Velocity Triangles Research Articles

Difference in perception of angular displacement according to applied waveforms

Conclusions: This study shows that the differences in the waveforms of angular rotation affect the perception and memory of angular displacement. Objectives: During daily life, when we turn our head during various activities, our brain calculates how much angular displacement our head has undergone. However, how we obtain an accurate estimation of this angular displacement remains unclarified. This study aims to clarify this issue by investigating the perception and memory of passive rotation for three different waveforms of angular velocity rotation (sinusoidal (sine), triangle, and step). Methods: Thirteen healthy young subjects sitting on a servo-controlled chair were passively rotated at 60° or 120° about the earth-vertical axis by using one of these three angular velocity waveforms. They then attempted to reproduce the rotation angle by rotating the chair in the same direction in which they had been passively rotated using a handheld controller. The gain (reproduced angle/passively rotated angle) was calculated and used for the evaluation of the perception and memory of angular rotation. Results: The gain for step rotation was larger than that for sine and triangle rotations, with statistical significance. This confirms that the difference in the waveforms of angular rotation affects the perception and memory of angular displacement.

Aeromechanical Control of High-Speed Axial Compressor Stall and Engine Performance— Part I: Control-Theoretic Models

General methodologies are proposed in this two-part paper that further phenomenological understanding of compressible stall inception and aeromechanical control of high-speed axial compressors and engine performance. Developed in Part I are strategies for passive stabilization of compressible rotating stall, using tailored structural design and aeromechanical feedback control, implemented in certain classes of high-speed axial compressors used in research laboratories and by industry. Fundamentals of the stability of various dynamically-compensated, high-speed compressors was set down from linearized, compressible structural-hydrodynamic equations of modal stall inception extended further in this study from previous work. A dimensionless framework for performance-based design of aeromechanically-controlled compression system stall mitigation and engine performance is established, linking specified design flow and work-transfer (pressure) operability to model stages or local blade components, velocity triangle environment, optimum efficiency, extended stall margin and operability loci, and aeromechanical detailed design. A systematic evaluation was made in Part II (Coleman and McGee, 2013, “Aeromechanical Control of High-Speed Axial Compressor Stall and Engine Performance—Part II: Assessments of Methodology,” ASME J. Fluids Eng. (to be published)) on the performance of ten aeromechanical feedback controller schemes to increase the predicted range of stable operation of two laboratory compressor characteristics assumed, using static pressure sensing and local structural actuation to rudimentary postpone high-speed modal stall inception. The maximum flow operating range for each of the ten dynamically-compensated, high-speed compression systems was determined using optimized or “tailored” structural controllers, and the results described in Part II of the companion paper are compared to maximum operating ranges achieved in corresponding low-speed compression systems.

The Effect of the Degree of Reaction on the Leakage Loss in Steam Turbines

The degree of reaction selected in designing steam turbines is of paramount importance. There has been competition between 50% reaction and impulse turbines over a century. It is, therefore, important to understand the effect of the degree of reaction on aerodynamic performance. In particular, a change in the degree of reaction affects the leakage flow substantially in both the stationary and rotating blades due to a change in the blade loading. The effect of the degree of reaction on the efficiency loss due to leakage flows is systematically investigated in this paper using analytical models. It is shown that the appropriate way to understand the efficiency loss due to leakage flows is to estimate the kinetic energy dissipation rather than the leakage mass flow rate, as demonstrated by Yoon et al. (Yoon, S., Curtis, E., Denton, J., and Longley, J., 2010, “The Effect of Clearance on Shrouded and Unshrouded Turbine at Two Different Levels of Reaction,” ASME Paper No. GT2010-22541). In order to estimate the efficiency loss due to leakage flows, the well-known Denton model (Denton, J. D., 1993, “Loss Mechanisms in Turbomachinery,” ASME J. Turbomach., 115, pp. 621–656) is extended by considering the velocity triangles in a repeating turbine stage. The extended model is compared with experimental data, at different degrees of reaction, and shows good agreement with measurements. It is shown that a reduction in the degree of reaction, at a fixed flow coefficient and a fixed work coefficient, results in an increase in the efficiency loss across the stationary blade but a decrease in that across the rotating blade. However, the efficiency loss across the stationary blade hub is estimated to be smaller than the efficiency loss across the rotating blade tip. A stationary blade can be better sealed than a rotating blade by applying multiple seals and using a leakage path with a low radius. The efficiency loss due to the tip leakage flow is substantially influenced by the choice of the tip configuration. Shrouded blades show several aerodynamic advantages over unshrouded blades in reducing the tip leakage efficiency loss. Employing multiple seals over the shroud decreases the tip leakage mass flow rate significantly. Moreover, as the degree of reaction approaches zero, the tip leakage mass flow rate over the shroud becomes small since the axial pressure drop across the rotating blade becomes small. In unshrouded blades, a reduction in the degree of reaction is shown to increase the leakage mass flow rate over the tip because the circumferential pressure difference between the blade pressure side and blade suction side generally increases when the pitch-to-chord ratio remains unchanged.

