Stagger Angle Research Articles

Performance Investigation of the Savonius Wind Turbine by Putting a Rotating Cylinder in the front of Advancing by Varying the Diameter and Stagger Angle

Performance Investigation of the Savonius Wind Turbine by Putting a Rotating Cylinder in the front of Advancing by Varying the Diameter and Stagger Angle

Flow induced vibration with forced convection of a stationary and oscillating filleted bluff bodies in a staggered position

Flow induced vibration (FIV) and forced convection heat transfer from staggered cylinders are numerically investigated with Re = 150 and Pr = 0.7. Cylinders are arranged in a staggered manner with three different stagger angles (α) = 15°, 30°, and 45°. The upstream cylinder (UC) is kept fixed while the downstream cylinder (DC) is mounted. The cross section of the bluff body is altered by parameter (r*) = 0 (square cylinder), 0.5, 0.75, and 1 (circular cylinder). For every stagger angle and r*, the reduced velocity is varied from 2 to 10. The mass ratio (m*) of the DC is kept at 10 and damping constant set to zero for maximum vibrational amplitude. The incompressible Navier–Stokes equations are coupled with Newton's equation for the mass-damper system of the vibrating cylinder. Flow induced vibration was studied with the help of frequency characteristics, dynamics response of cylinders, and instantaneous phase plots of lift and amplitude. Generally, in the case of square cylinders a delayed response can be observed as compared to other configurations. For α=15°, the DC is fully submerged into the wake of static UC. P + S (P: pair; S: singlet)-type vortices can be observed for r* = 0. For other configurations of filleted cylinders, such as r* = 0.5, 0.75, and 1 at Ur=4, 2 parallel row formation is formed due to negative sign vortices while the other one was a combination of positive and negative vortices in pseudo-P formation. At higher Ur=6 and 8, coalesced and irregular wakes can be noticed. As the stagger angle is increased to higher than 30°, the wake of both cylinders becomes more pronounced. Due to the change in stagger angle, fs (vortex shedding frequency) of UC and DC forces decouples. 2P-type vortex shedding can be observed at Ur=4 for r* = 0.75 and 1. Pairs of vortices are coupled from each cylinder in a row where negative vortices coalesce while losing energy. For lower r* = 0 and 0.5, there is a tendency for three row formation. Further increase in angle pushed the DC completely out of the wake of the UC although vortices from both cylinders are still found to interact and exhibit three row formation and 2P-type vortex shedding. Heat transfer from the DC is highly dependent on the stagger angle. For r* = 1 and 0.5 at Ur=2, the change in Nuavg is 15% and 14.7%, respectively, when the angle changed from 15° to 45°. Heat transfer from any FIV system can be directly influenced by dynamic response, position, shape, and flow topology. The generated results are provide insight for understanding the vibrational modes and heat transfer from two bluff bodies involving fluid–structure interactions.

Improving near-stall performance of axial flow compressors using variable rotor tandem stage. A steady analysis

This paper investigates the idea of substituting the first stage of a conventional axial-flow compressor and its inlet guide vane (IGV) row with a variable rotor tandem (VRT) stage to reduce the size and weight of axial-flow compressors. It is expected that a tandem stage gains higher pressure ratio than a conventional stage, and simultaneously, its variable stagger rotor provides more flexibility in handling unsteady phenomena at low mass flow rates. A three-dimensional numerical model based on Reynolds-Averaged Navier–Stokes equations is developed to conduct this investigation. To validate the numerical model, experimental tests are conducted on a tandem single-stage axial-flow compressor test bench in the Dana laboratory of Amirkabir University of Technology, to compare the performance map with numerical results. The validated numerical model is then employed to simulate the performance of both front and aft variable rotor blades. The proposed tandem stage effectively performs the IGV duty, suppresses instabilities at low mass flow rates, and eventually extends the compressor's stable operational range. This proves that a VRT stage is an efficient active surge-control system tool. The detailed survey of the three-dimensional flow field reveals that the aft tandem rotor blade stagger angle is more effective in increasing the stall margin and decreasing the minimum operational mass flow rate than the front row of blades. It is observed that when the aft blades rotate in the direction of decreasing the tandem blades' gap area, the flow momentum increases and causes the compressor stability at lower mass flow rates.

