collaboration between clients, sales teams, and development teams. The success of agile methodology was dissipating as teams could not do on-premise huddles. The company witnessed an overrun in the sprint schedule, increase of budgeted cost, and sliding customer satisfaction. Senior management could not manage process parameters properly, and therefore predictability of the processes waned. The start-up owners, through the application of the “dynamic capabilities framework,” focused on reconfiguring the agile working processes and improving the remote working capability of employees. This case shows the start-up’s agile development process transformation journey following the dynamic capabilities framework to overcome the challenges posed by the pandemic. The teaching case focuses on imparting knowledge on agile development and dynamic capabilities to Information Systems students.

Weak clogging in constricted channel flow.

We investigate simple models of a monodisperse system of soft, frictionless disks flowing through a two-dimensional microchannel in the presence of a single or a double constriction using Brownian dynamics simulation. After a transient time, a stationary state is observed with an increase in particle density before the constriction and a depletion after it. For a constriction width to particle diameter ratio of less than 3, the mean particle velocity is reduced compared to the unimpeded flow and it falls to zero for ratios of less than 1. At low temperatures, the particle mean velocity may vary nonmonotonically with the constriction width. The associated intermittent behavior is due to the formation of small arches of particles with a finite lifetime. The distribution of the interparticle exit times rises rapidly at short times followed by an exponential decay with a large characteristic time, while the cascade size distribution displays prominent peaks for specific cluster sizes. Although the dependence of the mean velocity on the separation of two constrictions is not simple, the mean flow velocity of a system with a single constriction provides an upper envelope for the system with two constrictions. We also examine the orientation of the leading pair of particles in front of the constriction(s). With a single constriction in the intermittent regime, there is a strong preference for the leading pair to be orientated perpendicular to the flow. When two constrictions are present, orientations parallel to the flow are much more likely at the second constriction.

Abstract 12848: Patient-Specific in silico Models Demonstrate Hemodynamic Effect of LAMPOON in Transcatheter Mitral Valve Replacement

Introduction: The purpose of this study was to investigate the hemodynamic impact of LAMPOON (Laceration of the Anterior Mitral leaflet to Prevent Outflow ObstructioN) in transcatheter mitral valve replacement (TMVR) using patient-specific in silico modeling. Methods: Eight subjects from the LAMPOON investigational device exemption trial were included. All subjects were at prohibitive risk of outflow tract obstruction from TMVR based on computed tomography (CT), and underwent successful LAMPOON immediately followed by TMVR. A validated computational fluid dynamics (CFD) model was used to compare simulated hemodynamics and 3D flow patterns between two modeled conditions: 1) TMVR with LAMPOON and 2) TMVR without LAMPOON. Using the post-procedure CT scans, anatomical models of TMVR with LAMPOON were created for each subject. The open transcatheter valve cells were then virtually closed to model TMVR without LAMPOON for each subject. Finally, CFD was performed for each condition to simulate the systolic flow fields. Results: As compared to TMVR without LAMPOON, TMVR with LAMPOON resulted in lower peak velocity, lower peak LVOT gradient, and higher peak LVOT effective orifice area by 13 ± 6% (p=0.004), 28 ± 14% (p=0.008), and 15 ± 8% (p=0.002), respectively. LAMPOON provided flow communication through exposed cells of the transcatheter valve, thereby decreasing the flow constriction and reducing flow stasis in the vicinity of the neo-LVOT (Figure). The hemodynamic benefit of LAMPOON was observed to be greater in subjects with a smaller neo-LVOT area measured post-implant (p&lt;0.001). Conclusions: In silico modeling allowed for a quantitative patient-specific comparison of TMVR with and without LAMPOON, which is impossible to study clinically. The LAMPOON procedure improved simulated hemodynamics in all subjects, with a greater hemodynamic impact observed in subjects with a smaller post-implant neo-LVOT area.

Abstract 11209: KER-012, a Novel Modified ActrII Ligand Trap, Attenuated Cardiac Pathology in a Pulmonary Arterial Banding Model of Right Ventricle Overload

Pulmonary arterial hypertension (PAH) is a debilitating disorder, characterized by right ventricle (RV) pressure overload, cardiac hypertrophy, and progressive RV dysfunction. PAH is associated with unbalanced TGFß signaling, favoring signaling of SMAD2/3 and opposing SMAD1/5/9. The result is an increase in vascular proliferation and disruption of vascular homeostasis. KER-012 is a modified ActRII ligand trap designed to inhibit ligands that signal through SMAD2/3 to promote restoration of vascular homeostasis. To investigate the cardio-protective effects of RKER-012, a research version of KER-012, we evaluated the effect of treatment in a pulmonary arterial banding (PAB) model. In this study, 8-week-old, male C57BL/6 mice underwent sham or PAB surgery to increase RV pressure and induce cardiac remodeling. The sham cohort received vehicle (VEH) treatment and PAB mice received either vehicle (VEH) or 10 mg/kg RKER-012 twice weekly for 3 weeks. Relative to sham mice, all PAB mice had elevated pulmonary arterial pressures on day 1 (all ps&lt;0.0001) that persisted until day 21 (all ps&lt;0.01), indicating that the PAB procedure was effective. VEH PAB mice also exhibited diminished cardiac function, including increased end systolic pressure volume relationship (ESPVR; +79.3%; p&lt;0.001) and increased myocardial performance index (MPI; +45.6%; p&lt;0.0001) compared to Sham VEH. Additionally, VEH PAB mice had markers of cardiac remodeling, including increased Fulton Indices (+54.8%; p&lt;0.0001), increased RV free wall thickness (RVFWT; +95.8%; p&lt;0.0001) and increased cardiac fibrotic tissue (+529.9%; p&lt;0.0001). In contrast, RKER-012 treatment was cardioprotective and prevented changes in cardiac function and tissue remodeling. In treated mice, there was a trend for decreased ESPVR (-14.2%), decreased MPI (-13.2%, p&lt;0.01), decreased Fulton Index (-13.5%; p&lt;0.01), and decreased RVFWT (-22.9%; p&lt;0.0001) compared to VEH PAB. Treated mice also had reduced cardiac fibrotic tissue (-38.9%, p&lt;0.01). Taken together, these data provide evidence that KER-012 has the potential to reduce cardiac remodeling and improve cardiac performance in pathologies involving constricted pulmonary arterial blood flow and could provide benefit in diseases such as PAH.

