Julian D Pauw
email: julian.pauw@ltf.mw.tum.de

Lucrezia Veggi

Bernd Wagner

Joydip Mondal

Maximilian Klotz

Oskar J Haidn

S Y Mpo

O Tatin

Design Procedure of a Turbopump Test Bench

Keywords:

e high complexity of turbopumps for liquid rocket engines and their demanding requirements necessitate that their design process is accompanied by extensive experimental investigations and validation tests. is paper presents the design procedure for a rocket turbopump test bench, where water is used as a surrogate for the cryogenic fluids usually used in rocket engines. Scaling methods, that allow for a comparison of tests under varying conditions, are reviewed from literature and applied to derive the necessary dimensions of the test bench. e resulting test bench design is shown in detail and its capabilities to support the turbopump design process are assessed. Further, the operational envelope of the derived test bench design is evaluated with respect to later tests of different pumps.

. INTRODUCTION e turbopumps of a liquid rocket engine (LRE) supply the combustion devices with fuel and oxidizer at high mass flow rates and at a high pressure level. Typically, fuel and oxidizer are pumped by separate pumps. e turbopumps increase the pressure from a low pressure level in the tank to a high pressure level needed for the combustion process. Consequently, the turbopumps are a substantial part of the rocket engine.

e dimension and the performance of the turbopumps depend highly on the desired engine operation point, the engine cycle and the requirements of the combustion chamber.

e work performed at the Division Space Propulsion of the Technical University of Munich (TUM) is embedded into the research project KonRAT, i.e. rocket propulsion engine components for applications in aerospace transportation systems.

e project aims at establishing competences in the development of turbopumps. [ , , , , ]. Key objective at the Division Space Propulsion, TUM, is the investigation of the design process of turbopumps and the investigation of fluid phenomena. Both parts are carried out numerically as well as experimentally.

e Division Space Propulsion, TUM, has established a design process for rocket engine turbo pumps based on well-known literature and commercially available so ware tools [ ]. In order to fully understand all design parameters and to ensure that those parameters desired can be reached, experimental validation of those design parameters is an indispensable step in the design loop of every rocket engine turbopump.

e fuel and the oxidizer of cryogenic liquid rocket engines are stored in liquid state under boiling conditions on-board the launcher and thus ground tests with cryogenic fluids are of very complex nature. Besides the difficult generation and storage of the cryogenic fluids, the demands on the turbopump under development are very high as the design needs to withstand high temperature loads and it needs to take into consideration material choices for cryogenic temperatures for every tests. Consequently, tests with fluids that are liquid at ambient temperature are highly desirable. Further, it would be beneficial to perform tests at lower rotational speeds without loosing information on the flow behaviour inside the pump. Test benches operated with water at ambient temperature have been established as a very good solution to this problem. A drawback of tests at ambient temperature with water is that the cavitational behaviour of turbopumps cannot be captured. Especially, the so called thermodynamic suppression head (TSH), an effect that can be observed at tests with cryogenic fluids, is not present at ambient temperature tests with water. A solution is provided by the findings of several research groups which show that similarity of the cavitational performance can be reached by heating the water up [ , , , , , ].

In literature, many different scaling and similarity methods are present. is paper will present a set of those methods based on a literature survey and makes use of the methods in order to define the operating conditions of a test bench for a liquid oxygen turbo pump developed at TUM. e derived test bench will be shown in detail and its properties will be evaluated for later usage. is is mostly done by making use of a numerical test bench representation in the commercially available so ware tool EcosimPro ® . In order to be able to use the test bench for other configurations as well, an outlook on the generalized operational envelope of the test bench will complete this paper, so that the possible use for future test campaigns with different configurations can be estimated.

.

SCALING METHODS

In order to test a pump in a test facility at conditions that differ from the normal operating conditions, the similarity of the flow passing through the pumps needs to be established both at the test bench and at the operational conditions. According to [ , , ], this similarity can be reached if four different parameters are comparable: ( ) the geometry under investigation, ( ) a comparable establishment of velocity triangles at pump inlet and outlet, ( ) a similar dynamic behaviour of the pump and ( ) comparable thermodynamic properties of the fluids.

Following Sigloch [ , ], geometric comparability of two turbo machines is fulfilled if the dimensions of the parts conducting the flow follow a certain ratio in all spatial dimensions. is offers not only comparable interaction of the fluid with the static and dynamic parts of the machine, but also yields similar velocity triangles at every corresponding point for friction-free conditions because the velocity vectors are then governed by passage dimensions and the rotational speed only. It is important to make sure that not only the rotor and blade geometries are comparable, but also the gap geometries and clearance distances between rotor and housing.

λ geometr y = dimension of prototype dimension of model = X m X a ( ) λ velocity = velocities of prototype velocities of model = v m v a ( )
In the case of single-phase flows, i.e. in the case of noncavitating flows, the forces acting on the pump are the following: inertia forces, pressure forces, viscous forces and the gravitational force. Additionally, forces resulting from the elasticity of the mechanical system, especially the sha , can act on the pump components. e flow through two different pumps can only be considered similar if the ratio of the forces acting on these pumps is constant in all spatial directions.

λ F or ce = forces at prototype forces at model = F m F a ( )
e forces acting in pumps with single-phase flows can be related by the Froude number, the Reynolds number and the Euler number. ese characteristic numbers should be the same for the model and the prototype.

e Froude number is defined as the ratio of inertia forces to gravitational forces. It is commonly used in hydro-mechanics to model flows with free surfaces where gravitational forces have a large impact.

Fr = inertia force gravitational force = v 2 gL c ( )
e Reynolds number relates between the acting inertia forces and the viscous forces. Equivalent Reynolds numbers predict a similar development of boundary layers inside two compared pumps. e generation of boundary layers is closely linked to the surface roughness of the parts that conduct the flow. Especially for geometrically scaled models it is difficult to generate a comparable surface roughness of all pump components. For the purpose of comparing different radial machines, the Reynolds number is o en defined as the product of peripheral velocity U 3 at the impeller outlet and the corresponding tip radius R 3 divided by the kinematic viscosity υ. When comparing the scaled measurements in detail, it is strongly recommended to calculate the Reynolds number locally to guarantee comparable boundary layers all over the pump [ , , , ].

Re = inertia force viscous force = U 3 R t,3 υ = ωR 2 t,3 υ ( )
e Euler number describes the ratio between pressure forces and inertia forces. For the scaling of pumps, it is inevitable to keep the Euler number the same for model and prototype.

Eu = pressure force inertia force = ∆p ρv 2 ( )
Further, the thermal properties of the fluids, i.e. the specific heat, the enthalpy and the thermal diffusivity, largely influence the flow characteristics. is is especially true for machines that exhibit a large pressure difference. It is advisable to make use of fluids with comparable properties and to closely track property changes.

e above scaling methods need to be incorporated in order to design a test bench that can be used to test a LOX turbopump with water. For ground tests of liquid rocket engine turbopumps, the gravitational effects are negligible. e differences in height and the resulting effects are comparably small. e Froude scaling is thus irrelevant. e Reynolds scaling is of high importance. At least for this application, it is sufficient to achieve fully turbulent conditions in the model and the prototype because the boundary layers that develop at turbulent conditions are assumed to be comparable. Fully turbulent conditions can be considered for Re t,3 > 10 6 . Due to the high rotational speeds of liquid rocket engine turbopumps, this requirement can be fulfilled without any problems. Figure sums up the properties that need to be scaled for liquid rocket engine turbopumps. Obeying the above given similarity conditions, the operating properties can be transferred between model and prototype For the volume flow rate:

Q m N m D t,m 3 = Q a N a D t,a 3 ( )
For the head rise:

H m N m 2 D t,m 2 = H a N a 2 D t,a 2 ( )
For the input power:

P m N m 3 D t,m 5 ρ m = P a N a 3 D t,a 5 ρ a ( )
. Scaling of Cavitation Phenomena e scaling methodology above is valid for ideal fluids, i.e. non-cavitating single-phase flows. In operational regimes where cavitation at the pump blades occurs, a two-phase flow is present as a phase change is triggered by a pressure drop where the local fluid pressure is below the vapour pressure of the fluid. Usually, a certain amount of cavitation can be accepted for every pump, but excessive cavitation results in a head break down of the whole pump and defines an operational limit of the pump when the local static pressure is much smaller than the vapor pressure of the pumped liquid. In rocket engine turbopumps, cavitation usually first occurs at the leading-edge of the inducer and it is for most appli- In order to show comparable behaviour with water as a surrogate compared to cryogenic fluids in terms of cavitation, it is necessary to match the same flow coefficient ϕ as well as the cavitation number σ [ , ].

