Mixing Plane Approach Research Articles

Integration of a transonic high-pressure turbine with a rotating detonation combustor and a diffuser

Abstract In this paper, a diffuser is used to integrate a transonic high-pressure turbine with a rotating detonation combustor (RDC). The paper focuses on the required design modifications to the turbine endwalls (EW) to enable high efficiency, while preserving the airfoil blade-to-blade geometry. The main challenge is the stator passage unstarting, due to the high inlet Mach number. First of all, steady Reynolds Averaged Navier Stokes simulations were performed to compare the efficiency of turbines with constant-radius EWs to turbines with axisymmetric EWs. A modified EW design prevented the unstarting of the stator passage, enabling a significant gain in performance. Afterward, the influence on the turbine efficiency and damping due to the unsteadiness from the diffuser-like fluctuations of the RDC was evaluated with unsteady Reynolds Averaged Navier Stokes simulations with a mixing plane approach (MPA). Full unsteady simulations were carried out on selected inlet conditions and compared to the mixing plane results. This parametric study provides turbine designers with recommended diffusion rates along the vane EWs. Additionally, we provide guidance on the upstream diffuser design, specifically the required damping and outlet Mach number.

Continuous adjoint‐based shape optimization of a turbomachinery stage using a 3D volumetric parameterization

AbstractThis work presents a novel volumetric parameterization technique along with the continuous adjoint method to support gradient‐based CFD shape optimization of turbomachinery stages. The proposed parameterization retains axisymmetry and periodicity by acting on a transformed coordinate system. The same volumetric model controls the shape and the computational volume mesh in a seamless manner, avoiding the additional use of a mesh deformation tool. Moreover, it is differentiated to compute mesh sensitivities (i.e., derivatives of nodal coordinates with respect to the design variables) and is combined with the flow and continuous adjoint, multi‐row solvers of the in‐house PUMA software. Flow field solutions in successive rows communicate based on the mixing plane approach; the development of continuous adjoint to the latter is also presented in this article. The adjoint to the turbulence model and distance‐from‐the‐wall (Hamilton–Jacobi) equations are solved, increasing the accuracy of the computed sensitivity derivatives. All these tools run on modern GPUs, accelerating both flow/adjoint solutions and shape/mesh manipulations. The capabilities of these tools are demonstrated in the shape optimization of the rotor blades of the MT1 high‐pressure, transonic, turbine stage, aiming at maximum stage isentropic efficiency with constraints on stage reaction and inlet capacity.

Implicit and Conservative Mixing-Plane Method for Multistage Turbomachinery Aerodynamic Analysis

A fully implicit Reynolds-averaged Navier–Stokes (RANS) flow solver and a corresponding adjoint solver using a Newton–Krylov algorithm has recently been developed and demonstrated to exhibit good solution robustness and efficiency for flow and adjoint aerodynamic analyses of single-row turbomachines at design and off-design conditions. To extend the algorithm to multistage applications, a robust mixing-plane technique and its fully implicit treatment are crucial. In this work, a mixing-plane approach featuring 1) flux conservation, 2) implicitness, 3) one-dimensional nonreflectiveness, and 4) robustness in handling reserve flow is proposed and incorporated into the existing Newton–Krylov turbomachinery computational fluid dynamics solver. Following a flux-based approach that ensures exact flux conservation, the algorithm of the proposed mixing-plane method is first rigorously derived, and implementation details into the existing single-row RANS solver are then discussed, with emphasis on the fully implicit treatment of the mixing-plane fluxes. Finally, the fully implicit multistage flow solution capability is extended to the corresponding adjoint solver. The resulting algorithms are tested on a subsonic and a transonic compressor to validate the flow solution accuracy, verify the adjoint sensitivity, and demonstrate its robustness in handling reverse flows.

