Static Pressure Coefficient Research Articles

Analysis of film cooling and flow resistance characteristics of turbine blades with thermal barrier coatings

This paper employs numerical simulation to investigate the influence of thermal barrier coatings' (TBCs) thickness and surface roughness on the cooling and flow resistance characteristics of turbine blades. The results indicate that the application of TBCs significantly enhances the surface cooling efficiency of the blades. Turbine blades coated with a 0.4 mm thickness of TBC compared to blades without thermal barrier coatings, the average cooling efficiency of the blade surface increases by 12.3 %, and the maximum temperature drop at the leading edge(LE) is 317.8 K. However, the small increment in TBCs thickness leads to an increase in aerodynamic losses in the vane passage. The static pressure coefficient continuously decreases in the suction side(SS) within the interval 0.3 < x/C < 1.0. The average flow coefficient of the film holes exhibits distinct variations in different regions of the blade. As surface roughness increases, the cooling efficiency on the SS and pressure side(PS) of the blade decreases, while the heat transfer enhancement at the LE and cooling efficiency improve. Compared to a smooth coated surface, when the surface roughness height increases to 20 μm, the blade surface cooling efficiency decreases by 1.12 %, and the average temperature rise is 10.3 K. Simultaneously, the energy loss coefficient and total pressure loss coefficient in the vane passage rise with the increase in surface roughness, while the variation in the average flow coefficient of the film cooling holes remains relatively small.

Control of Flow and Acoustic Fields Around an Axial Fan Utilizing Plasma Actuators

Abstract Small axial fans, commonly employed for cooling electronic equipment, are frequently housed within narrow ducts, where intense tonal sound with duct resonance can occur, particularly when the blade passing frequency or its harmonic frequency aligns with the duct's resonance frequency. To mitigate resonant sound, this study proposes a flow control using dielectric barrier discharge plasma actuators, which induce a flow along the generation of plasma in air. The control effects on flow field, acoustic radiation, and aerodynamic characteristics are evaluated through direct aeroacoustic simulations and experiments conducted at different flow rates. The computational results reveal that swirling flow occurs in the inflow due to fan rotations at low flow coefficients. This swirling flow is weakened by utilizing plasma actuators, which are arranged to induce flows in the circumferentially reverse direction compared to fan rotations. This control method weakens the resonant sound at low and intermediate flow coefficients, while intensifying it at high flow coefficients, all at the same rotational speed. Moreover, the static pressure coefficient decreases and increases at low and high flow coefficients, respectively, with the latter attributed to an increase in the relative inflow angle induced by the control. Experimental findings demonstrate that the acoustic resonance was reduced by the control at both low and high flow rates, achieved by adjusting the rotational speed to maintain the same flowrate and static pressure rise as in the baseline case.

Integrated Plug High-Strength Geocell Reinforcement in Foundation Design for Square Footing

This paper develops an analytical model to calculate the ultimate bearing capacity of the integrated plug high-strength geocell (IPGC)-reinforced foundation under a square footing. The high strength and stiffness of the geocell wall and the typical failure of the integrated plug-in joint tearing were considered. The ultimate bearing capacity of the IPGC-reinforced foundation was calculated in two separate parts. The ultimate bearing capacity of an unreinforced foundation was calculated using the modified Terzaghi equation. The increased bearing capacity of the IPGC was calculated as the function of the tearing force of the geocell wall, the height and the diameter of a geocell, the empirical static earth pressure coefficient, and the vertical additional stress coefficient under uniformly distributed rectangular loading. The results showed that the maximum error between the experimental and the theoretical results is less than 18%. The ultimate bearing capacity of IPGC-reinforced foundations decreases with larger geocell diameters. When the diameter of the geocell exceeds 1.8 times the foundation width, the confinement effect of IPGC becomes negligible. The findings of this study offer a robust analytical equation for predicting IPGC-reinforced foundations, along with valuable insights into the efficacy of IPGC reinforcement in enhancing foundation stability.

How much can roof-mounted bicycles on a following team car reduce cyclist drag?