Effects of Flow Rate and Viscosity on Slip Factor of Centrifugal Pump Handling Viscous Oils

Slip factor is an important parameter in the hydraulic design of centrifugal pump impeller for handling viscous oils. How to extract the factor from CFD computational results and how flow rate and liquid viscosity to affect it remain unclear. In the present paper, the flip factor was estimated by means of two approaches: one is from the velocity triangles at the impeller outlet and the other is due to the impeller theoretical head of 3D turbulent viscous fluid. The velocity of water and viscous oils in the impeller and volute computed by CFD was validated with LDV measurements at the best efficiency point. The effect of exit blade angle on slip factor was clarified. It was shown that the two approaches result into two different slip factors. The factors are significantly dependent of flow rate; however, the liquid viscosity seems to take less effect on them. Volute is responsible for reduction in tangential velocity of liquid at the outlet of impeller at low flow rates. The slip factor of impeller with large exit blade angle is not sensitive to flow rate.

Experimental Measurements of Ingestion Through Turbine Rim Seals—Part I: Externally Induced Ingress

This paper describes a new research facility which experimentally models hot gas ingestion into the wheel-space of an axial turbine stage. Measurements of the CO2 gas concentration in the rim-seal region and inside the cavity are used to assess the performance of two generic (though engine-representative) rim-seal geometries in terms of the variation of concentration effectiveness with sealing flow rate. The variation of pressure in the turbine annulus, which governs this externally-induced (EI) ingestion, was obtained from steady pressure measurements downstream of the vanes and near the rim seal upstream of the rotating blades. Although the ingestion through the rim seal is a consequence of an unsteady, three-dimensional flow field and the cause-effect relationship between the pressure and the sealing effectiveness is complex, the experimental data is shown to be successfully calculated by simple effectiveness equations developed from a previously published orifice model. The data illustrate that, for similar turbine-stage velocity triangles, the effectiveness can be correlated using a nondimensional sealing parameter, Φo. In principle, and within the limits of dimensional similitude, these correlations should apply to a geometrically-similar engine at the same operating conditions. Part II of this paper describes an experimental investigation of rotationally-induced (RI) ingress, where there is no mainstream flow and consequently no circumferential variation of external pressure.

Calculating the aerodynamics of vertical axis wind turbines

Vertical axis wind turbine technology has been applied last years, very long after horizontal axis wind turbine technology. Aerodynamic problems of vertical axis wind machines are discussible. An important problem is the determination of the incidence law in the interaction between wind and rotor blades. The focus of the work is to establish equations of the incidence depending on the blade azimuth, and to solve them. From these results, aerodynamic torques and power can be calculated. The incidence angle is a parameter of velocity triangle, and both the factors depend not only on the blade azimuth but also on the ratio of rotational speed and horizontal speed. The built computational program allows theoretically selecting the relationship of geometric parameters of wind turbine in accordance with requirements on power, wind speed and installation conditions.

Experiments and CFD Analyses for a New Reaction Microhydro Propeller with Five Blades

AbstractThis works aims to develop and study a new reaction microhydro tubular propeller turbine with five blades as a promising answer to solve the lack of energy in rural and remote areas. The first stage is to validate numerical and experimental tests made for the flow behavior for different values of head, discharge, and rotational impeller speed. Using specific mathematical formulations, a blade model configuration is developed based on the velocity triangles at the impeller inlet and outlet and experimental results based on pressure, discharge, and velocity profiles in different turbine sections. Through characteristic parameters, performance curves are obtained allowing comparisons between experimental and computational fluid dynamics (CFD) results. Also, an evaluation of the hydrodynamic behavior is made for a scaled model application by similarity turbo machines theory.

