Flow Boundary Conditions Research Articles

Navier-Stokes characteristic boundary conditions for high-enthalpy compressible flows in thermochemical non-equilibrium

This fundamental study presents Navier-Stokes characteristic boundary conditions (NSCBCs) for high-enthalpy hypersonic flows in thermochemical non-equilibrium. In particular, the relevant locally one-dimensional inviscid (LODI) relations are derived within a two-temperature framework for high-enthalpy hypersonic flows undergoing finite-rate thermochemical processes, including air dissociation and vibrational relaxation. Using these LODI relations, a set of NSCBCs are proposed and later demonstrated in canonical test cases, including the interaction of homogeneous isotropic turbulence with a shock wave subject to high-enthalpy thermochemical non-equilibrium effects.

The comprehensive research on the transcritical CO2 thermal management system used in thermostatic transport vehicles

Natural fluid CO2 has become the preferred target of refrigerant alternative in the electrified transportation field in recent years to replace positive temperature coefficient (PTC) heaters, reduce energy consumption, and respect the international ban on Hydrofluorocarbons (HFCs) refrigerants. Thermostatic transport vehicles (TTVs) are well suited to exploit the benefits of CO2 due to their working conditions with a broad range of ambient temperatures, extensive transit distances, and substantial heating capacity requirements in cold climates. In this paper, a transcritical CO2 heat pump air-conditioning system used in TTV was constructed initially with proper control logic. Then following the assessment of the system’s steady-state performance, the dynamic operation process under high thermal inertia was thoroughly examined and analyzed in detail. Ultimately, the optimization of the dynamic response process was realized under varying heat flow boundary conditions. The primary results demonstrated that the rationally designed CO2 thermal management system performed admirably in various operating conditions, particularly in the heating mode where the coefficient of performance (COP) exceeded 3.2. Addressing the high-frequency fluctuation caused by the cargo thermal inertia, the temperature could be maintained with only two starts and stops within 3×105 seconds when the system control logic was refined. The optimized thermal management system of TTV efficiently allowed cargo to achieve the proper temperature as quickly as possible and sustain stability. This study provides an effective theoretical basis for the promotion of the transcritical CO2 thermal management system in the field of TTVs.

Effects of lubricant rheology and flow turbulence on the dynamic properties of hydrodynamic bearing

The present numerical investigation, which takes into account the coexisted consequence of the turbulence domain and non-Newtonian flow rheology, predicts the dynamic properties of a finite hydrodynamic bearing. Under the proper flow boundary conditions, the turbulence (linear) and non-Newtonian hypotheses have revised the Continuity and Navier–Stokes equation. The finite element approach is acclimated to calculate the clearance extent of the finite hydrodynamic bearing using the Galerkin approach and a sturdy iteration strategy. The cylindrical coordinate's versions of continuity and momentum equations are bestowed for the lubricant field of the finite hydrodynamic bearing, postulating the turbulence domain and non-Newtonian flow rheology. Dynamic properties of a finite hydrodynamic bearing have been enumerated using cross-coupled and direct lubricant-film bearing coefficients, whirl ratio and critical mass at various eccentricity ratios for different ranges of Reynolds numbers and different values of flow behavior index of the non-Newtonian rheological model. In comparison to perfect turbulence and non-Newtonian rheological status, the mixed regime demonstrated improved properties. The direct and cross-coupled lubricant-film bearing coefficients are improved by 12.28% and 20.85% respectively while critical mass is enhanced by 20.55% at selected values of Reynolds number and power-law index. The proposed severe fluid film domain improves the stability of finite hydrodynamic bearings significantly.

