Distribution Of Flow Parameters Research Articles

Inverse Method of Centrifugal Pump Blade Based on Gaussian Process Regression

The inverse problem is always one of the important issues in the field of fluid machinery for the complex relationship among the blade shape, the hydraulic performance, and the inner flow structure. Based on Bayesian theory of posterior probability obtained from known prior probability, the inverse methods for the centrifugal pump blade based on the single-output Gaussian process regression (SOGPR) and the multioutput Gaussian process regression (MOGPR) were proposed, respectively. The training sample set consists of the blade shape parameters and the distribution of flow parameters. The hyperparameters in the inverse problem models were trained by using the maximum likelihood estimation and the gradient descent algorithm. The blade shape corresponding to the objective blade load can be achieved by the trained inverse problem models. The MH48-12.5 low specific speed centrifugal pump was selected to verify the proposed inverse methods. The reliability and accuracy of both inverse problem models were confirmed and compared by implementing leave-one-out (LOO) cross-validation and extrapolation characteristic analysis. The results show that the blade shapes within the sample space can be reconstructed exactly by both models. The root mean square errors of the MOGPR inverse problem model for the pump blade are generally lower than those of the SOGPR inverse problem model in the LOO cross-validation. The extrapolation characteristic of the MOGPR inverse problem model is better than that of the SOGPR inverse problem model for the correlation between the blade shape parameters can be fully considered by the correlation matrix of the MOGPR model. The proposed inverse methods can efficiently solve the inverse problem of centrifugal pump blade with sufficient accuracy.

Effect of water vapor condensation on the flow distribution in a PEM fuel cell stack

In this study, the effect of water vapor condensation on the flow distribution in the manifold of a PEMFC stack is investigated. A solver is developed in OpenFOAM software and is validated against experimental and numerical data. Due to the condensation, the water vapor concentration in the mixture decreases near the manifold walls. Thus, beginning and last cells receive more oxygen than the middle cells. The condensed water forms small droplets on the manifold walls. The small droplets coalesce into larger droplets. Descending large droplets into the last cell of the 26-cell stack leads to the formation of the slug. This process results in blockage of flow through the last cell, causing a significant increase in the flow non-uniformity. The non-uniformity index increases significantly from 0.046 to 0.94 in the water removal process. When the number of cells increases from 26 to 39, the large droplet detaches from the manifold and sinks into seven middle cells. The flow passing through these cells significantly reduces, resulting in a severe flow maldistribution. A comparison between flow distribution parameters indicates that the root mean square value of the deviation from the mean flow rate is a better criterion than the non-uniformity index to determine the severity of maldistribution.

Numerical investigation on vibration-induced two-phase distribution in a vertical annular channel

Earthquake vibrations have great impacts on two-phase flow in the reactor core. In this paper, numerical simulations were conducted to identify the air-water two-phase distribution in a vertical upward annular channel under horizontal vibration condition. The inner and outer diameter of the annular channel are 19.1 mm and 38.1 mm. The simulations were performed based on the two-fluid Euler-Euler modeling framework. Benchmark simulations for bubbly flow under stationary condition were firstly conducted to validate the up-to-date interfacial force models. Applicability of the interfacial force models were evaluated and a set of Ishii-Zuber drag force model, Tomiyama lift force model, Frank wall lubrication force model and Burns turbulent dispersion force model was found to provide the best agreement with experimental results. Based on this work, two-phase flow distributions under vibration condition were studied. Horizontal vibration of the annular channel was simulated by introducing simple harmonic motion. The vibration frequency and vibration amplitude were set to 1.97 Hz and 9.5 mm, respectively. Additional interfacial force caused by inertial effect was imposed on disperse bubbles under vibration condition, which promoted the lateral migration of bubbles. The numerical results showed that the distributions of local interfacial parameters varied periodically along the vibration direction. A maximum increase of about 32% was observed in the peak void fraction compared to that under stationary condition for case 3. But the distribution of local flow parameters remained unchanged in the direction perpendicular to the vibration. A good consistency between the simulation results and the experimental data was found. The comparison results indicate that the present modeling method is able to predict the two-phase distribution of bubbly flow under vibration condition. But an inhomogeneous model considering bubble interactions and grouping is suggested for two-phase flow beyond bubbly regime.