Steady-State Fluid-Solid Mixing Plane to Replace Transient Conjugate Heat Transfer Computations during Design Phase

The demand for increased turbomachinery performance, both, towards higher pressures and temperatures, leads to high thermal-loads of specific components and can critically affect mechanical integrity. In the particular case of rotating-disk configurations, like the back-side of wheels or in cavities, a very efficient way for cooling is jet impingement. An example for this situation are high pressure-ratio turbochargers, where cooling of the impeller disk (back wall) is introduced to achieve tolerable thermal loads. From the physical point of view, jet impingement on a rotating wall generates an unsteady heat transfer situation. On the other end, accurate values of time-averaged temperatures would be sufficient for design purposes. In general, obtaining circumferentially time-averaged solutions requires transient analysis of the conjugate heat transfer (CHT) process to account for the mean effect of jet cooling on solids. Such analysis is computationally expensive, due to the difference in information propagation time-scale for the solid and the fluid. In this paper, a new approach to directly compute circumferentially time-averaged (i.e., steady-state) temperature distributions for rotating-disk CHT problems is presented based on an adaption of the well known fluid-fluid mixing plane approach.

Numerical Investigation on the Aerodynamic Performance of a Low-Pressure Steam Turbine Exhaust Hood Using Design of Experiment Analysis

Abstract Nowadays, the rising interest in using renewable energy for thermal power generation has led to radical changes in steam turbine design practice and operability. Modern steam turbines are required to operate with greater flexibility due to rapid load changes, fast start-up, and frequent shutdowns. This has given rise to great challenges to the exhaust hood system design, which has a great influence on the overall turbine performance converting the kinetic energy leaving the last stage of low-pressure turbine into static pressure. The radial hoods are characterized by a complex aerodynamic behavior since the flow turns by 90 deg in a very short distance and this generates a highly rotational flow structure within the diffuser and exhaust hood outer casing, moreover, the adverse pressure gradient can promote the flow separation drastically reducing the hood recovery performance. For these reasons, it is fundamental to design the exhaust system in order to ensure a good pressure recovery under all the machine operating conditions. This paper presents a design of experiment (DOE) analysis on a low-pressure steam turbine exhaust hood through computational fluid dynamics (CFD) simulations. A parametric model of an axial-radial exhaust hood was developed, and a sensitivity of exhaust hood performance as a function of key geometrical parameters was carried out, with the aim of optimizing the pressure recovery coefficient and minimizing the overall dimensions of the exhaust casing. Since hood performance strongly depends on a proper coupling with the turbine rear stage, such a stage was modeled using the so-called mixing-plane approach to couple both stator–rotor and rotor-diffuser interfaces. A detailed analysis of the flow field in the exhaust hood in the different configurations was performed, detecting the swirling structures responsible for the energy dissipation in each simulation, as well as correlating the flow field with the pressure recovery coefficient.

Challenges Associated With Replicating Rotor Blade Deposition in a Non-Rotating Annular Cascade

Abstract A computational analysis is performed to determine if particulate impact events on the external surfaces of gas turbine engine rotor blades can be faithfully replicated in an experimental rotor cascade. The general electric (GE) energy efficient engine (E3) first-stage turbine flow-field at cruise conditions is first solved using a steady-state explicit mixing plane (MP) approach. To model flow in the cascade, a single E3 rotor periodic domain is then constructed with an inlet section matching the relative flow incidence angle from the mixing plane calculation. The mass-averaged relative flow conditions at the inlet and outlet of the mixing plane rotor section are imposed on the cascade boundaries and a steady solution is found. Particles with diameters ranging from 1 to 25 µm are tracked through each domain and the OSU deposition model is implemented to dictate the sticking and rebounding action of particles impacting solid surfaces. It is discovered that both the locations and parameters of the impacts in the cascade vary significantly from the engine environment. For smaller particles, this is credited to a stronger upstream influence of the blade on the cascade flow-field. As size increases, differences in deposition are instead driven by the interaction of the full-stage vane with the particles. The lack of a vane in the cascade causes drastically different particle inlet vectors over the rotor than are seen in the engine setting. The radial differences of particle impact locations are explored, and the role that pressure plays is considered.

Integration of a transonic high-pressure turbine with a rotating detonation combustor and a diffuser

Abstract In this paper, a diffuser is used to integrate a transonic high-pressure turbine with a rotating detonation combustor (RDC). The paper focuses on the required design modifications to the turbine endwalls (EW) to enable high efficiency, while preserving the airfoil blade-to-blade geometry. The main challenge is the stator passage unstarting, due to the high inlet Mach number. First of all, steady Reynolds Averaged Navier Stokes simulations were performed to compare the efficiency of turbines with constant-radius EWs to turbines with axisymmetric EWs. A modified EW design prevented the unstarting of the stator passage, enabling a significant gain in performance. Afterward, the influence on the turbine efficiency and damping due to the unsteadiness from the diffuser-like fluctuations of the RDC was evaluated with unsteady Reynolds Averaged Navier Stokes simulations with a mixing plane approach (MPA). Full unsteady simulations were carried out on selected inlet conditions and compared to the mixing plane results. This parametric study provides turbine designers with recommended diffusion rates along the vane EWs. Additionally, we provide guidance on the upstream diffuser design, specifically the required damping and outlet Mach number.