Dynamic simulations of post-stall performance in multistage axial compressors

In this contribution a quasi-one-dimensional tool for stationary and transient simulations of post-stall flows in multistage axial compressors is presented. An adapted version of the 1D Euler equations with additional source terms is discretized with a finite volume method and solved in time by a fourth-order Runge-Kutta scheme. The equations are discretized at mid-span both inside the blade rows and the non-bladed regions. The source terms express the blade-flow interactions and are estimated by calculating the velocity triangles for each blade row. Loss and deviation correlations are implemented and compared to experimental data in normal flow, stalled flow and reversed flow regions.

Numerical Simulation of Surge in Axial Compressor

The object of this paper is to provide a reliable tool to simulate the stationary and transient operation performances in multistage axial compression systems, especially poststall behavior. An adapted version of the 1D Euler equations with additional source terms is solved by a time marching and control volume method. The equations are discretized at midspan both inside the blade rows and the nonbladed regions, along the real flow path geometry. The source terms express the blade-flow interactions and are estimated by calculating the velocity triangles for each blade row. Loss coefficient and deviation models are supplied by empirical correlations and are compared to experimental data in all flow regions. Transient simulations are carried and compared to the experimental results for several values of parameterB. The flow mechanism inside the compressor during a surge cycle is also shown.

A physically based methodology to extrapolate performance maps of radial turbines

This paper details a physically based methodology to perform an extrapolation of the radial turbine performance maps, both mass flow characteristics and the efficiency curve. This method takes into account a narrow range of experimental data, which is usually the data available when such turbines are part of a turbocharger. Therefore, the extrapolation methodology is especially useful when data from third parties are being used or when the compressor of a turbocharger is used as the turbine brake in a gas stand. The nozzle equation is used to develop an interpolation and extrapolation of the mass flow rate trough the turbine. Then, specific information is extracted from this extrapolation and is fed into a total-to-static efficiency equation to carry out an extension of the efficiency curve. This equation is developed using the definition of the total-to-static efficiency, velocity triangles and thermodynamic and fluid fundamental equations. This procedure has been applied to five radial turbines of different sizes and types. Results are compared against experimental information available in the literature or provided by the turbine manufacturers and a good agreement has been found between theoretical and experimentally estimated data.

Steady Air Injection Flow Control in Centrifugal Compressor

In the present work steady air injection upstream of the leading edge was used in a centrifugal compressor, Whose preliminary design of compressor injection systems can be modeled by a geometrical relationship between user-specified yaw angle and resulting blade incidence angle based on simple velocity triangles, the error between the best yaw angle obtained from this relationship and that obtained from numerical simulation is less than 3%. To reveal the mechanism, steady numerical simulations were performed on high pressure ratio centrifugal compressor rotor operated with a rotor tip speed of 586 m/s. Parametric studies of the injection yaw angle was performed to determine the configuration that provide the best steady results for the compression systems studied in this work. The injectors were placed at short distance (ten percent of the inlet tip radius upstream of the compressor face) the objective of this was to achieve maximum control over the leading edge flow by varying individual injection parameters. The injection angle, α, was fifteen while the yaw angle, β, was parametrically varied. The results show that at design speed (n= 50 000 r/min) with injection flow rate equal to 3% of the main flow rate and 25 degree air injection yaw angle can lower the mass flow rate at stall for approximately 7.5%.

Aerodynamics design of two-stage vane-less counter-rotating turbinec

It is one of the most efficient ways to greatly improve aero-engines’ performance by utilizing vaneless counter-rotating turbine (VCRT) technology. To supply sufficient power, VCRT turns to be high Mach number, large flow angle at high-pressure turbine (HPT) rotor exit, and low blade camber angle, which increase difficulties to turbine design. As the axial velocity ratio of HPT rotor is much larger than the conventional ones, the optimal selection of VCRT velocity triangles based on theoretical analysis is developed, and how the efficiency varied by HPT stator/rotor exit flow angle is also figured out. The key points to design a high efficient practicable VCRT are to select velocity triangles that are characterized by low flow coefficient, high outlet flow angle and large axial velocity ratio of HPT rotor. Meanwhile, performance comparison between convergent blade and convergent-divergent blade shows the latter is more appropriate for VCRT.

