Julien Pohl
email: j.pohl@leeds.ac.uk

Harvey Thompson

Ralf Schlaps

Shahrokh Shahpar

Vincenzo Fico

Gary Clayton

S Y Mpo

O Tatin

Innovative Turbine Stator Well Design Using Design Optimisation

Keywords:

Nowadays, it is common practice to expose engine components to main annulus air temperatures exceeding the thermal material limit in order to increase the overall engine performance and to minimise the engine specific fuel consumption. To prevent overheating of the materials and thus the reduction of component life, an internal flow system is required to cool and protect the critical engine parts. Previous studies have shown that the insertion of a deflector plate in turbine cavities leads to a more effective use of reduced cooling air, since the coolant is fed more effectively into the disc boundary layer. This paper describes a flexible design parameterisation of an engine representative turbine stator well geometry with stationary deflector plate and its implementation within an automated design optimisation process using automatic meshing and steady-state CFD. Special attention and effort is turned to the flexibility of the parameterisation method in order to reduce the number of design variables to a minimum on the one hand but increasing the design space flexibility & generality on the other. Finally the optimised design is evaluated using a coupled FEA/CFD method and compared against the baseline design.

[ -] Non-dimensional near wall spacing β

[ -] Swirl ratio ω [rad s -1 ] Rotational speed

INTRODUCTION

Over the last decades the significance of internal cooling air systems have become increasingly important in the field of modern gas turbine engines. The main target for aeroengine manufacturers is an improvement of the overall engine efficiency, and thus a reduction in specific fuel consumption. This is mainly achieved by an increase of temperature of the exhaust gas coming from the combustion chamber, which enters the turbine main gas path. These gas temperatures exceed the thermal material limit of the engine components, both within (i.e. blades) and adjacent (i.e. cavities) to the main gas path. To prevent damage and to protect these components from overheating, secondary cooling air systems are designed.

The required cooling air is bled from compressor stages and introduced to the blade cooling channels and the exposed turbine cavities, which are inevitably formed by stationary and rotating walls. In order to maximise the overall cycle performance the minimum cooling air mass flow rate should be used that still ensures the required component life. There are mainly two reasons in favour of a reduction of the cooling air: first, the higher the amount of cooling air, the worse the engine thermodynamic cycle performance. Second, the higher the amount of cooling air re-entering the main gas path at a later stage, the lower is the stage efficiency [START_REF] Illingworth | 3D Fluid-Solid Heat Transfer Coupling of an Aero-Engine Preswirl System[END_REF][START_REF] Amirante | A Coupled Approach for Aerothermal Mechanical Modelling for Turbomachinery[END_REF]. As a follow up study of the work carried out during the MAGPI (Main Annulus Gas Path Interaction) project, subproject 7 of the EU FP7 project AMEDEO (Aerospace Multi-disciplinary Enabling Design Optimisation) specifically aims towards the development of a robust design optimisation strategy for turbine stator wells (TSW) in order to improve the cooling performance and reduce the required amount of coolant.

During the last couple of years some of the experimental data obtained during the MAGPI project has been analysed and validated. Dixon et al. [START_REF] Dixon | Heat Transfer in Turbine Hub Cavities Adjacent to the Main Gas Path[END_REF] did some preliminary analyses of different cooling configurations using adiabatic steady-state computational fluid dynamics (CFD) solutions in order to obtain an understanding of the different flow fields inside the cavities. With regard to the cooling effectiveness of the rotor disc and the front cavity, it has been concluded that it is desirable to get an entrainment of the cooling air along the rotor wall. This can be achieved either by axial lock plate inlets or a deflected radial coolant inflow. Similar conclusions have been made by da Soghe et al. [START_REF] Dasoghe | Turbine Stator Well CFD Studies: Effects of Coolant Supply Geometry on Cavity Sealing Performance[END_REF] and Coren et al. [START_REF] Coren | The Influence of Turbine Stator Well Coolant Flow Rate and Passage Configuration on Cooling Effectiveness[END_REF], who conducted parameter studies analysing different positions and inclinations of the radial drive arm hole.

Recently, Pohl et al. [START_REF] Pohl | Turbine Stator Well Cooling -Improved Geometry Benefits[END_REF] analysed in detail the test case with a mounted stationary deflector plate in the upstream cavity and proposed different modelling and meshing strategies. Using steady-state CFD, the flow physics as well as the cooling effectiveness on the upstream rotor disc were compared between the baseline (i.e. cavity without deflector) and the deflector plate geometry for two different amounts of coolant mass flow. Since the deflector directs the cooling air towards the disc, even small volumes of cooling air result in an improved cooling performance. It was concluded that the cooling air could nearly be halved by inserting the deflector into the cavity.

In a practical aero engine context, Young et al. [START_REF] Young | Turbine apparatus[END_REF] analysed the effect of a deflector plate attached to the rotating drive arm in order to improve the cooling effectiveness on the rotor disc. It was also found that due to the deflector the cooling air is entrained towards the disc, resulting in better cooling of that particular critical part. The outcome was so promising that it has been patented successfully.

Regarding the development and application of optimisation techniques to aero-engine components a lot of effort has been made in the field of main gas path aerodynamics (e.g. [START_REF] Shahpar | Large Scale Optimization of Transonic Axial Compressor Rotor Blades[END_REF][START_REF] Polynkin | Multidisciplinary Optimization of Turbomachinery Based on Meta-Model Built bt Genetic Programming[END_REF][START_REF] Schlaps | Automatic Three-Dimensional Optimisation of a Modern Tandem Compressor Vane[END_REF]). Whereas in main gas path aerodynamics the parameterisation of the blades or vanes is mainly realised by parameterising the main defining engineering parameters, such as chord length, camberline angle, pitch and thickness, the parameterisation of components forming the internal cooling systems is less consolidated.

Verstraete et al. [START_REF] Verstraete | Optimization of a U-Bend for Minimal Pressure Loss in Internal Cooling Channels -Part I: Numerical Method[END_REF] parameterised a 2D U-bend geometry, which is typical for internal cooling channels, using third order Bézier curves defined by four control points each. Every control point was given a particular degree of freedom in order to keep the design variables to a minimum but at the same time covering a large design space.

For the automatic optimisation of the baseline MAGPI TSW geometry, Lück et al. [START_REF] Lück | Thermal Fluid-Structure Interaction Based Optimization of Secondary Air Flows in Rotor Stator Cavities of Aircraft Turbines[END_REF] used a mixture of CAD-based parameterisation and mesh morphing from the output of the evaluation of a thermal-fluid structure interaction. With this approach it was possible to change the inclination of the cooling hole and also take thermo-mechanical effects into account.

In the following sections, first a short overview and introduction is given on the flow physics present in a TSW with a stationary deflector plate. Then, some theoretical background on general optimisation strategies and on response surface modelling approaches are presented. This is followed by the numerical methodology used in this work, consisting of the introduction to the test case geometry and the CFD evaluation technique. The latter includes a description of the discretised CFD model with its basic assumptions for boundary conditions and restrictions, as it is embedded in the automatic meshing process. The parameterisation of the deflector plate geometry with its necessary geometrical approximations is also presented, with the focus on the actual optimisation setup defining the objective function and the constraints. Results obtained from the optimisation are shown, interpreted and discussed. Finally, the main conclusions are drawn and recommendations for future work are given.

THEORETICAL BACKGROUND TSW Flow Theory

This section gives an overview of the flow behaviour in a TSW with an integrated stationary deflector plate and its benefits compared to a standard baseline geometry without a deflector. A schematic illustration of the typical TSW flow phenomena with an inserted stationary deflector plate can be seen in Fig. 1. The orange and black contour lines represent rotating and stationary parts, respectively. Cooling air is introduced into the upstream cavity radially through a drive arm hole. Other than for the standard geometry, the cooling air does not penetrate the cavity forming a core flow, but instead impinges the deflector plate and is turned towards the rotor disc, by forming a complex 3D vortex flow structure. The cooling air which reaches the disc is then entrained radially outwards by the rotating part of the turbine. The rim seal flow characterises the mixing zone between the hot gas coming from the main annulus and the cooling air. The interaction of these two flows strongly affects the temperatures inside the cavity. Three different flow scenarios can be distinguished depending on the amount of cooling air and the size of the interstage seal clearance [START_REF] Phadke | Aerodynamic Aspects of the Sealing of Gas Turbine Rotor-Stator Systems -Part 1: The Behaviour of Simple Shrouded Rotating Disk Systems in Quiescent Environment[END_REF][START_REF] Phadke | Aerodynamic Aspects of the Sealing of Gas Turbine Rotor-Stator Systems -Part 2: The Behaviour of Simple Seals in Quasi-Axisymmetric External Flow[END_REF]:

Net gas ingestion: If the amount of cooling air is small and/or the interstage seal clearance is large, the rim seal flow is dominated by hot gas entering the cavity.

