Turbomachinery Rotor Dynamics – Latest Modelling & Simulation CAE for Design and Analysis, using SoftInWay’s Integrated Tool

The Rotor-Dynamic System of a typical turbomachine consists of rotors, bearings and support structures. The aim of the designer undertaking analysis is to understand the dynamics of the rotating component and its implication. Today the industry practices and specifications rely heavily on the accuracy of rotor-dynamic simulated predictions to progressively reduce empirical iterations and save valuable time (as repeated direct measurements are always not feasible). Be it a centrifugal pump or compressor, steam or gas turbine, motor or generator, the lateral rotor-dynamic behavior is the most critical aspect in determining the reliability and operability. Such analytical predictions are often tackled using computer models and accuracy in representing the physical system is of paramount importance.  Prior to analysis it is necessary to create a detailed model, and hence element such as cylindrical, conical , inner bore fillet/chamfer, groove/jut, disk / blade root and shroud, copy/mirror option, bearing element and position definition are built. Stations (rather than nodes) having six DOF (degrees of freedom) are used to model rotor-dynamic systems. Typically for lateral critical analysis each station has four DOF, two each translational and rotational (angular). Decoupled analysis followed by coupled lateral, torsional and axial vibration makes prediction realistic and comprehensive. The mathematical model has four essential components, i.e. rotating shafts with distributed mass and elasticity, disks, bearing and inevitable synchronous imbalance excitation. Components such as impellers, wheels, collars, balance rings, couplings – short axial length and large diameter either keyed or integral on shaft are best modelled as lumped mass. Bearings, dampers, seals, supports, and fluid-induced forces can be simulated with their respective characteristics. Bearing forces are linearized using dynamic stiffness and damping coefficients and together with foundation complete the bearing model. The governing equation of motion for MDOF system require  determination of roots (Eigenvalue) and Eigen Vectors. Lateral analyses – such as static deflection and bearing loads, critical speed analysis, critical speed map, unbalance response analysis, whirl speed and stability analysis, torsional modal and time transient analyses are then performed.Aashish blog 1 image

Indeed rotor-dynamic modelling with practical experience and engineering judgement improves accuracy.  Its ability to model complexities such as flexible supports, foundation, rotor seal interaction, and instabilities while making the CAE model comprehensive, user friendly, and fully integrated with other well proven and mature suites for flow path and  blade design makes SofInWay’s software platform unique.

Integrated Approach within AxSTREAM® Platform

Suited to meet the diverse needs of designers, analysts and users of turbomachinery, SoftInWay’s webinar in collaboration with Test Devices Inc scheduled on Mar 2, 2017, 10 AM EST helps you to understand HOW rather than why. It will  cover rotor and bearing types, principles of an integrated approach to rotor-dynamics system design and simulation, purpose and procedures for rotor-dynamic and structural analysis. The software demonstration will include modelling features, import/export options, lateral and torsional capabilities, bearing analyses and modelling capabilities, and case studies. It will also briefly highlight fundamentals such as characteristic influence of shaft rotational on natural frequencies in comparison to classical natural frequencies and modes in structures, gyroscopic effects, rigid vs flexible rotors, free and forced vibration as applicable to turbomachine rotors, impact of bearing characteristics and concept of cross coupling, modes, Campbell diagram, stead and transient response, instabilities, condition monitoring, testing, evaluation and acceptance criteria (log dec and margins) and much more. Testing methods covered by Tech Devices Inc. highlight testing procedures and methods for design validation and building confidence that the design exceeds expectations.

 

Surge Conditions of Centrifugal and Axial Compressors

Centrifugal and axial compressors must operate within certain parameters dictated by both the constraints of the given application as well as a number of mechanical factors.  In general, integrated control systems allow compressors to navigate dynamically within their stable operating range.   Typical operating ranges for compressors are represented on a plot of volumetric flow rate versus compression ratio.  Compressors have a wide number of applications, from household vacuum cleaners to large 500 MW gas turbine units.  Compression ratios found in refrigeration applications are typically around 10:1, while in air conditioners they are usually between 3:1 and 4:1.  Of course, multiple compressors can be arranged in series to increase the ratio dramatically to upwards of 40:1 in gas turbine engines.  While compressors in different applications range dramatically in their pressure ratios, similar incidents require engineers to carefully evaluate what is the proper operating range for the particular compressor design.

