Variation Of Pressure Gradient Research Articles

Stationary flow driven by non-sinusoidal time-periodic pressure gradients in wavy-walled channels

The classical problem of secondary flow driven by a sinusoidally varying pressure gradient is extended here to address periodic pressure gradients of complex waveform, which are present in many oscillatory physiological flows. A slender two-dimensional wavy-walled channel is selected as a canonical model problem. Following standard steady-streaming analyses, valid for small values of the ratio ε of the stroke length of the pulsatile motion to the channel wavelength, the spatially periodic flow is described in terms of power-law expansions of ε, with the Womersley number assumed to be of order unity. The solution found at leading order involves a time-periodic velocity with a zero time-averaged value at any given point. As in the case of a sinusoidal pressure gradient, effects of inertia enter at the following order to induce a steady flow in the form of recirculating vortices with zero net flow rate. An improved two-term asymptotic description of this secondary flow is sought by carrying the analysis to the following order. It is found that, when the pressure gradient has a waveform with multiple harmonics, the resulting velocity corrections display a nonzero flow rate, not present in the single-frequency case, which enables stationary convective transport along the channel. Direct numerical simulations for values of ε of order unity are used to investigate effects of inertia and delineate the range of validity of the asymptotic limit ε≪1. The comparisons of the time-averaged velocity obtained numerically with the two-term asymptotic description reveals that the latter remains remarkably accurate for values of ε exceeding 0.5. As an illustrative example, the results of the model problem are used to investigate the cerebrospinal-fluid flow driven along the spinal canal by the cardiac and respiratory cycles, characterized by markedly non-sinusoidal waveforms.

History effects and wall-similarity of non-equilibrium turbulent boundary layers in varying pressure gradient over rough and smooth surfaces

Experimental investigations were conducted on non-equilibrium, turbulent boundary layers over rough and smooth surfaces. A NACA 0012 airfoil was systematically rotated to generate a family of bi-directional pressure fields on the research surface. The rough surface consisted of 2mm tall, staggered, circular cylindrical elements producing flow conditions that were in the fully rough regime. The velocity fields were measured using a custom Pitot-probe boundary layer rake and time-resolved particle image velocimetry (TR-PIV). The primary effect of the roughness was to increase the magnitude of the outer layer and skin friction parameters. Flows over both wall conditions exhibited “history effects” in the integrated boundary layer parameters, which indicates characteristic dependencies on the streamwise flow evolution. Indirect skin friction methods for non-equilibrium rough wall flows were sensitive to the regression fits of the empirical data, which were used in the absence of direct measurements. The effective sandgrain roughness parameter, ks, remained independent of pressure gradient flow history, within the uncertainty of empirical methods used for skin friction determination. Varying levels of wall-similarity were observed in the smooth and rough wall Reynolds stress profiles. Although past evaluations of wall-similarity have suggested that a sufficiently large boundary layer thickness to ks is sufficient for wall-similarity, the present results indicate a need for additional multivariable considerations including matching flow histories and considering local Reynolds numbers measurement resolution.

Effect of heat transfer on peristaltic flow of Newtonian fluid through eccentric cylinders

Heat transfer effect on peristaltic Newtonian flow in an annular region of eccentric cylinders is considered. An approximate solution for temperature and velocity is obtained using perturbation technique. For constant flow rate, the variation of pressure gradient and velocity with respect to several non-dimensional parameters is studied using graphical representation. It is seen in these graphs that velocity, pressure gradient and temperature enhance with raise in eccentricity and amplitude ratio. Heat diffuses with faster rate with depletion in area of cross section eccentric annulus through parameter inner cylinder radius. Also, velocity rises with increase in heat transfer parameters such as Grashof number and heat transfer co-efficient. Thus velocity of peristaltic flow in eccentric annulus enhances rapidly in presence of heat transfer compared to absence of heat transfer. A study of peristaltic flow in concentric annulus in presence of heat transfer is obtained analytically and compared with present study at eccentricity equal to zero, to validate the approximate solution. It is seen that flow rate increases more in case of eccentric annulus compared to concentric in presence of heat transfer. Present study has application in endoscope, which is important to diagnose problems in internal organs. Also, the variation of pressure gradient helps to maintain flow rate which is essential during insertion of catheter into artery.

