Pressure Coefficient Research Articles

AI-based predictive approach via FFB propagation in a driven-cavity of Ostwald de-Waele fluid using CFD-ANN and Levenberg–Marquardt

The integration of Artificial Intelligence (AI) and Machine Learning (ML) techniques into computational science has ushered in a new era of innovation and efficiency in various fields, with particular significance in computational fluid dynamics (CFD). Several methods based on AI and Machine Learning (ML) have been standardized in many fields of computational science, including computational fluid dynamics (CFD). This study aims to couple CFD with artificial neural networks (ANNs) to predict the fluid forces that arise when a flowing fluid interacts with obstacles installed in the flow domain. The momentum equation elucidating the flow has been simulated by adopting the finite element method (FEM) for a range of rheological and kinematic conditions. Hydrodynamic forces, including pressure drop between the back and front of the obstacle, surface drag, and lift variations, are measured on the outer surface of the cylinder via CFD simulations. This data has subsequently been fed into a Feed-Forward Back (FFB) propagation neural network for the prediction of such forces with completely unknown data. For all cases, higher predictivity is achieved for the drag coefficient (CD) and lift coefficient (CL) since the mean square error (MSE) is within ± 2% and the coefficient of determination (R) is approximately 99% for all the cases. The influence of pertinent parameters like the power law index (n) and Reynolds number (Re) on velocity, pressure, and drag and lift coefficients is also presented for limited cases. Moreover, a significant reduction in computing time has been noticed while applying hybrid CFD-ANN approach as compared with CFD simulations only.

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.

Design and demonstration of a sensing network for full-scale wind pressure measurements on buildings

There is a need for full-scale wind pressure measurements to evaluate the accuracy of peak wind load estimates from wind tunnel measurements, numerical simulations, or building codes. The objective of this study was to design a sensing network for obtaining long-term records of fluctuating wind pressures, and to demonstrate the network’s potential through deployment. A custom data-logger using the BMP388 absolute pressure sensor, which can measure pressure coefficients within ±0.1 at a wind speed of 10 m/s, was designed. The accuracy of the measured statistics was established through comparison with a standard differential sensor in a wind tunnel experiment. A network of 10 motes was deployed on the sloped roof of the 184 m tall Space Needle, obtaining over 1000 h of fluctuating pressure data. The measurements reveal a windward separation region with strong dependency of the approach wind turbulence on the pressure statistics, but positive skewness limits the peak values. The skewness becomes negative near the edge of a second, leeward separation region, resulting in peak factors up to 2.6 times larger than the code-prescribed value of 3.4. The results demonstrate that long-term full-scale measurements provide valuable insight into peak wind pressures and their dependence on approach wind characteristics.

Numerical investigation of nitrogen spontaneous condensation over airfoils in cryogenic wind tunnel

Cryogenic wind tunnels (CWT) provide the aerodynamic tests that occur at high Reynolds numbers by operating under cryogenic environment to meet the requirements of hypersonic flight simulation. However, condensation in cryogenic environment near the limited condition destroys the reliability of the test measurement results. Accordingly, research on condensation in CWT is imperative for devising effective control strategies. This study introduces a transonic non-equilibrium condensation model, tailored to evaluate the complex phenomena of nitrogen condensation over airfoils. The model was applied to assess condensation effects on the NACA 0012–64 airfoil and the RAE 2822 airfoil under various operating conditions. Furthermore, the study examined the effect of the angle of attack and airfoil shape on the condensation process. The result show that nitrogen condensation near the airfoil is observable only under operating conditions within the pre-condensation zone. Operating conditions of CWT can be tailored to prevent condensation with specific airfoil profiles. The effect of condensation on the pressure coefficient includes advancing the position of the pressure jump and increasing the pressure coefficient of the airfoil intermediate region, particularly within the 20 %–70 % chord length span on the airfoil's upper surface. This primarily affects the measurement of lift coefficients in CWT. In the operating conditions of this study, the lift coefficient exhibits a maximum deviation of 31.4 %, and the drag coefficient shows a maximum deviation of 2.4 %. The transonic spontaneous condensation model offers an approach to evaluate condensation's impact on airfoil tests within CWT. The findings introduce a methodological framework for effectively controlling condensation phenomena.

The Role of Turbulence Transport in Mechanical Energy Budgets

Abstract In this article, we study the role of turbulence transport on loss prediction using high fidelity scale-resolving simulations. For this purpose, we use eight high-fidelity simulation datasets and compute flux of entropy and stagnation pressure transport equation budgets for all the cases. We find that under certain unsteady inflow conditions, the stagnation pressure coefficient is not a reliable loss metric even at low Mach number conditions. This is due to the turbulence transport terms. The impact of these terms, typically assumed to be negligible, made stagnation pressure loss coefficient underpredict loss from 0% to over 40% when compared to entropy loss coefficient for cases considered here. This effect was most pronounced for the cases with highly unsteady inflow conditions and at low Reynolds numbers.