Dan Post 10
Figure 1- Typical Performance Map Limits – Compressor Ratio (Rc) vs. Volumetric Flow Rate (Qs)

For intensive applications of centrifugal and axial compressors, the phenomenon of surge resides as one of the limiting boundary conditions for the operation of the turbomachine. Essentially, surge is regarded as the phenomena when the energy contained in the gas being compressed exceeds the energy imparted by the rotating blades of the compressor. As a result of the energetic gas overcoming the backpressure, a rapid flow reversal will occur as the gas expands back through the compressor. Once this gas expands back through to the suction of the compressor, the operation of the compressor returns back to normal. However, if preventative measures are not taken by the appropriate controls system or any implemented mechanical interruptions, the compressor will return to a state of surge. This cyclic event is referred to as surge cycling and can result in serious damage to the rotor seals, rotor bearings, driver mechanisms, and overall cycle operation.

Because of surge and other phenomena such as stall, engineers must embed proper control systems that effectively handle different off-design conditions seen in particular compressor arrangements. Depending on the application, certain compressors will rarely operate away from their design point, and such control systems are not necessary. However, in advanced applications such as large gas turbine unit compressors, controls systems allow the compressor to navigate within a range between the choke, stall, minimum speed, and maximum speed limits. The chart seen in Figure 1 describes the operating range of a compressor using a Rc—Qs map. In many cases, an antisurge valve (ASV) working in conjunction with an antisurge PI controller will action open or closed based on varying transient conditions seen on the compressor. For design purposes, it is vital to understand compressor limits in order to properly develop or outsource a compressor based on the performance metrics needed for the application.

Computational Fluid Dynamics in Turbomachinery Design

The evolution of turbomachinery technology can be traced back several centuries and has resulted in the high efficiency turbomachines of today. Since the 1940s, turbomachinery development has been led mainly by gas turbine and aeroengine development, and the growth in power within the past 60 years has been dramatic. The development of numerical methods and the increasing computing capacity helped establish a strong design capability in the industry.

The first numerical methods related to turbomachinery were developed years before the use of digital computations. In 1951 Wu [1] introduced the blade-to-blade (S1) and hub-to-tip (S2) stream surfaces, which dominated the field until the 1980s when computer resources made it possible to account for 3D methods. The axisymmetric S2 calculations, also called “throughflow calculation” became the backbone of turbomachinery design, while the S1 calculation remains the basis for defining the detailed blade shape.

Fully 3D methods replaced the stream surface calculations by a single calculation for the whole blade row. This removed the modelling assumptions of the quasi three-dimensional approach but required far greater computer power and so was not usable as a routine design tool until the late 1980s. For similar reasons, early methods had to use coarser grids that introduced larger numerical errors than in the Q3D approach. Such limitations are now overcome with the rapid growth of computer technology.

Nowadays, the design of advanced turbomachinery components [2] is facing more demanding requirements. Higher performance must be achieved within shorter design cycles and at lower cost. Ambitious objectives in the reduction of weight, complexity and manufacturing cost lead to fewer compressor and turbine stages, and therefore to increased stage loading. For designers, this new situation implies the capability to control the very complex flow phenomena occurring in highly loaded stages, on the whole operating range of the engine, early in the design process. In addition to aerodynamic performance, the aggressive design of advanced, fully 3D blades also requires an early focus on all the aspects related to engine mechanical limitations such as blade flutter, forced response and thermal constraint.

The increased requirements on 3D CFD modelling lead to parallel processing of the flow phenomena. The majority of commercial CFD tools demands additional cost for parallel computing, which increase the total cost of the design process. With AxCFD, the users have the opportunity to use parallel calculation without the need to pay extra! AxCFD along with all design modules is fully integrated in the AxSTREAM Software Suite, the most complete engineering platform on the market. Try it now and enjoy the comfort of designing turbomachines from scratch to complete 3D CAD in a couple of hours.

