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While the consistent advance in computational power has enabled the Computational Fluid Dynamics (CFD) an effective tool for compressor performance characterization, the need for quick performance estimates at initial design phase of compressor still requires the use of low order models. Thus, the throughflow method remains the backbone of compressors design process. The accuracy of the throughflow calculation mainly depends on the adopted empirical correlations. However, the traditional empirical models are just accurate for the conventionally loaded compressor at normal working conditions. In this article, the mechanism of blade profile loss generation and the formation mode of existing empirical correlation are studied, and the reason why the traditional diffusion factor based empirical models are not applicable for modern high-loading compressors or conventional-loading blades at negative incidence is also discussed. Then, the Genetic Algorithm assisted Back Propagation Neural Network (GA-BPNN) is used to train the surrogate model for the design and off-design loss prediction along the blade span of the compressor. Based on the test data of four transonic compressor stages, a database containing 72 sets of blade element geometry and about 1400 sets of blade element performance data is established. Considering the different mechanisms of rotor and stator losses at different working conditions, the entire database and surrogate model are divided into four components according to the rotor and stator at positive incidence and negative incidence. Comparing the prediction results of the surrogate model with the traditional empirical correlations and experimental data, the results show that the GA-BPNN is an alternative solution for developing the empirical model.

In recent years, the computational fluid dynamics (CFD) techniques have attracted enormous interest in the throughflow calculations, and one of the major concerns in the CFD-based throughflow method is the modeling of blade forces. In this article, a viscous blade force model in the CFD-based throughflow program was proposed to account for the loss generation. The throughflow code is based on the axisymmetric Navier–Stokes equations. The inviscid blade force is determined by calculating a pressure difference between the pressure and suction surfaces, and the viscous blade force is related to the local kinetic energy through a skin friction coefficient. The viscous blade force model was validated by a linear controlled diffusion airfoil cascade, and the results showed that it can correctly introduce the loss into the CFD-based throughflow model. Then, the code was applied to calculate the transonic NASA rotor 67, and the calculated results were in good agreement with the measured results, which showed that the calculated shock losses reduce the dependence of the throughflow calculation on the empirical correlation. Last, the 3.5-stage compressor P&W3S1 at 85%, 100%, and 105% of the design speed was performed to demonstrate the reliability of the viscous blade force model in a multistage environment. The results showed that the CFD-based throughflow method can easily predict the spanwise mixing due to the inclusion of the turbulence model, and predicted results were in acceptable agreement with the experimental results. In a word, the proposed viscous blade force model and CFD-based throughflow model can achieve the throughflow analysis with an acceptable level of accuracy and a little time-consuming.

This paper presents the use of a conventional computational-fluid-dynamics-based throughflow method to model the effects of a bypass fan in a propulsion system (for example, nacelle) under the rest...

In this paper we have investigated the effect of throughflow on thermal convection in a viscoelastic fluid saturated porous media. The governing equations are modelled in the presence of throughflow. These equations are made dimensionless and the obtained nonlinear problem solved numerically. There are two types of throughflow effects on thermal instability inflow and outflow investigated by finite amplitude analysis. This finite amplitude equation is obtained using the complex Ginzburg-Landau amplitude equation (CGLE) for a weak nonlinear oscillatory convection. The heat transport analysis is given by complex Ginzburg-Landau amplitude equation (CGLE). The numerical results indicate that due to the non-uniform throughflow there is instability at the bottom plate and influence the heat transfer in the system. The vertical throughflow is having both stable and unstable modes depending on flow direction. The nature of viscoelastic fluid is having both effects either stabilize or destabilize. Further, it is found that the nonlinear throughflow effects have dual role on heat transport. The solutions of the present problem are obtained numerically by using Runge-Kutta fourth order method.

The supercritical carbon dioxide Brayton cycle is recognized as a promising candidate for the next generation of nuclear power and energy system. Among all the components in the cycle, the centrifugal compressor is one of the most important ones. This paper presents a streamline curvature throughflow method based on real gas properties and capable of dealing with condensation flows in the supercritical carbon dioxide compressors. A fluid thermodynamic property calculation method based on look-up tables is adopted to account for the real gas effects and fluid condensation and to reduce the computational time. For extending the simulation capability to the region below the saturation curve to assess the condensation possibility, the homogeneous equilibrium model is adopted. Finally, the real gas-based streamline curvature method is applied in the analysis of a supercritical carbon dioxide centrifugal compressor working near the critical point. Then, computational fluid dynamics calculations are performed to validate the method in detail. The results of the computational validation indicate that the real gas-based streamline curvature method presented in the paper can obtain an accurate enough flow field as that obtained by three-dimensional computational fluid dynamics simulations considering the coarse grid and the much less calculation time.

Achieving highly efficient extrication of the tunnel boring machine (TBM) cutter-head driving system from the collapsed surrounding rock has become a key problem globally, and significant effort has been directed to improve TBM cutter-head extricating ability. In this study, the characteristics of a hydro-viscous device have been investigated to improve extricating performance of the TBM cutter-head. A numerical method based on an explicit pressure-linked equation is presented for computing the film parameters of the HVC, which is then applied to investigate extrication characteristics of a TBM cutter-head with a hydro-viscous clutch (HVC). The explicit pressure-linked equation is derived from the Navier–Stokes equations and the conservation equation, where boundary conditions are involved. The model of a cutter-head driving system with an HVC is established, and the extrication characteristics of the cutter-head driving system are analyzed and compared with three extrication strategies. The variation in extrication torque shows that the linear strategy or positive parabolic strategy are preferred for their relatively high extrication efficiency and low rigid impact, and the effects of throughflow rate on torque transmission are also investigated. The test rig of the TBM cutter-head driving system was set up to validate the numerical method and the model of a cutter-head driving system, and the feasibility of the proposed numerical method for researching the extrication of the TBM cutter-head is verified.

