Int. J. Turbomach. Propuls. Power, Volume 4, Issue 3 (September 2019) – 17 articles

Axial turbines are the most common turbine configuration for electric power generation and propulsion systems due to their versatility in terms of power capacity and range of operating conditions. Mean-line models are essential for the preliminary design of axial turbines and, despite being covered to some extent in turbomachinery textbooks, only some scientific publications present a comprehensive formulation of the preliminary design problem. In this context, a mean-line model and optimization methodology for the preliminary design of axial turbines with any number of stages is proposed. The model is formulated to use arbitrary equations of state and empirical loss models and it accounts for the influence of the diffuser on turbine performance using a one-dimensional flow model. The mathematical problem was formulated as a constrained, optimization problem, and solved using gradient-based algorithms. In addition, the model was validated against two test cases from the literature and it was found that the deviation between experimental data and model prediction in terms of mass flow rate and power output was less than 1.2% for both cases and that the deviation of the total-to-static efficiency was within the uncertainty of the empirical loss models. Moreover, the optimization methodology was applied to a case study from the literature and a sensitivity analysis was performed to investigate the influence of several variables on turbine performance, concluding that: (1) the minimum hub-to-tip ratio constraint is always active at the outlet of the last rotor and that its value should be selected as a trade-off of aerodynamic performance and mechanical integrity; (2) that the total-to-static isentropic efficiency of turbines without diffuser deteriorates rapidly when the pressure ratio is increased; and (3) that there exist a loci of maximum efficiency in the specific speed and specific diameter plane (Baljé diagram) that can be predicted with a simple analytical expression. Full article

Annular diffusers are frequently used in turbomachinery applications to recover the discharge kinetic energy and increase the total-to-static isentropic efficiency. Despite its strong influence on turbomachinery performance, the diffuser is often neglected during the preliminary design. In this context, a one-dimensional flow model for annular diffusers that accounts for the impact of this component on turbomachinery performance was developed. The model allows use of arbitrary equations of state and to account for the effects of area change, heat transfer, and friction. The mathematical problem is formulated as an implicit system of ordinary differential equations that can be solved when the Mach number in the meridional direction is different than one. The model was verified against a reference case to assess that: (1) the stagnation enthalpy is conserved and (2) the entropy computation is consistent and it was found that the error of the numerical solution was always smaller than the prescribed integration tolerance. In addition, the model was validated against experimental data from the literature, finding that deviation between the predicted and measured pressure recovery coefficients was less than 2% when the best-fit skin friction coefficient is used. Finally, a sensitivity analysis was performed to investigate the influence of several input parameters on diffuser performance, concluding that: (1) the area ratio is not a suitable optimization variable because the pressure recovery coefficient increases asymptotically when this variable tends to infinity, (2) the diffuser should be designed with a positive mean wall cant angle to recover the tangential fraction of kinetic energy, (3) the mean wall cant angle is a critical design variable when the maximum axial length of the diffuser is constrained, and (4) the performance of the diffuser declines when the outlet hub-to-tip ratio of axial turbomachines is increased because the channel height is reduced. Full article

The paper presents the results of a computational study on the aerodynamics and the performance of a small-scale Vertical-Axis Wind Turbine (VAWT) for distributed micro-generation. The complexity of VAWT aerodynamics, which are inherently unsteady and three-dimensional, makes high-fidelity flow models extremely demanding in terms of computational cost, limiting the analysis to mainly 2D or 2.5D Computational Fluid-Dynamics (CFD) approaches. This paper discusses how a proper setting of the computational model opens the way for carrying out fully 3D unsteady CFD simulations of a VAWT. Key aspects of the flow model and of the numerical solution are discussed, in view of limiting the computational cost while maintaining the reliability of the predictions. A set of operating conditions is considered, in terms of tip-speed-ratio (TSR), covering both peak efficiency condition as well as off-design operation. The fidelity of the numerical predictions is assessed via a systematic comparison with the experimental benchmark data available for this turbine, consisting of both performance and wake measurements carried out in the large-scale wind tunnel of the Politecnico di Milano. The analysis of the flow field on the equatorial plane allows highlighting its time-dependent evolution, with the aim of identifying both the periodic flow structures and the onset of dynamic stall. The full three-dimensional character of the computations allows investigating the aerodynamics of the struts and the evolution of the trailing vorticity at the tip of the blades, eventually resulting in periodic large-scale vortices. Full article

