Flow Regime Transition Research Articles

POD Analysis of the Wake of Two Tandem Square Cylinders

This study aims to investigate the wake of two tandem square cylinders based on the Proper Orthogonal Decomposition (POD) analyses of the PIV and hotwire data. The cylinder centre-to-centre spacing ratio L/w examined is from 1.2 to 4.2, covering the four flow regimes, i.e., extended body, reattachment, transition and co-shedding. The Reynolds number examined was 1.3 × 104. A novel Proper Orthogonal Decomposition (POD) technique (hereafter referred to as PODHW) is developed to analyse data from single point hotwire measurements, offering a new perspective compared to the conventional POD analysis (PODPIV) based on Particle Image Velocimetry (PIV) data. A key finding is the identification of two distinct states, reattachment and co-shedding, within the transition flow regime at L/w = 2.8, which PODPIV fails to capture due to the limited duration of the PIV data obtained. This study confirms, for the first time, the existence of these states as proposed by Zhou et al. (2024), highlighting the advantage of using PODHW for capturing intermittent flow phenomena. Furthermore, the analysis reveals how the predominant coherent structures contribute to the total fluctuating velocity energy in each individual regime. Other aspects of the flow are also discussed, including the Strouhal numbers, the contribution to the total fluctuating energy of the flow from the first four POD modes, and a comparison between different regimes.

Hydrodynamic study of gas–liquid-solid mini-fluidization based on fluorescence PIV

The fluorescence-based tracer particle image velocimetry (fluorescence PIV) was used to obtain the flow regimes transition, bubble size and velocity, liquid and particle flow field characteristics of the 1 ∼ 3 mm GLSMFBs and 93 ∼ 195 μm glass beads. When the bed-to-particle diameter ratio increased, the bubble size and velocity distribution tended to be more concentrated. Bubble rose as straight line and S-shaped spiral trajectory. The divergence and vorticity of the flow field were preliminarily quantified. There showed a close relationship between the macroscopic hydromechanical behaviors such as bubble size and velocity and the mesoscopic behaviors such as the movement and development of vortices. The upward drag force of liquid and bubble on particles mainly affected the particle axial velocity, while the particle radial motion was mainly caused by bubble wake and surface force among particles. The results provide theoretical reference for the design and optimization of GLSMFB reactors.

Microconfined High-Pressure Transcritical Channel Flow Database: Laminar, Transitional & Turbulent Regimes

The potential of comprehending and managing microscale flows to enhance energy processes, especially in heat transfer and propulsion applications, remains largely untapped particularly for supercritical fluids, which have gained increased interest over the past years due to the higher power and thermodynamic efficiencies they provide. This work, therefore, presents the first comprehensive, open-source dataset carefully curated and structured for studying microconfined high-pressure transcritical fluid channel flows under various regimes. Particularly, the dataset contains 18 direct numerical simulations of carbon dioxide at different bulk pressures and velocities confined between differentially-heated walls. For all cases, the thermodynamic conditions selected impose the fluid to undergo a transcritical trajectory across the pseudo-boiling region. The data collection comprises an array of physical quantities that enable comprehensive parametric analyses spanning laminar, transitional, and turbulent flow regimes. This data repository is poised to provide access to the detailed study and modeling of the complex flow physics observed in high-pressure transcritical fluids, especially those closely linked to improving microfluidics performance.

Facile one-step functionalised graphene oxide-phytic acid coating towards effective wax inhibition in waxy oil transportation

Wax deposition in pipelines is a global issue during the production and transportation of oil. Recently, superhydrophilic/underwater superoleophobic coatings have garnered much attention due to their wax inhibition potential based on water film theory. Herein, carbon steel (CS) substrates were made superhydrophilic by coating phytic acid (PA) functionalised graphene oxide (GO) materials prepared by very simple process. The superhydrophilic GO-PA coatings induced the formation of a hydration layer on the surface, thus inherently showing underwater superoleophobic properties in a water-contained waxy oil system. The optimised GO-PA/CS surface possessed a water contact angle of nearly 0° and an underwater oil contact angle of ∼ 160°. This coating demonstrated up to 89.5 % enhancement in oil passing speed during the oil transportation test. This enhancement is particularly significant for reducing wax deposition in laminar and transitional flow regimes. Moreover, in the cold-finger wax deposition tests, a wax inhibition efficiency of 95.8 % was achieved with the optimised GO-PA/CS surface in the laminar flow regime. Therefore, this research provides insights into a mechanically and chemically stable GO-based coating achieved via a facile one-step functionalisation, which has not been previously reported in the literature for applications in waxy oil transportation.

