On Aerodynamic Loading of Linear Compressor Cascades

Transcription

1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47 St., New York. N.Y GT-275 The Society shall not be responsible for statements or opinions advanced in papers or in dis cusslon at meetings of the Society or of its Divisions or Sections, of printed in its publications. M Discussion is printed only if the paper is published in an ASME Journal. Papers are available ]ti from ASME for fifteen months after the meeting. Printed In USA. Copyright 1992 by ASME On Aerodynamic Loading of Linear Compressor Cascades JAN CITAVI( PCS spot. s r. o. Turbomachinery Dept. Praha. Czechoslovakia ABSTRACT A study is presented concerning a high loading of the pressure surface of a blade in a linear compressor cascade. Assuming the two- -dimensional incompressible flow, two cascades denoted as RK3 and VD17 have been designed using an inverse method developed previously at SVCTSS. Both cascades have similar aerodynamic loading over the blade suction surface, but the cascade RK3 has lower minimum velocity (i.e. higher loading) on the pressure surface than the cascade VD17. Both cascades have been tested at the design as well as at the off- -design incidence angles in a low-speed windtunnel. The results have been used for definition of the maximum permissible aerodynamic loading on both suction and pressure surfaces. NOMENCLATURE AVR = axial velocity ratio c = blade chord CVD = chosen velocity distribution c P = pressure coefficient D,Deq= diffusion factors according to Lieblein H = shape factor LBL = laminar boundary layer L.E. = leading edge LS = laminar separation Ma = Mach number p = pressure pt = total pressure PS = pressure surface R = re-attachment Re = Reynolds number RK3 = cascade from a rotor s = blade spacing SB = separation bubble (transitional)= =LS-TR-R SS = suction surface TBL = turbulent boundary layer TR = transition in the attached or separated shear layer T.E. = trailing edge TS = turbulent separation TSB = turbulent separation bubble=ts-r Tu = turbulence intensity VD = velocity distribution over blade surface VDss = velocity distribution over suction surface VDps = velocity distribution over pressure surface VD17 = cascade having VDss number 17 w = velocity x,y = coordinates Subscript 1 = inlet flow 2 = outlet flow INTRODUCTION Maximum permissible aerodynamic loading is closely related to boundary layer separation which is a key problem of cascade aerodynamics. This has been recognise very early by Howell (1942) who suggested the maximum flow deflection as an aerodynamic loading of a given cascade with C4 profile. The nominal values related to the maximum flow deflection have been earlier used for designing of axial flow compressors. Using a very simple boundary layer concept and experimental results on 65-series, Lieblein (1965) introduced diffusion factors. The values of D=0.6 or Deq=2.2 have been considered as the maximum permissible loading. It has been shown (Citavy, 1974) that the above values of the diffusion factors are valid only for the so-called triangle shapes of velocity distributions; the corresponding value of maximum diffusion factor is Deq=1.2 for the roof- -top velocity distribution. In spite of this Presented at the International Gas Turbine and Aeroengine Congress and Exposition Cologne, Germany June 1-4, 1992

2 limitation, the diffusion factors have been (and perhaps still are) widely used in designing axial-flow compressors. Substantial progress has been achieved by introducing more detailed boundary theory together with an inverse cascade problem. The boundary layer theory makes it possible to choose a suitable or even an optimum velocity distribution over the blade surface. For the chosen velocity distribution (VD) and given velocity triangle, the cascade geometry is determined from a solution to the inverse problem. Both compressor and turbine cascades have been designed by means of the inverse problem for a prescribed velocity distribution (PVD); these cascades used to be denoted as PVD cascades. Previous work of SVUSS (SpaL^ek, 1958, Citavy, 1974) as well as many other, e.g. Papailiou (1967), Liu (1983), Beknev (1990), etc. represents selected examples of designing the cascades with prescribed VD over the suction blade surface. Recently,the same approach applied to highly loaded cascades at high subsonic Mach numbers (e.g. Sanger, 1983 and other) is being called CDA (controlled diffusion aerofoil). Nearly all of the above works have been concentrated on the suction surface of a blade. The present paper deals with the aerodynamic loading of both suction and pressure surface. Loading of the pressure surface is important in several design applications, e.g. aerofoil with maximum lift coefficient. A suitable distribution of aerodynamic loading between the suction and pressure surfaces is also important in relation to off-design aerodynamic performance. In general, more loading on one side of a blade causes a smaller range of incidence angles between the design and surge or chocking. The main purpose of this paper is to demonstrate how a choice of velocity distribution over the suction, and in particular, over the pressure surface, affects the aerodynamic performance at the deign and also at off-design incidence angles. For simplicity, 2D incompressible flow is assumed. Some of the considerations are applicable up to the critical Mach number, providing the inverse method and boundary layer calculations are valid for the subsonic compressible flow. QUALITATIVE RELATION BETWEEN BOUNDARY LAYER DEVELOPMENT AND AERODYNAMIC LOADING. The term 'loading' means the state of boundary layers on blade surface in relation to how near they are to the separation. A permissible blade loading can be defined as such a state of boundary layer when separation is just avoided. However, under real flow conditions, small separated regions, like a closed separation bubble cannot be avoided. By the separation bubble one understand the following sequences in boundary layer development: laminar separation-transition in the separated shear layer - re-attachment of a re-developing turbulent boundary layer; in short: SB = LS+TR+R. It should be distinguished from the locally separated turbulent boundary layer, i.e. turbulent separation bubble TSB = TS+R. In the simplest case of 2D incompressible flow there are only two important parameters which control the boundary layer development over the whole blade surface: i) velocity distribution (VD) ii) Reynolds number (Re). (VD)II 2 ir KSB W/W2 II (VD)55I i-----i SB SB -- VDI ^^ TS VDII 1VD1 PsI ^i (VD)II 1 0 ' 0XM/C X/C 1 Fig. 1: Velocity distribution (VD) over the blade in cascade; VD I - moderate aerodynamic loading, VD II - high loading For a qualitative description of boundary layer development in relation to aerodynamic loading, let us consider a typical ('linearised') VD denoted as VD I in Fig. 1; the corresponding boundary layer development at say, Re=5.10, will be as follows: Suction blade surface: boundary layer is laminar (L) from the leading edge (L.E.) up to the point of laminar separation (LS) followed by transition (TR) in the separated shear layer with re-attachment (R) as the turbulent boundary layer (T) which develops up to the trailing edge (T.E.). Pressure surface: laminar boundary layer (L) is developing from the leading edge (L.E.) up to the trailing edge or up to a natural transition region which is followed by the turbulent boundary layer up to the trailing edge. At higher aerodynamic loading caused by the VD II, Fig. 1, the boundary layer development on a blade surface is described as follows: Suction surface: laminar boundary layer - separation bubble - turbulent boundary layer - turbulent separation Pressure surface: laminar boundary layer - separation bubble - turbulent boundary layer. The main differences between the boundary layer development in case of VD I and VD II are the separations with VD II near the trailing edge on the suction surface and near the leading edge on the pressure surface. These two areas are the most dangerous from the point of view of separation because of the largest gradients. Summary of possible boundary layer development on both sides of a blade in cascades with various aerodynamics loading is indicated in TABLE 1.

