Exit Location Research Articles

Microramp wake impinging on canonical shock/boundary-layer interaction

We analyze the influence of microramp vortex generators (mVGs) on a canonical oblique shock wave/turbulent boundary-layer interaction (SBLI) in terms of mean flow field and unsteady dynamics. The flow configuration of our wall-resolved large-eddy simulations (LES) reproduces the experiment of Bo et al. [“Experimental investigation of the micro-ramp based shock wave and turbulent boundary-layer interaction control,” Phys. Fluids 24, 055110 (2012)]: a rake of microramps is inserted upstream of the SBLI, protruding by 0.476δ in a turbulent boundary layer (TBL) at free-stream Mach number M = 2.7 and corresponding to a Reynolds number based on the displacement thickness of Reθ=3600. The long integration time of 1672 Lsep/U∞ allows an accurate characterization of the low-frequency dynamics of the SBLI under the influence of the microramps. With respect to the reference SBLI without control devices, the mean flow field shows a new spatial organization of the recirculation bubble due to the mVGs' wake. The alternating high and low-speed zones in the near-wall region of the incoming TBL, induced by the counter-rotating streamwise vortices generated by the mVGs, trigger spanwise corrugations of the separation and reattachment lines and locally alter the reverse flow region. Tornado-like vortices are found in the vicinity of these zones, yielding a new fluid collection mechanism of the reverse flow region. These vortices redirect the fluid coming from regions outside of the wake in the incoming TBL to three key spanwise exit locations located in between the mVGs and at their centerline. Interestingly, power spectral densities of wall-pressure probes show a damping of the low-frequency dynamics of the reflected shock foot for spanwise stations aligned with the mVGs' wake, whereas this activity appears to be reinforced in the planes located in between the mVGs. However, we found no evidence of unsteady forcing linked to the high-frequency shedding of the coherent structures developing in the wake of the microramps. Dynamic mode decomposition highlights a significant change in the low-frequency dynamics, mostly affecting the mass budget of the recirculation bubble. The breathing of the recirculation zone that occurs at StL=0.1 for the SBLI without control devices (with StL=fLsep/U∞) appears to shift toward a lower frequency of StL=0.05. Remembering that the reflected shock foot motion is related to frequencies in the range StL=[0.03−0.05], the SBLI with upstream mVGs seems to highlight a synchronization of this motion with the breathing of the separation bubble.

Effects of pressure side film cooling hole placement and condition on surface heat transfer coefficients along a transonic turbine blade tip

Considered is thermal performance for the squealer blade tip of four film cooling configurations, B1, B2, B3 and B4, with hole exits for each arrangement positioned along a different portion of the upper pressure side of a transonic turbine blade. Each upper pressure side configuration includes five film cooling holes, such that each hole has a compound angle of 45° with respect to the circumferential/axial plane, also with an angle orientation of 40° relative to the plane tangent to the exit cross sectional area of each hole. Results are given for blowing ratios ranging from 0.42 to 3.20 in the form of spatially-resolved and spatially-averaged surface distributions of heat transfer coefficients and heat transfer coefficient ratios. In regard to tip surface variations, surface heat transfer coefficient ratios distributions are a consequence of the manner in which the film coolant collects in a substantial manner along the pressure side rim and then advects above and across the squealer recess with little to no coolant collecting within the cavity, or along the recess surface, to then collect in a substantial manner further downstream along the suction side rim. Such flow characteristics affect heat transfer coefficient ratio variations for all four film cooling configurations, but are especially influential for the B3 arrangement. Considering local heat transfer coefficient ratio distributions along the upper pressure side surface, the most significant local variations in the vicinity of a film cooling hole exit locations. Here, heat transfer coefficient ratio distributions for the B1 and the B4 configurations, in particular, show evidence of a horseshoe-shaped vortex which forms around each emerging coolant concentration. The two downstream legs of each vortex are associated with a pair of locally augmented heat transfer coefficient streaks, often with a streak of locally-lower coefficient ratios positioned between. Local and line-averaged heat transfer coefficient ratios along the upper pressure side also vary significantly with blowing ratio, with additional periodic variations as the normalized circumferential/axial coordinate varies. Within the resulting distributions, local heat transfer coefficient ratio increases are associated with locally augmented mixing and turbulent transport, which are especially present near the exits of different film cooling hole locations.

