Multi-Dimensional Coupling CFD Method for Shrouded Turbines

Tip leakage is generated inevitably by the clearance between the rotating blades and the stationary casing of a turbine, and is responsible for both the aerodynamic losses in a turbine stage and the high heat-loads in the tip region [2]. To decrease tip leakage and improve component performance, shroud seal structures have been widely applied to modern turbine components, especially to low pressure turbines, because of their advantage on both aerodynamic and structural features. However, due to the complexity of the shroud geometry, the flow structures and thermodynamic process in shroud can be extremely complicated, that is interactions of vortices, separations, jet flow, etc. Thus, because of the complex geometry of shrouds, as well as strong interactions between the tip leakage and main flow, it is not easy to draw a numerical simulation with satisfactory accuracy and time-costing in shrouded turbines. This begs the question of what should the compromise be between using simplified loss models and full 3D CFD analysis for leakage modelling?

In the main flow path of a turbine the flow will always be dominated by the blades shape, while for leakage cases the flow will be dominated by the motion and evolution of small eddies. Rosic et al. [1] reviewed the importance of shroud leakage modelling in multistage turbines. The comparison of measurements and 3D calculations shows that the flow in shrouded low aspect ratio turbines is dominated by shroud leakage. This is especially true as regards the loss distribution. The rotor shroud leakage flow greatly increases the secondary flow in the downstream stators and drives low energy fluid towards mid-span. It was pointed out that with very low values of shroud leakage the flow is reasonably well modelled by a simple 1D model of the leakage flow, using sources and sinks on the casing. However, for more representative real clearances, full 3D modelling of the seal and cavity flows is necessary in order to obtain reasonable agreement. Given that developing a simulation method with both high precision and fast solving speed is imperatively demanded for engineers to assess new designs, Zhengping Zou et al. [2] suggested that one of the potential approaches for solving the problem is a method that couples low dimensional models, 1D and 2D models, of the shroud flow with 3D (three-dimensional) simulations of the main flow passage. Specifically, some boundary source and boundary sink is set on the interface between the shroud and the main flow passage, and the source term and sink term are determined by the shroud leakage model. The schematic of this process is given in Fig. 1. The results of his study [2] demonstrate that the proposed models and methods will contribute to pursue deeper understanding and better design methods of shrouded axial turbines.

cfd
Figure 1: (a) Schematic of full 3D computation; (b) Schematic of multi-dimensional coupling simulation. [2]
 Check out AxSTREAM CFD for your designing needs!

References:

[1] “The Importance of Shroud Leakage Modeling in Multistage Turbine Flow Calculations”, Budimir Rosic, John D. Denton, and Graham Pullan, Journal of Turbomachinery, Vol 128, pp. 699-707, October 2006

[2] “Shroud leakage flow models and a multi-dimensional coupling CFD (computational fluid dynamics) method for shrouded turbines”, Zhengping Zou, Jingyuan Liu, Weihao Zhang, and Peng Wang, Energy journal, Vol 103, pp. 410-249

Mesh Generation Characteristics for an Accurate Turbomachinery Design

This post will examine the meshing requirements for an accurate analysis of flow characteristics in terms of turbomachinery applications, based on Marco Stelldinger et al study [1]. Computational Fluid Dynamics (CFD) are widely used for the analysis and the design of turbomachinery blade rows.  A well-established method is the application of semi-unstructured meshes, which uses a combination of structured meshes in the radial direction and unstructured meshes in the axial as well as the tangential direction. Stelldinger’s paper presents a library for turbomachinery meshing, which enables the generation of semi-unstructured meshes for turbomachinery blade passages, including cavities, fillets and varying clearance sizes. The focus lies on the generation of a mesh that represents the real geometry as accurately as possible, while the mesh quality is preserved.

The above was achieved by using two different approaches. The first approach divides the blade passage into four parts. Inside of these parts, a structured grid is generated by solving a system of elliptic partial differential equations. The second approach is based on the domain being split into fourteen blocks. It has benefits concerning computational time towards the first one, because of a faster generation procedure as well as a faster performance of the inverse mapping.

Mesh View
Figure 1 Mesh View

Another key aspect in mesh generation is the improvement of the mesh quality applying suitable methods. Since mesh smoothing algorithms have been shown to be effective in improving the mesh quality, two smoothing algorithms, a constrained Laplace smoothing and an optimization-based smoothing were presented. Both algorithms showed benefits concerning the achieved mesh quality compared to the standard Laplace smoothing, while the computational time is longer. For the investigated turbomachinery meshes the constrained Laplace smoothing is exposed as the most feasible choice, because of a suitable combination of mesh quality and computational time.

