Flow Regime Research Articles

Convolutional neural network augmented soft-sensor for autonomous microfluidic production of uniform bubbles

Microfluidics has emerged as a foundational process for creating highly uniform emulsions and bubbles. To enable integration of microfluidic platforms into industrial processes, achieving precise control over the size uniformity of microfluidic-generated bubbles and emulsions is crucial. Even if the external variables such as flow rates or pressures are kept constant, microfluidic processes can be easily disturbed by unknown factors that would substantially compromise the uniformity of resulting emulsions and bubbles. In this study, we introduce a two-step soft-sensor approach that combines a convolutional neural network (CNN) and an image recognition algorithm for feature extraction to detect both the flow regime and the size and uniformity of resulting bubbles. By using a CNN to detect flow regimes, our controller is able to restore the bubble-producing flow regime in response to disturbances. Beyond self-recovery, our controller actively adjusts to minimize errors, maintain setpoints, mitigate disturbances, and ensure system stability over extended periods. 99.2% of bubbles produced during an 8-hour period remain within 5% of the setpoint with our controller acting. By leveraging the soft sensor and artificial intelligence-assisted feedback control, our work presents a widely applicable approach for precise and automated control of microfluidics in diverse applications.

Numerical Investigation of Flow Inside a Channel with Elastic Vortex Generator and Elastic Wall for Heat Transfer Enhancement

In the present investigation, a detailed numerical investigation of the flow and heat transfer characteristics of a channel with an elastic fin (vortex generator) and an elastic wall has been carried out using finite element method. The Fluid-Structure Interaction (FSI) model is used to capture the interaction between the fluid and the solid structure. A sinusoidal time dependent velocity profile has been imposed at the inlet of the channel and the right half of the upper wall of the channel is heated and exposed to constant temperature boundary condition. Due to the sinusoidal velocity profile at the inlet, the elastic fin oscillates periodically and act as a vortex generator, which causes more turbulence in the flow. The obtained results showed that the Nusselt number over the heated wall is affected by the position of the flexible fin, height of flexible fin and elasticity modulus of elastic fin. Moreover, due to the elasticity of the elastic wall and sinusoidal behavior of the inlet velocity, the elastic wall oscillates periodically upward and downward. The Nusselt number values over the heated wall are increased with decrease of the elastic modulus value of the elastic wall. However, the decrease in elastic modulus value of the elastic wall contributes to an increase in the pressure drop inside the channel. It should be added that the interplay between the fluid motion and the deformable structures leads to enhanced turbulence, as the flexible fin and elastic wall introduce additional disturbances and fluctuations into the flow regime. Consequently, this heightened turbulence level has profound implications for heat transfer processes within the system.

Study and Analysis of Flow Regime Transitions in Straight Channels Using the Lattice Boltzmann Method for Shallow Water

Study and Analysis of Flow Regime Transitions in Straight Channels Using the Lattice Boltzmann Method for Shallow Water

Anthropogenic activities mitigate the impacts of climate extremes on high flow regimes on the Loess Plateau

The hydrological cycle is anticipated to become increasing variable due to intensified global climate extremes and frequent floods. Understanding the evolution and driving mechanisms of floods in the context of climatic extremes is essential, particularly on the Loess Plateau (LP) where anthropogenic activities are significant. Here, we examined the spatiotemporal variability of climate extremes and their impacts on flood processes on the LP during 1956–2015. We employed a paired year approach to quantitatively assess the driving role of anthropogenic activities on flood changes in 11 major basins. Our findings indicated a general decline in extreme precipitation indices, while temperature has increased across most of the LP. Both annual runoff (Q) and high flow (Q5) magnitude significantly decreased in all basins. We identified that the major climatic indices driving Q5 included erosive precipitation amount, flood season precipitation, heavy precipitation amount, and maximum 7-day precipitation amount. Importantly, anthropogenic activities have mitigated the impact of climate extremes on Q5 regimes. Compared the post-2000 with reference period (1956–1979), under similar climatic conditions, we observed a reduction in the average Q5 magnitude by 30.19–78.14%, and a decrease in the average Q5 duration by 46.48–100.00% across the basins. The contributions of climate variability and anthropogenic activities to Q5 magnitude changes among 11 basins ranged from –37.58% to 22.02% and –56.84% to –15.08%, respectively, highlighting the crucial role of ecological restoration in reducing Q5 magnitude. These results underscore the importance of ecological restoration in flood regulation and offer valuable insights for basin management in the Yellow River Basin.