Theory and Experiment of the Limiting Current in Impinging Jet Electrodes

Recently, flow cells with a confined impinging jet type have emerged as a promising hydrodynamic electrochemical setup for non-conventional square model electrodes that cannot be measured in the commonly used rotating disk electrode (RDE) setup1. Due to the complex hydrodynamic flow profiles, these flow cell types usually rely on computational fluid dynamics (CFD) simulations for the description of the local current density profiles and overall current-potential characteristics2. In this work, we present an advanced analytical model of the limiting current in confined impinging jet electrodes and validate the model with experimental data and corresponding CFD simulations.Around 350 parameter sets of the confined impinging jet electrode arrangement were analyzed by varying the inlet diameter (d), distance between inlet-nozzle and electrode (H), electrode radius (RIII), and volume flow rate (V0). Figure 1 shows the proposed analytical solution which separates the electrode into three different diffusion regions: (i) wall-tube region (blue rectangle), (ii) wall-jet region (green rectangle), and finally (iii) radial channel-flow region (orange rectangle). The approach allows predicting the limiting current characteristics for a broad variety of impinging jet electrodes, including the confined impinging jet electrode type. The flow line profiles obtained by CFD simulations are in excellent agreement with the analytically determined regimes with radii RI and RII and flow regime transitions. Very importantly, for the construction of ideal wall-tube electrodes the transition point RI can now be described by our analytical model in high accuracy and requires no more in-depth numerical or experimental studies3. We determined an average relative error over all parameter points compared to the numerical CFD simulations to be 7.8 %. In contrast, the analytical formula for free wall-jets4 to the entire electrode is in the range of 29 %. Furthermore, using a 3D-printed flow cell geometry (H = 0.7 mm; d = 0.5 mm) with the confined impinging jet type, the obtained experimental data confirm the here developed analytical model. The experimental data for different electrode radii (1 mm < R < 3 mm) using the ferrocyanide/ferricyanide redox pair ([Fe(CN)6]4-/[Fe(CN)6]3-) also show good agreement to the analytical model with an average deviation of 6 %.In summary, we have developed an analytical model that allows an accurate prediction of the limiting current for different geometries of the impinging jet electrode. Based on numerical and experimental approaches, our model shows an accuracy of below 10 %, which is very remarkable compared to the current models reported in the literature. The results of this study help to improve the design and construction of electrochemical flow cells based on this electrode type as an alternative to the classic RDE setup.

Tilt effect on squeeze-film damping in electrostatic micro-actuators

In this study, we theoretically explore the impact of tilt on the switching dynamics of a MEMS device operated by a pair of electrostatic actuators and subject to pronounced squeeze-film damping in the transition and free molecular flow regimes. Our investigation reveals that inducing tilt, achieved through the application of uneven voltages on the electrodes, introduces additional source terms in the modified Reynolds equation governing the pressure distribution in the squeeze-film gap. These added terms result in an accelerated decay of the squeeze film force, facilitating faster device switching between the initial and target configurations.To analyze the device dynamics, we develop a coupled numerical model and employ evolutionary multi-objective optimization to determine an optimal actuation scheme. This optimization is carried out for scenarios where initially different voltages are applied to the electrodes during a certain pre-defined time interval before transitioning to the steady voltage corresponding to the target gap size at equilibrium. Our findings highlight that the suggested actuation strategy leads to substantial improvements in the switching time of the device. Furthermore, we provide insights into the conditions favoring tilt actuation over parallel-motion actuation where the initially applied voltages are equal.

A numerical study of Elasto-inertial particle-focusing in straight and serpentine microchannels

