Stagger Angle Research Articles

Semi-analytical modeling and experimental verification of a flexible varying section disk–blades system with elastic supports

A semi-analytical model of a flexible varying section disk–blades (FVSDBs) system with elastic supports is proposed, where the spin softening, centrifugal stiffening, and Coriolis force effects of the system are considered. Timoshenko beams with a stagger angle are used to simulate blades, and a varying section wheel based on plate theory is used to construct the disk. Hamilton’s principle and Galerkin method are utilized to derive the differential governing equations of the FVSDBs system. The proposed semi-analytical model accounts for the lateral vibration of the disk, and the longitudinal and lateral vibration of the blades. Besides, the validity of the proposed model has been verified by comparing the natural frequencies, mode shapes, and vibration responses obtained from the proposed model, finite element model (FEM), and experiment. The results indicate that the proposed semi-analytical model has high precision and computational efficiency, which can provide an alternative scheme for predicting the vibration characteristics of varying section disk–blades and overcoming the high computational cost of finite element models.

Flow and Heat Transfer Characteristics of Staggered Cylinders

Abstract Determining how the flow structure affects the heat transfer of a staggered cylindrical array was one of the objectives of this numerical study. The major flow patterns and the corresponding characteristics of heat transfer were investigated, including Shear Layer Reattachment (SLR), Induced Separation (IS), Vortex Pairing and Enveloping (VPE), Vortex Impingement (VI), and Synchronized Vortex Shedding (SVS). As the stagger angle is larger than 35°, the mean Nusselt numbers of array systems are larger than that of a single cylinder. The magnitude of Nu/Cd is suggested as a parameter to measure the efficiency of the heat transfer for an array system.

Effect of Stagger Angle of Rotor Channels on the Wave Rotor

A wave rotor optimizes the use of energy resources by enhancing thermodynamic cycles, and further optimization of wave rotor geometry is emerging as an attractive research area. Among the geometric features, the stagger angle of channels lacks sufficient study in spite of its important effects. To address this question, this work developed and applied the velocity triangle models to modify the basic geometry of wave rotors for different stagger angles, and investigated the flow fields with two-dimensional numerical methods. Results showed that: (1) different stagger angles worked out similar unsteady pressure wave systems and kept nearly constant compression and expansion ratios of the wave rotor; (2) increased stagger angle made the inlet and outlet flows turn toward the axial direction, which was beneficial to compact and light-weighted integration of the wave rotor to a gas turbine; (3) increased stagger angle made the wave rotor consume more shaft power, but even the maximum shaft power was small. This work revealed a critical mechanism how the velocity variation across an unsteady pressure wave produced rim work in a staggered channel, and made a recommendation to comprehensive optimization of wave rotor geometry for better integration in a gas turbine and acceptable shaft power consumption.

Multi-Parameter Optimization Design of Axial-Flow Pump Based on Orthogonal Method

The axial-flow pump is a widely used piece of general machinery which consumes large amounts of energy. In this study, an axial-flow pump with the specific speed of 536 is firstly designed and experimentally measured; then, the orthogonal method is employed to conduct the energy performance optimization. Five optimization parameters, including hub control point, hub stagger angle, shroud stagger angle, camber angle and centroid position were set with four levels. Sixteen individual pumps were designed according to the orthogonal method; then, a numerical simulation was implemented to obtain the energy performance and flow pattern. Results showed that the shroud stagger angle has the maximum influence on the pump head and efficiency, and the hub stagger angle and camber angle are also very important. At a design point of flow rate 70 kg/s, the efficiency of the optimal pump is 86.29%, which improved by 2.05% in comparison with the baseline pump. The pressure gradient of the optimal pump from blade inlet to outlet becomes more fluent than that of baseline pump, and the low-velocity region of the optimal pump at the blade head shrinks, compared to that of the baseline pump.

