Theoretical Estimation of Minimum and Maximum Allowable Rotational Speed of Supercritical CO2 Inward Flow Radial Turbine

Supercritical CO2 inward flow radial turbines necessitate high operating speeds due to the high density of sCO2, especially in sub-MW scale power generation where rotational speeds can be in the range of 50k to 150k rpm. Although designing the turbine at these high rotational speeds is reasonable from the aerodynamic efficiency point of view but generally not practical to operate. A theoretical framework based on 1-D meanline analysis is built to evaluate the minimum and maximum rotational speed limits corresponding to a set of boundary conditions and operating constraints. The results show that minimum allowable speed depends on the inlet velocity triangle (IVT) and is constrained by inlet Mach number, inlet blade height, and inlet flow angle. On the other hand, maximum allowable speed depends on the outlet velocity triangle (OVT) and is constrained by outlet relative Mach number, outlet hub radius, and blade speed. The theoretical models are demonstrated from kilowatt to megawatt power levels, and the results are compared with commercial software and Balje’s Ns-Ds diagram. Although this study is highlighted in the context of supercritical CO2 as the working fluid, in principle, the same models are equally valid for any working fluid.

On Choosing the Optimal Impeller Exit Velocity Triangles in Preliminary Design

Impeller discharge flow plays an important role in centrifugal compressor performance and operability for two reasons. First, it determines the work factor and relative diffusion for the impeller. Second, it sets the flow into the downstream stationary diffusion system. The choice made in the preliminary design phase for the impeller exit velocity triangle is crucial for a successful design. The state-of-the-art design approach for determining the impeller exit velocity triangle in the preliminary design phase relies on several empirical guidelines, i.e. maximum work factor and diffusion ratio for an impeller, the optimal range of absolute flow angle, etc. However, as modern compressors continue pushing toward higher efficiency and higher work factor, this design approach falls short in providing exact guidance for choosing an optimal impeller exit velocity triangles due to its empirical nature as well as the competing mechanism of the two trends. In light of this challenge, this paper introduces a reduced-dimension, deterministic approach for the design of the impeller exit velocity triangle. The method gauges the design of the impeller exit velocity triangle from a different design philosophy using a relative diffusion effectiveness parameter and is validated using 6 impeller designs, representative of applications in both turbochargers and aero engines. Furthermore, with the deterministic method in place, optimal impeller exit velocity triangles are explored over a broad design space, and a one-to-one mapping from a selection of impeller total-to-total pressure ratios and backsweep angles to a unique optimal impeller exit velocity triangle is provided. This new approach is demonstrated, and discussions regarding the influences of impeller total-to-total pressure ratio, isentropic efficiency, and backsweep angle on the optimal impeller exit velocity triangle are presented.

Fan Aerodynamics With a Short Intake at High Angle of Attack

Fans that are designed to maintain thrust at the high angle of attack (AOA) flight condition could exploit the cruise fuel burn benefit of a shorter intake design. This article considers how the fan rotor radial pressure ratio distribution and tip velocity triangle can be designed to improve thrust when coupled to a short intake operating at high AOA. Two AOA values are investigated using unsteady computational fluid dynamics: 20 deg (attached flow) and 35 deg (separated flow). Thrust at high AOA is governed by three key loss and work input mechanisms. (i) Rotor choking loss: flow is accelerated around the intake bottom lip and enters the rotor with high Mach numbers. Fans designed with a tip-high radial pressure ratio distribution reduced choking loss with a separated intake compared to a mid-high design, particularly when the tip velocity triangle was designed with high diffusion instead of high camber. (ii) Rotor–separation interaction loss: the rotor ingests low mass flow when operating inside the separation and the casing boundary layer separates. High diffusion tip designs strengthened the casing separation, but this penalty did not outweigh improved choking loss. (iii) Work input in radial flows: high AOA generates strong radial flows through the rotor, which alter both the amount and the way work is imparted on the flow. Fans designed with a mid-high radial pressure ratio distribution imparted high work on streamlines migrating toward the hub. Consolidating these findings, we propose two design philosophies for improved thrust at high AOA: high work (mid-high radial pressure ratio distribution) or low loss (tip-high radial pressure ratio distribution with high diffusion tip velocity triangle).