Poromechanics Modeling Forecasts Production, Analyzes Productivity Decline

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 212200, “Accurate Production Forecasting and Productivity Decline Analysis Using Coupled Full-Field and Near-Wellbore Poromechanics Modeling,” by Yan Li, Bin Wang, and Jiehao Wang, Chevron, et al. The paper has not been peer reviewed. _ Productivity index (PI) decline is caused by different mechanisms in both the wellbore region and the far field. Damage in the wellbore region can be simulated by detailed wellbore modeling. A newly developed full-field and near-wellbore poromechanics coupling scheme is used in the complete paper to model PI degradation against time. Near-wellbore damage and field and well interactions are identified when applying the coupling scheme for a deepwater well. History matching, production forecasting, and safe drawdown limits are derived for operational decisions. Full-Field Reservoir Model and Near-Wellbore Poromechanics Model Coupling Full-field and near-wellbore modeling involves coupling the simulation of a full-field reservoir model with one or more near-wellbore poromechanics models. In the coupled simulation, the full-field reservoir model dictates the changing flow or thermal boundary conditions for the embedded near-wellbore models. Meanwhile, near-wellbore phenomena affect well productivity in the full-field reservoir model, altering the flow and thermal boundary conditions on all near-wellbore models in the same field. While capturing the dynamic interactions between the full-field model and all embedded near-wellbore models is of vital importance, the traditional near-wellbore modeling work flow considers only one-way coupling. This work flow is labor-intensive and lacks the dynamic interplay between the reservoir and near-wellbore models. A novel near-wellbore coupling framework is developed to automate data exchange and capture dynamic interactions between the full-field model and the near-wellbore model. In the full-field reservoir and geomechanics coupling applications, only a reservoir simulator solves reservoir flow and thermal equations and a geomechanics simulator solves solid mechanics equations. The reservoir and geomechanics simulators exchange 3D field data. Because solid mechanics equations are quasistatic, the geomechanics simulator does not take timesteps in full-field coupling. In near-wellbore coupling, however, both reservoir and geomechanics simulators solve reservoir flow and thermal equations. The near-wellbore geomechanics model also may solve solid mechanics or other equations coupled to flow or thermal equations in the near-wellbore model. All physics are included in the near-wellbore model for the coupling. Both field properties (3D) and transient boundary conditions (2D) must be mapped onto the near-wellbore model. It is important to ensure that the full-field and near-wellbore models are consistent. A 3D data-mapping module is developed to map flow and rock properties and initial conditions from the full-field model to the near-wellbore model. During the simulation, the transient pressure/temperature boundary conditions (2D) at the external boundary of the near-wellbore model must be mapped from the full-field model to the near-wellbore model to update transient boundary conditions. The automated data mapping in the coupling scheme eliminates the need for manual mapping of field properties and transient boundary conditions.

A hybrid data-driven framework for loss prediction of MCA airfoils

The Multi Circular Arc airfoils family has gained significant popularity in axial compressor design due to its capability to achieve higher pressure ratios with lower losses compared to conventional NACA airfoils. However, modeling their aerodynamic performance for transonic axial compressors remains a challenging task. This research addresses this issue by developing a data driven model for Multi Circular Arc airfoils loss correlation utilizing an automated blade-to-blade flow solver, StarCCM, under specific flow boundary conditions. Since the data built in this research includes high dimensionality, it is subjected to dimensionality reduction using Principal Component Analysis while retaining as much of its important information as possible. What sets our research apart is the comparative analysis of hybrid machine learning approaches. We specifically combine classification techniques based on shock wave formation on the airfoil’s suction side with Multi-Layer Perceptron neural network methods. This unique combination allows for a comprehensive prediction of MCA loss as the main objective of the research. The results demonstrate that this surrogate-based approach provides accurate loss model with 97% of precision error for the classification which results in 0.99 and 0.94 of R2 for loss model related to the transonic and subsonic airfoils loss prediction.

Long-wave instabilities of sloping stratified exchange flows

We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin–Helmholtz instability and Holmboe wave instability, in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$ , which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number, Prandtl number, base flow profile and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin–Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

Entropy generation analysis of a micropolar fluid in a corrugated channel with convective and slip conditions

This study focuses on examining the entropy generation in a corrugated channel, considering convective boundary conditions and slip flow, with a micropolar fluid. The governing equations for the micropolar fluid flow, including linear and angular momentum equations, as well as the energy equation, are solved using the perturbation technique. The effects of corrugations, slipping flow, and convective boundary conditions on the entropy generation and the flow behavior are analyzed. The results show that the entropy generation enhanced with the corrugation amplitude, while it reduced for the slip flow. Moreover, entropy generation is affected by the convective boundary conditions, and it is an increasing function with the convective heat transfer coefficient. Additionally, the study demonstrates that micropolar fluid exhibits distinct flow characteristics in comparison to classical Newtonian fluids. These findings have practical implications for the design and optimization of microfluidic devices, as well as for gaining insights into the behavior of micropolar fluids in various engineering applications.

