Outlet Boundary Conditions Research Articles

Axial Flow Fan Performance in a Forced Draught Air-Cooled Heat Exchanger for a Supercritical Carbon Dioxide Brayton Cycle

Abstract An axial flow cooling fan has been designed for use in a concentrated solar power plant. The plant is based on a supercritical carbon dioxide (sCO2) Brayton cycle, and uses a forced draft air-cooled heat exchanger (ACHE) for cooling. The fan performance has been investigated using both computational fluid dynamics (CFD) and scaled fan tests. This paper presents a CFD model that integrates the fan with the heat exchanger. The objective is to establish a foundation for similar models and to contribute to the development of efficient ACHE units designed for sCO2 power cycles. The finned-tube bundle is simplified, with a Porous Media Model representing the pressure drop through the bundle. Pressure inlet and -outlet boundary conditions are used, meaning the air flowrate is solved based on the fan and tube bundle interaction. The flowrate predicted by the CFD model is 0.5% higher than the analytical prediction, and 3.6% lower than the design value, demonstrating that the assumptions used in the design procedure are reasonable. The plenum height is also found to affect the flowrate, with shorter plenums resulting in higher flow rates and fan efficiencies, and longer plenums resulting in more uniform cooling air flow.

Patient-specific compliant simulation framework informed by 4DMRI-extracted pulse wave Velocity: Application post-TEVAR

We introduce a new computational framework that utilises Pulse Wave Velocity (PWV) extracted directly from 4D flow MRI (4DMRI) to inform patient-specific compliant computational fluid dynamics (CFD) simulations of a Type-B aortic dissection (TBAD), post-thoracic endovascular aortic repair (TEVAR). The thoracic aortic geometry, a 3D inlet velocity profile (IVP) and dynamic outlet boundary conditions are derived from 4DMRI and brachial pressure patient data. A moving boundary method (MBM) is applied to simulate aortic wall displacement. The aortic wall stiffness is estimated through two methods: one relying on area-based distensibility and the other utilising regional pulse wave velocity (RPWV) distensibility, further fine-tuned to align with in vivo values. Predicted pressures and outlet flow rates were within 2.3 % of target values. RPWV-based simulations were more accurate in replicating in vivo hemodynamics than the area-based ones. RPWVs were closely predicted in most regions, except the endograft. Systolic flow reversal ratios (SFRR) were accurately captured, while differences above 60 % in in-plane rotational flow (IRF) between the simulations were observed. Significant disparities in predicted wall shear stress (WSS)-based indices were observed between the two approaches, especially the endothelial cell activation potential (ECAP). At the isthmus, the RPWV-driven simulation indicated a mean ECAP>1.4 Pa-1 (critical threshold), indicating areas potentially prone to thrombosis, not captured by the area-based simulation.RPWV-driven simulation results agree well with 4DMRI measurements, validating the proposed pipeline and facilitating a comprehensive assessment of surgical decision-making scenarios and potential complications, such as thrombosis and aortic growth.

Numerical assessment of using various outlet boundary conditions on the hemodynamics of an idealized left coronary artery model.

Vascular diseases are greatly influenced by the hemodynamic parameters and the accuracy of determining these parameters depends on the use of correct boundary conditions. The present work carries out a two-way fluid-structure interaction (FSI) simulation to investigate the effects of outlet pressure boundary conditions on the hemodynamics through the left coronary artery bifurcation with moderate stenosis (50%) in the left anterior descending (LAD) branch. The Carreau viscosity model is employed to characterise the shear-thinning behaviour of blood. The results of the study reveal that the employment of zero pressure at the outlet boundaries significantly overestimates the values of hemodynamic variables like wall shear stress (WSS), and time-averaged wall shear stress (TAWSS) compared with human healthy and pulsatile pressure outlet conditions. However, the difference between these variables is marginally low for human healthy and pulsatile pressure outlets. The oscillatory shear index (OSI) remains the same across all scenarios, indicating independence from the outlet boundary condition. Furthermore, the magnitude of negative axial velocity and pressure drop across the plaque are found to be higher at the zero pressure outlet boundary condition.