References:

[1] Wu, C. H. A general through flow theory of fluid flow with subsonic or supersonic velocities in turbomachines of arbitrary hub and casing shapes. NACA paper TN2302, 1951
[2] H. Joubert, H. Quiniou, “Turbomachinery designed used intensive CFD”, Snecma http://www.icas.org/ICAS_ARCHIVE/ICAS2000/PAPERS/ICA6104.PDF 

An Integrated Design System for Gas Turbines

In my earlier blog titled “Optimizing the Cooling Holes in Gas Turbine Blades, I wrote about how optimizing the cooling flow through turbine blades is important considering both performance and reliability. The design process differs between different designers and depends on a number of factors including expertise, availability of design tools, statistical or empirical data, corporate procedure and so on. That being said, the ultimate goal is to provide a design which is considered optimal. Though the designer is often satisfied on completion of a design and when the machine is put into operation, there is always the feeling  that we could have done better if there were more resources and time. Integrating the entire design process with multidisciplinary optimization provides a great opportunity to arrive at the optimal design rapidly with less manual intervention and effort.

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Figure 1: Integrated AxSTREAM® Platform

Figure 1 shows the integrated approach to design a cooled gas turbine using multidisciplinary tools in an optimization environment. The flow path design starts from the conceptual stage to arrive at the optimal flow path geometry, accounting for a preliminary estimate of the cooling flow. Detailed design requires accurate estimation of the cooling flow considering the actual geometries and the material temperatures. Using ID head and flow simulation tools such as AxSTREAM® NET, the cooling flow can be modelled to produce the optimal geometric dimension in an iterative process to further fine tune the flow path performance. To meet the performance and reliability objectives, multidisciplinary optimization can be achieved via the integrated modules. The process when further integrated with a CAD package can help in generating the optimized geometry that can be taken for prototype development.

To learn more about how the AxSTREAM® platform can help you obtain an optimized gas turbine design quickly and accurately, please contact sales@softinway.com; info@softinway.com.

Fatigue in Turbomachinery

This post is based on DeLuca’s publication about fatigue phenomena in gas turbines [1]. One of the most significant characteristics of a gas turbine is its durability. Especially for the aerospace industry where engines must meet not only propulsion but also safety requirements, the failure of gas turbine blades is a major concern. The “cyclic” loading of the components associated with generator excursions is one of the principal sources of degradation in turbomachinery. In addition, fatigue can be caused during the manufacturing of the components. There are three commonly recognized forms of fatigue: high cycle fatigue (HCF), low cycle fatigue (LCF) and thermal mechanical fatigue (TMF).The principal distinction between HCF and LCF is the region of the stress strain curve (Figure 1) where the repetitive application of the load (and resultant deformation or strain) is taking place.

gas-turbine-alloy
Figure 1 – The stress vs. strain curve for a typical gas turbine alloy

HCF is metal fatigue that results from cracking or fracturing generally characterized by the failure of small cracks at stress levels substantially lower than stresses associated with steady loading. HCF occurs as a result from a combination of steady stress, vibratory stress and material imperfections [2].  It is initiated by the formation of a small, often microscopic, crack. HCF is characterized by low amplitude high frequency elastic strains. An example of this would be an aerofoil subjected to repeated bending. One source of this bending occurs as a compressor or turbine blade passes behind a stator vane. When the blade emerges into the gas path it is bent by high velocity gas pressure. Changes in rotor speed change the frequency of blade loading. The excitation will, at some point, match the blade’s resonant frequency which will cause the amplitude of vibration to increase significantly.

In contrast, LCF is characterized by high amplitude low frequency plastic strains. A good example of LCF damage is of the damage which is caused by local plastic strains at the attachment surfaces between a turbine blade and the turbine disk. Most turbine blades have a variety of features like holes, interior passages, curves and notches. These features raise the local stress level to the point where plastic strains occur. Turbine blades and vanes usually have a configuration at the base referred to as a dovetail or fir tree.
In the case of thermal mechanical fatigue (present in turbine blades, vanes and other hot section components) large temperature changes result in significant thermal expansion and contraction and therefore significant strain excursions. These strains are reinforced or countered by mechanical strains associated with centrifugal loads as the engine speed changes. The combination of these events causes material degradation due to TMF.