The Effect of Reaction on Compressor Performance

Reaction is the fundamental parameter by which the asymmetry of the velocity triangle of a stage is set. Little is understood about the effect that reaction has on either the efficiency or the operating range of a compressor. A particular difficulty in understanding the effect of reaction is that the rotor and stator have a natural asymmetry caused by the centrifugal effects in the rotor boundary layer being much larger than that in the stator boundary layer. In this paper a novel approach has been taken: McKenzie's ‘linear repeating stage’ concept is used to remove the centrifugal effects. The centrifugal effects are then reintroduced as a body force. This allows the velocity triangle effect and centrifugal force effect to be decoupled. The paper shows the surprising result that, depending on how the solidity is set, a 50% reaction stage can either result in the maximum, or the minimum, profile loss. When the centrifugal effects are removed, 50% reaction is shown to minimise endwall loss, maximise stage efficiency and maximise operating range. When the centrifugal effects are reintroduced, the compressor with the maximum design efficiency is found to rise in reaction by 5% (from 50% reaction to 55% reaction) and the compressor with the maximum operating range is found to rise in reaction by 15% (from 50% reaction to 65% reaction).

Fan Aerodynamics With a Short Intake at High Angle of Attack

Future turbofan engines seek shorter intakes to reduce the cruise fuel burn of a low pressure ratio, large diameter fan. However, shorter intakes increase the level of flow distortion entering the rotor when the aircraft angle of attack (AOA) is high, reducing thrust when critically needed. This paper considers how the fan rotor radial pressure ratio distribution and tip velocity triangle can be designed to improve thrust at high AOA. Full annulus, unsteady CFD is performed on three rotor designs coupled to a short intake. We show that rotor design for high AOA should be guided by three flow mechanisms. Mechanism i) is caused by high Mach number flow over the bottom intake lip, which chokes the rotor leading to high loss. Mechanism ii) is the loss generation in the rotor tip as it passes through an intake separation. Mechanism iii) shows radial flows through the rotor change both the amount and the way work is imparted on the flow. Two comparable rotor design philosophies for high thrust are proposed; high work or low loss. Rotors designed to a mid-high radial pressure ratio distribution impart high work on streamlines that migrate radially towards the hub and exit the rotor at highly cambered sections. Meanwhile, tip-high designs reduce choking losses in the midspan when operating with a separated intake, particularly when the tip velocity triangle is designed to high axial velocity diffusion over high camber. However, such designs suffer with higher tip losses after exiting an intake separation.

The Effect of Reaction on Compressor Performance

Reaction is the fundamental parameter by which the asymmetry of the velocity triangle of a stage is set. Little is understood about the effect that reaction has on either the efficiency or the operating range of a compressor. A particular difficulty in understanding the effect of reaction is that the rotor and stator have a natural asymmetry caused by the centrifugal effects in the rotor boundary layer being much larger than that in the stator boundary layer. In this paper a novel approach has been taken: McKenzie’s ‘linear repeating stage’ concept is used to remove the centrifugal effects. The centrifugal effects are then reintroduced as a body force. This allows the velocity triangle effect and centrifugal force effect to be decoupled. The paper shows the surprising result that, depending on how the solidity is set, a 50% reaction stage can either result in the maximum, or the minimum, profile loss. When the centrifugal effects are removed, 50% reaction is shown to minimise endwall loss, maximise stage efficiency and maximise operating range. When the centrifugal effects are reintroduced, the compressor with the maximum design efficiency is found to rise in reaction by 5% (from 50% reaction to 55% reaction) and the compressor with the maximum operating range is found to rise in reaction by 15% (from 50% reaction to 65% reaction).