Effects of rotational speed on transient cooling performance of nozzle spray with liquid nitrogen in a rotor-stator cavity

This paper presents the results of an experimental investigation into the cooling performance of a rotor-stator cavity with liquid nitrogen spraying. The experiments were conducted under varying rotational Reynolds numbers ranging from 1.70 × 106 to 5.12 × 106. The effects of rotational speed on temperature drop rate are studied and compared in detail, as well as the heat transfer coefficient distribution. Sufficient data, such as heat flux, injection rate, and injection pressure, were collected to provide a basis for further study in explaining the spray and evaporation over the cavity. It was found that the cooling performance of the rotating disc is strongly affected by the rotational speed. The short-term period exhibits a peak cooling rate of 14°C/s, in contrast to the sustained cooling rate during the spray process at rotational speeds of 500r/min, which amounts to 0.9°C/s. The occurrence of cavitation and evaporation within the nozzle results in a reduction of flow coefficient and fluctuation of the injection differential pressure. The transient cooling performance is well-explained by the temperature changes and cooling-down time under different rotational speeds. The analysis of the heat transfer coefficient is further enhanced through an evaluation of the convective and conductive heat transfer rates using a one-dimensional theoretical approach. The average temperature of the disc is expected to decrease by 100°C within a time frame no longer than 120 s. Additionally, after a duration of 120 s, the average heat transfer rate on the cold side is anticipated to surpass 8000 W/(m·K).

Analytical Method for the Deformation-Based Design of Retaining Walls in Asymmetric Excavation

Conventional methods for designing retaining structures are not applicable to asymmetric excavation or deformation-based designs. This study proposes a quadruple-line displacement-dependent earth pressure coefficient model. Based on the proposed model, an analytical solution was developed to facilitate the deformation-based design of the asymmetric length of retaining walls propped at the crest. Furthermore, the effects of the soil internal friction angle, strut stiffness, excavation asymmetry level, and deformation control value on the embedment ratio (Re) of retaining walls were investigated. The results showed that Re determined by the classical equivalent-beam method is unsafe due to its basis on the ultimate-state earth pressure theory. The Re value of the shallower side exhibited greater sensitivity to asymmetric excavation than that of the deeper side. The retaining structure’s required Re decreased with an increase in the excavation asymmetry level. The required Re on either side of the retaining structure decreased as the deformation control values increased. The controlled deformation had a more obvious effect on the Re value of the retaining structure on the deeper side. The proposed method can be used for the deformation-based design of asymmetric wall lengths of retaining structures propped at the crest, considering the different excavation depths on both sides.

Effects of Leading-Edge Blowing Control and Reduced Frequency on Airfoil Aerodynamic Performances

Abstract Airfoil leading-edge fluid-blowing control is computationally studied to improve aerodynamic efficiency. The fluid injection momentum coefficient Cμ (the ratio of injection to incoming square velocities times the slot's width to airfoil's half chord length) varies from 0.5% to 5.4%. Both static and dynamic conditions are investigated for a NACA0018 airfoil at low speed and Reynolds number of 250 k based on the airfoil's chord length. The airfoil is dynamically pitched at a reduced frequency (the pitching tangential speed to the freestream speed ratio), varying between 0.0078 and 0.2. Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) is used in the simulations as based on the Transition SST and Spalart–Allmaras models, generally achieving good agreement with experimental results in lift and drag coefficients and in the pressure coefficient distributions along the airfoil. It is found that oscillating the airfoil can delay stall, as expected, in dynamic stall (DS). Leading-edge blowing control can also significantly delay stall both in static and dynamic conditions as long as sufficient momentum is applied to the control. On the other hand, for a small Cμ such as 0.5%, the leading-edge control worsens the performance and hastens the appearance of stall in both static and dynamic conditions. The airfoil's oscillation reduces the differences between pitch-up and pitch-down aerodynamic performances. Detailed analysis of vorticity, pressure, velocity, and streamline contours is given to provide plausible explanations and insight to the flow.