Experimental investigation on a diffusion jet flame performance using a developed flame holder supplied with air from a concentric pipe

In this study, a diffusion jet flame consisting of a newly developed flame holder with three coaxial pipes to transfer air and fuel to the combustion zone, is investigated experimentally to simulate the ramjet effect. The flame holder is a double cone with three fuel ports on the top cone to improve the mixing of fuel and air. The inner pipe transfer fuel and is connected to the flame holder (which serves as a fuel injection point) and the middle pipe transfer primary air and the outer pipe transfer secondary air to the combustion zone (to investigate the impact of removing still air from around the flame as in ramjet applications). The flame holder and the primary air exit were at fixed positions (Datum Z4= 0) while the secondary air exit position changed many times below and above the datum line. The results showed that the secondary air exit location had an effect on the flame temperature distribution, flame shape, flame length, and flame width. The optimum position of the secondary air pipe was found above the datum line at Z5 = 7.5 mm, where the flame temperature and length are considered relatively high compared to other secondary air pipe positions.

Calculating Cooled Turbine Efficiency With Weighted Cooling Flow Distributions

Abstract The ability to accurately characterize the thermal efficiency of turbine stages with cooled components is essential to advance turbine technologies. There are many methods for calculating aerodynamic efficiency of turbomachinery components, with most encompassing either single point or simple integrated values at the inlet and exit locations. For cooled turbine stages, there is an added complexity of how to incorporate cooling flow streams. Although these techniques may include multiple cooling flows, a fully mixed assumption is often invoked without directly accounting for distributions of cooling flow in the annulus. However, the distribution of cooling flows in turbine stages may vary significantly depending on the location and nature of injection. This study addresses how calculated efficiency may vary depending upon how cooling flows are injected and the manner in which these cooling flows are accounted. The analyses utilize experimentally measured cooling flow concentration profiles to motivate a new approach for calculating cooled turbine efficiency with weighted cooling flow distributions. Validation data for a one-stage high-pressure turbine geometry from the energy efficient engine (E3) program are assessed to determine the range of influence for cooling flow distributions. Results show that cooling flows injected at similar axial positions can have unequal influences on integrated stage efficiency based on known distributions of cooling flow and other properties at the turbine stage exit plane. In some cases, deviations approaching half a point of efficiency can be observed relative to traditional equations, and the magnitude of influence is shown to increase as stage total pressure ratio decreases.

The Poincaré maps of a slow-fast stochastic system

This work is concerned with the Poincaré maps of a slow-fast stochastic system. Applying the random manifold reduced theory and the moving orthonormal system argument, it derives the effective construction of the stochastic Poincaré map. Moreover, employing the geometric distribution of the first exit time, it builds the stability of the stochastic Poincaré maps, that is, the stochastic Poincaré maps return to a small neighborhood of a fixed point of a deterministic Poincaré map with one time or even infinite times as the noise intensity tends to zero. It further investigates the limit distribution of the first exit location on the boundary of the domain via the harmonic measure.

Role of office layout typology in saving time and distance spent by users: Case of office buildings in Erbil city

Space organization and space layout in buildings are complex issues in architectural design. People spend most of their lives in offices, yet office buildings still get little attention. This paper examines the potential role of office space typologies in saving distance and time spent by users communicating between these spaces. The study adopts multiple methodologies to scrutinize users’ paths and track their movement. Diversity in methodologies provides a deep understanding of how spatial configurations of these spaces affect users’ movement. Three office buildings were selected in Erbil city to represent three different office space typologies. The study revealed the effective role of office space typologies in influencing the level of user satisfaction and comfort, concluding that the most influential factors in providing distances and time are circulation patterns, entry and exit locations that require considering function, organizational and administrative structure of building spaces, and balancing between horizontal and vertical accessibility.

Field Experiments to Identify and Eliminate Recirculation Zones to Improve Indoor Ventilation: Comparison with CFD.