New propulsive concepts, such as boundary layer ingestion, involve stronger interactions between the engine and its environment, and are thus more complex flows compared to classical architectures. Usual turbomachinery design tools are inadequate, and new numerical methodologies are needed to accurately predict the engine performance with affordable CPU resources. The present paper examines the relevance of a reduced-order modeling approach—the body force modeling (BFM) method—for a low-speed cooling fan with inflow distortion. The formulation itself accounts for the blade metal blockage and compressibility effects, and it relies on a semiempirical loss model, independent of computational fluid dynamics (CFD) calibration. The BFM results obtained in the present work are assessed against full-annulus unsteady Reynolds-averaged Navier-Stokes (URANS) results and experiments. The comparison shows that the BFM approach successfully quantifies the fan stage performance. Furthermore, the distortion transfer across the stage is examined and the flow patterns observed are found to be the same as in the URANS results and in the measurements. Hence, this methodology, coming at a low CPU cost, is well-adapted to the early design phase of an innovative propulsion system. Full article

This paper presents an innovative design for reducing the impact of secondary flows on the aerodynamics of low-pressure turbine (LPT) stages. Starting from a state-of-the-art LPT stage, a local reshaping of the stator blade was introduced in the end-wall region in order to oppose the flow turning deviation. This resulted in an optimal stator shape, able to provide a more uniform exit flow angle. The detailed comparison between the baseline stator and the redesigned one allowed for pointing out that the rotor row performance increased thanks to the more uniform inlet flow, while the stator losses were not significantly affected. Moreover, it was possible to derive some design rules and to devise a general blade shape, named ‘snaked’, able to ensure such results. This generalization translated in an effective parametric description of the ‘snaked’ shape, in which few parameters are sufficient to describe the optimal shape modification starting from a conventional design. The “snaked” blade concept and its design have been patented by Avio Aero. The stator redesign was then applied to a whole LPT module in order to evaluate the potential benefit of the ‘snaked’ design on the overall turbine performance. Finally, the design was validated by means of an experimental campaign concerning the stator blade. The spanwise distributions of the flow angle and pressure loss coefficient at the stator exit proved the effectiveness of the redesign in providing a more uniform flow to the successive row, while preserving the original stator losses. Full article

This paper provides an investigation of a casing treatment (CT) approach for pressure ratio improvements of centrifugal compressors between peak efficiency and surge. Results were experimentally verified for a variety of automotive turbocharger compressors and analyzed with 3D CFD. The CT design is an adaptation from an axial high-pressure compressor, which was successfully applied and intensively investigated in recent years. The aerodynamic working principle of the applied CT design and the achievable improvements are shown and described. The demand of operating range for automotive applications typically dictates high inlet shroud to outlet radius ratio (high trim) and past experiences indicate that a recirculation zone is formed in the inducer for those centrifugal compressors. This recirculation at the inlet shroud causes losses, a massive blockage and induces a co-rotating swirl at the inlet of the impeller. The result is a reduced pressure ratio, often leading to flat speed lines between the onset of recirculation and surge. This paper provides an understanding of inducer recirculation, its impacts and suggests countermeasures. The CT design for centrifugal compressors only influences flow locally at the inducer and prevents recirculation. It differs substantially in design and functionality from the classical bleed slot system commonly used to increase operating range. An experimental and CFD comparison between these designs is presented. While the classical bleed slot system often provides a massive increase in operating range, it often fails to increase the pressure ratio between onset of inducer recirculation and surge. In contrast, the CT design achieves a gain in pressure ratio near surge. Full article

This paper aims at evaluating the characteristics of the wakes periodically shed by the rotating bars of a spoked-wheel type wake generator installed upstream of a high-speed low Reynolds linear low-pressure turbine blade cascade. Due to the very high bar passing frequency obtained with the rotating wake generator (f_bar = 2.4−5.6 kHz), a fast-response pressure probe equipped with a single 350 mbar absolute Kulite sensor has been used. In order to measure the inlet flow angle fluctuations, an angular aerodynamic calibration of the probe allowed the use of the virtual three-hole mode; additionally, yielding yaw corrected periodic total pressure, static pressure and Mach number fluctuations. The results are presented for four bar passing frequencies (f_bar = 2.4/3.2/4.6/5.6 kHz), each tested at three isentropic inlet Mach numbers M_1,is = 0.26/0.34/0.41 and for Reynolds numbers varying between Re_1,is = 40,000 and 58,000, thus covering a wide range of engine representative flow coefficients (ϕ = 0.44−1.60). The measured wake characteristics show fairly good agreement with the theory of fixed cylinders in a cross-flow and the evaluated total pressure losses and flow angle variations generated by the rotating bars show fairly good agreement with theoretical results obtained from a control volume analysis. Full article