Numerical investigation of the wet steam condensation flow characteristics in stator cascade with blade surface heating

The scientific and effective control of steam wetness in steam turbines is of great significance for improving power generation efficiency. Based on the research status of wet steam, the influence of different surface heating intensity in a stator cascade was studied. The distribution of condensation flow parameters in White cascade under 0–700 kW/m2 surface heating intensity is calculated. On this basis, the positive heating intensity region was determined and refined to obtain the best heating condition with higher accuracy. The results show that the condensation is restrained and the outlet wetness is decreased as the blade surface heating intensity increases. The steam wetness and droplet diameter in the flow field can be controlled by adding heating intensity. Additionally, at the initial stage of applying heat to the blade, an increasing enthalpy drop occurs, and the entropy increase experiences a decline, while negative effects rapidly emerge if the heating intensity is too high. The optimum heating intensity is 120 kW/m2. Compared with the 0 kW/m2, the average outlet wetness, total pressure loss coefficient and entropy increase of 120 kW/m2 surface heating intensity can be reduced by 1.1266%, 15.5% and 1.7%, respectively, and the enthalpy drop can be increased by 1.7%.

Proračun sile trenja i toplotnog uticaja mlaza mlaznog motora na unutrašnju površinu lansirne cevi

Introduction/purpose: To study the dynamics of launchers with sources of high-energy gas jets, it is relevant to calculate shear forces from the action of a high-temperature supersonic jet on the inner surface of a cylindrical channel and the temperature of the channel walls. The aim of this work is to develop a comprehensive method for calculating aerodynamic friction and heating on the inner surface of a tubular guide of a rocket. Methods/results: The research method is based on the theory of supersonic gas flows in cylindrical channels and the theory of the boundary layer. The gas jet is considered continuous, stationary and axisymmetric. The system of differential equations of motion of the projectile in the guide integrates numerically over time. The flow parameters in the pipe sections are found according to the dependences of the theory of supersonic gas flows, taking into account friction losses. To calculate shear stress on the guide wall, we use the relations of the asymptotic theory of the turbulent boundary layer, the theory of turbulent spots of Emmons of the transition boundary layer, and data on the Reynolds numbers of the beginning of the laminar-turbulent transition in wind tunnels. At the same time, the differential equation for heating the thin wall of the guide in the range of contact between the surface of the guide and the jet is numerically integrated. The calculations of the distribution of flow parameters, friction force and the temperature of the wall of the tubular guide during the movement of the projectile inside the jet from the moment the engine is started to the moment the shell exits completely from the guide are performed and graphically presented. Conclusions: This method of calculating aerodynamic friction and heating on the inner surface of a tubular guide of a rocket due to a high temperature supersonic gas jet - taking into account the effects of nonisothermality, compressibility and laminar-turbulent transition in the boundary layer - can be used to study the dynamics of the launch of rockets from launchers equipped with tubular guides.

Analysis of Peak Flow Distribution for Bridge Collapse Sites

Bridge collapse risk can be evaluated more rigorously if the hydrologic characteristics of bridge collapse sites are demystified, particularly for peak flows. In this study, forty-two bridge collapse sites were analyzed to find any trend in the peak flows. Flood frequency and other statistical analyses were used to derive peak flow distribution parameters, identify trends linked to flood magnitude and flood behavior (how extreme), quantify the return periods of peak flows, and compare different approaches of flood frequency in deriving the return periods. The results indicate that most of the bridge collapse sites exhibit heavy tail distribution and flood magnitudes that are well consistent when regressed over the drainage area. A comparison of different flood frequency analyses reveals that there is no single approach that is best generally for the dataset studied. These results indicate a commonality in flood behavior (outliers are expected, not random; heavy-tail property) for the collapse dataset studied and provides some basis for extending the findings obtained for the 42 collapsed bridges to other sites to assess the risk of future collapses.

Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study

An ejector containing phase changing gas-liquid flow process acts as a popular and decisive device in multiple industrial applications, including the hydrogen production, electricity production, fuel cells, refrigeration, petroleum industry and desalination systems. However, non-condensable gas is inevitable for the usual operation of phase-changing gas-liquid ejector in the trigeneration or electrolyzer system for hydrogen production, and rarely research is concerned with this issue. In the present study, the effect of non-condensable gas contained in the condensable gas on the characteristics of gas-centered water ejector is presented, with steam, water and air acting as the gas, liquid and non-condensable gas, respectively. Experimentally, the flow rate of steam is controlled to be 1.45 g/s with an absolute pressure of 120 kPa, the air flow rate varies from 0 to 0.14 g/s, resulting in a non-condensable gas concentration ranging from 0 to 9%, and the resulted water flow rate at 100 kPa and 282.15 K changes from 34.7 to 37.3 g/s. Combined with the numerical methods, the performance of ejector expressed in ejected water flow rate was found to increase firstly with a small amount of non-condensable gas, and decrease when the non-condensable gas reaches a certain amount. In addition, the distributions of multiple local flow parameters including pressure, condensation rate and gas volume fraction, velocity and temperature inside the ejector were shown for different non-condensable concentration, by which the mechanism for the change of ejector performance under varying non-condensable concentration was demonstrated. These findings are initiative and insightful for the ejector design optimization in the trigeneration system for hydrogen production and the proposed numerical models can be utilized in analysis and design of steam ejector with non-condensable gas involved.

Effective Asymptotic Model of Two-Phase Flow through Fractured-Porous Media

The solution of the Buckley-Leverett problem classical for the theory of flow through a porous medium, generalized to the case of two-phase flows in fractured-porous media, is considered. In this case, immiscible displacement of fluid in the porous medium is complicated by the absence of local capillary equilibrium between pore spaces of different scales and in the generic case the solution of problem is not self-similar. The flow through a porous medium is considered in the limiting case of large time scales when capillary equilibrium is established and the flow parameter distributions, as shown in the study, tend to self-similar asymptotics. For the effective ordinary porous medium the average equations of equilibrium flow through the porous medium which describe these asymptotics are obtained

Influence of flow conditions over the forebody of a hypersonic air inlet on the flow of air in a boundary-layer bleed channel

In the present paper, we report on the results of a study that was performed as part of the program for developing a method for calculating the flow and the mass-flow-rate coefficient in narrow cylindrical bleed channels under conditions of impingement of a thick boundary layer. For setting the boundary conditions at the inlet boundary of the computational domain, we used the pressure and temperature profiles obtained at the outlet boundary of the simulation domain for the flow around the forebody of a hypersonic air inlet. Numerical modeling of the 3D flow around that forebody was carried out in the range of Mach numbers from 3 to 6 at an angle of attack of 6°. The distributions of static pressure calculated along the symmetry plane and in the transverse direction were compared with experimental data. A satisfactory agreement between the calculated and experimental data is shown. The simulation of the flow was carried out within the framework of the Reynolds-averaged stationary Navier-Stokes equations using the k-ω SST model of turbulence. The obtained distributions of flow parameters and flow streamlines have allowed us to perform an analysis of specific features of the flow structure on the forebody of the model air inlet and in a boundary-layer bleed channel. The calculations showed that, in the examined range of Mach numbers, a sonic flow in boundary-layer bleed channels could be realized to ensure a maximum rate of the mass flow of air through the channels.

Efficiency of Mixture Separation in Distillation Columns with Structured Packings under Different Ways of Dynamically Controlled Irrigation

The paper presents results of an experimental study of separation efficiency and distribution of flow parameters over the cross section of the distillation columns. The experiments were carried out on the large-scale research setup “Large Freon Column” with diameter of packing of 0.6 m and 0.9 m. The mixture of refrigerants R114 and R21 was used as the working liquid at a pressure of 3 bar in the column. Experimental data were obtained at uniform and nonuniform irrigation of the Mellapak 350.Y and Sulzer 500X structured packings by a controlled liquid distributor. The liquid distributor with independently controlled valves for each drip point was used for controlled packing irrigation. The newmethod for dynamically controlled irrigation of the packing by an operated liquid distributor is suggested. This method is aimed at the destruction of large-scale maldistribution areas (flows) inside the column and the achievement of higher separation efficiency through periodic irrigation of the entire packing or its individual areas under the liquid distributor. The use of dynamically controlled irrigation of the packing allows an increase in efficiency of mixture separation of up to 20%.

Flow in a Narrow Channel with Chemical Reactions on the Wall

The solution of the problem of gas flow in a narrow plane or cylindrical channel with the internal rod on the axis and chemical reactions on the walls is obtained. The problem reduces to solution of an ordinary differential equation for the transverse flow parameter distribution. In a certain degree, this example simulates flows in chemical reactors used sometimes for investigation of heterogeneous chemical reactions.