Identification of continuous twin-screw melt granulation mechanisms for different screw configurations, process settings and formulation

Twin-screw melt granulation (TSMG) is a promising continuous manufacturing technology for the processing of high drug load formulations and to formulate heat- and moisture-sensitive active pharmaceutical ingredients (APIs). This study evaluates the influence of process parameters for TSMG, mainly focusing on the effect of the screw configuration combined with screw speed, throughput and barrel temperature, to elucidate the melt granulation mechanisms. For the kneading zone, the stagger angle was varied between 30°, 60° and 90°, and investigated for both the forward and the reversed direction. In addition to the process parameters, the influence of the formulation differing in their API-binder miscibility was evaluated. As responses, the granule (size, friability and porosity) and process properties such as torque were evaluated, indicating that the screw configuration is the most influential factor. Nucleation, consolidation and breakage are the granulation mechanisms for the forward and the neutral configuration, while consolidation and densification with shear elongation are identified for the reversed configuration. The formulations differ mainly in the forward and neutral configuration since the immiscible formulation shows a bimodal granule size distribution with a larger fraction of fines and weaker granules is obtained. For the reversed configuration, similar granulation mechanisms are seen for both formulations.

Numerical Characterization of Mixing in a Kneading Element Channel of Dual‐Speed Corotating Non‐Twin Screws Using Lagrangian Statistics Method

AbstractA novel kind of dual‐speed corotating non‐twin kneading elements with a zero stagger angle is designed to improve mixing ability. The physical model considering several narrow gaps is developed where the inlet and outlet transition sections are also included. Finite element method associated with the mesh superposition technique is further applied to solve the time‐dependent flow field where fluid is assumed to obey the Carreau constitutive model. The tracers initially from different locations are tracked using a self‐developed fourth‐order Runge–Kutta scheme. Distributive mixing is evaluated through evolution of tracer droplets and decaying of variance index with time. In addition, a Lagrangian statistics method is used to characterize the dispersive mixing in terms of the statistical distributions of mixing index and their integration areas within the range of mixing index larger than 0.5. In contrast, the kneading elements of a conventional twin screw configuration are also modeled to show the mixing difference.

The Optimal Blading Design and CFD Analysis of Axial Flow Fan

This study proposes a method to optimize the blade angle and chord length distributions of axial flow fan rotor blade, and applied it to the design of the actual industrial axial flow fan. The present design model of the axial flow fan rotor blade is to construct and stack the section profiles using single circular arc and airfoil thickness distribution with the camber and stagger angles as design variables along the blade span height from hub to tip, and the chord length distribution is designed in a parabolic fashion from hub to tip. The performance and efficiency of the fan rotor blades are predicted by applying a through-flow analysis method to the 3D fan blade geometry obtained from the design variables of the camber angle, stagger angle, and chord length of the blade sections. These fan design and through-flow analysis methods are used as the simulation engine for optimization problem. Through applying the optimization algorithm, an optimal axial flow fan rotor is obtained with maximum efficiency and computational fluid dynamics analysis is performed to verify the result of the present optimal design. From the computational fluid dynamics calculation results, it can be seen that the present optimal design model has an efficiency improvement of about 2% compared to the initial design, and maintains relatively high efficiency even under partial load conditions.

Effects of Flow Coefficient on Turbine Aerodynamic Performance and Loss Characteristics

The effects of flow coefficient on the gas flow and loss characteristics inside the high-pressure turbine is investigated using a numerical simulation. In this paper, the midspan of the first stator of the “Lisa” 1.5 stage high-pressure turbine is used as a prototype to obtain different flow coefficients by changing the stagger angle and the exit angle. The boundary conditions of all cases are consistent with the experimental data of “Lisa”. The results show that the flow coefficient is decreased from 0.478 to 0.374 as the stagger angle is varied from 44.2° to 56.2° and from 0.630 to 0.341 as the exit angle is varied from 63° to 75°. Large stagger angle or large exit angle both cause an increase in turbine aerodynamic losses. The similarity between the two is that both cause enhanced effect of transverse secondary flow in the passage. The difference is that with large stagger angle, the adverse pressure gradient affects a large area, resulting in large boundary layer losses; with large exit angle, the passage vortex is weakened but with a large influence area.