Effect of Impeller Parameters on the Flow inside the Centrifugal Blower using CFD

A numerical analysis is carried out to understand the flow characteristics for different impeller configurations of a single stage centrifugal blower. The volute design is based on constant velocity method. Four different impeller configurations are selected for the analysis. Impeller blade geometry is created with point by point method. Numerical simulation is carried out by CFD software GAMBIT 2.4.6 and FLUENT 6.3.26. GAMBIT work includes geometry definition and grid generation of computational domain. This process includes selection of grid types, grid refinements and defining correct boundary conditions. Processing work is carried out in FLUENT. The viscous Navier-Stokes equations are solved with control volume approach and the k-ε turbulence model. In this three dimensional numerical analysis is carried out with steady flow approach. The rotor and stator interaction is solved by mixing plane approach. Results of simulation are presented in terms of flow parameters, at impeller outlet and various angular positions inside the volute. Also, the contours of flow properties are presented at the outlet plane of fluid domain. Results suggest that for the same configurations of centrifugal blower, as we change geometrical parameter of impeller the flow inside the blower get affected.

Comparative Study on Steady and Unsteady Flow in a Centrifugal Compressor Stage

Steady Reynolds-averaged Navier-Stokes (RANS) simulation with the mixing-plane approach is the most common procedure to obtain the performance of a centrifugal compressor in an industrial development process. However, the accurate prediction of complicated flow fields in centrifugal compressors is the most significant challenge. Some phenomena such as the impeller-diffuser flow interaction generates the unsteadiness which can affect the steady assumption. The goal of this study is to investigate the differences between the RANS and URANS simulation results in a centrifugal compressor stage. Simulations are performed at three operating points: near surge (NS), design point (DP), and near choke (NC). The results show that the RANS simulation can predict the overall performance with reasonable accuracy. However, the differences between the RANS and URANS simulation are quite significant especially in the region that the flows are highly unsteady or nearly separated. The RANS simulation is still not very accurate to predict the time-dependent quantities of the flow structure. It shows that the URANS calculations are necessary to predict the detailed flow structures and performance. The phenomena and mechanisms of the complex and highly unsteady flow in the centrifugal compressor with a vaned diffuser are presented and analyzed in detail.

Thermal Performance Prediction in the Air Gap of a Rotor-Stator Configuration: Effects of Numerical Models

This study is dedicated to a numerical investigation of convective heat transfer on the rotor surfaces of a rotor-stator configuration that is typically found in large hydro-generators. The computational fluid dynamics calculations with two turbulence modelling approaches are used to predict the flow structure and heat transfer in the air gap of the rotor-stator configuration. The steady state mixing plane approach is employed at the interface to couple the rotor and stator components. Results show that the location of mixing plane interface in the air gap plays an important role in the prediction of heat transfer on the pole face. Also, it is indicated that the prediction of temperature distribution on the pole face is greatly affected by the turbulence models used. Furthermore, through a comparison between the pure convective and conjugate heat transfer methodologies, it is shown that the inclusion of solid domain into the numerical model significantly improves the thermal prediction of the solid components of the machine.

