Dynamic Pressure Coefficient Research Articles

Machine Learning for Dynamic Pressure Coefficient Prediction in Vertical Water Jets

Vertical water jets present significant challenges for hydraulic structures due to their potential to cause erosion and structural damage. This study aimed to predict the dimensionless pressure coefficient (Cp) of vertical water jets by examining the relationships between experimental parameters, such as Froude number, slope, and the ratio of waterfall height over the product of the Froude number and diameter, referred to as α, using machine learning models. Two hundred forty controlled experiments were conducted, with pressure data collected. To address the problem’s non-linearity, six machine learning models were tested: linear regression, K-nearest neighbors, decision tree, support vector regression, random forest, and XGBoost. The XGBoost model outperformed others, achieving an R-squared of 0.953 and a Root Mean Squared Error (RMSE) of 0.191. Residual analysis validated its better performance, demonstrating that it delivered the most accurate predictions with minimal bias. Feature importance analysis revealed the Froude number was the most significant predictor, followed by slope and diameter. This study emphasizes the importance of the Froude number in predicting jet behavior and shows the efficacy of advanced machine learning models in capturing complex fluid dynamics, providing valuable insights for optimizing engineering applications such as water jet cutting and cooling systems.

A novel specialized material removal rate model considering the synergistic effect of dynamic pressure and shear stress for the permanent-magnet small ball-end magnetorheological polishing

Permanent-magnet small ball-end magnetorheological polishing is often used to process small glass workpiece. During polishing, the pressure and shear stress are generated by magnetorheological fluid on the workpiece surface. When conducting fixed-point polishing experiment on fused silica plane workpiece, it was found that the polished pits were mainly distributed on one side of the polishing head's rotation axis. However, the available material removal model considering only a single force cannot explain the cause of polished pit offset phenomenon. It is speculated that the synergistic effect of the two forces on material removal may lead to the offset phenomenon. In order to accurately describe the material removal mechanism of this polishing method, a novel material removal rate model is established in this research. First, a group of actual polished pits are obtained through fixed-point polishing experiment. Then, a novel pressure-shear stress synergistic material removal rate model with unknown coefficients is established. Based on this model, the fixed-point polishing process is simulated by finite element method. The simulated polished pits under different model coefficients are obtained, and the influence rules of model coefficients on the polished pit contour is analyzed. Finally, by seeking the minimal fitting error between the simulated and actual contours, a group of optimal model coefficients are determined, namely, the shear stress coefficient is 1, the dynamic pressure coefficient is 1.2, and the weight coefficient of polishing velocity is 1.9. Through verification, the relative error between the simulated and actual contours can be as low as −9.12 % to 7.13 %. The novel model reveals that the material removal is caused by both shear stress and dynamic pressure. The dynamic pressure is distributed on one side of the polishing head axis and plays a leading role in material removal, which can well explain the cause of offset phenomenon. This research fills the blank of material removal mechanism of this polishing method, and the novel model provides a theoretical basis for process optimization research.

Multi-scale flume investigation of the influence of cylindrical baffles on the mobility of landslide debris

Debris flows travel downslope at high speed and often cause damage to the infrastructure of societies around the world. With increasing extreme rainfall events and urbanization in mountainous regions, effective structural countermeasures are in increasing demand. Over recent years, engineers have proposed the installation of an array of cylindrical columns, called baffles, to reduce the velocity of debris flows in catchments. However, existing design methods are highly empirical in nature, so it is unclear whether they are adequate or over designed, and appropriate specifications and arrangement of cylindrical baffles have still not been suggested. Moreover, previous experimental studies have predominantly modeled debris flows as dry granular flows at a laboratory scale. In this study, to investigate the effect of cylindrical baffles on the dynamic characteristics of debris flow, a series of small-scale flume tests was conducted using a flume equipped with devices to measure the flow interaction between baffles and the dynamic loads of debris flow. In addition, to investigate the scale effect of debris flows and cylindrical baffles on flow characteristics, large-scale tests were also performed according to different numbers of rows of baffles for similar baffle configurations confirmed by small-scale tests. Using the small- and large-scale test results, this study analyzed the energy dissipation and dynamic impact characteristics according to the height and number of rows of baffles. The analysis results showed that the use of baffles increased the energy dissipation of debris flows, and an additional row of baffles produced greater effects on the energy dissipation in the debris flows. Based on the test results, the average dynamic pressure coefficient for cylindrical baffles was 0.31.

