Computational Fluid Dynamics Techniques Research Articles

Combining Computational Fluid Dynamics and Experimental Data to Understand Fish Schooling Behavior.

Understanding the flow physics behind fish schooling poses significant challenges due to the difficulties in directly measuring hydrodynamic performance and the three-dimensional, chaotic, and complex flow structures generated by collective moving organisms. Numerous previous simulations and experiments have utilized computational, mechanical, or robotic models to represent live fish. And existing studies of live fish schools have contributed significantly to dissecting the complexities of fish schooling. But the scarcity of combined approaches that include both computational and experimental studies, ideally of the same fish schools, has limited our ability to understand the physical factors that are involved in fish collective behavior. This underscores the necessity of developing new approaches to working directly with live fish schools. An integrated method that combines experiments on live fish schools with computational fluid dynamic (CFD) simulations represents an innovative method of studying the hydrodynamics of fish schooling. CFD techniques can deliver accurate performance measurements and high-fidelity flow characteristics for comprehensive analysis. Concurrently, experimental approaches can capture the precise locomotor kinematics of fish and offer additional flow information through particle image velocimetry (PIV) measurements, potentially enhancing the accuracy and efficiency of CFD studies via advanced data assimilation techniques. The flow patterns observed in PIV experiments with fish schools and the complex hydrodynamic interactions revealed by integrated analyses highlight the complexity of fish schooling, prompting a reevaluation of the classic Weihs model of school dynamics. The synergy between CFD models and experimental data grants us comprehensive insights into the flow dynamics of fish schools, facilitating the evaluation of their functional significance and enabling comparative studies of schooling behavior. In addition, we consider the challenges in developing integrated analytical methods and suggest promising directions for future research.

Leveraging the Supercomputer Fugaku for the Assessment of Droplet/Aerosol Transmission Risks in COVID‐19 Mitigation Efforts

This work delves into the significant advancements in epidemiological modeling and public health policy driven by detailed, quantitative analyses of COVID‐19 aerosol transmission utilizing the capabilities of the supercomputer Fugaku, the world's fastest supercomputer in 2020. By integrating novel computational fluid dynamics (CFD) techniques integrated in the multi‐physics solver CUBE, we achieved scalable, high‐resolution simulations essential for modeling micrometer‐sized virus‐containing aerosols, revolutionizing our understanding of transmission risks in various societal contexts. This innovation significantly reduced the time‐to‐solution for these intricate simulations and allowed for the quick creation of digital twins that captured a broad range of social scenarios with substantial transmission risks. These efforts required a significant amount of computational resources, which were provided for through Fugaku, during COVID‐19. The detailed transmission risk assessments that were produced through this work had a significant impact on public health policies and public behavior throughout Japan, exemplifying a pivotal shift in the digital transformation of epidemiology and the proactive management of pandemic‐related challenges. © 2024 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

CFD for the optimization of spiral wound film assembly

In this paper, a conventional mesh shim for a spiral wound membrane assembly is structurally optimized by adding jet holes to achieve the jet function, and the effect of curvature on fluid flow is investigated. The three different gaskets are compared with each other and the performance of the optimized gaskets is investigated by using computational fluid dynamics (CFD) techniques and analyzed parametrically. This knowledge can be supplemented by the use of CFD techniques for spacers, whereby the geometry of the spacer can be optimized and the corresponding performance of the spiral wound film assembly can be improved.

Validation of ultrasound velocimetry and computational fluid dynamics for flow assessment in femoral artery stenotic disease.