Earlier research demonstrated that a car following a cyclist can provide an aerodynamic benefit to this cyclist. This effect could be large enough to potentially influence the outcome of individual time trials. This incited the International Cycling Union (UCI) in 2023 to raise the minimum distance from 10 to 25 m. However, this previous research work did not consider the bicycles typically mounted on the roof of a team car. Indeed, some teams have mounted up to ten bicycles on the roof, possibly in an attempt to optimise the aerodynamic benefit by their team car, even in individual time trials. This study employs CFD simulations validated by wind tunnel measurements to assess the benefit provided by different rooftop bicycle configurations. It is shown that the extra benefits are substantial and extend up to a distance of at least 25 m between cyclist and car, which could trigger new rules by the UCI. This study also shows that the cyclist drag reduction by a following car and for any car-cyclist separation distance d, can be estimated by the static pressure coefficient at position d in front of the isolated car, which can be obtained by a single CFD simulation.

Investigation of control effects of end-wall self-adaptive jet on three-dimensional corner separation of a highly loaded compressor cascade

To overcome the limitations posed by three-dimensional corner separation, this paper proposes a novel flow control technology known as passive End-Wall (EW) self-adaptive jet. Two single EW slotted schemes (EWS1 and EWS2), alongside a combined (COM) scheme featuring double EW slots, were investigated. The results reveal that the EW slot, driven by pressure differentials between the pressure and suction sides, can generate an adaptive jet with escalating velocity as the operational load increases. This high-speed jet effectively re-excites the local low-energy fluid, thereby mitigating the corner separation. Notably, the EWS1 slot, positioned near the blade leading edge, exhibits relatively low jet velocities at negative incidence angles, causing jet separation and exacerbating the corner separation. Besides, the EWS2 slot is close to the blade trailing edge, resulting in massive low-energy fluid accumulating and separating before the slot outlet at positive incidence angles. In contrast, the COM scheme emerges as the most effective solution for comprehensive corner separation control. It can significantly reduce the total pressure loss and improve the static pressure coefficient for the ORI blade at 0°-4° incidence angles, while causing minimal negative impact on the aerodynamic performance at negative incidence angles. Therefore, the corner stall is delayed, and the available incidence angle range is broadened from −10°–−2° to −10°–4°.This holds substantial promise for advancing the aerodynamic performance, operational stability, and load capacity of future highly loaded compressors.

Numerical Study on the Corner Separation Control for a Compressor Cascade via Bionic Herringbone Riblets

Bionic herringbone riblets are applied to relieve the flow near the blade endwall in a linear compressor cascade under the incidence angle of −4° to 6° at a Reynolds number of 382,000. The herringbone riblets are placed at the endwall upstream of the blade, and the Reynolds-averaged Navier–Stokes simulations are performed to explore their effects on corner separation and the control mechanism. The results show that the herringbone riblets can effectively improve the corner separation over the stable operating range, and the control effect is affected by the riblet height and the yaw angle. The implementation of herringbone riblets with a height of only 0.08 boundary layer thickness and a yaw angle of 30 degrees can reduce the total pressure loss by up to 9.89% and increase the static pressure coefficient by 12.27%. Flow details indicate that small-scale vortices in the riblet channels can accumulate and form a high-intensity large-scale vortex close to the bottom of the boundary layer downstream. Compared with traditional vortex generators, the herringbone riblets induce a vortex closer to the wall due to their smaller size, which can reduce the damage of an induced vortex to the mainstream and enhance its control over the bottom of the boundary layer, thereby effectively reducing additional losses. The induced vortex enhances mixing and injects kinetic energy into the low-energy fluid, thus inhibiting the transverse migration of low-energy fluid in the endwall boundary layer, delaying the formation of the separating vortex, further suppressing the development of corner separation and improving the aerodynamic performance of the cascade.

Large-Eddy Simulation of Flow Separation Control in Low-Speed Diffuser Cascade with Splitter Blades

The passive flow control technology of using splitter blades in low-speed diffuser cascade was investigated in this study. Based on the Reynolds average Navier-Stokes calculations, the arrangement parameters of the splitter blades were studied in detail to determine the optimal parameters. The large-eddy simulation was performed on the base case and the optimized splitter blade case to obtain the transient vortex structures and unsteady flow characteristics of the cascade. The results show that the aerodynamic performance of the cascade was susceptible to the position of the splitter blades. The optimal position of the splitter blades was located in the middle of the main blades near the leading edge. When the cascade was arranged with optimized splitter blades, the static pressure coefficient was improved and the stall occurrence was delayed. The scale and intensity of the separation vortices generated on the suction surface of the main blade decreased. In addition, the separation vortices of the main blade and the splitter blade interacted and rapidly decomposed into small-scale vortices downstream of the cascade, reducing the flow loss. The stability of the cascade was enhanced.