Net gas egress: If the amount of cooling air is large and/or the interstage seal clearance is tight, the rim seal flow is dominated by cooling air leaving the cavity in the main annulus.

Local ingestion/egress: If the cavity flow is balanced locally hot gas enters the cavity but also cool air enters the main annulus. This phenomenon is driven by the rotorstator interaction in the main gas path and the turbulent mixing in the rim region.

The portion of air/gas mixture staying in the cavity then finds its way to the interstage seal clearance since the deflector plate is mounted to the stator foot by a few pins, spacers or bolts in order to allow air to pass between these parts. This flow is driven by the presence of a pressure gradient from outer to inner radii between the stator wall and the deflector plate. Interstage seals are used to reduce the flow of air from upstream to downstream stator well cavities. This seal flow is, as mentioned above, largely influenced by the clearance size and also the pressure drop across the seal, which is a function of the upstream and downstream conditions including the pressure drop over the stage in the main annulus. The flow structure in the downstream cavity can then again be described as a traditional rotor-stator flow, consisting of a disc entrainment flow, a core flow and a rim seal exchange flow.

Optimisation Theory

Within this subsection, some theoretical background on a typical optimisation strategy is described as it is used for many complex engineering or aero-engine problems. Also, the response surface modelling technique, a method on how to choose the initial database, as well as the actual optimisation method used in this work are presented.

Optimisation Strategy

The optimisation is conducted using the Rolls-Royce SOPHY system (SOFT, PADRAM, HYDRA) [START_REF] Shahpar | SOPHY: An Integrated CFD Based Automatic Design Optimisation System[END_REF]. SOFT (Smart Optimisation For Turbomachinery) [START_REF] Shahpar | SOFT: A New Design And Optimisation Tool for Turbomachinery[END_REF] provides a library of different optimisation algorithms and communicates through python scripts with the other codes in order to execute them in batch mode, to evaluate the results of the simulation. In general, these computations are run in parallel on an HPC cluster in order to reduce the overall run time.

The 2D geometry is generated parametrically using a python programme and then fed to the meshing tool PADRAM (Parametric Design and Rapid Meshing) [START_REF] Shahpar | PADRAM: Parametric Design and Rapid Meshing System for Turbomachinery Optimisation[END_REF]. PADRAM then generates automatically and robustly 3D structured and unstructured meshes for the main annulus and for the cavity domain, respectively. The discretised 3D model is passed to the HYDRA system [START_REF] Lapworth | Hydra-CFD: A Framework for Collaborative CFD Development[END_REF] for pre-processing and finally solving the Reynolds-Averaged Navier-Stokes equations (RANS). The converged CFD solution is then fed to the post-processing tool Paraview, where the solution is evaluated with respect to the figure of merit, i.e. the objective function, then passed to the optimiser. In general, an optimisation problem is defined by an objective function f (x), which is sought for minimum values, while satisfying a number of problem dependent constraints g(x):

Minimise Subject to f m (x), g j (x) ≥ 0, x l i ≤ x i ≤ x u i , m = 1, 2, ..., M; j = 1, 2, ..., J; i = 1, 2, ..., n. ( 1
)
where x is the design vector containing n design parameters x 1 , ..., x n . The superscripts l and u define the lower and upper limit of a particular design parameter x i . The details on how these parameters are defined in this work is described in a later section.

Initial Database -Design of Experiments

In order to carry out an optimisation and to explore the design space in an efficient way, it is necessary to start from an initial database. In this study, the initial database is created with a Design of Experiment (DOE) approach where the DOE is generated automatically using a Latin Hypercube sampling technique (LHS), which distributes a desired amount of initial database points homogeneously within the design space in such a way that each point is the only one in a certain axisaligned hyperplane [START_REF] Mckay | A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code[END_REF][START_REF] Stein | Large Sample Properties of Simulations Using Latin Hypercube Sampling[END_REF]. From a stochastic point of view, this method provides the best interpolation dataset for an unknown behaviour of an objective function within a defined design space.

In order to choose the number of database points for the initial DOE, the recommendation given by Baerts et al. [START_REF] Baert | Surrogate-Based Optimisation for a Mixed-Variable Design Space: Proof of Concept and Opportunities for Turbomachinery Applications[END_REF] is followed: for a purely continuous design space of a surrogate based optimisation, the authors took five times the number of design variables (5 × n) for an initial DOE. This also seemed to be a reasonable approach for this study, due to the defined low dimensional space.

Surrogate Based Optimisation

For complex engineering problems, either 2D or 3D, the aim is to get to the optimum solution as fast as possible, i.e. with a minimum number of simulations. Therefore, mathematical or statistical approximation models are used to speed up the optimisation. In the technical literature, these models are known as surrogate models, metamodels or response surface models (RSM). In this study, the optimisation is conducted by using the so called Kriging technique, which is able to replicate accurately a complex multi-dimensional function. It is out of the scope of this paper to derive the equations in detail of the Kriging method. Therefore the reader is referred to the early literature of Krige [START_REF] Krige | A Statistical Approach to Some Basic Mine Valuations and Allied Problems at the Witwatersrand[END_REF] and Matheron [START_REF] Matheron | Principles of Geostatistics[END_REF] and for practical guidance in engineering to the book of Forrester et al. [START_REF] Forrester | Engineering Design via Surrogate Modelling: A Practical Guide[END_REF].

In this work regressing Kriging [START_REF] Forrester | Design and Analysis of "Noisy" Computer Experiments[END_REF][START_REF] Brooks | Multi-Fidelity Design Optimisation of a Transonic Compressor Rotor[END_REF] is used, which is based on the classical Kriging approach with an additional parameter to filter out scatter or noise coming from numerical calculations such as CFD. A schematic representation of the optimisation process based on Kriging as it is implemented in SOFT, can be seen in Fig. 2. Starting from an initial LHS DOE set, the obtained initial designs are evaluated in parallel and saved in a database or in case of failure, in a failure database. Once the designs are evaluated, a RSM is built using Kriging and the convergence of the RSM is checked using the efficient leave-one-out cross-validation method (see [START_REF] Brooks | Multi-Fidelity Design Optimisation of a Transonic Compressor Rotor[END_REF][START_REF] Dubrule | Cross Validation of Kriging in Unique Neighbourhood[END_REF]). If that is the case, the optimisation stops. Otherwise, the initial DOE is updated by additional points in order to iteratively get to a more accurate solution.

In order to refine the DOE and to find a new set of update points, the RSM is searched using global and local optimisation techniques. Therefore, two optimisation algorithms are chosen from the SOFT library: an adaptive range multiobjective genetic algorithm (ARMOGA) [START_REF] Sasaki | Efficient Search for Trade-Offs by Adaptive Range Multi-Objective Genetic Algorithms[END_REF] and sequential quadratic programming (SQP) [START_REF] Gill | Practical Optimization[END_REF][START_REF] Powell | Variable Metric Methods for Constrained Optimization[END_REF]. The searching criteria follow a list of preferences until the maximum number of update points, also known as infill points, is reached (six points per update). First it is searched for the best constrained generalised expected improvement (CGEI) [START_REF] Forrester | Engineering Design via Surrogate Modelling: A Practical Guide[END_REF]. In a second step -if no CGEI could be found or the maximum number of update points is not yet reached -the maximum Kriging error is sought to find the location of maximum uncertainty. In a third step a search is made for the best Kriging prediction.

NUMERICAL METHODOLOGY

This section introduces the reader to the numerical methods used in this study. An introduction to the analysed test case geometry and its discretisation is given, followed by the para-

CFD Evaluation

The geometry used in this work is based on the MAGPI rig test facility, which has already been analysed thoroughly in recent years [START_REF] Dixon | Heat Transfer in Turbine Hub Cavities Adjacent to the Main Gas Path[END_REF][START_REF] Dasoghe | Turbine Stator Well CFD Studies: Effects of Coolant Supply Geometry on Cavity Sealing Performance[END_REF][START_REF] Coren | The Influence of Turbine Stator Well Coolant Flow Rate and Passage Configuration on Cooling Effectiveness[END_REF][START_REF] Pohl | Turbine Stator Well Cooling -Improved Geometry Benefits[END_REF][START_REF] Guijarro-Valencia | An Investigation Into Numerical Analysis Alternatives For Prediciting Re-Ingestion in Turbine Disc Rim Cavities[END_REF][START_REF] Eastwood | Experimental Investigation of Turbine Stator Well Rim Seal, re-Ingestion and Interstage Seal Flows Using Gas Concentration Techniques and Displacement Measurements[END_REF][START_REF] Dixon | Main Annulus Gas Path Interactions -Turbine Stator Well Heat Transfer[END_REF][START_REF] Eastwood | Investigaton of Rim Seal Exchange and Coolant Re-Ingestion in Rotor Stator Cavities Using Concentration Techniques[END_REF]. For a full overview of the rig geometry with its instrumentation and running conditions the reader is referred to the work of Eastwood [START_REF] Eastwood | Investigaton of Rim Seal Exchange and Coolant Re-Ingestion in Rotor Stator Cavities Using Concentration Techniques[END_REF]. From a numerical point of view the experimental data was used to develop and validate reliable methods to predict both the flow phenomena in TSWs for different amounts of cooling mass flow, and also the conjugate heat transfer on the life critical rotor parts.