Experimental investigation of storm sewer geyser using a large-scale setup

The storm sewer geyser is a process where an air–water mixture violently erupts from a manhole. Despite the low hydrostatic pressure, violent eruptions can achieve a height of tens of meters above the ground. This current study experimentally investigates large-scale violent geysers using a large air pocket inserted from a pressurized air tank. The total length of the pipe system is approximately 88 m with a 0.1572 m diameter pipe. This large-scale experiment facilitates the investigation of spontaneous geyser eruptions. This study identifies the role of air–water volume ratio and coefficient of pressure (ratio of absolute initial static pressure to initial dynamic pressure) on the geyser intensity using eruption images and pressure plots. A total of 116 cases are tested, in which the volume ratio is parametrically increased from 0 to 1.1 under various operating conditions. A geyser score is defined to quantify the geyser eruption nature based on visual observations. The key findings are as follows: first, a sharp transition in geyser intensity is observed at the critical volume ratio of 0.5, and pre-transition and post-transition intensity exhibit a linear relationship with the volume ratio; and second, the critical volume ratio linearly varies with the coefficient of pressure.

Experimental and numerical study on the local crosswind environment of a wide streamlined bridge deck equipped with wind barriers at different angles of attack

In this study, the effects of wind barriers on the crosswind environment of vehicle safety on a long-span bridge with a streamlined bridge deck were investigated at different angles of attack (AOA). The profiles of the mean and the root mean square (RMS) of the wind pressure coefficients above different traffic lanes were obtained through synchronous pressure measurements. The mean pressure fields around the bridge decks were investigated by computational fluid dynamics (CFD) simulations. The crosswind environment of vehicle safety between the deck with railings and the deck with wind barriers was compared and analyzed in detail at different AOA. The results showed that the wind barriers produce a thicker separation shear layer above the bridge deck and result in a larger negative pressure region in comparison with the case with railings. This leads to a notable reduction in the mean wind pressure coefficients above the deck. The increase in the AOA enhances the above-mentioned reduction effect. It was also found that the wind barriers significantly increase the RMS of the wind pressure coefficients above the deck compared with the railings. The increase in the AOA inhibits this enhancement effect. The results of the equivalent mean pressure coefficients show that the wind barriers reduce the vehicle sideslipping risk more effectively than the vehicle overturning risk. It was also found that the effect of the wind barriers on the reduction of the overturning risk is more sensitive to the change in AOA than the effect on the reduction of the vehicle sideslipping risk.

A multi-region analysis of unsteady Oseen's equation for accelerating flow past a circular cylinder

It is difficult to find a valid high-order (of Reynolds number) analytical approximation to the uniform viscous flow past an infinite circular cylinder by applying perturbation techniques. In this study, we show that by accelerating flow past a circular cylinder with taking unsteady Stokes' solution as an initial approximation, higher-order approximation solutions to unsteady Oseen's equation can be obtained by an iteration scheme of perturbation, which exactly satisfy the boundary conditions. As a matter of fact, the nonlinear (convective) term linearized by Oseen's approximation is overweighted especially near the body surface. To eliminate the overweight, a multi-region analysis is proposed in this study to improve analytical unsteady Oseen's solution so as to extend the valid range of Reynolds numbers. In other words, the flow region is hypothetically divided into several annular regions, and the linearized convective term in each region is modified by multiplying with a Carrier's coefficient c (0 < c ≤ 1). The results show that, when the accelerating parameter in the range of 0.5 ≤ a ≤ 4, the maximum effective Reynolds number Reeff of the fourth-order five-region solution is both much larger than that of Stokes' and Oseen's ones. For example, when a = 0.5, Reeff = 22.26 is roughly eight times that of Stokes' solution (Reeff = 2.67), and nine times that of Oseen's solution (Reeff = 2.41). Moreover, when the instantaneous Reynolds number Re(t) is smaller than the Reeff, the flow separation angle and the wake length are both consistent with the numerical results obtained by accurately solving the full Navier-Stokes equations. In addition, the flow properties, including the drag coefficients, streamline patterns, and the pressure coefficients, as well as the vorticity distributions also agree well with the numerical results. This study represents a significant extension of our previous study for unsteady Stokes' equation [Xu et al., Phys. Fluids 35, 033608 (2023)] to unsteady Oseen's equation and its generalization.