Study of dynamic debris impact load on flexible debris-resisting barriers and the dynamic pressure coefficient

The use of steel flexible barriers to mitigate landslide risk on natural hillsides is becoming common in the past decade in Hong Kong. The current design approach for this kind of barrier structure involves the adoption of the hydrodynamic load model to predict dynamic impact forces, followed by non-linear structural analyses of flexible barriers using numerical programs based on the pseudo-static force method. From local design guidelines, the dynamic pressure coefficient, a critical input parameter in the hydrodynamic load model, is taken as 2.0. This empirically considers the effect of impacts from boulders up to 2.0 m in diameter. With a view to rationalising the design approach, a series of physical impact tests and numerical analyses was conducted to investigate the dynamic debris impact on flexible barriers and the resulting barrier response. The physical impact tests involved up to 9 m3 of debris resisted by a 1.5 m high steel ring-net barrier. The tests were conducted in the 28 m long large-scale flume facility at the Kadoorie Centre in Hong Kong. Numerical modelling using computer programs LS-DYNA and NIDA-MNN was conducted to analyse the dynamic response of flexible barriers with different structural forms. The study aims to evaluate the dynamic pressure coefficient and to verify the current design approach based on the suggested dynamic pressure coefficient from this study. Results indicate that a dynamic pressure coefficient of 1.0 is, in general, appropriate for design purposes if the debris comprises primarily water and fine-grained particles.

A new insight into the dynamic impact between geophysical flow and rigid barrier

Understanding the interaction between complicated geophysical flows and barriers remains a critical challenge for hazards countermeasures in engineering design. In this study, the impact of geophysical flows on a rigid barrier is studied numerically using coupled computational fluid dynamics and discrete element method (CFD-DEM). Three types of fluid: Bingham, Herschel-Bulkley, and water are chosen as the fluid phase to mix with particles in the simulation, corresponding to Case B-P, Case HB-P, Case W-P, respectively. The results of two-phase simulations are then compared with initial volume controlled dry granular flow (Case P) under the same Froude condition. Two impact mechanisms, namely pileup and runup mechanisms, are recognised in flow-barrier interaction. The effects of fluid properties including viscosity and density on the impact force against the flume base and barrier and inter-particle contacts are also systematically examined. In addition, the dynamic pressure coefficient α is also predicted by a newly proposed analytical model, which has been validated by the data from experimental and numerical tests. Findings indicate that the new model may provide a useful reference to calculate the impact force for the design of a rigid barrier in intercepting hazardous geophysical flows.

Numerical Calibration and Investigation of the Influence of Reynolds Number on Measurements With Five-Hole Probes in Compressible Flows

Abstract This paper presents an investigation into the numerical and experimental calibration of a five-hole probe and effects of Reynolds number variations on the characteristics of the probe. The test object is a cone-type drilled elbow probe with a head diameter of 1.59 mm and a cone angle of 60 deg. The experimental calibration maps of four different probes of the same type and nominal geometry are compared. A significant variation of the curves can be observed especially at high yaw angles. This led to a visual inspection of the probes with a 3D measurement system. The actual geometry of the three used probes and the surface and radii in particular varied significantly from that of the unused spare probe. Furthermore, a numerical calibration map of the ideal probe was generated for a Mach number of Ma = 0.3. A comparison between the experimental and numerical calibration coefficients revealed that total pressure, yaw and pitch angle were reproduced reasonably well. The dynamic pressure coefficient, however, has a considerable offset. Finally, a parameter study of the effect of varying the Reynolds number over different yaw angles was conducted. The calibration Reynolds number is of the order of Re = 1 · 104 and was varied between 0.5 · 104 < Re < 6 · 104. While the results suggest that only minor measurement errors occur for yaw angle, total pressure and static pressure, a relatively large error was observed for pitch angle measurements.