In the present study, the full-coverage film cooling characteristics of the fan-shaped holes with a constant lateral width at the exits are investigated under a wide range of blowing ratio from 0.5 to 7.5. The fan-shaped holes with inclination angles of 20°, 25° and 30° and expansion angles of 10° and 13° are considered. Adiabatic film cooling effectiveness of the holes is measured using thermo-chromic liquid crystal technology. Meanwhile, the corresponding flow characteristics are illustrated by numerical simulation. Effects of the inclination angle and the expansion angle as well as the blowing ratio on the cooling effectiveness and discharge coefficient of the holes are analyzed. Compared to cylindrical holes, the fan-shaped holes have obvious advantages in terms of adiabatic film cooling effectiveness and discharge coefficient. The inclination angle of the fan-shaped hole shows a dominant impact on the separation motion inside the hole, which then governs the vortex structure and the film cooling effectiveness downstream. The row-by-row interaction of the coolant jets, as one of the important features of full-coverage film cooling, normally leads to the weakness of the vortices downstream the holes and therefore the better cooling performance. In order to further quantify the full-coverage film cooling performance and throughflow losses of the holes, correlations of experimental data for area-averaged effectiveness and discharge coefficient are developed.

A time-marching throughflow method for the off-design performance analysis of axial compressors is described. The method is based on the Euler equations, and a new inviscid blade force model is proposed in order to achieve desired flow deflection. The flow discontinuity problems at the leading and trailing edges are tackled by automatic correction of blade mean surface using cubic spline interpolation. Empirical loss models have been integrated into the throughflow model in order to simulate the viscous force effects in the real three-dimensional flow. Two test cases have been presented to validate the throughflow model, including the transonic fan rotor – NASA Rotor 67 working at a near-peak-efficiency point and a 1.5-stage high-speed axial compressor with inlet guide vane operating at 68% nominal speed. Reasonable flow parameters distributions have been obtained in the Rotor 67 fan calculating results, and accurate overall performance characteristics have also been predicted at the strong off-design condition for the 1.5-stage axial compressor. The CPU time of both cases cost less than one minute at one operating point. The results indicate that the developed time-marching throughflow model is effective and efficient in the turbomachinery performance analysis.

In this article, the joint effect of pulsating throughflow and magnetic field on the onset of convective instability in a nanofluid layer, bounded in a Hele-Shaw cell is presented within the context of linear stability theory and frozen profile approach. The model utilized for nanofluid combines the impacts of Brownian motion and thermophoresis, while for Hele-Shaw cell, Hele-Shaw model is considered. The Galerkin technique is utilized to solve the eigenvalue problem. The outcome of the important parameters on the stability framework is examined analytically. It is observed that the pulsating throughflow and magnetic field have both stabilizing effects. The impact of increasing the Hele-Shaw number [Formula: see text], the modified diffusive ratio [Formula: see text] and the nanoparticle Rayleigh number [Formula: see text] is to quicken the convective motion, while the Lewis number [Formula: see text] has dual impact on the stability framework in the existence of pulsating throughflow. It is also established that the oscillatory mode of convective motion is possible only when the value of the magnetic Prandtl number [Formula: see text] is not greater than unity.

An analysis is made for the effect of throughflow on the onset of convection in a rectangular box under the assumption that total flux (sum of diffusive, thermophoretic, and convective) is zero on the boundaries. A linear stability analysis and Galerkin weighted residual method are used to obtain the Rayleigh number and stability curves for the onset of convection. Three dominating combination of parameters are extracted from the non-dimensional analysis. All rescaled parameters promote the convection. Aspect ratios, throughflow, and nanoparticles play an important role in the formulation of cell distribution and development of convection. Oscillatory convection is possible for permissible range of nanofluid parameters. It is also found that the size of a cellular mode is altered by throughflow and nanoparticles.

Dry lakes covered with a salt crust organised into beautifully patterned networks of narrow ridges are common in arid regions. Here, we consider the initial instability and the ultimate fate of buoyancy-driven convection that could lead to such patterns. Specifically, we look at convection in a deep porous medium with a constant throughflow boundary condition on a horizontal surface, which resembles the situation found below an evaporating salt lake. The system is scaled to have only one free parameter, the Rayleigh number, which characterises the relative driving force for convection. We then solve the resulting linear stability problem for the onset of convection. Further exploring the nonlinear regime of this model with pseudo-spectral numerical methods, we demonstrate how the growth of small downwelling plumes is itself unstable to coarsening, as the system develops into a dynamic steady state. In this mature state we show how the typical speeds and length scales of the convective plumes scale with forcing conditions, and the Rayleigh number. Interestingly, a robust length scale emerges for the pattern wavelength, which is largely independent of the driving parameters. Finally, we introduce a spatially inhomogeneous boundary condition – a modulated evaporation rate – to mimic any feedback between a growing salt crust and the evaporation over the dry salt lake. We show how this boundary condition can introduce phase locking of the downwelling plumes below sites of low evaporation, such as at the ridges of salt polygons.