To investigate the accuracy of high-framerate echo particle image velocimetry (ePIV) and computational fluid dynamics (CFD) for determining velocity vectors in femoral bifurcation models through comparison with optical particle image velocimetry (oPIV). Separate femoral bifurcation models were built for oPIV and ePIV measurements of a non-stenosed (control) and a 75%-area stenosed common femoral artery. A flow loop was used to create triphasic pulsatile flow. In-plane velocity vectors were measured with oPIV and ePIV. Flow was simulated with CFD using boundary conditions from ePIV and additional duplex-ultrasound (DUS) measurements. Mean differences and 95%-limits of agreement (1.96*SD) of the velocity magnitudes in space and time were compared, and the similarity of vector complexity (VC) and time-averaged wall shear stress (TAWSS) was assessed. Similar flow features were observed between modalities with velocities up to 110 and in the control and the stenosed model, respectively. Relative to oPIV, ePIV and CFD-ePIV showed negligible mean differences in velocity (), with limits of agreement of (control) and (stenosed). CFD-DUS overestimated velocities with limits of agreements of and for the control and stenosed model, respectively. VC showed good agreement, whereas TAWSS showed similar trends but with higher values for ePIV, CFD-DUS, and CFD-ePIV compared to oPIV. EPIV and CFD-ePIV can accurately measure complex flow features in the femoral bifurcation and around a stenosis. CFD-DUS showed larger deviations in velocities making it a less robust technique for hemodynamical assessment. The applied ePIV and CFD techniques enable two- and three-dimensional assessment of local hemodynamics with high spatiotemporal resolution and thereby overcome key limitations of current clinical modalities making them an attractive and cost-effective alternative for hemodynamical assessment in clinical practice.

Mixing Time Prediction in a Ladle Furnace

This paper presents a study on the effectiveness of two turbulence models, the large eddy simulation (LES) model and the k-ε turbulence model, in predicting mixing time within a ladle furnace using the computational fluid dynamics (CFD) technique. The CFD model was developed based on a downscaled water ladle from an industrial ladle. Corresponding experiments were conducted to provide insights into the flow field, which were used for the validation of CFD simulations. The correlation between the flow structure and turbulence kinetic energy in relation to mixing time was investigated. Flow field results indicated that both turbulence models aligned well with time-averaged velocity data from the experiments. However, the LES model not only offered a closer match in magnitude but also provided a more detailed representation of turbulence eddies. With respect to predicting mixing time, increased flow rates resulted in extended mixing times in both turbulence models. However, the LES model consistently projected longer mixing times due to its capability to capture a more intricate distribution of turbulence eddies.

Computational fluid dynamics analysis of the fluid environment of 3D printed gradient structure in interfacial tissue engineering

Mass transport properties within three-dimensional (3D) scaffold are essential for tissue regeneration, such as various fluid environmental cues influence mesenchymal stem cells differentiation. Recently, 3D printing has been emerging as a new technology for scaffold fabrication by controlling the scaffold pore geometry to affect cell growth environment. In this study, the flow field within scaffolds in a perfusion system was investigated with uniform structures, single gradient structures and complex gradient structures using computational fluid dynamics (CFD) method. The CFD results from those uniform structures indicate the fluid velocity and fluid shear stress within the scaffold structure increased as the filament diameter increasing, pore width decreasing, pore shape decreased from 90° to 15°, and layer configuration changing from lattice to stagger structure. By assembling those uniform structure as single gradient structures, it is noted that the fluid dynamic characterisation within the scaffold remains the same as the corresponding uniform structures. A complex gradient structure was designed to mimic natural osteochondral tissue by assembly the uniform structures of filament diameter, pore width, pore shape and layer configuration. The results show that the fluid velocity and fluid shear stress within the complex gradient structure distribute gradually increasing and their maximum magnitude were from 1.15 to 3.20 mm/s, and from 12 to 39 mPa, respectively. CFD technique allows the prediction of velocity and fluid shear stress within the designed 3D gradient scaffolds, which would be beneficial for the tissue scaffold development for interfacial tissue engineering in the future.

Water quality assessment using Bi-LSTM and computational fluid dynamics (CFD) techniques