Novel adjustable backflow structure in electric coolant pump for balancing hydraulic performance and reducing temperature rise

An electric coolant pump serves as the source for coolant circulation in the thermal management of electric vehicles. To address the thermal issues for the printed circuit board integrated within the electric coolant pump, a novel backflow structure with an adjustable orifice diameter is designed from the impeller outlet to the printed circuit board to promote convective heat dissipation. Eventually, this flow returns to the impeller inlet, thereby altering the hydraulic performance of pump The balance between hydraulic performance and temperature rise is achieved by adjusting the orifice diameter. Considering the variations in coolant properties with respect to temperature, numerical simulations of the electric coolant pump are performed using the unsteady compressible Reynolds-Averaged Navier-Stokes Equations. There is good agreement between experimental and numerical simulations results in both cases with and without an orifice. On an average, by increasing the orifice diameter by 1.5 mm which results in a 1.11 % decrease in efficiency, a 0.008 decrease in pressure coefficient, and a reduction of temperature by 2.98 K on printed circuit board. As the orifice diameter increases, leakage losses in the rear side chamber increases with the improvement of heat dissipation. The clash between the backflow jet and the inflow from the suction pipe results in significant entropy generation, forming jet vortices and increasing in pressure fluctuation. However, when the orifice diameter exceeds 3 mm, the cooling advantages no longer justify the trade-off in hydraulic performance. Thus, 3 mm orifice diameter is an optimal compromise between hydraulic performance and temperature control.

Estimating nonlinear wind-induced response of roof cable nets by aeroelastic experiments and ML modeling

The paper examines the structural engineering challenges related to the assessment of the wind-induced vertical displacements of lightweight, hyperbolic-paraboloid cable-supported membrane roofs. Analysis and comparisons are conducted using three distinct methods for calculating the roof vertical, out-of-plane displacements. Finite-element model (FEM) analysis is employed using: (i) estimated static nodal forces obtained from wind pressure coefficients determined by aerodynamic wind tunnel tests on a rigid building model, and (ii) loads found from wind pressure coefficients, estimated through machine learning (ML) methods, and (iii) measured roof response found from aeroelastic wind tunnel tests on a flexible model. The study examines three different roof geometries (square, rectangular and circular) and two distinct membrane curvatures for each geometry. Furthermore, wind directionality (three mean-wind incidence angles) and Reynolds number effects (seven mean wind velocities) are studied. Comparisons show that the non-linear FEM analysis, based on estimated static wind loads, underestimates the roof displacements at the roof center, compared to the direct measurements on the aeroelastic model. The main contribution of the study consists of a novel application of ML models, and Artificial Neural Networks (ANNs) in particular, which are employed to correct roof displacement estimations, found by simplified aerodynamic test pressure measurements on rigid roof models. The goal is to better describe the complex fluid-structure interaction of the roof membranes, which can only be achieved by direct aeroelastic tests that are difficult to design and execute. Finally, the study demonstrates that ANNs can be used not only for preliminary design of the full-scale structure but also for construction of wind tunnel scale models.

Numerical Study on Failure Mechanisms of Deep Roadway Sidewalls with Different Height-Width Ratios and Lateral Pressures

Numerical Study on Failure Mechanisms of Deep Roadway Sidewalls with Different Height-Width Ratios and Lateral Pressures

Influences of strain rate on mechanical behaviors of unsaturated and quasi-saturated loess under varying drainage conditions

Although time-dependent deformation of geomaterials underpins slope-failure prediction models, the influence of strain rate on shearing strength and deformation behavior of loess remains unclear. The consolidated undrained (CU) and drained (CD) triaxial testing elucidated the impact of strain rate (0.005-0.3 mm/min) on strength envelopes, deformation moduli, pore pressures, and dilatancy characteristics of unsaturated and quasi-saturated loess. Under drained conditions with a controlled matric suction of 50 kPa, increasing strain rates from 0.005 mm/min to 0.011 mm/min induced decreases in failure deviatoric stress (qf), initial deformation modulus (Ei), and cohesion (c), while friction angles remained unaffected. Specimens displayed initial contractive volumetric strains transitioning to dilation across varying confining pressures. Higher rates diminished contractive volumetric strains and drainage volumes, indicating reduced densification and strength in the shear zone. Under undrained conditions, both unsaturated and quasi-saturated (pore pressure coefficient B=0.75) loess exhibited deteriorating mechanical properties with increasing rates from 0.03 mm/min to 0.3 mm/min. For unsaturated loess, reduced contractive volumetric strains at higher rates manifested relatively looser structures in the pre-peak stress phase. The strength decrement in quasi-saturated loess arose from elevated excess porewater pressures diminishing effective stresses. Negative porewater pressures emerged in quasi-saturated loess at lower confining pressures and strain rates. Compared to previous studies, the qf and Ei exhibited rate sensitivity below threshold values before attaining minima with marginal subsequent influence. The underlying mechanism mirrors the transition from creep to accelerated deformation phase of landslides.