Microfluidic devices have gained popularity in recent years due to their low cost and simplicity. Cell focusing linked with cell counting and cell separation used in clinical tests and point-of-care devices stands towards the top of every list of microfluidic applications. To focus and manipulate particles in a Newtonian medium, inertial microfluidics has been widely used. There is a requirement to replace a significantly more efficient approach given various particle-focusing positions near the channel walls recorded by inertial microfluidics. Here, the synergetic effect of elastic and inertial forces in relatively low-concentration viscoelastic fluids was investigated numerically. Utilizing particle-focusing behavior in straight and serpentine channels with different corner angles, by applying the numerical results obtained using the developed direct numerical simulation method (DNS) for elastic and inertial forces, we created a microchannel with a remarkable performance. As the flow regime transitions to elasto-inertial, where inertial forces are comparable to elastic forces in a straight microchannel, particles tend to concentrate at the channel centerline. As the flow rate increases, however, particle defocusing develops, and shear gradient lift forces ultimately overcome elastic forces in the channel's central region. Given that fluid flows at a higher velocity in the serpentine channel with a corner angle of 75° than in other channels, the Dean drag force induced by secondary flow serves to reduce particle defocusing rate at a given flow rate, making this channel a desirable platform for Elasto-inertial microfluidics. Particle focusing in a vertical direction was noticed as a benefit of elasto-inertial microfluidics, regardless of the geometry or flow rate of the particles passing through the channel. Finally, the impact of particle diameter on focusing behavior was studied. As particle diameter decreases, focusing width decreases and the focusing band shifts to the left side of the cross-section. We expect that the numerical evaluation of using viscoelastic medium in complex geometries can contribute to accelerate the three dimensional particle-focusing mechanism and enhance the efficiency of microdevices for cell and particle manipulation.

Flow regime transition maps and pressure loss prediction of gas, oil and water three-phase flow in the vertical riser downstream 90° bend using data driven approach

The simultaneous flow of gas, oil & water is frequently encountered in pipelines during upstream petroleum operations. The multiphase flow results in different types of flow patterns based on the flow rates of fluids, physical properties and geometry of the flow domain. The flow behavior is characterized based on the governing flow patterns. Hence, the information about the flow patterns, regime maps and resulting pressure loss are important for multiphase flow system design and optimization. The current work is focused on construction of gas, oil and water, three-phase flow regime maps and developing pressure loss prediction correlations for the flow through vertical riser downstream 90° bend. The pipe internal diameter (ID) is 6 inch and the bending radius to pipe diameter ratio is 1. The observed gas-liquid flow patterns are slug, churn, and semi-annular churn flow at the given range of superficial velocities of fluids. The flow pattern data has been used to construct flow regime maps to analyze the variation in flow patterns with flow rates of fluids and compared with the available works in the literature. In addition, the change in pressure loss with respect to flow patterns has been analyzed. Previous models are used for the prediction of pressure loss. However, according to the assessment, the models underpredicted the pressure loss. Based on three-phase pressure loss data, multiple linear regression analysis has been carried out to propose new correlations for pressure loss prediction. Comparison of the calculated and experimental data showed good agreement between the results. The knowledge of flow regime variation and pressure loss correlations can help flow assurance engineers in designing and optimization of multiphase flow systems.

Flow regimes of the reactive submerged gas jet from the Laval nozzle into liquid

The reactive submerged gas jet into a liquid bath is used in numerous industrial processes. The jet is featured with violent gas–liquid interface fluctuations. Previous studies showed that the most prominent feature is the cyclic formation and disappearance of the “gas cavity” near the nozzle. This near-nozzle interface fluctuation causes the “back attack” which is usually hazardous in actual applications. In the current study, another flow regime was observed: the near-nozzle interface is stable, and the most violent interface oscillation and the main reaction zone are away from the nozzle. In this regime, the “gas cavity” fluctuation is detached to the nozzle, the gas phase break-off position is pushed downstream (L/d0 from <3.0 to >6.0), and the “back attack” vanishes. This regime is termed as the “Detached Reaction Regime” (if the previous regime is the “Attached Reaction Regime”). The transition from the Attached Reaction Regime to the Detached Reaction Regime is usually caused by an increase in gas momentum. Laval nozzles with different divergent angles (10°, 15° and 20°) were tested. For each Laval nozzle, the effects of the gas total pressure and liquid temperature were investigated. The length and width of the jet were analyzed. Results show that the length and width of the gas jet suddenly decrease because of an enhancement of the gas–liquid mixing rate at the regime transition. In addition, the length-to-width ratio is approximately 3.0 for both regimes and all nozzles. Finally, a criterion for predicting the flow regime transition was proposed.