Numerical simulations on the flow regime characteristics of horizontal pneumatic conveying using CFD-DEM

To elucidate the flow regime characteristics and boundary conditions of gas-solid two-phase flow in horizontal pipe pneumatic conveying, the flow characteristics were studied based on the four-way coupled CFD-DEM method. Based on the experimental verification of flow regimes, the flow characteristics at different superficial gas velocities were analyzed from three perspectives. The results showed that the mean value of the pressure at the inlet and the standard deviation of the pressure fluctuation decreased with the superficial gas velocity, as well as the mass of the standard volume particles. The conveying flow regimes of slug flow, dune flow and stratified flow in the pipe were presented in turn, and the particle distribution in the pipe gradually shifted from filling the entire pipe to the bottom of the pipe. The particle velocity in the middle part of the pipe was the highest for slug flow.

Numerical investigation of flow past a cylinder using cumulant lattice Boltzmann method

This paper presents simulations of flow past a circular cylinder within the subcritical Reynolds number (Re) range from 3900 to 2 × 105, utilizing the parameterized cumulant lattice Boltzmann model. In this study, a three-dimensional characteristic boundary condition for incompressible flow has been integrated into the lattice Boltzmann method at the outflow boundary to minimize spurious reflection. The flow field, wake statistics, hydrodynamic force, and power spectra results of Re = 3900 from the cumulant lattice Boltzmann model are exhaustively compared with the laboratory data and other numerical models. Relative to other numerical models employing turbulence closure, the cumulant lattice Boltzmann simulations demonstrate enhanced agreement with the experimental data even with relatively coarser grid resolution. The resolution-spanning feature for the cumulant lattice Boltzmann model in turbulent flows, without using explicit turbulence model, aligns with the previous benchmark case studies. The stability-preserving regularization process in the present model is analyzed. Results indicate that the influence of the regularization parameter is mitigated with improved grid resolution. A specific regularization parameter for flow around cylinder simulations is recommended. Variations in flow properties and hydrodynamic forces within the subcritical Reynolds number range of 3900 to 2 × 105 are analyzed. The results confirm that the parameterized cumulant lattice Boltzmann model can accurately simulate practical engineering flows, characterized by complex separation and recirculation, within the subcritical range. Moreover, the computational efficiency and parallel scalability are compared with other numerical methods.

On the computation of the Basal Envelope Surface of Talwegs using the Analytic Element Method

The stream network is a major feature of a landscape, conveying water, sediment, and solute from hillslopes to the ocean. Noticeably, from a large-scale point of view, the elevation of the talwegs of perennial streams is an important head boundary condition for both surface and groundwater flow originating from hillslopes. Assuming a wireframe (1D) representation of talweg lines, the problem of interpolating elevation between talwegs has received attention for applications such as flood mapping using Height Above Nearest Drainage (HAND, [Nobre et al., 2011]), or groundwater level interpolation in low-conductivity aquifer systems. In this study we propose an alternate definition of this large-scale base level concept introduced by [Wyns et al., 2004], namely the Basal Envelope Surface of Talwegs (BEST) and the associated Height Above the Basal Envelope Surface of Talwegs (HABEST), along with a procedure to compute it using the Analytic Element Method (AEM). It can be defined as the head distribution satisfying Laplace equation (Darcy flow with vanishing divergence), with stream segments set as Dirichlet boundary conditions. The BEST is thus the real part of a complex analytic (holomorphic) function which can be modeled using analytic slit elements, with very low computational requirements and without the need for kriging, as it is often seen in the literature. This analytic model is extended to the case of a non-zero, uniform divergence flow (head distribution satisfying a Poisson equation) which can be useful to analyse groundwater levels at catchment scale.

