Fluid Dynamics Analysis Research Articles

Ruptured Vertebral Artery Dissection Treated with Endovascular Intervention

A retrospective study of cases of endovascular treatment of dissection of the vertebral artery with subarachnoid hemorrhage was conducted. Data were 11 cases of vertebral artery dissecting aneurysm (VADA) among 291 consecutive subarachnoid hemorrhage patients who underwent clipping or endovascular treatment at Ota Memorial Hospital. Classified into 4 patterns based on the location of the dissection and posterior inferior cerebellar artery (PICA): pre-PICA, post-PICA, involved PICA, and non-PICA. And one of the cases had bilateral vertebral artery dissection, and computational fluid dynamics analysis was included in the study. Ruptured VADA occurred in 11 of the 291 patients (3.8%). Endovascular treatment was performed in 8 of these 11 patients. Postoperative diffusion-weighted imaging detected no high-intensity lesions and no postoperative ischemic complications or rebleeding occurred in any patient. In a case of bilateral VADA, computational fluid dynamics analysis of very low or high wall shear stress at the dissection, low aneurysm formation indicator, and high oscillatory shear index may be considered rupture factors. Treatment strategies for each branching pattern of PICA can prevent rupture and avoid ischemic complications. And prediction of the rupture side is important in patients with bilateral dissection to consider the appropriate treatment and timing.

Experimental and Computational Fluid Dynamics Analysis of Industrial Water Desalination with High Salinity by Adsorption Chlorine on Resin in a Packed Column

AbstractTo investigate chlorine adsorption from water onto resins, some batch adsorption tests were considered. The mechanisms and characteristic parameters of the adsorption process were analyzed using isotherm models which revealed the following order (based on the coefficient of determination): Flory–Huggins (0.99) > Fowler‐Guggenheim (0.98) >, and Langmuir (0.38).The experimental data were examined using two kinetic models, including first‐ and second‐order ones with R2 value of 0.88, 0.1 respectively. According to the adsorption isotherm study, the Flory–Huggins isotherm model better fit adsorption on the surface of resin, as compared to other models. Assessing the thermodynamic parameters found out that the adsorption of Cl onto resins became an exothermic and spontaneous process. The results were then obtained. Similarly, the results of the experiment were provided via the computational fluid dynamics evaluation. Moreover, the results obtained by computational fluid dynamics were compared with the experimental data, and their accuracy was proved. Subsequently, the effects of changing the design and operating parameters, including flow rate (3, 6, 10 L min−1) and bed height (10, 20, 40 cm) on the performance of this tower were studied. The results showed that by reducing the adsorbent, the adsorbed Cl increased and a longer bed was required for adsorption, which was not cost‐effective. The amount of adsorption decreased as the flow rate increased, indicating that there was little contact between the Cl and the adsorbent.

Clinical and Hemodynamic Features of Aneurysm Rupture in Coil Embolization of Intracranial Aneurysms.

Intraprocedural rupture (IPR) during coil embolization (CE) of an intracranial aneurysm is a significant clinical concern that necessitates a comprehensive understanding of its clinical and hemodynamic predictors. Between January 2012 and December 2023, 435 saccular cerebral aneurysms were treated with CE at our institution. The inclusion criterion was extravasation or coil protrusion during CE. Postoperative data were used to confirm rupture points, and computational fluid dynamics (CFD) analysis was performed to assess hemodynamic characteristics, focusing on maximum pressure (Pmax) and wall shear stress (WSS). IPR occurred in six aneurysms (1.3%; three ruptured and three unruptured), with a dome size of 4.7 ± 1.8 mm and a D/N ratio of 1.5 ± 0.5. There were four aneurysms in the internal carotid artery (ICA), one in the anterior cerebral artery, and one in the middle cerebral artery. ICA aneurysms were treated using adjunctive techniques (three balloon-assisted, one stent-assisted). Two aneurysms (M1M2 and A1) were treated simply, yet had relatively small and misaligned domes. CFD analysis identified the rupture point as a flow impingement zone with Pmax in five aneurysms (83.3%). Time-averaged WSS was locally reduced around this area (1.3 ± 0.7 [Pa]), significantly lower than the aneurysmal dome (p < 0.01). Hemodynamically unstable areas have fragile, thin walls with rupture risk. A microcatheter was inserted along the inflow zone, directed towards the caution area. These findings underscore the importance of identifying hemodynamically unstable areas during CE. Adjunctive techniques should be applied with caution, especially in small aneurysms with axial misalignment, to minimize the rupture risk.