Visual depiction and numerical characterization of intricate flow in triply periodic minimal surface foams

Benefiting from the structural specificity and programmability, the bioinspired triply periodic minimal surfaces (TPMSs) bring excellent physicochemical properties that are distinct from conventional topologies. Especially with the rapid development of additive manufacturing and high-performance computing capacities, function-oriented design and synthesis of smart TPMS materials or devices have become feasible. Therefore, understanding the flow characterizations induced by TPMS foams is of remarkable importance to the successful design and practical operation. However, the in-depth studies and theoretical guidance on the relationship between structure and flow characterizations of TPMS foams are still limited. In this study, an Eulerian and Lagrangian coupled model is developed to investigate the internal flow behaviors and flow regime transition mechanism from creeping to inertial flow in four representative TPMS foams. The simulation accuracy is then validated by a high-resolution pore-scale flow field observation. Results show that the flow morphology and pressure drop characteristics are highly influenced by TPMS geometry and Re. Among which, Schwarz Diamond (D), Schoen Gyroid (G), and Fischer-Koch S (S) foams are more susceptible to radial flow disturbance, while Schoen inverted Weissenberg periodic foam to axial flow disturbance. In addition, higher porosities delay the transition to transitional regime of the flow. This work establishes firm theoretical and methodological foundations for the customization and intelligent development of bioinspired TPMS foam materials in broad fluidic applications.

The flow regimes of two parallel-connected chambers respectively with a mechanical extractor and a buoyancy source

This research studies the ventilation flow patterns and density stratification in two parallel-connected chambers which respectively have a mechanical extractor and a localized buoyancy source. Two parallel-connected chambers are denoted as the forced and extracted chambers. The forced chamber having a continuous localized buoyancy source is located upstream, and the extracted chamber having a mechanical extractor is located downstream. Two chambers are interconnected by an internal connection opening and are connected to the exterior in a parallel manner through their own connection openings. The effects of the adjoining chamber having a mechanical extractor on the ventilation flow patterns and density stratification in the space are investigated in this study. The flow driving forces include the buoyant and inertial forces in this ventilated space. The buoyant force results from the buoyancy source, and the inertial force is due to the mechanical extractor. This research uses the theoretical analysis approach and the laboratory reduced-scale model to investigate this problem. This paper focuses on the ventilation flow patterns in the steady state and discusses different flow regimes due to the adjoining extracted chamber effect. The internal connection opening level and orientation between two chambers are discussed in this study. Three flow regimes, the small (or reduced), transition, and large (or enhanced) flow regimes, are found in two parallel-connected chambers and there is a range of critical flow rates to determine the flow regime when the internal connection opening is located in a partition wall as investigated in this research. If the internal connection opening is located in a horizontal ceiling, a clear-cut critical flow rate is expected and only two flow regimes exist. This study discusses the characteristics of different flow regimes in the space of two parallel-connected chambers. The paper presents three derived theoretical models and analogous salt-bath experimental results for three flow regimes, and comparisons between them show reasonable agreement.

Consequence analysis of vapour cloud explosion from the release of high-pressure hydrogen storage

Gaseous hydrogen is commonly stored under high pressures due to its low volumetric storage density. The safety concerns about its release and potential accidents, such as vapour cloud explosions, were of the highest importance in industries. This research work established a methodology for consequence analysis of compressed hydrogen releases, considering various stages of event escalation, including high-pressure gas release, gas jet dispersion, and overpressure evaluations. Specifically, compressed hydrogen release was defined as an under-expanded flow, characterised by a transition from sonic to supersonic velocities. The notional nozzle theory was employed to tackle the flow regime transition and provide revised nozzle size and gas velocity as inputs to the CFD model for gas jet dispersion. The model was validated against experimental results, exhibiting a good agreement with a deviation of less than 20%. The flammable gas mass in the cloud was determined using the dispersion model and then used for overpressure predictions. This approach proved to be more realistic than relying solely on the total hydrogen release amount. In a case study, release parameters such as release direction, wind speed and release hole size were investigated. It was observed that a downward release resulted in less gas dissipation, leading to larger overpressures compared to other release directions. Wind speed had a relatively lower impact compared to other parameters. The release hole size had the most significant influence on explosion overpressure, with the case of a larger release size (e.g., 50.8 mm) exhibiting a few hundred times higher of hazardous area compared to a small hole size (e.g., 3 mm).

Liquid–liquid flow characteristics and mass transfer enhancement in a Taylor–Couette microreactor

AbstractThe liquid–liquid immiscible flow and mass transfer were investigated in a novel Taylor–Couette microreactor (TCMR). Due to the rotation shear and microscale effects, each phase flowed in the form of helical strips/bands, instead of dispersion droplets as in conventional equipment. Based on the movement and inclination of the bands, the helical vortex (HV), mixed helical vortex (MHV) and stationary helical vortex (SHV) were distinguished. The characteristics of the regimes were strongly influenced by rotation speed and flow rate, but the specific surface area only slightly varied. The flow regimes also influenced the two phase mass transfer. It was shown that the mass transfer coefficient kLa monotonically increased with the rotation speed in the HV regime, while it slightly decreased when the flow shifted into the MHV/SHV regime. According to the parametric studies, empirical correlations were developed for the flow regime transition and mass transfer prediction.