Hemodynamic Insights into Abdominal Aortic Aneurysms: Bridging the Knowledge Gap for Improved Patient Care

Background: Abdominal aortic aneurysms (AAAs) present a formidable public health concern due to their propensity for localized, anomalous expansion of the abdominal aorta. These insidious dilations, often in their early stages, mask the life-threatening potential for rupture, which carries a grave prognosis. Understanding the hemodynamic intricacies governing AAAs is paramount for predicting aneurysmal growth and the imminent risk of rupture. Objective: Our extensive investigation delves into this complex hemodynamic environment intrinsic to AAAs, utilizing comprehensive numerical analyses of the physiological pulsatile blood flow and realistic boundary conditions to explore the multifaceted dynamics influencing aneurysm rupture risk. Our study introduces novel elements by integrating these parameters into the overall context of aneurysm pathophysiology, thus advancing our understanding of the intricate mechanics governing their evolution and rupture. Methods: Conservation of mass and momentum equations are used to model the blood flow in an AAAs, and these equations are solved using a finite volume-based ANSYS Fluent solver. Resistance pressure outlets following a three-element Windkessel model were imposed at each outlet to accurately model the blood flow and the AAAs’ shear stress. Results: Our results uncover elevated blood flow velocities within an aneurysm, suggesting an augmented risk of future rupture due to increased stress in the aneurysm wall. During the systole phase, high wall shear stress (WSS) was observed, typically associated with a lower risk of rupture, while a low oscillatory shear index (OSI) was noted, correlating with a decreased risk of aneurysm expansion. Conversely, during the diastole phase, low WSS and a high OSI were identified, potentially weakening the aneurysm wall, thereby promoting expansion and rupture. Conclusion: Our study underscores the indispensable role of computational fluid dynamic (CFD) techniques in the diagnostic, therapeutic, and monitoring realms of AAAs. This body of research significantly advances our understanding of aneurysm pathophysiology, thus offering pivotal insights into the intricate mechanics underpinning their progression and rupture, informing clinical interventions and enhancing patient care.

Heat transfer enhancement of nanofluids in a four-blade LPD static mixer

The heat transfer performance of nanofluids within a four-bladed LPD static mixer was investigated using a combination of experiments and simulations under constant heat flow boundary conditions with Re ranging from 3519 to 16719. Al2O3-H2O nanofluid with volume fraction φ = 0.3 % was prepared experimentally and the stability of the nanofluid was analyzed by settling observation method and Dynamic light scattering (DLS). Numerical simulations were adopted to analyze the effects of nanoparticle types, volume fractions and types of mixing nanofluids on the heat transfer enhancement inside the four-bladed LPD static mixer. The results show that the maximum error of Nusselt number (Nu) between the predicted values of Mixture model and experimental values was 7.39 %. Because of the combined heat transfer performance coefficient PEC more than 1 with the increasing of Re, the mixers with α = 30° and β = 45° instead of KSM could be recommended when Re > 5279. The PEC of Al2O3-H2O nanofluids gradually increases with the increasing φ. At the same Re and φ, the flied synergy number Fc and PEC of the mixed nanofluids are 1.01–1.47 times and 1.15–3.35 times higher than those of the single nanofluids.

Validation of wall boundary conditions for simulating complex fluid flows via the Boltzmann equation: Momentum transport and skin friction

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited the extent of numerical validation studies to simple, often two-dimensional, flow problems. Recent algorithmic advancements for the Boltzmann–Bhatnagar–Gross–Krook equation introduced by the authors [Dzanic et al., J. Comput. Phys. 486, 112146 (2023)], consisting of a highly efficient high-order spatial discretization augmented with a discretely conservative velocity model, have made it feasible to accurately simulate unsteady three-dimensional flow problems across both the rarefied and continuum regimes. This work presents a comprehensive evaluation and validation of wall boundary conditions across a variety of flow regimes, primarily for the purpose of exploring their effects on momentum transfer in the low Mach limit. Results are presented for a range of steady and unsteady wall-bounded flow problems across both the rarefied and continuum regimes, from canonical two-dimensional laminar flows to unsteady three-dimensional transitional and turbulent flows, the latter of which are the first instances of wall-bounded turbulent flows computed by directly solving the Boltzmann equation. We show that approximations of the molecular gas dynamics equations can accurately predict both non-equilibrium phenomena and complex hydrodynamic flow instabilities and show how spatial and velocity domain resolution affect the accuracy. The results indicate that an accurate approximation of particle transport (i.e., high spatial resolution) is significantly more important than particle collision (i.e., high velocity domain resolution) for predicting flow instabilities and momentum transfer consistent with that predicted by the hydrodynamic equations and that these effects can be computed accurately even with very few degrees of freedom in the velocity domain. These findings suggest that highly accurate spatial schemes (e.g., high-order schemes) are a promising approach for solving molecular gas dynamics for complex flows and that the direct solution of the Boltzmann equation can be performed at a reasonable cost when compared to hydrodynamic simulations at the same level of resolution.