Assessment of water quality is imperative for informed decision-making, ecological preservation, and sustainable water resource management, particularly in light of escalating anthropogenic pollution. Traditional approaches often face complexities and inaccuracies in forecasting, necessitating advancements in modelling techniques. Machine learning methods, particularly deep learning, present promising avenues for accurate water quality estimation, albeit with challenges. This study aims to enhance water quality forecasting through the integration of deep learning, specifically Bi-directional Long Short-Term Memory (Bi-LSTM) networks, with computational fluid dynamics (CFD). The objective is to address the limitations of existing methods by leveraging the synergies between deep learning and fluid dynamics simulations, thereby improving predictive accuracy and efficiency. By proposing a novel framework that combines Bi-LSTM networks with computational fluid mechanics, this study introduces an innovative approach to water quality assessment. The integration of these techniques offers a comprehensive solution to overcome the complexities inherent in traditional methods, promising greater reliability and efficiency in predicting water quality parameters. The study employs Bi-LSTM networks alongside CFD simulations to model contaminant movement and diffusion in water bodies, particularly focusing on the Yamuna River. Utilizing empirical data on Chemical Oxygen Demand (COD) and Biological Oxygen Demand (BOD), the framework aims to predict key factors influencing water quality. The ANSYS software, operating within a Windows environment, facilitates the execution of the proposed methodology. Evaluation of the proposed model demonstrates superior performance compared to traditional methods, exhibiting higher predictive reliability and lower margins of error. Through a comprehensive comparison study, the Bi-LSTM and CFD-based approach surpasses existing techniques in accurately forecasting water quality parameters, thus highlighting its efficacy and potential for practical application. The integration of Bi-LSTM networks with computational fluid dynamics presents a promising avenue for enhancing water quality evaluation. The study underscores the significance of leveraging advanced computational techniques to address the challenges associated with forecasting water quality, ultimately contributing to informed decision-making and sustainable water resource management.

Study on the Improvement of Droplet Penetration Effect by Nozzle Tilt Angle under the Influence of Orthogonal Side Wind.

This study investigates the impact of varying side wind velocities and nozzle inclination angles on droplet penetration during plant protection spraying operations, focusing on citrus trees. Experiments were conducted across four wind speed levels (0, 1, 2, 3 m/s) perpendicular to the nozzle direction and seven nozzle inclination levels (0°, 8°, 15°, 23°, 30°, 38°, 45°) to evaluate droplet distribution under different spraying parameters. A baseline condition with 0 m/s wind speed and a 0° nozzle angle served as the control. Utilizing Computational Fluid Dynamics (CFD) and regression analysis techniques in conjunction with field trials, the droplet penetration was analyzed. Results indicate that at constant wind speeds, adjusting the nozzle inclination angle against the direction of the side wind can significantly enhance droplet deposition in the canopy, with a 23° inclination providing the optimal increase in deposition volume, averaging a change of +16.705 μL/cm2. Multivariate nonlinear regression analysis revealed that both wind speed and nozzle inclination angle significantly affect the droplet penetration ratio, demonstrating a correlation between these factors, with wind speed exerting a greater impact than nozzle angle. Increasing the nozzle inclination angle at higher wind speeds improves the penetration ratio, with the optimal parameters being a 23° angle and 3 m/s wind speed, showing a 12.6% improvement over the control. The model fitted for the impact of nozzle angle and wind speed on droplet penetration was validated through field experiments, identifying optimal angles for enhancing penetration at wind speeds of 1, 2, and 3 m/s as 8°, 17°, and 25°, respectively. This research provides insights for improving droplet penetration techniques in plant protection operations.

Dynamic temperature distribution characteristics of a large glasshouse with cooling system during the start-stop stage

Excessive heat accumulation leads to high temperature in the glasshouse, the high temperature directly affects the normal growth of crops. This research based on the cooling system as the cooling method of glasshouse, experimental and computational fluid dynamics technique were used to investigate the cooling effect in the start-stop stage. CFD was used to simulate and optimize the temperature dynamics during the start-stop phase of the glasshouse cooling system in the most common summer climates (rainy and sunny). A glasshouse test platform was built in Wuhan in order to conduct temperature experiments to verify the effectiveness of the simulation. The results show that starting the cooling system in summer can effectively reduce the temperature inside the glasshouse in a short time (when it is rainy, the temperature is reduced by 8.1 °C; when it is sunny, the temperature is reduced by 5 °C). During the start-stop stage, the temperature trend of the horizontal and vertical planes is the same. Until the system is running stably, the indoor temperature is maintained uniform and stable, with little fluctuation. In order to create the best growing environment for crops, the air velocity of the air supply outlet is increased to 6.0 m/s on sunny days, which is helpful to increase crop yield and reduce greenhouse gas emissions.

Computational fluid dynamics method for determining the rotational diffusion coefficient of cells

This work presents a straightforward computational method to estimate the rotational diffusion coefficient (Dr) of cells and particles of various sizes using the continuum fluid mechanics theory. We calculate the torque (Γ) for cells and particles immersed in fluids to find the mobility coefficient μ and then obtain the Dr by substituting Γ in the Einstein relation. Geometries are constructed using triangular mesh, and the model is solved with computational fluid dynamics techniques. This method is less intensive and more efficient than the widely used models. We simulate eight different particle geometries and compare the results with previous literature.