Variability and predictability of a reduced-order land–atmosphere coupled model

Abstract. This study delves into the predictability of atmospheric blocking, zonal, and transition patterns utilizing a simplified coupled model. This model, implemented in Python, emulates midlatitude atmospheric dynamics with a two-layer quasi-geostrophic channel atmosphere on a β plane, encompassing simplified land effects. Initially, we comprehensively scrutinize the model's responses to environmental parameters like solar radiation, surface friction, and atmosphere–ground heat exchange. Our findings confirm that the model faithfully replicates real-world Earth-like flow regimes, establishing a robust foundation for further analysis. Subsequently, employing Gaussian mixture clustering, we successfully delineate distinct blocking, zonal, and transition flow regimes, unveiling their dependencies on surface friction. To gauge predictability and persistence, we compute the averaged local Lyapunov exponents for each regime. Our investigation uncovers the presence of zonal, blocking, and transition regimes, particularly under conditions of reduced surface friction. As surface friction increases further, the system transitions to a state characterized by two blocking regimes and a transition regime. Intriguingly, periodic behavior emerges under specific surface friction values, returning to patterns observed under low friction coefficients. A model resolution increase impacts the system in such a way that only two regimes are then obtained with the clustering: the transition phase disappears and the predictability drops to roughly 2 d for both of the remaining regimes. In accordance with previous research findings, our study underscores the fact that when all three regimes coexist, zonal patterns exhibit a more extended predictability horizon compared to blocking patterns. Remarkably, transition patterns exhibit reduced predictability when coexisting with the other regimes. In addition, within a specified range of surface friction values where two blocking regimes are found, it is observed that blocked atmospheric situations in the west of the applied topography are marked by instabilities and reduced predictability in contrast to the blockings appearing on the eastern side of the topography.

Development of explainable recognition models for ADMFB flow regimes based on ensemble learning

The spatiotemporal characteristics of fluidization within an Air Dense Medium Fluidized Bed (ADMFB) are critical for its heat and mass transfer, as well as for mixing and separation processes. Yet, detailed analyses of the dynamic behavior of flow regimes during progressive transformations are scarce. This study captured synchronous pressure drop signals at multiple points along the sidewall of the bed using a non-intrusive measurement technique. Statistical analyses were utilized to extract the pressure drop's characteristic parameters and examine the statistical features' spatiotemporal fluctuations during fluidization state transitions. We proposed a method to quantitatively characterize the bed's real-time fluidization state through the combined use of multiple-point pressure characteristics. Following this approach, a multidimensional spatio-temporal matrix was constructed to depict the flow regime transitions quantitatively. Concurrently, ensemble learning techniques were applied to classify flow regimes based on various feature parameters and sample lengths. In the final phase, comprehensive interpretations and detailed visual analyses were deployed on the inputs to the optimized ensemble learning model, XGBoost, utilizing the Shapley Additive Explanations (SHAP) framework. This study provides additional insights and methodologies for managing the transition and intelligent control of flow regimes within an ADMFB.

The study of solid particles effect on the gas bubble dispersion dynamics of complex gas-liquid mixtures at the intake screen of submersible pump

The study of gas phase dispersion at the intake of submersible pumping equipment is an actual issue, since changes in gas phase dispersion can lead to changes in natural separation. At the same time, the gas separation efficiency can be affected by the presence of solid phase in the well products, which would change the structure of gas-liquid mixture and operation mode of electric submersible pump. The results of the research are novel, which takes into account the influence of the properties of multi-component gas-liquid mixture on the character of operation of ESP well. The new dependences of gas bubble diameter at the submersible equipment intake on gas content for four model gas-liquid mixtures: «water – air», «water – surfactants – air», «water – air – solids» and «water – surfactants – air – solids» with the concentration of suspended particles in the flow of 1.0 g/l have been experimentally obtained in conditions of gauge pressure at the intake 0.04 - 0.05 MPa, gas content of mixture was increased up to 71%, liquid flow rate was changed in the range of values from 13 to 68 m3/day. High-speed video recording with fixing the structure of gas-liquid mixture in the near-intake space of the ESP was carried out during the tests. Visualization allows us to clarify the boundary of the flow regime transition from «bubble» to «slug/churn» compared to the Caetano method. There were developed new correlations of natural gas separation coefficient taking into account the influence of solid phase at different operating modes of ESP well. Keywords: gas-liquid mixture (GLM); gas bubble; natural gas separation; solid particles; surfactants.