The effects of upstream flexible barrier on the debris flow entrainment and impact dynamics on a terminal barrier

The destructive nature of debris flows is mainly caused by flow bulking from entrainment of an erodible channel bed. To arrest these flows, multiple flexible barriers are commonly installed along the predicted flow path. Despite the importance of an erodible bed, its effects are generally ignored when designing barriers. In this study, three unique experiments were carried out in a 28 m long flume to investigate the impact of a debris flow on both single and dual flexible barriers installed in a channel with a 6 m long erodible soil bed. Initial debris volumes of 2.5 and 6 m3 were modelled. For the test setting adopted, a small upstream flexible barrier before the erodible bed separates the flow into several surges via overflow. The smaller surges reduce bed entrainment by 70% and impact force on the terminal barrier by 94% compared to the case without an upstream flexible barrier. However, debris overflowing the deformed flexible upstream barrier induces a centrifugal force that results in a dynamic pressure coefficient that is up to 2.2 times higher than those recommended in guidelines. This suggests that although compact upstream flexible barriers can be effective for controlling bed entrainment, they should be carefully designed to withstand higher impact forces.

Pressure reduction in plunge pools by triangular wedges at high-head overfall spillways

Overfall spillways are important hydraulic structures for the release of overtopping water flows downstream of a dam. To reduce the effects of the impact of falling water in plunge pools, an overfall spillway outlet design that produces a longitudinally spreading jet is required. This study examined the effects of a triangular wedge placed at the end of an overfall spillway to deflect the water flow in the lateral direction, making the jet longitudinally diffuse before reaching the plunge pool. Laboratory data on the mean pressure coefficient were used to analyse the effects of various design parameters. An increase in the deflection ratio and a decrease in the weir crest length reduced the jet impact pressure. Compared with the impact of a rectangular jet falling into a plunge pool, an appropriate triangular wedge structure was found to improve the spreading of the impingement jet and reduce the mean dynamic pressure coefficient. By optimising the geometric design to accomplish jet impact control, the results of the present investigation may help engineers to design overfall spillways in high-head dam projects.

The wet-towing resistance of the composite bucket foundation for offshore wind turbines

The composite bucket foundation (CBF) is a new and environmentally-friendly foundation for offshore wind turbines. This foundation can be prefabricated in batches onshore followed by integrated transport and installation at sea. The structure itself has a subdivision air cushion structure that enables the foundation to float stably on the water surface and realize long-distance towing of the foundation. The mechanism of this air-liquid-solid coupling towing process is complicated, and the influence of the bulkheads on the towing resistance is not clear. In this paper, the influence of the subdivision structure on the towing resistance of the CBF is compared with the tow test in hydrostatic water. The structural motion characteristics and the change of the cushion pressure are also analysed. Experiments are used to verify numerical calculation results. The flow field difference between the CBF with bulkheads, the CBF without bulkheads and the real floating structure was analysed. The dynamic pressure coefficient was used to analyze the force at surfaces of different CBF's. For the tow test and numerical calculation of multiple CBFs, the optimal multi-CBF tow distance and towage number are obtained through the calculation of energy consumption rate.

Experimental investigations on wave induced dynamic pressures over slotted vertical barriers in random wave fields

Experimental investigations were carried out to assess the wave induced pressures on slotted vertical barriers. Thirty six different wave barrier configurations (10%, 20%, 30%, 40%, 50% and 60% porosities and 1 to 6 numbers of slotted walls) were tested in random wave fields of JONSWAP spectra for different combinations of significant wave heights and peak periods. It is found that on the dynamic pressure on vertical slotted wave barrier reduces progressively from the seaside to the rear side. In general, the dynamic pressure coefficient Ps/(ρgHis/2) reduces with an increase in relative water depth, d/Lp. where Ps is the significant dynamic pressure, ρg is the weight density of water, His is the significant incident wave height, d is the water depth and Lp is the wave length corresponds to peak wave period. It is also found that the highest value of measured Ps/(ρgHis/2) is about 1.5. The barrier with 3 walls and 10% porosity and for d/Lp of 0.3, the seaside wall panel experience dynamic pressure coefficient of 1.44, the first rear wall with 0.82 and the lee side porous wall with 0.58. The results can be used for the optimal design of the panels of multiple slotted vertical wave barriers.