In order to keep the computational requirements within the capability of available computer facilities, it was decided to reduce the size of the discretised domain to a minimum. As in the previous numerical study on the original deflector plate geometry [START_REF] Pohl | Turbine Stator Well Cooling -Improved Geometry Benefits[END_REF], in this work a 1/39th sector model was chosen, which is a reasonable approximation due to the periodicity of the 78 blades and 39 vanes per stage. Furthermore, the two stage domain was reduced to only one rotor blade pair from the first stage and the upstream cavity including the deflector plate until the first fin of the interstage seal. The rotational Reynolds number Re φ is roughly 1.6 × 10 6 .

The mesh was generated using the automatic Rolls-Royce in-house meshing tool PADRAM (see Fig. 3). The main annulus domain was generated using a multi-block structured approach, following the mesh sensitivity study of Dixon et al. [START_REF] Dixon | Heat Transfer in Turbine Hub Cavities Adjacent to the Main Gas Path[END_REF], whereas the cavity was meshed in an hybrid unstructured way, following some assumptions made and verified for its suitability by Pohl et al. [START_REF] Pohl | Turbine Stator Well Cooling -Improved Geometry Benefits[END_REF]. In order to generate the mesh automatically with PADRAM and to make it feasible for HYDRA the cavity domain was meshed in a single reference frame, meaning that the connecting bolt between stator

Rim region

Complete cavity

Cooling inlet region The cavity mesh was then merged conformally at the rim to the main rotor mesh, which results in an overall mesh size of around six million cells. The boundary layer was resolved, ensuring y + values of around 1 in the most of the near wall regions. Only the regions around the first fin as well as at the stator and deflector plate, where the bolt used to connect both parts, did not match this criterion.

At this stage the Rolls-Royce in-house CFD code HYDRA was used to solve the RANS equations using a second order finite volume discretisation of the domain in double precision. The turbulence closure was done using the k -ω turbulence model with adaptive wall functions of Launder and Spalding [START_REF] Launder | The Numerical Computation of Flows[END_REF] in the regions where the near wall resolution was large. The cooling air inlet was defined as a mass flow inlet with a fixed temperature. The inlet for the main annulus was defined as a pressure inlet, where the total pressure was read across from the solution of the complete main annulus. The same approximations were taken for the outlets in the main annulus and the fin, where the static pressure distributions were taken from the full sector model run. The walls were defined as adiabatic, to keep the computation within a reasonable time scale. During the early design phase of the MAGPI test rig, similar stand-alone adiabatic CFD simulations were carried out to get an idea of the impact on the disc temperature using different geometries and varying amounts of cooling air [START_REF] Dixon | Heat Transfer in Turbine Hub Cavities Adjacent to the Main Gas Path[END_REF].

In order to validate the outcome of the optimisation using stand-alone adiabatic CFD, a well established coupled FEA/CFD method [START_REF] Verdicchio | The Validation and Coupling of Computational Fluid Dynamics and Finite Element Codes for Solving Industrial Problems[END_REF] was applied to the final geometry to extract metal temperatures. These results were based on the coupling between the in-house FEA solver SC03 and the commercially available CFD code FLUENT. The two codes communicate through a Rolls-Royce proprietary communication library. For details on the method and the FEA model with the deflector included it is referred to the work of Pohl et al. [START_REF] Pohl | Turbine Stator Well Cooling -Improved Geometry Benefits[END_REF]. Both stand-alone CFD solutions from the two different CFD solvers, HYDRA and FLUENT, were compared beforehand. Since no significant differences were found in the temperature predictions inside the cavity, the change in between solvers was possible.

Parametric Geometry Definition

The cavity geometry and the rotor geometry were not changed in this study. Only the shape and the position of the deflector plate were modified. The parameterisation of the deflector plate was done in 2D and is shown in Fig. 4 (a). It was chosen to define the midsection of the deflector plate by four control points, defining three separate B-spline curves (1-3), which in this work were defined as straight lines. There were mainly two reasons for this: first, to make the parameterisation as general as possible by avoiding hard-coded values. Second, to generate a manufacturable solution, which also could be mounted to the stator foot, meaning that it was necessary to have a vertical curve 2.

The points of the B-splines of the midsection were then projected orthogonally in positive and negative direction with a distance of half the thickness t/2 of the deflector plate. It can also be seen that the angle of curves 1 and 2 did not have to be the same. The degrees of freedom of the four control points are depicted in Fig. 4 (b). In total seven geometrical design parameters were defined:

• d U, x and d U,r , which define the axial and radial degree of freedom of the upper point

• d D,
x , which defines the axial distance of curve 2 to the stator foot

• d D,r , which defines the radial degree of freedom of the point connecting curve 1 to curve 2 with respect to the outer radii of the stator foot

• l D , which defines the length of curve 2

• d L, x and d L,r , which define the axial and radial degree of freedom of the lower point Before setting up the optimisation it was checked that the generated geometry after applying the thickness to the midsection would not cut or touch lines of the remaining non-changed cavity geometry. Second, checks were made to ensure that the most extreme geometries, i.e. the one with the tightest gaps between parts, could be reliably meshed in PADRAM without corrupting the defined boundary layer.

Optimisation Setup

In order to finally setup the automated optimisation loop, an objective function as well as the constraints have to be defined, both depicted in Fig. 4 (b) in blue and red, respectively. The objective of this optimisation is to minimise the cooling air

d U,r d U, x l D d D, x d D,r d L, x d L,r ṁcool T di sc t / 2 t / 2 c u r v e 1 c u r v e 3 curve 2 t / 2 t / 2 (a) (b)
f (x) = ṁcool (2)
with x being the design vector consisting of eight design parameters (seven geometrical and one for the cooling air mass flow rate). Also one constraint g j (x) is defined (see Fig. 4 (b)):

g j (x) = T ma x di sc -T di sc, j ≥ 0 ( 3
)
where T ma x di sc is the maximum allowable area mean adiabatic wall temperature at the disc and T di sc, j the computed value for a particular design j. The maximum value was taken from the results of a numerical simulation of the baseline geometry and an initial cooling mass flow rate of 55gs -1 .

The actual optimisation is conducted in parallel, where each CFD simulation is run on 24 cores. At first a DOE of 40 design points is generated (n = 8).

RESULTS AND DISCUSSION

Optimisation Results

This section gives an overview of the results of the optimisation. Fig. 5 shows the convergence history of the Kriging assisted optimisation, where the circles represent feasible and the crosses non-feasible solutions. A design is considered feasible when the solution stays within the limits of the constraint. Overall, 98 design points have been evaluated, where five mesh failures were recorded, one in the DOE and four in the optimisation process. Although, at first, only non-feasible designs were found, the optimiser managed to find feasible designs for small amounts of cooling air. The optimised deflector design only needs 19gs -1 of cooling air compared to 55gs -1 for the baseline geometry without deflector, which is a reduction of around 65%. Compared to the non-optimised deflector, where earlier studies showed that 30gs -1 achieves a similar performance to the baseline geometry [START_REF] Pohl | Turbine Stator Well Cooling -Improved Geometry Benefits[END_REF], the optimised deflector reduces the coolant by another 40%.

A different representation of the evaluated results is presented in Fig. 6, where the amount of cooling air is plotted against the area mean averaged adiabatic wall temperature All points below that line are considered feasible, the others non-feasible. A linear trend is observed in this representation.

d D,x [-] 0 1 0 1 d U,r [-] d D,r [-] d L,r [-] d D,x [-] l D [-] d U,x [-] d U,x [-] d L,x [-] (a) (b) (c) (d)
The cooling performance shrinks with a reduction of coolant air, as one would expect. Interestingly, for all cooling mass flow rates above the value of around 37gs -1 (cutting point between trendline and constraint), all deflector designs meet the required cooling performance of the disc. Figures 7 (a) -(d) show the Kriging predictions coming from the optimisation for all geometrical design parameters. The response surfaces are obtained from the optimisation process as presented above. The four different plots are coloured by the near disc temperature T di sc and represent slices through the eight dimensional design space. With these plots it is possible to analyse the influence of each design parameter on the cooling performance of the disc. Examining the values of the optimised design, which are highlighted by the red dots, it is clearly visible that the optimiser moves the design points to the extreme values of the design space. Two design variables (d U,r and d D, x in Fig. 7 (a) and (d)) were optimised without reaching the limits of the design space. These variable define From this information, the new position and design of the deflector was modelled and included in the complete two stage sector geometry. Steady-state adiabatic CFD were then carried out in order to analyse the optimised TSW flow in detail and to verify the outcome of the optimisation.