ϕ = 2Q AD t ω ( ) σ = (p st -p v ) 2ρ l D 2 t ω 2 ( )
However, in experiments with several fluids, especially with cryogenic fluids, that operate close to their critical point like liquid hydrogen and liquid oxygen, it was possible to observe that the inducers of pumps are operating without cavitation at NPSH values smaller than the NPSH R which would be expected for an ideal fluid. is effect is commonly called thermal suppression head (TSH). By definition, the TSH calculates to the difference between the available NPSH A and the NPSH ideal f luid that would be expected for an ideal fluid. NPSH ideal f luid equals the NPSH t ank minus friction losses in the inlet tubing [ ].

TSH = NPSH available -NPSH ideal f luid ( ) e mechanism of bubble formation, growth and collapse in cavitation depends largely on the instantaneous heat transfer between the bubble and the surrounding fluid, the size of the pump and the speed of the pump. us, additional scaling methods are needed to allow for a prediction of the mechanisms related to thermodynamic effects. Several parameters and models have been suggested in order to describe and predict the occurrence of cavitation in this regard [ , , , , , ].

Brennen [ ], by simply looking at a heat balance between the vapor and liquid phases, established a dimensional parameter that, as he claimed, should be identical for replicating identical cavitation behavior in two liquids. He assumed that the heat-transfer between the bubble and its surrounding is of conductive nature. e developed parameter Σ is widely used. ereby, he tried to show the different ranges within which the cavitation behavior of different fluids resembled the cavitation behaviour of water.

Σ = ρ 2 v h 2 f g ρ 2 l √ α l C p,l T l ( )
Ehrlich and Murdock [ ] further developed this parameter to a non-dimensional thermal scaling parameter called Dimensionless Bubble (DB) parameter by considering bubble growth over a time-varying pressure field. e resulting DB parameter is similar to the formulation suggested by Ruggeri and Moore [ ] and is considered very convenient for estimating the thermal operational boundaries of the test bench at an early stage in the test bench design process, as it is based solely on thermodynamic properties of the bulk fluid rather than empirical correlations. For the detailed investigation of a specific pump, it is of high importance to take into account all available prediction models, especially those for which be er validation data is available in literature.

DB = R t ω 3 /2 C p,l T l ρ 2 l √ α l h 2 fg ρ 2 v ( )
. TEST OBJECT

One main goal of the test bench under construction is to establish a result validation loop within the numerical design process for turbopumps at TUM. e pump to be developed is a liquid oxygen turbopump designed for a liquid hydrogen and liquid oxygen expander cycle engine. e desired operational parameters are given in Table . e resulting thrust level is in the order of magnitude of the VINCI upper stage engine. A preliminary CAD sketch of the pump assembly with inducer, impeller and turbine is shown in Figure . e test bench is designed in such a way as to investigate the pump detached from the turbine system. e parts of the pump assembly that are relevant for the test bench design are highlighted.

Table . LOX turbopump nominal operating conditions

. TEST BENCH DESIGN e main properties of the test bench can be selected based on the dimensions of the pump under development and the general scaling methods for pumps, which have both been introduced in the sections before.

e following section erefore, it is necessary to acquire the following data: the pressure difference over the investigated pump, the mass flow rate, the sha torque and the rotational speed of the sha . e torque measurements give information about the efficiency of the pump under investigation. A second goal is to experimentally observe the cavitation behaviour of the inducer and the pump with water tests in order to predict the cavitation behaviour under liquid oxygen conditions. erefore, as evident from the cavitation scaling theory, the water needs to be heated up in order to operate the facility with a liquid which is close to its boiling point.

. Test Facility Dimensioning

For an operation of the pump in non-cavitating conditions, the scaling methods of equation , equation and equation have to be applied. e maximal rotational speed of the motor that drives the pump has been chosen to N max = 5500 r pm.

e following considerations will approve this choice. Further, it is in good agreement with the rotational speeds of comparable test facilities. Consequently, sub-scale tests will be performed.

e geometry stays the same as in the LOX hardware. e hardware designed for the LOX turbopump will be used on the test bench without any scaling: λ geom = 1. e efficiency of the pump on the test bench and the efficiency of the original LOX pump are assumed to be equal:

η m = η a .
With the properties of the pump under development at TUM, given in

Q m, N ma x ≈ Q a N max N a = 24.75 m 3 /h ( )
e scaled design head rise at N max equals

H m, N ma x ≈ H a N m 2 N a 2 = 33.30 m ( )
At the same operating point, the sha power calculates to

P m, N ma x ≈ P a N m 3 ρ m N a 3 ρ a = 3.29 kW ( )
e dimensions of the new test facility have to be chosen in such a way that those parameters can be satisfied. A wider range of operation above those limits is desirable for potentially subsequent expansions of the test facility. In order to test the cavitation performance of the pump inducer, it is necessary that the mass flow coefficient ϕ, the cavitation number σ and the thermodynamic properties match the ones of the LOX application. Further, the turbopump has to be operated in regions where Re > 10 6 . As for noncavitating conditions, the geometry of the LOX hardware is used without dimensional scaling.

e minimal necessary rotational speed for which Re = 10 6 is satisfied can be described, according to Equation , by

ω ≥ υRe R 2 t,3
= 400.55 r ad /s or N ≥ 3825.00 r pm ( ) e thermodynamic properties are assumed to be comparable if the Dimensionless Bubble (DB) parameter, as denoted in Equation , is equal or close to equal. For the LOX turbopump, with the operational parameters given in Table and the dimensions of the impeller given in Table , this parameter calculates to DB LOX,re f = 0.306 for the impeller of the TUM design.

e plot in Figure shows the LOX DB reference value DB LOX,re f as a constant line. Together with this constant value, the DB value calculated for different rotational speeds is shown in dependence of the water temperature. It is clearly visible that for each rotational speed of the turbopump on the test bench, a specific water temperature has to be set in order to satisfy the equality of the Dimensionless Bubble (DB) parameter. With increasing rotational speed, the required water temperature rises. For the maximal chosen rotational speed of the motor N max , the water temperature iteratively calculates to T N max = 368 K. It has to be pointed out that this value for the bulk water temperature at the pump inlet only serves as design constraint to the water heating system at this early point in the test bench design procedure. .

Detailed Test Bench Design

Water is selected as the test medium. e use of water offers several advantages. e most important advantage is the easy handling. is allows for a comparably cheap operation of the test facility. Compared to tests with cryogenic fluids, the safety of tests is also improved. Further, only very few material incompatibilities are known. e system is designed as a closed circuit. is is especially advantageous for tests with heated water: a er preheating the water up to the desired temperature, the heater only needs to keep the temperature at the desired level. is can improve the temperature control accuracy. e use of a closed water loop is also in good agreement with other test facilities for pumps at different institutes and national standards [ , , , , , , , , ].

