> = CwRe, 0.5 laminar throughflow parameter A, = CwRe, g turbulent throughflow parameter

Transcription

1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y. 117 r The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the 7Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published 95-GT-212 in an ASME Journal. Authorization to photocopy material for internal or personal use under circumstance not falling within the fair use provisions of the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of $.3 per page is paid directly to the CCC, 27 Congress Street, Salem MA 197. Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright Q 1995 by ASME Al Rights Reserved Printed in U.S.A. SIMPLE DESIGN METHODS FOR THE PREDICTION OF RADIAL STATIC PRESSURE DISTRIBUTIONS IN A ROTOR -STATOR CAVITY WITH RADIAL INFLOW Kenneth J. Hart Mechanical, Aerospace and Automotive Engineering University of Hertfordshire England. Alan B. Turner School of Engineering University of Sussex England. ABSTRACT Research has been conducted into the effects of component geometry and air bleed flow on the radial variation of static pressure and core tangential velocity in a rotor-stator cavity of the type often found behind the impeller of a gas turbine engine centrifugal compressor. A CFD code, validated by rig test data for a wide range of rotor-stator axial gaps and throughflows, has been used to generate pressure and velocity data for typical gas turbine operating conditions. This data has been arranged as a series of simple design curves which relate the rotational speed of the core of fluid between rotor and stator boundary layers, and hence the static pressure distribution, to primary cavity geometry, rotational Reynolds number and bleed throughflow with particular attention to radial inflowing bleeds. Details are provided on the use and limitations of these curves. Predictions using this method have been compared successfully with measured data from engine test and a compressor test rig, modified to facilitate variable quantity and direction of impeller rear face bleed flow, at typical gas turbine operational power conditions. Data generated by these curves can be used directly in the design process and to validate integral momentum methods which can provide relatively simple computation of rotor-stator cavity pressure and velocity distributions independently or within air system network programs. This approach is considered to be a cost and time effective addition to the analytical design process especially if validated CFD code, which can accommodate rotational flows consistently and accurately, is not available. NOMENCLATURE Cw = m/µr, non-dimensional mass flow G = sir,, axial gap ratio L = 1>. scaled turbulent throughflow parameter in bleed mass flow rate p static pressure r radius ri inner radius of rotor-stator cavity r, rim radius of rotor Rem = pwro /µ rotational Reynolds number s axial rotor-stator gap Sw = v/cjro flow inlet swirl fraction v, tangential velocity of core flow v m tangential velocity X = r/r, radius ratio = v,,/r,.ro core tangential velocity factor Q- Q for zero cavity mass throughflow > = CwRe,.5 laminar throughflow parameter A, = CwRe, g turbulent throughflow parameter p W absolute viscosity of air density of air angular velocity of rotor 1. OBJECTIVE The design of gas turbine internal air systems demands accurate knowledge of velocity and pressure distributions across the faces of rotating components for the reliable assessment of bleed flows, component temperatures and bearing thrust loads. This knowledge can be acquired, for specific design configurations, by component rig testing and/or detailed CFD analysis. Presented at the International Gas Turbine and Aeroengine Congress and Exposition Houston, Texas - June 5-8, 1995