Several methods for the modelling of fillets between blade and the casing were also presented. The methods provide meshes with different qualities, that results into different convergence rates and residuals. Furthermore, the axisymmetric surfaces are dependent on the axial position that enables the modelling of clearances with a variable size. CFD simulations for a variable stator vane with a constant clearance size between blade and inner casing as well as with a variable clearance size were performed. The results show a different flow behavior near the clearance. This emphasizes the requirement of an accurate representation of the real geometry for CFD simulations of turbomachinery flows.

mesh-view
Figure 2: AxCFD mesh view

The AxCFD module of the AxSTREAM platform allows the user to employ an automatic turbomachinery-specific, structured hexagonal meshing by customization in the setup period. Different types of mesh generation are available and can be refined in each direction. Take some time to use AxSTREAM and enjoy the design process!

Enhanced Design Capabilities Using CFD

The use of computational fluid dynamics (CFD) in turbomachinery design is getting more and more popular given the increased computational resources. For the design process, however, there is no need for extensive CFD capabilities as the effort is put on minimizing engineering time while obtaining a design which is about 90% optimized. Here we are presenting two cases where CFD is used to derive significant information for pump design.

First, the influence of the blade shape on the parameters of the single blade hydrodynamic pump was studied by Knížat et al [1]. The investigation of the pump properties was carried out experimentally with a support of CFD methods. The accuracy of applied steady-state calculations was satisfactory for the process of design of a single blade pump, because of the good agreement between measured and calculated power curves.

For the CFD the Menter SST (shear stress transport) model of turbulence was chosen. This model effectively combines robustness and accuracy of the k-ω model in regions close to the wall with the model k-ε working better in a free stream away from the wall. These improvements make the SST model more accurate and reliable compared with the standard k-ω model. The CFD calculations served for the estimation of pump power curves. The specific energy, torque and hydraulic efficiency were evaluated for each flow rate.

This studied showed that the position of the best efficiency point is sensitive on the blade shape. Thus, it is necessary to form the blade more carefully than in a case of a classical multi-blade pump. It also follows from the calculations that the pump flow is non-symmetrical and it may cause increased dynamical load of the shaft.

In a second study conducted by Yang et al, a double volute centrifugal pump with relative low efficiency and high vibration was redesigned to improve the efficiency and reduce the unsteady radial forces with the aid of unsteady CFD analysis. The concept of entropy generation rate was proposed to evaluate the magnitude and distribution of the loss generation inside the pump. It was found that the wall frictions, wakes downstream the blade TE, flow separation near hub on pressure surface side, and mixing loss in volute are the four main sources leading to significant entropy generation in baseline pump. In the redesigned model, the entropy generation near the hub on pressure surface side was diminished and the loss in the volute was also reduced, while the loss generated by wall friction was increased with the blade number increasing. In general, the entropy generation rate was a useful technique to identify the loss sources and it is really helpful for the redesign and optimization of pumps. The local Euler head distribution (LEHD) obtained in viscous flow was proposed to evaluate the flow on constant span stream surfaces from the hub to shroud. It was found that Kutta condition was not necessarily satisfied at blade leading edge in viscous flow. A two-step-form LEHD was recommended to suppress flow separation and secondary flow near the hub on pressure side of the blade in a centrifugal impeller. The impeller was redesigned with two-step-form LEHD, and the splitter blades were added to improve hydraulic performance and to reduce unsteady radial forces.

The use of CFD integrated in a streamline engineering platform like AxSTREAM would be a valuable tool for every engineer. Try AxSTREAM and AxCFD to conduct your own research and lead to significant outcomes related to turbomachinery design, analysis and optimization!

 

[1] Impeller design of a single blade hydrodynamic pump, Knížat,B. and Csuka,Z. and Hyriak,M., AIP Conference Proceedings, Volume 1768, 016

[2] Computational fluid dynamics- based pump redesign to improve efficiency and decrease unsteady radial forces. Yan, P., Chu, N., Wu, D., Cao, L., Yang, S., & Wu, P. (2017).  Journal of Fluids Engineering, Transactions of the ASME, 139(1)

Gaining Turbomachinery Insight Using a Fluid Structure Interaction Approach

Existing research studies for the corresponding flow-induced vibration analysis of centrifugal pumps are mainly carried out without considering the interaction between fluid and structure. The ignorance of fluid structure interaction (FSI) means that the energy transfer between fluid and structure is neglected. To some extent, the accuracy and reliability of unsteady flow and rotor deflection analysis should be affected by this interaction mechanism.