Unsupervised physics-informed deep learning for assessing pulmonary artery hemodynamics

Deep learning advancements have significantly benefited medical applications. One such helpful application is noninvasive fractional flow reserve (FFR) evaluation along the pulmonary artery tree, which aids in planning optimal balloon pulmonary angioplasty. This study proposes a surrogate model that employs an unsupervised physics-informed neural network (UPNN) to predict FFR based on pulmonary CT angiography. To ensure the UPNN strictly follows the unique solution of the governing equations, we implemented a hard boundary conditions enforcement approach. Subsequently, a finite difference convolutional filter was developed to enhance connectivity among neighboring points. This allows the neural networks to propagate boundary conditions into the unseen vessel interior and perceive the geometric structure of the computational domain. We also introduced regularization constraints on the three components contributing to pressure drop within the artery tree. A total of 4500 synthetic pulmonary artery trees were used to train the UPNN with impedance outlet boundary conditions. We found that the limits of agreement of FFR trained by UPNN ranged from −0.05 to 0.04 with computational fluid dynamics (CFD) simulation results. The testing results showed that the correlation coefficient between FFR predicted by UPNN and CFD were 96.1% and 94.7% for synthetic and patient-specific data, respectively. Using invasive FFR as reference, the accuracy of FFR predicted by UPNN and CFD was 81.4% and 84.8%, respectively. These results demonstrate that our UPNN-based surrogate model’s performance in evaluating FFR aligns closely with CFD simulations.

A fully coupled Pressure-Based method for compressible flows at all Mach numbers

When extending the fully coupled pressure-based method to resolve compressible flows, the effective treatment of the boundary conditions is crucial due to the inherent characteristics of compressible flows. Failure to properly account for this can result in numerical instability and divergence. In this article, a detailed treatment of boundary conditions for compressible flows has been formulated in terms of the boundary face’s contribution to the discretization equation of the boundary element. These boundary conditions involve subsonic inlet, supersonic inlet, subsonic outlet, and supersonic outlet boundary conditions. The analysis has been focused on test cases of flow through a bumped arc channel and a converging–diverging nozzle including quasi-incompressible, subsonic, transonic, supersonic and hypersonic speed regimes, where the Mach number ranges from 0.1 to 10. The results indicate the robust performance of the fully coupled method in resolving compressible flows. The computational results obtained from the fully coupled algorithm exhibit a high degree of consistency with available literature cases and analytical solutions, with a maximum error of less than 5%. Moreover, the findings also suggest that the coupled solver presents promising potential in handling hypersonic flows.

Deflection and control of the mixing region in membraneless vanadium micro redox flow batteries: Modeling and experimental validation

Membraneless micro redox flow batteries operate within the laminar flow regime to mitigate the convective mixing between catholyte and anolyte. The absence of an ion-exchange membrane reduces manufacturing costs and overall cell resistance, thereby enhancing battery performance. However, it also poses a new challenge: the precise control of the thin mixing layer established between the two co-flowing electrolytes. Undesired displacements of the mixing region lead to increased crossover losses and significant liquid transfer between tanks. This work addresses the deflection of the mixing region under varying flow conditions, considering electrolyte viscosity variations due to the changes in the local state of charge arising during battery operation. This is achieved through a combination of mathematical analysis, numerical simulations, and experimental results. The conservation equations and non-dimensional parameters governing the problem are first written and discussed. The model is then integrated numerically incorporating different inlet and outlet boundary conditions to simulate the effect of various flow control strategies. Next, the numerical results are validated against experimental realizations of the flow. Finally, three case studies are presented and discussed. This work highlights the relevance of variable viscosity in the operation of co-laminar membraneless micro redox flow batteries, and proposes for the first time feasible control methods to mitigate undesired disturbances in the hydraulic circuit, thereby minimizing crossover losses.