Features of design calculation of compressor spool flow path of a twin-shaft gas turbine engine core on the basis of 1D and 2D models of their working process

The features of the stages of parameter design calculation for the formation of the initial design of the flow path of the compressor spool of a twin-shaft engine core of a gas turbine engine are presented and substantiated. The article contains recommendations for choosing values of the pump head coefficient, efficiency and other important parameters for the stages of medium-pressure and high-pressure spools at the stage of thermodynamic calculation. At the stage of design gas-dynamic calculation of the compressor at the middle diameter, typical distributions of axial velocity component and degree of reaction along the flow path of compressor spools should be taken into consideration. At the same time, it is necessary to provide requirements for reducing the flow velocity and static pressure coefficients in the rotor wheels and stator blades, head coefficients and Stepanov coefficients. The design gas-dynamic calculation of the compressor along the radius of the flow path is characterized by a variety of flow swirl laws at the inlet to the rotor wheels, distributions of the pressure increase and efficiency over the height of the blades. In conclusion, an example of a three-dimensional model of a compressor flow path taking into consideration the features of design calculation of the parameters of compressor spools of a twin-shaft engine core of a gas turbine engine on the basis of the appropriate flow path diagram in the meridional plane is presented.

Effects of Synthetic Jets on Swirl Inflow in a Variable-Geometry Twin Air-Intake

Air intakes are an integral part of contemporary passenger and military aircraft engines. Their impact on aerodynamic performance across the entire flight envelope is critical to aircraft flight safety, efficiency, and manoeuvrability, especially at high Mach numbers due to shock waves. The high demand for reductions in aircraft weight and size and enhancements in durability, comfort, and thermal and radar signatures compel researchers and engineers to explore new designs and develop efficient air intakes for high-performance aircraft engines. Although a number of studies on air intake have been conducted and reported in the open literature, there is little information available in the public domain on bifurcated twin air intakes using synthetic jet. As a result, the primary goal of this research is to use computational fluid dynamics modelling to investigate the effects of synthetic jets on swirl inflow variable geometry twin air intake aerodynamic performance over a range of Reynolds numbers. Some important parameters (distortion coefficient, non-uniformity index, swirl coefficient, and static and total pressure coefficients) were investigated. Both static and total pressure recovery have been increased at all swirl numbers. A significant decrease in distortion coefficient and swirl coefficient has also been achieved, reaching a 53% reduction in the distortion coefficient and a 62% reduction in the swirl coefficient. The reduction in the non-uniformity index is achieved by 62% for the controlled flow case. The findings show that synthetic jets are effective in controlling the flow separation in the twin air intakes and enhancing aerodynamic performance.

Effect of uncertain operating conditions on the aerodynamic performance of high-pressure axial turbomachinery blades

The objective existence of uncertain operating conditions can cause significant variations in the aerodynamic performance of turbomachinery. This study presents a comprehensive investigation into the impact of six uncertain operating conditions on the aerodynamic performance of a turbine. Additionally, a global sensitivity analysis was performed to identify the most important operating condition parameters. To reduce the computational cost of uncertainty quantification (UQ), a new UQ framework, the Nested Sparse-grid Stochastic Collocation Method (NSSCM), is used. It has been observed that uncertain operating conditions can lead to significant variations in energy loss, which in turn directly impacts the operating efficiency of the turbine. This research finds that the suction surface and trailing edge of the blade are particularly sensitive to uncertain operating conditions. The impact of uncertainty on the static pressure coefficient decreases as the flow develops, while the uncertainty of the Mach number and energy loss coefficient increases. Inlet total pressure and outlet static pressure are the primary factors impacting turbomachinery aerodynamics, as determined by sensitivity analysis. This study provides new insights into the impact of uncertain operating conditions on turbine efficiency and can guide the development of more robust turbine designs in the future.