Investigating the In-Flow Characteristics of Multi-Operation Conditions of Cross-Flow Fan in Air Conditioning Systems

Cross-flow fans are widely used in numerous applications such as low-pressure ventilation, household appliances, laser instruments, and air-conditioning equipment. Cross-flow fans have superior characteristics, including simple structure, small size, stable airflow, high dynamic pressure coefficient, and low noise. In the present study, numerical simulation and experimental research were carried out to study the unique secondary flow and eccentric vortex flow characteristics of the internal flow field in multi-operating conditions. To this end the vorticity and the circumferential pressure distribution in the air duct are obtained based on the performed experiments and the correlation between spectral characteristics of multiple operating conditions and the inflow state is established. The obtained results show that when the area of the airflow passage decreases while the area of the eccentric vortex area gradually increases, then the airflow of the cross-flow fan decreases, the outlet expands, and the flow pattern uniformity reduces. It was found that wakes form in the vicinity of the blade and the tail of the volute tongue, which generate pressure pulsation, and aerodynamic noise. The pressure distribution along the inner circumference shows that the total minimum pressure appears in the eccentric vortex near the volute tongue and the volute returns near the zone. Moreover, it was found that the total pressure near the eccentric vortex is significantly smaller than that of the main flow zone. As the flow rate decreases, the pressure pulsation amplitude of the eccentric vortex region significantly increases, while the static and total pressure pulsation amplitudes are gradually increased. Close to the eccentric vortex on the inner side of the blade in the volute tongue area, total pressure is low, total pressure on the outside of the blade is not affected, and pressure difference between the inner and outer sides is large. When the flow rate of the cross-flow fan is 0.4 Qd, there is no obvious peak at the harmonic frequency of the blade passage frequency. This shows that the aerodynamic noise is caused by the main unstable flow.

Physical Modeling of Ski-Jump Spillway to Evaluate Dynamic Pressure

The effects of changes in the angle of pool impact plate, plunging depth, and discharge upon the dynamic pressure caused by ski-jump buckets were investigated in the laboratory. Four impact plate angles and four plunging depths were used. Discharges of 67, 86, 161, and 184 L/s were chosen. For any discharge, plunging depth and impact plate angle were regulated, and dynamic pressures were measured by a transducer. The results showed that with the increase in the ratio of drop length of the jet to its break-up length (H/Lb), and with an increase in the impact plate angle, the mean dynamic pressure coefficient decreased. An inspection of the plunging depth (Y) ratio to the initial thickness of the jet (Bj) revealed that when Y/Bj > 3, the plunging depth of the downstream pool reduced dynamic pressure. At the angle of 60°, the dynamic pressure coefficient due to increasing in plunging depth varied from 34% to 95%.

Experimental Research on Dynamic Evolution Characteristics of Roof Movement and Mining-Induced Stress of Superimposed Mining in a Close Distance Coal Seam Group

To obtain the evolution characteristics of roof movement and mining-induced stress, the evolution of roof movement and mining-induced stress are investigated during the mining of close coal seams based on 2# and 3 + 4# coal seams in Shaqu coal mine. The results show that characteristics of macro-migration for overlying strata by superimposed mining in close coal seams are similar to that in a single coal seam. Roof strata present coordinated migration of multiple strata, and the displacements increase progressively. Roof strata can alleviate ground pressure as a cushion due to 2# coal seam mining, which reflects the stress-weakening effect under superimposed mining in close coal seams. Compared with 2# coal seam mining, the interval, support load, and dynamic pressure coefficient are reduced during periodic weighting in the 3 + 4# coal seam, and some parts of the rock undergo step-like sink. Based on above results, the hydraulic supports with high-rated working resistance are selected for superimposed mining. Finally, there was no failure among hydraulic supports or other dynamic disasters because of auxiliary measures implemented, and intensive management attention, during periodic weighting.