Investigation on outlet boundary conditions in lattice Boltzmann simulations of flow boiling heat transfer

Investigation on outlet boundary conditions in lattice Boltzmann simulations of flow boiling heat transfer

Optimization Based on Computer Fluid Dynamics Finite Element Method Automotive Cooling Fan Structure

With the continuous improvement of vehicle comprehensive technology, the heat load generated by automotive engine systems, hydraulic systems, and other devices also increases. Therefore, improving the heat dissipation efficiency of the cooling system is a key technology that cannot be ignored in the current vehicle development process. The car cooling fan is an important component of the cooling system, and its working characteristics will directly affect the cooling effect of the engine. This article uses the finite volume method of computer fluid dynamics to optimize the structure of a heat dissipation fan, analyze and define the flow field control volume required for its numerical calculation, use structured and unstructured grids to discretize the internal flow field region, select pressure inlet and pressure outlet boundary conditions, and simulate and analyze the fluid flow in the radiator based on fluid dynamics theory calculations. The orthogonal experimental method was used to analyze various performance indicators during the experimental process. The results showed that the comprehensive performance of the No. 3 optimized cooling fan was the best, with a 10.45% increase in static pressure efficiency, a 14.03% increase in dynamic pressure efficiency, and an 11.26% increase in maximum flow velocity. The optimized fan flow field streamline became more full and uniform, significantly improving the fluid dynamics performance of the air in the cooling system.

A hemodynamic model of artery bypass graft considering microcirculation function.

The incidence of arterial stenosis is increasing year by year. In order to better diagnose and treat arterial stenosis, numerical simulation technology has become a popular method. A novel model is constructed to investigate the influence of microcirculation on the hemodynamics of artery bypass graft. In this paper, a severely narrow artery bypass graft model is considered. The geometric shape includes a narrow artery tube and a bypass graft of the same diameter with a 45° suture angle. The fluid-structure interaction model is considered by finite element numerical calculation, and the flow is simulated with microcirculation as the outlet boundary condition. The changes of blood flow velocity, pressure and wall shear stress are analyzed. The results show that blood almost entirely flows into the graft tube and there is no recirculation area at the anastomosis. The artery bypass graft model considering microcirculation function could simulate the physiological characteristics of blood flow more reasonably, and it provide helps for clinicians to diagnose and treat arterial stenosis.

Evaluating the accuracy of cerebrovascular computational fluid dynamics modeling through time-resolved experimental validation

Accurate modeling of cerebral hemodynamics is crucial for better understanding the hemodynamics of stroke, for which computational fluid dynamics (CFD) modeling is a viable tool to obtain information. However, a comprehensive study on the accuracy of cerebrovascular CFD models including both transient arterial pressures and flows does not exist. This study systematically assessed the accuracy of different outlet boundary conditions (BCs) comparing CFD modeling and an in-vitro experiment. The experimental setup consisted of an anatomical cerebrovascular phantom and high-resolution flow and pressure data acquisition. The CFD model of the same cerebrovascular geometry comprised five sets of stationary and transient BCs including established techniques and a novel BC, the phase modulation approach. The experiment produced physiological hemodynamics consistent with reported clinical results for total cerebral blood flow, inlet pressure, flow distribution, and flow pulsatility indices (PI). The in-silico model instead yielded time-dependent deviations between 19–66% for flows and 6–26% for pressures. For cerebrovascular CFD modeling, it is recommended to avoid stationary outlet pressure BCs, which caused the highest deviations. The Windkessel and the phase modulation BCs provided realistic flow PI values and cerebrovascular pressures, respectively. However, this study shows that the accuracy of current cerebrovascular CFD models is limited.

Eulerian- lagrangian dense discrete phase model (DDPM) of stenotic LAD coronary arteries in comparison with single phase modeling

In computational fluid dynamic studies related to blood flow, investigating the behavior of blood particles is crucial, especially red blood cells as they constitute a significant proportion of blood particles. Additionally, studying red blood cell movements is necessary, especially in stenotic artery geometries. A new multiphase scheme was utilized to demonstrate the effect of red blood cells on hemodynamics in complex coronary arteries and investigate the consequence of their motion. To investigate the effect of red blood cell movement on flow, the dense discrete phase model (DDPM) was used. This simulation was performed in 3D coronary arteries with different degrees of stenosis, utilizing blood pressure as inlet and outlet boundary conditions while assuming the arterial wall to be rigid. The model prediction shows good agreement with experimental data. Velocity values were comparable in both single-phase and two-phase flow simulations, but the shear stress in two-phase modeling had higher values. In the two-phase DDPM modeling, the recirculation areas indicated a higher probability of atherosclerosis plaque re-formation in the pre-stenosis area compared to the stenosis and post-stenosis areas. The DDPM model was found to be more effective in obtaining shear stress values in the artery. Additionally, this model provides good results compared to the single-phase model in investigating the movement of particles along the artery as well as recirculation areas that lead to the deposition of particles.