In recent years, more and more applications of FSI are found in the reliability research of turbomachinery. Most of them are about turbines, and a few of them address pumps. Kato [1] predicted the noise from a multi-stage centrifugal pump using one-way coupling method. This practical approach treats the fluid physics and the solid physics consecutively.

cent-pump
Figure 1: Multistage centrifugal pump [1].
In the CFD computations of the internal flows, Kato could successfully predict the pressure fluctuations despite turbulent boundary layer in the impeller passages was not resolved. The computed pressure fluctuations on the internal surface agreed well with the measured ones not only at the blade passing frequencies, (BPF) but also on the base level. By visualizing the distributions of the pressure fluctuations at the BPFs, it was found that the fluctuation was especially high at the second harmonics of the BPF. This was consistent with the vibration velocity measured on the outer surface. On the other hand, he overpredicted the total head by about 10%. This is because turbulent boundary layer in the impeller passage was not resolved, and therefore, the blockage effect was not taken into account appropriately at this stage of the research.

Vibration of the structure portion was then calculated by a dynamical structural analysis with the calculated pressure fluctuations on the internal surface as input data. It was clearly shown that the dominant vibrations of the pump originate from the rotor-stator interaction. The trivial vibrations were damped off over time. The vibration levels of the BPF on the outer surface of the pump structure agreed reasonably well with the  measured ones. The computations revealed the feasibility of the fluid-structure coupled simulation for flow-induced noise generated in turbomachinery.

Another example of fluid-structure interaction was presented by Pei et. Al [2] when an axial-flow pump device with a two-way passage was studied. A coupled solution of the flow field and structural response of the impeller was established using a two-way coupling method to study the distribution of stress and deformation in the impeller and quantitatively analyze that on the blade along the wireframe paths had different flow rates. This studied showed that the maximum equivalent stress and maximum total deformation in the impeller are greatly influenced by flow rate, and its values drops with an increasing flow rate and a decreasing head. In addition, the total deformation in the impeller is greater near the blade rim, where the maximum value can be found. The equivalent stress is greater near the blade hub, where the maximum value can be obtained.

The above studies are the best proof that by using the right methods, tools and expertise you can get an insight for any kind of turbomachinery. Try AxSTREAM using the CFD and FEA integrated modules to design your machine and understand the fundamentals of its operation in depth.

References:

[1] Prediction of the Noise From a Multi-Stage Centrifugal Pump, Chisachi Kato, Shinobu Yoshimura, Yoshinobu Yamade, Yu Yan Jiang, Hong Wang, Ryuta Imai, Hiroyuki Katsura, Tetsuya Yoshida and Yashushi Takano , ASME 2005 Fluids Engineering Division Summer Meeting, Volume 1: Symposia, Parts A and B, Houston, Texas, USA, June 19–23, 2005

[2] Fluid–structure coupling analysis of deformation and stress in impeller of an axial-flow pump with two-way passage, Ji Pei, Fan Meng, Yanjun Li, Shouqi Yuan, Jia Chen, National Research Center of Pumps, Jiangsu University, Zhenjiang, China

A Reasonable Approach to Pump Design While Avoiding Resonance

For the majority of pump application, the growing use of variable speed operation has increased the likelihood of resonance conditions that can cause excessive vibration levels, which can negatively impact pump performance and reliability. Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations (external excitation source) matches the system’s natural frequency of vibration more than it does at other frequencies. To avoid vibration issues, potential complications must be properly addressed and mitigated during the design phase.

Some of the factors that may cause excitation of a natural frequency include rotational balance, impeller exit pressure pulsations, and gear couplings misalignment. The effect of the resonance can be determined by evaluating the pumping machinery construction. All aspects of the installation such as the discharge head, mounting structure, piping and drive system will affect lateral, torsional and structural frequencies of the pumping system. It is advised that the analysis be conducted during the initial design phase to reduce the probability of reliability problems and the time and expense associated.

Natural frequencies of a pump and motor can be calculated by performing a modal analysis using the Finite Element Method Analysis (FEA). The finite element modelling and analysis techniques provide an understanding of the mechanical system behaviour, including the natural frequency values during design phase.

Understanding the predicted natural frequency values allows an evaluation of the expected separation between the pump natural frequency and excitation frequencies, such as pump operation speed. The separation is established by the pump manufacturer to avoid mechanical resonance.