Effects of endwall clearances of variable diffuser vane on centrifugal compressor performance

To ensure the variable diffuser vane can rotate around a pivot fluently in practical applications, there have to be clearances between vanes and diffuser walls. As the compressor pressure ratio increases, the effects of the vane endwall clearances are enhanced and cannot be ignored. This paper investigates the effects of both-side vane endwall clearances on the centrifugal compressor performance. Results show that the existence of endwall clearances mainly enlarges the flow capacity of the vane diffuser and decreases the compressor efficiency, and these effects are more significant as the vane stagger angle decreases. A one-side endwall clearance of 2.7% of the diffuser width increases the choke mass flow rate by as much as 20% and decreases the compressor peak efficiency by 2.7%. Due to the non-uniform flow along span at the impeller outlet, the shroud-side vane endwall leakage plays a more important role than the hub-side in affecting the compressor performance. In additions, the respective contributions of the vane throat, the hub-side and the shroud-side endwall clearances to the increases of the vane choke mass flow rate are quantitatively studied. The flow physics and loss mechanisms of the endwall leakage are revealed.

First principles study of electronic structure of x-form phthalocyanine crystals doped with one-dimensional iodine atomic chains

The x-form phthalocyanine (Pc) crystal is composed of a square-lattice arrangement of one-dimensional and double-period molecular chains with molecular planes normal to the stacking direction, and doped iodine (I) atomic chains between these molecular chains are known to induce the insulator-metal transition. Using the van der Waals density functional method, we investigate the electronic structure of a single x-form silicon Pc (x-SiPc) chain and the x-SiPc crystal undoped and doped with I atomic chains in a comparative manner. Although a SiPc molecule has a Si pz derived orbital just above the LUMO, the aligned Si atoms in x-crystals, each of which is at the center of the molecular plane, dimerize in the stacking direction, which prevents formation of a Si metallic band. In a single SiPc chain, two molecules in each primitive unit cell are stacked face-to-face with a staggering angle of 45°. However, when these molecular chains aggregate to create x-crystals, the staggering angle deviates from 45° to about 40° to form H–H bonding orbitals like H2 molecules between neighboring molecular planes in the lateral direction. Doping of the I atomic chains converts half-filling of the doubly degenerate bands to a lower band occupancy, which corresponds to the insulator-metal transition observed experimentally. The equally spaced I atomic chains create a metallic band due to pz-orbital overlapping with an effective-mass ratio of 0.15. Although the SiPc chains operate to create equally spaced I atomic chains, the effect of I atoms trying to trimerize is larger. This trimerization prevents pz orbitals of I atoms from making a metallic band.

Numerical and experimental study on the critical geometric variation based on sensitivity analysis on a compressor rotor

Abstract Different types of geometric variations often appear coupledly in manufactured blades. It is desired to identify the ones that have the strongest impact on the performance. In this paper, the influence of multiple geometric variations on the compressor rotor blade at the design point is studied. Two hundred and nine varied blades are constructed by adding variation data to the design-intent blade and assessed using steady-state Reynolds-Averaged Navier–Stokes (RANS) simulations. It is shown that the region near the lower and upper end of the blade is more sensitive to geometric variations. Spearman’s rank correlation coefficient is used to measure the sensitivity of rotor performance to geometric variations. The results show that the stagger angle variation is the most influencing variation. Local sensitivity analysis at different spans also shows that the stagger angle variation is an important geometric variation that needs more attention during blade manufacturing. Also, the influence of geometric variations can reach further than nearby regions. Consequently, experiments on linear cascades at different spans of the rotor are carried out to study the effect of stagger angle on flow characteristics. Results show that the stagger angle variation could lead to different changes in performance depending on the specific cascade profile.

Flow structure and heat transfer of a two-cylinder array

Two cylinders in staggered and tandem configurations were experimentally investigated to understand how the flow structure influences heat transfer. The results indicate the heat transfer of downstream cylinder exhibits more variability than that of the upstream cylinder as the stagger angle changes. The heat transfer characteristics for each flow pattern and the mechanisms governing heat transfer for the cylindrical array were clarified. Additionally, the significant effects of flow motion on the local Nusselt number of the cylinder surfaces resulting from varying stagger angles were elucidated. The overall Nusselt number in a staggered array system increases with the stagger angle, whereas in a tandem array system, it increases with the distance ratio. Notably, staggered cylinder arrangements exhibited a more pronounced enhancement in heat transfer compared to the tandem arrangement.