This paper presents large-eddy and direct numerical simulations of buoyancy-driven convection in sealed and open rapidly rotating cavities for Rayleigh numbers in the range 107–109, and axial throughflow Reynolds numbers 2000 and 5600. Viscous heating due to the Ekman layer scrubbing effect, which has previously been found responsible for the difference in sealed cavity shroud Nusselt number predictions between a compressible N-S solver and an incompressible counterpart using the Boussinesq approximation, is discussed and scaled up to engine conditions. For the open cavity with an axial throughflow, laminar Ekman layer behaviour of the mean flow statistics is confirmed up to the highest condition in this paper. The Buoyancy number Bo is found useful to indicate the influence of an axial throughflow. For the conditions studied the mean velocities are subject to Ra, while the velocity fluctuations are affected by Bo. A correlation, Nu′ = 0.169(Ra′)0.318, obtained with both the sealed and open cavity shroud heat transfer solutions, agrees with that for free gravitational convection between horizontal plates within 16% for the range of Ra′ considered.

The study aimed to determine the linkage between soil exchangeable potassium (K+) concentration and stream water K+ concentration during rainfall and snowmelt events. The research was performed in small catchments with different land use (i.e. woodland, traditional agriculture, experimental agriculture, mixed-use) in the Carpathian Foothills (Poland). All of the studied catchments whose hillslopes were covered with fragipan soils had a markedly lower hydraulic conductivity (Ksat) in the fragipan (Btx) than in the horizons lying above (A and E). These highly permeable horizons determine the K+ influx to streams during most event types except snowmelts with frozen soil. In the woodland catchment, stream water K+ concentrations during events are determined by a high vertical variability in Ksat and exchangeable K+ concentrations in soil profiles. Rapid flushing of K+ from the topsoil Ah horizon with higher Ksat and higher exchangeable K+ concentrations than in the lying lower E horizon resulted in a clockwise hysteresis of K+ in stream water during most events. In the agricultural catchments, changes in stream water K+ concentration during events were determined by distinct differences between soil exchangeable K+ concentrations on hillslopes and in riparian areas. For example, during rainfall events under dry antecedent conditions, exchangeable K+ concentrations in topsoil horizons on hillslopes were distinctly higher than concentrations of exchangeable K+ in riparian area soils. The inflow of alluvial water with a low dose of K+ before the inflow of throughflow from hillslopes with a high dose of K+ thus resulted in wide counterclockwise hystereses for streamwater K+.

The computational method in throughflow simulation is investigated in this paper. The present investigation reported the current research status and compared the advantages and disadvantages between different computational models including streamline curvature method, matrix method and throughflow calculation based on time marching. For the most commonly used time marching method, we discussed one key issue in application in engineering reality which is called as the simulation of blade force, which was divided into two categories according to whether to solve the circumferentially momentum equation as master equation or not. In conclusion, compared with other methods, time marching method has more advantages in transonic flow adaptability, shock capture ability and calculating accuracy, so that it has more potentials and prospects in the future research. The blade force model, as a key link in the time marching method, has developed rapidly. However, there is still no unified highprecision model and the modeling of blade force needs more study. With further development, this method is expected to become a standard tool during the aeroengine compressor design stage.

Gas turbine engines are highly intricate machines, and every component of them is closely associated with one another. In the traditional engine developing process, vast experiment tests are needed. To reduce unnecessary trials, a whole gas turbine engine simulation is extremely needed. For this purpose, a compressor simulation tool is now developed. Considering the inherent drawbacks of 0D analysis and 3D CFD (Computational Fluid Dynamics) calculation, the 2D throughflow method is an indispensable tool. Based on the circumferential average method (CAM), 3D Navier&ndash, Stokes is transformed into a 2D method. One phenomenon arising is that the lack of description about circumferential motion leads to the need for the blade force modeling in compressor simulation. Previous models are based on the assumption that flow passes through the average stream surface without entropy increasing, which is not applicable in the CAM. An improved model is proposed based on the result analysis from CAM and NUMECA method in a linear cascade. Whereafter, the model is applied in a highly loaded and low-speed fan, which has been tested for its performance characteristics. Utilizing the new model, the error of the adiabatic efficiency between CAM and experiment decreases from 4.0% to 1.0% and the accuracy of the mass flow, and pressure ratio remains unchanged. The time involved in the CAM simulation is nearly 70 times faster than that of the 3D simulation.

The joint effect of pulsating throughflow and external electric field on the outset of convective instability in a horizontal porous medium layer saturated by a dielectric nanofluid is investigated. Pulsating throughflow alters the basic profiles for temperature and the volumetric fraction of nanoparticle from linear to nonlinear with layer height, which marks the stability expressively. To treat this problem, the Buongiorno’s two-phase mathematical model is used taking the flux of volumetric fraction of nanoparticle is vanish on the horizontal boundaries. Using the framework of linear stability theory and frozen profile approach, the stability equations are derived and solved analytically applying the Galerkin weighted residuals method with thermal Rayleigh-Darcy number as the eigenvalue. The effect of increasing the external AC electric Rayleigh-Darcy number , the modified diffusivity ratio and the nanoparticle Rayleigh number is to favorable for the convective motion, while the Lewis number and porosity parameter have dual influence on the stability scheme in the existence of pulsating throughflow. The frozen profile method shows that the result of pulsating throughflow in both directions is stabilizing. An enlarged amplitude of throughflow fluctuations offers to increased stability by an amount that vary on frequency. It is also found that the oscillatory mode of convection is not favorable for nanofluids if the vertical nanoparticle flux is vanish on the boundaries.