Performance variation study on bulb turbines with different water head under considering free surface and water gravity

The maximum and minimum water head difference of bulb turbine is only a few meters to ten meters, and the performance is highly sensitive to the change of water head, especially in low head operation, the bulb turbine performance deteriorates and vibration intensifies, this seriously affect the normal operation of the power station. Therefore, considering the free surface and water gravity, a numerical method is adopted to study the performance of prototype bulb turbines at different water head, by analysing the distribution of flow parameters with water head in hydraulic turbine, it is revealed that the stress of blade is uneven and the cause of cavitation and vibration at low head operation. The results show that: with the decrease of water head, the cavitation performance of the runner becomes worse, the low pressure area moves from the suction side to the pressure side of blade; the water torque of the guide vanes and the runner blades in different positions is different, which could cause the guide vane and blade angle asynchronism during adjustment; with the decrease of water head, the torque difference generated by the blades at different positions on the rotating shaft of the hydraulic turbine increase, the blades experience dynamic stresses, It threatens the strength of the blade and the stable operation of the unit.

Effect of rough inner wall of nanochannel on fluid flow behavior

Flow system on a nano scale, as an effective and economic system, has been widely employed. While on a macroscopic scale, for the non-slip boundary, the velocity of the fluid at the surface is assumed to be consistent with the surface. This approximation may become invalid on a smaller length scale pertinent to the operation of microfluid devices. The interface slip effect has a significant influence on the flow because of its higher ratio of surface to volume. In this paper, the Poiseuille flow, which is composed of two infinite parallel asymmetric walls, is studied by the molecular dynamics method. The influence of wall roughness and surface wettability of channel on fluid flow in the channel are analyzed. The results show that the asymmetric upper and lower wall can lead to an asymmetric distribution of flow parameters. The change of wall roughness and wettability would affect the flow characteristics of fluid atoms near the wall. Due to the influence of wall grooves, the number density distribution near the rough wall is lower than that on the smooth wall side. As the rib height and wall wettability increase, the number density of fluid atoms in the groove increases gradually, and the change of the rib spacing does not substantially affect the number density distribution of fluid atoms near the rough wall. For different structure types of walls, the real solid-liquid boundary positions are determined by simulating the velocity field distribution in the channel under both Couette flow and Poiseuille flow, which can help us to better analyze the interface slip effect. The variation of wall roughness and wettability can affect the position of the solid-liquid interface. The change of rib height and wettability can greatly influence the velocity distribution in channel, and the position of the solid-liquid boundary as well. Conversely, the rib spacing has a less effect on the boundary position. The difference in boundary position can affect the interface slip effect. We can find the slip velocity and the slip length on one side of the rough wall to be smaller than those on the smooth wall side, and as the rib height and wall wettability increase, the slip velocity and the slip length significantly decrease near the rough wall side. The effect of rib spacing on fluid flow is trivial, and the interface slip velocity and length are relatively stable.

An Automated Flow Traversing Measurement System in the Last Stages of Large-Capacity Steam Turbines

The article presents the results from putting a new automated flow traversing measurement system (AFTMS) in an experimental turbine intended for testing steam paths of the low-pressure cylinders (LPC) of large-capacity steam turbines into use. Modern computerized facilities have been used in developing the system. Such an approach has been implemented for the first time in the full-scale test bench available at PJSC Power Machines in carrying out experimental investigations of an LPC double stage compartment (on a 1 : 1 scale) equipped with a new, ultimately long last stage blade (LSB) developed for a steam turbine plant for ultrasupercritical steam conditions. The investigations were aimed at confirming the effectiveness of the developed system in measuring the flow parameters in the last LPC stage. The necessity of making a shift from nonautomated and semiautomatic systems to the use of automated measurement systems is substantiated. The article describes a system that makes it possible, with automated setting of the gas dynamic probe head position on the traversing line, to determine the steam flow direction; to measure the stagnation pressure, static pressure, and stagnation temperature; and to record the measures indicators with exactly assigned time tags. The results from measurements of flow parameters upstream of the last LPC stage in a partial load mode are given. A comparison between the experimental and calculated flow parameter distribution data over the stage radius in the control section is shown.