Weak and strong chirality-anomaly-manipulations in a superconducting Weyl semimetal sandwich structure

We investigate the quantum interference of the electron–hole conversions from the two interfaces in a Weyl semimetal (WSM)-based hybrid structure, in which a superconducting WSM is sandwiched in between two normal ones. The quantum interference is characterized by the chirality-anomaly-manipulation (CAM). It is found that only low energy is in favor for s-wave BCS pairing states. The Andreev reflection (AR) chirality blockade can be tuned by the stagger angle α for the relative orientation of paired Weyl points, accompanied by an AR bipolar chirality diode. Thus, a strong CAM is indicated for the electron–hole conversion. However, the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing states have no energy preference, with the weak and strong CAMs being near and far away from the zero energy, respectively. More interestingly, a perfect AR with the normal reflection suppressed thoroughly can be obtained at any α as a result of the FFLO paring with the same chirality. In addition, the conductance or noise power, which incorporates the contributions of the two paired Weyl nodes, not only, in turn, embodies the respective features of their contributions but also can be experimentally measured to discern between the BCS and FFLO paring states.

Improving part-load performance of combined-cycle gas turbines by optimizing variable geometry control strategy for compressor and power turbine combined adjustment

The variable geometry methods currently used in combined-cycle gas turbines are compressor variable inlet guide vanes (VIGV) or power turbine variable area nozzles (VAN). On this basis, this study presents the optimal variable geometry control strategy for compressor and power turbine combined adjustment ([Formula: see text]) using the Differential Evolutionary Algorithm with the LM2500+ gas turbine. The aim is to further improve the part-load performance of the combined-cycle gas turbine. Firstly, a part-load performance prediction model for variable geometry gas turbines is established based on the component method. Subsequently, a variable geometry gas turbine part-load performance optimization model is developed by combining the Differential Evolution Algorithm. Finally, the optimum combination of stagger angles for the compressor inlet vane and power turbine nozzle is calculated at each part-load condition. Compared to the VIGV and VAN control strategies, the [Formula: see text] control strategy proposed in this paper shows a higher stability margin and better economy. The [Formula: see text] control strategy maintains a constant exhaust temperature within a part load range from 20% to 100% with the stability margin exceeding 14%. In comparison with the VAN control strategy, the fuel flow rate decreases by 1.152% at 45% relative load power and by 3.435% at 20.0% relative load power with the [Formula: see text] control strategy.

Numerical study on aerodynamic performance improvement and efficiency enhancement of the savonius vertical axis wind turbine with semi-directional airfoil guide vane

The growth of greenhouse gases increased the need for wind energy resource. Savonius vertical axis wind turbines (VAWT) have high potential as a turbomachine. Optimization methods such as flow injection on the rotor suction side to flow control on buckets developed as Savonius VAWTs operating range and efficiency are lower than other VAWTs. In this study, the semi-directional airfoil guide vane (SDAGV) was introduced to improve the aerodynamic performance and increase the efficiency of Savonius VAWT. The results indicate that the vane installation at the lower upstream of the rotor yields a power coefficient (Cp) of 0.12, representing a 140% growth compared to a single Savonius rotor. Furthermore, this installation extended the operating range of the turbine from a tip speed ratio (TSR) of 0.51–0.8. According to the results, it was found that more passages could improve efficiency. Five types of symmetrical airfoil profiles were evaluated for the guide vane. The NACA0010 airfoil profile, which has lower thickness than the others, obtained 7% higher efficiency than the base case consisting of NACA0012. Also, the optimal stagger angle for configurations NACA0021, NACA0018 was found to be 45°, and for NACA0010 and NACA0012 was determined to be 30°, respectively.