Ventilation of shared indoor spaces is crucial for mitigating air-borne infection spread among its occupants. Replacing the air in a room with fresh air is key to minimize the concentration of potentially infectious aerosol generated in the room. Recirculating air flow present at corners and around obstacles can trap air and infectious aerosol. This can significantly delay their evacuation by the ventilation system. Knowing the location and extent of such recirculation zones is, therefore, important. In this work, we present flow visualization experiments to identify recirculation zones in an enclosed space. It is based on the deflection of the smoke streak generated by an incense stick. We use particle image velocimetry (PIV) post-processing to quantify the deflection of the smoke streak and use it as an indicator of the direction of local air flow. Positive deflection, defined as the deflection towards the exit location, is associated with primary flow present in well-ventilated regions of the room. On the other hand, negative deflection indicates reversed flow in recirculation zones, where the smoke streak is defined away from the exit location. The technique is applied to a public shared washroom, where the toilet seat is found to be in a well-ventilated region, while the washbasin is in a large recirculation zone. We compare the experimental point measurements with flow field solution obtained using computational fluid dynamics (CFD). We also explore geometry modifications as a strategy to eliminate the recirculation zone over the washbasin.Supplementary InformationThe online version contains supplementary material available at 10.1007/s41403-022-00335-1.

Improving the Percutaneous Approach for the Management of Trigeminal Neuralgia

Trigeminal neuralgia, a debilitating pain disorder affecting the trigeminal nerve distribution, is often treated through percutaneous procedures using the route of Härtel. Miscannulation and excessive attempts at traversing the foramen ovale can negatively affect surgical outcomes. Complications attributed to miscannulation include blindness, brainstem hematoma, temporal lobe hematoma, and carotid artery hemorrhage. Currently, there is disagreement regarding the best skin entry point for the percutaneous approach. However, identifying an optimum entry point for cannulation can decrease the number of attempts necessary for a successful cannulation and also decrease the amount of fluoroscopic radiation exposure for both the patient and the surgeon. Therefore, this cadaveric study assessed a total of 56 cadavers to identify the optimum skin entry point. Calvariae, brains, and trigeminal nerves were removed, and the foramina ovalae were exposed. A lumbar needle was inserted through each porous trigeminus and foramen ovale at varied angles. The cannulation procedure was “reversed” by inserting the needle from the interior of the cranium through the porous trigeminus, foramen ovale, and skin. The exit location of the needle relative to facial structures was assessed. The exit points from the facial skin, which would otherwise represent the optimal entry points for the percutaneous procedure, were recorded. The results of this study represent an improvement in the percutaneous approach for the management of trigeminal neuralgia.

IoT-Enabled Vehicle Speed Monitoring System

Millions of people lose their lives each year worldwide due to traffic law violations, specifically, over speeding. The existing systems fail to report most of such violations due to their respective flaws. For instance, speed guns work in isolation and cannot measure speed of all vehicles on roads at all spatial points. They can only detect the speed of the vehicle the line of sight of the camera. A solution is to deploy a huge number of speed guns at different locations on the road to detect and report vehicles that are over speeding. However, this solution is not feasible because it demands a large amount of equipment and computational resources to process such a big amount of data. In this paper, a speed detection framework is developed to detect vehicles’ speeds with only two speed guns, which can report speed even when the vehicle is not within the camera’s line of sight. The system is specifically designed for an irregular traffic scenario such as that of Pakistan, where it is inconvenient to install conventional systems. The idea is to calculate the average speed of vehicles traveling in a specific region, for instance, between two spatial points. A low-cost Raspberry Pi (RPi) module and an ordinary camera are deployed to detect the registration numbers on vehicle license plates. This hardware presents a more stable system since it is powered by a low consumption Raspberry Pi that can operate for hours without crashing or malfunctioning. More specifically, the entrance and exit locations and the time taken to get from one point to another are recorded. An automatic alert to traffic authorities is generated when a driver is over speeding. A detailed explanation of the hardware prototype and the algorithms is given, along with the setup configurations of the hardware prototype, the website, and the mobile device applications.