The Optimised Deflector Plate -Steady-State CFD

A comparison of the optimised deflector (left) against the non-optimised deflector (right) with respect to the position and shape based on the findings presented in the previous subsection can be seen in Figs. 8 and9: the upper tip of the deflector is moved close to the rotor disc, whereas the lower parts are moved close to the stator foot. The depicted midplane cuts are contoured by swirl fraction β (= v θ (ωr) -1 ) and relative total temperature. Both simulations were run with the reduced cooling mass flow rate of 19 g s -1 . For the optimised geometry, it can be seen that the cooling air enters the cavity swirled at disc speed ( β = 1) and keeps its swirl as long as it does not impinge the deflector. This maintenance of swirl due to the position of the deflector close to the stator foot is beneficial for the cooling performance of the disc. Having a look at the non-optimised deflector, the cooling air loses all its swirl quickly after entering the cavity even before impinging the deflector. Another interesting phenomenon can be seen at the lower tip of the deflector plate, where -for the optimised design -part of the highly swirled cooling air seems to move to the interstage seal straight away without cooling the disc. This ensures that the gap between the deflector lower tip and the rotor wall is sealed against hot gas coming from higher radii. This is not the case for the non-optimised geometry.

Examining the temperature contours inside the cavity for the optimised design, it can be seen that the cooling air enters the cavity and then partially splits up, as one could infer from the swirl ratio contours. The disc is cooled all along the area enclosed by the deflector. It can also clearly be seen that hot gas from the main annulus ingests through the rim into the upstream cavity since the amount of cooling air does not meet the sealing requirements anymore. This results in a strong heat-up of the area between the deflector and the stator foot as well as the downstream cavity. The cooling air however does seal the region between the lower tip of the deflector and the rotor wall avoiding hot gas to enter the critical area between deflector and rotor disc.

In the non-optimised geometry, the air, which is used to cool the disc, is of higher relative total temperature than that in the optimised design. This is mainly due to two reasons: firstly, the cooling air loses all its swirl after entering the cavity, which results in an increase in relative total temperature. Secondly, the gap between the lower deflector tip and the rotor disc is not sealed, which results in hot air coming from higher radii entering the area between the deflector and the rotor disc. However, the air temperatures along the stator wall are slightly lower for the non-optimised design than those for the optimised one. While in the former the entire cooling flow penetrates the upstream cavity and mixes with the ingested flow, in the latter a fraction of the coolant is directly diverted towards the interstage seal.

Having analysed the steady-state CFD results for the optimised deflector, it can be concluded that the optimisation converged to a better deflector design, keeping the rotor disc cool while reducing the amount of cooling air. However, the fact that a large amount of hot gas enters the cavity, which inevitably results in a heat-up of the metal, needed further investigation. Therefore, coupled FEA/CFD analyses were carried out in order to extract the metal temperatures for the optimised design, the non-optimised deflector plate (both for a cooling air mass flow rate of 19 g s -1 ) and the baseline design without a deflector (55 g s -1 ). Also it is worth mentioning that the simulations were run with a constant interstage seal clearance only. The thermo-mechanical impact of the stator heating on the interstage seal clearance was not considered. [START_REF] Eastwood | Investigaton of Rim Seal Exchange and Coolant Re-Ingestion in Rotor Stator Cavities Using Concentration Techniques[END_REF]. From the contours and the plots, it can be seen that the temperatures inside the upstream rotor disc are very similar (positions 80, 101, 98, 92) for the optimised deflector and the baseline geometry, which was the requirement to the optimisation. The non-optimised deflector is slightly worse, especially at the lower radii of the rotor disc.

FEA/CFD Coupling -Metal Temperature Predictions

Then, moving further downstream inside the cavity (positions 110, 116, 125, 128, 130) the rotors of the deflector designs are hotter compared to the baseline geometry. A reason for that, as mentioned before, is due to the hot gas from the main annulus ingesting into the upstream cavity, which then heats up the interstage seal as well as the downstream cavity compared to the baseline geometry. This has also an effect on the metal temperature. Having a look at the temperature distribution along the rotor, it can be seen that despite the increase in temperature of the downstream rotor in the optimised design, the temperatures are still lower than in the upstream region. Hence, as a whole, from the thermal perspective, the optimised design with a reduced amount of cooling air is no worse than the baseline with the higher amount of cooling air. And for the same amount of coolant, the optimised deflector geometry performs better than the non-optimised deflector design.

The comparison of the stator metal temperatures shows larger differences between the deflector and the baseline de-signs due to the reasons mentioned above. Due to the hot gas ingestion, the stator temperatures are nearly constant over the radius and the axial position whereas in the baseline geometry the stator is cooled. Due to the higher amount of ingestion for the optimised design compared to the non-optimised deflector, the upstream stator (positions [START_REF] Shahpar | SOFT: A New Design And Optimisation Tool for Turbomachinery[END_REF][START_REF] Shahpar | PADRAM: Parametric Design and Rapid Meshing System for Turbomachinery Optimisation[END_REF][START_REF] Lapworth | Hydra-CFD: A Framework for Collaborative CFD Development[END_REF][START_REF] Mckay | A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code[END_REF] is also slightly hotter for the optimised deflector design, which also agrees with the findings from the steady-state CFD in the previous section. Since the stator foot is not a life limiting part and the temperatures are still lower compared to the rotating components, it can be concluded that the insertion of the optimised deflector provides an efficient distribution of cooling air inside the cavity, keeping the critical parts cool and the non-critical parts in a reasonable temperature range.

The comparison of the optimised to the non-optimised deflector design for this rig test case shows a small improvement in disc cooling and differences in the flow physics, which might be more significant for real engine running conditions, where temperatures as well as temperature gradients are much higher. Especially, the fact that ingested hot gas is able to pass through the gap between the lower deflector tip and the rotor disc for the non-optimised design, might cause life threatening conditions.

CONCLUSION

In this study an automated design optimisation using Kriging of a 3D sector model of a TSW test rig geometry with an inserted stationary deflector plate has been conducted. The geometry has been parameterised in such a way that flexibility of the design is ensured: different shapes and positions of the deflector plate inside the cavity have been generated automatically.

The outcome of the optimisation using adiabatic steadystate CFD has shown that the overall amount of cooling air can be reduced by approximately 65% compared to the baseline geometry without a deflector plate by still ensuring similar rotor disc cooling. This outcome has been verified using the coupled FEA/CFD method to compare metal temperatures for the new design to those for the baseline design. These results were in agreement with the stand-alone CFD results.

Another very important aspect for the new design and the reduced amount of cooling air is the fact that hot gas from the main annulus is ingested into the cavity, since the introduced amount of cooling air does not meet the sealing requirements of the cavity. This results in a metal temperature rise of the stator foot and also of the rotating downstream cavity components, but still keeps them at a temperature lower than the upstream components.

For future work in this research area, some recommendations are given here. When applying this method to real engine running conditions, it is essential -due to much higher temperatures and temperature gradients -to define an additional constraint to control and monitor the amount of ingested flow to the downstream cavity. Also the thermo-mechanical movements are of high importance. Not only, is it likely that a variation in seal size affects the final flow solution, but also the very extreme positions of the deflector should be chosen very carefully in order to prevent rubbing and damage at the most critical running conditions. The authors are also aware of the limitations of steady-state CFD in order to accurately predict the correct level of hot gas ingestion. For future work -in order to minimise these uncertainties -it is recommended to implement unsteady CFD or higher order turbulence models in the proposed optimisation strategy.

Figure 1 .

 1 Figure 1. Stator well flow structure with stationary deflector plate

Figure 2 .

 2 Figure 2. Schematic representation of the Optimisation strategy using Kriging in SOFT

Figure 3 .

 3 Figure 3. Mesh of upstream TSW cavity with deflector plate merged to the main annulus

Figure 4 .

 4 Figure 4. Definition of the geometrical parameters of the deflector plate: (a) shape definition, (b) position inside the cavity

Figure 5 .

 5 Figure 5. Convergence history of the Optimisation

Figure 6 .

 6 Figure 6. Objective function plotted against constraint for evaluated simulations

Figure 7 .

 7 Figure 7. Overview of the Kriging prediction contoured by the temperature near the rotor disc T di sc

Figure 8 .