A conceptual model for talik dynamics and icing formation in a river floodplain in the continuous permafrost zone at Salluit, Nunavik (Quebec), Canada

AbstractIcing occurs each winter along the floodplain of the Kuuguluk River in the continuous permafrost zone at Salluit in Nunavik (Quebec), Canada. The source of successive water overflows which thicken and enlarge this ice cover over time is suprapermafrost groundwater discharging from a talik below the riverbed. Electrical resistivity tomography was used to delineate the talik, while water level and temperature dataloggers were used to assess the thermo‐hydraulic conditions of the riverbed. The mean annual riverbed temperature was 1.8°C in 2016 while the mean annual air temperature was −6.0°C. Hydraulic heads below the ice cover as high as 2.8 m and events of abrupt decreases in hydraulic head due to suprapermafrost groundwater overflow through cracks in the ice cover were monitored. An analytical solution based on beam mechanics theory was used to assess the water pressure‐induced stresses which are sufficient to fracture the ice cover. A detailed conceptual model of the talik and icing dynamics is proposed to explain the cryo‐hydrogeological processes taking place in this complex groundwater–river system. The groundwater pressure buildup in the talik during the winter is due to constricted flow of suprapermafrost groundwater in the talik. These results have implications for understanding the dynamics of river taliks and their use as potential water supplies in northern communities.

Algorithm for flow of highly-concentrated emulsions through a narrow constriction

A multipole-accelerated 3D boundary-integral algorithm is developed to model pressure-driven flow of a highly-concentrated emulsion of many deformable drops through a periodic channel with tight constrictions. The drops are monodisperse, free from surfactant, and the Reynolds number is small for Stokes equations to apply. The channel surface consists of four solid panels: front and back parallel to each other, and band-like top and bottom panels with an arbitrary profile. The algorithm is for arbitrary channel aspect ratios, but the results are obtained for extreme cases, when the channel depth (front-back distance) is the same as the minimum channel height and both can be much smaller than the non-deformed drop diameter, making the drops flow as a monolayer. Strong hydrodynamic interactions (especially, drop-wall) necessitate very high surface resolutions combined with novel desingularization tools for the boundary integrals. Multipole acceleration gives, at least, two orders of magnitude gain over direct summations and facilitates long-time simulations, with many drop rearrangements. Examples for homoviscous emulsions with 40-92 drops in two types of channels at 80-90% drop volume fractions and different capillary numbers demonstrate single-file drop motion intermittent with pairs or triplets of drops in the constriction. Such squeezing interactions can result in extreme drop elongations, but are still not sufficient to promote breakup for the channel geometries, capillary numbers and drop confinements considered. Integral properties (the entire drop-phase and constriction flow velocities) are also analyzed.

Aeroacoustic differences between the Japanese fricatives [ɕ] and [ç

To elucidate the linguistic similarity between the alveolo-palatal sibilant [ɕ] and palatal non-sibilant [ç] in Japanese, the aeroacoustic differences between the two consonants were explored via experimentation with participants and analysis using simplified vocal tract models. The real-time magnetic resonance imaging (rtMRI) observations of articulatory movements demonstrated that some speakers use a nearly identical place of articulation for /si/ [ɕi] and /hi/ [çi]. Simplified vocal tract models were then constructed based on the data captured by static MRI, and the model-generated synthetic sounds were compared with speaker data producing [ɕ] and [ç]. Speaker data demonstrated that the amplitude of the broadband noise of [ç] was weaker than that of [ɕ]; the characteristic peak amplitude at approximately 4 kHz was greater in [ç] than in [ɕ], although the mid-sagittal vocal tract profiles were nearly identical for three of ten subjects in the rtMRI observation. These acoustic differences were reproduced by the proposed models, with differences in the width of the coronal plane constriction and the flow rate. The results suggest the need to include constriction width and flow rate as parameters for articulatory phonetic descriptions of speech sounds.

Investigation of flow through curved constrictions for leakage flow modelling in hydraulic gear pumps

The internal leakage flows in external gear and gerotor pumps are often represented by flow through curved constrictions. The nature of this flow can vary from laminar to turbulent and the flow can experience localized cavitation too. In the current literature, there is a scarcity of techniques for accurately modelling such curve-constricted flows which limits the accuracy of the current simulation tools for gear pumps.This paper presents a novel flow model for curve-constricted geometries that is applicable over a wide range of flow regimes including localized cavitation. Using a dimensionless form, the proposed model characterizes the constriction flow velocity as the function of the constriction shape, the pressure difference, and a properly defined cavitation indicator. The functional relationships between these dimensionless parameters are developed based on CFD simulations. The flow model is validated by the means of several experiments conducted on a custom test apparatus.The model presented in this paper can be incorporated in the lumped parameter simulation tools widely used for modelling gear pumps, improving their accuracy in predicting the internal leakages. Consequently, this model will also aid the development of novel energy efficient gear pump designs, where such leakages are kept to a minimum.