Hall effects on steady rotating MHD flow of heat generating fluid through porous medium with variable pressure gradient

This research analyses a steady rotating MHD flow in a parallel plate bounded by a porous medium under the influence of a uniform magnetic field of strength B0 that is inclined at an angle of inclination α with normal to the boundaries in the transverse xz-plane, taking hall current into account, along with pressure gradient. The study also examines heat and mass transfer over a continuously moving permeable surface with constant velocity through power-law fluids at rest. To create perturbations, a constant pressure gradient is applied along the plates and non-torsional oscillations are induced in the upper plate, while the lower plate remains at rest. The flow in the porous medium is governed by the Brinkman's equations. Using perturbation techniques, velocity and temperature diagnostic solutions are obtained and discussed computationally with respect to flow parameters through graphs. The paper also evaluates skin friction and Nusselt number, and discusses them in detail with reference to relevant parameters.

Dynamics of unsteady fluid-flow caused by a sinusoidally varying pressure gradient through a capillary tube with Caputo-Fabrizio derivative

This paper presents a study of the unsteady flow of second grade fluid through a capillary tube, caused by sinusoidally varying pressure gradient, with fractional derivative model. The fractional derivative is taken in Caputo-Fabrizio sense. The analytical solution for the velocity profile has been obtained for non-homogenous boundary conditions by employing the Laplace transform and the finite Hankel transform. The influence of order of Caputo-Fabrizio time-fractional derivative and time parameter on fluid motion is discussed graphically.

Pore-scale analysis of two-phase nanofluid flow and heat transfer in open-cell metal foams considering Brownian motion

Simultaneous use of porous media and nanofluids will increase the convective heat transfer multiple times compared to non-porous and pure fluid conditions. Heat transfer and flow transport of nanofluids inside porous media are usually simulated in large-scale with average properties, which are typically highly uncertain. Pore-scale simulation as an alternative approach can capture the characteristics of flow and heat transfer more accurately. Only few studies have been conducted to study nanofluid flow through porous media in pore-scale, and most of them employed single-phase approach without focus on different affective forces. This paper uses a pore-scale approach to investigate the flow characteristics and convective heat transfer of two-phase nanofluid flow in open-cell metal foams (OCMFs). Simulation of fluid flow and heat transfer is achieved by Buongiorno’s model. Therefore, a computational code through the OpenFOAM library that operates by a direct numerical simulation (DNS) approach and the finite volume method (FVM) is used. The momentum, energy, continuity, and nanoparticle distribution equations are discretized, and the SIMPLE algorithm is utilized for pressure and velocity coupling. In the present study, three OCMFs with a constant porosity (0.86) and various pore densities are investigated. Also, variations of pressure gradient, Nusselt number, and Darcy velocity are investigated as a function of pore density (as a geometric parameter), nanoparticle diameter, concentration, and Brownian motion force. The results indicate that the Brownian force enhances the heat transfer in OCMFs from 2% by up to 14% for the nanofluid flowing with 3% nanoparticle concentration. Also, increasing the diameter of nanoparticles reduces the Darcy velocity and heat transfer by up to 4%. On the other hand, increasing particle concentration from 3% to 5%, increases heat transfer by up to 10% and reduces the Darcy velocity by up to 9%. Finally, doubling the pore density demonstrates the complex behavior of the flow patterns, in which the heat transfer increases by up to 30% and permeability and velocity are reduced by up to 70%.