Soft abrasive flow polishing based on the cavitation effect

The fluid medium used for soft abrasive flow (SAF) is of low viscosity and high flow velocity. The conventional SAF processing method is widely used due its ability to avoid damage and its adaptability of the workpiece surface. However, the current SAF method also suffers from limitations such as long polishing times and low processing efficiency. To address these issues, this paper proposes a method based on the cavitation effect to assist the soft abrasive flow polishing, termed CSAF. First, the working mechanism of CSAF is introduced through a schematic diagram. In addition, a CSAF fluid mechanic model is configured on the basis of the mixture multiphase model and cavitation model. Then, the distribution of key flow parameters, such as the velocity, dynamic pressure, and turbulent kinetic energy, is obtained and compared through computational fluid dynamic software. Numerical analysis results show that the flow field assisted by the cavitation effects shows better processing performance than SAF. Finally, particle imaging velocity (PIV) observation and experimental processing platforms are established, and extensive experiments are conducted. The processing comparison experiments showed that the abrasive flow assisted by the cavitation effect can lower the workpiece surface roughness to 3.46 nm with a satisfactory surface quality over a shorter time than the SAF method. The numerical analysis results are aligned with the PIV observation and the polishing experiment results. The SAF polishing method based on the cavitation effect significantly increases the polishing efficiency.

Dynamics of a change in the local density of liquid flow rate and efficiency of mixture separation at periodic irrigation of the structured packing

The use of modern structured packing in the distillation columns allows much more even distribution of the liquid film over the packing surface, but it does not completely solve the problem of uniform distribution of flow parameters over the entire height of the packing. Negative stratification of vapor along the packing height caused by different densities of vapor mixture components and higher temperature in the lower part of the column leads to formation of large-scale maldistributions of temperature and mixture composition over the column cross-section even under the conditions of uniform irrigation of packing with liquid. This work presents the experimental results obtained at periodic packing irrigation with total blocking of the spray nozzle. The experiments were carried out in the distillation column with the diameter of 0.6 m on 10 layers of the Sulzer 500X packing with the total height of 2.2 m. The mixture of R-21 and R-114 was used as the working liquid. To irrigate the packing, the liquid distributor with 123 independently controlled solenoid valves overlapping the holes with the diameter of 3.6 mm, specially designed by the authors, was used. Response of the column to the action of liquid distributor was observed in real time according to indications of 3 groups of thermometers mounted in 3 different cross-sections of the column. The flow meter located at a fixed point of the column cross-section allowed registration of dynamics of a change in the local flow rate density of liquid flowing from the packing.

Efficiency of Mixture Separation in Distillation Columns with Structured Packings under Conditions of Dynamically Controlled Irrigation

The paper presents the results of an experimental study of separation efficiency and distribution of flow parameters over the cross-section of the distillation columns. The experiments were carried out on the large-scale research setup “Large Freon Column” with the diameter of 0.6 and 0.9 m. Experimental data were obtained at uniform and non-uniform irrigation of the Mellapak 350.Y and Sulzer 500X structured packings by the controlled liquid distributor. The mixture of refrigerants R114 and R21 was used as the working liquid at the pressure of 3 bar in the column. The liquid distributor with independently controlled valves for each drip point was used for controlled packing irrigation. Local temperature distributions of the liquid phase and counter-current vapor flow in the cross-section and over the packing height were recorded using a sequence of fast-response temperature sensors. Periodic irrigation of the structured packing can affect large-scale non-uniformity of mixture composition and flow parameter distribution over the cross-section and height of the transfer unit. Significantly non-uniform packing irrigation within a separate semiperiod leads to rearrangement of the structure of large-scale non-uniformity inside the packing.The new method for dynamically controlled irrigation of the packing is suggested. This method is aimed at destruction of stationary large-scale maldistribution over the column cross-section and achievement of higher separation efficiency of a completely wetted packing.