Analysis of Fluid Pressure Drop through a Globe Valve using Computational Fluid Dynamics and Statistical Techniques

Fluid mechanics plays a crucial role in everyday life, enabling the selection of accessories, materials, and various components essential for a system through which fluid flows. Pressure drop stands out as one of the most relevant factors in the design of fluid flow systems. However, analytical and experimental physical methods can increase these analyses' costs and time. Hence, in this study, statistical tools are employed to carry out specific experiments supported by numerical fluid simulation, aiming to comprehend the pressure drop behavior in a fluid as it passes through a globe valve. This valve, in turn, possesses distinct operating and manufacturing characteristics. The methods employed encompass a complete factorial system of response surface as support to construct the experimental design path through computational fluid dynamics. Among the key findings, it is demonstrated that, for systems with relatively low flow rates, the valve opening percentage does not exhibit a significant relationship with fluid pressure drop. Conversely, significant effects are observed for systems with relatively high flow rates regarding the valve opening percentage and pressure drop, reaching values of up to 73% pressure drop in this study. It can be inferred that the integration of statistical experimental design techniques and computational fluid dynamics constitutes a valuable resource for studying the pressure drop of a fluid passing through a system.

Optimizing metal part distortion in the material extrusion-thermal debinding-sintering process: An experimental and numerical study

The thermal debinding-sintering process plays an essential role in the context of material extrusion-based additive manufacturing (AM) for producing parts using metal injection molding (MIM). During thermal debinding, metal parts often experience material distortion and porosity, which negatively impacts their mechanical properties. Slowing down the debinding speed is a common approach to mitigate material distortion and porosity. However, this leads to a significant increase in the debinding time. In this study, we carried out debinding-sintering experiments to optimize the distortion and porosity in metal parts. These metal parts were manufactured utilizing bronze/polylactide (PLA) blend filaments and placed in crucibles of different sizes (small, medium, and large), with different heating rates and holding times. The results revealed that the small crucible yielded higher porosity levels in the metal parts, which could be reduced from 23% to 12% by extending both the heating and holding times. In contrast, the medium crucible managed to reduce porosity to approximately 15% without requiring an extension of the processing time. The large crucible, on the other hand, couldn't achieve further porosity reduction due to challenges in reaching the desired temperature. To gain a deeper insight into temperature distribution during the debinding process, we performed numerical simulations using the computational fluid dynamics (CFD) technique and obtained temperature profiles within the kiln using the three crucibles. Ultimately, we carried out standard mechanical tests on the resulting metal parts and evaluated the thermal debinding procedure under various conditions. The approach we employed, combining experiments and numerical simulations, demonstrated significant promise for enhancing the quality of metal parts in the thermal debinding-sintering process.

CFD Analysis of Automobile Radiator Performance: Investigation of Heat Input, Mass Flow Rate, and Coating Thickness Effects

This research paper delves into the realm of Computational Fluid Dynamics (CFD) analysis to optimize the thermal performance of automobile radiators through the application of coatings. The study focuses on the impact of three different coating sizes, namely 50 micrometres, 80 micrometres, and 100 micrometres, aiming to enhance heat transfer efficiency and overall radiator performance. To systematically investigate the influence of these coatings on thermal behaviour, the L9 Orthogonal array is employed as a robust experimental design. The experimental methodology involves simulating the radiator's heat dissipation capabilities using CFD techniques, considering the interaction of fluid dynamics and heat transfer within the coated radiator. The L9 Orthogonal array provides a systematic and efficient approach to conducting experiments, allowing for the exploration of various coating combinations and their effects on thermal performance. The research not only analyses the impact of different coating sizes on the overall heat transfer efficiency but also seeks to identify optimal combinations that yield superior results. Insights gained from this study contribute to the development of advanced thermal management strategies in automotive engineering, aiming to enhance the cooling efficiency of radiators while maintaining operational and material constraints. Key findings highlight the significant role that coating thickness plays in augmenting the heat dissipation capabilities of automobile radiators. The outcomes of this research bear implications for the automotive industry, guiding future design considerations for improved radiator performance in terms of heat transfer efficiency, energy consumption, and overall system sustainability.