Effect of Ohmic heating on magnetohydrodynamic flow with variable pressure gradient: a computational approach

ABSTRACT Ohmic heating, which significantly affects magnetohydrodynamic flow, is one of the exciting effects to be experienced. This study looks at the significance of Ohmic heating on two-dimensional flow and dissipative heat transfer of a viscous fluid over a flat surface. The mainstream flow is subjected to a pressure gradient and externally oriented inclined magnetic field. An implicit finite difference method has been used to obtain the convergent solutions and the graphical results have been obtained using MATLAB software. A positive correlation is found between temperature and viscous dissipation parameter. Further, the flow encountered higher resistance due to the magnetic field, which is more prominent when the magnetic field is normal to the flow direction .

Effect of pore water on the depressurization of gas hydrate in clayey silt sediments

Marine gas hydrate always occurs in clayey silt sediments partially or fully saturated with water. Pore water is involved in gas hydrate formation and decomposition, which plays an important role in gas recovery from hydrate during depressurization. In this work, the depressurization of methane hydrate in the clayey silt sediments was experimentally investigated in a one-dimensional reactor. The variation of gas production and pressure gradient under the gas-rich and water-rich condition were studied. It was found that the gas production in water-rich environment was much lower than that in gas-rich environment as the movement of hydrate dissociating front is slower in water-rich environment. The permeability of the clayey silt sediments was measured before hydrate formation and after hydrate decomposition, which indicated that there was a large depression in the permeability of the clayey silt sediments after hydrate decomposition, which could be attributed to the hydration swelling of clay minerals with the expansion of diffuse double layer caused by the release of water with lower salinity from gas hydrate dissociation. And the permeability depression of the clayey silt sediments caused by hydrate decomposition was more obvious in water-rich environment, reaching up to ∼50%, and increased with the content of clay minerals. In addition, inorganic salt-based clay stabilizer solution was pre-injected into the clayey silt gas hydrate-bearing sediments before depressurization to mitigate the formation damage during gas hydrate production. The results showed the permeability of the sediments pre-saturated with NH4Cl was maintained at ∼75% of the initial values after gas hydrate decomposition as the exchange of Na+ with NH4+ in sediments was proved to decrease the bound water in montmorillonite interlayers by NMR analysis and inhibit the hydration swelling of clay particles.

Numerical modeling and parametric sensitivity analysis of heat transfer and two-phase oil and water flow characteristics in horizontal and inclined flowlines using OpenFOAM

Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to the temperature difference between the fluids and the surroundings. Heat transfer analysis is very important for the prediction and prevention of deposits in oil and water flowlines, which could impede the flow and give rise to huge financial losses. Therefore, a 3D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to explore the complex mechanisms of the two-phase oil-water transportation and heat transfer in different flowline inclinations. In this work, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is utilized to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns and the local heat transfer coefficients (HTC) for two-phase oil-water flow at different flowlines inclinations (0°, +4°, +7°) are validated by the experimental literature results and the relative errors are also compared. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the performance of the produced two-phase hydrocarbon systems for effective subsea fluid transportation. Thereafter, HTC and flow patterns for oil-water flows at downward inclinations of 4°, and 7° can be predicted by the models. The velocity distribution, pressure gradient, liquid holdup, and temperature variation at the flowline cross-sections are simulated and analyzed in detail. Consequently, the numerical model can be generally applied to compute the global properties of the fluid and other operating parameters that are beneficial in the management of two-phase oil-water transportation.

Numerical study and sensitivity analysis of two-phase oil-water flow and heat transfer in different flowline orientations using OpenFOAM

Evaluating the oil-water temperatures in flowlines is demanding mostly in deep offshore applications where flow assurance issues and dramatic heat transfer are anticipated to occur. Consequently, a 3-D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to investigate the mechanisms of the two-phase oil-water transportation and heat transfer in horizontal and inclined flowlines. In this study, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is employed to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns, local heat transfer coefficients (HTC), and relative errors for two-phase oil-water flow at different flowline orientations (0o, +4o, +7o) are compared with the experimental literature results. The model was also employed to ascertain the effect of input water cuts and flowline inclinations on the flow regimes, and the results were validated in literature with a high accuracy level. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the output temperature and pressure of the produced two-phase hydrocarbon systems. Subsequently, HTC and flow patterns for oil-water flows at different inclinations of −10o, -4o, and +10o can be predicted by the model. The velocity distribution, liquid holdup, pressure gradient, and temperature variation at the flowline cross-sections are simulated and analyzed extensively.