The boundary conditions assumed during FEA are essential to the accuracy of predicted results. In some cases, the final as-built conditions (such as foundation stiffness) significantly affect the analysis accuracy if they differ from those conditions assumed during the analysis. In such case a pump test is recommended. Tests like that indicate that increasing the natural frequency of the system is the best solution. This increase in natural frequency could be accomplished by modifying two of the pump system’s physical characteristics, reducing mass or increasing stiffness of the system.

It is therefore important to know the type of acceptable solution that will provide the best pump operation. And this is where AxSTREAM adds significant value at the design process. Using SoftInWay fully integrated engineering platform the customers are able to optimize the pumping machine, and next to perform all the necessary structural analysis using AxSTRESS, our express structural, modal and harmonic analysis FEM solver with a customizable, automatic turbomachinery-specific mesh generation.

Source:

http://empoweringpumps.com/lateral-torsional-structural-analyses-pumps-can-avoid-vibration-problems-pump-issues-related-resonance-conditions/

http://www.pumpsandsystems.com/topics/pumps/vertical-turbine-pumps/structural-resonance-problems-vertical-pumps

The Importance of Turbulence Modelling

What is the importance of turbulence modelling in capturing accurate 3D secondary flow and mixing losses in turbomachinery? An investigation on the effect of return channel (RCH) dimensions of a centrifugal compressor stage on the aerodynamic performance was studied to answer this question by A. Hildebrandt and F. Schilling as an effort to push turbomachinery one step further.

W. Fister was among the first to investigate the return channel flow using 3D-CFD. At that time the capability of commercial software was not extended and any computational effort was limited by the CPU-capacity. Therefore, only simplified calculations that included constant density without a turbulence model (based on the Prandtl mixing length hypothesis) embedded in in-house code, were performed.

Although separated flow without a predominant flow direction could not have been calculated, the method indicated separated flow regions with relatively accurate precision, and it predicted the magnitude of loss coefficients to a higher degree than experimental data. The study was further
simplified using incompressible flow, and an axial U-turn inlet flow.AxCFD

The biggest drawback of using inverse methods for return channel design refers to the question of appropriate flow distribution across the RCH surface. Furthermore, flow separation cannot be predicted with the help of singularity methods. In order to circumvent the problem of predicting flow separation, nowadays compressible viscous 3D-CFD applied with different highly complex turbulence modeling is the state of the art even at the conceptual stage of the design.

Hildebrandt and F. Schilling analyzed three different centrifugal stages regarding the return channel system performance. All three stages featured the same impeller type, two of them being applied with a 3D-RCH at different flow coefficient and one impeller being applied with a 2D-RCH system. The 3D-RCH stage featured both CFD calculated and measured superior aerodynamics over the 2D-RCH stage regarding the overall performance as well as regarding the outlet flow angle. The comparison between the measured and the CFD-predicted performance showed agreement both when it comes to overall performance (efficiency, pressure rise coefficient) and also regarding detailed flow field (outlet flow field). The 3D secondary flow and mixing losses of the entire domain downstream the vaneless diffuser were either underestimated or overestimated by the CFD-calculations, depending on the turbulence modeling and the impeller fillet radii-modeling which affects the RCH-inlet flow conditions. The effect of fillet radii-modeling on the RCH-exit flow angle spanwise distribution was found to be significant in order to better match the experimental results.

It is worth noting that the rather simple Spalart–Allmaras turbulence model provided better agreement with the measured RCH-exit flow angle distribution than the more sophisticated k-epsilon model, which on the other hand, outputted a closer fit with the measured surface vane pressure distribution. Regarding the RCH total pressure loss distribution, none of the models showed a perfect agreement with the measurement data.

Moreover, the incident losses of the 3D-RCH system seemed to play a minor role within the overall RCH-loss which is significantly dominated by the 3D-secondary losses.

Interested in learning more? Check out AxSTREAM and AxCFD!

[1] A. Hildebrandt and F. Schilling, 2017 “Numerical and Experimental Investigation of Return Channel Vane Aerodynamics With Two-Dimensional and Three-Dimensional Vanes”, Journal of Turbomachinery Vol. 139 / 011010-1

[2] Fister, W., Zahn, G., and Tasche, J., 1982, “Theoretical and Experimental Investigations About Vaneless Return Channels of Multi-Stage Radial Flow Turbomachines,” ASME Paper No. 82-GT-209.