Особенности работы звеньев газодымозащитной службы при массовом спасении людей

Introduction. It is well known that in case of fire at facilities with a massive presence of people, there are difficulties in evacuating or rescuing the victims. The reason is the following factors: 1) Visitors do not know the location of the emergency exits, in addition to this, people experience a feeling of fear that suppresses logical thinking; 2) Due to the time spent on concentrating the forces and means of fire departments, rescue of people from smoky premises is not organized in time, which can lead to tragic consequences; 3) Insufficient time of the protective action of breathing apparatus with compressed air and dense smoke do not allow to quickly find the victims. This paper presents the results of modeling and an experiment carried out by the authors to rescue the victims. During the experiment, the necessary number of gas and smoke protection service units was concentrated in advance and ready to rescue the victims, which is almost impossible in a real fire. The paper investigates the difficulties of the work of gas and smoke protection service units in rescuing people at facilities with a massive stay of people, not taking into account the impact of fire hazards. The aims and objectives. The aim of the work is to investigate the features of functioning of the gas and smoke protection service units during mass rescue operations. Methodology. The mechanism of the work of the gas and air search and rescue units during mass rescue works is studied. The work time of the gas and smoke protection service units, spent on the rescue of victims, is described. The experiment was carried out practically under ideal conditions, allowing to concentrate the forces and means of the fire-rescue garrison in the amount hypothetically sufficient for carrying out rescue operations in an unbreathable environment at facilities with mass stay of people. The results of the study. The mechanism of link operation is investigated and presented during mass rescue operations. Difficulties of mass rescue are visually shown. In the conditions of the largely idealized experiment within twenty minutes on two routes simultaneously could be conditionally extracted from the smoke-filled rooms no more than 18 people. The time difference between the first and the last rescued was more than 20 minutes. Conclusion. The results of the study determine the need for significant adaptation of methods and development of technical means for solving problems during mass rescue operations in an unbreathable environment. Keywords: rescue works, gas and smoke rescue unit, breathing apparatus, time, distance, victim.

A systematic approach to calibrate spray and break-up models for the simulation of high-pressure fuel injections

A novel calibration methodology is presented to accurately predict the fundamental characteristics of high-pressure fuel sprays for Gasoline Direct Injection (GDI) applications. The model was developed within the Siemens Simcenter STAR-CD 3D CFD software environment and used the Lagrangian–Eulerian solution scheme. The simulations were carried out based on a quiescent, constant volume, computational vessel to reproduce the real spray testing environment. A combination of statistic and optimisation methods was used for spray model selection and calibration and the process was supported by a wide range of experimental data. A comparative study was conducted between the two most commonly used models for fuel atomisation: Kelvin–Helmholtz/Rayleigh–Taylor (KH–RT) and Reitz–Diwakar (RD) break-up models. The Rosin–Rammler (RR) mono-modal droplet size distribution was tuned to assign initial spray characteristics at the critical nozzle exit location. A half factorial design was used to reveal how the various model calibration factors influence the spray properties, leading to the selection of the dominant ones. Numerical simulations of the injection process were carried out based on space-filling Design of Experiment (DoE) schedules, which used the dominant factors as input variables. Statistical regression and nested optimisation procedures were then applied to define the optimal levels of the model calibration factors. The method aims to give an alternative to the widely used trial-and-error approach and unveils the correlation between calibration factors and spray characteristics. The results show the importance of the initial droplet size distribution and secondary break-up coefficients to accurately calibrate the entire spray process. RD outperformed KH–RT in terms of prediction when comparing numerical spray tip penetration and droplet size characteristics to the experimental counterparts. The calibrated spray model was able to correctly predict the spray properties over a wide range of injection pressure. The work presented in this paper is part of the APC6 DYNAMO project led by Ford Motor Company.

Utilising Natural Attributes of Tropical Islands for Beach Protection

This study reveals the coastal protection benefits of small artificial reefs on tropical islands. A monitored case study involving field and computer modelling investigations, as well as construction of a 95 m long reef and 12,000 m3 of local sand nourishment in a tropical lagoon on the north-east coast of Mauritius, is presented. Monitoring showed that a large salient widened the beach by 50 m in one year. The salient has continued to grow slowly and has remained stable for four years, including during a cyclone. Only a simple and inexpensive artificial reef was needed in the shallow lagoon to rebalance the shoreline wave conditions, because most wave energy was lost by breaking further offshore on the natural reef. With rising sea levels, inshore reefs with nourishment can overcome increases in wave height, wave set-up and wave run-up at the shoreline, which are jointly responsible for erosion and the flooding of homes by erosion and over-topping. To find suitable nourishment sources, regional computer modelling identified the following dominant circulation patterns: currents both coming into the lagoon over the reef crest (driven by breaking wave energy) and exiting via relict river channels or zones of lower waves. Sand for nourishment may be extracted from the exit locations with reduced environmental impact, because net currents are driving sand out of the lagoon system into deeper water. These relict sands have the same grain size as the natural beach and are readily accessible.