Has unsustainable groundwater use induced low flow regimes in the Urucuia Aquifer System? An urgent call for integrated water management

Groundwater depletion in the Urucuia Aquifer System (UAS) has concerned the Brazilian water agencies since it is the principal water source in the arid length of the São Francisco river. In contrast, the irrigation fields increasing and uncertainty regarding climate variability have impaired the management of this important hydrograph region of Brazil. Therefore, the proper management of the UAS relies on the correct definition of the factors that are impacting most of the ground and surface waters, i.e., whether they are from climate or anthropogenic activities. Relying on Artificial Intelligence (AI) modeling and hydrological signatures, this study proposed a methodology to disentangle the role of climatic variability and groundwater pumping on streamflow dynamics by rebuilding natural time series in four watersheds within the UAS’s boundaries. By comparing the natural to the observed streamflow time series, the long-term 90th percentile (Q_90) discharge, from which 80% can be granted for multiple uses in the State of Bahia, decreased by up to 50% in the UAS. Yet, the watersheds’ productivity, given by the 90% specific yield, ranged from -52.3% (3.8 L/s.km2 to 1.8 L/s.km2) to -74.0% (23.4 L/s.km2 to 6.1 L/s.km2). Low flow duration was ∼ 1,650 days in natural conditions and increased to 10,354 days in the current land use and cover scenario. Changes in the maximum low flow duration length ranged from 191.7% to 1,315.7%, and in the low flow, deficits were up to 7,150%. These results highlight that groundwater pumping is the principal factor of the UAS’s dryness since climate variability could not track streamflow decreases. However, climate variability is secondary because of the intensification of the atmosphere demand. Although it is a Brazilian application, the proposed methodology can be applied in other aquifer systems to guide decision-makers' management strategies worldwide.

Comparative Study on the Application Efficacy of Small Disturbance Equation versus One-Dimensional Euler Equation in Nozzle Flow Analysis

This paper presents a numerical simulation study of subsonic and supersonic nozzle flow regimes utilizing the Small Disturbance Equation (SDE), implemented through Python to analyze flow stability under various boundary conditions. The SDE, extensively applied in aerospace, meteorology, and fluid mechanics, offers a critical framework for examining aircraft stability and maneuverability, essential for ensuring flight safety. Additionally, its application extends to spacecraft stability and control in aerospace science. The findings from this study reveal that subsonic flows, characterized by their stability and smoothness, respond more predictably under varying boundary conditions compared to their supersonic counterparts. Conversely, supersonic flows demonstrate increased sensitivity to changes in boundary conditions, resulting in more complex flow patterns. This sensitivity underscores the need for precise control mechanisms in supersonic applications to maintain flow stability and ensure the safety and efficiency of aerospace operations. The simulations underscore the practical importance of the SDE in advancing the understanding of dynamic flow problems across different scientific and engineering disciplines.

Research and Analysis of the Small Disturbance Equation in Subsonic, Transonic, and Supersonic Regimes

This paper explores the application of the Small Disturbance Equation (SDE) across subsonic, transonic, and supersonic flow regimes. Derived from the Euler and Navier-Stokes equations, the SDE offers an efficient framework for analyzing aerodynamic behaviors, particularly through the utilization of discretization techniques and iterative solving methods executed in Python. The study assesses the accuracy and limitations of the SDE in detailing essential flow characteristics, revealing that while the equation performs effectively in subsonic and transonic flows, it encounters challenges in supersonic regimes. Nonlinear effects such as shock waves significantly hinder its performance at high speeds. Compared with conventional computational fluid dynamics (CFD) methods, the SDE stands out in scenarios where computational efficiency is paramount. However, its limitations in handling high-speed flows must be carefully considered, highlighting the need for further refinement in its application to supersonic dynamics. This analysis suggests that while the SDE is beneficial for certain aerodynamic studies, its scope and utility are constrained by the inherent complexities of high-speed fluid dynamics.