Seven-Sensor Fast-Response Probe for Full-Scale Wind Turbine Flowfield Measurements

The unsteady wind profile in the atmospheric boundary layer upstream of a modern wind turbine is measured. The measurements are accomplished using a novel measurement approach that is comprised of an autonomous uninhabited aerial vehicle (UAV) that is equipped with a seven-sensor fast-response aerodynamic probe (F7S-UAV). The autonomous UAV enables high spatial resolution (∼6.3% of rotor diameter) measurements, which hitherto have not been accomplished around full-scale wind turbines. The F7S-UAV probe developed at ETH Zurich is the key-enabling technology for the measurements. The time-averaged wind profile from the F7S-UAV probe is found to be in very good agreement to an independently measured profile using the UAV. This time-averaged profile, which is measured in moderately complex terrain, differs by as much as 30% from the wind profile that is extrapolated from a logarithmic height formula; therefore, the limited utility of extrapolated profiles, which are commonly used in site assessments, is made evident. The time-varying wind profiles show that at a given height, the velocity fluctuations can be as much as 44% of the time-averaged velocity, therefore indicating that there are substantial loads that may impact the fatigue life of the wind turbine’s components. Furthermore, the shear in the velocity profile also subjects the fixed pitch blade to varying incidences and loading. Analysis of the associated velocity triangles indicates that the sectional lift coefficient at midspan of this modern turbine would vary by 12% in the measured time-averaged wind profile. These variations must be accounted in the structural design of the blades. Thus, the measurements of the unsteady wind profile accomplished with this novel measurement system demonstrate that it is a cost effective complement to the suite of available site assessment measurement tools.

English

The main objective of the paper is creating a method on how one can model an axial flow compressor. A systematic design approach has been used in the present study in order to design an axial flow compressor. The design calculations were based on thermodynamics, gas dynamic, fluid mechanics, aerodynamic and empirical relations. A two- dimensional compressible flow is assumed with constant axial and rotor blade velocities. A free-vortex swirl distribution was used in the design. These calculations include thermodynamic properties of the working fluid, number of rotor and stator blades, tip and hub diameters, blade dimensions (chord, length and space) for both rotor and stator, velocity triangles before and after the rotor and stator, mach number, solidity, flow and blade angles (blade twist). A repeated stage calculation is made to calculate the above parameters along compressor stages. The twist of the blades can be calculated along the blade length at any required number of sections selected by the designers to obtain smooth blade twist profile. NACA 65010 has been selected as a blade profile for the compressor at root, mean and tip. Here it is calculated at three main sections, the hub, the mean and the tip. The blade selected for this study is NACA 65010. The data obtained from the systematic approach has been utilised to generate three dimensional compressors.

Contrarotating Turbine Aerodesign for an Advanced Hypersonic Propulsion System

Contrarotating turbomachinery is part of a novel airbreathing system to power a vehicle from takeoff to hypersonic speeds. The turbine-based combined cycle precools the inlet air before compression, with the hydrogen fuel as the heat-rejection sink. To ensure a safe engine operation, a helium loop is introduced between the air and hydrogen cycles; the helium drives the turbines of the main turbocompressor. The high speed of sound and low compressibility of the helium results in subsonic blading with low divergence of the endwalls. This paper describes in detail the aerodesign procedure of contrarotating helium turbines, which allows a net reduction in turbine size while augmenting the turbine efficiency. The design methodology is reviewed starting from the preliminary velocity triangle analysis. Studies were conducted to determine the effect over efficiency, outlet swirl and periodicity of the blade height, degree of reaction, and work distribution. The three-dimensional optimizer demands efficient parameterization techniques to account for the lean/sweep/twist geometry. The present multidisciplinary design includes the calculation of the centrifugal stresses. Three different helium turbine architectures have been designed and optimized, with special care to ensure an adequate performance at offdesign operation, and particular attention was devoted to minimize the secondary flows.

Applications of traditional pump design theory to artificial heart and CFD simulation

A novel heart pump model was obtained by improving the traditional axial pump design theory with the consideration of working and hydraulic situations for artificial hearts. The pump head range and the velocity triangle were introduced and an iterative approach was utilized for the initial model. Moreover, computational fluid dynamics (CFD) simulations were performed to determine relevant model parameters. The results show that this procedure can be used for designing a series of high-efficiency artificial heart pumps.