3 TABLE 1: Relation between loading and boundary layer development RK3 Suction surface: low loading LBL - TR - TBL moderate loading LBL - SB - TBL high loading LBL - SB - TBL - TS very high loading LBL - SB - TBL - TS Pressure surface: low loading LBL moderate loading LBL - TR - TBL high loading LBL - SB - TBL very high loading LBL - SB - TBL - TS - R The above considerations can serve as a guide to choose such a velocity distribution on both the suction (VDss) and the pressure (VDps) surfaces for which extensive separation is avoided. Such a chosen velocity distribution (CVD) = (VDss) + (VDps) is the most suitable for given requirements. The CVD is related to the velocity triangle (i.e. inlet and outlet flow angles) and blade spacing through the known circulation coefficient. This makes it possible to determine the relative blade spacing providing, the velocity triangle and CVD are known. Three typical design problems are as follows: i) The simplest and most common requirement for a given velocity triangle is a minimum loss. This can be satisfied by CVD for which there is no extensive separation on either side of a blade. ii) More typical problem is to design a cascade for maximum flow deflection and the lowest loss. Different cascades will be obtained depending on wether the inlet or the outlet flow angle is kept constant. iii) The most interesting problem is to design a cascade for maximum flow deflection, maximum critical Mach number and minimum loss at the same time. This can be accomplished by choosing a moderate loading on the suction surface and a high loading of pressure surface. Fig. 2: Geometry of cascades VD17 and RK3 and discontinuity position xm from which the velocity decreases up to the trailing edge. The same value of H = 2 were chosen for both cascades, but the values of xm differed and were equal to 0.7 and 0.5 for the cascade RK3 and VD17, respectively. Because of the discontinuity, the idealised VD has to be smoothed out using Fourier series. This is noticeable as "waves" on the VD with cascade RK3. After smoothing, the values of maximum velocity are equal to 1.25 and 1.3 for RK3 and VD17 cascades, respectively. The corresponding values of Deq = 1.65 and The chosen VD corresponds to the moderate loading (i.e. VDss I in Fig. 1.) and the particular shapes for both cascades are shown in Fig. 3 in terms of pressure coefficient distributions. Once the VDss is chosen, an estimate of the critical Mach number can be made using the known rules for compressibility correction, e.g. according to Prandtl-Glauert or Karman-Tsien. DESIGN OF TWO CASCADES HAVING CVD Two linear compressor cascades denoted as RK3 and VD 17 have been designed for testing the above qualitative model. Two-dimensional incompressible flow has been assumed. Velocity Triangles. The inlet and outlet flow angles are given in Fig. 2. It is seen that the inlet flow angles do not differ more than 3 deg. for both cascades. However, the outlet flow angles are substantially different, so that the flow deflection is much higher with cascade RK3, see Fig. 2. Chosen Velocity Distribution (CVD). Suction surface. Both cascades have a velocity distribution chosen from a family of "idealised" velocity distributions (Spa6ek 1958 and Citavy 1974). The aerodynamic loading with this idealised VD is specified by choosing the values of the boundary layer form parameter H \ o 0,5 (7S'..SS RK3,ai=-43 \ o CALCULATION 1 ^\ o EXPERIMENT Re =1,67 X 10 5 C P \ 0,5 \ otu =2% o 0 0 o o x/c 1 Fig. 3: Chosen VD/pressure distribution for two compressor cascades RK3 and VD17 Pressure surface. The VDps is chosen to be nearly constant over most of the pressure surface. However, values of the constants differs for the two cascades and are equal to 0.85 and C

4 0.99 for RK3 and VD17 cascades, respectively. The lower value of minimum velocity with cascade RK3 causes a higher circulation, but also a steeper unfavourable gradient near the L.E. Inverse Problem. A simple inverse method developed earlier (Citavy, 1974) from Polasek's singularity analysis method has been used to determine the cascades coordinates. The chosen velocity distribution VDss is approximated by Fourier series and system of algebraic equations is solved for the unknown Fourier coefficient for the distribution of circulation, mean=line and profile shape. The stagger angle, space-chord ratio and maximum thickness are chosen and the velocity triangle and velocity distribution VDps over pressure surface is determined. The resulting profile shapes of both cascades are given in Fig. 2. It can be seen that the leading edge radius of RK3 cascade is small and it has not been especially treated for the assumed incompressible flow. The table of coordinates is given in Appendix. EXPERIMENTAL INVESTIGATION Blades of Tested Cascades. The blade chord of both cascades is c = 60 mm, the height h = 300 mm which gives the aspect ratio equal to 5. The blades have been produced from aluminium alloy using standard technology on NC-machines (a model blade on MAHO 1000 controlled by CNC432, the tested blades on HESACOP50 controlled by Gettys). The blade geometry is checked on SIP 422 M (controlled by HP 9831A) and is kept within ±0.05 mm. Surface roughness along the chord and along the blade height is 0.6 and 1.5 gm, respectively. Two blades in each cascade have been provided with pressure tapping. Wind-tunnel. Low-speed cascade wind-tunnel having variable incidence angle working section has been used. It is of open type with