This paper studies the computational modelling of the flow separation over the engine nacelle lips under the off-design condition of significant crosswind. A numerical framework is set up to reproduce the general flow characteristics under crosswinds with increasing engine mass flow rate, which include: low-speed separation, attached flow and high speed shock-induced separation. A quasi-3D (Q3D) duct extraction method from the full 3D (F3D) simulations has been developed. Results obtained from the Q3D simulations are shown to largely reproduce the trends observed (isentropic Mach number variations and high-speed separation behaviour) in the 3D intake, substantially reducing the simulation time by a factor of 50. The agreement between the F3D and Q3D simulations is encouraging when the flow either fully attached or with modest levels of separation but degrades when the flow fully detaches. Results are shown to deviate beyond this limit since the captured streamtube shape (and hence the corresponding Q3D duct shape) changes with the mass flow rate. Interestingly, the drooped intake investigated in the current study is prone to earlier separation under crosswinds when compared to an axisymmetric intake. Implications of these results on the industrial nacelle lip design are also discussed. Full article

Due to manufacturing tolerance and deterioration during operation, fan blades in the same engine exhibit geometric variability. The absence of symmetry will inevitably exacerbate and contribute to the complexities of running geometry prediction as the blade variability is bound to be amplified by aerodynamic and centrifugal loading. In this study, we aim to address the fan blade untwist related phenomenon known as alternate passage divergence (APD). As the name suggests, APD manifests as alternating passage geometry (and hence alternating tip stagger pattern) when the fan stage is operating close to/at peak efficiency condition. APD can introduce adverse influence on fan performance, aeroacoustics behaviour, and high cycle fatigue characteristics of the blade. The main objective of the study is to identify the parameters contributing to the APD phenomenon. In this study, the APD behaviours of two transonic fan blade designs are compared. Full article

Rotor tip film cooling is investigated at the Large Scale Turbine Rig, which is a 1.5-stage axial turbine rig operating at low speeds. Using pressure sensitive paint, the film cooling effectiveness $\eta$ at a squealer-type blade tip with cylindrical pressure-side film cooling holes is obtained. The effect of turbine inlet swirl on $\eta$ is examined in comparison to an axial inflow baseline case. Coolant-to-mainstream injection ratios are varied between 0.45% and 1.74% for an engine-realistic coolant-to-mainstream density ratio of 1.5. It is shown that inlet swirl causes a reduction in $\eta$ for low injection ratios by up to 26%, with the trailing edge being especially susceptible to swirl. For injection ratios greater than 0.93%, however, $\eta$ is increased by up to 11% for swirling inflow, while for axial inflow a further increase in coolant injection does not transfer into a gain in $\eta$ . Full article

A four stage helicoaxial pump was tested under varying operating conditions. A range of inlet pressures, rotational speeds (3000, 3600 rpm), and gas void fractures (GVFs) were considered for two fluid viscosities. The head developed and power input to run the pump were recorded. Head, power input and efficiency decrease as the GVF increases with best efficiency point (BEP) moving towards lower flow rate conditions. Dimensional analysis was conducted to evaluate the applicability of current affinity laws to the two-phase flow performance of the pump under consideration. Dimensionless head coefficient and power coefficients were defined for two-phase flow, considering the homogeneity in the two-phase fluid properties. Deviations in the two-phase affinity coefficients from the common law curve increases with GVF. To bridge this gap, a new correlation is proposed with a revised flow coefficient that allows all the head coefficient data to collapse on a single line with a greater degree of accuracy. Full article

Depending on a dynamical energy market dominated by the influence of volatile energies, the operators of hydro-power plants are forced to extend the operating range of their hydraulic machines to stay competitive. High flexibility towards low-load, a rising number of start-ups and fast response times are required for better control of the electrical grid. The major downside of these operating regions is that pressure pulsations, which are induced by the means of flow phenomena, lead to higher fatigue damage regarding the runner. Therefore, site measurements in combination with numerical methods can be used to gain a deeper understanding of the runner lifetime. This paper presents a numerical approach to understand the critical operation zones and access fatigue damage, including steady state, unsteady and transient computational fluid dynamic (CFD) one-way coupled with a transient finite element method (FEM). Full article

This paper aims to give an understanding of an effect which stabilizes the inlet conditions of compressors for supercritical CO₂ (sCO2) operating close to the critical point. The effect was observed during testing of the turbomachine within the sCO2-HeRo project, and is caused by the sCO2 real gas properties close to the pseudocritical line. Under theoretical consideration, strong gradients in the fluid properties around this line—dependent on the static temperature and pressure of sCO2—can result in strong variation of compressor performance and finally lead to unstable cycle behavior. However, this paper demonstrates reduced gradients in density at the compressor inlet when varying the cooling power and taking advantage of a stabilizing effect. The applicable range and the significance of this stabilizing effect depended on the cooler inlet temperature and pressure, and was used to evaluate the relevance for individual cycles. Controlling the cooling power and the measurement of the inlet density allowed control of the compressor inlet conditions equally well, independent of the operating point, even close to the critical point. Full article