Analysis of Fluid Dynamics and Heat Transfer in a Rectangular Duct with Staggered Baffles

This computational fluid dynamic analysis attempts to simulate the incompressible steady fluid flow and heat transfer in a solar air channel with wall-mounted baffles. Two ꞌSꞌ-shaped baffles, having different orientations, i.e., ꞌSꞌ-upstream and ꞌSꞌ-downstream, were inserted into the channel and fixed to the top and bottom walls of the channel in a periodically staggered manner to develop vortices to improve the mixing and consequently the heat transfer. The analyses are conducted with the Commercial CFD software FLUENT using the finite volume method for Reynolds number varying from 12,000 to 32,000. The numerical results are presented in terms of streamlines, velocity-magnitude, x-velocity, y-velocity, dynamic pressure coefficient, turbulent kinetic energy, turbulent viscosity, turbulent intensity, temperature field, coefficient and factor of normalized skin friction, local and average numbers of normalized Nusselt, and thermal performance factor. The insertion of the S-shaped baffles in the channel not only causes a much high friction loss, f/f0 = 3.319 - 32.336, but also provides a considerable augmentation in the thermal transfer rate in the channel, Nu/Nu0 = 1.939 - 4.582, depending on the S-baffle orientations and the Reynolds number. The S-upstream baffle provides higher friction loss and heat transfer rate than the S-Downstream around 56.443 %, 55.700 %, 54.972 %, 54.289 % and 53.660 %; and 25.011 %, 23.455 %, 21.977 %, 20.626 %, and 19.414 % for Re = 12,000, 17,000, 22,000, 27,000, and 32,000, respectively. In addition, the result analysis shows that the optimum thermal performance factor is around 1.513 at the highest Reynolds number and S-downstream.

Heat Transfer in Air Flow Past a Bottom Channel Wall-Attached Diamond-Shaped Baffle – Using a CFD Technique

A computational analysis has been conducted to investigate turbulent flow and convective thermal transfer characteristics in a two-dimensional horizontal rectangular section channel with a hot lower wall-mounted diamond-shaped baffle. The calculations are based on the finite volume method, by means of Commercial Computational Fluid Dynamics software FLUENT, standard k-epsilon turbulence model with QUICK numerical scheme, and the SIMPLE discretization algorithm has been applied. The fluid flow and heat transfer characteristics, i.e., dynamic pressure coefficient, stream function, mean, axial, and transverse velocities, turbulent viscosity, temperature field, skin friction coefficients, local and average Nusselt numbers, and thermal enhancement factor are presented for flow Reynolds numbers based on the aeraulic diameter of the computational domain ranging from 12,000 to 32,000 at constant surface temperature condition along the upper and lower walls. Effect of the diamond configuration of the insulated baffle is studied numerically and the data obtained from this same baffle model are also compared with that of the simple flat rectangular baffle under similar operating conditions. Over the range under investigation, the improvements are found to be around 3.962 and 29.820 times higher than the smooth air channel with no baffle for heat thermal transfer and skin friction factor, respectively. The maximum TEF is around 1.292 at the highest Reynolds number value, Re = 32,000.

Impulse load characteristics of bouldery debris flow impact

Boulders entrained in debris flows are the main cause of damage to debris-resisting structures. Poly-dispersity leads to grain-size segregation, which causes boulders to migrate to the free surface and then accumulate at the front of the flow. Despite the importance of grain-size segregation, the current design of debris-resisting structures does not explicitly consider its effects on impact. In this study, two series of centrifuge tests were carried out to investigate the impact behaviour of mono-disperse bouldery flows and bi-disperse flows comprising boulders mixed with fine debris material. The diameter of the boulders was varied to study the effects of boulder size on the dynamic response of an instrumented model rigid barrier. The results reveal that, as the boulder size increases, a transition from progressive loading to predominantly impulse loading is observed. Boulders floating on the fine debris can induce even higher peak loads compared with mono-disperse bouldery flow. A new relationship between an equivalent dynamic pressure coefficient for the hydrodynamic approach and boulder size is established. This new relationship serves as a criterion for distinguishing between the boulders and fine debris in the design of structural countermeasures.