A streamline curvature method based integrated throughflow analysis approach is newly developed to deal with component matching problems of variable cycle compression systems. The construction of variable cycle compression system is modularly modelled in the procedure. Splitting and confluent flow are elaborately disposed. A numerical method based on the “streamline floating” character of streamline curvature method is developed to model the function of forward variable area bypass injector. Moreover, extensive models used in the throughflow calculations, including minimum loss incidence, deviation and loss models were assessed, selected and modified. Finally, code validations were conducted on three representative traditional compressors, i. e. NASA rotor 67, NASA stage 37 and a custom-designed low-speed repeating four-stage compressor. Both the predicted overall characteristics and spanwise profiles agree reasonably well with the experimental data. The validated procedure was finally used to sketch the performance maps of a double bypass compression system under two different control rules, i. e. the first bypass throttling and the second bypass throttling. The results show some aspects of the difficulties and complications in operating a variable cycle compression system, and meanwhile, demonstrate the superiority of the newly developed integrated throughflow method.

There are overwhelming proofs of how urbanization contributes to the increase of carbon emissions. However, it has been unclear how structural and functional changes in urban carbon flows evolve with socioeconomic development in a long run, which is important for a more systemic and efficient carbon mitigation policy. The present study probes into the interaction between urban carbon metabolism and socioeconomic activities from a systems perspective. Taking Beijing as a case study, we model the dynamics between the changing carbon metabolism and variation in socioeconomic conditions over 1985–2030, based on a collection of system-based indicators from ecological network analysis. We find an “inverted V curve” carbon transition in Beijing, and the turning point occurred around 2010. This transition is widely observed in the variation in total embodied emission, total system throughflow, boundary flow and system capacity. Continuing improvement in efficiency is expected to lessen the pressure from carbonization in 2020 and 2030 without sacrificing the diversity of economic activities. We suggest that network analysis has a unique potential in unfolding the interplay between carbon transition and socioeconomic development that most “accounting approaches” fail to penetrate.

The effect of vertical throughflow on the onset of bio-thermal convection in a water-based nanofluid containing gyrotactic microorganisms is investigated using more realistic boundary conditions. The Galerkin weighted residual method is used to obtain numerical solutions of the mathematical model. The effects of bioconvection Rayleigh number, gyrotaxis number, bioconvection Péclet number, Lewis number, Péclet number, particle density increment number, modified diffusitivity ratio, and nanoparticle Rayleigh number on thermal Rayleigh number are examined.The combined effect of Brownian motion and thermophoresis of nanoparticles, vertical throughflow, and gyrotactic microorganisms on the thermal Rayleigh number is found to be destabilizing and its value is decreased by first to third orders of magnitude as compared to regular fluids. Critical wave number is dependent on bioconvection parameters, nanofluid parameters as well as throughflow parameter. The results obtained using passive boundary conditions are compared with those of active boundary conditions. The present study may find applications in seawater convection at the ocean crust.

The temperature rise of hydro-viscous film in rotating parallel disks is usually controlled by imposing throughflow for keeping high film viscosity, but the Coriolis effect induced by throughflow can resist hydro-viscous transmission in return. In this work, the combined effects of Coriolis force and temperature-viscosity dependency on the hydro-viscous transmission are investigated. Firstly, the momentum and energy equations are established and the temperature-viscosity relationship is given, meanwhile, the numerical method is introduced. Then the combined effects on temperature rise and viscous transmission are analyzed and partly validated in experiment. The results reveal that with throughflow rate increasing the resistant effect of Coriolis force can be more and more significant relatively to temperature-viscosity effect, so their balance should be highlighted.

The stability of a flow subjected to an inclined temperature gradient (Hadley-type flow) in a horizontal porous media is studied in the presence of a basic horizontal mass flow (Prats flow). Therefore, the basic flow is called the Hadley–Prats flow. A weak vertical heterogeneity in permeability and conductivity is considered. The effect of viscous dissipation is taken to be non-negligible. The Rayleigh number corresponding to the vertical thermal gradient RaC is considered as an eigenvalue. Other parameters are the Peclet number (Pe) associated with the horizontal through flow, horizontal Rayleigh number (RaH) associated with the horizontal temperature gradient, Gebhart number (Ge) associated with viscous dissipation; parameters γ1 and γ2 represent the changes in permeability and conductivity, respectively. A linear stability analysis is done and the governing equations are solved numerically to obtain the critical Rayleigh number and wave number. Longitudinal and transverse rolls are discussed. Longitudinal rolls are the preferred modes for instability in most scenarios. It is found that when throughflow is present, the heterogeneity in permeability can show a stabilizing effect for longitudinal rolls but destabilizing effect for transverse rolls and vice versa depending on the direction of the throughflow. Increase in conductivity also may stabilize or destabilize the flow depending on the mass flow and viscous heating. The horizontal thermal gradient shows interesting effects in the presence of weak heterogeneity and horizontal throughflow. Significant change in the critical Rayleigh number is observed even for small values of the horizontal Rayleigh number.

The imposed throughflow into rotating parallel disk system is to decrease temperature rise of hydro-viscous film flow, but the induced Coriolis effects are usually underestimated on torque transmission. The analytical expressions of thin-film parameters are obtained based on Navier-Stokes equations with the method of approximate analytical iteration. The Coriolis force and the corresponding influence on torque transmission are analyzed by analytical calculation and experimental verification. The results show that the tangential Coriolis force serves as resistance to the viscous torque transmission and the Coriolis torque loss can lead to primary reduction of efficiency among all motion effects. Therefore, the Coriolis effects should be paid more attention for the practical designs and applications of rotating hydro-viscous parallel-disk systems with imposed throughflow.