Developing and correction methods for a one-dimensional axial flow compressor model

This paper establishes a one-dimensional model of an axial flow compressor using the Average Mid-Diameter Method and employs polynomials to adjust the off-design stagger angle and off-design loss models. Furthermore, a model stepwise correction strategy based on the Particle Swarm Optimization (PSO) algorithm is proposed. The accuracy of the corrected one-dimensional axial flow compressor model was verified and integrated into the overall engine model for validation. Simulation results indicate that the maximum error in calculating the characteristics of the established one-dimensional axial flow compressor model does not exceed 6%, and the maximum error in simulating the overall engine model remains below 4%. These findings validate the effectiveness of modeling and correction methods for a one-dimensional axial flow compressor model targeting aero-engine component-level model.

A shock loss reduction method for the low-pressure rotor of a vaneless counter-rotating turbine using circulation redistribution

This paper proposes the circulation redistribution for the low-pressure (LP) rotor of a highly-loaded vaneless counter-rotating turbine (VCRT) to reduce the LP shock losses. The method is to decrease the mid-span circulation and increase the tip circulation at the exit of the LP rotor with unchanged high-pressure (HP) and LP power output. The LP Blade-to-Blade flow field can be considered as a Laval nozzle model. And the high static pressure drop from the throat to the exit results in strong trailing edge (TE) shocks near the LP mid-span. Also, the suction side TE shock (ST) and the reflected shock of the pressure side TE shock (RPT) near the LP mid-span merge into a relatively strong shock very close to the TE. These two factors result in high shock losses. To reduce the shock losses under the design condition, decreasing the stagger angle and the blade exit angle near the LP mid-span are adopted to reduce the LP mid-span exit circulation. This changes the throat area to exit area ratio near the LP mid-span, prompting the actual static pressure drop from the throat to the exit to be reduced and closer to the theoretical value, so that the TE shock strength is reduced. Besides, the intersection of the RPT and the ST is delayed owing to the improved flow angle distributions near the TE, further contributing to the LP mid-span shock loss reduction. Since the LP power output is decreased and the LP tip-leakage flow (TLF) losses are far lower than the HP TLF losses, increasing the stagger angle and the blade exit angle in LP tip regions are employed to increase the LP exit circulation and decrease the HP exit circulation in tip regions. Then the HP and LP efficiency are both raised with unchanged HP and LP power output after optimizing the blade profiles near the mid-span and in tip regions of the LP rotor. The remarkable thing is that the TE shock strength in LP tip and root regions are both reduced after improved because of the decreased ratio of the exit area to the throat area. And the intersection of the RPT and the ST in LP tip and root regions are also both delayed, leading to reduced shock losses. The reduced TE shock losses along the whole LP span appreciably raise the LP and VCRT efficiency by 0.96% and 0.32% respectively.

Investigating the effect of axial fan shrinkage obtained by centrifugal casting technology on aerodynamic characteristics

Centrifugal casting technology was developed for the application of manufacturing axial fans. In the literature, these fans were usually manufactured by injection molding, mechanical processing or heat pressing. The main characteristic of this molding technology allows the creation of thick and hollow blades. This characteristic of the blades gives useful advantages of the fan that cannot be achieved by conventional methods. The centrifugal casting technology has been applied to fabricate axial fans in recent research. However, the issue of quality control and especially the shrinkage of the resulting fan compared to the molding has not yet been considered. Therefore, more in-depth studies and approaches are required. In this study, 3D scanning method is used to evaluate the shrinkage of the blades. The used 3D scanner is the Comet L3D 5M type based on structured light (blue LED) with a 5-megapixel sensor. This device achieves high accuracy and reliability (resolution 18 μm). The theoretical basis for determining fan shrinkage compared to CAD molds is based on the following main parameters: Chord line L (mm), relative thickness Emax (%), and stagger angle ( (degrees). In addition, the aerodynamic characteristics of the proposed fan are compared to those of a fan made of aluminum (blades are identical, but different in fabricating technology). Characteristics of this aluminum rigid-fan are assumed as reference. The results showed that the difference was not large between the blades. Besides, the results of aerodynamic testing on the test bench of the two fans are almost similar. This indicates the good adaptability of the axial fan received by the centrifugal casting technology.