Effects of composite structures on internal flow field and particle classification performance of hydrocyclone

ABSTRACT Hydrocyclones are commonly used solid – liquid separation apparatuses extensively adopted in various sorting industries owing to their unique advantages. However, the intrinsic constraints of their structures result in comparatively low-classification precision. Therefore, this study proposes a series of composite-structured hydrocyclones to augment their classification accuracy. Employing computational fluid dynamics techniques, this study provides a numerical analysis of hydrocyclones with varying structures, thus resulting in a series of valuable findings. Initially, the introduction of the composite structures effectively strengthened the centrifugal force in a manner directly proportional to the number of inlets. Internal turbulence provides effective turbulent scouring of the particles, simultaneously offering enhanced flow-field stability. Finally, the cutting ability and classification precision of the composite structures were substantially enhanced compared with those of traditional hydrocyclones. This was most evident in the structures that utilized four inlets, a parabolic cone section, and a thick-walled overflow pipe structure which resulted in superior product quality.

Enhancing accuracy and efficiency: A novel implicit–explicit approach for fluid dynamics simulation

This study presents an innovative implicit–explicit time-stepping algorithm based on a first-order temporal accuracy method, addressing challenges in simulating all-regimes of fluid flows. The algorithm's primary focus is on mitigating stiffness inherent in the density-based “Roe” method, pivotal in finite volume approaches employing unstructured meshes. The objective is to comprehensively evaluate the method's efficiency and robustness, contrasting it with the explicit fourth-order Runge–Kutta method. This evaluation encompasses simulations across a broad spectrum of Mach numbers, including scenarios of incompressible and compressible flow. The scenarios investigated include the Sod Riemann problem to simulate compressible Euler equations, revealing the algorithm's versatility, and the low Mach number Riemann problem to analyze system stiffness in incompressible flow. Additionally, Navier–Stokes equations are employed to study viscous and unsteady flow patterns around stationary cylinders. The study scrutinizes two time-stepping algorithms, emphasizing accuracy, stability, and computational efficiency. The results demonstrate the implicit–explicit Runge–Kutta algorithm's superior accuracy in predicting flow discontinuities in compressible flow. This advantage arises from the semi-implicit nature of the equations, reducing numerical errors. The algorithm significantly enhances accuracy and stability for low Mach number Riemann problems, addressing increasing stiffness as Mach numbers decrease. Notably, the algorithm optimizes computational efficiency for both low Mach number Riemann problems and viscous flows around cylinders, reducing computational costs by 38%–68%. The investigation extends to a two dimensional hypersonic inviscid flow over cylinder and double Mach reflection case, showcasing the method's proficiency in capturing complex and hypersonic flow behavior. Overall, this research advances the understanding of time discretization techniques in computational fluid dynamics, offering an effective approach for handling a wide range of Mach numbers while improving accuracy and efficiency.

Design optimization of a cylindrical UV-C LED reactor for effective water disinfection with numerical simulations and test reactor fabrication

Ultraviolet C-band light-emitting diodes (UV-C LEDs) provide effective water disinfection and flexible reactor design. In this study, the disinfection performance of the cylindrical UV-C LED reactor was optimized using a new computational fluid dynamics (CFD) technique and validated experimentally with test reactors. The CFD technique provided UV doses for individual particles representing microorganisms, which were integrated along their trajectories using the discrete phase method within the radiation field acquired through the Monte Carlo method. Utilizing the minimum UV dose as a criterion, four key design parameters were evaluated: reactor aspect ratio (L/D) (in the range of 2.5−6), LED power angle (15−55°), wall reflectivity (0.6−0.94), and water flow rate (1−4 l/min). The optimal L/D of 4.2 was determined and subsequently applied to fabricate the test reactors. The polytetrafluoroethylene (PTFE) test reactor exhibited superior disinfection performance for E. coli O157:H7 compared to the one made of SUS304, due to its high wall reflectivity. Furthermore, a lower water flow rate enhanced disinfection performance by extending the residence time. The predicted log reductions exhibited a consistent trend with the measured values, confirming the efficacy of the CFD methodology applicable to various reactor designs and LED configurations.