Numerical simulation of two-dimensional plain flap ground effect based on NACA4412 airfoil

Based on the NACA4412 airfoil, by solving a two-dimensional unsteady Reynolds-averaged N-S equation and using the k-ωSST model, this paper analyzes the influence of near-ground altitude change on different configuration flow fields under moving ground conditions and explores the variation law of wing pressure coefficient at different near-ground altitudes. The results show that the attraction of the upper airfoil is weakened by the GE (ground effect), the pressure of the lower airfoil is increased, and the upper and lower airfoils influence the lift change of the airfoil. With the decrease of near-ground altitude, at a certain AOA (angle of attack), the greater the flap angle is, the faster the suction loss on the upper wing surface is and the slower the pressure increases on the lower wing surface, and the lower the near-ground altitude corresponding to the minimum lift coefficient is. With the decrease of near-ground altitude, at a certain flap angle, the greater the AOA is, the faster the suction loss on the upper wing surface is and the slower the pressure increases on the lower wing surface, and the lower the near-earth altitude corresponding to the minimum lift coefficient is.

Research on the air-infiltration rate shelter coefficient of building complexes based on building parameter clustering

The configuration of a building complex can significantly influence the air-infiltration rate, which subsequently affects the energy consumption for heating and cooling. Given the diversity of parameters associated with a building complex, it is challenging to study all combinations. This study proposed the k-means clustering method to identify representative building clusters, thereby facilitating the derivation of correction coefficient for the air-infiltration rate within a complex. Initially, data pertaining to district characteristics, such as the complex density, height, and building aspect ratio, were collected and clustered to obtain several representative groups of building clusters. Subsequently, a validated computational fluid dynamics program with the renormalization group (RNG) k–ε turbulence model was employed to investigate the spatial characteristics of the pressure coefficient (Cp) on building surfaces across various groups within the complex. Finally, the shelter coefficient (SAIR), which represents the ratio of an individual building to those in different groups, was determined to correct for the air-infiltration rate in diverse district types. The results show that SAIR varies considerably (from 0.15 to 0.53) owing to the different densities, heights, and layouts between buildings. The applicability of SAIR was further demonstrated and verified in a case study of a building in Dalian, China. The research results can provide a method for predicting the air-infiltration rate of building complex.

Partitioning of wind pressure coefficients on a tall building under interference effect: a cluster analysis approach

This study proposed a cluster analysis-based approach for partitioning wind pressure on tall buildings in densely-packed areas, considering interference effects. By utilizing a modified GK cluster algorithm and leveraging the coordinate positions of pressure taps along with their corresponding wind pressure coefficients (WPC), the study aimed to distinguish different parts of the building surface exhibiting varying wind load characteristics. The adoption of cluster validation indices (CVIs) allowed for the determination of the optimal number of clusters, enhancing the accuracy and reliability of the partitioning process. The resulting clusters effectively captured the distribution of wind pressure, providing valuable insights for wind-resistant design considerations. Overall, the proposed approach demonstrates promising potential in facilitating the design and analysis of tall buildings subjected to complex wind loads in urban environments.

Convolutional neural network-based wind pressure prediction on low-rise buildings

A new model of wind pressure prediction for low-rise buildings is built based on deep convolutional neural network (CNN), and the model is trained and tested by the aerodynamic data from international open database. The prediction accuracy is compared with that of the literature, and then comprehensive error analysis on all 335 predicted taps under 3 untrained wind directions are carried out for mean and RMS pressure coefficients by various error metrics. The study shows that the distributions of mean and RMS coefficients predicted by the CNN model are closer to the experimental results in comparison with those predicted by the traditional artificial neural network (ANN) model and the common deep neural network (DNN) model without the convolution and pooling layers. The relative error on the corner tap is 13.5%, 4.3% and 0.1% by the ANN, DNN, and CNN models respectively. The mean-square-error (MSE) of the corner bay and the whole roof are also eminently reduced by the CNN model. By introducing the convolutional and pooling layers, more prediction errors are confined within 5% and basically no errors exceed 20%. Consequently, the CNN algorithm can be applied in solving various wind pressure prediction problems on buildings in the future work.

The Triple Product Rule and the Subtleties of the Mathematical Tools Used in Thermodynamics

We have clarified several formulas from mathematics and physics. Specifically, we have shown that several standard concepts from thermodynamics, which have been recently investigated and rejected in some papers, continue to be valid. Thus, we have studied the triple product rule, the first law of thermodynamics, Mayer's relation, work, function of state, the relationship between the coefficient of thermal expansion, coefficient of isothermal compressibility and thermal coefficient of pressure. We have used multivariable calculus and properties of Jacobians and other mathematical tools. Likewise, we have provided several didactic examples concerning the interpretation of thermodynamical and mathematical formulas. We have concluded that the basement of several thermodynamical formulas is correct but full of subtleties. Thus, those formulas continue to be valid despite some claims in the recent literature.