2 The aim of this research was to use data from experimental rig tests and CFD predictions to produce a series of general design curves relating the rotational speed of the core fluid in the cavity to primary geometry, rotational Reynolds number and bleed through flow for the types of rotor-stator cavities found behind the impeller of a gas turbine engine centrifugal compressor. These curves could find use directly, or as validation data for integral methods, in the early stages of the engine design process when data from costly and time consuming rig testing or CFD analysis may not be available. Further validation of these design curves was to be achieved using test data from engines and engine component rigs performing at customary gas turbine operating conditions. 2. INTRODUCTION The higher compression ratios and turbine entry temperatures prevalent in modem gas turbine engines present increased demands on the internal cooling air system. To achieve satisfactory cooling and sealing with minimum expenditure of valuable cooling air requires an understanding of the complex airflow mechanisms which exist within the engine, especially in the vicinity of high speed rotating components. The work reported here relates primarily to the prediction of velocity and pressure variations in rotor-stator cavities with imposed throughflows. Although such cavities are found extensively throughout the gas turbine engine this work focuses upon those found typically between the backplate of a gas turbine centrifugal compressor impeller and its adjacent stator. 2.1 Impeller Rear Face Rotor-Stator Cavity Configurations The centrifugal compressor is used extensively in helicopter, light aircraft and business jet gas turbine engines. However, engines differ significantly in the design of local component geometries and air bleed arrangements which are often dictated by the dynamics of the rotor system and the need to provide adequate cooling, sealing and thrust load control throughout the engine. Figure 1 shows some typical arrangements for impeller rear face rotor-stator cavities. It can be seen that the presence of labyrinth seals, stiffening rings and balancing features result in a variety of shapes of rotor-stator cavity. Depending upon the overall engine air system design, the air flow through the cavity typically varies between 1.% of mainstream compressor flow bled radially inwards to 1.% bled radially outwards; some engines have no imposed bleed at all. A substantial number of engines designed in recent years have adopted a 'centripetal' inflow bleed through the impeller rear face cavity to help dissipate windage, provide a source of bleed air for the internal air system, yield lower impeller metal temperatures and give local pressure distributions generally more favourable to bearing axial thrust load control. In the case of bearing thrust load control, very large loads are generated in the core of the engine by the action of high pressures on large surface areas of rotor. Axial loads acting in forward and rearward directions are generally balanced out such that the net load experienced by the thrust bearing is only 1-2% of the largest contributor to this summation of loads. The largest load is often that generated by air pressures acting on the rear face of an impeller and a small percentage error in the calculation of this pressure load can result in a net bearing thrust load substantially below or above its design capacity. This can lead to ball skidding, load reversal or overload problems within the bearing thereby affecting engine integrity and reliability. FIGURE 1 TYPICAL IMPELLER REAR FACE ROTOR-STATOR CAVITY CONFIGURATIONS

3 Hence an understanding of the variation in static pressure distribution as bleed air is passed through the impeller rear face cavity is of extreme importance to the design of the internal air system of the engine. This may be achieved for each particular design case by the use of component test rigs or detailed CFD analysis such as that performed by Liu and Patel (1993). However, there is a need in industry for simpler but adequate analysis methods that can be used frequently in the parametric studies associated with the preliminary design process. These methods should be available for rapid analysis on relatively small computing devices or as subroutines in network solver computer programs. Integral momentum methods are often used in industry to achieve this purpose although they require prior knowledge of the flow structure, assumptions for the boundary layer profiles and rely heavily on validation against test data. Dadkhah et al (1992) = v, and thus 1 8p = ( 2 w2r also shows r evidence of momentum integral methods p ar underestimating