Quantitative Computational Fluid Dynamics Analyses of Particle Deposition in a Heavy-Duty Subsonic Axial Compressor

Solid particle ingestion is one of the principal degradation mechanisms in the compressor and turbine sections of gas turbines. In particular, in industrial applications, the microparticles not captured by the air filtration system can cause deposits on blading and, consequently, result in a decrease in compressor performance. In the literature, there are some studies related to the fouling phenomena in transonic compressors, but in industrial applications (heavy-duty compressors, pump stations, etc.), the subsonic compressors are widespread. It is highly important for the manufacturer to gather information about the fouling phenomenon related to this type of compressor. This paper presents three-dimensional (3D) numerical simulations of the microparticle ingestion (0.15–1.50 μm) in a multistage (i.e., eight stage) subsonic axial compressor, carried out by means of a commercial computational fluid dynamic (CFD) code. Particles of this size can follow the main air flow with relatively little slip, while being impacted by flow turbulence. It is of great interest to the industry to determine which zones of the compressor blades are impacted by these small particles. Particle trajectory simulations use a stochastic Lagrangian tracking method that solves the equations of motion separately from the continuous phase. The adopted computational strategy allows the evaluation of particle deposition in a multistage axial compressor thanks to the use of a mixing plane approach to model the rotor/stator interaction. The compressor numerical model and the discrete phase model are set up and validated against the experimental and numerical data available in the literature. The number of particles and sizes is specified in order to perform a quantitative analysis of the particle impacts on the blade surface. The blade zones affected by particle impacts and the kinematic characteristics (velocity and angle) of the impact of micrometric and submicrometric particles with the blade surface are shown. Both blade zones affected by particle impact and deposition are analyzed. The particle deposition is established by using the quantity called sticking probability (SP), adopted from the literature. The SP links the kinematic characteristics of particle impact on the blade with the fouling phenomenon. The results show that microparticles tend to follow the flow by impacting on the compressor blades at full span. The suction side (SS) of the blade is only affected by the impacts of the smallest particles. Particular fluid dynamic phenomena, such as corner separations and clearance vortices, strongly influence the impact location of the particles. The impact and deposition trends decrease according to the stages. The front stages appear more affected by particle impact and deposition than the rear ones.

Assessment of Steady and Unsteady Full Annulus Simulations Predictivity for a Low-Speed Axial Fan at Load-Controlled Windmill

A steady mixing plane approach is compared with the time-averaged solution of an unsteady full annulus calculation for a conventional fan operating at load-controlled windmill. The objective is to assess the added value of a complete unsteady calculation compared with a more classical approach, especially concerning the effect of the spatial and temporal periodicity release in such an unusual operation as windmill. Experiment with global steady measurements and rotor radial characterizations was conducted. Numerical analysis demonstrates that windmilling global performances obtained with the time-averaged solution of the unsteady simulation are not far different from the steady case, especially in the rotor. Some differences arise in the stator, particularly regarding the velocity field. Temporal periodicity release in this row has clearly a significant effect on the flow unsteady response. A detailed analysis highlights that generic patterns of windmilling flows recorded on a steady approach are also reported on the unsteady case.

Design of radial turbomachinery for supercritical CO2 systems using theoretical and numerical CFD methodologies

In high temperature waste heat to power conversion applications, bottoming thermodynamic cycles using carbon dioxide in supercritical phase (sCO2) have recently become a promising developing technology that could outperform conventional Organic Rankine Cycle systems in terms of efficiency and compactness. Moreover, carbon dioxide is a fluid chemically stable, reliable, low-cost, non-toxic, non-flammable and readily available. Supercritical CO2 power generation systems have been investigated by scientists and engineers mostly for large scale applications. However, when the electrical target output power is lower (50-100 kW), there are additional challenges on the turbomachinery design that need to be addressed. In the current research work, with reference to simple regenerative cycle architecture, the design of small scale sCO2 radial compressor and turbine are firstly addressed through the similarity approach. Further to this study, numerical CFD simulations are performed to optimize the 3D design of the impellers and of the stators. In particular, steady state RANS simulations using the mixing plane approach are carried out taking into account real gas properties for CO2.

Multiple-Frequency Phase-Lagged Unsteady Simulations of Experimental Axial Compressor

This paper presents an evaluation of the multiple-frequency phase-lagged approach, which enables the performance of unsteady Reynolds-averaged Navier–Stokes simulations on multistage turbomachinery configurations using a time-marching method. The major advantage of this approach is to reduce the computational domain to one single blade passage per row. The first part of the paper presents the method and discusses the associated assumptions and limitations. The method is then evaluated on the axial compressor configuration “Compresseur de Recherche pour l’Etude des effets Aérodynamiques et TEchnologiques” investigated experimentally at Laboratory of Fluid Mechanics and Acoustics. The computational fluid dynamics results are analyzed and compared both with experimental data and with a reference multipassage computation based on a sliding mesh approach. These comparisons enable the highlighting of the interests of this approach but also the underlining of its limits. The multiple-frequency phase-lagged approach enables the simulation of unsteady effects on a multistage turbomachinery and access to unsteady information that would not be available with a mixing-plane approach. However, if the method is capable of capturing unsteady effects linked to the adjacent upstream and downstream blade rows passing frequency, it fails modeling clocking effects, i.e., the relative influence between rows and .