Particle image velocimetry study of the flow control effects of singular and multiple curved serration models

This paper reports on preliminary observations of an investigation of flows associated with models that mimic serrations on the leading edge of barn owl feathers. The objective was to use particle image velocimetry measurements to determine the capacity of singular and multiple curved (three-dimensional) serration models to modify the noise-reducing indicators of a narrow-channeled flow past a cylinder. Four models were tested: 3 singular serration models of respective angles of inclination, α = 24°, 27.5° and 31°, and a model consisting of an array of 3 serrations of α = 24°, 27.5° and 31°. Each case was subjected to flow of Reynolds number (based on the serration height and maximum velocity of the flow) of ∼2,000, simulating the flow regime of local flow around barbs of real barn owl flights. A planar particle image velocimetry technique was used to capture the midspan plane velocities to determine the effects of each model. The results show that using singular serration models of inclination angles than 30° may lead to disorganized spatial structures and enhanced turbulence levels. On the other hand, an array of only 3 curved serrations of different geometries can modify the spatial flow structure into a well-ordered one, resulting in a 50% reduction in turbulence intensities. These initial results suggest that under complex flow conditions, the insertion of single and multiple curved serrations can lead to significant flow changes that may result in potential noise modifications.

Relative size matters: Spawning substrate roughness size and spacing affect egg dislodgement and retention in the benthos

AbstractThe consequences of hydrodynamic effects on survival of embryonic benthic organisms remain unknown. This is because the interaction of hydrodynamics and substrate roughness is complex, but it can be conceptualized in two dimensions by roughness flow regimes (isolated, wake interference, and skimming flow) or roughness types (k‐ and d‐type). We examined the effect of different roughness flow regimes/roughness types and roughness heights (k) on the dislodgement of walleye (Sander vitreus) eggs (2 mm diameter, ⌀) using a wall jet apparatus. We expected that lower wall shear stress (τw) would be required for dislodgement in more‐exposed/less‐sheltered roughness type/flow regimes (i.e., k‐type/isolated roughness flow) and when k ≤ ⌀. Surprisingly, the opposite was found, indicating that other mechanism(s) are also responsible for egg dislodgement on these rough surfaces. Hydrodynamic sheltering occurred when flow was directed over exposed eggs (k ≤ ⌀) adjacent to roughness elements effectively increasing their width, and thus requiring higher τw for rolling and then ejection. When k > ⌀, eggs dislodgement likely occurred via the lower pressure in the eddies recirculating in the groove width between roughness elements, rather than due to τw. These results indicate the relevance of heterogeneous sorting and sizing of substrate elements to provide suitable spawning habitats in benthic environments.

Flow regimes in a melting system composed of binary fluid: transition from penetrative convection to diffusion

In a horizontally heated melting system, where a solid substance is subject to melting by a warmer liquid beneath, the presence of solute in the liquid introduces a complex interplay between temperature and concentration dynamics. Employing a recently developed sharp interface method (Xue et al., J. Comput. Phys., vol. 491, 2023), we conduct direct numerical simulations to investigate the transient behaviour of the system across a broad range of Rayleigh numbers and solute concentrations. Our observations reveal distinct flow regimes: at low concentrations, the system resembles a temperature-driven melting problem, characterized by vortex rolls beneath the melting interface. As the solute concentration increases, a stably stratified layer emerges beneath the interface, leading to the transition from thermal convection to penetrative convection, which resembles those flow characteristics observed in the double-diffusive convection. This shift results from the competition between the stabilizing effect induced by solute concentration gradient and the destabilizing effect caused by temperature gradient. Otherwise in the diffusion regime, characterized by very high solute concentrations, the flow becomes static due to the complete suppression of convection by the stably stratified layer. This regime further exhibits two distinct patterns: ‘melting’ and ‘dissolution’. Beyond characterizing diverse flow patterns, our study conducts a quantitative analysis, examining heat/mass transfer, melting rates, and the evolution of temperature and concentration at the interface. These insights contribute to a better understanding of the intricate interplay between temperature and solute concentration during phase change, with implications for accurately estimating melting rates in binary fluid systems.