Core impact force of vertical water jets on smooth and rough surfaces

A normal way to dissipate energy of the dam released high velocity jets is to allow them to free-fall in to a plunge pool or impact a plane surface in case of dam site limitations. The water jets have an undisturbed core from nozzle outlet to a certain falling height, which has more impact force and less turbulent intensity than the developed part of the free jet. Experiments are conducted to determine core impact pressure coefficient of a vertical jet on smooth and rough plane surfaces. The experiment results for different jet diameters and falling heights showed considerable increase of the mean dynamic pressure coefficient with increase of the jet Froude number for both smooth surface and rough surface. A simple Froude based mathematical model is correlated for estimation of jet core impact force on the smooth and rough plane surfaces. In addition, a considerable increase of the jet core length was indicated with increase of the jet Froude number. Results also showed a strong correlation between turbulence intensity coefficient and the jet core length.

Analysis of Mining-induced Response for Floor Roadway Engineering and Surrounding Rock Control

For problem of surrounding rock control and instability of floor roadway under the influence of mining, the combination of site investigation, theoretical analysis, numerical calculation and field measurement methods are used. Firstly, the simplified calculation model of surrounding rock stress for floor roadway was established, and the calculation formula of that was theoretically derived. Secondly, the mining-induced responsive laws and deformation mechanism of surrounding rock stress for floor roadway were deeply analyzed. The results show that in the mining-induced neighborhood, the response of surrounding rock stress for floor roadway is extremely sensitive, and dynamic pressure coefficient of major principal stress is continuously increasing, which is the main stage for deformation occurred in surrounding rock. It is also found that mining response value of horizontal stress of floor roadway is much higher than that of vertical stress, which easily causes serious deformation in places where high deviatoric stress exists for two sides of roadway, as well as damage to bracing structure of roof load. Moreover, that can lead to instability of surrounding rock and collapse disaster of roof. Finally, engineering practice for roadway supporting shows that the compound control technology proposed (i.e. anchor with grouting - pressure relief cable - floor cable) is effective for stability controlling of rockmass around floor roadway.

Plunge pool dynamic pressures: a temporal analysis in the nappe flow case

ABSTRACTRectangular jet, or nappe flow, constitutes one of the energy dissipation methods used in the overtopping of dams. This paper reports new laboratory data on pressures, velocities and air entrainment and analyses the degree of break-up of a rectangular jet before entering the basin and the pressure fluctuations on the bottom of the pool. It is found that the maximum mean dynamic pressure coefficient of 0.86, which is valid for circular jets, is reduced to 0.83 for a rectangular jet. The study has also led to a relationship between the fluctuating pressure coefficient and the degree of the jet break-up. The peak pressure coefficient occurred for break-up length ratios (i.e. falling height/length) in the range of 1.00–1.20. The scaling effects are negligible for scales less than 1:10. The new set of characteristics given in the paper fills the current knowledge gap related to rectangular jets.

Analyses of Actual Measurement and Numerical Simulation on Gently Inclined Thin Seam

Based on the numerical simulation method and actual measurement analyses, characteristics of working face mineral pressure of the River Mouth Mine has been analyzed and this paper has obtained the following results: First weighting step of the main roof is 23.2 m, the average dynamic pressure coefficient is 1.54~1.74, mine strata behaviors is fiercer; hydraulic prop’s average working resistance is 45.72 KN of each, which indicates hydraulic prop’s working resistance has larger surplus coefficient, some measures should be taken to increase utilization ratio; advanced support length of return airway and mechanical roadway should reach to 30 m, the method and results can be used to improve support pattern of working face and guide safety production.