Purpose The purpose of this paper is to study the effects of vertical throughflow on the boundary layer flow and heat transfer of a nanofluid driven by a permeable stretching/shrinking surface. Design/methodology/approach Similarity transformation is used to convert the system of boundary layer equations into a system of ordinary differential equations. The system of governing similarity equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. The generated numerical results are presented graphically and discussed based on some governing parameters. Findings It is found that dual solutions exist in both cases of stretching and shrinking sheet situations. Stability analysis is performed to determine which solution is stable and valid physically. Originality/value Dual solutions are found for positive and negative values of the moving parameter. A stability analysis has also been performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible.

The annular gap between rotor and stator is an inevitable flow path of a throughflow ventilated electrical machine, but the flow entering the rotor-stator gap is subjected to the effects of rotation. The pressure loss and volumetric flow rate across the rotor-stator gap were measured and compared between rotating and stationary conditions. The experimental measurements found that the flow entering the rotor-stator gap is affected by an additional pressure loss. In the present study, the rotational pressure loss at the entrance of rotor-stator gap is characterised. Based upon dimensional analysis, the coefficient of entrance loss can be correlated with a dimensionless parameter, i.e. rotation ratio. The investigation leads to an original correlation for the entrance loss coefficient of rotor-stator gap arisen from the Coriolis and centrifugal effects in rotating reference frame.

The effect of throughflow and temperature modulation on a rotating porous medium is investigated. The generalized Darcy model is used for the momentum equation. Heat transfer analysis is based on weakly nonlinear thermal instability. It is computed numerically in terms of the Nusselt number, which is governed by a non-autonomous complex Ginzburg-Landau equation. Both concepts, rotation and throughflow are used as an external mechanism to regulate heat transfer. The effect of amplitude and frequency of modulation on heat transport is discussed and presented graphically. The effect of throughflow has duel by nature on heat transfer, the outflow enhances and inflow diminishes the heat transfer. It is found that, high rotational rates promotes heat transfer than low rotational rates. Further, the effect of modulation on mean Nusselt number depends on both the phase difference and frequency rather than on only the choice of the frequency of small amplitude modulation.

In the last decades, the consolidation of 3D CFD approaches in the industrial design practices has progressively moved throughflow codes from the top of design systems to somewhere in between first development stages and the final aerodynamic optimizations. Despite this trend and the typical limitations of traditional throughflow methods, designers tend to still consider such methods as fundamental tools for drafting a credible aero-design in a short turnaround time. Recently a considerable attention has been devoted to CFDbased throughflow codes as suitable means to widen the range of applicability of these tools while smoothing the predictive gap with successive threedimensional flow analyses.The present paper retraces the development and some applications of a modern and complete CFD-based throughflow solver specifically tuned for multistage axial turbine design. The code solves the axisymmetric Euler equations with an original treatment of tangential blockage and body force. It inherits its numerical scheme from a state-of-the-art CFD solver (TRAF code) and incorporates real gas capabilities, three-dimensional flow features (e.g. secondary flows, tip leakage effects), coolant flow injections, and radial mixing models. Also geometric features of actual blades, like fillets, part-span shrouds, and snubbers, are accounted for by suitable models.The capabilities of the code are demonstrated by discussing a significant range of test cases and industrial applications. They include single stage configurations and entire multistage modules of steam turbines, with flow conditions ranging from subsonic to supersonic. Computational strategies for design and off-design analyses will be presented and discussed. The reliability and accuracy of the method is assessed by comparing throughflow results with 3D CFD calculations and experimental data. A good agreement in terms of overall performance and spanwise distributions is achieved in both design and off-design operating conditions.

This paper is aimed to investigate the transition to absolute instability in a porous layer with horizontal throughflow. The importance of this analysis is due to the possible experimental failure to detect growing perturbations which are localised in space and which may be convected away by the throughflow. The instability of the uniform flow in a horizontal rectangular channel subject to uniform heating from below and cooled from above is studied. While the lower wall is modelled as an impermeable isoflux plane, the upper wall is assumed to be impermeable and imperfectly conducting, so that a Robin temperature condition with a given Biot number is prescribed. The sidewalls are assumed to be adiabatic and impermeable. The basic state considered here is a stationary parallel flow with a vertical uniform temperature gradient, namely the typical configuration describing the Darcy–Benard instability with throughflow. The linear instability of localised wavepackets is analysed, thus detecting the parametric conditions for the transition to absolute instability. The absolute instability is formulated through an eigenvalue problem based on an eighth–order system of ordinary differential equations. The solution is sought numerically by utilising the shooting method. The threshold to absolute instability is detected versus the Peclet number associated with the basic flow rate along the channel.