Scaling behaviour of rotating convection in a spherical shell with different Prandtl numbers

Rayleigh–Bénard convection in a rotating spherical shell provides a simplified model for convective dynamics of planetary and stellar interiors. Over the past decades, the problem has been studied extensively via numerical simulations, but most previous simulations set the Prandtl number $Pr$ to unity. In this study we build more than 200 numerical models of rotating convection in a spherical shell over a wide range of $Pr$ ( $10^{-2}\le Pr \le 10^2$ ). By increasing the Rayleigh number $Ra$ , we characterise four different flow regimes, starting from the linear onset to multiple modes, then transitioning to the geostrophic turbulence and eventually approaching the weakly rotating regime. In the multiple modes regime, we show evidence of triadic resonances in numerical models with different $Pr$ , which may provide a generic mechanism for the transition from laminar to turbulence in rotating convection. We analyse scaling behaviours of the heat transfer and convective flow speeds in numerical simulations, paying particular attention to the $Pr$ dependence. We find that the so-called diffusion-free scaling for the heat transfer cannot reconcile all numerical models with different $Pr$ in the geostrophic turbulence regime. However, the characteristic flow speeds at different $Pr$ roughly follow a unified scaling that can be described by visco-Archimedean–Coriolis force balances, though the scaling tends to approach the Coriolis-inertial-Archimedean force balance at low $Pr$ . We also show that transition behaviours from rotating to non-rotating convection depend on $Pr$ . The transition criteria based on heat transfer and flow morphology would be rather different when $Pr>1$ , but the two criteria are consistent for cases with $Pr\le 1$ . Both scaling behaviours and transition behaviours suggest that the heat transfer is controlled by the boundary layers while the convective flow speeds are mainly determined by the force balance in the bulk for cases with $Pr>1$ , which is in line with recent experimental results with moderate to high $Pr$ . For cases with $Pr \le 1$ , both the heat transfer and convective velocities are approaching the inviscid dynamics in the bulk. We also briefly analysed the magnitude and scaling of zonal flows at different $Pr$ , showing that the zonal flow amplitude rapidly increases as $Pr$ decreases.

Point-enhanced convolutional neural network: A novel deep learning method for transonic wall-bounded flows

Low order models can be used to accelerate engineering design processes. Ideally, these surrogates should meet the conflicting requirements of large design space coverage, high accuracy and fast evaluation. Within the context of aerospace applications at transonic conditions, this can be challenging due to the associated non-linearity of the flow regime. Different methods have been investigated in the past to predict the flow-field around shapes such as airfoils or cylinders. However, they usually have reduced spatial resolution, limiting the prediction capabilities within the boundary layer which is of interest for transonic wall-bounded flows. This work proposes a novel Point-Enhanced Convolutional Neural Network (PCNN) method that combines the advantages of the well-established PointNet and convolutional neural network approaches. The PCNN model has relatively low memory requirements in the training process, preserves the spatial correlation in the domain and has the same resolution as a traditional computational method. The architecture is used for the flow-field prediction of civil aero-engine nacelles in which it is demonstrated that the flow features of peak isentropic Mach number (Mis), pre-shock isentropic Mach number and shock location (X/Lnac) are captured within ΔMis = 0.02, ΔMis=0.04, ΔX/Lnac=0.007, respectively. The PCNN model successfully predicts the integral parameters of the boundary layer, in which the incompressible displacement thickness, momentum thickness and shape factor are typically within 5% of the CFD. Overall, the PCNN method is demonstrated for transonic wall-bounded flows for a range of flow physics that include shock waves and shock-induced separation.

Direct numerical simulation of turbulent, generalized Couette–Poiseuille flow

We present direct numerical simulation (DNS) and modelling of incompressible, turbulent, generalized Couette–Poiseuille flow. A particular example is specified by spherical coordinates $(Re,\theta,\phi )$ , where $Re = 6000$ is a global Reynolds number, $\phi$ denotes the angle between the moving plate, velocity-difference vector and the volume-flow vector and $\tan \theta$ specifies the ratio of the mean volume-flow speed to the plate speed. The limits $\phi \to 0^\circ$ and $\phi \to 90^\circ$ give alignment and orthogonality, respectively, while $\theta \to 0^\circ,\ \theta \to 90^\circ$ correspond respectively to pure Couette flow in the $x$ direction and pure Poiseuille flow at angle $\phi$ to the $x$ axis. Competition between the Couette-flow shear and the forced volume flow produces a mean-velocity profile with directional twist between the confining walls. Resultant mean-speed profiles relative to each wall generally show a log-like region. An empirical flow model is constructed based on component log and log-wake velocity profiles relative to the two walls. This gives predictions of four independent components of shear stress and also mean-velocity profiles as functions of $(Re,\theta,\phi )$ . The model captures DNS results including the mean-flow twist. Premultiplied energy spectra are obtained for symmetric flows with $\phi =90^\circ$ . With increasing $\theta$ , the energy peak gradually moves in the direction of increasing $k_x$ and decreasing $k_z$ . Rotation of the energy spectrum produced by the faster moving velocity near the wall is also observed. Rapid weakening of a spike maxima in the Couette-type flow regime indicates attenuation of large-scale roll structures, which is also shown in the $Q$ -criterion visualization of a three-dimensional time-averaged flow.