 8 Figure 8. Contours of swirl ratio for the optimised (left) and non-optimised deflector plate (right) in a mid-plane cut

Figure 9 .

 9 Figure 9. Contours of fluid temperature for the optimised (left) and non-optimised deflector plate (right) in a mid-plane cut

Figures 10 and 11 Figure 10 .Figure 11 .

 111011 Figures 10 and 11 summarise the results of the FEA/CFD coupled analyses. In Fig.10contours of metal temperature of the optimised (left) and non-optimised deflector (middle) with a reduced cooling air mass flow rate of 19 g s -1 as well as the baseline geometry (right) with a cooling air mass flow rate of 55 g s -1 are depicted. Figure11shows a comparison of discrete metal temperature values from these models at the

ACKNOWLEDGEMENTS

The present investigations were supported by the European Commission within the AMEDEO Marie Curie initial training network (grant reference 316394) and the authors want also to thank the European Commission for its support within the Framework 6 Programme, Research Project MAGPI, AST5-CT-2006-030874 for the use of the test rig geometry.


Sebastian Haueisen
email: sebastian.haueisen@tu-berlin.de

Paul Uwe Thamsen

Sebastian Wulff

Experimental Investigation on Material Selection for Pumps and Machinery to Remove Ochre Deposits

Keywords:

Samples were exposed to create an artificial ochre layer on the surface of it. This was done for different materials and coatings as well as exposure times. The thickness of the ochre layer were in a technical relevant range and similar to layers that were found on technical systems like pumps and machinery. These samples were cleaned by water flows with increasing velocities to determine the velocity when ochre detached. The velocities, which were detected in this experiment, were the input conditions for tests afterwards. The velocity distribution in the near of the surface of the sample sheets was measured. A solid body was implemented in the near of the surface to reach high velocities in a technical relevant flow rate. Measurements of the velocity profiles were performed.

INTRODUCTION

Ochre deposits i.e. iron clogging, is one of the main reasons for downtime and maintenance demand by pumping from wells. In addition it leads to a significantly increase of friction losses in the involved system and causes thereby increased energy costs. Affected of iron clogging are the fields of openpit mining as well as the industry of drinking water production. Figure 1 shows an example of ochre deposits on the diffusor of a pump and compared it to a clean part. This demonstrates the challenges with iron clogging. The influence of the ochre deposits on the pump's performance and efficiency was investigated by Wulff [START_REF] Dvgw | Reinigung und Desinfektion von Wasserverteilungsanlagen (Cleaning and disinfection of water distribution systems)[END_REF].

An example for the pump performance is shown in Figure 2.

The ochre deposits cause an increase of hydraulic losses in the pump. This leads to a reduced head, a shift of Best Efficiency Point to smaller flow rates and a decrease of efficiency.

Figure 2: Influence of ochre deposits on the pump's performance by [START_REF] Dvgw | Reinigung und Desinfektion von Wasserverteilungsanlagen (Cleaning and disinfection of water distribution systems)[END_REF].

Further, Apfelbacher et al. [START_REF] Apfelbacher | Langzeitverhalten von Unterwassermotorpumpen im Lausitzer Revier (Long-term behavior of submersible motor pump in the mining area Lausitz) In German[END_REF] showed by a long-term observation of submersible pumps used in an opencast mining that the flow rate decreased continually over only a period of 2 years if no action is taken against the ochre deposits. Figure 3 shows the decrease of flow rate over the whole test period in relation to the pump's performance curve and the delivery condition. Figure 4 displays the linear decreasing of efficiency as a function of the decreasing flow rate. This shows the massive drop in effectiveness and therefore the energy saving potential of a cleaning process. The current common methods of cleaning iron clogged systems and submersible motor pumps are done by shutting down the well and the removing of pump. Afterwards, various methods are used to remove the ochre deposits. These are mechanical methods, chemical methods or the combination of both. The cleaning by mechanical processes is for example done by high pressure water jets, the drying and subsequent knocking out of ochre deposits, vibratory grinding or sandblasting. If items have to be cleaned from the inside, they have to be dissembled. The cleaning by chemical processes is done by pumping or by bathing the items in a cleaner [START_REF] Wulff | Ansätze zur Modellierung eines komplexen Ableitersystems für die Grundwasserabsenkung (Approaches for modeling a complex deriving system for groundwater lowering)[END_REF]. For both cases, a neutralization of the cleaner is required. This particularly applies to the pump. Mechanical cleaning methods are also known for the well and used in the context of cleaning the well interior (well tubes, filter gravel, borehole wall) [START_REF] Wulff | Ansätze zur Modellierung eines komplexen Ableitersystems für die Grundwasserabsenkung (Approaches for modeling a complex deriving system for groundwater lowering)[END_REF][START_REF] Dvgw | Brunnenregenerierung (Regeneration of Wells)[END_REF].

The chemical methods can also be applied to the well, but may need a special approval process. Again, the hydraulic components should be removed from the well for these methods.

Therefore, an approach is preferable by which the system is not only prevented from ochre depositions, but rather to develop a simple concept to clean a system in-situ if it is already iron clogged. This has the advantage of a reduced maintenance time as well as the possibility to operate the system more economical since purification is frequently possible. Methods for the in-situ purifying of clogged system exist already. For example, the process of flushing water or a water-air-mixture proposed by the German Technical and Scientific Association for Gas and Water (DVGW) [START_REF] Dvgw | Reinigung und Desinfektion von Wasserverteilungsanlagen (Cleaning and disinfection of water distribution systems)[END_REF]. However, these methods are not yet applicable to ochre deposits as for example, necessary flow velocities are unknown. Further, in general terms, it is unknown for which flow velocities ochre detaches and how this relates to the used material. Therefore, this paper experimentally examines the flow velocities for which ochre resolves and relates this in addition to different materials and coatings. The investigations were made in three steps: The first step included the creations of artificially ochre layers on sample sheets of different materials and coatings. The goal of the second step was to determine the flow velocity at which the ochre detached from the sample sheets. It was found that these necessary flow velocities were higher than technically relevant flow velocities. Hence, the last step involved measurements at which a sample is installed in a flow channel and the velocity distribution on its surface was measured by a Laser-Doppler-Anemometry system (LDA). A solid body conditioning in shape of a nozzle was adapted until the necessary flow velocity for ochre detachment was reached. For that propose the velocity profiles around the sample sheet were measured by LDA. For each material and coating were three sample sheets utilized in order to ensure reproducibility. The sample sheets were mounted on a rack during the exposure time (cf. Figure 5) The rack offered enough space to install 8 sets of sample sheet, 24 samples over all. The samples were installed vertical with equal space between them in a depth of 150 mm. The exploration time was 12 weeks, in one repetition experiment it was 24 weeks.

Flow Velocity of

Results

The grown layers of ochre were comparable to those which are normally found at iron clogged, hydraulic components in wells e.g. pumps or machinery. Thus, on the surface of the samples was an inertial layer, which was hard and aged. Furthermore, there was a second layer, which was soft and could be easily detached. Likewise to hydraulic components was the grown ochre of the samples inhomogeneous in texture. There are some materials and coating which stick out. For example, the results of Coating 4 and the Polyenthylene spread across a wide range. A first inspection showed that these materials were grown with a thicker and also harder ochre layer. The materials Copper, Brass and Coating 5 stick out too. The ochre layers on these materials are very smooth. Only small vibration by lifting the rack out of the water led to a loss of ochre layer parts on these materials. 1.2 Determine the Velocity of Ochre Detachment

1.2.

Methods

The aim of the experiments was to determine the flow velocity at which the ochre layer on the sample's surface detached. Therefore, the samples with ochre layer were mounted in a transparent pipe section of 100 mm diameter on a test rig which is shown in Figure 7.

It consisted of a test basin with 9 m³ water reservoir, submersible motor pump, transparent pipe section to mount the sample sheets, a flow measurement device, a flow control valve and venting valves on different places to obtain air in the test section. The transparent pipe section allowed to observe the sample sheets during the experiment. After starting the pump the volumetric flow velocity was increased each 20 seconds starting with 0.35 m/s. Each measurement was finished when the sample sheet was completely cleaned or the maximum flow speed of 9.6 m/s was reached. During the measurements, sticking out events and their flow velocity were determined:

• First ochre particle were mobilized.

• Bigger areas were mobilized.

• Only the ground layer-the initialized ochre layer-was present. • No more ochre particles were mobilized.

Figure 8 shows a sample before and after the in-situ cleaning. not scaled

Results

The experiments for obtaining the velocity of ochre detachment show the context between exploration time, ochre layer thickness, necessary velocity to remove the ochre deposits and material. Figure 9 show that all material and coatings could be cleaned up to a remaining ochre thickness less than 3 mm with one outliner at 5 mm. The volumetric average velocity was in all tests between 0 and 9 m/s. Assuming a technical relevant velocity of 2 m/s, it can be stated, that the necessary average velocities to detach ochre from the sample sheets were significantly higher.