Patient-Specific Haemodynamic Analysis of Virtual Grafting Strategies in Type-B Aortic Dissection: Impact of Compliance Mismatch

IntroductionCompliance mismatch between the aortic wall and Dacron Grafts is a clinical problem concerning aortic haemodynamics and morphological degeneration. The aortic stiffness introduced by grafts can lead to an increased left ventricular (LV) afterload. This study quantifies the impact of compliance mismatch by virtually testing different Type-B aortic dissection (TBAD) surgical grafting strategies in patient-specific, compliant computational fluid dynamics (CFD) simulations.Materials and MethodsA post-operative case of TBAD was segmented from computed tomography angiography data. Three virtual surgeries were generated using different grafts; two additional cases with compliant grafts were assessed. Compliant CFD simulations were performed using a patient-specific inlet flow rate and three-element Windkessel outlet boundary conditions informed by 2D-Flow MRI data. The wall compliance was calibrated using Cine-MRI images. Pressure, wall shear stress (WSS) indices and energy loss (EL) were computed.ResultsIncreased aortic stiffness and longer grafts increased aortic pressure and EL. Implementing a compliant graft matching the aortic compliance of the patient reduced the pulse pressure by 11% and EL by 4%. The endothelial cell activation potential (ECAP) differed the most within the aneurysm, where the maximum percentage difference between the reference case and the mid (MDA) and complete (CDA) descending aorta replacements increased by 16% and 20%, respectively.ConclusionThis study suggests that by minimising graft length and matching its compliance to the native aorta whilst aligning with surgical requirements, the risk of LV hypertrophy may be reduced. This provides evidence that compliance-matching grafts may enhance patient outcomes.

Outlet boundary condition and mean temperature gradient effects on the minimum acoustics disturbances energy in triggering nonlinear thermoacoustic instability

In this study, we theoretically investigate the impact of outlet boundary conditions and mean temperature gradients on the maximum transient growth rate of acoustical energy and the critical energy required for triggering. Our analysis encompasses open–open and open–closed thermoacoustic systems. The theoretical models developed focus on horizontal ducts with a mean temperature jump over the heat source, employing the modified King's law. By linearizing the unsteady heat release, the nonlinear thermoacoustic equations transform into linearized-delay ones. This approach enables us to predict optimal initial perturbations for linearized-delay and nonlinear systems, corresponding to maximum transient growth rates of acoustic energy over short and long periods, respectively, thus providing insights into critical energy for triggering. We find that a closed outlet leads to higher transient energy growth and a lower critical energy for triggering compared to an open outlet. The increased mean temperature gradient has a “destructive” impact on triggering in open–open systems but a “constructive” effect in open–closed systems. Raising the mean temperature ratio generally increases the critical energy for triggering in the open–open system, whereas it decreases the critical energy in the open–closed system. The critical energy for nonlinear optimal initial perturbations is notably affected by the minimum energy of critical unstable periodic solutions, while the critical energy for linearized-delay optimal initial perturbations is closely tied to the energy level of stable periodic solutions. Due to the transient energy growth rate, the critical energy for nonlinear optimal initial perturbations is significantly lower than that for linearized-delay optimal initial perturbations.

Effects of preoperative aortic tortuosity and postoperative hypertension on patient-specific hemodynamics of abdominal aortic aneurysm

Abdominal aortic aneurysm (AAA) is a serious dilated vascular disease. The risk factors of aneurysm rupture and postoperative blood pressure are the major clinical concerns. The purpose of this work is to analyze the hemodynamic difference between preoperative and postoperative AAA using patient-specific boundary conditions and explore the rupture risk of AAA with different torsion and to simulate the blood flow of different degrees of hypertension. A three-element Windkessel model is utilized as the outlet boundary condition. 20-sim software and self-developed user-defined functions are used to calibrate the parameters. To analyze the influence of aortic tortuosity on hemodynamics, five AAA geometries with different torsion degrees are modified and obtained. We also grade the hypertension and explore the effect of hypertension after operation. The analysis results are consistent with the patient-specific situation. The results show that stent implantation for aneurysms reduces the pressure at the lesion site and increase the speed and wall shear stress. Vessels with high torsion have lower time-averaged wall shear stress (TAWSS), higher oscillatory shear stress index (OSI) and relative retention time, and more disordered blood flow. After stent implantation, with the increase in blood pressure, TAWSS and OSI continue to increase, and the blood flow speed is also faster. AAA with high torsion is more likely to rupture. In clinical practice, attention should be paid to the degree of torsion of the lesion site. Furthermore, blood pressure should be monitored and controlled in time to prevent postoperative complications.

Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique

In this work, we present a lower-dimensional model for flow and transport problems in thin domains with rough walls. The full-order model is given for a fully resolved geometry, wherein we consider Stokes flow and a time-dependent diffusion–convection equation with inlet and outlet boundary conditions and zero-flux boundary conditions for both the flow and transport problems on domain walls. Generally, discretizations of a full-order model by classical numerical schemes result in very large discrete problems, which are computationally expensive given that sufficiently fine grids are needed for the approximation. To construct a computationally efficient numerical method, we propose a model-order-reduction numerical technique to reduce the full-order model to a lower-dimensional model. The construction of the lower-dimensional model for the flow and the transport problem is based on the finite volume method and the concept of numerical averaging. Numerical results are presented for three test geometries with varying roughness of walls and thickness of the two-dimensional domain to show the accuracy and applicability of the proposed scheme. In our numerical simulations, we use solutions obtained from the finite element method on a fine grid that can resolve the complex geometry at the grid level as the reference solution to the problem.

Elucidating the Role of Flow Fields in Bubble Removal from Porous Transport Layers

Accelerating bubble removal from the porous transport layer (PTL) will be the key to reaching high current densities and cell efficiencies for polymer electrolyte membrane (PEM) water electrolyzers by improving catalyst utilization through reduced bubble accumulation for enhanced water transport to reach reaction sites 1,2. Previous studies have reported non-uniform bubble distributions within the PTL, where bubble saturation under the flow field lands was higher than that under the channel 3–5. This bubble distribution heterogeneity was attributed to the PTL/flow field interface and PTL/catalyst layer interface, which caused non-uniform outlet and non-uniform inlet conditions for bubble transport within the PTL, respectively. As such, determining the impact of the interfacial conditions on bubble removal from the PTL is critical for optimizing designs for next generation PTLs that need to exhibit low reactant mass transport resistances for PEM water electrolyzers.In this study, we elucidated the effects of the PTL/flow field interface on bubble transport in the PTL and specified the role of flow fields in bubble removal from the PTL. First, X-ray computed tomography (CT) was employed to reconstruct the microstructure of a titanium fibre-based PTL. Pore network modelling was then implemented to simulate and analyze the multiphase flow behaviour within the PTL under two kinds of outlet boundary conditions, i.e., with and without a flow field. We showed a dramatic non-uniform bubble distribution within the PTL when using an outlet condition with a flow field, while a uniform bubble distribution occurred in the PTL when using an outlet condition without a flow field. We attributed this to the existence of flow fields that lead to longer gas transport pathways through the PTL regions under the flow field lands. This study demonstrates the effects of flow fields on hindering bubble transport within the PTL and informs the need of tailored designs of the PTL/flow field interface for accelerating bubble transport in the PTL. References J. K. Lee and A. Bazylak, Joule, 5, 19–21 (2021).S. Yuan et al., Prog. Energy Combust. Sci., 96, 101075 (2023).J. K. Lee et al., Cell Reports Phys. Sci., 1, 100147 (2020).C. H. Lee et al., J. Power Sources, 446, 227312 (2020).S. De Angelis et al., J. Mater. Chem. A, 9, 22102–22113 (2021).

Analytic solution for pulse wave propagation in flexible tubes with application to a patient-specific arterial tree