Regenerative pumps are characterized by a low specific speed that place them between rotary positive displacement pumps and purely radial centrifugal pumps. They are interesting for many industrial applications since, for a given flow rate and a specified head, they allow for a reduced size and can operate at a lower rotational speed with respect to purely radial pumps. The complexity of the flow within regenerative machines makes the theoretical performance estimation a challenging task. The prediction of the leakage flow rate between the rotating and the static disks has the greatest impact on the prediction of global performance. All the classical approaches to the disk clearance problem assume that there is no relevant circumferential pressure gradient. In the present case, the flow develops along the tangential direction and the pressure gradient is intrinsically non-zero. The aim of the present work is to develop a reliable approach for the prediction of leakage flows in regenerative pumps. A preliminary numerical simulation on a virtual model of a regenerative pump where the disk clearance is part of the control volume has been performed for three different clearance aspect ratios. The outcome of that campaign allowed the authors to determine the behavior of the flow in the cavity and choose correctly the baseline hypotheses for a mathematical-physical method for the prediction of leakage flows. The method assumes that the flow inside of the disk clearance is two-dimensional and can be decomposed into several stream-tubes. Energy balance is performed for each tube, thus generating a system that can be solved numerically. The new methodology was tuned using data obtained from the numerical simulation. After that, the methodology was integrated into an existing one-dimensional code called DART (developed at the University of Florence in cooperation with Pierburg Pump Technology Italy S.p.A.) and the new algorithm was verified using available numerical and experimental data. It is here demonstrated that an appropriate calibration of the leakage flow model allows for an improved reliability of the one-dimensional code. Full article

This paper presents the results of integral heat transfer measurements taken in a square ribbed cooling channel configuration for evaluating heat transfer and turbulent flow characteristics in convective cooled gas turbine blades and draws a comparison with numerical results. The heated section of the channel is either smooth or equipped with 45 ${}^{\circ }$ crossed ribs on two opposite walls. The first part of the paper describes the instrumentation and experimental setup in detail. The second part compares the numerical calculations with the experimentally determined results. The turbulent heat transfer is calculated using two common algebraic models and three implemented explicit algebraic models, each time in combination with an explicit algebraic Reynolds stress model. The numerical calculations show that the use of higher-order models for the turbulent heat flux provides a higher accuracy of the heat transfer prediction for both configurations. The best model is able to predict almost all results within the experimental uncertainties. Full article

The effect of rotational speed and pressure rise on the leakage flow noise radiated by a low-speed axial fan, provided with rotating shroud, has been systematically investigated. The flow in the gap region has been studied by means of particle image velocimetry (PIV) measurements taken in the meridional plane. At low blade loading, the leakage flow is restrained close to the rotor ring and, at higher loading, it forms a wide recirculation zone. In the latter conditions, an unsteady flow separation likely takes place in the blade tip region which may be observed in the instantaneous flow field only. The leakage flow noise generally increases with the blade loading, but is non-monotonic, as the overall sound pressure level (OASPL) growth is interrupted by local minima; such a trend is qualitatively independent of the rotational speed. As the loading increases, the sound pressure level (SPL) spectrum shows important modifications, since the characteristic frequency of the subharmonic narrowband humps related to the leakage noise decreases; furthermore, height and width of the humps vary non-monotonically. Such a complicated behavior is likely related to the modifications in the leakage flow pattern and also to the appearance of the flow separation at the blade tip. Full article

Subject of discussion are simulations and experimental investigations on the acoustic characterization of three single stage centrifugal pumps of different specific speed. In operation, these pump-types generate pressure pulsation at blade passing frequency, primarily due to rotor-volute-interaction. In order to determine the acoustic excitation it is necessary to know about the pumps’ acoustic transmission parameters. In this paper, a one-dimensional numerical model for transient time-domain simulation is presented, which takes into account the pump geometry as well as the volutes’ structural behaviour by means of the local effective speed of sound. Numerical results for the transmission characteristics of the three different pumps are shown in terms of scattering matrices and evaluated against parameters calculated from measurement results. The experimental analyses are carried out using dynamic pressure sensors in both the suction and the discharge pipe. Assuming solely plane wave propagation, the complex acoustic field on each side is evaluated independently. The so called “two source” method is then used to determine the transmission parameters of the pumps in standstill for a range of frequencies experimentally. Subsequently, the acoustic excitation at varying rotational speed is evaluated by means of measurements at the pumps in operation and presented as monopole and dipole source types for cavitation-free conditions. Full article