the core rotation at large rates of outflow bleed. Both complex and more basic methods need to be fully where, w = angular velocity of rotor supported by research data which covers all of the likely design options. Whilst a substantial amount of research has been published on the effects of 'centrifugal' outflow bleeds through rotor-stator cavities on core velocity and pressure distributions, 2(r22 - r,2) P2 - PI = /3 the effects of inflowing bleeds are less well understood..5pw 2 The aim of work' reported here is to provide a set of curves herefore:- which will enable rotor-stator cavity velocity and pressure 2 (p2 - pt).5 distributions to be predicted to a reasonable accuracy early in the engine design process without the need for time consuming and costly rig testing or CFD work. Informed judgements can then be made on the effects of the magnitude and direction of air bleed flows through any rotor-stator cavity within the engine and design decisions made accordingly. The work concentrates on inflowing bleeds although zero cavity throughflow and outflowing bleed data, which have been more fully researched and correlated by other workers, is included to give a more complete picture to the engine designer regarding the overall effect of bleed flow on rotor-stator cavity behaviour. 3. THEORY AND REVIEW OF PREVIOUS WORK. A substantial amount of work has been performed by numerous researchers on the flow of fluid close to rotating discs. Hart and Turner (1994) contains a basic chronological review of some of this work and its relevance to rotor-stator cavity velocity and pressure variations. Most practical rotor-stator cavities occurring in a gas turbine engine consist of separate boundary layers adjacent to the rotor and stator walls separated by a rotating core of fluid; classified by Daily and Nece (196) as Regime 4. This rotating core of fluid is fundamental to the presentation of experimental and theoretical data reported here. Viscous and turbulent effects are negligible except in thin boundary layers close to the rotor and stator and also in the entry and exit regions of the cavity. The remaining core of fluid can be considered to rotate at a constant angular velocity which is some proportion of the velocity of the rotor. Assuming negligible radial and axial velocities with incompressible flow in the inviscid core region of a rotor-stator cavity, radial equilibrium gives the relationship between the radial pressure gradient (ap/8r) and the tangential velocity (v t) of the air at radius r in the form:- 1 op = v^z p 8r r Since the radial pressure distribution is controlled principally by the tangential velocity of the core region (Owen & Rogers 1989) an accepted approximation is to use a core tangential velocity factor 16, which is the ratio of the tangential velocity of the air core to that of the rotor at the same radius. Integrating with respect to r between radii r, and r2 gives: a = (1) pw2(r22 - r1 2) Hence, from measured values of static pressures p t and P2 at radii r, and r2, at a known rotational speed w, a value of (3 can be derived which applies to some mean radial position. The use of this dimensionless core rotation factor has been adopted by several workers to establish and compare relationships between (3 and parameters such as rotational Reynolds number, geometry and cavity throughflow. It is not applicable to regions where there is no 'core' structure such as in the inlet source region or the outlet sink region. The basic cavity geometry is presented as a dimensionless gap ratio G which is equal to the axial gap divided by the rim radius. The cavity mass throughflow is presented as a dimensionless throughflow parameter X. For laminar flow X, = CwRe m-.5 and for turbulent flow X b = CwRem 8 Cw is itself a dimensionless flow parameter equal to m/µr, and is essentially a coolant flow Reynolds number. This was proposed by Daily et al (1964) and confirmed by many other researchers. A net radial outflow of air through the cavity has the effect of reducing the tangential velocity of the core, ultimately to zero if sufficient throughflow is supplied, and of extending the central source region further into the cavity if the throughflow is supplied close to the centre of rotation. For inflow, the conservation of angular momentum causes a substantial increase in core tangential velocity producing values of /3 well above unity. The values of (3 are also strongly affected by the inlet swirl of the bleed flow.