As the water is supposed to stay within the circuit for the duration of multiple test campaigns, deionized water is used. is is beneficial as depositions on water circuit components are limited. Especially for heated water, the sedimentary deposition of limescale is reduced significantly [ ]. It has to be taken into account that the water needs a minimal conductivity greater 20 µS /cm to guarantee the operation of inductive mass flow meters. e decay of the water quality is slowed down as well due to the fact that no permanent access of light is present in the system. A major drawback of a closed-loop system is that, in case of occurring cavitation, vapour bubbles can persist in the system and be sucked into the inlet again. e drawing in Figure shows an overview of the circuit. Necessary sensor positions, actuators and their positions within the loop are shown as well.

e water reservoir is realized by a stainless steel tank with a volume of V tank = 2000 l. It is designed to withstand the mechanical and thermal loads of water at p tank,max = 4 bar and T tank,max = 100 • C. e tank is equipped with a EPDM membrane filled with pressurized air. is membrane has a volume of V membr ane = 500 l. e air pressure within this membrane and therefore also within the tank is variable and can be controlled and regulated electronically. In operational modes where cavitation occurs, it is very likely that bubbles are transported into the tank and might disturb the pump measurements if they are sucked into the pump again. In order to significantly reduce this effect, it is desirable to maximize the residence time of the water in the reservoir.

is is a ained by redirecting the inlet flow in circumferential direction. In addition, the amount of dissolved oxygen can be measured in order to a ain a good repeatability of the test conditions. Further, the tank can be depressurized up to a negative pressure of p t,tank = 0.9 bar to remove dissolved oxygen. is is especially important for tests with heated water. For safety reasons, the tank is also equipped with an over-pressure valve.

e controllable static inlet pressure allows to perform NPSH R evaluations on the test pump.

e inlet to the pump from the main reservoir and the outlet piping from the pump to the main tank is created by stainless steel tubes with circular cross-section and standard flange connectors. e tube dimension has been chosen to equal the standard dimension DN80. is results in an internal pipe diameter of all tubes of D tube = 80.8 mm. It is favourable to have a fully turbulent flow within the tubes present at all times.

is is feasible with D tube for mass flow rates from m min = 0.6 kg s on. Based on the head rise scaling considerations in Equation , all tubes have been designed in the pressure class DN80-PN25. Due to restrictions of the sensors and auxiliary equipment in the loop, the static pressure in the inlet section, including the tank, is limited to p 1,max = 4 bar. e pressure in the outlet section is limited to p 3,max = 10 bar. In order to avoid possible sources of cavitation in the tubing, all transitions and redirections of flow are manufactured as smooth as possible. Further, all sources of flow disturbance are avoided in all tubes in front of sensors and in the tube in front of the pump inlet at a tube length of L min = 10 D tube .

e head rise of the pump needs to be reduced to the pressure level of the tank. is is done by a thro le valve configuration in-between the pump and the tank. In order to reduce the risk of cavitation at the thro ling system, two identical valves are arranged in a daisy-chain configuration. Both valves are equipped with an electronically controllable actuation unit. is makes it possible to set the pressure drop across each valve independently. Further, the mass flow rate can be controlled.

is feature is needed in order to do a performance mapping of the pump under investigation and it is a crucial requirement for cavitation scaling.

e mass flow rate is sensed at two locations. One inductive mass flow meter is placed in the inlet tubing directly in front of the pump inlet. A second inductive mass flow meter is placed a er the pump. At the same position, a measurement orifice is placed.

is is where the pressure drop across a defined through-flow area is measured. us, for a given fluid density, the mass flow rate can be calculated in a second, independent way. is allows for a comparison of measurement results and the improvement of the measurement accuracy in all measurement ranges. For the controlled operation of the test bench, pressures and temperatures are captured at different locations of the water circuit. e static pressure is monitored, as depicted in Figure

, in the pump inlet section, in the pump outlet section and directly a er the main thro le valve configuration. At all three locations, the pressure measurements are averaged over the circumference of the horizontally placed pipes in order to compare for gravity effects. e measured static pressure difference between pump inlet and pump outlet can be used to calculate the head rise of the pump. e static pressure difference over the thro ling valve configuration allows for a safe operation of the same. In addition, the tank pressure is also monitored. Additionally, temperatures are detected at all mentioned pressure sensor locations. Especially for tests with heated water, these temperature readings yield valuable information for the thermal control system. e pump is driven by a three-phase alternating current (AC) electric motor with a maximal power of P shaf t,max = 12 kW.

e motor reaches its maximal torque T shaf t,max = 27 Nm at its design speed N ref = 3100 r pm. e maximal speed of the motor, without the use of any additional transmission, is N max = 5500 r pm. e motor is connected to the sha by a flexible coupling that dampens the temporary high torque during start-up. e sha is held in position by a bearing unit in overhung configuration -the bearings are positioned between the pump and the drive unit. e bearing unit is designed as an arrangement of a fixed bearing close to the pump and a floating bearing close to the drive unit. All loads on the drive unit are closely monitored. is includes the torque of the sha , the rotational speed and the axial force acting on the fixed bearing. Further, a bearing monitoring system is established by permanent observation of the bearing race temperatures. All bearings are run with grease lubrication and the grease quality is observed in fixed intervals. Further, the pump housing is equipped with three acceleration sensors for the investigation of potential instabilities. e data obtained from those sensors can also be used to monitor the bearing operation. As shown in section , in order to reproduce the cavitation behaviour of the LOX turbopump, it is necessary to run tests with heated water. erefore, a water heating system is included in the test bench setup. is heating system is designed as a second auxiliary circuit that can be decoupled from the pump circuit. us, it is possible to heat the water contained in the main tank to a desired temperature. e water is heated up by an electrical heater with a power of P ht,el = 60 kW.

e water in the second auxiliary water circuit is driven by a separate pump. e heating system is designed to control the temperature within ∆T 1 = ±1 K and can a ain a maximal water temperature of T max = 100 • C. For means of flow control in the auxiliary heating circuit, the water temperature at the heater outlet, the static pressure at heater inlet and heater outlet as well as the mass flow rate are closely monitored. e mass flow rate is detected by a measuring orifice. e bladder inside the main tank serves as a compensation reservoir for volumetric changes due to the heating of the water. A dedicated cooling system is not implemented, but the insulation of the tank and the tubing is designed in a way that continuous heating is necessary to a ain a constant high temperature.

. Numerical Design Methods

In order to enhance the test facility development described in the previous sections, the test bench was modelled numerically in parallel with the physical setup. erefore, the water circuit including all pipes, valves and the tank have been modelled in the so ware tool EcosimPro ® . Especially all components that are foreseen to be electronically controlled were investigated numerically in detail.

erefore, the heating system and the tank, including the membrane bladder, were represented as detailed numerical models. For all components, the pressure drop across those components is implemented for different mass flow rates as core functionality. Further, for investigations on the thermal control of the test bench, empirical correlations for heat losses at all surfaces have been added. e so ware suite EcosimPro ® offers many tubing and piping elements readily available in its libraries that have been adapted to the properties of the test bench.

Q [m 3 /h]
ey can be combined in a modular way. e EcosimPro ® library ESPSS expands the building blocks by components for rocket engines. is includes special tank configurations as well as a generic turbopump model. e graph in Figure shows a numerically obtained system performance chart for different positions of the thro le valve assembly. For the generation of this chart, the thro le valve configuration was opened at a fixed percentage and the mass flow rate was varied. e static pressure at the pump inlet and the pump outlet was measured and the resulting head of the system was calculated. Especially the performance for the fully opened thro le valve configuration is of high interest as this curve describes the minimal head that a pump has to generate in order to be tested on the test bench. Further, a numerical evaluation of the pump operation within the circuit has been evaluated. erefore, the generic pump model has been initialized with a specific speed of N S = 24.34, a total head of H tot = 602.3 m, the design rotational speed of N LOX = 20000 r pm and an estimated efficiency of η = 0.887.

e graph in Figure shows the computed pump characteristic for N = 1500 r pm, the motor design speed N ref = 3100 r pm and the maximal rotational speed of the motor N max = 5500 r pm. Additionally, the system performance map is partially shown. is makes it possible to identify the resulting operation points.

is chart has been created by varying the opening level of the thro le valve configuration from 0% to 100%. e rotational speed of the pump has been kept constant for each curve. e head rise across the pump has been measured. .