Performance Improvement of A Low Aspect Ratio Axial Flow Compressor Rotor by Means of Turbulence Generator

The present paper reports results of an experimental investigation aimed at improving the performance and operating range of an axial flow compressor using a simple passive means. A total of four configurations are tested, namely, (i) basic rotor configuration without any passive means, (ii) rotor with modified partial shroud (MPS), (iii) rotor with MPS and turbulence generator, TG, placed on the casing at the leading edge of the rotor blade and (iv) rotor with MPS and turbulence generator, TG1, placed on the casing at 44 mm upstream of the leading edge of the rotor blade. The turbulence generators are made of velcro tape. The rotor performance is determined by measuring static pressure on the casing, upstream and downstream of the rotor blade. In addition, five hole probe traverses are made at the rotor exit at five flow coefficients (at, above and below design flow coefficients). From the casing static pressure measurements, stall flow coefficient of rotor (with MPS + TG1) is found to be decreased. From the five hole probe measurements, rotor (with MPS + TG1) is found to have improved total and static pressure coefficients compared to rotor (with MPS). Slightly reduced performance of this rotor compared to the basic configuration is attributed to the adverse effects of MPS. The improved performance of the rotor (with MPS + TG1) is attributed to the energization of the casing wall boundary layer at the rotor inlet, due to vortexes generated by TG1.

Analysis of Airflow Patterns and Pressure Distribution Characteristics on Cars with Variations of Under Front End Tilt Angle

The airflow across the underbody of the car will affect the lift and drag of a car. Part under front end car vehicle is one of the factors in the car that causes drag and also lift. This research was conducted to determine the airflow pattern and pressure distribution characteristics, such as static pressure, dynamic pressure, and pressure coefficient, which affect the performance of the test vehicle with variations in the angle of the under-front end. Experimental testing was carried out on 4 specimens, namely car vehicles with variations in tilt angles under front end 0°, 5°, 10°, and 15° inside the wind tunnel with a speed of 5.47 m/s. The results showed that the under front end of the 0° tilt angle is an area with low pressure, where the lift that occurs is relatively smaller than the under front end area which varies the angle of inclination. However, pressure fluctuations experienced by an angle of 10° are more stable than 0°.

Computational Investigation of Effect of Tip Clearance in an Annular Turbine Rotor Impulse Cascade

This paper describes three dimensional computational investigations of the effect of the tip clearance on the secondary and tip clearance flows in an annular turbine rotor cascade with non uniform inlet flow. In the actual turbine, the flow at inlet of the rotor is non uniform due to radial pressure gradient acting from the hub to casing. To provide non uniformity at the rotor cascade inlet, an annular nozzle cascade is provided at the upstream. The studies are carried out with the help of a commercially available CFD package. The studies have been carried out for four values of clearance, i.e. 0%, 1%, 3% and 5% of chord. Detailed comparison of the leakage flow direction, pressure gradient, and leakage vortex size, losses, location and interaction with other flow features is carried out. The results are presented in terms of static pressure coefficient distribution on the blade surfaces and total pressure loss coefficient contours in the passage. Spanwise distributions of the circumferentially averaged loss coefficient and flow angle are presented. The extent of losses in the circumferential direction is increased with the increase in the height of the tip clearance but reduced in the spanwise direction. The mass averaged loss coefficient increases rapidly from 0.24 at zero clearance to 0.42 at 1% tip clearance. As the tip clearance is further increased, the losses increase slowly (0.54 at 3% tip clearance to 0.58 at 5% tip clearance). The mass averaged flow angle decreases from 66.3° at zero clearance to 63.7° at 1% clearance to 60.1° at 3% clearance and to 57.3° at 5% clearance.

Look Up Table Method for Five Hole Probe Data Reduction

A lookup method for extracting flow field information from five hole probe measurements is presented. The look up table method consists of two step interpolation. In the first step, the calibration space is divided into a large number of small intervals of yaw and pitch coefficients (0.1, 0.05 or 0.01) and the required quantities are interpolated using local cubic spline interpolation technique. The interpolated values are stored in a large square matrix. In the second step, the measured values of yaw and pitch coefficients are used to determine yaw and pitch angles by linear interpolation. Same procedure is used to determine total and static pressure coefficients. Additional data taken during the calibration is used for validating lookup table method and spline interpolation method. The errors from the look up table method, particularly with the interval of 0.01 are about the same or lower than those obtained from the spline interpolation method. The computational times for lookup table method are found to be lower than that for the spline interpolation method. The lookup table method seems to be attractive when a large amount of five hole probe data is to be processed and in cases where online data processing is required.