Mechanisms of hydrodynamic parameters regulating sinking volume in ship navigation

Abstract Ships navigating in the water need to consider their safety first, and the abnormal sinking amount of the ship will be a great threat to the navigation safety of the ship. In this paper, the relationship between hydrodynamic parameters and ship sinking amount is studied in order to realize the reasonable control of the ship by setting different hydrodynamic parameters so as to ensure the safety of ship navigation. Through Taylor’s formula to calculate the hydrodynamic parameters of the ship navigation, and through the combination of potential flow theory and boundary conditions, finally using Green’s function method in the surface element method, it is calculated that the sinking amount of the ship from hydrodynamic parameter 35000 to hydrodynamic parameter 3200000 is a gently increasing trend, and in the case of h/d=2.5, the ship’s speed Fn=0.25, the ship’s sinking amount appears to be oscillating changes.

Lumped model for a quasi-continuously operating open metal hydride heat pump system

Hydrogen as a potential future fuel for fuel cell vehicles is mostly stored in high-pressure tanks at 350 or 700 bar, which requires energy-intense compression of typically 15 % of the lower heating value. For the recovery of parts of the compression work, a promising possibility is the usage of an open metal hydride heat pump. Similarly to other sorption-based heat pump systems, in order to reach high specific thermal power, it is crucial to find a trade-off in the design and operation of the reactor between two main factors: enabling fast reaction dynamics and reducing losses due to temperature switches. The present work introduces a steady-state model with lumped metal hydride and reactor mass considering one-dimensional heat and mass transfer, which is able to quickly predict the corresponding specific thermal power and efficiency. A special focus is on the calculation of the non-complete conversion due to an operation at constant gas flow. The model is validated with existing experimental data over a broad range of operation conditions in terms of metal hydride specific hydrogen mass flow (1.6–7.6 gH2 min−1 kgMH-1) and temperature boundary conditions (cold side temperature: 13–25 °C, hot side temperature: 24–42 °C). It is capable of describing the specific thermal power and the efficiency as the two main performance indicators with a suitable accuracy. To give an example of the applicability of the developed tool, a generic discussion of the performance limitations of the selected reactor design is carried out, indicating that the reactor of the validation experiment is mainly mass transport limited.

Analysis of the absorbing boundary condition for the Maxwell fluid flow over a semi-infinite plate with considering the magnetic field

In this paper, we analyze the flow mechanism of the Maxwell fluid over a semi-infinite plate. To handle the semi-infinite boundary, the artificial boundary method is employed and the absorbing boundary condition in the form of convolution is derived. Besides, the stability of the absorbing boundary condition is analyzed. Solutions are obtained numerically using the finite difference method and the accuracy is verified by introducing a source term to construct the exact solution. To demonstrate the validity and reasonableness of the absorbing boundary condition, a comparison with the direct truncation boundary is discussed. Our study examines the effects of the magnetic field, relaxation parameter, oscillation frequency and plate amplitude on the velocity distribution and flow mechanism of the Maxwell fluid.

Thermal analysis of thermoelectric active cooling including external thermal resistances

Thermoelectric active cooling uses nontraditional thermoelectric materials with high thermal conductivity, high thermoelectric power factor, and relatively low figure of merit (ZT) to transfer large heat flows from a hot object to a cold heat sink. However, prior studies have not considered the influence of external thermal resistances associated with the heat sinks or contacts, making it difficult to design active cooling thermal systems or compare the use of low-ZT and high-ZT materials. Here, we perform a non-dimensionalized analysis of thermoelectric active cooling under forced heat flow boundary conditions, including arbitrary external thermal resistances. We identify the optimal electrical currents to minimize the heat source temperature and find the crossover heat flows at which low-ZT active cooling leads to lower source temperatures than high-ZT and even ZT→+∞ thermoelectric refrigeration. These optimal parameters are insensitive to the thermal resistance between the heat source and thermoelectric materials, but depend strongly on the heat sink thermal resistance. Finally, we map the boundaries where active cooling yields lower source temperatures than thermoelectric refrigeration. For currently considered active cooling materials, active cooling with ZT < 0.1 is advantageous compared to ZT→+∞ refrigeration for dimensionless heat sink thermal conductances larger than 15 and dimensionless source powers between 1 and 100. Thus, our results motivate further investigation of system-level thermoelectric active cooling for applications in electronics thermal management.

