From the water wheel to turbines and hydroelectricity. Technological evolution and revolutions

Since its appearance in the first century BC, the water wheel has developed with increasing pre-industrial activities, and has been at the origin of the industrial revolution for metallurgy, textile mills, and paper mills. Since the nineteenth century, the water wheel has become highly efficient. The reaction turbine appeared by 1825, and continued to undergo technological development. The impulsion turbine appeared for high chutes, by 1880. Other turbines for low-head chutes were further designed. Turbine development was associated, after 1890, with the use of hydropower to generate electricity, both for industrial activities, and for the benefits of cities. A model “one city + one plant” was followed in the twentieth century by more complex and efficient schemes when electrical interconnection developed, together with pumped plants for energy storage.     

Three-dimensional analysis of the flow in a curved hydraulic turbine draft tube

The three-dimensional turbulent flow in a curved hydraulic turbine draft tube is studied numerically. The analysis is based on the steady Reynolds-averaged Navier–Stokes equations closed with the κ-ε model. The governing equations are discretized by a conservative finite volume formulation on a non-orthogonal body-fitted co-ordinate system. Two grid systems, one with 34 × 16 × 12 nodes and another with 50 × 30 × 22 nodes, have been used and the results from them are compared. In terms of computing effort, the number of iterations needed to yield the same degree of convergence is found to be proportional to the square root of the total number of nodes employed, which is consistent with an earlier study made for two-dimensional flows using the same algorithm. Calculations have been performed over a wide range of inlet swirl, using both the hybrid and second-order upwind schemes on coarse and fine grids. The addition of inlet swirl is found to eliminate the stalling characteristics in the downstream region and modify the behaviour of the flow markedly in the elbow region, thereby affecting the overall pressure recovery noticeably. The recovery factor increases up to a swirl ratio of about 0˙75, and then drops off. Although the general trends obtained with both finite difference operators are in agreement, the quantitative values as well as some of the fine flow structures can differ. Many of the detailed features observed on the fine grid system are smeared out on the coarse grid system, pointing out the necessity of both a good finite difference operator and a good grid distribution for an accurate result.     

Two-equation turbulence models for prediction of heat transfer on a transonic turbine blade

Two versions of the two-equation k–ω model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier–Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k–ω models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multi-block grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.     

Exact calculation of the flow of a staggered tandem cascade with moving second blade row

Summary  The plane flow around a tandem cascade of flat plates is calculated by means of conformal mapping. The blades of the two rows are perpendicular to each other. The first row is stationary, the second row moves with constant velocity. The conformal mapping will be constructed by a “mapping flow”. The blades of one row are stream lines and those of the other row are potential lines of the flow. By conformal mapping, the physical flow around the tandem cascade of the physical ζ-plane is converted into a flow between infinitely long straight walls in the z-plane, each wall corresponding to one of the blades. The conditions far upstream and far downstream of the cascade are represented by source-vortices. In the z-plane, the boundary conditions may be easily fulfilled by reflection and repetition of the source-vortices, and the flow may be calculated by well-known methods. The physical flow searched for is then obtained by inverse mapping. Received 24 July 2000; accepted for publication 6 December 2000     

Turbulent boundary layer separation control and loss evaluation of low profile vortex generators

The present paper analyses the results of a detailed experimental study on low profile vortex generators used to control the turbulent boundary layer separation on a large-scale flat plate with a prescribed adverse pressure gradient, typical of aggressive turbine intermediate ducts. This activity is part of a joint European research program on Aggressive Intermediate Duct Aerodynamics (AIDA). Laser Doppler Velocimetry and a Kiel total pressure probe have been employed to perform measurements in the test section symmetry plane and in cross-stream planes to investigate the turbulent boundary layer, with and without control device application.Velocity fields, Reynolds stresses, and total pressure distributions are analysed and compared for the controlled and non controlled flow conditions to characterize the mean flow behaviour. The detail and the accuracy of the measurements allow the evaluation of the deformation works of the mean motion in the test section symmetry plane. Normal and shear contributions of viscous and turbulent deformation works have been analysed and employed to explain the distribution of the total pressure loss. For the controlled flow the discussion of the flow field is extended considering the effects of the vortex generated in the cross-stream planes. The experimental data allow the evaluation of the global amount of losses, considering a balance of total pressure fluxes in the different measuring planes.     