Numerical Investigation of the Interaction between Mainstream and Tip Shroud Leakage Flow in a 2-Stage Low Pressure Turbine

The pressing demand for future advanced gas turbine requires to identify the losses in a turbine and to understand the physical mechanisms producing them. In low pressure turbines with shrouded blades, a large portion of these losses is generated by tip shroud leakage flow and associated interaction. For this reason, shroud leakage losses are generally grouped into the losses of leakage flow itself and the losses caused by the interaction between leakage flow and mainstream. In order to evaluate the influence of shroud leakage flow and related losses on turbine performance, computational investigations for a 2-stage low pressure turbine is presented and discussed in this paper. Three dimensional steady multistage calculations using mixing plane approach were performed including detailed tip shroud geometry. Results showed that turbines with shrouded blades have an obvious advantage over unshrouded ones in terms of aerodynamic performance. A loss mechanism breakdown analysis demonstrated that the leakage loss is the main contributor in the first stage while mixing loss dominates in the second stage. Due to the blade-to-blade pressure gradient, both inlet and exit cavity present non-uniform leakage injection and extraction. The flow in the exit cavity is filled with cavity vortex, leakage jet attached to the cavity wall and recirculation zone induced by main flow ingestion. Furthermore, radial gap and exit cavity size of tip shroud have a major effect on the yaw angle near the tip region in the main flow. Therefore, a full calculation of shroud leakage flow is necessary in turbine performance analysis and the shroud geometric features need to be considered during turbine design process.

Assessment of an implicit mixing plane approach for pump-turbine applications

In the design process of pump-turbines, both in pump and turbine mode, the assessment of the components matching is very important. In order to be fast in this task, the usual procedure is based on steady-state methods, like the frozen-rotor or the mixing-plane method.The frozen-rotor approach is straight forward and relatively easy to implement, but can produce unphysical behavior, mainly depending on the relative position of the components. On the other hand, the mixing-plane has a more physical background, delivering to the downstream component the mixed-out state of the upstream flow. On how the mixed-out state is computed and imposed to the downstream component there are different methodologies.In the present paper a novel, fully-implicit mixing-plane method is presented and applied to pump-turbine applications, both in pump and turbine mode.The major advantage of this approach is its robustness, including the ability to handle back flow at the interface, and accuracy. Compared to currently available methods, both in proprietary and commercial codes, the implicit approach leads to a consistent treatment of the interface, enforcing natively the idea of the mixing-plane, i.e. constant spanwise-distribution of the quantities. This allows to obtain excellent results also at part- and over-load.

The Influence of Inlet Asymmetry on Steam Turbine Exhaust Hood Flows.

It has been widely recognized for some decades that it is essential to accurately represent the strong coupling between the last stage blades (LSB) and the diffuser inlet, in order to correctly capture the flow through the exhaust hoods of steam turbine low pressure cylinders. This applies to any form of simulation of the flow, i.e., numerical or experimental. The exhaust hood flow structure is highly three-dimensional and appropriate coupling will enable the important influence of this asymmetry to be transferred to the rotor. This, however, presents challenges as the calculation size grows rapidly when the full annulus is calculated. The size of the simulation means researchers are constantly searching for methods to reduce the computational effort without compromising solution accuracy. However, this can result in excessive computational demands in numerical simulations. Unsteady full-annulus CFD calculation will remain infeasible for routine design calculations for the foreseeable future. More computationally efficient methods for coupling the unsteady rotor flow to the hood flow are required that bring computational expense within realizable limits while still maintaining sufficient accuracy for meaningful design calculations. Research activity in this area is focused on developing new methods and techniques to improve accuracy and reduce computational expense. A novel approach for coupling the turbine last stage to the exhaust hood employing the nonlinear harmonic (NLH) method is presented in this paper. The generic, IP free, exhaust hood and last stage blade geometries from Burton et al. (2012. "A Generic Low Pressure Exhaust Diffuser for Steam Turbine Research,"Proceedings of the ASME Turbo Expo, Copenhagen, Denmark, Paper No. GT2012-68485) that are representative of modern designs, are used to demonstrate the effectiveness of the method. This is achieved by comparing results obtained with the NLH to those obtained with a more conventional mixing-plane approach. The results show that the circumferential asymmetry can be successfully transferred in both directions between the exhaust hood flow and that through the LSB, by using the NLH. This paper also suggests that for exhaust hoods of generous axial length, little change in Cp is observed when the circumferential asymmetry is captured. However, the predicted flow structure is significantly different, which will influence the design and placement of the exhaust hood internal "furniture."