SUMMARY AND OUTLOOK

e key characteristics of the developed test facility are summarized in Table . e designed test bench provides a valuable facility to test radial pumps with inducers in a sub-scale environment. According to the presented scaling methods, the results obtained here can be used to predict the non-scaled pump performance of the original application. Additionally, the possibilities to heat up the water, to control the flow rate and to control the inlet pressure separately, allow for the investigation of the occurrence of cavitation at the inducer blades. 11 e presented test facility has been designed to meet the test criteria for the LOX-turbopump which is currently under development here at TUM. All dimensions and characteristics of the components have been chosen accordingly. Nevertheless, the test bench can be used to investigate any pump of similar constructive form, as long as it stays within the constraints given in Table . Based on the Barber-Nichol's chart for pumps [ ], the operational boundaries of the test e numerical implementation of all components with EcosimPro ® in parallel with the physical construction of the test facility has shown to be beneficial. It was possible to investigate component dimensions at question numerically and the a priori understanding of the test facility was greatly improved. Especially the dimensioning of the water heating system and the development of the inlet pressure control system in the tank were supported by numerical studies. Implementations of simple circuit components like straight and bent pipes, valves and tanks are available and the empirical correlations are of good quality for the full operating region of the test bench. e preliminarily calculated performance chart derived from the generic pump model shows the same order of magnitude as the analytically scaled values. Anyhow, especially the implementation of the pump, based on the generic pump component from the ESPSS library, does not yield the desired amount of details. Two possibilities have been identified in order to perform improved numerical analyses: ( ) Experimental measurement of the pump performance map and implementing this information in a module or ( ) detailed modeling of the single pump components. Both approaches are currently being followed at TUM.

For the second approach, a detailed model of the inlet, the inducer, the impeller, the diffusor and the volute of the pump developed at TUM are under development.

NOMENCLATURE

Figure .

 . Figure .Comparable properties for fluid-dynamic similarity

  cations best described by heterogeneous nucleation due to fluid impurities [ ]. By definition, the net positive suction head (NPSH) calculates to the difference between the total pressure and the fluid's vapor pressure at the inlet divided by the local density of the fluid. [ ]. NPSH = P st -P v ρg ( ) e required net positive suction head (NPSH R ) is commonly defined as the point where operation of the pump is still feasible. e minimal required NPSH R has to be smaller than the available NPSH A . NPSH R ≤ NPSH A ( )

  pump outlet p t,3 70 bar A radial-type impeller was selected based on the suction specific speed N SS value of the pump. Additionally, in order to avoid cavitation in the radial impeller stage, a high head inducer with cylindrical tip shape was positioned in front of the impeller. [ , ] A summary of the design details at nominal operating conditions with liquid oxygen is given in Table .

Figure .

 . Figure . Dimenionless Bubble (DB) parameter at different rotational speeds. e DB reference value has been calculated for the a LOX pump as described in Table . e LOX geometry is used without any changes for the water tests. e DB values are calculated for p t,1 = 1 bar.

  Figure shows a CAD plot of the main circuit of the test facility that is currently being constructed at the Division Space Propulsion, TUM.

Figure .

 . Figure . CAD view of the turbopump test bench at TUM

Figure .

 . Figure . Numerically obtained system performance chart.e percentile values denote the level of opening of the thro le valve configuration.

Figure .

 . Figure . Numerically obtained pump performance chart for N = 1500 r pm, N = 3100 r pm & N = 5500 r pm. e system performance chart for different opening levels of the thro le valve configuration are plo ed in gray.

Figure .

 . Figure . Operational envelope of the turbopump test facility at TUM is figure is composed by overlaying the Barber Nichols chart for pumps [ ] with the operational boundaries of the test facility at the Division Space Propulsion, TUM.

Table .

 . LOX turbopump detailed design parameters

	Electrical Optional Water Heating System	Pressure	Temperature	Main Throttle Valve	Property Pump Characteristics Specific speed N S Design head coefficient ψ st, pump Temperature F Massflowmeter Pressure		Value 24.34 0.56	Unit -r pm • m 2 / √ Water Pipe Pump Shaft	s
	Auxiliary Pump Water Heater	System Pressure Control Main Tank			Hydraulic efficiency η hyd Pump overall efficiency η tot Sha power P shaf t Investigation Impeller under Inducer &	0.88 0.75 -197 Unit Bearing	--kW Motor
	Inducer Characteristics Design suction specific speed N SS Design head coefficient ψ tot,inducer Design flow coefficient ϕ inducer Number of blades Z inducer Hub-to-tip ratio, inlet D h,1 /D t,1 Hub-to-tip ratio, outlet D h,2 /D t,2 Tip diameter D t,1 Impeller Characteristics Design head coefficient ψ tot,impeller Design flow coefficient ϕ impeller Pressure Temperature Bearing Figure . Drawing of the test bench layout Massflowmeter rates and rotational speeds in order to generate a pump per-Number of blades Z F formance chart.	Data	421.42 0.11 0.089 2 0.40 0.64 70.83 0.50 0.10 Torque	Speed	r pm • m 2 / √ -----mm --	s

impeller 6 -Tip-to-outlet ratio D t2 /D t3 0.72 -Hub-to-outlet ratio D h2 /D t3 0.46 -Tip diameter D t3 100.284 mm Figure . Preliminary CAD view of the developed turbopump at TUM without housing and volute. e pump components are highlighted. identifies the test objectives which are of interest and the implementation in the test bench.

.

Test Objectives

One of the key objectives of the test facility is to provide performance validation data for the turbopump development at the Division Space Propulsion, TUM. is can be yielded by measuring the pump's head rise at varied volume flow

  Table and Table , the maximal mass flow rate at N max based on the design point of the original LOX hardware calculates to

Table .

 . Operational Characteristics of the Test Facility at TUM

	Property	Value Unit
	Rotational speed N Pump Power P Inducer Diameter D t,1 Impeller Diameter D t,3 Fluid Temperature T Total pressure at pump inlet p tot,1 Total pressure at pump outlet p tot,3 Cavitation Number σ	≤ 5500 rpm ≤ 12 kW ≤ 80 mm ≤ 150 mm • C ≤ 100 ≥ 1 bar ≤ 10 bar 0.02 ...0.45 -
	Flow coefficient ϕ	≤ 0.

  E. Rapposelli, A. Cervone, Ch. Bramanti, and L. d'Agostino. A new cavitation test facility at centrospazio. th International Conference on Launcher Technology Space Launcher Liquid Propulsion, . [ ] E. Rapposelli, A. Cervone, and L. d'Agostino. A new cavitating pump rotordynamic test facility. th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, . AIAA -. [ ] J. Kim, H. H. Song, and S. J. Song. Measurements of the non-dimensional thermal parameter effects on cavitation in a turbopump inducer. ISROMAC, . [ ] S.-L. Ng. Dynamic response of cavitating turbomachines. California Institute of Technology, . Report No. E . . [ ] Stephen Skelley. Summary of Recent Inducer Testing at MSFC and Future Plans. presentation, . ermal and Fluids Analysis Workshop, August -, NASA/Marshall Space Flight Center. [ ] O. E. Balje. Turbomachines: A Guide to Design, Selection, and eory. John Wiley & Sons, New York, . [ ] H. Sigloch. Strömungsmaschinen: Grundlagen und Anwendungen. Hanser, München, . [ ] J. F. Gülich. Centrifugal Pumps. Springer, Berlin Heidelberg, . [ ] C. Pfleiderer and H. Petermann. Strömungsmaschinen. Springer, Berlin, edition, . [ ] R. A. van den Braembussche. Radial compressor design and optimization: March . von Karman Institute, Rhode-Saint-Genèse, . [ ] S. L. Ceccio and S. A. Mäkiharju. Experimental methods for the study of hydrodynamic cavitation. In L. d'Agostino and M. V. Salve i, editors, Cavitation Instabilities and Rotordynamic Effects in Turbopumps and Hydroturbines, volume of CISM International Centre for Mechanical Sciences courses and lectures, pages -. Springer, Wien, New York, . [ ] Liquid rocket engine turbopump inducers. NASA Space Vehicle Design Criteria (Chemical Propulsion), . NASA SP-. ] H. A. Stahl and A. J. Stepanoff. ermodynamic aspects of cavitation in centrifugal pumps. Journal of Basic Engineering, : -, . [ ] S. R. Ruggeri and R. S. Moore. Method for prediction of pump cavitation performance for various liquids, liquid temperatures, and rotation speeds. NASA Technical Note, . NASA TN D-. [ ] H. Kato, H. Yamaguchi, K. Okada, S.and Kikuchi, and M. Myanaga. Suppression of sheet cavitation inception by water discharge through slit. International Symposium on Cavitation Inception, . [ ] S. Watanabe, T. Hidaka, H. Horiguchi, A. Furukawa, and Y. Tsujimoto. Analysis of thermodynamic effects on cavitation instabilities. ASME Journal of Fluids Engineering, J. P. Franc and C. Pellone. Analysis of thermal effects in a cavitating inducer using rayleigh equation. ASME Journal of Fluids Engineering, ( ): -, . [ ] C. E. Brennen. Hydrodynamics of Pumps. Oxford science publications. Concepts ETI, Norwich, Vt., . [ ] D. A. Ehrlich and J. W. Murdock. A dimensionless scaling parameter for thermal effects on cavitation in turbopump inducers. Journal of Fluids Engineering, ( ), . [ ] C. Bramanti. Experimental study of cavitation and flow instabilities in space rocket turbopumps and hydrofoils. doctoral thesis, Università degli Studi di Pisa, . [ ] A. Pasini. Pumping Performance Similarity, Cavitation-Induced Instabilities and Fluid-Induced Rotordynamic Forces in Tapered Inducers. doctoral thesis, Università degli Studi di Pisa, . [ ] DIN EN ISO . Rotodynamic pumps -Hydraulic performance acceptance tests -Grades , and . German version EN ISO : , . DIN Deutsches Institut für Normung e.V. Beuth Verlag, Berlin. [ ] H. Bendlin. Reinstwasser von A bis Z : Grundlagen und Lexikon. VCH, Weinheim [u.a.], . [ ] E. Kenneth and P.E. Nichols. How to select turbomachinery for your application. Barber-Nichols Inc.