Tip gap flow characteristics in a turbine cascade equipped with pressure-side partial squealer rims

Tip gap flow characteristics and aerodynamic loss generations in a turbine cascade equipped with pressure-side partial squealer rims have been investigated with the variation of its rim height-to-span ratio (h_p/s) for a tip gap height of h/s = 1.36%. The results show that the tip gap flow is characterized not only by the incoming leakage flow over the pressure-side squealer rim but also by the upstream flow intrusion behind the rim. The incoming leakage flow tends to decelerate through the divergent tip gap flow channel and can hardly reach the blade suction side upstream of the mid-chord, due to the interaction with the upstream flow intrusion as well as due to the flow deceleration. A tip gap flow model has been proposed for h_p/s = 3.75%, and the effect of h_p/s on the tip surface flow is discussed in detail. With increasing h_p/s, the total-pressure loss coefficient mass-averaged all over the present measurement plane decreases steeply, has a minimum value for h_p/s = 1.88%, and then increases gradually. Its maximum reduction with respect to the plane tip result is evaluated to be 11.6%, which is found not better than that in the cavity squealer tip case.     

An investigation of the heat transfer and static pressure on the over-tip casing wall of an axial turbine operating at engine representative flow conditions. (I). Time-mean results

The over-tip casing of the high-pressure turbine in a modern gas turbine engine is subjected to strong convective heat transfer that can lead to thermally induced failure (burnout) of this component. However, the complicated flow physics in this region is dominated by the close proximity of the moving turbine blades, which gives rise to significant temporal variations at the blade-passing frequency. The understanding of the physical processes that control the casing metal temperature is still limited and this fact has significant implications for the turbine design strategy. A series of experiments has been performed that seeks to address some of these important issues. This article reports the measurements of time-mean heat transfer and time-mean static pressure that have been made on the over-tip casing of a transonic axial-flow turbine operating at flow conditions that are representative of those found in modern gas turbine engines. Time-resolved measurements of these flow variables (that reveal the details of the blade-tip/casing interaction physics) are presented in a companion paper. The nozzle guide vane exit flow conditions in these experiments were a Mach number of 0.93 and a Reynolds number of 2.7 × 10⁶ based on nozzle guide vane mid-height axial chord. The axial and circumferential distributions of heat transfer rate, adiabatic wall temperature, Nusselt number and static pressure are presented. The data reveal large axial variations in the wall heat flux and adiabatic wall temperature that are shown to be primarily associated with the reduction in flow stagnation temperature through the blade row. The heat flux falls by a factor of 6 (from 120 to 20 kW/m²). In contrast, the Nusselt number falls by just 36% between the rotor inlet plane and 80% rotor axial chord; additionally, this drop is near to linear from 20% to 80% rotor axial chord. The circumferential variations in heat transfer rate are small, implying that the nozzle guide vanes do not produce a strong variation in casing boundary layer properties in the region measured. The casing static pressure measurements follow trends that can be expected from the blade loading distribution, with maximum values immediately upstream of the rotor inlet plane, and then a decreasing trend with axial position as the flow is turned and accelerated in the relative frame of reference. The time-mean static pressure measurements on the casing wall also reveal distinct circumferential variations that are small in comparison to the large pressure gradient in the axial direction.     

An investigation of the heat transfer and static pressure on the over-tip casing wall of an axial turbine operating at engine representative flow conditions. (II). Time-resolved results