The tests showed also, that the remaining ochre thickness is independent of the ochre thickness and the exploration time. However, the necessary velocity increases with the exploration time and the ochre thickness.

The removal velocities were categorized to different classes for further tests. Figure 10

Discussion

The tests showed that it is possible to clean ochre deposits by help of high flow velocities of water. This was shown for all tested materials and coatings. Therefore, an in-situ cleaning of ochre deposits i.e. iron clogged systems is principal possible. Some materials, such as e.g. brass and copper, show particularly good ocher-repellent properties. These should be preferred for ocher endangered pumps and machines.

On the other hand, the studies show that Coating 4 is not suitable for use in this application area. The measurements also show that a flow rate of Class 4 or higher is most often necessary to replace the ocher of the plates. These speeds do not normally occur in technical systems. For in-situ cleaning this speed should be ensured to force a cleaning.

Velocity Profiles 2.1 Methods

The outcome of the first experiments showed that there are higher velocities necessary for detaching ochre from pumps or machines than these that are normally found in technical systems. It was the idea to use a conditioning in shape of a nozzle around the sample sheets. This increases the velocity at the sample sheets surface whereby the system velocity has a low technical relevant value. The resulting velocity profiles were measured and provide information about the boundary layers and the required design of conditioning. These tests were done by mounting a clean sample sheet in a closed flow channel. Figure 12 shows this flow channel which had a pipe diameter of DN 400. It contained a tank with an axial pump and an etoile straightener directly after the pump on the lower pipe level. The tank was connected to water storage tanks, a cooler and a filter rack. Next to the tank were two butterfly valves. In flow direction followed on the lower level a flow measurement device and two elbows with guide vanes. On the top level was a settling chamber with an installed straightener and a nozzle. The nozzle had a contraction ratio of 2 and transformed the flow cross section to a rectangle with a height of 300 mm and a width of 210 mm with a corner radius of 8 mm. Before and after the transparent test section were two pressure measurement devices installed. After the test section followed a diffusor and a wake back to the tank.

Figure 11 shows the test setup in the measuring section. The parts of the conditioning are a basement, a spacer with different thickness and the profile of the conditioning.

In this case, a nozzle with a quarter circle shape of radius 40 mm and a diffusor with a 6° angle were used. The thickness of the spacer variated the conditioning. The conditioning fills the test section's width with 210 mm. The measuring section was equipped with transparent side walls to allow optical access.

Figure 11. Experimental Setup.

A LDA system was used to measure the flow profiles around the sample sheet. The LDA System is a statistical, laser optical system to measure the flow velocity in a small control volume. The used system was a one dimensional fp50-shift LDA System from Intelligent Laser Application (ILA) that consisted of an integrated nd:YAG Laser with 532 nm wavelength and a focal length of 250 mm [START_REF]HANDbook Laser Doppler Velocimetry fp50shift[END_REF]. The used particles are Silver Hollow Glass Spheres with a diameter of 15 μm. The minimum bursts per point were 500 and the minimum measuring time was 120 seconds. The LDA System was used to detect the flow velocity in different points over the sample sheet's surface to measure the velocity distribution in this way. The first measuring plane is upstream, 50 mm in front of the leading edge; here the incident velocity distribution was detected. The next plane was directly on the leading edge, the planes following in the length of 5, 10, 20, 40, 60, 80, 120, and 240 mm over the sample sheet's length. All planes were in the middle of the depth of the sample sheet. On the planes, the points of measuring are in the height of 0.5, 1, 2, 4, 8, 16, 32 mm. On the upstream plane in addition -5, -2.5 and 0 mm.

Results

Figure 13 shows an example for the measured normed velocity distributions of class 4. Further, the normed velocity distribution was measured for each of the six classes. The incident flow is in an area around 99% of the adjusted velocity. For the position x=10 mm, the first measured velocities is in the boundary layer. At least, on position x=240 mm, the first four velocities are in the boundary layer.

For the next step the velocity distribution on the position x=40 mm is the reference distribution. On this position the transition between the nozzle and the diffusor is located. Figure 14 to 19 illustrate the results of the test with the conditioned flow. The aim was to know the level of conditioning that led to ochre detachment velocities. Figure 14 shows one velocity distribution in the near of the sample sheet's surface at the position x=40 mm as a reference. In addition the distribution of the technical relevant flow rate is shown and four levels of conditioning: Reducing the cross section area in the test section to 63%, 50%, 37% and 23%.

The velocity for the first class is less than the technical relevant flow velocity of 2.0 m/s. Therefore the local velocity is higher without a conditioning of the flow. The class 2 is reached with a conditioning level of 63%. The local velocities of class 3 could reach with a conditioning level of 37%. The velocities of class 4 and 5 are reached with a conditioning level of 23%. A conditioning level of 23% was not big enough to reach the local velocities of class 6.

The same investigations were also done with the technical relevant velocity of 0.75 m/s. In this case only the first two classes could be reached with a conditioning level of maximum 23%.

Conclusion and Discussion

The described tests show that it is possible to grow artificial ochre layers on test specimen. This ochre layers are similar to layers found in hydraulic systems and clogged pumps. It was found that the grown artificial ochre layers depended on the used materials and coatings of the sample sheets in respect to its adhesiveness. Positively sticking out were mainly copper and brass because the ochre layer were easily to remove from it.

The tests focused on a cleaning process by flushing water to the sample sheets with artificial ochre layers. This was successful and demonstrate the cleaning is in principle possible. However, the necessary flow velocities to remove the ochre layers were higher than normally found in technical systems. Again, the tests showed that the ochre layers and their adhesions depended on the material and coatings. For example, the sample sheets of cooper were easy to clean, i.e. low velocities, and in contrast the ochre adheres particularly strong on coating 4.

The tests were followed by measuring the velocity fields around the sample sheets and the use of a so called conditioning. This created locally the examined velocity to remove ochre whereby the flow velocity in the system had a technical relevant value.

However, it remains unclear by these tests whether these conditioned flows actually would clean an iron clogged system. During these tests, the process of iron clogging has been simplified. Thus, the geometry of the sample sheets do not correspond to the geometries usually found in hydraulic systems. In addition, the process of iron clogging is sometimes a long process with years of operation as the above mentioned long term experiments show. During such a period, the boundary conditions for a cleaning can change. For example, the surface roughness of new parts is not equal to old parts under iron clogging conditions. This was not considered during this investigations. Also, the ideal conditions in terms of the velocity distribution and the pressure distribution in the measuring section does not correspond to those that occur in real systems.

Outlook

Further investigations consider now the influence of surface roughness of the tested sample sheets. This will be done by sample sheets of same material but different in surface roughness ranging from a polished surface to an aged casting surface. Additionally, the next step will be to evaluate the conditioned flow with ochre samples. These investigations showed that the in-situ cleaning of iron clogged surfaces by a water flow is possible. The results of these investigations will be used in the further research to develop an in-situ cleaning for hydraulic machine and machinery by water flow or water-air mixture. First laboratory test in this field were successful. Figure 20 shows on the left side an iron clogged entry into the diffusor of a submersible motor pump before the attempt. On the right side the same component is displayed after the in-situ cleaning test with a water-air mixture.

Figure 1 .

 1 Figure 1. Example of Ochre Deposits on the Diffusor of a Submersible Pump

Figure 3 :

 3 Figure 3: Characteristic curve of pump and variation of operating point during entire test period [2].

Figure 4 :

 4 Figure 4: Variation of relative efficiency eta/etaopt as a function of the volumetric delivery during the test periode [2].

Figure 5 .

 5 Figure 5. Rack for Sample Sheets, Sample Sheets Clean (left) and Iron Clogged (right).

Figure 6 .

 6 Figure 6. Ochre Thickness over Exploration Time.

Figure 6

 6 Figure6illustrates that the samples differ in ochre layer with thickness from 0 and 32 mm after exploration times of 12 or 24 weeks. It shows that the ochre layer is grown with the exploration time. The samples of 1.4571, Coating 1, Coating 2 and Coating 3 were examined twice, first with an exploration time of 12 weeks and second with an exploration time of 24 weeks. These samples had an ochre layer with thicknesses between 15 and 30 mm after 24 weeks and in contrast the same samples had thicknesses

Figure 7 .

 7 Figure 7. Test Rick for Detachment Experiments.

Figure 8 .

 8 Figure 8. Sample sheet with ochre Layer (top) and Sample Sheet after in-situ cleaning (bottom).

Figure 9 .