In this paper, we present an analytic solution for pulse wave propagation in a flexible arterial model with tapering, physiological boundary conditions and variable wall properties (wall elasticity and thickness). The change of wall properties follows a profile that is proportional to $r^\alpha$ , where $r$ represents the lumen radius and $\alpha$ is a material coefficient. The cross-sectionally averaged velocity and pressure are obtained by solving a hyperbolic system derived from the mass and momentum conservations, and they are expressed in Bessel functions of order $(4-\alpha )/(3-\alpha )$ and $1/(3-\alpha )$ , respectively. The solution is successfully validated by comparing it with numerical results from three-dimensional (3-D) fluid–structure interaction simulations. Subsequently, the solution is employed to study pulse wave propagation in an arterial model, revealing that the wall properties and the physiological outlet boundary conditions, such as the resistor–capacitor–resistor (RCR) model, play a crucial role in characterizing the input impedance and reflection coefficient. At low-frequency range, the input impedance is found to be insensitive to the wall properties and is primarily determined by the RCR parameters. At high-frequency range, the input impedance oscillates around the local characteristic impedance, and the oscillation amplitude varies non-monotonically with $\alpha$ . Expressions for the input impedance at both low-frequency and high-frequency limits are presented. This analytic solution is also successfully applied to model flow inside a patient-specific arterial tree, with the maximum relative errors in pressure and flow rate never exceeding $1.6\,\%$ and $9.0\,\%$ when compared with results from 3-D numerical simulations.

Numerical simulation of two-phase slug flows in horizontal pipelines: A 3-D smoothed particle hydrodynamics application

A fundamental difficulty of studying gas–liquid pipe flows is the prediction of the occurrence and characteristics of the slug flow regime, which plays a crucial role in the safety design of oil pipelines. Current empirical methods and one-dimensional computational models only achieve limited success. While 3-D numerical simulations are highly recommended, they have been very seldom used. We perform 3-D Lagrangian numerical simulations of gas–liquid pipe flows by adapting an existing multi-phase smoothed particle hydrodynamics (SPH) method based on a Riemann solver to achieve an efficient solver. To realize the high inlet velocities of gas and liquid an in- and outlet boundary condition is presented. The results are validated against existing experimental data, numerical simulations and analytical solutions. Multiple gas–liquid pipe flow patterns are predicted, namely, smooth stratified, stratified wavy, bubble flow, slug flow and bubble flow. Several principle characteristics of slug flows, e.g., pressure gradient, slug development and slug frequency are analyzed in a 3-D fully Lagrangian framework.

Theoretical model of azimuthal combustion instability subject to non-trivial boundary conditions

The problem of evaluating the sensitivity of non-trivial boundary conditions to the onset of azimuthal combustion instability is a longstanding challenge in the development process of modern gas turbines. The difficulty lies in how to describe three-dimensional in- and outlet boundary conditions in an artificial computational domain. To date, the existing analytical models have still failed to quantitatively explain why the features of the azimuthal combustion instability of a combustor in laboratory environment are quite different from that in a real gas turbine, making the stability control devices developed in laboratory generally lose the effectiveness in practical applications. To overcome this limitation, we provide a novel theoretical framework to directly include the effect of non-trivial boundary conditions on the azimuthal combustion instability. A key step is to take the non-trivial boundary conditions as equivalent distributed sources so as to uniformly describe the physical characteristics of the inner surface in an annular enclosure along with different in- and outlet configurations. Meanwhile, a dispersion relation equation is established by the application of three-dimensional Green’s function approach and generalized impedance concept. Results show that the effects of the generalized modal reflection coefficients on azimuthal unstable modes are extremely prominent, and even prompt the transition from stable to unstable mode, thus reasonably explaining why the thermoacoustic instability phenomena in a real gas turbine are difficult to observe in an isolated combustion chamber. Overall, this work provides an effective tool for analysis of the azimuthal combustion instability including various complicated boundary conditions.

An analytical method informed by clinical imaging data for estimating outlet boundary conditions in computational fluid dynamics analysis of carotid artery blood flow

Stroke occur mainly due to arterial thrombosis and rupture of cerebral blood vessels. Previous studies showed that blood flow-induced wall shear stress is an essential bio marker for estimating atherogenesis. It is a common practice to use computational fluid dynamics (CFD) simulations to calculate wall shear stress and to quantify blood flow. Reliability of predicted CFD results greatly depends on the accuracy of applied boundary conditions. Previously, the boundary conditions were estimated by varying values so that they matched the clinical data. It is applicable upon the availability of clinical data. Meanwhile, in most cases all that can be accessed are arterial geometry and inflow rate. Consequently, there is a need to devise a tool to estimate boundary values such as resistance and compliance of arteries. This study proposes an analytical framework to estimate the boundary conditions for a carotid artery based on the geometries of the downstream arteries available from clinical images.