Effects of centrifugal stiffening and spin softening on nonlinear modal characteristics of cyclic blades with impact–friction coupling

This paper aims to interpret the coupling modal properties of cyclic blades under impact–friction interactions and their evolution mechanism versus operating points. Therefore, a coupling analytical model of cyclic blades is developed based on a Lagrange method and the assumed mode method (AMM), after considering centrifugal stiffening, spin softening, stagger angle, and twist angle. Then a mixed modal analysis method (MMAM) for this analytical model is extended by combining the extended periodic motion concept (EPMC) with AMM. Wherein a classic alternating frequency/time method (AFT) and the continuation method are employed to overcome the numerical divergence problem. Then damped nonlinear normal modes (dNNMs), including eigenfrequencies, modal damping ratios, and mode shapes, of the coupling system with shroud joints are finally computed and discussed under different excitation levels and contact conditions through a modal synthesis algorithm. After that, the influence laws of centrifugal stiffening and spin softening on the dNNMs are explored to reveal its evolution mechanism versus operation speeds. Finally, the Campbell diagrams of dNNMs are successfully obtained to discuss the effects of the impact–friction coupling on critical speeds (CSs) of the shrouded blades system.

Numerical investigation of a variable stator vane with nonuniform partial radial gaps in an annular compressor cascade

Abstract A variable stator vane (VSV) with nonuniform partial radial gaps is numerically investigated in an annular compressor cascade. Five adjusting angles (α = −5.5°, −5°, 0°, 5° and 10°) are chosen to simulate different working conditions. The VSV is adjusted in negative direction means that the stagger angle increases and the VSV is more closed. Since the VSV is installed in an annular cascade, the heights of the partial gaps are nonuniform and reaches 3.8% of the span. Results show that as the VSV is adjusted negatively, the total pressure loss rises by 20.3% and a huge area of corner separation appears. The outflow angle is also more distorted along radial direction. Comparisons with a fixed-configuration stator show that although the VSV would cause higher loss, it indeed plays an important role in adjusting the outflow angle.

A data-driven non-intrusive polynomial chaos for performance impact of high subsonic compressor cascades with stagger angle and profile errors

The impact of geometric variations due to manufacturing errors on the aerodynamic performance of compressor blades is considerable in engineering practice. Accurate uncertainty quantification (UQ) of aerodynamic performance based on actual statistical information of manufacturing errors is helpful for error detection, aerodynamic shape design, etc. However, the actual manufacturing errors may not be independent of each other, and their marginal distributions are often not standard. To apply UQ to dependent input variables with arbitrary distributions, the present paper first introduced a decorrelation algorithm and proposed a novel data-driven Non-Intrusive Polynomial Chaos (DNIPC) model. The subsequent tests based on high-dimensional function experiments and UQ of the performance for a high subsonic compressor cascade have validated its generality, effectiveness, and efficiency. Then, the simultaneous impact of stagger angle and profile errors on the performance of the compressor cascade was investigated by the proposed DNIPC and Sobol's sensitivity analysis. The distributions of manufacturing error were determined by kernel density estimation based on finite measurement data, then using the parametric B-spline and Bezier curves to build the manufactured geometry of the cascade. Finally, the influence of the manufacturing errors on aerodynamic performance was further discussed through the UQ of the cascade flow field. The results show that the performance impact in the off-design conditions, especially for those below the design incidence, is the most important. It suggested that the uncertainty of profile error should be checked carefully in the process of detecting machining error when the operation condition is at or below the design incidence; in contrast, the influence of stagger angle error calls for more attention when the cascade works at high incidences. The fluctuation of the overall aerodynamic loss is mainly associated with the manufacturing error near the leading edge, for it affects the velocity spike and the development of its downstream boundary layer. Therefore, the leading edge error should be the top focus.