Computational fluid dynamics analysis of scaled Thermo-Compressor Performance in Multi-effect Distillation plants with Thermal Vapor Compression

This paper investigates scaled Thermo-Compressors for Multi-Effect Distillation with Thermal Vapor Compression (MED-TVC) desalination plants using Computational Fluid Dynamics (CFD). Initial validation compared CFD predictions with a real MED-TVC plant. Scaled-down Thermo-Compressors exhibited constant entrainment and pressure ratios, validating design scalability. The study expanded to test with compressed air as a practical substitute for steam under identical conditions. Results showed minimal deviation in entrainment and pressure ratios, affirming the feasibility of air testing. To account for temperature differences, a correction factor was introduced for accurate prediction when testing with air. Crucially, we explored substituting high-temperature steam with compressed air for testing. Lowering the air temperature allowed a reduced pressure of 13.12 bar while maintaining equivalent performance ratios compared to steam at 16 bar and 474.7 K. These findings are pivotal for developing small-scale Thermo-Compressor prototypes, facilitating testing with steam or air, and reducing risks and costs associated with full-scale fabrication. The study contributes practical insights for optimizing Thermo-Compressor designs in MED-TVC desalination, presenting compressed air as a viable alternative for efficient and cost-effective testing.

Analysis of Tesla CyberTruck Speed on the Velocity and Pressure Distribution Using SimFlow Software

This work presents a comprehensive Computational Fluid Dynamics (CFD) analysis of the external flow around the Tesla CyberTruck, focusing on its aerodynamic characteristics under varying conditions. The primary objectives are to study velocity and pressure distributions. The simulation considers two independent parameters: vehicle speed (20, 40, and 80 m/s) and the type of turbulent flow (k-ω SST and k-ε). The simulation provides insights into complex flow patterns through meticulous meshing, boundary condition setup, and solver configuration, highlighting areas of interest such as flow separation, recirculation, and turbulence. Parametric variations are analyzed to determine how turbulent flow type and speed affect critical parameters like pressure and velocity. The results of this CFD analysis offer valuable information about the vehicle's aerodynamic performance, contributing to design optimization, handling and stability enhancements, and improved fuel efficiency. The findings from this study are expected to enhance visualization and understanding of the aerodynamic aspects of the Tesla CyberTruck.

Effects of Race Car's Speed on the Aerodynamic Aspect Using Computational Fluid Dynamics Analysis

This research employs Computational Fluid Dynamics (CFD) methods to investigate the intricate relationship between race car speed and external aerodynamics during high-performance racing competitions. The primary objectives encompass the application of CFD in pre-processing and analyzing external aerodynamic aspects, coupled with a comprehensive examination of the external flow around a race car for a nuanced understanding of its aerodynamic performance. Various car speeds were considered with the RANS (k-ω SST) turbulent model. The results unveiled a direct correlation between inlet velocity and the maximum velocity attained by the race car. The aerodynamic design intricately directs the airflow, leading to higher velocities predominantly along the upper part of the car body. Noteworthy is the revelation that the highest recorded maximum velocity of 231.06 m/s coincides with a peak inlet velocity of 200 m/s, suggesting a consistent increase in maximum velocity with rising inlet velocity. This research emphasizes the pivotal role of inlet velocity in achieving peak car speed performance. It sheds light on the significance of turbulent model selection in capturing the complexities of external flow dynamics. This knowledge contributes to optimizing the external aerodynamics of race car body design, ultimately enhancing performance and competitiveness in the dynamic world of Formula 1 racing.

Simulation of the Collapse Mechanism of a Minaret under the Effect of Strong Wind

In this study, the collapse mechanism of a destroyed minaret under strong wind influence was simulated to understand such structural interactions and identify potential risky regions. Wind profiles were defined according to Eurocode and Turkish Standards and were used in Computational Fluid Dynamics analyses. The pressure and suction stresses obtained with these wind analyses were applied on the minaret’s surface with Abaqus and the nonlinear finite element analyses were performed. As a result of the numerical analyses, displacements, stresses, plastic strains, and damages were obtained and results were comparatively presented. The results obtained with both standards are quite close and top displacements exceed the limit value specified in the Italian Building Code and Eurocode 8. Besides, many mesh elements in the minaret’s transition segment were damaged with tension stresses in nonlinear finite element analyses. Finally, the minaret’s failure behaviour was successfully simulated with the used methods.