Numerical simulation of direct methanol fuel cells using computational fluid dynamics

Recently, there has been a research trend towards clean energy sources such as fuel cells, owing to their high efficiency and close-to-zero emissions. However, the efficiency level depends on the design, and physical experiments are time-consuming requiring expensive materials; therefore, a realistic numerical simulation is crucial to test different designs and conditions. In this paper, the fluid dynamics and electrochemical reactions in direct methanol fuel cells (DMFC) are mathematically modeled and numerically simulated using computational fluid dynamics (CFD) techniques within the OpenFOAM software. The profiles of temperature, reactants, and products flow through the anodic and cathodic chambers of DMFC are derived from the equations of continuity, momentum, species transport, and electrochemical reactions are simulated to study two flow field geometries of a DMFC, parallel channels, and a serpentine channel. A methodology to obtain the crossover current density is presented, and its effect is evaluated on the DMFC behavior. The accuracy and confidence of the results are validated with a case reported in the literature.

Simulation of Nanofiltration Mass Transfer for Magnesium and Lithium Separation in Salt Lakes.

A mass transfer model to predict the transport processes of magnesium and lithium ions through porous media in salt lakes has been proposed, which is a combination of the extended Nernst-Planck equation and Donnan effect, accounting for ion diffusion, electromigration, and convection within membrane pores. First, the morphological structure, thickness, surface roughness, and hydrophilicity of the membrane were characterized as fixed parameters, indicating that the surface of the nanofiltration membrane is smooth with low roughness and strong hydrophilicity, resulting in a lower desalination rate but higher water flux. Subsequently, numerical calculations based on the model were conducted to establish a reasonable transport equation for predicting the concentration and retention rate of the main magnesium and lithium ions. When compared with the experimental results, a deviation of less than 5.5% is obtained, confirming the accuracy of the model in describing ion mass transfer. Finally, computational fluid dynamics techniques were employed to simulate the model equations in both the feed and permeate subdomains, demonstrating that the flow characteristics align with reality. Thus, the established transport model exhibits higher predictive accuracy for NF ion separation than one-dimensional models.

Recent Advances in CFD-based Bridge Fire Evaluations: A Brief Review

Bridges, as the main elements of transportation networks, demand significant attention due to their unique structural characteristics and high consequences of fire incidents. So, it is crucial to enhance the fire resilience of these structures. Various studies have focused on the integration of advanced fire modeling techniques, including computational fluid dynamics (CFD), the finite element method (FEM), and artificial intelligence (AI) to improve the fire responses of the bridges. This article provided an overview of recent advancements in bridge fire modeling and addressing methodologies, challenges, and future directions for enhancing the fire resilience of bridge structures. Natural language processing (NLP) was employed for an in-depth exploration of bridge fire engineering topics and integrated CFD, FEM, and AI techniques. It has highlighted the importance of AI in enhancing real-time fire prediction and reducing related computational demands, emphasizing the importance of developing AI integrated approaches for the accelerated and effective post-fire assessment of bridge structures, considering their unique structural challenges and high impact of fires.

Prediction of turbine gas Meter error in high-pressure by CFD techniques: A novel approach to reduce high-pressure calibration (HPC) costs

Calibrating gas meters to their operating conditions are ideal for defining accuracy, but obstacles like economics, time, physical limitations, and a lack of high-pressure calibration facilities often prevent this. A Computational Fluid Dynamics (CFD) model was created using the motion equations simultaneously angular momentum balance in steady state and the standard k-ε turbulence model to improve the prediction of Turbine Gas Meter (TGM) performance at both high-pressure and atmospheric conditions. Utilizing the Multiple Reference Frame (MRF) model, numerical simulations for a 2-inch turbine gas meter (DN 50, G65, and PN/ANSI 150) were conducted, and the proposed model's accuracy was validated by comparing atmospheric calibration simulation results with experimental data, demonstrating a Weighted Mean Error (WME) of −0.162%. According to the performance analysis results, the accuracy of the turbine gas meter deteriorated as pressure increased, and the rotor's maximum rise in angular velocity increased by 12% compared to atmospheric pressure. Additionally, it was discovered that pressure variations had a more significant impact on angular velocity at lower flow rates. Also, it was found that pressure has a considerable effect on gas turbine meter performance up to 50 bar (Re = 2.5 × 106). Angular velocity variations are negligible at more tremendous pressures and can be disregarded. Finally, a correlation for turbine gas meter was developed, which can be used to forecast angular velocity at various pressures and the error percentage compared to atmospheric conditions.