Computational tool for teaching learning velocity triangle of hydraulic turbines

This paper presents an investigation about utilizing computational tools applied to specific issues of the Turbo machinery. This subject is concentrated by third-year understudies in B.S. Mechanical Engineering Program. These understudies have previously learned the Fluid mechanics, which is required in structuring distinctive machine components. While teaching Turbo machinery, understudies frequently become overpowered by an incredible number of hypothetical ideas, loads of recipes, and references from information handbooks. In some cases it is helpful to utilize an intuitive learning condition, for example, a computing environment. In this way, activities utilizing computers are required to upgrade dynamic learning. This paper will give another method of showing the turbo machinery through Excel/VBA. A capable computer program which can change the method of your comprehension of the subject and assignments which won't be restricted to the classroom. This tool can be introduced among the students as well as among teachers. Providing students with this tool help them in getting rid of large calculations and it will also help them to see different variations in values which will help them to understand the concepts as well as it is a good way to improve the motivation of students towards the subject. It will also help teachers to teach different types of concepts not only just few concept as it takes time due to its lengthiness. Students can also use it as a tool in designing parts of the project. Besides solving the equations this tool can also provide how each parameter affects different forces. Therefore students can perform as many calculations just with a single click and without any mistake or being bored.

The compound bowing design in a highly loaded linear cascade with large turning angle

Numerical simulation was carried out to study the influences of blade-bowing designs based on a highly loaded cascade with large turning angle, while the compound bowing design showed much lower endwall loss than the conventional design in this study. Generally, it showed that the increased turning angle would strengthen the adverse pressure gradient on the suction surface, so the side effect of negative blade bowing angle would be enhanced because of the reduced flow filed stability near suction–endwall corner. However, the positive corner bowing angle that applied in the compound bowing design would enhance the flow field stability near the suction–endwall corner by adjusting spanwise pressure gradient and velocity triangle, so the side effect of negative blade bowing angle would be suppressed and lead to weaker secondary flow. In detail, the blade bowing angle (as well as the corner bowing angle in the conventional bowed cascades) was varied from −5° to −30° in this study, while the reductions of the loss coefficient in the compound bowed cascades were about 0.662.16 times higher (the absolute differences were about 0.0067 0.0097) than the corresponding conventional bowed cascades. Moreover, the Reynolds number and Mach number at the outlet plane were kept at 2.4 × 105 and 0.6, respectively, during the bowing design to ensure the comparability.

Design of Multi-Stage Axial Flow Compressor and Validation using Numerical Simulations

The optimum yield of gas turbine engines has so far been driven on and around the operational efficiency of the compressor and in essence around the efficiency of the compressor blade. The efficacy of a compressor is ascertained substantially by the smoothness of the air flowing through it. In this present work, a multi-stage axial compressor in the Turbojet engine with an application for propulsion is designed based on thermodynamic calculations. The calculations were carried out employing the principles of thermodynamics, and aerodynamics along the mean streamline based on the technique of a velocity triangle in the lack of inlet guide vanes. The coordinates for the blade profile has been calculated on and around the premise of the calibrated blade base profile. The model for the seven-stage axial flow compressors based on thermodynamic calculations was devised and analyzed utilizing computational fluid dynamics methodology. The multiple reference frame approach was used to represent the impact of both rotating and stationary components and the simulation for the first stage was conducted using a periodic approach. For the intent of the verification, a comparison was made between the analytical values and the simulated values and the variation between these values was found to be 16.7%. Validation results demonstrate that the proposed method is valid and can be used for multi-stage axial compressor design and performance evaluation.

Investigation of the effect of gaps between the blades of open flume Pico hydro turbine runners

This study will analyze the impact of gap size in two different runners called runner A (five blades) and B (six blades) to provides recommendations in design and manufacture of open flume turbine runners so that maximize the conversion of kinetic and potential energy. There are three methods was used to investigate its: analytical method is used to design the turbine; experimental to determine the actual turbine performance; computational fluid dynamics (CFD) to study the physical phenomena and re-check the velocity triangle on the runner to validate the design and manufacturing process. Using the results obtained, gaps between the blades can alter the velocity vector on the outlet and unbalance the rotation of runner; this imbalance could cause cavitation. Then, the decreasing torque is assumed because water pressure in the draft tube is similar to atmospheric pressure. Two conditions must be satisfied to maximize the performance of the turbine: swirling flow is required after the water flows past the runner in order to minimize the radial velocity on the outlet so that the draft tube can function properly; the dimensions of the blade must be carefully selected to avoid the formation of gaps between the blades.