Influence of Periodic Unsteady Effects on Flow and Performance Prediction on an Axial High Pressure Compressor

A numerical assessment of unsteadiness and information losses due to boundary conditions, especially the rotor-stator interface treatment in an axial high pressure compressor (HPC) is proposed. Steady and unsteady computations are performed on a three-stage axial HPC with a 3D Navier-Stokes code. The steady simulation is based upon periodic boundary condition for azimuthal frontiers and the mixing plane approach which averages circumferentially the information coming from the adjacent blade row. The unsteady one uses the phase-lag method for both azimuthal frontiers and rotor-stator interface. The unsteady simulation highlights the wake effects in the stator passage due to the wakes released by the rotor and the potential effects on the wall pressure of the rotor blades due to the stator blades. The comparison between the steady and the time-averaged unsteady simulations shows a good agreement in the information transfer at the rotor-stator interface. The main discrepancy appears in the static pressure field on the rotor side of the interface, due to the inability of the steady computation to capture the potential effects. The radial profiles and the performances obtained with these two simulations are very similar. Thus a steady computation results in flow field and performance predictions with a sufficient accuracy. This comparison confirms the validity of using the mixing plane approach for HPC design.

Assessment of various rotor tip geometries on a single stage gas turbine performance

Tip leakage loss introduces major part of losses of the rotor in axial gas turbines. Therefore, the rotor blade tip has a considerable effect on rotor efficiency. To understand the flow physics of the rotor tip leakage, we solve the flow field for different tip platforms (passive flow control) and by considering coolant tip injection (active flow control). Various blade tip configurations such as squealers and extensions on both pressure and suction sides, partial PS-squealer and flat tip with various tip clearances are generated. The computational domains are generated using unstructured prism layers for boundary layer resolution and unstructured, tetrahedral mesh for main flow. By using a finite volume CFD solver capable of solving RANS equations in an unstructured domain, the transonic compressible flow in the domain is solved. To capture the turbulent field in blade tip, shear stress transport (SST) k-ω model is employed. By using mixing plane approach, it is possible to couple outlet boundary of stator and inlet boundary of rotor and investigate the stator-rotor interaction in the rotor flow field and its consequence tip leakage flow. To investigate the combined effects of active and passive flow control measures in blade tip region, we simulate baseline geometry with and without tip coolant to show the effects of geometrical features of the rotor tip as well as the effect of tip coolant mass flow rate. Taking into account various rotor tip configurations and their tip leakage losses, it is possible to propose an optimum configuration.

Numerical assessment on improving multistage centrifugal impeller performance by changing inlet skew angle at impeller inlet

Multistage centrifugal impellers with four different skew angles were investigated by using computational fluid dynamics. The purpose of this work is to investigate the influences of lean angle at the blade tip of the impeller inlet. Four variations of lean angles, that is, 8°, 10°, 15° and 20°, were made at first stage impeller. Reynolds Average Navier Stokes equation was used in simulation together with a shear-stress transport (SST) k-w turbulence model and mixing-plane approach, respectively. Three dimensional fluid flows were simplified using periodic model to reduce the computational cost and time required. A good performance was expected that the secondary flow can be effectively reduced in the flow passage of the impeller without excessive increase in manufacturing cost caused by the secondary flow. The results show that secondary flow affects the main flow intricately to form vortices or having non-uniform velocity in the flow passage, which in turn results in substantial fluid energy loss not only in the impeller but also in the guide vane downstream of impeller. The numerical solutions were performed and allowed the optimum design and operating conditions to be obtained.