In this paper large-eddy simulation is used to study buoyancy-induced flow in a rotating cavity with an axial throughflow of cooling air. This configuration is relevant in the context of secondary air systems of modern gas turbines, where cooling air is used to extract heat from compressor disks. Although global flow features of these flows are well understood, other aspects such as flow statistics, especially in terms of the disk and shroud boundary layers, have not been studied. Here, previous work for a sealed rotating cavity is extended to investigate the effect of an axial throughflow on flow statistics and heat transfer. Time- and circumferentially-averaged results reveal that the thickness of the boundary layers forming near the upstream and downstream disks is consistent with that of a laminar Ekman layer, although it is shown that the boundary layer thickness distribution along the radial direction presents greater variations than in the sealed cavity case. Instantaneous profiles of the radial and azimuthal velocities near the disks show good qualitative agreement with an Ekman-type analytical solution, especially in terms of the boundary layer thickness. The shroud heat transfer is shown to be governed by the local centrifugal acceleration and by a core temperature, which has a weak dependence on the value of the axial Reynolds number. Spectral analyses of time signals obtained at selected locations indicate that, even though the disk boundary layers behave as unsteady laminar Ekman layers, the flow inside the cavity is turbulent and highly intermittent. In comparison with a sealed cavity, cases with an axial throughflow are characterised by a broader range of frequencies, which arise from the interaction between the laminar jet and the buoyant flow inside the cavity.

A computational fluid dynamics (CFD)-based throughflow solver is applied to the meridional analysis of low-pressure steam turbine modules. The throughflow code inherits its numerical scheme from a state-of-the-art CFD solver (TRAF code) and incorporates real gas capabilities, three-dimensional flow features, and spanwise mixing models. Secondary flow effects are introduced via a concentrated vortex model. Tip gap and shroud leakage effects are modeled in terms of source vectors in the system of governing equations. The impact of part-span shrouds and snubbers are accounted for, on a local basis, through suitable body force fields. The advection upstream splitting method (AUSM+-up) upwind strategy has been adopted as a basis to construct a numerical flux scheme explicitly suited for throughflow applications. The original formulation has been adapted to handle real gas flows and to embed the treatment of body force fields in a fully consistent framework. The capability of the procedure is assessed by analyzing the low-pressure modules of two large steam turbines designed and manufactured by Ansaldo Energia. These modules include rotor tip shrouds and part-span snubbers and feature supersonic flow and large blade twist. Throughflow predictions in terms of main performance figures and radial distributions of flow quantities are compared with experimental data and 3D steady viscous analyses. It will be shown how the proposed CFD-based throughflow model can be fruitfully used in the early stages of the design as it delivers predictions of comparable accuracy with 3D CFD analyses at a fraction of the computational time.

A detailed study on the linear stability of plane porous-Couette flow in the presence of a uniform vertical throughflow using the Brinkman–extended Darcy equation has been presented. The equivalent of the Orr–Sommerfeld eigenvalue problem is formulated and solved numerically using the Chebyshev collocation method. The throughflow introduces an asymmetry in the basic flow amounting to the existence of a different set of onset modes. The contributions of the throughflow dependent modified Reynolds number and the modified porous parameter on the critical values defining the threshold for the onset of instability are presented. It is found that the stability characteristics of plane Couette flow in a porous medium in the presence of throughflow are remarkably different from no throughflow and non-porous cases.

With the increasing importance of renewable energy sources in the power generation scenario, traditional fossil-fuel power generation systems are subjected to relevant and rapid load variations. Consequently, designers have become more and more interested at predicting the transient behavior of fossil fuel power plants. Tools allowing off-design performance predictions of turbomachines have consequently become desirable even in the first design phases. The paper presents the development of a strategy for gas turbines off-design analyses that exploit a novel CFD-based throughflow method, and its application to a heavy-duty, medium size, F-Class, 4-stage gas turbine designed and manufactured by Ansaldo Energia. The throughflow code is based on the axisymmetric Euler equations with tangential blockage and body forces, and inherits its numerical scheme from a state-of-the-art CFD solver (TRAF code), including real-gas capabilities. The strategy starts from the calibration of the throughflow method in order to match the results of 3D CFD analyses at design point, whereupon the computational framework is frozen and used for off-design simulations. The proposed methodology is fairly general and will be discussed in details in the paper. The analysed operating conditions of the turbine encompass a wide range of expansion ratios and corrected rotational speeds. The feasibility of the procedure is assessed by a detailed comparison with 3D CFD results in terms of span-wise distributions and performance figures. It will be shown how the generality and reliability of the proposed method demonstrates its feasibility for an intensive use in the design of gas turbines. In particular, throughflow predictions can compete with the ones provided by state-of-the-art 3D CFD approaches and can be obtained with a small fraction of the computational time.

An extension of Carreau and Carreau–Yasuda rheological models to porous media is proposed to study the onset of mixed convection of both pseudoplastic fluids (PF) and dilatant fluids (DF) in a porous layer heated from below in the presence of a horizontal throughflow. In comparison with Newtonian fluids, three more dimensionless parameters are introduced, namely, the Darcy–Weissenberg number Wi, the power–law index n, and the Yasuda parameter a. Temporal stability analysis of the basic state showed that in the absence of a throughflow (Wi = 0), the critical Rayleigh number and the critical wavenumber at the onset of convection are the same as for Newtonian fluids, namely, R a c = 4 π 2 and k c = π, respectively. When the throughflow is added (Wi > 0), it is found that moving transverse rolls (stationary longitudinal rolls) are the dominant mode of the instability for PF (for DF). Furthermore, depending on Wi, two regimes of instability were identified. In the weakly non-Newtonian regime (i.e., W i < W i t ≈ 1), a destabilizing effect is observed for PF, while the reverse occurs for DF. These effects are more intense by reducing (increasing) the index n for PF (for DF). In this regime, a significant qualitative difference is found between the Darcy–Carreau model and the power–law model. However, in the strongly non-Newtonian regime, the two models lead to similar results. A mechanical energy budget analysis is performed to understand the physical effects of the interaction between the basic throughflow and the disturbances. It is also shown that the intrinsic macroscale properties of the porous medium may play a key role in the stabilizing/destabilizing effect. Finally, a comparison is made between the present theoretical predictions and recent mixed convection experiments in a Hele–Shaw cell.