Hemodynamic Factors Affecting Carotid Sinus Atherosclerotic Stenosis

Carotid atherosclerotic plaque occurs predominantly at the outer wall of the carotid sinus, and computational fluid dynamics (CFD) plays an important role in explaining plaque formation. The present study investigated the hemodynamic factors affecting carotid atherosclerotic stenosis. Sixteen patients with normal carotid arteries and 16 with symptomatic stenotic carotid sinus underwent 3-dimensional angiographic imaging evaluations and were studied with CFD to simulate the complete 3-dimensional blood flow and hemodynamic parameter distribution in the carotid bifurcations. The hemodynamic parameters, including wall shear stress (WSS), dynamic and total pressure, total pressure gradient, strain rate, velocity, and velocity angle, were investigated. The atherosclerosis-prone outer lateral walls of the carotid sinus and the external carotid artery at its start had significantly (P < 0.05) low dynamic pressure, WSS, strain rate, and total pressure gradient but high static pressure. The blood flow near these walls with flow separation had significantly (P < 0.05) decreased velocity and dynamic pressures but a high velocity angle. The carotid divider had significantly (P < 0.05) elevated dynamic and total pressure, WSS, strain rate, and total pressure gradient but reduced static pressure. Additional stenosis occurred at the downstream area of stenosis with significantly (P<0.05) decreased dynamic pressure, WSS, strain rate, and total pressure gradient similar to the wall at the sinus and the start of the external carotid artery. Significantly decreased vascular WSS, dynamic pressure, strain rate, and total pressure gradient are key to atherosclerotic plaque formation at the carotid sinus.

Adaptive water infrastructure planning for nonstationary hydrology

Abstract The uncertainty of a changing climate raises challenges for water infrastructure planning and design. Not accounting for nonstationarity may result in under-designed structures that fail too frequently, or over-designed structures that are economically inefficient. This concern is magnified by uncertainty in the long-term frequency and magnitude of future extreme events. Planning strategies that allow adaptations over a structure's life could improve both reliability and economic efficiency. This study develops a method to inform adaptive water infrastructure planning with uncertain hydrologic and other forms of nonstationarity, applied to levee system planning. A stochastic dynamic programming model including a Markov process is developed for infrastructure planning with uncertain nonstationarity in flood frequency. Bayes' theorem is used to update peak flow probabilities conditioned on observed past peak flows and to update expected residual flood damages over time. A levee system planning problem with a numerical example from California illustrates the approach to derive optimal levee heights over time, and economic values of adapting to uncertain nonstationary flood risk. The projected range of probabilistic hydrology scenarios affects the optimal results, particularly in later planning stages as hydrology scenarios diverge with time. Adaptive planning strategies allowing more levee upgrades over time slightly lowers the overall cost and provides better flood protection than one-time construction under nonstationary hydrology for any climate in the example. Compared to a known future nonstationary hydrology, incorporating uncertain nonstationary climate results in higher levees being planned for observed severe hydrology scenarios in later stages. The overall present value cost with uncertain nonstationary climate depends on rates of change in peak flow distribution parameters in future hydrology scenarios.

Computational Study on the Effect of Shroud Shape on the Efficiency of the Gas Turbine Stage

The last stages of powerful power gas turbines play an important role in the development of power and efficiency of the whole unit as well as in the distribution of the flow parameters behind the last stage, which determines the efficient operation of the exhaust diffusers. Therefore, much attention is paid to improving the efficiency of the last stages of gas turbines as well as the distribution of flow parameters. Since the long blades of the last stages of multistage high-power gas turbines could fall into the resonance frequency range in the course of operation, which results in the destruction of the blades, damping wires or damping bolts are used for turning out of resonance frequencies. However, these damping elements cause additional energy losses leading to a reduction in the efficiency of the stage. To minimize these losses, dampening shrouds are used instead of wires and bolts at the periphery of the working blades. However, because of the strength problems, designers have to use, instead of the most efficient full shrouds, partial shrouds that do not provide for significantly reducing the losses in the tip clearance between the blade and the turbine housing. In this paper, a computational study is performed concerning an effect that the design of the shroud of the turbine-working blade exerted on the flow structure in the vicinity of the shroud and on the efficiency of the stage as a whole. The analysis of the flow structure has shown that a significant part of the losses under using the shrouds is associated with the formation of vortex zones in the cavities on the turbine housing before the shrouds, between the ribs of the shrouds, and in the cavities at the outlet behind the shrouds. All the investigated variants of a partial shrouding are inferior in efficiency to the stages with shrouds that completely cover the tip section of the working blade. The stage with a unshrouded working blade was most efficient at the values of the relative tip clearance less than 0.9%.