Loss model of low pressure compressor for mechanical vapor recompression system

Abstract Low pressure compressor (LPC) serves the role of enhancing pressure levels of secondary steam at nominal pressure ratios (1.5), procured from the evaporator as a primary thermal energy source. A loss model has been proficiently proposed to rapidly predict the performance of the LPC. Instead of conventional lump sum loss equations, the model adopts well-established one-dimensional (1D) loss formulations scattered across scholarly publications. Given an explicit configuration of the LPC, the environmental conditions, rotational velocity, and capacity, static and total temperatures, static and total pressures, pressure reductions, polytropic head, and efficiencies of each individual segment of the compressor can be calculated. Validation of this model was done using computational fluid dynamics (CFD) analysis. This model renders it feasible to conduct a parametric examination of the impact of each loss apparatus on the LPC’s capability, thereby aiding designers in substantiating design choices that minimize these losses and consequently positively influencing the comprehensive efficiency.

Aerodynamic and Structural Assessment of Floating Wind Turbine Rotor Under Varying Tilt Angle

Predicting the aerodynamic performance of floating offshore wind turbines (FOWTs) proves challenging due to platform motion induced by waves. The effect of wind and waves results in a six-degree-of-freedom motion of the platform, directly influencing turbine performance. Understanding the impact of specific degrees of freedom (DOF) motions on aerodynamics and structural response is crucial for effective wind turbine design. This research examines the impact of rotor tilt on both aerodynamic performance and structural response. The investigation employs computational fluid dynamics (CFD) analysis and mapping aerodynamic loads onto the finite element (FE) mesh for structural analysis. The study employs a comprehensive 3D simulation, utilizing the moving reference frame (MRF) method for the NREL 5 MW reference wind turbine CFD simulations. It explores different rotor tilt angles (5°, 10°, 15°, and 20°) encountered by offshore structures during their operation and examines their impact on aerodynamic performance. Predicted aerodynamic loads were mapped onto the blade FE mesh using the radial basis function (RBF) interpolation technique and solved using the open-source FE solver CalculiX. The analysis shows that the turbine performance is relatively unaffected up to a tilt angle of 10°. However, further increase in rotor tilt angle adversely impacts turbine performance, leading to notable reductions in thrust and power output. The fluid-structure coupled analysis provided insights into the deformations and stresses experienced by the turbine blade, indicating a notable increase in flap-wise displacement for larger tilt angles, while edge-wise displacement is not as significantly affected. The maximum stress location on the blade generally correlates well with actual observations.

Axial flow impeller design and simulation for negative pressure adsorption climbing robot

Abstract Axial flow impeller is broadly applied in negative pressure adsorption climbing robots, but its design method and procedure are rarely reported. This paper used a wind turbine blade climbing NDT robot as case study, presented a comprehensive design process of the axial flow impeller, and evaluated the adsorption performance of the impeller by carrying out simulation experiments. Firstly, analysing the force equilibrium of the robot and determining minimum adsorption force required by the robot. Secondly, defining design parameters of the axial flow impeller by using fluid dynamics analysis method. Thirdly, specifying structural parameters of the impeller blades using impeller design theory and developing the CAD model of the impeller. Finally, evaluating the adsorption performance of the impeller by carrying out a series of Fluent simulation experiments. Research results showed that the total adsorption force of the impeller reached 80.30N as rotational speed is 6000rpm, which satisfied design requirements of the climbing robot. This research provides a methodological framework in designing axial flow impellers for the purpose of negative pressure adsorption.