The gas–liquid flow in a rotor-stator spinning disc reactor, with co-feeding of gas and liquid, is studied for high gas volumetric throughflow rates and high gas/liquid volumetric flow ratios. High speed imaging and spectral analysis of pressure drop signals are employed to analyse the flow. Two mechanisms of bubble formation are observed, one due to gas overpressure leading to large irregular bubbles, and one due to liquid turbulent vortices leading to small, well-defined bubbles. The two mechanisms lead to three distinct gas dispersion regimes, distinguished by their characteristic oscillations in pressure drop. At low rotational Reynolds numbers ( Re ω 6 ), in the gas spillover regime, the gas is dispersed as large bubbles only. Above this critical Re ω , small bubbles are sheared off as well, thus forming a heterogeneous dispersion. At sufficiently high Re ω , depending on the gas flow rate, the gas is homogeneously dispersed as small bubbles. The maximum gas flow that can be dispersed as small bubbles is linearly proportional to the local energy dissipation rate. The understanding of the bubble formation mechanisms and pressure signature allows prediction and detection of the prevailing hydrodynamic regime in scaled up spinning disc reactors and for different reaction fluids.

The effect of vertical throughflow and time-periodic gravity field has been investigated on Darcy convection. The amplitude of gravity modulation is considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the stationary mode of convection. As a consequence heat transport evaluated in terms of the Nusselt number, which is governed by the non-autonomous Ginzburg-Landau equation. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The amplitude and frequency of modulation, Prandtl Darcy number on heat transport have been analyzed and depicted graphically. Further, the study establishes that the heat transport can be controlled effectively by a mechanism that is external to the system. Finally flow patterns are presented in terms of streamlines and isotherms.

The cooling air in a rotating machine is subject to windage as it passes over the rotor surface, particularly for cases where nonaxisymmetric features such as boltheads are encountered. The ability to accurately predict windage can help reduce the quantity of cooling air required, resulting in increased efficiency. Previous work has shown that the steady computational fluid dynamics solutions can give reasonable predictions for the effects of bolts on disc moment for a rotor–stator cavity with throughflow but flow velocities and disc temperature are not well predicted. Large fluctuations in velocities have been observed experimentally in some cases. Time-dependent computational fluid dynamics simulations reported here bring to light the unsteady nature of the flow. Unsteady Reynolds-averaged Navier–Stokes calculations for 120° and 360° models of the rotor–stator cavity with 9 and 18 bolts were performed in order to better understand the flow physics. Although the rotor–stator cavity with bolts is geometrically steady in the rotating frame of reference, it was found that the bolts generate unsteadiness which creates time-dependent rotating flow features within the cavity. At low throughflow conditions, the unsteady flow significantly increases the average disc temperature.

In this paper, thermal instability in a horizontal nanofluid-saturated porous layer with vertical through flow and quadratic drag is investigated. The important effects of Brownian motion and thermophoresis are included in the model of nanofluid, while for porous medium the modified Forchheimer-extended Darcy model is employed. The criterion for both stationary and oscillatory convection is derived analytically with and without through flow and quadratic drag effects. It is found that oscillatory convection is possible only for the case of a bottom-heavy nanoparticle distribution.

This paper investigates the influence of a uniform vertical throughflow on the stability of Poiseuille flow in a Newtonian fluid-saturated Brinkman porous medium. The solution to the stability eigenvalue problem is obtained numerically using the Chebyshev collocation and the Galerkin methods. The vertical throughflow, irrespective of its direction, imparts an identical stabilizing/destabilizing effect on the fluid flow. The throughflow dependent Reynolds number RT instills both stabilizing and destabilizing effects in a fluid saturated channel of porous medium and the range of RT up to which the system gets destabilized increases with increasing porous parameter. The results for the clear fluid case are also obtained as a particular case from the present study, and contrary to the porous case, throughflow always displays a stabilizing effect. Moreover, the numerical solutions presented will be useful for checking the performance and accuracy of any numerical methodologies.