Profile Loss Reduction of High-Lift Turbine Blades With Rough and Ribbed Surfaces

Abstract Transitional boundary layers on low-pressure turbines (LPTs) are prone to separation on the suction surface of the blade under strong local adverse pressure gradients. Intermittent freestream turbulence, periodic wakes shed by the upstream blades, and surface roughness due to in-service degradation of the blades are shown to suppress the separation. Although this generally leads to a profile loss reduction, some of the benefits are offset by a loss increase associated with an increased turbulent wetted area. In this work, we explore a strategy where the losses in both the transitional and turbulent boundary layers can be reduced. In particular, we employ surface roughness in the transitional regime to reduce the separation bubble-related losses and riblets in the turbulent regime to further reduce the losses due to the turbulent wetted area. The efficacy of this ‘rough-riblet blade surface’ is studied using high-fidelity eddy resolving simulations on the configuration of a flat surface subjected to streamwise varying pressure gradients. Two riblet shapes, sawtooth and scalloped, are considered. When compared to the roughness alone configuration, scalloped riblets reduced the skin friction drag by ≈10% and are much more effective than the sawtooth riblets. Through the streamwise evolution of the boundary layer parameters such as trailing edge momentum thickness, maximum turbulent kinetic energy, and Reynolds stresses, the additional losses incurred at the junction between the smooth wall and riblet leading edge are highlighted.

Reply.

We thank Luo et al. for the interest in our manuscript, although all answers to the raised concerns are found in the published manuscript. We agree that baseline liver function correlates with mortality, and we reported in detail no significant differences in baseline characteristics between groups; in particular, Model for End‐Stage Liver Disease, Child‐Pugh score, and age did not differ significantly, whereas albumin was higher in the groups with higher mortality (table 4). Moreover, Luo et al. stated that bilirubinemia >7 mg/dl is not a contraindication for transjugular intrahepatic portosystemic shunt (TIPS) insertion for ascites. This is a dangerous and misleading statement because studies so far have excluded those patients.1 There is evidence that bilirubin below 3 mg/dl is a good biomarker to predict outcome in patients with ascites.2 The strong association of bilirubin levels with post‐TIPS outcome reinforces the recommendation of guidelines for extreme caution for TIPS insertion for ascites if bilirubin >3–5 mg/dl.3,4 Although the quality of stents has improved over time, we included many patients and followed them over a long period of time. Indeed, we have reported the stent types used here (figure S7). Luo et al. raised an important issue of portal hepatic pressure gradient (PPG) variation and changes over time in our patients. It is very unlikely that in the real world outside of clinical trials longitudinal invasive measurements of PPG after TIPS are routinely performed. Ultrasound‐based assessment of patency is the routine follow‐up of choice. Therefore, we try to elaborate an easy‐to‐obtain surrogate marker at the time of TIPS insertion that is applicable for most cases in real‐life practice. Hereby, percentage decrease in PPG is a good marker for response to treatment in ascites control in our cohort. Finally, we agree that in recently compensated cases with ascites as the first decompensating event, the amount of ascites may be prognostic.5 However, all patients in our study received TIPS for therapy of recurrent and refractory ascites. Thus, the cited study does not apply to our patients and therefore the concern is unjustified. We thank again Luo et al. and hope that our answers could address their concerns and avoid confusion in further readers.