Comparative Analysis of Different Burner Concepts in a Locally Manufactured Bread-Baking Oven

The supply and control of heat within an oven with minimal loss is an integral process in optimizing the bread-baking process. Research over the years reports on measures to control heat, however, there is limited data on optimizing burner designs for efficient heat supply. Challenged with enhancing the functionality of a bread baking oven made locally, three different burner concepts (i.e., U, H and Rectangular shaped) were designed, fabricated and evaluated in a locally manufactured bread baking oven. The study investigated the three burner configurations to enhance the locally manufactured ovens&amp;apos; environmental sustainability, cost-effectiveness, and efficiency. The study also assessed each burner design concept&amp;apos;s performance in relation to heat distribution, fuel consumption, and emissions through thorough experimentation and analysis. Thermocouples were used to determine the temperature differences within the oven and outside the oven walls to verify heat losses. The results showed that the concept burner design can be used to bake bread with good quality parameters like colour, texture and taste within efficient baking time. Computational Fluid Dynamic (CFD) analysis performed on the proposed burner design concepts in relation to heat flow show that continuous flow of heat was assured during baking. Also, simulation performed on the baking trays show an acceptable stress and strain levels as well as favorable factor of safety, indicating that the designs proposed is suitable for the purpose. Data analysis performed on the heat generated within the oven chamber considering the lower and upper trays for all the burners evaluated can be ranked in terms of percentage as RB &amp;gt; HB &amp;gt; UB (41.39% &amp;gt; 30.72% &amp;gt; 27.89%). Based on the study conducted, the authors can suggest the best design concept for heat generation in locally manufactured ovens should be rectangular-shaped.

Flow Diversion Effect in a Saphenous Vein Graft Aneurysm Using a Double-Layer Micromesh Stent: A Case Report.

A double-layer micromesh stent is designed for the treatment of carotid artery stenosis that has been reported to potentially provide a flow diversion effect. However, the actual flow diversion effect of stents remains unclear. Here, we present a case of a growing saphenous vein graft (SVG) aneurysm treated with the placement of the double-layer micromesh stent using its flow diversion effect. A 66-year-old woman, who underwent high-flow bypass using a SVG for a blister-like internal carotid artery aneurysm 13 years earlier at our institute, was referred to our hospital with a pulsatile cervical mass. Magnetic resonance angiography showed a 9-mm aneurysm on the left SVG, although the aneurysm was a small pouch 4 years earlier. Digital subtracted angiography demonstrated a 9.4 × 8.3-mm aneurysm from the SVG at the auricular level. Because the diameter of the graft was larger than that of the available flow diverter stents in Japan, we decided to place the double-layer micromesh stent (CASPER RX, 7 × 25 mm MicroVention) using its flow diversion effect. Computational fluid dynamics analysis before and after stent deployment showed a significant reduction in the average flow velocity and wall shear stress in the aneurysm, indicating actual flow diversion. An angiogram 2 months postoperatively showed complete obliteration of the aneurysm. Obliteration of the saphenous vein aneurysm was achieved because of the flow diversion effect of the double-layer micromesh stent. The stents might be a feasible alternative for treating cervical carotid aneurysms.

Analysis and Optimization of the Performances of the Tandem Blade Radial Compressor Using the CFD

Centrifugal compressors are frequently used in both military and commercial areas because they can be easily manufactured and reach high-pressure compression ratios. The factor that limits the performance and operating range of compressors is flow instability. Many ideas have been put forward for performance improvement, but tandem blade radial compressors, which do not require an extra air system, have attracted the most interest. In this study, computational fluid dynamics (CFD) analyses were carried out on various parameters of the tandem blade (TB) radial compressor, and an optimization study was carried out to find the best design using a genetic algorithm on a whole operating curve. It was investigated how these parameters affected the efficiency and total pressure ratio between the determined lower and upper limits. The numerical analyses of the optimum design obtained as a result of the iterations were carried out. As a result of the iterations, three optimum designs were obtained and numerical analysis was carried out according to one of them, and then they were compared with the results in the literature. The general agreement of computational fluid dynamics and the literature data served as a validation for the computational approach. The error rates between the numerical analysis results and the experimental results in the literature were calculated for different flow rates and were found to be 1.98% as the highest and 0.35 as the lowest. The work carried out in this article will provide a valuable reference for future advanced tandem blade compressor designs.