	R	radius		sion systems -first minimal models and experimental
	ρ	density		validation. Space Propulsion Conference,	.
	Re Σ T υ v ω X Z	Reynolds number cavitation parameter (Brennen) temperature kinematic viscosity velocity rotational speed [ r ad /s] length number of blades	[ ] Ch. Wagner, B. Proux, A. Krinner, T. D. Rixen. Rotordynamik: Modellierung und Einfluss ümmel, and von Schrägkugellagern für Hochdrehzahlanwendungen. Second IFToMM D-A-CH Conference, . [ ] L. Veggi, J. D. Pauw, B. Wagner, and O. J. Haidn. A study on the design of lox turbopump inducers. Manuscript submi ed for publication, .
	Subscripts	[ ] D. A. Ehrlich, J. Schwille, R. P. Welle, J. W. Murdock,
	A	available		and Hardy B. S. A water test facility for liquid rocket
	a	application prototype (not scaled)		engine turbopump cavitation testing. Proceedings of the
	c	characteristic		th International Symposium on Cavitation,	.
	el h	electrical hub [ ] ( ): -, .
	ht [ ]	heating circuit
	hyd	hydraulic
	l	liquid
	m	model for tests
	R	required
	SS	suction specific
	st	static
	t	tip
	tot	total
	v	vapor
		inducer inlet
		interface between inducer and impeller
		impeller outlet
	Abbreviations
	NPSH Net Positive Suction Head
	AC	Alternating Current
	CAD Computer Aided Design DB Dimensionless Bubble parameter LH Liquid Hydrogen LOX Liquid Oxygen LRE Liquid Rocket Engine TSH ermodynamic Suppression Head TUM Technical University of Munich	Symbols A area α thermal diffusivity C p specific heat D diameter DB Dimensionless Bubble parameter η efficiency
			Eu	Euler number
			F	force
			Fr	Froude number
			g H	gravitational acceleration. g = 9, 81 m /s 2 head rise
			h fg	heat of vaporization
			λ	scaling factor
			m	mass flow rate
			N N S N SS P	rotational speed min -1 specific speed. N S = N • suction specific speed. N SS = N • √ Q H 0.75 power	√ N PSH 0.75 Q
			p	pressure
			ψ ϕ	3 head coefficient. ψ = 2gH /U 2 flow coefficient
			U	peripheral velocity
			Q	volume flow rate

[

ACKNOWLEDGMENTS

is project is supported by the Ludwig Bölkow Campus, funded by the Bavarian government. e authors greatly appreciate the good cooperation with the consortium partners.


Omer Hodzic

Martin Sinkwitz

Andreas Schramm

Senad Iseni

David Engelmann

Francesca Di Mare

Ronald Mailach

S Y Mpo

O Tatin

Design of a low pressure turbine stage with control stage characteristics for investigations of partial admission effects

Keywords:

Partial admission is commonly used to control the power, especially of small scale steam turbines. However, asymmetric flow field results at the inlet of a turbine stage with part load control when one or more nozzles are closed. In this case a highly transient flow field with specific partial admission effects occurs. Especially the control stage of the turbine is high loaded in case of partial admission and therefore, additional losses result in the flow field. Those effects are investigated insufficiently, especially experimental data are rare. In this paper the reconstruction of an existing low pressure test facility to a control stage will be presented at first. According to the new stage design three dimensional CFD calculations are carried out with focus on the estimation of unsteady fluctuations and field of influence due to partial admission. Also the positions, where the important effects are noticeable are determined. After the numerical based design process and the numerical investigation to partial admission the test facility was modificated and the measurement positions in the test facility are established.

INTRODUCTION

Due to the decentralization of energy supply in the future, small scaled steam turbines will be more often used. Further, common and promt load change must be ensured and the power output must be adapted to fit the needs of the consumers. For this an appropriate method to control the power output have to be chosen considering efficiency, economy and ecology. Partial Admission is in terms of efficiency at part load operation points an effective method to control the power output of small scale steam turbines. In this case upstream of the turbine a so called control stage is applied. The load of the stage is controlled by a group of nozzles, each with control valves, which are located in circumferential direction. At part load operation one or more nozzle groups can be partially or completely closed resulting in a asymmetric flow distribution in circumferential direction. As a result the static pressure and static enthalpy drop are increased over the control stage and simultaneously reduced downstream of the control stage. Additionaly flow losses and an increasing stage load, especially on the rotor blades, occur. The mixing effects at the boundary between the admitted and non admitted annulus arc lead to specific losses at partial admission. Furthermore, pump effects in the rotor passages downstream of the non admitted area as well as filling and emptying of rotor passages that pass the non admitted area cause additional losses. Several research investigations of partial admission effects are described in literature. Most of these investigations are numerical studies whereas experimental investigations are rare. Hushmandi [7] and Kalkkuhl [9] present detailed numerical simulation results. Fridh et al. [START_REF]Experimental Investigation of Performance, Flow Interactions and Rotor Forcing in Axial Partial Admission Turbines[END_REF] and references [START_REF]Strömungsvorgänge und Verlustanteile in ungleichförmig beaufschlagten Turbinenstufen[END_REF], [15], [START_REF]Experimental Investigations Into the Nonuniform Flow in a 4-Stage Turbine With Special Focus on the Flow Equalization in the First Turbine Stage[END_REF] presents experimental results to partial admission effects. The mentioned experimental investigations comprise mainly traverses in different planes of the control stage and the turbine. In the work of Fridh unsteady loading of a rotor blade due to the part load is investigated with time resolved pressure transducers and strain gauges. Although numerical investigations ( [START_REF]Unsteady flow and load in 50% partial admission control stage with different admitting arc distributions[END_REF] [10] [6] [14][13]) are given in detail, experimental data are necessary to validate the numerical models. In order to understand effects resulting from part loading more experimental investigations to partial admission effects are essential. At the Chair of Thermal Turbomachinery, Ruhr-Universität Bochum a large scale low pressure test facility is proposed to used for the above mentioned experimental investigations. To achieve comparable flow conditions between the test rig and a control stage of industrial turbine the test rig has to be modified. Additionally, the characteristics of the necessary measurement technique has to be specified. The aim of this work is the design of a suitable stage geometry with characteristics of a control stage as well as the estimation of the unsteady fluctuations at full and partial admission conditions. For this, a numerical based design process is conducted. In a first step steady state simulations are performed using a reduced numerical model with one stator and two rotor passages to reconstruct the low pressure air test stage. The reduced numerical model was investigated for a number of different blade numbers, channel heights and operating points. These investigations result in a final construction, which was used for the subsequent studies. In a next step steady state and transient simulations of a 360 degree model of the designed stage for the full admitted case (reference case) and a case with partial admission are carried out. Based on this results the time dependent fluctuations are estimated and the field of influence caused by partial admission are determined. Subsequently, the reconstruction of the existing test facility to the new control stage design and the implementation of the measurement setup are realized. In the following two sections a description of the existing test facility and the detailed design process are discussed.