Modeling Two-Phase Flow Caused by Hydrate Dissociation in a Reservoir on the Concept of Global Pressure

Summary The classic Darcy’s two-phase flow equation has a variety of mathematically equivalent formats, such as pressure/saturation (PS), two-phase pressure (PP), and global pressure/saturation (GP). Based on the concept of global pressure, we derive a new formulation for two-phase flow caused by hydrate dissociation in porous media, coupled with the mass and energy conservation equations, thereby offering a novel theoretical frame for gas hydrate extraction simulation. The new model provides in-depth insights into complex flow fields: The dissociation of hydrates under thermal stimulation may lead to two flow fields of gas and water with different directions in the reservoir. The simulation results are in good agreement with the recorded data set of Masuda’s and Chong’s experiments, which verifies the correctness and applicability of the new model. Based on numerical simulations of the same hydrate dissociation experiments, the efficiency of the GP method was compared with the PP method published in our previous work. The results show that the GP method has more than two times the timestep size of the PP method for unsteady flow and 1.5 times for steady flow. Furthermore, the relative residual of the GP method is even two orders of magnitude lower than that of the PP method for two-phase flows with complex variations of pressure gradient and fluid flux. Therefore, the GP method is significantly more efficient than the PP method for simulating gas hydrate development. The proposed GP method improves the computational efficiency of hydrate extraction simulation at the laboratory scale and understanding the mechanisms of two-phase flow in reservoirs caused by hydrate dissociation. It may have potential advantages for field-scale simulation of hydrate development, which requires further studies to demonstrate.

Modification of Segment Structure Calculation Theory and Development and Application of Integrated Software for a Shield Tunnel

From the aspect of calculation theory, the beam–spring model method and modified routine method of shield tunnel segment structure calculation were improved, and an efficient integrated software system for segment structure calculation of shield tunnel was developed. The beam–spring method is generally calculated according to the assumption of continuous displacement between beams and joints, and the existing modified routine method assumes that the lateral pressure gradient is constant generally, which does not consider the variation in lateral pressure gradient caused by the difference in the lateral pressure coefficient of soil layers or the water level height, which has a certain deviation from the actual situation. The existing beam–spring method and modified routine method theory were improved, the discontinuous displacement between beams and joints in the beam–spring method was taken into account, and the problem of lateral pressure gradient change in the modified routine method was solved. The calculation software system developed by C# and python programming language was proposed to improve the accuracy and efficiency of segment structure calculation. Based on the actual monitoring data of the internal force of the shield tunnel segment and the adjacent shield tunnel segments under construction in Changsha, China, the segments of the shield tunnel with different cross-section sizes and different hydrogeological conditions are calculated to verify the reliability of the calculation software system. At the same time, combined with the calculation results of the software system and field test data, the stiffness reduction coefficient and equivalent foundation resistance coefficient in the modified routine method were derived to further improve the accuracy of the calculation results, which provided a new idea for the calculation of segment structure of shield tunnel with different diameters under different hydrogeological conditions.

On the Kármán momentum-integral approach and the Pohlhausen paradox: Extension to a cylinder in crossflow with a potential farfield motion

In this work, the Kármán–Pohlhausen (KP) momentum-integral approach based on optimized fourth-order (MX4) polynomial approximations of the velocity and temperature profiles is applied to a classical benchmark problem, namely, that of a cylinder in crossflow with a variable pressure gradient. This enables us to extract closed-form expressions for both hydrodynamic and thermal boundary-layer parameters and then compare the newly found solutions to their counterparts obtained using Pohlhausen's cubic (KP3) and quartic (KP4) polynomials. As usual, the farfield around the cylinder is modeled using potential flow theory and the momentum-integral analysis is paired with Walz's empirical expression for the momentum thickness, which is based on a wide collection of experiments. This procedure permits retrieving explicit relations for the pressure-sensitive KP3, KP4, and MX4 velocity profiles across the boundary layer; one also obtains accurate approximations for the pressure distribution around the cylinder as well as an improved prediction of the separation point, namely, to within 0.87% of the actual location. In this process, refined estimates are produced for several characteristic parameters whose distributions are found to be in favorable agreement with experimental measurements and numerical simulations. These include the disturbance, momentum, and displacement thicknesses as well as the skin friction, pressure, and total drag coefficients. Finally, the thermal analysis is undertaken using both isothermal and isoflux boundary conditions. For each of these cases, closed-form analytical solutions are obtained for the local Nusselt number distribution around the cylinder, and these distributions are found to exhibit noticeably reduced errors relative to their classical values.