A quasi-one-dimensional CFD model for multistage turbomachines

The objective of this paper is to present a fast and reliable CFD model that is able to simulate stationary and transient operations of multistage compressors and turbines. This analysis tool is based on an adapted version of the Euler equations solved by a time-marching, finite-volume method. The Euler equations have been extended by including source terms expressing the blade-flow interactions. These source terms are determined using the velocity triangles and a row-by-row representation of the blading at mid-span. The losses and deviations undergone by the fluid across each blade row are supplied by correlations. The resulting flow solver is a performance prediction tool based only on the machine geometry, offering the possibility of exploring the entire characteristic map of a multistage compressor or turbine. Its efficiency in terms of CPU time makes it possible to couple it to an optimization algorithm or to a gas turbine performance tool. Different test-cases are presented for which the calculated characteristic maps are compared to experimental ones.

Shaft Power Matching and Performance Prediction for Contra-Rotating Axial Flow Fans

The purpose of shaft power matching of contra-rotating axial flow fans (CRAFF) is to ensure the best utilization of the motors at their rated power while not to overload them at the operation.Usually it requires a lot of time and effort due to lack of theoretical guidance and, thus, becomes a major problem for the application of CRAFF. Through analyzing velocity triangle, the authors have found a nondimensional parameter k, defined as the tangential ratio of two relative outflow angles for two impellers, to be critical for successful shaft power matching and aerodynamic design. The authors then performed a numerical simulation of the flow field for a design of CRAFF, of which the performance prediction was validated very well by test data. Based on the analysis of the flow filed data, the result obtained from the velocity triangle analysis is further improved and some values for k and deviation angle δ are recommended. In order to determine the approximate optimum of blade pitch angles of two impellers, a guideline for shaft power matching is then presented. Finally, a comparison of the blade pitch angles obtained from the guideline with that obtained from the optimum using numerical simulation are carried out for six designs of CRAFF. The errors are only within 2 degrees.

Influence of Loading Distribution on the Off-Design Performance of High-Pressure Turbine Blades

Linear cascade measurements for the aerodynamic performance of a family of three transonic, high-pressure (HP) turbine blades have been presented previously by the authors. The airfoils were designed for the same inlet and outlet velocity triangles but varied in their loading distributions. The previous papers presented results for the design incidence at various exit Mach numbers, and for off-design incidence at the design exit Mach number of 1.05. Results from the earlier studies indicated that by shifting the loading towards the rear of the airfoil an improvement in the profile loss performance of the order of 20% could be obtained near the design Mach number at design incidence. Measurements performed at off-design incidence, but still at the design Mach number, showed that the superior performance of the aft-loaded blade extended over a range of incidence from about −5.0deg to +5.0deg relative to the design value. For the current study, additional measurements were performed at off-design Mach numbers from about 0.5 to 1.3 and for incidence values of −10.0deg, +5.0deg, and +10.0deg relative to design. The corresponding Reynolds numbers, based on outlet velocity and true chord, varied from roughly 4×105 to 10×105. The measurements included midspan losses, blade loading distributions, and base pressures. In addition, two-dimensional Navier–Stokes computations of the flow were performed to help in the interpretation of the experimental results. The results show that the superior loss performance of the aft-loaded profile, observed at design Mach number and low values of off-design incidence, does not extend readily to off-design Mach numbers and larger values of incidence. In fact, the measured midspan loss performance for the aft-loaded blade was found to be inferior to, or at best equal to, that of the baseline, midloaded airfoil at most combinations of off-design Mach number and incidence. However, based on the observations made at design and off-design flow conditions, it appears that aft-loading can be a viable design philosophy to employ in order to reduce the losses within a blade row provided the rearward deceleration is carefully limited. The loss performance of the front-loaded blade is inferior or at best equal to that of the other two blades for all operating conditions.

Potential of flow pre-whirl at the compressor inlet of automotive engine turbochargers to enlarge surge margin and overcome packaging limitations

Due to the packaging constraints to which turbocharged engines are submitted in passenger cars, the inlet duct of the centrifugal compressor often requires a 90° bend. The compressor inlet perpendicular to its axis disturbs the flow and reduces the compressor performance. This paper presents an interesting solution based on a specifically designed inlet swirl-generator device (SGD) that palliates these negative effects. In addition, the SGD can be used to extend the surge margin of the compressor if the position of the SGD blades is modified in function of the reciprocating engine operation conditions. The paper describes how the swirl level and the pressure losses generated by the device have been characterized in a continuous flow test rig. After this the SGD plus a centrifugal compressor from a turbocharger unit have been tested in a specific turbocharger test bench. The results obtained show the influence of the SGD blades position on the compressor performance. In order to better understand the influence of the SGD on the turbocharger behaviour, the flow velocity triangles near the inducer have been reconstructed using an approach based on CFD calculations.