ON WELL-POSED BOUNDARY CONDITIONS AND ENERGY STABLE FINITE-VOLUME METHOD FOR THE LINEAR SHALLOW WATER WAVE EQUATION

Abstract We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite-volume method is developed based on the summation-by-parts framework with the boundary conditions implemented weakly using penalties. Stability is proven by deriving a discrete energy estimate analogous to the continuous estimate. The continuous and discrete analysis covers all flow regimes. Numerical experiments are presented verifying the analysis.

An Experimental Study of Flow and Turbulence Properties near the Rising Sector Gate Mouth Considering the Gate Opening with a PIV Measuring System

Hydraulic structures, such as movable weir gates, are widely installed in rivers and streams for various purposes. Among these is the rising sector gate, which is the focus of this study. This research investigated how different gate openings affect flow velocity and turbulence distributions at the gate mouth. A hydraulic analysis of flow and turbulence characteristics near the mouth of a rising sector gate model was conducted through laboratory experiments with various flow conditions and gate openings utilizing a Particle Image Velocimetry (PIV) system. Experimental tests were carried out with two gate-opening angles (30 and 45 degrees). The PIV measurements revealed significant variations in flow velocity and turbulence properties in response to the gate openings and flow conditions. Notably, in the vicinity of the gate mouth, where the flow regime changes rapidly between the upstream and downstream regions, the turbulence properties in the upstream part of the gate mouth were more than twice those in the downstream part. Additionally, the streamwise distribution of depth-averaged relative turbulence intensity was analyzed. The results showed that the depth-averaged relative turbulence intensity decreased by nearly half as the gate opening increased from 30 to 45 degrees, with the lowest values observed at the gate mouth, followed by an increase downstream. A functional relationship between the maximum flow velocity at the gate mouth during underflow operation and the Froude number was established to guide practical gate operation in the field.

Linking curve number with environmental flows: a novel approach.

Change in flow regime is one of the major reasons which influence the services offered by rivers and integrity of their aquatic ecosystems requiring certain amount of flow in the river known as environmental flow. In this study, the environmental flows described by Tennant's method are correlated with a very versatile index defined in terms of Curve Number (CN) that incorporates hydrometeorological and geomorphological characteristics of catchment. Parameter CN is commonly known to be closely related with catchment characteristics (viz., land use, soil type, etc.). The rainfall-runoff data of 17 catchments from five major Indian river basins (i.e., Brahmani-Baitarani, Godavari, Mahanadi, Mahi, and Narmada) of low flow season (October-June) are used to derive the relationship between percentage of average annual flow (%AAF) and CN. The %AAF is seen to increase linearly with increasing CN, and vice versa, for all catchments and the correlation (R) is found to be greater than 0.7 for 16 (out of 17) catchments. The correlation between %AAF and CN is maximum for Dhariawad (R2 = 0.899) and Baronda (R2 = 0.814) catchments, indicating excellent relationship between %AAF and CN, which can be useful for the environmental flow prediction based on catchment characteristics. The existence of such a relationship is further strengthened by the relation established between the standard normal deviate of CN and the Standard Flow Index (SQI), a variation of %AAF, using the same field data.

Effects of offset jet width on periodic flow in a dual jet

The primary aim of this work is to investigate the impact of the offset jet width on the unsteady flow characteristics of a turbulent dual jet, which consists of a wall jet and an offset jet. A computational fluid dynamics code is developed to solve the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. The width of the offset jet is varied while keeping the width of the wall jet constant at the separation distance between the two jets. When the ratio of the offset jet width (w) to the separation distance (d) is w/d=0.5, the flow field exhibits a periodic vortex shedding phenomenon. Conversely, when w/d=0.4, the flow field remains steady. The shedding phenomenon is discernible even when w/d=2. The instantaneous velocity components display sinusoidal oscillations at 0.5≤w/d≤2. Applying the fast Fourier transform to these sinusoidal signals yields a distinct frequency peak at the vortex shedding frequency. Within the range of 0.5≤w/d≤2, the shedding frequency decreases as the width of the offset jet increases. This trend continues until it reaches a constant value at w/d=1.4. This indicates that the width of the offset jet has a notable influence on the shedding phenomenon within the range of 0.5≤w/d≤1.4. For 1.4<w/d≤2, the shedding frequency remains unaffected by the offset jet width variation. Depending on the value of w/d, the shedding phenomenon is characterized by three flow regimes: a steady flow regime (forw/d≤0.4), an outer share layer-influenced shedding regime (for w/d=0.5−1.4), and an outer shear layer-free shedding regime (for w/d>1.4).