 9 Figure 9. Remaining Ochre Thickness over Velocity.

  displays the class diagram to order the tested materials and coatings to the defined velocity classes. The class wide Δv is fixed on 1.5 m/s. Therefore, the class boarders and the choosen class velocities follow to: • Class 1: 0≤v<1.5 m/s, v m =0.75 m/s. • Class 2: 1.5≤v<3.0 m/s; v m =2.25 m/s. • Class 3: 3.0≤v<4.5 m/s; v m =3.75 m/s. • Class 4: 4.5≤v<6.0 m/s; v m =5.25 m/s. • Class 5: 6.0≤v<7.5 m/s; v m =6.75 m/s. • Class 6: 7.5≤v<9.0 m/s; v m =8.25 m/s. In an ideal case each material or coating could be assign to one class. In this experiments, it was only possible for 1.4571 (t=24 weeks, class 6), Teflon (class 5) and Coating 3 (t=12 weeks, class 4). There are some more material and coatings in two neighbored classes (double counted classes are underlined): Brass (class 4/5), Polyethylene (class 3/4), Coating 1 (t=12 weeks, class 3/4), Coating 2 (t=12 weeks, class 4/5) and Coating 3 (t=24 weeks, class 4/5). The class diagram (Fig. 10) shows that most materials and coatings belong to class 4 and 5 i.e. high velocity classes.

Figure 10 .

 10 Figure 10. Results of the Experiments ordered by Velocity Classes.

Figure 12 .Figure 13 .

 1213 Figure 12. Closed Flow Channel.1000 mm

Figure 14 .

 14 Figure 14. Reference Class 1, vpipe=2.0 m/s, Position x=40 mm.

Figure 15 .

 15 Figure 15. Reference Class 2, vpipe=2.0 m/s, Position x=40 mm.

Figure 16 .

 16 Figure 16. Reference Class 3, vpipe=2.0 m/s, Position x=40 mm.

Figure 17 .

 17 Figure 17. Reference Class 4, vpipe=2.0 m/s, Position x=40 mm.

Figure 18 .

 18 Figure 18. Reference Class 5, vpipe=2.0 m/s, Position x=40 mm.

Figure 19 .

 19 Figure 19. Reference Class 6, vpipe=2.0 m/s, Position x=40 mm.

Figure 20 .

 20 Figure 20. Submersible motor Pump's Iron Clogged Entry of the Diffusor. Before in-situ cleaning (left) and after the test (right)

Ochre Detachment 1.1 Sample Sheets

	1.1.1 Methods
	Layer of artificial ochre were grown on sample sheets of
	different materials and coatings. This was done by
	exposing them to an open flow channel that transported
	mine water of an open pit mine. The sample sheets were
	rectangular with dimensions of 130 mm x 300 mm x 5 mm.
	The considered materials and coatings were:
	• Stainless steel 1.4571.
	• Polyethylene.
	• Copper.
	• Brass.
	• Teflon.

• Coating 1 (Epoxi Coating). • Coating 2 (Epoxi Coating). • Coating 3 (Epoxi Coating). • Coating 4. • Coating 5. new pump's performance with ochre

ACKNOWLEDGMENTS

This research was supported by Bundesministerium für Bildung und Forschung (BMBF). We thank all involved colleagues, especially our colleagues from the Vattenfall Europe Minig Group, who provided insight and expertise that greatly assisted the research. The authors would like to thank Michael Poehler and Carsten Strauch for their support during the field and laboratory tests. We thank Angela Gerlach for assistance and comments that greatly improved the manuscript.


Xiaoran Zhao

Zhengwei Wang

Yexiang Xiao

Yongyao Luo

Lei Cao

Unsteady Flow and Pressure Pulsation Characteristics Analysis of Rotating Stall in Centrifugal Pumps under Off Design Conditions

Keywords:

Unsteady flow phenomena like rotating stall frequently occur in centrifugal pumps under off design conditions. Rotating stall could lead to flow instabilities and pressure pulsation, which affect the normal operation of pumps. The mechanism of rotating stall has not been sufficiently understood in previous researches. This paper aims to simulate the unsteady flow characteristics in a centrifugal pump by CFD, analyze pressure pulsations caused by rotating stall and explore the propagation mechanism of rotating stall. In current study, 3D unsteady numerical simulations were performed to model the unsteady flow within the entire flow passage of a centrifugal pump under conditions of 0.4QBEP and 0.6QBEP. Though flow characteristics research, the generation and propagation of rotating stall are discovered. Additionally, frequencies and amplitudes of pressure pulsations related to rotating stall are investigated by spectrum analysis.

INTRODUCTION

Centrifugal pumps are widely used in industry. To ensure efficient utilization, it is important to operate centrifugal pumps in stable conditions. Unsteady flow phenomena, including rotating stall, rotor-stator interaction (RSI) and reverse flows, exist in centrifugal pumps under off design conditions. All of above flow patterns could possibly lead to instabilities and pressure pulsations. During the past few years, rotor-stator interaction is regarded as the most important factor for strong pressure pulsations with blade passing frequency. Rotating stall is also a primary cause of low frequency pressure fluctuations in centrifugal pumps.

When flow rate decreases sharply, flow separation develops, resulting to the passage blockage. This blockage will cause adjacent passage stalled, like the stall cell is propagating circumferentially. This phenomenon is called rotating stall. Rotating stall was firstly discovered and extensively studied in compressor turbines [START_REF] Emmons | Compressor Surge and Stall Propagation[END_REF][START_REF] Day | Stall inception in axial flow compressors[END_REF]. Much attention has been paid to the study on flow structures of rotating stall in pumps by both numerical and experimental methods. Yoshida [START_REF] Yoshida | Rotating Stalls in Centrifugal Impeller/Vaned Diffuser Systems[END_REF] observed rotating stall in the vaned diffuser of a centrifugal pump in experiment. Sinha [START_REF] Sinha | The Flow Structure During Onset and Developed States of Rotating Stall Within a Vaned Diffuser of a Centrifugal Pump [J][END_REF] described rotating stall phenomenon at the exit part of a centrifugal pump with vanned diffusers and revealed the relationship between rotating stall and pressure pulsation by PIV measurements. Sano [START_REF] Sano | Numerical Study of Rotating Stall in a Pump Vaned Diffuser [J][END_REF] used CFD technology to explore rotating stall and pressure variation in a vaned diffuser of a pump and proved that the clearance between impeller and diffuser had an effect on occurrence regions of rotating stall.

Recently, more researchers concentrate on rotating stall studies. Li [START_REF] Li | Dynamic Characteristics of Rotating Stall in Mixed Flow Pump [J][END_REF] built an understanding on rotating stall in mixed flow pump and found that adverse pressure gradient in the flow passage increased with stall development and influenced stall in turn. Yuan [START_REF] Yuan | Experimental investigation on the flow-induced noise under variable conditions for centrifugal pumps[END_REF] investigated broadband noise and resonance caused by rotating stall in a centrifugal pump under small flow rate condition though frequency analysis. Lucius [START_REF] Lucius | Numerical Simulation and Evaluation of Velocity Fluctuations During Rotating Stall of a Centrifugal Pump [J][END_REF] argued that rotating stall could excite structural vibrations in pumps through numerical simulations. Despite those studies, the mechanism of rotating stall has not been sufficiently understood in previous researches.

In centrifugal turbomachinery research, both flow pattern study and pressure pulsation analysis are necessary. Cao [START_REF] Lei | Effect of axial clearance on the energy performance of an enclosed-impeller centrifugal pump with vice blades[END_REF] described three-dimensional turbulent flow in the entire flow passage of a shrouded centrifugal pump to understand energy losses caused by different factors. Yang [START_REF] Jing | Unsteady internal flow field simulations in a double suction centrifugal fan[END_REF] investigated vibration and noise generation mechanism of a double suction centrifugal fan based on analysis of the pressure fluctuations. The present paper applies CFD technology to simulate flow characteristics in a centrifugal pump, analyzes pressure pulsations caused by rotating stall and explores propagation mechanism of rotating stall.

Calculation Model 1.1 Parameters of Centrifugal Pump

The studied model is a centrifugal pump with three impeller blades. Computational domains are showed in Figure 1, including volute, impeller and suction pipe. The main parameters of this pump are presented in Table 1.

Turbulence Model and Boundary Conditions

In this research, ANSYS CFX is used to solve Reynoldsaveraged Navier-Stokes (RANS) equations. RANS equations can analyze on both statistical average turbulence parameters and random fluctuating quantities. There are several turbulent models to describe turbulence program, including standard k-ε, RNG k-ε, standard k-ω, SST k-ω, and Reynolds stress model (RSM). The incompressible continuity equation and the Reynolds time averaged Naviere-Stokes equations with the SST k-ω turbulence model was adopted in this paper.