As you can see, it is important to take into account stresses on gas turbine blades in order to determine the viability of the component. AxCFD and AxSTRESS are both vital tools that can help you quantify the stresses on your blades and make the correct decision for the choice of materials and operation conditions of the machine.

Reference:

[1] D.P.DeLuca, “Understanding fatigue”, United Technologies Pratt & Whitney;
[2] Sanford Fleeter, Chenn Zhou, Elias N. Houstin, John R. Rice, “Fatigue life prediction of turbomachine blading”, Purdue University.

Component Matching of Industrial Gas Turbines

An important first step in understanding the gas turbine design process is the knowledge of how individual components act given their particular boundary conditions. However, in order to effectively leverage these individual design processes, a basic knowledge of how these components interact with each other is essential to the overall performance of a gas turbine unit. The power and efficiency outputs of a gas turbine are the result of a complex interaction between different turbomachines and a combustion system. Therefore, performance metrics for a gas turbine are not only based on the respective performances of each turbine, compressor, and combustion system, but also on their interactions. The concept of component matching becomes crucial in understanding how to deal with these systems simultaneously.

two-shaft-gas-turbine
Figure 2 – Simplified Two-Shaft Gas Turbine Arrangement Modeled in AxCYCLE

In general, gas turbines for industrial applications consist of a compressor, a power turbine, and a gas generator turbine designed into one of two arrangements. The first arrangement invokes the use of the gas generator turbine to drive the air compressor, and a power turbine to load the generator on a separate shaft. This two-shaft arrangement allows the speed of the gas generator turbine to only depend on the load applied to the engine. On a single-shaft arrangement, the system obviously cannot exist at varied speeds and the power turbine coupled with the gas generator turbine would be responsible for driving both the generator and the compressor. A simplified diagram of each arrangement is displayed in Figures 1 and 2.

gas-turbine-arrangement-in-axcycle
Figure 1- Single-Shaft Gas Turbine Arrangement in AxCYCLE (Power Turbine and Gas Generator Turbine Considered One Turbine)

The efficiency of gas turbine engines can be improved substantially by increasing the firing temperature of the turbine, however, it is important to remember that the surface of the components exposed to the hot gas must remain below a safe working temperature consistent with the mechanical strength and corrosion resistance of the employed materials. Along with this firing temperature limit, obvious upper bounds exist on the speed of the gas generator due to mechanical failures and reduced lifetimes at high RPMs. These two limits help construct a particular range at which the engine can perform. There is a certain “match” temperature that controls whether the engine will be operating at its maximum gas generator speed (speed toping) or its maximum firing temperature (temperature topping). At ambient temperatures above the match temperature, the engine will operate at its max firing temperature and below its max generator speed. In a similar vein, the engine will operate at its max generator speed and below its max firing temperature at ambient conditions below the match temperature. The match temperature is the ambient temperature at which the engine reaches both limits, and it represents the highest efficiency of that engine.

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Figure 3 – Off-Design Analysis for an Axial Turbine using AxSTREAM’s AxMAP Module

This match temperature is not a trivial or fixed value. Several auxiliary factors cause changes in the gas engine’s match temperature, which must be appropriately accounted for in the gas turbine design. The following factors alter the match point of any gas engine

  • – Changes in the fuel properties
  • – Reduction in compressor or turbine efficiency due to fouling, increased leakage, tip clearance, and material roughness variations
  • – Accessory loads imparted by pumps and other secondary systems
  • – Inlet and Exhaust losses

These auxiliary factors along with the routine changes described by varying ambient temperature, ambient pressure, humidity, load, and power turbine speed all contribute to the complexity involved in properly designing a gas turbine.  Correctly analyzing off-design conditions becomes an art of variable manipulation and generally requires the use of cohesive design and analysis platforms for proper evaluation.  SoftInWay’s integrated software platform allows for streamlined manipulation of your gas turbine design together with immediate off-design analysis based on any prescribed changes.  If you would like to learn about how our AxSTREAM platform assists with off-design analysis in gas turbines and other turbomachinery, please visit our software page.