TEST FACILITY

An existing low pressure test facility is applied for the planned experimental investigations to partial admission effects. In the original configuration this facility includes up to two stages and is supplied with air by a radial blower positioned downstream of the stage. The test turbine operates in a suction mode. At the inlet of the test facility the air is under ambient conditions. Due to the large test rig the disturbance caused by the installed measurement equipment is negligible. The test section consists, depending on the configuration, of one or more stationary or rotating replaceable components. The benefit of this modular construction is that investigations to other unsteady effects can be carried out with moderate retrofit effort. For example, experimental investigations of the interaction of different secondary flows are carried out by Sinkwitz et al. [12]. The inlet casing includes two rectifiers to adjust the air in the axial direction. Behind the inlet casing different stage configurations can be realized. The rotor is mounted on the machine shaft which contains of a outer component and a inner component. The rotor is fixed on the outer shaft whereas measurement devices are able to implement in the inner hollow shaft. Two pivoted casings occupy several accesses for measurement probes and allow a stepwise circumferentially move. Additionally, the probes can be traversed in radial direction. The inlet casing and the outlet casing include accesses for pressure probes or temperature measurement devices. Further, the outlet casing includes 10 evenly distributed pressure taps in circumferential direction for measuring the static pressure at the stage outlet. In combination with the total pressure at the turbine inlet the operating point can be monitored and controlled. In addition, the flow rate can be determined by measuring the difference of static pressure downstream and upstream of a channel contraction in the inlet casing.

CONCEPTUAL METHODS

Step 1: Design of a control stage geometry

The stator and rotor blade design as well as the stage configuration are determined by scaling an existing blade geometry used in a control stage of an industrial steam turbine and by variation of the blade numbers in the stator and rotor row simultaneously. The purpose of this blade variation was the adjustment of the dimensionless stage variables e.g. the distribution of the pressure coefficient c p along the blade chord, degree of reaction ρ y,s and the stage loading Ψ y to corresponding values of a control stage in a industrial steam turbine. The mentioned variables are defined as:

ρ y,s = y ′′ s y s Ψ y = 2 y u 2 2
For that, at first an existing blade geometry was scaled up to the channel heigth of 170mm and several combinations of the blade number ratio z r ot or z s t at or were investigated by numerical simulations. Therefore, two numerical models, one for the industrial steam turbine under origin conditions and one for the test facility under ambient conditions are calculated and compared. For both numerical investigations a one stator and two rotor passage blade passage model are used. The SSTturbulence model is used and steady state simulations for both numerical setups are carried out. The scaling of the origin geometry results in very large dimensions so the assembly in the existing low pressure turbine is not realizable. Therefore, the channel height (origin height: 170mm) was customized and simultaneously the blade number of the stator and rotor row were noticeably increased. A raised number of blades allows, a larger number of blocking configurations. Due to a smaller pitch, more suitable degrees of blocking adjusted to a stable operating point of the blower are realizible. In contrast the test rig channel decreased and consequently, the influence by the endwalls will be raised. To avoid strong influence by the endwalls of the test facility as well as the influence by the measurement probes a channel height of 80mm was chosen. After determination of the channel height, the operating point with the best efficiency (design point) was to be determined. Therefore, different variations of rotational speed of the rotor and of the massflow rate as well as variations of the blade number ratio z r ot or z s t at or are carried out. Here, a stable operation of the blower has to be ensured. Especially at partial admission conditions caused by additional losses a large shift in the compressor map of the blower can be expected as shown in the next section. At the same time, the stage characteristics should be comparable with corresponding values of above mentioned steam turbine control stage at midspan. In conclusion, it is necessary to achieve similar velocity triangles in the relative frame for similar distribution of the pressure coefficient c p,rel as well as the reaction of degree and the stage loading. Additionally, the best efficiency will be achieved at this conditions for a given rotational speed of the rotor. The best efficiency point raises with increasing rotational speed n T and massflow rate m as long as the velocity triangles are not changed. However, the pressure and enthalpy drop over the stage increase simultaneously. At the limit of the blower power a stable operation point can not be ensured.

The determination of the design point based on results of steady state calculations at full admission conditions. The rotational speed and the massflow were defined first and will be changed if the resulting pressure drop over the stage is to high considering the expected increasing of the pressure drop caused by flow losses at partial admission conditions. So the suitable operating point results from a iterative process. Thus, the design point is defined at a massflow rate of m = 7kg/s and a shaft speed of n T = 500r pm with a blade number combination of 44 stator and 75 rotor blades even though better efficiency can be achieved at higher massflow. The pressure coefficient is determined by referencing on velocity in the relative frame. So the definition of c p,rel is:

c p,rel = p -p 2 1 2 ρw 2
Due to this definition, the influence by the different rotational speed in industrial steam turbines and in the presented LP turbine will be unconsidered. At that operating point the degree of reaction is ρ y < 0.1 and the stage loading Ψ h ≈ -2.92.

Figure 1 shows the corresponding distribution of the pressure coefficient on the rotor blade at midspan for the investigated cases. A good agreement between origin and RUB control stage is recognizable except a small area at the suction side near leading edge. Based on these studies, the configuration with 44 stator and 75 rotor blades will be used for further numerical investigations. In the following, the allowed degree of blocking for the partial admission investigations has to be estimated. Moreover, a sufficient large area near the blockage can be investigated by traversing along the blockage till approximatly ≈ 33 degrees from the blokage borders. A large shift of the pressure difference due to partial admission compared to full admission is recognizable whereby increasing of the massflow results in a increased shift. However, a stable operation under partial admission condition is ensured. Step 3: Design adjustments of modified facility

In this section the retrofitted test facility is described and depicted. To reduce the channel height from 170mm to 80mm in the inlet casing a ramp is constructed based on CFD preinvestigations. The rotor and stator blades are mounted on wheels whereby the hub diameter is adjusted to achieve a channel height of 80mm. The hub ring of rotor wheel is connected with the shaft ring by 8 struts and the shaft ring is fixed on the shaft by slot and key. Different from the rotor construction, the stator casing is fixed at the facility frame and the hub is carried by the stator blades. In figure 3 the setup of the retrofitted test facility is depicted. Next to the inlet casing the first pivot-mounted casing (TR I) is integrated followed by the stator casing. Behind the stator casing the rotor wheel is fixed on the shaft, whereby the axial distance between stator trailing edge and rotor leading edge amounts to l ax,rotor = 38mm. The second pivot-mounted casing (TR II) is located coaxial above the rotor. This allows traverses between the stator and rotor row as well as traverses in three planes behind the rotor. The outlet casing is placed downstream of the stage and before the air blower. As mentioned, 10 pressure taps at the casing are used to monitoring and controlling the operating point.

Step 4: CFD and FEM calculations of the designed stage

The design process is completed by performing steady state as well as transient simulations of a 360 degrees model of the control stage. For full and partial admission case evaluation at the measurement locations are carried out to determine the influence of the perturbation areas caused by the stage geometry e.g. the blockage construction. Especially the impact of the blockage construction on the velocity and pressure field has to be captured. Furthermore, the stage load at full and partial admission conditions should be determined. Therefore, rotor blade forces will be monitored and compared for both admission cases. The results from this calculations allow specification of suitable measurement components for the experimental investigations. A detailed description of this step follows in the next section.

NUMERICAL INVESTIGATONS FOR PARTIAL ADMISSION

In this section numerical investigations are presented by using CFD and FEM analysis for calculation of the flow field as well as the structural behavior. The CFD investigations include steady state and transient calculations at full and partial admission conditions considering the proposed measurement campaigns. The evaluation of the results are carried out at the proposed measurement positions. Additional, structural analysis by using FEM methods are performed for different speed of rotation to capture the structural response frequencies of the system by comparing with frequencies of excitation due to flow field. Hereafter, the intended measurement campaigns and the corresporending probe positions will be shown in detail and then the numerical setup will be presented.