Investigation of the controlling mechanisms of blade slotting technology on the shock-wave-induced corner separation

Three-dimensional corner separation usually gets worse under the mutual interaction between the boundary layer and shock wave, thus greatly influencing supersonic compressor blades in aerodynamic performance. This study proposed adopting the blade slotting technology to control the serious shock-wave-induced corner separation and investigated the effects of the slot height. The results showed that, the low-energy fluid accumulated in the corner region can be enough re-energized by the slot jet with high momentum, thus effectively reducing its mutual interference with the shock wave and suppressing its separation. The velocity and mass-flow of the slot jet get larger as the slot height increases. But when the momentum contained in the slot jet has been able to enough re-energize the local boundary layer, a larger jet mass-flow will slightly worsen the aerodynamic performance. To better improve the overall aerodynamic performance in a wide inlet airflow angle (β1) range, it is better to choose the slot height that can just resist the migration of hub secondary flow at the maximum β1. In the current study, this suitable slot height can increase the static pressure coefficient by an average of 26.0% and reduce the total pressure loss by 10.8% on average in the β1 range of 57.1°∼61.5°. It is significantly beneficial for the future higher-load compressor to achieve a larger total pressure ratio, higher efficiency, and better working stability.

Calculation of Rock Pressure in Loess Tunnels Based on Limit Equilibrium Theory and Analysis of Influencing Factors

The research on the calculation method of tunnel envelope pressure is a key issue in the design of tunnel engineering support structure. Based on the limit equilibrium theory, this paper proposes a method to calculate the surrounding rock pressure in shallow buried loess tunnels. Firstly, based on the investigation of the damage mode of the loess tunnel surrounding rock and the field measurement results of the surrounding rock pressure, the damage mode of the loess tunnel is proposed, and then a method of calculating the surrounding rock pressure applicable to the shallow buried loess tunnel is derived according to the limit equilibrium condition of the tunnel square soil body and the side wedge; the basic mechanical parameters are known in this method, so only the rupture angle β needs to be determined, and the rupture angle calculation model in the shallow buried loess tunnel is proposed Three assumptions are made in the rupture angle calculation model, and the rupture angle calculation formula is derived according to the stress state on the slip surface of the surrounding rock; the pressure of the surrounding rock in the loess tunnel obtained by this method is compared with four methods, namely, the pressure theory of the surrounding rock in the existing loose body of Taishaki, the pressure formula of the deeply buried surrounding rock in the railroad tunnel design code, the Beer Baumann method, and the Xie Jiayi method, in order to verify the correctness and validity of the calculation method used, and to analyze the influence of different parameters on the surrounding rock pressure. The innovation of this paper lies in the derivation of a method for calculating the pressure in the surrounding rock of a shallow buried loess tunnel using the limit equilibrium theory, and also further proposes a formula for calculating the rupture angle. The pressure of surrounding rock decreases with the increase of static earth pressure coefficient, lateral pressure coefficient, friction angle and cohesion in soil, but the static earth pressure coefficient has a greater influence on the surrounding rock pressure. With the increase of sagittal span ratio, tunnel burial depth and soil weight, the surrounding rock pressure peaked with the increase of tunnel burial depth, and the surrounding rock pressure curve increased first and then decreased.