 

References:

http://turbolab.tamu.edu/proc/turboproc/T29/t29pg247.pdf

Heat Recovery Steam Generator Design

Heat recovery steam generators (HRSGs) are used in power generation to recover heat from hot flue gases (500-600 °C), usually originating from a gas turbine or diesel engine. The HRSG consists of the same heat transfer surfaces as other boilers, except for the furnace. Since no fuel is combusted in a HRSG, the HRSG have convention based evaporator surfaces, where water evaporates into steam. A HRSG can have a horizontal or vertical layout, depending on the available space. When designing a HRSG, the following issues should be considered:

hrsg-boiler
Figure 1: Schematic of a HRSG boiler
  • The pinch-point of the evaporator and the approach temperature of the economizer
  • The pressure drop of the flue gas side of the boiler
  • Optimization of the heating surfaces

The pinch-point (the smallest temperature difference between the two streams in a system of heat exchangers) is found in the evaporator, and is usually 6-10 °C, which can be seen in Figure 2. To maximize the steam power of the boiler, the pinch-point must be chosen as small as possible. The approach temperature is the temperature difference of the input temperature in the evaporator and the output of the economizer. This is often 0-5 °C. The pressure

hrsg-boiler-2
Figure 2: Example of a heat load graph for HRSG boiler

drop (usually 25-40 mbar) of the flue gas side also has an effect on the efficiency of power plant. The heat transfer of the HRSG is primarily convective. The flow velocity of the flue gas has an influence on the heat transfer coefficient. The evaporator of heat recovery boiler can be of natural or forced circulation type. The heat exchanger type of the evaporator can be any of parallel-flow, counter-flow or cross-flow. In parallel-flow arrangement the hot and cold fluids move in the same direction and in counter-flow heat exchanger fluids move in opposite direction.

 

The Significance of Quantifying Uncertainties in Turbomachinery CFD

The increased use of CFD for turbomachinery design is an outcome of the increasing accuracy thanks to high computational resources. Although the benefits of such computations are strong, the approximations and errors derived from CFD could significantly affect the prediction of crucial parameters such as flow temperature and heat transfer. This article will present the challenges related to uncertainties in turbomachinery CFD, based on “Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines” [1]

The exact definition of boundary conditions presents one of the biggest challenges in CFD and turbomachinery given the high accuracy needed to determine the distributions of the non-uniform conditions to which turbomachinery components are subjected [2].

An additional limitation related to CFD is known as geometric uncertainty. It should be noted that, in a geometric model, a lot of details are neglected for simplicity and speed or because they are unknown, which leads to differences between the real model and the simulated one. However, even if all the details are included along with secondary air systems, they could be affected by manufacturing of the components. A study [3] quantified the change of the stage efficiency due to manufacturing errors in the rotor end-wall and to different interaction between the purge flow and the main flow.

Moreover, grid dependence analysis is a fundamental task of every numerical simulation and must be considered as such. In fact, grid spacing effects can be responsible for the poor prediction of both flow structures (i.e. von Karman Vortex Street, shock intensity and position, secondary flows…) and integral parameters such as stagnation losses. For those reasons, the effects of computational grid on the obtained results must be accounted for, when performing high-fidelity computational fluid dynamics.

Another uncertainty arises due to the improper selection between steady and unsteady simulations. For instance, when it comes to losses prediction, Pullan [4] demonstrated that a steady simulation generates 10 % less losses compared with the unsteady one. Another classical error caused by a steady simulation is the analysis of the redistribution for a hot spot in the rotor row [5].

cfd-post-processing

Along with the use of accurate boundary conditions to analyze turbomachinery flows, the simulation of component interaction is equally important. For example, an accurate methodology for the exchange of turbulence information across the interfaces is essential, especially concerning the evaluation of the turbulent length scale.

Finally, attention must be paid to the simulation of cooling devices since design is affected by geometrical uncertainty, numerical accuracy, fluid/solid interaction and boundary conditions variability [6]. It could be argued that the numerical simulation of a cooled, transonic high-pressure vane is one of the most challenging topics in CFD. Geometric uncertainty is so high that a 10 % variation of cooling hole diameter would generate an increase of 40 K in the local metal temperature of the vane [7].

Most of the described problems are related to the stochastic uncertainty, which is a function of the knowledge problem physics and the complexity of the algorithm. Then, numerical accuracy can rise with an improved knowledge of the physics and with the computational resources, while uncertainty quantification should be a strong support in the analysis and design of turbomachinery.