Developing an Explainable Variational Autoencoder (VAE) Framework for Accurate Representation of Local Circulation in Taiwan

AbstractThis study develops an explainable variational autoencoder (VAE) framework to efficiently generate high‐fidelity local circulation patterns in Taiwan, ensuring an accurate representation of the physical relationship between generated local circulation and upstream synoptic flow regimes. Large ensemble semi‐realistic simulations were conducted using a high‐resolution (2 km) model, TaiwanVVM, where critical characteristics of various synoptic flow regimes were carefully selected to focus on the effects of local circulation variations. The VAE was constructed to capture essential representations of local circulation scenarios associated with the lee vortices by training on the ensemble data set. The VAE's latent space effectively captures the synoptic flow regimes as controlling factors, aligning with the physical understanding of Taiwan's local circulation dynamics. The critical transition of flow regimes under the influence of southeasterly synoptic flow regimes is also well represented in the VAE's latent space. This indicates that the VAE can learn the nonlinear characteristics of the multiscale interactions involving the lee vortex. The latent space within VAE can serve as a reduced‐order model for predicting local circulation using synoptic wind speed and direction. This explainable VAE binds the physical reasoning to the predictions of the local circulation that ensures the physical examination of the uncertainty in accelerating the local weather assessments under various climate change scenarios.

Gas-liquid flow regimes in a novel rocking and rolling flow loop

Predicting two-phase flow pattern characteristics and flow transition is fundamental to address several industrial problems, e.g. for the oil and gas industry. In order to fulfil the upscaling from the laboratory to the industrial scale, resource-efficient flow testing facilities which closely replicate industrial flow characteristics are needed. To address this, we introduce a new experimental device named as the Rocking and Rolling Ring Flow Loop (3RFL), which is size, cost, and time-efficient. In the present work, we employ the 3RFL apparatus at atmospheric pressure and temperature, with air and water as working fluids. However, the ultimate goal of our work is to build an experimental set-up capable of capturing the under-pressure reactive multiphase flow (gas-liquid–solid) dynamics typical of flow assurance in oil production and transportation. At the moment, the 3RFL can induce different flow regimes by adjusting the system control parameters such as rocking angle, rocking rate, and liquid volume fraction, all without requiring a pump. We observe three flow regimes, and analyse the impact of control parameters on their emergence. Our findings reveal that flow regime transitions are influenced by the competition between gravitational and centrifugal forces, which arise due to the curvature of the tube. Among three employed modelling strategies, namely mechanistic modelling, total energy minimization and a combined approach, we find that the total energy minimization model best compares to the experimental liquid height.

A critical review on various factors affecting the thermohydraulic performance in transition-flow regime

A critical review on various factors affecting the thermohydraulic performance in transition-flow regime

Empirical heat transfer correlations of high-pressure transcritical fluids at low Reynolds numbers

Empirical heat transfer correlations serve as indispensable tools for predicting and optimizing the thermal performance of a wide range of engineering devices, like for example in energy conversion and propulsion applications. Although a remarkable number of correlations exist for systems at low (atmospheric) pressures, accurately quantifying heat transfer under high-pressure transcritical conditions poses a notable challenge, especially at low Reynolds numbers due to the scarcity of correlations available in the literature. This difficulty has prompted the widespread use of general empirical correlations, which are inadequate for such flow conditions, and hold significant implications, for instance, in fields like microfluidics technology. In this regard, the aim of this study is to develop novel heat transfer correlations tailored for high-pressure transcritical fluids at relatively low Reynolds numbers. These correlations are derived from a dataset of 18 direct numerical simulations of carbon dioxide confined between differentially heated walls, which induce a transcritical trajectory through the pseudo-boiling region. The correlations are developed for both the cold liquid-like and hot gas-like regions, resulting in a total of 6 correlations that encompass the laminar, transitional, and turbulent flow regimes. In particular, as a function of Reynolds, Prandtl, Eckert and Mach numbers, the proposed empirical correlations provide accurate estimations with relative errors below 8%, which significantly surpass existing literature correlations.