Experimental Study of Stagger Angle Effect on the Performance of Marine Savonius Vertical Axis Water Turbine

This paper investigates the performance of Savonius vertical axis water turbine by varying its stagger angles. In this study, the shape of the turbine blade is modified based on the Myring equation as well as adding a disturbance in the form of a circular cylinder placed in front of the advancing blade as a barrier. The method used in this research is an experimental study in a water tunnel at a velocity of 0.22 m/s. The turbine has size of 0.4 m in height and 0.4 m in diameter. The experiment results show that the use of a circular cylinder in front of the advancing blade has a significant effect on increasing turbine performance. This can be proven by placing a circular cylinder with , , and where the angular speed achieved is , torque coefficient and the result of maximum power coefficient is about 0.4356.

Smart Blade Count Selection to Align Modal Propagation Angle with Stator Stagger Angle for Low-Noise Ducted Fan Designs

The rotor–stator interaction noise is a major source of fan noise. Especially for low-speed fan stages, the tonal component is typically a dominant noise source. A challenge is to reduce this tonal noise, as it is typically perceived as unpleasant. Therefore, in this paper, we analytically, numerically and experimentally investigate an acoustic effect to lower the tonal noise excitation. Our study on an existing low-speed fan indicates a reduction in tonal interaction noise of more than 9 dB at the source if the excited acoustic modes propagate parallel to the stator leading edge angle. Moreover, a design-to-low-noise approach is demonstrated in order to apply this effect to two new fan stages with fewer stator than rotor blades. The acoustic design of both fans is determined by an appropriate choice of the rotor and stator blade numbers in order to align the modal propagation angle with the stator stagger angle. The blade geometries are obtained from aerodynamic optimization. Both fans provide similar aerodynamic but opposing acoustic radiation characteristics compared to the baseline fan and a significant tonal noise reduction resulting from the impact of the modal propagation angle on noise excitation. To ensure that this effect can also be applied to other low-speed fans, a design rule is derived and validated.

Multi-objective design optimization of a transonic axial fan stage using sparse active subspaces

In this paper, a multi-objective optimization strategy for efficient design of turbomachinery blades using sparse active subspaces is implemented for a turbofan stage design. The proposed strategy utilized sparse polynomial chaos expansion on a limited dataset to generate a function from which the differential and the covariance matrix can be obtained. Active subspace was used to compute the active variables via singular value decomposition and a hybrid polynomial correlated function expansion was used to construct a surrogate model on the active subspace. Coupled with freeform method and multi-objective genetic algorithm, an automated optimization loop was run at a single operating condition. An improvement in stage efficiency and total pressure ratio of 2.97% and 1.15% was achieved for the optimum design compared with the baseline. Additionally, total pressure loss coefficient decreased by 5.88%, exit flow angle by 34.65% and shock strength by 5.32%. The coupled effect of change in stagger angle, forward sweep, forward lean, and chord length reduced the recirculation at the hub, and blockage at the shroud due the tip leakage flow by decreasing the blade loading. The threshold value hyperparameter was found to be the most influential and must be accurately determined.

Inlet Guide Vane Stagger Effects on Multistage Compressor Performance and Stall Inception

The effects of variable inlet guide vanes on compressors have been evaluated throughout the turbomachinery industry for decades. These vanes improve both the performance and stability of a machine—the extent to which is highly dependent on the individual machine and the conditions of operation. Evaluating their effects on compressor stall inception via experimental investigations can inform model development and validation since commonly used RANS and URANS tools face limitations in accurately predicting and modeling stall events. The current literature on variable inlet guide vane restaggering, however, is dominated by numerical investigations. This study offers a unique experimental investigation into restaggering effects on compressor stall behavior by evaluating experimental results from different variable inlet guide vane stagger angles in a high-pressure axial compressor. Previous investigations have shown that variable inlet guide vane restaggering may change the stall inception mechanism of axial flow compressors. This investigation found a distinct change in the stage matching of the machine without altering the stall inception mechanism, further demonstrating the need for experimental investigations to inform the specific effects that restaggering inlet guide vanes offers comparable compressors.