References:

[1] F. Montomoli et al., Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines, SpringerBriefs in Applied Sciences and Technology, DOI 10.1007/978-3-319-14681-2_2
[2] Salvadori, S., Montomoli, F., Martelli, F., Chana, K. S., Qureshi, I., & Povey, T. (2012). Analysis on the effect of a nonuniform inlet profile on heat transfer and fluid flow in turbine stages. Journal of Turbomachinery, 134(1), 011012-1-14. doi:10.1115/1.4003233.
[3] Adami, P., Martelli, F., & Cecchi, S. (2007). Analysis of the shroud leakage flow and mainflow interactions in high-pressure turbines using an unsteady computational fluid dynamics approach. Proceedings of the IMechE Part A: Journal of Power and Energy, 21. doi:10.1243/09576509JPE466.
[4] Pullan, G. (2006). Secondary flows and loss caused by blade row interaction in a turbine stage. ASME Journal of Turbomachinery, 128(3), 484–491.
[5] Butler, T. L., Sharma, O. P., Joslyn, H. D., & Dring, R. P. (1989). Redistribution of an inlet temperature distortion in an axial flow turbine stage. AIAA Journal of Propulsion and Power, 5, 64–71.
[6] Montomoli, F., Massini, M., & Salvadori, S. (2011). Geometrical uncertainty in turbomachinery: Tip gap and fillet radius. Elsevier Computers and Fluids, 46(1), 362–368. doi:10.1016/j.compfluid.2010.11.031.
[7] Bunker, R. S. (2009). The effects of manufacturing tolerances on gas turbine cooling. ASME Journal of Turbomachinery, 131, 041018-1-11. doi:10.1115/1.3072494.

The Economic Optimization of Renewable Energy

clean-blog-postGlobal warming is a very popular topic at the present time. With the upwards trend of clean technology and the realization that strict climate policy should be implemented, demand of renewable energy has sky-rocketed while conservative plant popularity continues to fall. Additionally, the number of coal power plants have significantly dropped since its peak era, as they are now known as the largest pollutant contribution, producing nitrogen, sulfur oxide and carbon dioxides.

Renewable energy comes from many sources: hydropower, wind power, geothermal energy, bioenergy and many more. The ability to replenish and have no limit on usage and application makes renewable energy implementation attractive. To make this even better, it also produces low emission. Theoretically, with the usage of renewable energy, human-kind should be able to meet their energy needs with minimal environmental damage. With growth rates ranging from 10% to 60% annually, renewable energy is getting cheaper through the technological improvements as well as market competition. In the end, the main goal is to maximize profit while minimizing our carbon footprint.  Since the technology is relatively new, capital costs are still considerably higher compared to more traditional (–and naturally harmful) implementations. This begs the question of exactly how we maximize the economic potential of a renewable energy power generation plant.

Living up to the full potential of any power generation plant starts with the design process. Solar power plants are one environmentally friendly option.  During the design process, designers should take into consideration the type and quality of the solar panels as it is important to see the economic-efficiency tradeoff before jumping into an investment. Looking into the power conversion is also one of the most important steps one should take into consideration since it would be worthless to produce more energy than what is able to be transferred and put to use and low energy generation would mean less gross income.

Geothermal power plants are another option. Many studies have shown that boundary conditions on each component play a big role in determining the plant’s capacity and efficiency. High efficiency is definitely desired to optimize the potential of a power plant and minimized the energy loss. That being said, it is important to take into account the economic sacrifice. Regardless of how good the technology is, if it doesn’t make any profit, it would not make sense for one to invest in such technology. Low capital cost but high operating expenses would hurt the economic feasibility in the long run, whereas high capital cost and low operating expense could still be risky since that would mean a higher lump sum of investment upfront which may or may not breakeven or be profitable depending on the fluctuation of energy market.

Modern technology allows investors and the engineering team to make this prediction based on models developed by the experts. SoftInWay just recently launched our economic module, so check out AxCYCLE to optimize your power plant!

Reference:
[1] http://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=4483&context=etd
[2] http://www.sciencedirect.com/science/article/pii/S0038092X12002022

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.

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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