Mesh Generation and Time Step Set

Mesh generation is a key step in the process of finite element modeling. Grid number, type and quality of the mesh affect the numerical simulation. Structure mesh cells generated by ANSYS ICEM were utilized in pump volute and suction pipe. Impeller structure mesh cells were produced by ANSYS Turbogrid. Cells near the solid wall were denser to capture the flow structure precisely, especially on blade surfaces. To ensure both accuracy and efficiency of this simulation, mesh independent check was performed at optimum operating condition of 200 m 3 /h flow rate and 32 m head. The finally adopted mesh element amount in transient calculations was 3.35 million (0.7 million in suction pipe, 1.59 million in impeller and 1.06 million in volute). The structure mesh of impeller is showed in The results of steady flow simulations were used as the initial flow flied of the unsteady simulations. The time step was set as 0.004138s, which is 1% of pump rotation period. Each pump revolution was calculated in a time sequence of 100 time steps.

Monitor Points Arrangement

Monitor points were set in each channel in the rotating impeller to record signals of pressure pulsation. Monitor points are set at pressure side, suction side and midpassage of 0.5 span. Flow direction is from 11 to 16.

Monitor points arrangement at one passage is presented in Figure 3.

RESULTS AND DISCUSSION

In order to study flow patterns and pressure pulsation characteristics, unsteady simulations were performed for two different working conditions of 0.4QBEP and 0.6QBEP.

Rotating Stall Flow Pattern Analysis

For the purpose of analyzing the impeller inner flow, numerous rotating periods were simulated. For 0.6QBEP working condition, Figure 4 -criterion is used to present the vortex structures to identify internal flow of the impeller. -criterion [START_REF] Chakraborty | On the relationships between local vortex identification schemes[J][END_REF] was proposed by Jeong and Hussain in 1995. When ignoring the effect of disturbance and viscosity, the symmetrical parts in gradient of incompressible Navier-Stokes equations can be expressed as ).

When comparing the two working conditions, it is demonstrated that rotating stall is more fully developed under 0.4QBEP working conditions, which is farther from the optimum condition.

Unsteady Pressure Pulsation Characteristics Analysis

In order to investigate unsteady characteristics of rotating stall, pressure pulsation signals of 54 monitor points under both 0.4QBEP and 0.6QBEP working conditions are collected and analyzed. Besides these frequencies, it is found that a frequency (f = 0.6fn) appears at monitor points M14-M16, P14-P16, which is considered as the frequency of rotating stall. Many researches have shown that the spread speed of stall cells is less than rotating speed of the impeller, which means the characteristic frequency of rotating stall is lower than rotation frequency. Results mentioned above agree well with this conclusion. The spectra also imply that the pressure pulsation amplitudes of rotating stall are more obvious at monitor points P14-P16. This finding indicates that stall cells appear downstream at the pressure side, which accords with the flow pattern analysis in Figure 4.

Bisides the pressure pulsation of stall cells propagating, rotating stall could impact on pressure pulsations caused by RSI. Amplitudes of frequency (f = 3fn) at monitor points P15 and P16 are higher than that of frequency (f = 2fn), which could be explained as follows : when stall cells pass by the volute tongue, the flow interaction will lead to pressure pulsations. The acting mechanism and influence needs further study. Figure 9 is pressure spectra of monitor point P15 under two working conditions. The unsteady pressure pulsation characteristics under 0.4QBEP working conditions is similar to 0.6QBEP. The frequency components are more complicated and the amplitudes of rotating frequency and its harmonic frequencies are higher under 0.4QBEP working conditions. It is demostrated that flow patterns are more complex when the flow rate is smaller apart from the optimal working condition.

(a) 0.4QBEP (b) 0.6QBEP Figure 6. Flow vortex structures under 0.4QBEP and 0.6QBEP working conditions ( )

Conclusions

Numerical simulations of the internal unsteady flow in a centrifugal pump reasonably illustrate the flow characteristics inside the pump. When operating at part load condition (60% BEP and 40% BEP), there exists obvious rotating stall phenomenon in the pump impeller.

(1) In flow pattern analysis, it is found that stall cells appear, expand, shrink and disappear sequentially in one flow passage. Due to the blockage caused by rotating stall, flow separation occurs at the impeller inlet, which leads to stall cells propagation between passages. The vorticity research implies that rotating stall develops more seriously under lower flow rate working condition.

(2) Since the unsteady pressure pulsation inside the pump could cause variations, the pressure signals at various monitor points in the impeller were analyzed. The results indicate that rotating stall frequency is lower than rotating frequency and that the interaction between stall cells and volute tongue could have an influence on RSI pressure pulsation. There is evident pressure amplitudes from rotating stall downstream at the pressure side, which agrees well with the flow pattern analysis.

Figure 1

 1 Figure 1 Computational pump

Figure 2 .

 2 Figure 2.

Figure 2 .Figure 3 .

 23 Figure 2. Structure mesh of impeller

  (a) t = 0.5379s ( 0° ) (b) t = 0.5421s ( 36° ) (c) t = 0.5462s ( 72° ) (d) t = 0.5504s ( 108° ) (e) t = 0.5545s ( 144° ) (f) t = 0.5586s ( 180° ) (g) t = 0.5628s ( 216° ) (h) t = 0.5669s ( 252° ) (i) t = 0.5710s ( 288° ) (j) t = 0.5752s ( 324° ) (h) t = 0.5793s ( 360° ) Figure 4. Streamline in span-wise = 0.5 plane of 14th rotating period under 0.6QBEP working condition (a) t = 0.5379s ( 0° ) (b) t = 0.5462s ( 72° ) (c) t = 0.5545s ( 144° ) (d) t = 0.5628s ( 216° ) (e) t = 0.5710s ( 288° ) (f) t = 0.5793s ( 360° ) Figure 5. Vector in span-wise = 0.5 plane of 14th rotating period under 0.6QBEP working condition Assume that eigenvalues of the symmetric tensor is , and , , .

  Figure 6 shows vortex structures in the impeller under 0.4QBEP and 0.6QBEP working conditions (

  Figure 7 reveals change rules of pressure signals with time in 4 rotating periods, taking monitor points P14 and S14 for example. Time domain charts of pressure pulsation indicate that pressure changes periodically with time and has one wave crests and troughs in one rotating period, which are mainly caused by rotor-stator interaction.

Figure 7 .Figure 8

 78 Figure 7. Change rules of pressure signals with time of monitor point np112 and np122 Figure 8 presents pressure spectra of monitor points in one passage C. As observed, dominant frequencies of pressure pulsation on blade points are rotating frequency (f = fn) and other harmonic frequencies (f = 2fn, 3fn, …).Besides these frequencies, it is found that a frequency (f = 0.6fn) appears at monitor points M14-M16, P14-P16, which is considered as the frequency of rotating stall. Many researches have shown that the spread speed of stall cells is less than rotating speed of the impeller, which means the characteristic frequency of rotating stall is lower than rotation frequency. Results mentioned above agree well with this conclusion. The spectra also imply that the pressure pulsation amplitudes of rotating stall are more obvious at monitor points P14-P16. This finding indicates that stall cells appear downstream at the pressure side, which accords with the flow pattern analysis in Figure4.Bisides the pressure pulsation of stall cells propagating, rotating stall could impact on pressure pulsations caused by RSI. Amplitudes of frequency (f = 3fn) at monitor points P15 and P16 are higher than that of frequency (f = 2fn), which could be explained as follows : when stall cells pass by the volute tongue, the flow interaction will lead to pressure pulsations. The acting mechanism and influence needs further study. Figure9is pressure spectra of monitor point P15 under two working conditions. The unsteady pressure pulsation characteristics under 0.4QBEP working conditions is similar to 0.6QBEP. The frequency components are more complicated and the amplitudes of rotating frequency and its harmonic frequencies are higher under 0.4QBEP working conditions. It is demostrated that flow patterns are more complex when the flow rate is smaller apart from the optimal working condition.

Table 1

 1 Main parameters of computational pump

ACKNOWLEDGMENTS

Special thanks are due to the State Key Program of National Science of China (Grant No. 51439002), National Natural

(a) P11, M11 and S11 (b) P12, M12 and S12 (c) P13, M13 and S13 (d) P14, M14 and S14 (e) P15, M15 and S15 (f) P16, M16 and S16 Figure 8. Pressure spectra of 54 monitor points in the impeller under 0.6QBEP working condition (a) P15 (b) S15 Figure 9. Pressure spectra of monitor points P15 and S15 under 0.4QBEP and 0.6QBEP working conditions Science Foundation of China (No. 51279083), Special Funds for Marine Renewable Energy Projects (Grant No. GHME2012GC02), State Key Laboratory of Hydroscience and Engineering (Grant No. 2014-KY-05) for supporting the present work.