Unsteady Analysis of a Pulsating Alternate Flow Pattern in a Radial Vaned Diffuser

In centrifugal compressors, Mild Surge (MS) leads to unstable operation. Previous experimental work on a centrifugal compressor designed and built by Safran Helicopter Engines (SafranHE) showed that MS corresponds to the pulsation of an alternate stall pattern at the Helmholtz frequency of the test rig on two channels in the radial diffuser. The present contribution experimentally investigates the impact of the Inlet Guide Vane (IGV) stagger angle on this alternate flow and numerically studies the topology of this pulsating alternate flow. The experimental investigation is performed with unsteady pressure sensors, and shows that the IGV stagger angle only impacts the pulsation frequency of the alternate flow pattern. This change is explained by the dependence of the Helmholtz frequency on the compressor inlet section. The topological analysis of the average flow field, computed from wall-resolved Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations, demonstrates that the saddle point (major critical point) in the corner hub/suction side of the stalled blade migrates upstream while staying in the corner if the mass flow rate decreases. One main blade over two is stalled on both sides because the flow originating from this corner separation circumvents the trailing edge and migrates upstream along the pressure side. In the simulation, the pulsation of the alternate stall is coupled with the reflection of acoustic waves on the inlet and outlet planes, regarded as an environmental effect.

Numerical modeling of the dynamic unsteadiness with global mode decomposition approach in a high-speed compressor with abnormal diffuser vane

Adjustable vane diffuser is addressed as one of the main techniques in centrifugal compressor in seeking of wider stability margin. Flow instabilities, however, may be driven by the three-dimensional flow separation induced by the abnormal vane in the diffuser. In the present work, a numerical investigation of the radial vaned diffuser with abnormal vane was applied to identify the correlation between stall inception and asymmetric flow distribution. Unsteady numerical simulations of the centrifugal compressor with vaned diffuser was carried out and validated against experimental data. Then, the aerodynamic characteristics and evolution process of the flow instabilities in vaned diffuser was analyzed with the compressed dynamic mode decomposition in term of perturbation frequency and dominating flow mode. Finally, concerning the relative position of the volute tongue and abnormal vane, the influence of the abnormal vane on the matching between the diffuser and volute regarding the stall mechanism was summarized. The results indicate that the abnormal vane needs to be altered large enough, which is above 10°, to trigger the flow instability of vaned diffuser before the spike stall in impeller. With the increase of stagger angle alternation, the stall mechanism turns from a global flow separation in multiple passages into a regional and abrupt phenomenon in limited passages. With the mode composition approach, the flow separation near diffuser outlet and the tornado-type vortices at the leading edge of the abnormal vane are responsible for the flow instability of the case with 15° vane alternation. When combined with the volute, the case with abnormal vane close to the volute tongue tends to be more unstable than that 180° away from volute tongue. The tornado-type vortices are also moved to the trailing edge rather than the leading edge under the influence of the asymmetric volute.

A tip-leakage loss reduction method using a front-loaded blade profile for the high-pressure rotor of a vaneless counter-rotating turbine

To reduce tip-leakage losses, this paper presents a front-loaded blade profile design method for the high-pressure (HP) rotor of a highly loaded vaneless counter-rotating turbine (VCRT). The method is to decrease the blade exit angle and increase the stagger angle with unchanged throat area to obtain front-loaded blade profiles at both the tip-leakage vortex upper and lower boundaries. As the relative exit Mach numbers in the tip region of the VCRT’s HP rotor are all over 1.5, the shearing of the high-speed leakage jet and passage flow near the trailing edge is very strong. To reduce the shearing losses, decreasing the blade exit angle of the HP rotor is adopted to reduce the tip loading near the trailing edge. This means the leakage jet mass-flow rate and speed near the trailing edge are reduced. Hence, the shearing strength and losses of the leakage jet and passage flow near the trailing edge are lower. Since decreasing the blade exit angle of the HP rotor results in increased throat area, increasing the stagger angle is employed to maintain unchanged throat area. Increasing the stagger angle also reduces the tip loading near the trailing edge, leading to reduced high-speed leakage jet mass-flow rate. Thus, the shearing strength and losses of the high-speed leakage jet and passage flow near the trailing edge are further reduced. The efficiency of the HP rotor and VCRT are raised by 0.45% and 0.53% respectively.