4 4. ACQUISITION OF NUMERICAL DATA 4.1 University of Sussex Small Rotor-Stator Rig. This is an experimental rig (Figure 2) consisting of a 4mm diameter rotor spinning at up to 44rpm and separated from a shrouded stator by an axial air gap which can be varied from 2mm to 23mm in width. Various measured quantities of air can be bled centrifugally (outflow) or centripetally (inflow) through the cavity between the rotor and the stator. For radial inflow the air can be either drawn into the cavity, with no initial swirl, through tubes in the stationary shroud or, with a swirl fraction of unity through holes in the rotor containing foam plugs. Static pressures are measured on the stator at 11 different radii repeated at 3 circumferential positions and also on the stator shroud. INFLOW Inlet Swirl 4.2 Computational Fluid Dynamics (CFD). In order to extrapolate the data acquired from experimental rig tests to cover the range of rotational Reynolds numbers exhibited by normal operational gas turbine impeller rear face rotor-stator cavities use was made of a CFD code. The CFD code was developed as SURF at the University of Sussex (Vaughan, 1987) and modified, as VU4, for use at Rolls- Royce plc. VU4 solves the partial differential equations modelling laminar or turbulent flow and convective heat transfer in an axisymmetric wheelspace. Although developed specifically for rotating disc flows it can also be used for other geometrically axisymmetric problems. Either axisymmetric or 3D solutions may be obtained for both compressible or incompressible flows. The governing partial differential equations are represented within the program by finite difference equations on a userdefined grid. Although a k-e turbulence model is available, a simpler mixing length model was used since it provides significant savings in computer time and has been shown by Chew (1985) to be very effective in dealing with rotating flows. The grid used was a 97 x 49 rectangular mesh with a geometric expansion factor of 1.2 away from each boundary. This grid has been shown to be sufficiently fine to provide a suitable number of grid points in the turbulent boundary layers and laminar sublayers and thereby minimise any grid dependency effects. Convergence was monitored by the observation of residuals, RMS changes and values of each variable (velocities and pressure) at appropriate grid points. In order to promote confidence in the use of this CFD code for the assessment of impeller rear face rotor-stator cavity geometries and through flows, CFD models were produced to validate the code at most of the geometry and flow conditions tested on the experimental rig. This validation process was reported in Hart and Turner (1994). 4.3 Rolls-Royce 4D Compressor Rig. This is a rig (Figure 3) designed primarily to test the performance of centrifugal compressors used for small turboprop/turboshaft engines. The rig includes the facility to vary the direction and quantity of air flow bleed across the rear face of the impeller. Instrumentation consists of static pressure and total temperature measurements at 5 different radii in the impeller rear face cavity, rotating thermocouples on the impeller backplate and measured flows in the cooling system inlet and exit ducts as well as the normal performance and safety instrumentation associated with a rig of this type. FIGURE 2 ROTOR-STATOR EXPERIMENTAL RIG 4

5 iii I \i' I Al \t /) FIGURE 3 ROLLS-ROYCE 4D COMPRESSOR RIG 4.4 Ranges for Experimental Testing and CFD Modelling.rotor-stator rig, modelled by CFD, tested on the 4D compressor Table 1 shows the ranges of basic rotor-stator axial gap ratio, rig and found typically in gas turbine impeller rear face rotor rotational Reynolds number and bleed throughflow tested on the stator cavities. Axial Gap Ratio Rotational Re Bleed Throughflow G = s/ro Rey = po,r,zlµ A, = Cw Re, Rotor-Stator Rig x x 16 5 x x 1-2 inflow outflow CFD x16-1.X17 5x x1-2 inflow outflow 4D Compressor mid rad 3.9 x x 16 4 x x outer rad inflow outflow Typical Operational x 1'- 1.2 x 17 4 x 1' x 1-2 Gas Turbine inflow outflow TABLE 1 RANGES FOR EXPERIMENTAL TESTING, CFD MODELLING AND ENGINE OPERATION. 5