Hydraulic assessment of different types of piano key weirs

ABSTRACT Piano Key Weir (PKW) is a non-linear weir with a small foundation footprint that allows large discharges through a narrow channel. The presence of overhangs classifies it into A, B, C, and D. For different PKW types, this study aims to assess the discharge, hydraulic characteristics (flow regimes, water surface profile, and nappes interference), and energy dispersion. This study employs the FLOW-3D software and validated by comparing experimental types A and D PKW with numerical simulations. Experimental and simulation results agreed well, with lower MAPE values for both types. After that, eight simulations for each PKW type were run, with headwater ratios (H t /P) from 0.13 to 0.85 (H t : total upstream head above crest, P: PKW height). Regarding discharge performance, type-B was superior to all other PKW types at lower heads (H t /P ≤0.40) due to longer upstream overhangs. While at higher heads (H t /P > 0.40), type-A became the highest PKW type. Since PKWs disperse energy more effectively than linear weirs, they acquire new performance as energy dissipators. Type-C had the highest energy dispersion rate, followed by type-A, type-D, and type-B. Finally, an empirical equation was provided to predict energy dispersion rates over PKW types as a function of discharge coefficient.

Data-driven effects of human activities and environmental factors on inland aquatic dissolved organic matter in China: Insights from machine learning

Aquatic DOM, a major carbon pool in inland waters, plays a key role in the global carbon cycle and is influenced by human activities and environmental factors. While watershed surveys have identified some drivers of aquatic DOM changes, national-scale knowledge remains limited. Spectral monitoring data from 721 aquatic DOMs in inland China were collected to predict and quantify the spectral properties of aquatic DOMs and the coupled effects of human activities and environmental factors by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), random forest (RF) and structural equation modeling (SEM). Our results show that the dataset is relatively evenly distributed in terms of flow regimes, and the data are adequately representative of various types of water in China. Although the performance of CEEMDAN is affected by the skewed distribution of data sampling points (453 and 449 for eastern regions and eutrophic waters, respectively), CEEMDAN effectively processes the spatial sequences of aquatic DOM spectra, which significantly improves the reliability of the machine learning model (by 13%–68%) and reduces the error (by 63%–92%). CEEMDAN-RF and SEM results indicate that longitude and latitude are the most important environmental factors affecting the spectral properties of aquatic DOM through temperature, light and land cover differences, reducing the biogenic properties of aquatic DOM. Unlike observations in small watersheds and estuaries, environmental factors of season, precipitation and salinity have weak effects on aquatic DOM. Furthermore, the biogenic character of aquatic DOM is enhanced by urban human activities, represented by urbanization, population, and impervious land fraction, which have long-lasting and strong impacts on aquatic DOM by driving water eutrophication and enhancing phytoplankton and microbial activity. Our study informs the prediction and quantification of coupled environmental and anthropogenic impacts on aquatic DOM at large scales.

Non-Newtonian fluids effects on the steady-state performance of two-lobe journal bearings

This research aims to investigate the behavior of non-Newtonian fluid obeying the power law model in a laminar flow regime for a two-lobe journal bearing. The investigation involves calculating the static characteristics in terms; of load-carrying capacity, attitude angle, friction coefficient, friction force, and side leakage, for various values of the power law index and different eccentricity ratios. To determine the static characteristics, the pressure distributions are obtained by the numerical solution of the modified Reynolds equation considering the effect of non-Newtonian behavior of the fluids using the finite difference method. This study reveals that increasing both the eccentricity ratio and power law index produce an increase in the load-carrying capacity, friction force, and side leakage while lead to a decrease in the attitude angle and friction coefficient for the two-lobe journal bearing. In addition, compared to Newtonian fluid the results show that the using of non-Newtonian fluids as lubricants improves the static characteristics of the two-lobe journal bearing especially for the shear-thickening lubricants.