A data-driven polynomial chaos method for uncertainty quantification of a subsonic compressor cascade with stagger angle errors

The probability-based uncertainty quantification (UQ) methods require a large amount of sampled data to construct the probability distribution of uncertain input parameters. However, it is a common situation that only limited and scarce sampled data are available in engineering applications due to expensive tests. In the present paper, the Data-Driven Polynomial Chaos (DDPC) method is adopted, which can propagate input uncertainty in the case of scarce sampled data. The calculation accuracy and convergence of the self-developed DDPC method are validated by a nonlinear test function. Subsequently, the DDPC method is applied to investigate the uncertain impact of stagger angle errors on the aerodynamic performance of a subsonic compressor cascade. A family of manufacturing error data of stagger angles was obtained from the real compressor blades. Based on the limited measurement data, the DDPC method combined with Computational Fluid Dynamics (CFD) simulation is employed to quantify the performance impact of the compressor cascade. The results show that the performance dispersion under off-design conditions is more prominent than that under design conditions. The actual aerodynamic performance deviating from the nominal performance is not a small probability event, and the probability of deviating from the nominal loss coefficient and exit flow angle by more than 1% can reach up to 47.6% and 36.8% under high incidence i = 7°. Detailed analysis shows that stagger angle errors have a significant effect on the flow state near the leading edge, resulting in variations in separation bubble size and boundary layer thickness.

Performance analysis of a novel small-scale radial turbine with adjustable nozzle for ocean thermal energy conversion

Ocean thermal energy is acknowledged as one of the most promising ocean renewable energy sources in low latitude sea areas. In the ocean thermal energy conversion system, the turbine plays a significant role, and it is responsible for converting the working medium enthalpy into the shaft output power. The present study is focused on the performance analysis of a novel radial inflow turbine with an adjustable nozzle in the OTEC system in order to adapt to the changing operating conditions of the turbine, which vary with the change in seawater temperature. At the design point, the predicted overall isentropic efficiency is 86.5%, and the shaft output power is 15.3 kW, slightly higher than the expected 15 kW. Furthermore, a parametric study is performed, respectively, for the nozzle vane stagger angle and the nozzle-impeller radial clearance to explore the favorable geometric parameters for different conditions. The turbine’s overall efficiency increases slightly with deceasing nozzle-impeller radial clearance, and the variation of the nozzle vane stagger angle is much more influential on the turbine shaft power and overall efficiency. The optimum stagger angle point moves from 32° to 36° gradually with the increase in nozzle-impeller clearance. Finally, the feasibility of an adjustable nozzle for the turbine under off-design conditions was verified by combining the radial clearance and nozzle stagger angle.

On the Flow Physics During the Transition of a Variable Pitch Fan From Nominal Operation to Reverse Thrust Mode

Abstract The flow field during the transition of variable pitch fans (VPFs) from nominal operation to reverse thrust mode at typical “Approach Idle” engine power setting and aircraft touchdown speed of 140 knots is described in this work. An integrated airframe-engine-VPF research model that features a future 40,000 lbf geared high bypass ratio engine installed on a twin-engine airframe in landing configuration is used to explore the flow field in a fully transient unsteady Reynolds-averaged Navier–Stokes (URANS) simulation with imposed wall motion. A novel methodology that implements an adaptation of a mesh displacement equation to mimic the fan blade airfoil rotation is developed. The implementation of this method with gradual, small-step deformation along with an automated mesh update routine enables a high quality, near “real-time” simulation of the complete transition. The flow field during transition is characterized by the evolution from full typical forward flow through the engine to the development of massive recirculation regions at the feather pitch setting and finally to development of a reverse flow from the bypass nozzle to the fan passages. In the paper, the transient development of the various flow features through different stations of the engine flow path apropos the fan blade airfoil rotation to reverse thrust mode are discussed in detail. Also, the temporal development of the mass flow ingested through the engine, airframe decelerating force, and distorted flow at the core engine inlet are described. A hitherto unresolved fan power peaking during the middle of the transition and higher power requirement at reverse thrust mode is captured. The effect of fan rotational speed in terms of engine power setting and the aircraft touchdown velocity on the transition flow physics is explored. A comparison of this fully transient approach with discrete steady-state runs for different stagger angle settings is presented. The flow physics during transition to reverse thrust mode as described in this study is critical in understanding the feasibility of using VPF for reverse thrust in future aircraft. The new capability to study the transition in a fully transient simulation can be used as a design development aid to define design and control characteristics of the reverse thrust VPF.