6 5. DESIGN CURVES Using data acquired from the rotor-stator rig and CFD simulation, a series of design curves have been produced relating core rotational factor (,8), rotational Reynolds number (Re m), turbulent throughflow parameter (JJ, inlet swirl (Sw), axial gap ratio (G) and radius ratio (r/r,). For the outflow bleed cases the data showed some grouping onto a common characteristic, at values of 13//3 similar to those obtained by the Dadkhah (1989) correlation:- The validation exercise reported in Hart and Turner (1994) compared values of from rig test and CFD at an Re m of 1. x 16 with various throughflows. In many cases there was little difference between rig and CFD values but where there is discrepancy, and until it can be fully resolved, the user of these design curves is advised to perform a sensitivity check using Table 2 which shows ^,;8'CFD for all gap ratios and throughflows tested at an Re, of 1. x ,6' =.87{exp[5.2(.486-N(X) -13'5)] -1.) but some 15%-25% greater than those predicted by the Daily, Ernst and Asbedian (1964) correlation:-,61,6' = [ X(X)-1v5 ] -t. However, the Dadkhah correlation was for a constant axial gap ratio of.1 and a Re, range up to 3 X 1 6. The rig testing and CFD work displayed in the design curves for a radius ratio of.7, gap ratio range and Rem range 1. X X 17 shows an increase in 3' with reduced axial gap ratio in line with the work of Daily and Nece (196). The curves also however show slight reductions in 13' and [3/3' with increased Re,. Although the'outflow data was of secondary importance to inflow in this particular research study, further comparison with established non-dimensional correlations and momentum-integral solutions may prove useful. Attempts were made to condense the inflow data using correlations of Q/^' against [X,/X 13J5] in a manner similar to that adopted for rotor-stator cavities with outflowing bleeds (Daily et al, 1964). It became apparent, from the very large scatter of points, that this approach was not appropriate for cavities with a substantial inflowing bleed throughflow. In order to make these curves available for use they are therefore presented here in this raw, unsmoothed manner. The points on the graphs indicate the conditions at which the CFD investigations were performed. Some interpolation has been employed to complete the curves but straight lines have been drawn when only 2 data points exist and interpolation with adjacent curves provides no obvious trend. The curves, although somewhat cumbersome, are readily usable in this form for direct design activity or momentum integral method validation and have therefore been published. Further work is necessary to try and collapse the data into a reduced number of variables which may be more amenable to a computer based method. Such an exercise would also allow anomalous points and trends to be more clearly identified and dealt with. Figure 4 gives the design curves for an axial gap ratio of.115 and considers radius ratios.25,.5,.7, 5 and.96. Figures 5, 6, and 7 show similar information for axial gap ratios.5,.25 and.1 respectively. In these plots the identifying parameters at the end of the individual curves relate to the direction [ = outflow, Z = inflow with zero inlet swirl, 1 = inflow with 1% inlet swirl, zf = zero flow] and quantity [value of L (L=1h)] of the cavity bleed throughflow. Axial Flow jg,yjgc n $.y^/scth Pn1/ C v $.y/bon $d1/ C,D Gap In/out r/r, r/r, r/r, r/r, r/r Ratio - SW Z I-3Z I-1Z ZERO Z I-3Z I-1Z ZERO I Z I-3Z I-1Z ZERO Z Z I-IZ ZERO O TABLE 2 COMPARISON OF /3 FROM ROTOR-STATOR RIG TEST AND CFD PREDICTION AT RE, = 1.X16.

7 3.2 /3 RATIO = :-----'" Z : : Z Me RADIUS RATIO = _ -._._ Zfl O OS LO /3 RATIO = Ø 1S /^ RADIUS RATIO =.96 -_15.75 f Z5.6 Z 'Zl " * ^ zf.3 Ol F' RADIUS RATIO = _ - Z3 ZI zf.3 Ol ROTATIONAL REYNOLDS NUMBER X 1` Key: zi zf Z3 ^, 1 ^ Z Throughtlow Direction Z = Inflow Inlet swirl % 3 Throughflow Quantity Value of L 1 = Inflow where Inlet swirl 1% L = 1, O = Outflow zf = Zero Flow FIGURE 4 CORE ROTATION DESIGN PREDICTION CURVES FOR AXIAL GAP RATIO.115 7