Performance Optimization on 3D Diffuser of Volute Pump Using Kriging Model

In order to enhance the hydraulic performance of the volute pump, the Kriging model and genetic algorithm (GA) were used to optimize the 3D diffuser of the volute pump, and the hydraulic performance of the optimized model was compared and analyzed with the original model. The volute pump diffuser model was parameterized by BladeGen software. A total of 14 parameters such as the distance between the leading and trailing edges and the central axis, and the inlet and outlet vane angle were selected as design variables, and the efficiency under the design condition was taken as the optimization objective. A total of 70 sets of sample data were randomly selected in the design space to train and test the Kriging model. The optimal solution was obtained by GA. The shape and inner flow of the optimized diffuser were compared with those of the original diffuser. The research results showed that the Kriging model can effectively establish the high-precision mathematical function between the design variables and the optimization objective, and the R2 value is 0.95356, which meets the engineering needs. The optimized geometry model demonstrated a significant change, the vane leading edge became thinner, and the wrap angle increased. After optimization, the hydraulic performance of the volute pump under design and part-load conditions were greatly improved, the efficiency under design conditions increased by 2.65%, and the head increased by 0.83 m. Furthermore, the inner flow condition improved, the large area of low-speed and vortex disappeared, the pressure distribution in the diffuser was more reasonable, and the pressure gradient variation decreased.

On the added value of statistical post-processing of regional climate models to identify homogeneous patterns of summer rainfall anomalies in Germany

A fuzzy classification scheme that results in physically interpretable meteorological patterns associated with rainfall generation is applied to classify homogeneous regions of boreal summer rainfall anomalies in Germany. Four leading homogeneous regions are classified, representing the western, southeastern, eastern, and northern/northwestern parts of Germany with some overlap in the central parts of Germany. Variations of the sea level pressure gradient across Europe, e.g., between the continental and maritime regions, is the major phenomenon that triggers the time development of the rainfall regions by modulating wind patterns and moisture advection. Two regional climate models (REMO and CCLM4) were used to investigate the capability of climate models to reproduce the observed summer rainfall regions. Both regional climate models (RCMs) were once driven by the ERA-Interim reanalysis and once by the MPI-ESM general circulation model (GCM). Overall, the RCMs exhibit good performance in terms of the regionalization of summer rainfall in Germany; though the goodness-of-match with the rainfall regions/patterns from observational data is low in some cases and the REMO model driven by MPI-ESM fails to reproduce the western homogeneous rainfall region. Under future climate change, virtually the same leading modes of summer rainfall occur, suggesting that the basic synoptic processes associated with the regional patterns remain the same over Germany. We have also assessed the added value of bias-correcting the MPI-ESM driven RCMs using a simple linear scaling approach. The bias correction does not significantly alter the identification of homogeneous rainfall regions and, hence, does not improve their goodness-of-match compared to the observed patterns, except for the one case where the original RCM output completely fails to reproduce the observed pattern. While the linear scaling method improves the basic statistics of precipitation, it does not improve the simulated meteorological patterns represented by the precipitation regimes.