Pneumatic-Probe Measurement Errors Caused by Fluctuating Flow Angles

Pneumatic probes such as five-hole probes (5HP) can conveniently measure three-dimensional flow angles, plus total and static pressure. In most applications, transducers are connected using pneumatic tubes, allowing the probe head to be highly miniaturized and robust. However, such “steady” probes are often used in unsteady flows, where they measure a pneumatically averaged flowfield that can differ from the time mean. To better understand these pneumatic averaging effects, an analytical framework is constructed using a quasi-steady model. Total and static pressure coefficients have a symmetric response to both positive and negative incidence. When incidence fluctuates, there is therefore a bias in the pneumatic average. These errors are evident in a shedding wake experiment, where a 5HP overestimates total pressure loss by up to 44% compared to a Kiel probe. These effects can be predicted by coupling an unsteady Reynolds-averaged Navier–Stokes calculation with the quasi-steady model. By predicting pneumatic averaging errors, the quasi-steady model can be used to obtain like-for-like validation of calculations against experimental data. Measurement data can also be corrected, provided that flow angle fluctuations can be measured or estimated. This approach can be readily used to postcorrect the large body of historical data likely to have been corrupted by pneumatic-averaging errors.

Influence of nozzle geometry on wall static pressure coefficient of the submerged turbulent jet impinging on a smooth flat surface

The experimental work is carried out to study the influence of nozzle geometry on the flow characteristics of the submerged turbulent jet impinging on a smooth flat surface. Three nozzle geometry configurations, viz. parabolic, conical and exponential, are considered. Depending upon the nozzle exit diameter, the Reynolds number of 12,000–23,500 and jet-to-plate distance of 0.5–6 is considered. At a higher jet-to-plate distance (z/d = 6), a secondary peak was observed at a radial distance around r/d = 0.4 from the stagnation point. It is due to the transition of fluid flow from laminar to turbulent on the impingement surface. At all Re and z/d, parabolic nozzle geometry resulted in maximum value as compared with other nozzle geometry configurations. This may be attributed to higher pressure losses in the conical nozzle and exponential nozzle than the parabola nozzle because of streamlined flow and this information can be used for local heat transfer phenomena for optimum conditions.

The investigation on a hybrid interpolated additional zonal method for a conventionally calibrated five-hole probe

For the highly three-dimensionality and large-span Mach number properties in modern turbomachinery, the five-hole probe calibrated by the conventional method might be incapable of accurate measurement. An additional zonal calibration method which can extend the valid deviation angle from 30° to 60° with low workload was introduced in this study. Besides, the data reduction process was modified to improve the measurement precision. Firstly, the Grubbs criterion and the spline interpolation approach were used to correct the gross error of calibration coefficients. Secondly, under the condition with a known Mach number, the univariate linear interpolation method was found to be more stable than the bivariate biharmonic spline interpolation method in restoring the real flow properties, especially in extended sectors. In addition, the investigation of the calibration coefficients behavior in the Mach-number range of 0.3 to 0.7 showed that the sensitivity of angle and total pressure coefficients to Mach number only appeared near the boundary of the five sectors, while the sensitivity of the static pressure coefficient remained seriously throughout the calibration region. When the measured and calibrated Mach numbers were placed within 0.4 or close to each other, the error caused by the compressibility effect could be ignored. Accordingly, the hybrid interpolation algorithm was developed to minimize the measurement error. Moreover, the hybrid interpolated additional method was confirmed in the measurement of the outlet flow field of the highly loaded compressor cascade. The measurement accuracy of the yaw angle and the total pressure loss were improved by 7.5° and 11.63%, respectively.

An Experimental Facility with the High-Speed Moving Endwall for Axial Compressor Leakage Flow Research

The moving endwall has a great influence on the development and stability of axial compressor leakage flow. This paper presents a novel experimental facility with a high-speed moving endwall for studying axial compressor leakage flow. The uniqueness of the design concept is that using a large disk simulates the high-speed moving endwall. When R/Cx = 16, theoretical analysis shows that the maximum linear velocity difference is about 2.5% while the maximum axial velocity difference of the mid-three passages is less than 5%. Single-passage simulations show that the disk radius of R/Cx = 16 can achieve an acceptable accuracy in terms of static pressure, total pressure, and density flow. Seven-passage simulations confirm that the mid-three passages have small errors from the axial velocity difference. Subsequently, preliminary experimental results obtained from the experimental facility are presented. The results reveal that the moving endwall significantly changes the distributions of the total pressure loss and static pressure coefficient. The relative difference in the averaged total pressure loss between the experiment and CFD is 11.33% and 7.69% for the static and moving endwall, respectively. It is expected that the experimental facility will make more useful contributions to the understanding of axial compressor leakage flow in the future.