8 2.8 R RADIUS RATIO = N RADIUS RATIO = Z ' Z3 - -_ 11.Z1 _ "zf ROTATIONAL REYNOLDS NUMBER X t` na. -_ Zf RADIUS RATIO =.5 RADIUS RATIO = ^ Z5.7 --: 13 ^ Z : ' _ _. a zf.3.5 Z3 ' ' 3.1 ^ Z5 RADIUS RATIO = Z3 1 zl.4 r + -. _ { zf ' Key: Throughflow Direction Z = Inflow Inlet swirl % 5 Through flow Quantity Value of L 1 = Inflow where Inlet swirl 1% L = 1>, O = Outflow FIGURE 5 CORE ROTATION DESIGN PREDICTION CURVES FOR AXIAL GAP RATIO.5 zf = Zero Flow 8

9 a RADIUS RATIO = Z5 RADIUS RATIO = ' Z _ 'Z RADIUS RATIO = (3 RATIO = Z _ zf zf ' -+- Z _ Zl,zf ; ZS ROTATIONAL REYNOLDS NUMBER X 1` 3 5 Z RADIUS RATIO = = ZSZ f Key: Throughflow Direction 5 Through flow Quantity.1L d i--^ r i I FIGURE 6 CORE ROTATION DESIGN PREDICTION 3 5 CURVES FOR AXIAL GAP RATIO.25 Z = Inflow Inlet swirl % Value of L 1 = Inflow where Inlet swirl 1% L = 1X, O = Outflow zf = Zero Flow 9

10 3.2RADIUS RATIO = z* zx o 8 RADIUS RATIO =.5 1. uv uo uo ur uo us.4 us m m o ^. RADIUS narzo~n es ' o c/ ' o u«us ITTTIIT1TIIT.75.7 u* _ ' ----u m u^.55. z^.5 o1 o Z3 /3 RADIUS RATIO =.7.35 Z ROTATIONAL REYNOLDS NUMBER x/.5 /m us m m o 1 Key: Direction Z = Inflow Inlet swirl % Quantity Value of L 1 = Inflow where Inlet swirl 1% FIGURE 7 CORE ROTAT ION DESIGN PREDICTION CURVES FOR AXIAL GAP RATIO.1 zf = Zero Flow 1

11 5.1 Use of Design Curves As stated previously, the aim of these design curves is to provide guidance on the effect of geometry and bleed flows on rotor-stator cavity core tangential velocities to enable preliminary design and analysis work to be performed without recourse to expensive rig test and/or CFD work. It is expected that, in order to assess the velocity and pressure distributions in an impeller rear face cavity, these curves would be used in the following manner. 1). Ascertain the axial gap ratio for the cavity in question. It should be remembered that the design curves are for rectangular rotor-stator cavities with static outer shroud and plain disc surfaces so some approximation will probably be necessary. Select the design curves that are closest to the gap ratio calculated. If the calculated axial gap ratio lies between 2 sets of plots then some interpolation will be required. 2). Calculate Ree for the condition(s) to be analysed using static pressure and temperature at the impeller tip for the air properties. 3). Using data from Figures 4, 5, 6 and 7 produce curves of J3 against radius ratio and throughflow parameter (example shown in Figure 9). 4). Using the curves produced in 3). above, convert the values of /3 into a pressure - radius characteristic in the following manner. Re-arranging equation 1 at radius ri the pressures at radii ri, 1 and r, a small distance either side of r ;, can be calculated using the formula:- 5.2 Design Method Shortfalls Although this method is useful in assessing the effects of throughflow on rotor-stator cavity velocity and pressure distributions it does not cover all of the many detailed geometry and flow features likely to be encountered by an engine designer. Although these shortfalls in knowledge will be addressed in future work on this subject, some advice is given below on how to make suitable approximations to account for them Effect of Inflow Inlet Swirl Rotor-stator rig and CFD data has been acquired for nominal % and 1% inlet swirl. However for practical rotor-stator situations the inlet swirl is likely to lie between these values. Using computational work carried out by Ong and Vaughan at the University of Sussex for a centripetal bleed flow through a rotorstator cavity with 3 different values of inlet swirl it can be shown that interpolation using an effectiveness based upon (inlet swirl) -g gives good agreement with the measured results. (Figure 8). It is therefore recommended that the expression:- = [Swo.s X ((3 - i3)1 + (3s,.o is used to derive values of (3 for inflow with inlet swirl of Sw from the design method data values for inlet swirls of and 1. = ^so. = [^ x (d 9 )] -.27Jsus so.nsos^ P 1 - P,_1 =.5J31,pc,2(rs+12 - rt-12) (2) The impeller tip static pressure can be found from cycle/aerodynamic data with an allowance, if necessary, for any pressure drop across the gap between the impeller tip and diffuser structure, and assigned to P;+1. Computed Radial Variation of /3 in a Rotor-Stator System for