Transient electroosmotic-driven ionic current magnetic fields in a charged nano-capillary

Transient electrokinetic analysis can provide practical insights on the evolution of dynamic phenomena in micro and nano-capillaries, which are often ignored in a steady-state analysis. In this paper, a numerical model is proposed for the transient electrokinetic analysis of electroosmotic flows in a charged nanocapillary. In addition, the transient effects of ionic currents and the magnetic field generated both inside and outside the nanochannel were evaluated, and the results were compared with a simplified analytical model. Results showed that the peak of the magnetic field strength occurs in the vicinity of the charged walls at the outer surface of the nanochannel, which was associated with the distribution of the total current density flowing within the channel. The magnetic flux density was also compared at three different sections; entry, mid, and exit locations. This comparison proved that the nature of the longitudinal changes in the electric double layer distribution has significant effects on the decay rate of the magnetic field outside of the nanochannel walls. The obtained results confirm that the generated magnetic field, detected outside of the nanochannels, could be used as a secondary electromagnetic signal for biomolecules as a part of a sequencing technique.

Internet of Things–Based Command Center to Improve Emergency Response in Underground Mines

BackgroundUnderground mines have several hazards that could lead to serious consequences if they come into effect. Acquiring, evaluating, and using the real-time data from the atmospheric monitoring system and miner's positional information is crucial in deciding the best course of action. MethodsA graphical user interface–based software is developed that uses an AutoCAD-based mine map, real-time atmospheric monitoring system, and miners' positional information to guide on the shortest route to mine exit and other locations within the mine, including the refuge chamber. Several algorithms are implemented to enhance the visualization of the program and guide the miners through the shortest routes. The information relayed by the sensors and communicated by other personnel are collected, evaluated, and used by the program in proposing the best course of action. ResultsThe program was evaluated using two case studies involving rescue relating to elevated carbon monoxide levels and increased temperature simulating fire scenarios. The program proposed the shortest path from the miner's current location to the exit of the mine, nearest refuge chamber, and the phone location. The real-time sensor information relayed by all the sensors was collected in a comma-separated value file. ConclusionThis program presents an important tool that aggregates information relayed by sensors to propose the best rescue strategy. The visualization capability of the program allows the operator to observe all the information on a screen and monitor the rescue in real time. This program permits the incorporation of additional sensors and algorithms to further customize the tool.

Investigation on the properties of sine-Wiener noise and its induced escape in the particular limit case D → ∞

Sine-Wiener (SW) noise is increasingly adopted in realistic stochastic modeling for its bounded nature. However, many features of the SW noise are still unexplored. In this paper, firstly, the properties of the SW noise and its integral process are explored as the parameter D in the SW noise tends to be infinite. It is found that although the distribution of the SW noise is quite different from Gaussian white noise, the integral process of the SW noise shows many similarities with the Wiener process. Inspired by the Wiener process, which uses the diffusion coefficient to denote the intensity of the Gaussian noise, a quantity is put forward to characterize the SW noise’s intensity. Then we apply the SW noise to a one-dimensional double-well potential system and the Maier–Stein system to investigate the escape behaviors. A more interesting result is observed that the mean first exit time also follows the well-known Arrhenius law as in the case of the Gaussian noise, and the quasi-potential and the exit location distributions are very close to the results of the Gaussian noise.

Save reservoirs of humid subtropical cities from eutrophication threat.

Reservoir water is the most important freshwater resource for many cities, especially in densely populated humid subtropical areas. Economic growth, population increase, and urbanization have been putting reservoir water of Shenzhen (China), a humid subtropical city, under severe threat of eutrophication and water supply shortage. In this study, we focused on an upstream reservoir of Shenzhen and established a 3-dimensional hydrodynamic-ecological model to investigate the water dynamics and nutrient budget. Tributaries to the reservoir were identified as the greatest contributors to nitrogen and phosphorus loads. Zones with weak flows and high nutrient concentration have high risks of causing blooms. Several mitigation measures were proposed, including improving flow by adding additional water exit locations in the reservoir, reducing nutrients in tributaries, and enhancingalgal predation, and were evaluated with the established model. The strategies combining hydrodynamic improvement and phosphorus reduction were suggested to decision makers and government managers for short-term management. However, for future water safety, excessive nitrogen is a potential danger. This study provides a modeling framework that can be applied to anthropogenic-influenced reservoirs elsewhere.