Flows past airfoils for the low-Reynolds number conditions of flying in Martian atmosphere

Fixed-wing aircraft with potential for long-duration flight and efficient manoeuvrability is expected to be the next frontier of Mars surface exploration. However, the feasibility of such an aircraft demands for wing airfoil suitable for low Reynolds flight conditions. In this framework, the paper deals with the computational study of two wing sections specifically designed for Mars exploration aircraft. Two-dimensional steady Reynolds-averaged Navier–Stokes simulations, using the computational fluid dynamics tool SU2 with the γ−Reθ transition model and the XFoil panel flow solver, are performed to address airfoils’ aerodynamics. Computational tools are validated by simulating flow past the Eppler 387 airfoil at Re∞=60×103, and comparing the results with experimental data collected in wind tunnel experiments. Aerodynamic performances of optimal wing sections are investigated at Re∞=3.4×104 by considering pressure coefficients and skin friction coefficients. The application of a literature-based correlation, specifically tailored to identify transition and reattachment locations, is extended to separation point detection. Computational Fluid Dynamics analysis conducted on the studied airfoils revealed that separation occurs within the laminar regime. Additionally, examination of turbulent shear stresses highlighted the role of airfoil curvature in counterbalancing the suction defect produced by the laminar separation bubble. This curvature-induced effect was found to play a crucial role in optimizing airfoil efficiency.

Improving the sustainability and effectiveness of photovoltaic evaporative cooling greenhouse in the Sahel

Anthropogenic climate change has caused worldwide extreme weather events including droughts, floods and heatwaves. It disproportionately affects developing countries through food insecurity. Greenhouse is important and relevant to the food-energy-water security in many regions. This study investigates the thermal behavior of photovoltaic evaporative cooling greenhouse made with eco-friendly coolers. The cooling potential of local plant materials was assessed under ambient conditions. Experimental thermal data obtained from optimized evaporative cooling system equipped with Hyphaene thebaica fibers (HF-pad) and conventional Celdek pad (C-pad), were used in heat and mass transfer equations to derive the greenhouse cooling performances. Computational fluid dynamics analysis software was used to investigate the refrigerant fluid distribution in the greenhouse. Cooler using HF-pad allows to keep the microclimate below 25 °C, with maximum moisture rate up to 80%, under harsh ambient conditions (temperature: 30–45 °C, humidity: 10–15%). HF-pad had the highest cooling coefficient of performance (COP = 9 against 6 for C-pad), the best cost to efficiency ratio (CER = 5; 4 times less than C-pad) and the lowest outlet temperature (20.0 °C). Due to higher outlet air velocity (1.116 m/s against 0.825 m/s for HF-pad), C-pad cooler spread cool air (20.5 °C) up to 1.25 m farther than its counterpart, creating higher pressure in the atmosphere (1.42 Pa against 0.71 Pa), with 2 times turbulent kinetic energy (0.014 J/kg). HF-pad presented cooling performances that compete with conventional pads. Moreover, optimization of HF-pad frame engineering and the technology scaling up to industrial level can allow better thermal and economic performances.

Improving sensible heat storage in a vertical annular pipe subject to variable inlet boundary condition using TiO2/water nanofluid: Numerical study

A computational fluid dynamics (CFD) analysis is conducted to investigate the thermal performance of unsteady free convection of TiO2/water nanofluids. The study process within a coaxial heat exchanger system. The model is based on the mixture Buongiorno approach. Due to the axisymmetric conditions, the study is carried out in two dimensions, and the conservation equations are reformulated in dimensionless form. The obtained PDE system is Discretized using the finite element method. The TiO2 concentration heterogeneity, resulting from thermophoresis and Brownian motion is considered. The presentation of the results encompassed isotherms, nanoparticle volume fraction distributions, and streamlines. The validation of the model shows a good agreement with the experimental results. The impact of the mass fraction’s nanoparticles ( 0.01 ≤ ϕ ≤ 0.04 ) and the Rayleigh number ( 10 3 ≤ Ra ≤ 10 8 ) on the heat transfer performance are analyzed. The parametric study shows that an increase in the Rayleigh number has no effect on heat transfer enhancement. Unlike for Ra = 10 6 where an increase in Nusselt number is observed. It was found also that the effect of nanofluid concentration on the Nusselt number was more noticeable in high Rayleigh cases due to the convection-driven heat transfer.