Turbulent Inflow of Varying Inlet Swirl I (Ong & Vaugha `^ ^. Inlet Swirl Therefore, with the value of 6 from the appropriate graph for a particular throughflow at a radius ratio of.96:-.11 r/r, P LO - P.92 =.5$ 2 2r 2((1.)2 - (.92)1 :. P1. - Po.92 =.768poi 2/32.96 Using the known values of P,. o (impeller tip static), p, co, r, and.96 then the pressure at radius.92 can be calculated. This central difference approach can be used in a similar manner to calculate the pressure at other inboard radii using the appropriate value of j3. For example, the pressure difference between radius ratios.92 and.78 can be calculated using equation (2) and the value of /3 at radius ratio 5. Hence static pressure against radius curves can be produced for the whole rotor-stator cavity for a selection of throughflows. 5). Analyse the cooling air system design, using an appropriate network solver computer program if available, to ascertain the effect of this overall pressure drop on flows within the system and iterate where necessary until a converged solution is achieved for the impeller rear face flow and the static pressure at the inner radius of the cavity. FIGURE 8 APPROXIMATION FOR INFLOW INLET SWIRL Effect of Non-Zero Inner Radius and Centrifugal Bleed Flow Inlet Swirl All of the data acquired from the rotor-stator rig and CFD simulation had an inner cavity radius of zero. (ie the rotational axis) However, many practical examples have a finite value for the cavity inner radius. Chew (1988) derived an integral solution for the flow entrainment on a rotating disc with a rim radius r, and a non-zero inner radius r; of the form:- Entrained flow with inner cavity radius r i = 1 r, 5 Entrained flow with zero inner cavity radius r,, For zero flow and inflow with r i/r, <.5 it is therefore suggested that the cavity inner radius position has only a second order effect on the flow structure in the cavity other than in the region local to where the flow exits. It is recommended that, in the first instance, the /3 -radius curves are deemed to apply unchanged down to the cavity inner radius. 11

12 Outflowing bleeds tend to have a braking effect on the rotating core. This braking effectiveness will depend upon the angular momentum of the inlet bleed compared to the angular momentum of the core. Hence local allowances should be made for outflowing bleeds entering the rotor-stator cavity at a finite radius and/or a finite swirl when constructing S - radius characteristics Effect of Non-Rectangular Cavity Shape and Protrusions Where a rotor-stator cavity is significantly conical in shape it has been found that the best agreement with a limited sample of measured data is achieved if the local axial gap ratio is used for calculating at each radius. Although it is likely to be significant, no advice is available at present on the effect of local protrusions on cavity velocity and pressure distributions. However a substantial amount of research has been carried out elsewhere on the effects of protrusions on rotor windage etc which may provide useful information. e.g. Millward and Robinson (1989), Zimmermann et al (1986) Effect of Ingestion at the Outer Radius of the Cavity For many cases where the cavity throughflow bleed is nominally outwards, there will also be a flow in and out of the cavity at its outer radius. This is because the amount of outflow bleed may not be sufficient to satisfy the rotor entrainment flow requirements with the particular shape and size of cavity tip gap. As a result the core tangential velocities near to the outer radius of the cavity could be substantially higher than those for a cavity perfectly sealed by the purging of the rotor-stator rim gap with outflow. It may also be assumed that as ingestion increases, its effects will be felt further inward into the cavity..9 R Innow, L = ; pwe.n^a Inflow, L = 3 7 pr d cted ' o...ca Designers are advised to consult some of the many papers on ingestion control to quantify this effect for particular applications Effect of Rotor/Stator Radial Temperature Gradients Since the inertia forces provided by the rotor are far higher than buoyancy effects it is thought unlikely that disc temperature gradients would have a significant effect on core tangential velocity distributions within the cavity. 