Optimization of Building Exit Layout: Combining Exit Decisions of Evacuees

Exits are essential to the efficiency of building evacuation due to its irreplaceable function, and the layout of multiple exits has always been the key concern for architectural design. To accurately evaluate the evacuation efficiency of different multiexit layouts and optimize the design rules, a dynamic exit decision model integrating an exit selection strategy and the social force model is developed to simulate the practical evacuation. And our proposed model outperforms the original social force model in terms of evacuation efficiency. Accordingly, different layouts are analyzed for evacuation in a single room with two exits. The analysis results reveal that evacuation time will be improved with the changes of exit locations and two parallel exits are validated as the most efficient layout among the three common categories. Affected by walking time and queuing time of evacuees, it is not conducive to evacuation whether the separation of two exits is too large or too small. Furthermore, an even symmetry is found more efficient than an asymmetric distribution of exits under some conditions. This work provides a basis for architectural designs of multiple exits and a foundation for further study of evacuation simulation.

Analysis on the Motorcycle-Exclusive Lane Implementation for the Urban Arterial Road in Banda Aceh City

A motorcycle-exclusive lane was implemented since 2015 at busiest urban arterial road in the city center of Banda Aceh. However, this policy seen to be ineffective as indicated by the low obedience by the motorcycle users. This study was, therefore, conducted to analyze the determinant of the implementation of motorcycle-exclusive lane. This involved infrastructure observation and road user direct interview through questionnaires survey. Target respondent was motorcyclist who used motorcycle-exclusive lane within the study area. A total volume of these users was observed to be 364 vehicles/day and drawn the sample as much as 170 samples were selected for data analysis using the Principal Component Analysis (PCA). The PCA found that the main factors influencing the implementation of the motorcycle-exclusive lanes include the sign, lane support, motorbike, and speed factors with each having its significant explanatory level. Finding depict that greatest factor had 26.419% variant of Factor 1 with technical improvement delivers to aspect of motorcycle-exclusive lanes must have traffic signs showing the entry and exit locations of motorbikes, must have motorcycle-exclusive lanes with information prohibiting the motorbikes from stopping, and motorcycle-exclusive lane signs must install in the needed place and easily visible to users.

Evaluation of Rapid Exit Locations Based on Veer-Off Risk for Landing Aircraft

Rapid exit taxiways enhance runway operational capacities by means of reducing the runway occupancy times of aircraft. The selection of rapid exit taxiway locations is important to achieve the optimum runway capacity. This paper presents a methodology for locating rapid exits based on excursion risk. Considering the level of severity and frequency of historical runway-related accidents and emerging use of rapid exit taxiways in the future, this study explores the associated veer-off risk at rapid exits. The proposed methodology estimates veer-off risk using three successive steps such as event probability, location probability, and severity estimation. An existing logistic regression model developed for landing overrun probability estimation is adapted for the exit taxiway facility to estimate event probability. Aircraft touchdown speed, deceleration, and runway criticality factor are the important operational parameters of this model adaptation. The aircraft turn path radius and kinetic energy at the time of veer-off are used to estimate the respective location probabilities and accident severities. As the sample analysis proves, the associated veer-off risk increases when the exits are closer to the runway threshold. The paper recommends wider taxiways and larger taxiway radii to compensate for increasing veer risks. The methodology helps for planning risk-based rapid exit taxiways for varying design, operational, and weather conditions.

Emergency Evacuation Planning via the Point of View on the Relationship Between Crowd Density and Moving Speed

Emergency evacuation is concerning to both industry and academics. This work applied the technology of a wireless sensor network to design and propose a nonlinear mathematical model and heuristic approach to fire emergency evacuation problem. The proposed model first considers basic factors including the distribution of people in each area, possible safe exit locations, possible hazard locations, rooms, open spaces, doors, and junctions. Based on these common factors and the proposed heavy smoke diffusion, the objective of the proposed model is to evacuate all people in the shortest time through the concept of load balance coming from the relationship between crowd density and moving speed. The algorithm of simulated annealing is finally applied to solve the evacuation planning problem derived from the proposed model. Experimental results verify the efficiency of the proposed model and the resulting solution.