Intended measurement campaigns

Evaluation of the numerical results were carried out in the corresponding measurement planes of the proposed experimental investigations. Additionally, the specification of the measurement technique will be determined based on the numerical results presented in this paper. Thus, the proposed measurement campaings will be presented in this section. The experimental investigations include three successively executed measurement campaigns. In the first campaign four planes of the stage will be investigated, whereby time averaged data will be measured by a five hole probe and time resolved data will be measured by two different hot wire probes. Figure 4 shows the measurement planes. The hot wire probes of type 55R56 will be used for measuring axial and radial velocity components and the type 55R57 for measuring axial and circumferential components. Traverses in spanwise and circumferential direction in the investigation planes ME1 as well as ME2-ME4 are intended. In these planes wall pressure will be measured by using pressure taps attached on the mentioned pivotable casings. This enables a high spacial resolution in the circumferential direction. Therefore, two different attachments will be mounted at the pivotable casing. The first one features pressure taps and the second one allows mounting of a screw-on Kulite pressure transducer. This allows aquisition of accurate time averaged as well as time resolved data at the casing of the stage.

In the second campaign pressure tabs at rotor midspan and flush mounted Kulite transducers (Kulite LQ-125) are used to measure the static pressure on the blade surface. Figure 5a and 5b shows the rotor blade with pressure tabs and the rotor blade with mounted Kulite transducers. The circumferetial position of the rotor can be determined by a trigger signal, which is measured for each revolution. To avoid the stochastic influences the sampling rate is defined by a measurement study with different count of sampling data. The data transfer from relative frame to the reference frame of the rotor system is realized with a slip ring system and a compact data logger system, implemented in the hollow shaft. For the time averaged pressure measurements on the rotor blade, the pressure taps are connected with a 64 channel pressure trancducer ZOC 33/64 (Scanivalve) and subsequently the analog data are transfered by the slip ring. Pressure fluctuation on the Kulite transducers are recorded as analog signals by the data logger system (Delphin ExpertVibro) and transformed to digital signal by a A-D converter. The digital data are stored on the internal hard drive and sended as one sampling for each circumferential position to the computer. Measurement of the velocity field by the Particle Image Velocimetry (PIV) method completes the experimental investigations. A concept for the PIV system is mounted on the pivot-mounted casings and allows a traverse in circumferential direction and the positioning of the system in the four different measurement planes. These concept allows the measuring of the velocity at the midspan area between the stator and rotor row, in the rotor passage and downstream of the stage.

Numerical setup

CFD analysis

In this section the numerical setup for the CFD and subsequently the setup for the FEM analysis will be described. Due to the partial admission configuration with a degree of a blockage of 40.90 degree a periodic boundary condition in circumferential direction is not possible, so the control stage have to be modeled as a full annulus model. All numerical investigations are carried out for the full admitted case (as reference) as well as for the part admitted case. The grids of stator and rotor passages as well as the inlet and outlet domains are generated with the inhouse meshing tool AxTurboMesh [8] [START_REF] Tatin | Fan casing contouring under consideration of aeroacoustics, mechanics, aeroelasticity and whole engine performance[END_REF]. Overall a mesh with approximately 20 million elements is used whereby the blockage are assumed as infinity thin with no slip wall conditions. In addition, all hub, shroud and blade walls assumed as no slip walls. A detailed grid independent study was conducted within a master thesis by Mutlu [11]. The results of this study show a grid independency at approximatly 20 million elements (figure 6). The inlet domain with the stator row as well as the outlet domain are stationary whereas the rotor domain is rotating with a shaft speed of 500 rpm. For the reference case, at inlet total pressure is set to pressure of ambient whereas at outlet boundary a massflow of m = 7kg/s is set first. Based on a steady state simulation the corresponding static pressure at outlet was determined by averaging. In the next step the averaged static pressure is defined as the outlet boundary condition. The same total pressure at inlet as well as the same static pressure at outlet were defined for the partial admission case. Thus, the pressure drop at part as well as at full loading is same. As a result, the blade forces in the admitted arc of the partial admitted configuration and of the full admitted configuration are equal. This allows a usefull comparison of forces at partial admission and full admission because all forces can be related to common reference value.

Air assumed under ideal gas conditions is used as working medium and the total temperature is set to ambient temperature of approximately 25 • C. The SST-tubulence model is used and steady state and transient simulations are carried out. Steady state simulations are performed with the so called frozen rotor interface in order to connect rotating and non rotating parts. For transient simulations a total number of 16 and 32 timesteps per blade passing of the stator blade has been chosen for a timestep study. The differences between the forces calculated with the mentioned timesteps are negligible for the partial admission and full admission case. Based on these results, further increasing of the timestep count is not necessary. Additional steady state simulations are carried out to determine the performance and efficiency of the test facility and to estimate the losses at different operating points.

FEM analysis

In addition to the CFD analysis a modal analysis was carried out to determine the eigenfrequencies of the rotor blades. The eigenfrequencies are plotted in a Campbell diagram over the rotational speed as well as the graphs of excitation frequencies (figure 13). The excitation results from stator wakes caused by trailing edges and from partial admission caused by interaction of admitted and non admitted arcs. For the modal analysis material data are used from data sheets to ensure the correct behaviour of the rotor components. Figure 7 shows the materials of the rotor components

RESULTS AND DISCUSSION

In this section CFD and FEM results are presented and discussed for the full and partial admission case. Initially, results from steady state simulations will be described and evaluated. Afterwards, results from the transient calculations will be discussed, especially the time history of blade forces is explained in detail. Finally, the blade passing frequency and the frequency of disturbance caused by the partial admission will be plotted in a frequency spectra and compared with the eigenfrequencies of the rotor wheel. Further frequencies occurring in the spectra are assessed in terms of importance for the investigations, so that dominated frequencies can be captured.

Results from steady state simulations

Results from steady state calculations are presented in corresponding planes of the proposed measurement campaigns. The figures 8 and 9 show the pressure distribution in the plane ME1-ME4 for full and partial admission. Although in plane ME1 the field of influcence by partial admission is limited mainly to the arc of blockage, transporting of losses by the rotor in circumferential direction are noticeably. Therefore, it can be considered that losses are transported in circumferential direction in the ME2, ME3 and ME4 planes. A remarkable disturbance due to the part loaded stage occurs up to ME4. The rotation of the rotor and the stagger angle of stator induce a momentum in circumferential direction. These effects cause an increase of the mixing intensity between the admitted and non admitted arc. Figure 10 shows the distribution of static entropy at midspan. Far downstream of the stage the field of influence by part loading decreases noticable. The entropy production caused by the stator wakes is distinctly less than the losses caused by the specific effects results from the partial admission. It has to be mentioned that the momentum in circumferential direction causes the disturbance to propagate in direction of the rotation even though, a sufficient range can be traversed by rotation of the pivotable casings.

Results from transient simulations

Results from steady state simulations provide time averaged data of the flow field but are not suitable to describe the highly unsteady flow field at partial admission conditions. Especially the influence by the rotation of the rotor row, the interaction between the rotor and stator blades as well as the disturbances caused by stator wakes and the blockage have to be described based on transient data. Therefore, in the following results from transient calculations of the full admitted and part admitted case are presented and compared. These investigations are carried out to determine the force response of the rotor blades due to excitation by passing through stator wakes as well as through the non-admitted section at partial admission. Furthermore, data from transient calculations allow estimation of unsteady fluctuations in the flow field and therby the specification of necessary measurement equipment can be determined.