Impact of thermodynamical rotational flow of cerebrospinal fluid in the presence of elasticity

ObjectiveTo explore the experimental justification of cerebrospinal fluid (CSF) amplitude and elastic fluctuations of ventricles, we extend our previous computational study to models with rotational flow and suitable boundary conditions. In the present study, we include an elastic effect due to the interaction with the thermal solutal model which accounts for CSF motion which flows rotationally due to hydrocephalus flows within the spinal canal.MethodsUsing an analytical pertubation method, we have attempted a new model to justify CSF flow movement using the influences of wall temperature difference.ResultsThis paper presents results from a computational study of the biomechanics of hydrocephalus, with special emphasis on a reassessment of the parenchymal elastic module. CSF amplitude in hydrocephalus patients is 2.7 times greater than that of normal subjects.ConclusionsThis finding suggests a non-linear mechanical system to present the hydrocephalic condition using a numerical model. The results can be useful to relieve the complexities in the mechanism of hydrocephalus and can shed light to support clinically for a convincing simulation.

Developing a Computational Fluid Dynamics-Finite Element Method Model to Analyze Thermal-Mechanical Stresses in a Heavy-Duty Medium-Speed Diesel Engine Piston During Warm-Up

Abstract Pistons play a vital role in internal combustion engines, affecting both performance and reliability, and are subjected to intense thermal-mechanical loads that have become more challenging due to improved engine efficiency and power. This study examines the thermal and mechanical stress experienced by a piston in a heavy-duty medium-speed diesel engine during warm-up. The heavy-duty diesel engines are typically used in heavy trucks, locomotives, and ships. A combination of computational fluid dynamics, finite element method, and matlab was used to consider factors such as oil temperature and flowrate, coolant temperature, component temperature, and boundary conditions during engine transient conditions. The results highlight the significant variations in the thermal and mechanical stress on the piston, particularly in the piston head under different warming-up conditions. It is noted that the variation in oil temperature is a crucial factor affecting the thermal stress on the piston. Low oil temperature can result in reduced heat exchange coefficient and inadequate cooling of the piston due to low flowrate of the cooling oil. During engine warm-up, both thermal and combined stresses reach maximum values and then decrease when the engine reaches stable operating conditions. By selecting appropriate warming-up modes, the quality of the warm-up process and the strength and longevity of the engine could be improved. This study also provides useful insights for technicians to prevent critical conditions that may damage the piston and reduce its strength and lifespan.

Analysis of Steady Groundwater Flow in Confined Aquifer Due to Long-Strip Pit Dewatering with Suspended Cut-Off Wall

This study investigates the steady flow resulting from dewatering by a partially penetrating well in a confined aquifer with a cut-off barrier. By considering flow in both horizontal and vertical directions and incorporating the barrier and pumping well as flow boundary conditions, separate mathematical models are established for the inside and outside of the cut-off barrier. The interaction between these zones is ensured through continuous conditions along the opening of the two zones. A semi-analytical solution is derived for the problem using the finite Fourier cosine transform and boundary transformation methods. The effectiveness of the method is verified by comparing it with the finite element numerical results and pumping test data respectively. Based on the proposed solutions, we proceed to analyze the influence of some relevant factors: the extent to which the cut-off wall is embedded within the confined aquifer, the depth of the partially penetrating well, and the distance to the lateral head boundary. Results indicate that a greater depth of the cut-off wall leads to a reduced pumping rate requirement for achieving a desired drawdown of the confined water level within the excavation. According to the presented solution, placing pumping wells near the top of the confined aquifer in excavation dewatering projects can facilitate a faster reduction of the confined water head at the excavation bottom. Additionally, proximity of lateral head boundary could significantly impact dewatering, with closer boundaries reducing dewatering effectiveness due to improved aquifer recharge. Finally, the use of the Fourier method showcases impressive convergence properties in the approach presented in this study. The computed results maintain a high level of approximation quality, even with extremely coarse discretization.