Step-induced transition in compressible high Reynolds number flow

The effect of sharp forward-facing steps on boundary-layer transition is systematically investigated in this work in combination with the influence of variations in Mach number, Reynolds number and streamwise pressure gradient. Experiments have been conducted in a quasi-two-dimensional flow at Mach numbers up to 0.77 and chord Reynolds numbers up to 13 million in the Cryogenic Ludwieg-Tube Göttingen. The adopted experimental set-up allows an independent variation of the aforementioned parameters and enables a decoupling of their respective effects on the boundary-layer transition, which has been measured accurately and non-intrusively by means of a temperature-sensitive paint. The functional relations determined between a non-dimensional transition parameter and the non-dimensional step parameters allow the step effect on transition to be isolated from the influence of variations in Mach number, Reynolds number and pressure gradient. Criteria for acceptable heights of forward-facing steps on natural laminar flow surfaces for the examined test conditions are derived from the present functional relations. The measured transition locations are also correlated with the results of linear, local stability analysis for the smooth configuration, enabling the estimation of the step-induced increment of the amplification factor ΔN of Tollmien–Schlichting waves, which can be incorporated in the eN transition prediction method.

Prediction of pressure gradient for oil-water flow: A comprehensive analysis on the performance of machine learning algorithms

Pressure gradient (PG) in liquid-liquid flow is one of the key components to design an energy-efficient transportation system for wellbores. This study aims to develop five robust machine learning (ML) algorithms and their fusions for a wide range of flow patterns (FP) regimes. The MLs include Support Vector Machine (SVM), Gaussian Process (GP), Random Forest (RF), Artificial Neural Network (ANN), k-Nearest Neighbor (kNN), and fusions of these five MLs. A total of eleven hundred experimental data points for nine FPs (two stratified and seven dispersed patterns) in horizontal wellbores are used to develop the MLs. The MLs' performance is evaluated using the metrics including mean absolute percentage error (MAPE), median absolute percentage error (MdAPE), coefficient of variation of root mean squared error (CV-RMSE), and adjusted coefficient of determination. The evaluation metrics are cross-validated using a repeated train-test split strategy. Seven important predictor variables are identified using a supervised feature selection approach: oil and water velocities, FP, input diameter, oil and water density, and oil viscosity. The results show that the high PG prediction accuracy can be achieved using GP compared to other MLs except for the ML-fusions (p < 0.05). A Friedman's test and Wilcoxon Sign-Rank post hoc analysis with Bonferroni correction show that PG prediction errors using GP are significantly lower than using the ANN model (p < 0.05). The values are 18.44 % and 23.9 % for CV-RMSE, 11.6 % and 10.06 % for MAPE, and 7.5 % and 6.75 % for MdAPE, using ANN and GP, respectively. While the previous studies mostly used ANN to demonstrate the capability of MLs to predict PG over the mechanistic or correlation-based models, the present research has shown that GP is even better than ANN using a wide range of FPs and a large data set. • Machine-learning algorithms are developed to predict the pressure gradient. • The Gaussian Process model produces significantly lower prediction error. • The median absolute percentage error using Gaussian Process is 6.75 %. • More than 95 % variation of pressure gradient can be explained using seven variables.

INTENSIFICATION AND STUDY OF HEAT TRANSFER AND FRICTION IN THE PLATE HEATING SURFACES OF THE KMS-2 AIR HEATER WITH A PRESSURE GRADIENT

A numerical study of heat transfer and friction in the heat exchanger channels in the presence of a variable pressure gradient is performed. The research was carried out in software complexes (Code_Saturne, Salome). The results of the validation of the research method are presented and they showed that the deviation of the numerical simulation results from the calculation data according to the known criterion equations is within the error of generalization of the experimental data by the criterion equations. According to the results of studies at Red=3000, Red=4177, Red=6000, it was found that the average value of the heat transfer coeffi cient of the channel of variable cross-section is up to 20 % higher than for the channel at dp/dx0. At the same time, the thermal-hydraulic effi ciency of the alternating channel (L=117 mm, l=58.5 mm, n=2) in the initial section at x =0...0.08 is lower than in the channel with dp/dx&gt;0 by 26.7 %, and at x =0.08...1 it is higher by 5 ... 15 %, at dp/dx