Blade forces

At full admission conditions the wakes of the stator row cause excitation of the rotor blades. The forces are determined by the rotational speed of the rotor and the blade count in the stator row. Due to partial admission of the control stage additional excitation is caused by filling and emptying of the rotor passages when a rotor blade enters and leaves the non-admitted area respectively. The following two equations are used to determine the frequencies of excitation caused by stator wakes and part admitted channel. As above mentioned, due to the same total (stage inlet) to static (stage outlet) pressure ratio amplitudes of forces in admitted arc of the partial admission case are comparable with forces of the full admission case. However, amplitudes of the forces which occur when rotor blades enter and leave the admitted arc increase significantly. Furthermore, a change of sign occurs by passing through the not admitted arc. When a rotor blade leaves the admitted arc first of all, the suction side of the blade enter the arc downstream of the blockage. On this side the passage can not be supplied by the working medium, so the static pressure decreases whereas the pressure side is still admitted. As a result, a raised tangential force in rotational direction can be observed whereby the amplitude is one order of magnitude higher compared to the amplitude of force caused by stator wakes. However, when the rotor leaves the blocked arc the suction side will be admitted with the working medium. Simultaneously, on the pressure side of the blade a pressure drop can be observed caused by the emptying of the rotor passage during passing of the blockage area. Due to the change of sign the tangential force the single blade counteracts the rotor wheel and acts as a compressor. Therefore, for each revolution the rotor blades are loaded alternating towards and opposite the rotational direction respectively. Figure 12 shows the frequency spectra of the tangential force. Although, the excitation frequency due to part loading is considerably lower than the excitation caused by the stator wakes the amplitudes are obviously larger and dominate the frequency spectra. Additional frequencies caused by constructional components do not occur, however linear combination of the first both can affect on the frequency spectra. Further excitation frequencies occur in the frequency spectra but the two effects mentioned above dominate. A noticeable shift between the first crossing point, where resonance can be expected and the intended operating point is recognizable, so that resonance problems in the system can be excluded. The first critical mode occurs at the frequency of approximatly 550Hz as the bending mode of the rotor struts. Another operating points including resonance can be leave out of consideration, because of a large shift to the design point.

f stator = Ω • z stator = 2 • π • N T • z stator f partial = Ω • z block = 2 • π • N T • z block

Estimation of fluctuations:

Besides the safety aspect of the structural analysis, these investigation is necessary for consideration of forced response effects. The positions of the piezoresistive transducers on the rotor blades are specified based on the transient results of the simulations at full and partial admission. Therefore, local evaluation points at different positions at midspan of the rotor blade are defined in the numerical model. A total of 12 positions along the blade profile are evaluated for one revolution of the rotor blade. The figure 14 shows the corresponding results. A noticeably difference of the pressure level on suction and pressure side can be observed. Furthermore, the influence by the stator wakes are distinctly less compared to the disturbance due to part admitted channel. Nevertheless, the amplitudes are not negligible and are neccessary to determine all excitations on the rotor blades. Two turning points in the graph of the transient behaviour of pressure occur while passing the blockage region, when the rotor entries and leaves the not admitted area respectively. First, at beginning of the blockage a minimum of the pressure is recognizable, whereas at the end of the blockage a maximum appears. Immediately, as the rotor blade enters the blockage, the emptying process of the rotor passage causes a reduced pressure. The interruption of the air supply downstream of the blockage causes the momentum of the remaining medium to decrease until the end of the blockage. When entering the admitted area, the high momentum flow impinges the rotor passage and will decelareted due to the low momentum flow in the passage. The stagnation of the fluid causes an increasing of the static pressure raising up to the maximum value. The emptying and filling process between the entering and leaving of the blockage is observable for each position of the rotor blade but with different intensity. Close to the rotor trailing edges the amplitudes of the pressure signal are one order of magnitude weaker than the amplitudes far from the traling edge or near to the leading edge repectively. The positions of the points DS 4 and 5 correspond to two points near to the traling edge and show the lowest response not only in the admitted but also in the not admitted area. In figure 15 the frequency spectra of the pressure history is depicted and shows the predominant frequencies for pressure and suction side of the rotor blade. On pressure and suction side the low frequency excitation due to the blockage causes the highest amplitudes, whereby the magnitude of the amplitudes on the suction side are generally higher. In addition, the high frequency disturbance caused by the stator wakes are clearly recognizble at the frequency of f = 366.66Hz as well as the multiple magnitude at f = 733.33Hz. Even higher frequencies are not noticeable, so the maximum sampling rate of 50kHz per channel performed by the A-D converter is sufficient for the proposed investigations.

CONCLUSION

In this paper the redesign of an existing low pressure test facility to a single stage facility for investigations to partial admission effects is described. In the first step, a suitable stage with characterstics of a control stage at design point was designed successful. The degree of reaction as well as the stage loading are comparable to corresponding values of a control stage in actual steam turbines. In doing so, the dominating effects of partial admitted stages can be measured even though the flow conditions in the test facility are not comparable to conditions of a control stages in steam turbines. After determination of a stage with characteristics of a control stage, numerical investigation with CFD and FEM methods were carried out. The CFD calculations have included steady state and transient simulations under full and partial admission conditions. Based on these results fields of influence and importance for the later following experimental investigations are determined. Furthermore, excitation sources caused by the unsteady flow are determined and compared with eigenfrequencies of the rotor wheel in a Campbell diagram. This indicates that neither at the design point nor at other proposed operating points the frequencies of excitation corresponds with any eigenfrequency. Thus, an operating point under resonance conditions can be excluded for all operating points which have to been investigated. In addition, to specify the characteristics of the measurement technique fluctuations of the velocity and pressure field were estimated. Therefore, the frequency spectra was evaluated for different positions in the flow field and dominant frequencies and amplitudes could be identified and at once the positions where the measurment has to been placed. Based on the flow conditions in the test facility highly sensitive measurement is demand to resolve the fluctuations and to ensure small measurement errors. In addition to the successfull design process of the test facility, the results shows the importance of the investigations of partial admission effects in the design process of control stages once more. The intended measurement at the retrofitted test facility as well as the corresponding numerical investigations have to give a wide indication of the unsteady flow in a part admitted control stage. Redesign of the low pressure test facility to a control stage enables extensive experimental investigations of partial admission effects in the future. An incomparable spatial as well as temporal resolution of a partly admitted control stage will ensure high quality data for further numerical validation and increase the comprehension of the phenomena, which occur at partial admission.

Figure 1 .

 1 Figure 1. Pressure coefficient distribution for the origin and scaled geometry RUB

Figure 2 .

 2 Figure 2. Air blower map

Figure 3 .

 3 Figure 3. Retrofitted low pressure test facility

Figure 4 .

 4 Figure 4. Measurement planes

( a )Figure 5 .

 a5 Figure 5. a) Rotor blade with 12 pressure tabs on pressure side (15 tabs on suction side) b) Rotor blade with 5 Kulite transducers on pressure side (7 Kulite transducers on suction side)

Figure 6 .

 6 Figure 6. Grid independeny study (Total pressure in plane between stator and rotor)

Figure 7 .

 7 Figure 7. Material of rotor components

Figure 8 .

 8 Figure 8. Absolute pressure in plane ME1 at partial admission

Figure 9 .

 9 Figure 9. Absolute pressure in plane ME2, ME3 and ME4 at partial admission

Figure 10 .

 10 Figure 10. Static entropy under partial admission condition

  Results of tangential forces from transient calculations at the full and partial admission case are depicted in figure11. These forces are calculated for each circumferential position by integrating the pressure on a single blade surface with the post processing tool Ansys CFX-POST.

Figure 11 .

 11 Figure 11. Tangential force at rotor blade for one revolution

Figure 12 .

 12 Figure 12. Frequency spectra of tangential force at rotor blade

Figure 13 .

 13 Figure 13. Campbell diagram of structural analysis of rotor

Figure 14 .

 14 Figure 14. Static pressure at rotor blade for one revolution

Figure 15 .

 15 Figure 15. Rotor frequency spectra at different positions (top: pressure side=PS, bottom: suction side=SS

  NOMENCLATURE m [ kg s ] Massflow ǫ [-] Degree of admission Ω [ 1 s ] Angular velocity Ψ [-] Stage loading ρ [ kg m 3 ] Density ρ y [-] Degree of reaction Θ [deg] Circumferential position F Θ [N] Tangential Force l ax [m] Axial distance c [ m s ] Velocity c p [-] Pressure coefficient f [ 1 s ] Frequency Ma [-] Mach number n [ rev s ] Rotational speed p [Pa] Static pressure P [W] Power of blower Re [-] Reynolds number w [ m s ] Velocity in relative frame z [-] Blade number

Table 1 .

 1 Test facility characteristics (before design process)

	Power of blower P blower [kW]	150
	Massflow m [kg/s] (at DP 1)	12.8
	Shaft speed of turbine n T [r pm] (at DP)	500
	Velocity at stage inlet c 0 [m/s] (at DP)	15
	Mach number at stage inlet Ma 0 [-]	≈ 0.1
	Reynolds number at stage inlet Re 0 [-]	≈ 200000