Optimization of screw design for continuous wet granulation: A case study of metoprolol succinate ER tablets

This study aimed at understanding the effect of screw design on the critical characteristics of granules and tablets of an extended-release (ER) formulation for twin screw granulation process. The screw design parameters assessed included number of kneading elements (KEs) per kneading zone, distance separating kneading zones, staggering angle (SA) of kneading elements and number of sizing elements (SEs). These input variables were varied using a design of experiment (DoE) approach to manufacture granules. Particle size distribution (PSD), flow and bulk properties of the granules, breaking strength and dissolution of tablets manufactured using these granules were characterized.The results of least square fitting showed that KEs, SA, and SEs of the screws significantly (p -values < 0.05) affected the PSD, cohesion, compressibility (CPS), conditioned bulk density (CBD) and permeability of the granules. The KEs and SEs significantly (p -value < 0.05) affected the dissolution, which was attributed to their effects on CPS and CBD of the granules. The distance between kneading zones had no significant effect on granules and tablet characteristics. These results may be used to further study the interaction of the identified critical screw design parameters with other processing parameters for continuous manufacturing of this ER matrix-based tablet formulation.

An improved stall prediction model for axial compressor stage based on diffuser analogy

Stall represents a limit to the useful operation of the axial compressor. Despite its difficulty, a rational and effective stall prediction model is an urgent requirement for compressor designers. In this paper, a stall prediction model for determining the maximum static pressure rise capability of axial flow compressor stage is presented based on Koch's two dimensional diffuser analogy concept. Compared with the original Koch's model, where the flow angles are only used to consider the increase of inlet dynamic pressure factor caused by high stagger angle, this paper takes into account the effect of flow angles on the diffusion length, and derives the mathematical expression of the modified non-dimensional diffusion length. A semi-empirical correlation is presented to account for the effect of camber angle on the stalling static-pressure-rise coefficient of axial compressor stages. By re-evaluating the Reynolds number effect, a blockage indicator is proposed to determine the effect of boundary layer blockage on stalling capability. Good agreement is demonstrated between the predicted and test stalling pressure rise data for a wide range of axial compressor stages and a 4-stage low speed research compressor. Compared with the original Koch's model, the relative error of the modified model in predicting the stall margin is reduced from 22.5% to 3.5%. This model has a guiding significance for the selection of initial design variables in the axial compressor design process.

Design and performance of very low head water turbines using a surface vorticity model algorithm

This study explores the numerical optimization of water turbine runner profile performance using a surface vorticity model algorithm. The turbine is designed on a laboratory scale and operates at a net head of 0.09 m, 400 rpm, and a water flow rate of 0.003 m3/s. The initial design of the turbine runner was optimized to minimize losses in the hydrofoil. The optimization algorithm is coded in MATLAB software to obtain the optimal stagger angle that will be used in the water turbine design. Furthermore, design validation was performed using computational fluid dynamics analysis ANSYS CFX to determine the water turbine performance. The settings used in ANSYS CFX include the reference pressure of 1 atm, turbulence model shear stress transport, and inlet boundary conditions using total pressure and static pressure outlet boundary conditions. The computational fluid dynamics analysis reveals that by optimizing the design, the efficiency of the water turbine increases by approximately 2.6%. The surface vorticity model algorithm can be applied to optimize the design of the water turbine runner.