6. DESIGN METHOD VALIDATION USING ENGINE AND COMPONENT RIG TEST DATA 6.1 Rolls-Royce 4D Compressor Rig Figure 9 shows - radius ratio characteristics predicted using the design methods described above and derived from static pressures measured on the 4D compressor rig at typical engine operating conditions. For the test data in this figure Re + = 4. X 16 and the rotor-stator axial gap ratio varied from.33 to.133. Computed and measured aerodynamic data for the main compressor flow indicated that the inflowing air entered the cavity with an initial swirl of around 75% of the impeller tip tangential velocity. It can be seen that there is good agreement between predicted and measured data especially with large amounts of inflowing bleed. The outflow predictions show best agreement at the inner radii of the cavity. The variance at the outer radii is believed to be due to ingested flows entering the cavity at the impeller tip. Calculations applying basic ingestion prediction methods (Phadke 1982) to the cavity tested suggest that some ingestion of highly swirled flow is likely to occur at the impeller tip for all amounts of outflow bleed up to around L = 4 (ie X, = 4X1-2)..6 Zero flow.5,/// ' ^.ca Mcd.4 r/r, (3,,,^ ca.5 Outflow, L = 1 pwd tee.6 /.4.51 r/r..3f r/re OS Q Inflow, L = 1 maso ce Outflow, L = 3 / ^,4 / RaK e ^;.3.2 r/r.4 1 r/r, FIGURE 9 /3 - r/r o FROM DESIGN PREDICTION CURVES COMPARED TO 4D COMPRESSOR RIG DATA 12

13 68 kpa Pressure static pressures 58 = Measured Results Gw 569, 62316rpm 56 Inner Radius or Cavoy Key: = Values from Design Prediction Curves lt^ains mn, FIGURE 1 STATIC PRESSURE-RADIUS FROM DESIGN PREDICTION CURVES COMPARED TO ENGINE TEST DATA 6.2 Rolls-Royce Gem Engine Test Data Figure 1 shows a prediction of the radial static pressure distribution in the rotor-stator cavity behind the impeller of a Rolls-Royce Gem engine compared to data measured directly from an engine operating on a test bed at a high power condition. This rotor-stator cavity has an axial gap ratio varying from approximately.8 to.25 and the test data is shown for a particular engine standard and operating condition where Re, = 8.X16 and )\ = 1. X 1-2 inflow (77% inlet swirl). It can be seen that the design method performs satisfactorily. 7. CONCLUSIONS AND PLANS FOR FURTHER WORK The main objective of this research package was to assess the effects of inflowing air bleeds on the velocity and pressure distributions in a rotor-stator cavity in a quantitative form of direct use in the design of gas turbine engine cooling air systems. A simple design method has been constructed from solutions produced by a partially validated CFD code with consideration given to the effects of other factors not yet fully investigated. This method has performed well in predicting radial static pressure distributions in rotor-stator cavities found in actual engines operating at typical high power conditions. Future work includes non-dimensional grouping of data into a reduced number of variables to promote better identification and explanation of trends and facilitate computerisation of the design methods, either directly from the data or as validated integral methods. Further rig testing and CFD work is envisaged to investigate the effects of more complex geometric arrangements representing typical engine design features such as balancing lands, rings of bolts and tapered surfaces. This work would also consider, in more detail, the effects of the radial position and initial swirl of the air at entry to the cavity. Data provided from the existing and future work programmes could be readily incorporated into the early stages of the engine component and cooling system design process, when rig test and CFD data may not be available, to essentially quantify the core tangential velocity distributions significant in the prediction of pressure gradients, moment and heat transfer coefficients. ACKNOWLEDGEMENTS The authors wish to thank Rolls-Royce plc for funding the work described in this paper. REFERENCES Chew J.W., 1985, 'Prediction of Flow in a Rotating Cavity with Radial Outflow using a Mixing Length Turbulence Model.' Proc. 4 ' Int. Conf. of Nwn. 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