This article reports the measurements of time-resolved heat transfer rate and time-resolved static pressure that have been made on the over-tip casing of a transonic axial-flow turbine operating at flow conditions that are representative of those found in modern gas turbine engines. This data is discussed and analysed in the context of explaining the physical mechanisms that influence the casing heat flux. The physical size of the measurement domain was one nozzle guide vane-pitch and from −20% to +80% rotor axial chord. Additionally, measurements of the time-resolved adiabatic wall temperature are presented. The time-mean data from the same set of experiments is presented and discussed in Part I of this article. The nozzle guide vane exit flow conditions in these experiments were a Mach number of 0.93 and a Reynolds number of 2.7 × 10⁶ based on nozzle guide vane mid-height axial chord. The data reveal large temporal variations in heat transfer characteristics to the casing wall that are associated with blade-tip passing events and in particular the blade over-tip leakage flow. The highest instantaneous heat flux to the casing wall occurs within the blade-tip gap, and this has been found to be caused by a combination of increasing flow temperature and heat transfer coefficient. The time-resolved static pressure measurements have enabled a detailed understanding of the tip-leakage aerodynamics to be established, and the physical mechanisms influencing the casing heat load have been determined. In particular, this has focused on the role of the unsteady blade lift distribution that is produced by upstream vane effects. This has been seen to modulate the tip-leakage flow and cause subsequent variations in casing heat flux. The novel experimental techniques employed in these experiments have allowed the measurement of the time-resolved adiabatic wall temperature on the casing wall. These data clearly show the falling flow temperatures as work is extracted from the gas by the turbine. Additionally, these temperature measurements have revealed that the absolute stagnation temperature within the tip-gap flow can be above the turbine inlet total temperature, and indicates the presence of a work process that leads to high adiabatic wall temperatures as a blade-tip passes a point on the casing wall. It is shown that this phenomena can be explained by consideration of the flow vectors within the tip-gap, and that these in turn are related to the local blade loading distribution. The paper also assesses the relative importance of different time-varying phenomena to the casing heat load distribution. This analysis has indicated that up to half of the casing heat load is associated with the over-tip leakage flow. Finally, the implications of the experimental findings are discussed in relation to future shroudless turbine design, and in particular the importance of accounting for the high heat fluxes found within the tip-gap.     

Pressure drop characteristics in a rotating smooth square channel with a sharp 180° bend

The results of an experimental study to investigate the local pressure drop characteristics in a square cross-sectioned smooth channel with a sharp 180° bend rotating about an axis normal to the free-stream direction are reported here. The sharp 180° turn was obtained by dividing a rectangular passage into two channels using a divider wall with a rounded tip at the location where the flow negotiates the turn. The study was carried out for three ratios of divider wall thickness to hydraulic diameter (W/D), namely, 0.24, 0.37 and 0.73 all with a rounded tip divider wall and only for a bend with a W/D ratio of 0.37, the influence of a sharp tip divider wall was studied. Experiments were conducted for a Reynolds number varying from 10 000 to 17 000 with the rotation number (ωD/V) varying from 0 to 0.38. The pressure drop distribution, normalized with the mainstream fluid dynamic pressure head, is presented for the leading, trailing and the outer surfaces. The results indicate that the local pressure drop characteristics in the bend region are significantly affected by a change in the rotation number but the influence of the Reynolds number is weak. The friction factor is less sensitive to rotation for the bend with a W/D ratio of 0.24 when compared to bends with W/D ratios of 0.37 and 0.73. Friction factor correlations are presented which fit the experimental data within 10% for the range of parameters studied.     

Performance-based design and analysis of flexible composite propulsors

Advanced composite propellers, turbines, and jet engines have become increasingly popular in part because of their ability to provide improved performance over traditional metallic rotors through exploitation of the intrinsic bend–twist coupling characteristics of anisotropic composite materials. While these performance improvements can be significant from a conceptual perspective, the load-dependent deformation responses of adaptive blades make the design of these structures highly non-trivial. Hence, it is necessary to understand and predict the dependence of the deformations on the geometry, material constitution, and fluid–structure interaction responses across the entire range of expected loading conditions.The objective of this work is to develop a probabilistic performance-based design and analysis methodology for flexible composite propulsors. To demonstrate the method, it is applied for the design and analysis of two (rigid) metallic and (flexible) composite propellers for a twin-shafted naval combatant craft. The probabilistic operational space is developed by considering the variation of vessel thrust requirements as a function of the vessel speed and wave conditions along with the probabilistic speed profiles. The performance of the metallic and composite propellers are compared and discussed. The implications of load-dependent deformations of the flexible composite propeller on the operating conditions and the resulting performance with respect to propeller efficiency, power demand, and fluid cavitation are presented for both spatially uniform and varying flows. While the proposed framework is demonstrated for marine propellers, the methodology can be generally applied for any marine, aerospace, or wind energy structure that must operate in a wide range of loading conditions over its expected life.