The basic tool set to design multi-stage axial compressors consists of fast codes for throughflow and blade-to-blade anal-ysis. Detailed blade row design is conducted with 3D CFD,mainly to control the end wall flow. This work focuses on the interaction between through-flow and blade-to-blade design and the transition to 3D CFD.A design strategy is presented that is based on a versatile air-foil family. The new class of airfoils is generated by optimizing a large number of airfoil shapes for varying design requirements. Each airfoil geometry satisfies the need for a wide working range as well as low losses. Based on this data, ma-chine learning is applied to estimate optimal airfoil shape and performance. The performance prediction is incorporated into the throughflow code. Based on a throughflow design, the air-foils can be stacked automatically to generate 3D blades. On this basis, a 3D CFD setup can be derived. This strategy is applied to study upgrade options for a15-stage stationary gas turbine compressor test rig. At first, the behaviour of the new airfoils is studied in detail. After-wards, the design is optimized for mass flow rate as well as efficiency. Selected configurations from the Pareto-front are evaluated with 3D CFD., {"references":["Aulich, M., Voss, C. and Raitor, T. (2014), 'Optimization Strategies demonstrated on a Transonic Centrifugal Compressor', ISROMAC 15 .","Banjac, M., Petrovic, V. and Wiedermann, A. (2015), 'Secondary Flows, Endwall Effects and Stall Detection in Axial Compressor Design', ASME J. Turbomach 137 (5), 051004.","Becker, K., Heitkamp, K. and Kügeler, E. (2010), 'Recent Progress in a Hybrid-Grid CFD Solver for Turbomachinery Flows', ECCOMAS CFD 2010 .","Carter, A. D. S. (1950), 'The low speed performance of related aerofoils in cascade', Aeronautical Research Council (CP29).","Denton, J. D. and Cumpsty, N. 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The buoyancy-induced flow and heat transfer inside the compressor rotors of gas-turbine engines affects the stresses and radial growth of the compressor disks, and it also causes a temperature rise in the axial throughflow of cooling air through the center of the disks. In turn, the radial growth of the disks affects the radial clearance between the rotating compressor blades and the surrounding stationary casing. The calculation of this clearance is extremely important, particularly in aeroengines where the increase in pressure ratios results in a decrease in the size of the blades. In this paper, a published theoretical model—based on buoyancy-induced laminar Ekman-layer flow on the rotating disks—is extended to include laminar free convection from the compressor shroud and forced convection between the bore of the disks and the axial throughflow. The predicted heat transfer from these three surfaces is then used to calculate the temperature rise of the throughflow. The predicted temperatures and Nusselt numbers are compared with measurements made in a multicavity compressor rig, and mainly good agreement is achieved for a range of Rossby, Reynolds, and Grashof numbers representative of those found in aeroengine compressors. Owing to compressibility effects in the fluid core between the disks—and as previously predicted—increasing rotational speed can result in an increase in the core temperature and a consequent decrease in the Nusselt numbers from the disks and shroud.

For many medical and industrial applications, measurement of flow is essential for continuous dosing of fluids. When other physical quantities of fluids are sensed next to flow, e.g. density and viscosity, the composition of the fluid can be obtained. Miniaturization of these sensors using microtechnology offers advantages in terms of resolution, mass production, channel wall material and internal volume. The research described in this dissertation spans roughly two subjects: • resolution limit analysis and improvement of microfabricated Coriolis mass flow sensors; • Integration of flow, pressure, density, viscosity and relative permittivity sensors on a single chip.

In this paper, a novel engineering platform for throughflow analysis based on streamline curvature approach is developed for the research of a 5-stage compressor. The method includes several types of improved loss and deviation angle models, which are combined with the authors’ adjustments for the purpose of reflecting the influences of three-dimensional internal flow in high-loaded multistage compressors with higher accuracy. In order to validate the reliability and robustness of the method, a series of test cases, including a subsonic compressor P&W 3S1, a transonic rotor NASA Rotor 1B and especially an advanced high pressure core compressor GE E3 HPC, are conducted. Then the computation procedure is applied to the research of a 5-stage compressor which is designed for developing an industrial gas turbine. The overall performance and aerodynamic configuration predicted by the procedure, both at design- and part-speed conditions, are analyzed and compared with experimental results, which show a good agreement. Further discussion regarding the universality of the method compared with CFD is made afterwards. The throughflow method is verified as a reliable and convenient tool for aerodynamic design and performance prediction of modern high-loaded compressors. This method is also qualified for use in the further optimization of the 5-stage compressor.

The paper describes the development and validation of a novel CFD-based throughflow model. It is based on the axisymmetric Euler equations with tangential blockage and body forces and inherits its numerical scheme from state-of-the-art CFD solver (TRAF code), including real-gas capabilities. A crucial aspect of the numerical procedure is represented by an adaptive approach for the meridional flow surface, which employs a new time-dependent equation to accommodate incidence and deviation effects, and which allows the explicit calculation of the blade body force. A realistic distribution of entropy along the streamlines is proposed in order to compute dissipative forces on the basis of a distributed loss model. The throughflow code is applied to the investigation of the NASA rotor 67 transonic fan and of a four stage low-pressure steam turbine at design conditions. The performance of the method is evaluated by comparing predicted operating characteristics and spanwise distributions of flow quantities with the results of CFD, steady, viscous calculations and experimental data.

A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.

This paper outlines the aerodynamic performance of a highly loaded 5-stage compressor in a conceptual semi-closed cycle. An in-house throughflow computation procedure that has been proven to be a powerful tool in aerodynamic analysis for modern compressors is applied to simulate the compressor. The influences of changes in physical properties of the working medium with varying ratios of exhaust CO2 recirculation are considered in the computation. A series of numerical simulations is conducted with two settings depending on whether the rotational speed is set to obey the criterion of similarity. For the identical non-dimensional speed parameter, the compressor can operate stably with pure CO2 as the working fluid. The distributions of aerodynamic parameters undergo no big differences under various CO2 contents; however, a somewhat little higher loss is observed for the 5th stage. When the absolute rotational speed is set according to the originally designed value, the compressor can bear a 25% CO2 content at the cost of a substantially narrowed working range, and a recirculation ratio of approximately 10% is a safe threshold value. The aerodynamic configuration also undergoes a notable redistribution given these circumstances; the load of the front stages is reduced, but the rear stages become the risk factors at near stall condition. This research reveals that from the compressor design point of view, a semi-closed cycle is feasible using existing technology and that compressor modifications are needed according to situational requirements. © 2015 Society of Chemical Industry and John Wiley & Sons, Ltd