Experimental and numerical investigation on the hydroelastic response of barge and KVLCC2 ship

In this paper, the hydroelasticity of two segmented ship models (Barge and KVLCC2) is investigated by experimental and numerical methods. A two-way Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) coupled method is adopted and further validated its accuracy against experimental results. The current approach emphasizes the overall convergence between two solvers, maintaining a strongly coupled manner to comprehensively address the fluid-structure interaction phenomenon, including the added mass effect. A series of experiments of a segmented Barge and KVLCC2 under various wave conditions were firstly conducted. The motions of the models are measured and the displacement Response Amplitude Operators (RAOs) are calculated. The CFD-FEA coupled method is demonstrated in agreement with experimental results by comparing the numerical prediction with the tank test results in terms of motion, affirming the validity and robustness. Finally, the hydroelastic response is discussed and investigated.

Numerical investigation of blunt body's resistance and heat reduction with combination of airway spike and root jet

Aerodynamic heating and impact resistance present significant challenges for hypersonic aircraft. This study introduces a novel multi-jet strategy to enhance both resistance reduction and thermal protection performance of hypersonic aircraft. Computational Fluid Dynamics (CFD) analysis is employed for the aerodynamic evaluation. The results demonstrate that this novel strategy effectively mitigates the shock waves, the peak pressure coefficient and Stanton number have been reduced by 64.3 % and 73.2 %, respectively. Through a comprehensive analysis of the influencing factors, it has been found that increasing the pressure ratio of the root jet significantly lowers the heat flux and pressure on the blunt body, albeit at the cost of an increased total flight resistance. When the nozzle on the side of the airway is oriented perpendicularly to the incoming flow direction, a notable reduction in resistance and aerodynamic heating on the blunt body is noted. By increasing the length-diameter ratio of the spike, a significant decrease in the pressure coefficient of the blunt body is achieved, the Stanton number remains largely unaffected. This study offers insights into the engineering application of strategies for reducing resistance and heat in hypersonic aircraft.

On dark energy effects on the accretion physics around a Kiselev spinning black hole

Kiselev metric in the static and rotating form is widely used to test different aspects of the dark energy (DE) effects. We consider a DE Kiselev spacetime, predicting the reduction to the Kerr black hole (BH) solution under suitable conditions on the DE parameters and in this frame we study the effects of the dark energy on BHs and disks accretion. Elaborating a close comparison with the limiting vacuum Kerr spacetime, we focus on thick accretion disks around the central BH in the Kiselev solution, both co-rotating and counter-rotating with respect the central BH. We examine different aspects of BH accretion energetics by focusing on quantities related to the accretion rates and cusp luminosity, when considered the DE presence, related to the pure Kerr central BH. Our findings show that in these conditions heavy divergences with respect to the vacuum case are expected for the DE metrics. A known effect of the Kiselev metric is to lead to a false estimation the BH spin, we confirm this characteristic from the fluids dynamics analysis. Remarkably our results show that DE is affecting differently the accretion physics, and particularly the accretion rate, according to the fluid rotation orientation with respect to the central spinning attractor, leading in some cases to an under-estimation of the BH spin mass ratio. These contrasting aspects emerging in dependence on the fluids rotational orientation can be a distinguishing general DE feature which could lead to a revised observational paradigm where DE existence is considered.

Investigation of the use of new fin on the melting time of the phase change material stored in the heat exchanger by computational fluid dynamics analysis

In this study, RT35 and RT42 are used as phase change materials (PCM) for latent thermal energy storage (LTES) in a double-tube concentric heat exchanger. A different fin model from the literature was used, and the fin efficiency was calculated with the help of computational fluid dynamics (CFD) analysis using a different method. The thermal behavior of PCM in the melting process was simulated by CFD analysis for the models with/without fins using ANSYS Fluent commercial software. The models were analyzed at 60 °C temperature and 0.5 m/s flow rate of the heat transfer fluid, which was selected as the optimum analysis parameter, and 6, 9, 12, and 15 fins were added to the finless model. It was determined that the melting time decreased by 72.91 %, 76.25 %, 81.66 %, and 85 % for RT-35 phase change material and by 76.33 %, 79.33 %, 83 %, and 86.33 % for RT-42 with an increasing number of fins compared to the finless model. The shortest complete melting time of PCM was 240 and 36 min for RT35 with no fins and an optimum number of fins of 15, respectively. The simulation findings showed that a rise in the temperature of the heat transfer fluid (HTF) and the number of fins shortened the PCM melting time. As a result, it was observed that the fin model with a different geometry from the literature was more effective in the complete melting time of PCM than the fin models in the literature.