Selection Criteria for Biplane Wing Geometries by Means of 2D Wind Tunnel Tests

This paper presents a study based on wind tunnel research on biplane configurations. The objective of this research is to establish an experimental basis for relationships between the main geometrical parameters that define a biplane configuration (stagger, decalage, gap, and sweep angle) and the aerodynamic characteristics (CL, CD). This experimental study focuses on a 2D approach. This method is the first step towards dealing with the issue, and it allows the variables involved in the tests to be reduced. The biplane configuration has been compared with the monoplane configuration to analyze the viability for implementing the biplane configuration in the field of application for micro air vehicles (MAV). At present, the biplane and other unusual configurations have not been a common design for MAV; however, they do have unlimited future potential. A set of experimental tests were carried out on various biplane configurations at low Reynolds numbers, which allowed the criteria for selecting the best wing configuration to be defined. The results obtained here show that the biplane configuration provides a higher maximum lift coefficient (CLmax) than the planar wing (monoplane). Furthermore, it has a larger wetted surface than the planar configuration, so the parasitic drag increases for the biplane configuration. This research is focused on a drone flight regime (low Reynolds number), and in this case, the parasitic drag (profile drag) has an important role in the total drag of the airplane. This study considers whether the reduction in the induced drag due to three–dimensional configuration (biplanes, box–wings, and joined–wings) can reduce the total drag or if the increase in the parasitic drag is bigger. Additionally, the increase in lift and the decrease in parasitic drag (profile drag) will be studied to determine if they have a greater influence on the performance of the airplane than the increase in structural weight. Further research is planned to be performed on 3D prototypes, with the selected configurations, and applied to nonconventional wing planforms.

Investigation of unsteady pressure fluctuations and methods for its suppression for a double suction centrifugal pump

Double suction centrifugal pumps find their usage in a variety of applications because of their ability to deliver good performance at higher flowrates and heads. The main issue with these devices is the occurrence of large pressure pulsations which cause noise, vibration, and unstable operation. The present work makes an effort using steady and unsteady computational fluid dynamics (CFD) approach to minimize these pulsations and also to improve the hydraulic performance of the considered pump. The CFD methodology and obtained results were validated by the experimental data to ensure reliability of the study. Fast Fourier Transform (FFT) analysis was performed to calculate the amplitude of these pressure pulsations. A parametric study was undertaken to find the effect of impeller stagger angles in reducing these pulsations and finding the most desirable stagger angle. Then, the performance of reference non-staggered impeller design was evaluated with the use of split volute arrangement and its comparison was done with the staggered impeller design. Finally, a combination of staggered impeller design with the split volute arrangement was tested to find its utility in suppressing pressure pulsations. It was observed that the best hydraulic performance could be obtained by the staggered 30° design with reduced pulsations; however, the least pressure pulsations were delivered by the combination of staggered 30° design with the split volute. The use of CFD helped in better visualization of the inherent flow physics associated with these designs.

Effect of Non-Uniformity of Rotor Stagger Angle on the Stability of a Low-Speed Axial Compressor

It is well known that variations in stagger angle between rotor blades affect compressor performance. In this paper, the stagger angle of blade No. 8 is increased or decreased by six degrees for non-uniformity, and the influence of rotor non-uniformity caused by the change in only one blade stagger angle on the performance and stability of the compressor is investigated. The experimental results show that whether the local rotor stagger angle increases or decreases, the compressor stability will deteriorate. If the stagger angle of blade No. 8 is reduced by six degrees, the flow coefficient at the stall point increases by 8.5%. If the stagger angle of blade No. 8 is increased by six degrees, the flow coefficient at the stall point increases by 1.5%. The reason for the deterioration of compressor stability caused by the local non-uniform rotor stagger angle is explored. When the stagger angle of rotor blade No. 8 deviates from the designed state, the load of blade No. 8 and the surrounding blades will change. The load on rotor blade No. 8 increases when the stagger angle decreases. In the near-stall condition, blade No. 8 becomes the “dangerous blade” that triggers the stall. As the stagger angle of rotor blade No. 8 increases, the load on blade No. 8 decreases. However, the load on blade No. 9 increases due to flow redistribution and blade No. 9 becomes a “dangerous blade” that triggers stall. The “dangerous blade” caused by the non-uniformity of stagger angle is the direct reason for the advance of the compressor rotating stall.