the outlet from the measured cascade into the ambient air. The velocity upstream of cascades could be changed within the range of 15 to 50 m per s. The Reynolds number and turbulence intensity was 1.7*10 5 and 0.002, respectively. The solid walls are used in the working section, so that axial velocity ratio (AVR) is not the independent variable. Upstream flow uniformity was checked by side walls pressure tapping, while the downstream wake periodicity was checked by traversing outlet flow behind three blades. Procedure and evaluation. Both cascades have been tested at the design inlet flow angle and then within a range of both higher (positive) and lower (negative) incidence angles until the loss coefficient was at least twice as large as the minimum one (at the design incidence angle). From the wake measurements, the loss coefficient and flow deflection have been evaluated: Pt1-Pt2 (1) pti -P1 E =a 2 -a 1 (2) The pressure coefficient c. has been determined from readings of pressure taps: cp= (3) P-P1 P tl -Pl Surface flow visualisation has been made on two blades (with pressure tapping) coated with wall paper on which a mixture of lamp black with oil was pained. Then the tunnel was run until the mixture stopped moving. The photographs were taken from each run. EXPERIMENTAL RESULTS AND DISCUSSION Pressure Distribution. The measured pressure distributions at the design incidence angle for both cascades are shown in Fig. 3. Experiments differs from the designed distributions, in particular with the cascade RK3 on the suction surface near the sharp leading edge. Unpublished re-calculations using three different methods have shown much better agreement (i. e. more smooth pressure distribution) near L.E. on a profile in cascade RK3. The differences between measured and calculated pressure distributions on the pressure surface for both cascades are explained, at least qualitatively, by the tunnel flow contraction (Citav2,1974). The measured variation of flow contraction expressed as AVR (according to Horlock) for cascades RK3 and VD 17 with incidence angle is illustrated in Fig. 4. As can be seen, the AVR is higher than 1 at positive incidence angles while at negative incidence angles it is less than 1 (i.e. flow divergence). Thus, the effect of AVR is more pronounced at positive incidence angles for both cascades when comparing to calculated pressure distribution at AVR=l. A\ Fig. 4: AVR in dependence of incidence angle The effect of off-design incidence angles is illustrated in Fig. 5. for positive and negative incidence angles. As expected, the differences between experiment and calculation are larger at positive incidence angle when the separation on the suction surface takes place near T.E.

5 \^ o -0,5 \ ' CALCULATION RK3, \ a,=-48'0 EXPERIMENT \ Re C P \ \ o Tu=2% \ o xlc 1 effect as is the case with the separation on the suction surface. In the latter case, the separated region extends into the near-wake and thus affects (increases) the outlet flow angle. Since the separation on the suction blade surface with cascade RK3 is of a larger extent, the increase of outlet flow angle at positive incidence angles is more pronounced than with the cascade VD17. 0,: ^P :ULATION :RIMENT 1,67 x xic Fig. 6: Loss coefficient and outlet flow angle in dependence of incidence angle Fig. 5: Pressure distribution at off-design incidence angles; a) high positive incidence angle b) low negative incidence angle Loss Coefficient and Outlet Flow Angle. The dependence of loss coefficient and outlet flow angle on inlet flow/incidence angle is shown in Fig. 6. Higher value of loss coefficient with cascade RK3 at the design incidence angle is due to a higher loading of the blade pressure surface. This is supported by flow visualisation, Fig. 7 which indicates a closed separation region near the leading edge on the pressure surface. The effect of off-design incidence angles can also be observed from Fig. 6. The loss coefficient increases with both higher and lower incidence angle as it is usual; the increase is steeper with the incidence angles higher than the design one. Incidentally, the working range for incidence angles (defined according to Howell as twice of the minimum/design loss) is nearly the same for both cascades (16 deg.). The outlet flow angle does not depend on incidence angle at lower incidence than the design ones. This is explained by a fact that the closed separated region on the pressure surface does not cause as large displacement Surface Flow Visualisation. From the photographs of flow visualisations, the lines of both laminar and turbulent boundary layer separation as well as re-attachment have been determined at each inlet flow angle. The separation bubbles were equally distributed along the blade span, except small regions near the side walls. The length of bubbles have been determined at mid-- span. An example of flow visualisations is illustrated in Fig. 7 for both cascades at the design incidence angle. The summary of these observations are indicated in Fig. 8 for the suction and pressure blade surfaces, respectively. The observed positions of LS, TR, TS and R are shown as a function of inlet flow/incidence angle for both cascades. The separated regions are indicated as the shaded area. Suction surface. At the design incidence angle, the separation bubble occurs on both cascades; the only difference is in the position and length of the bubble. Similarity in the boundary layer development exist also at both positive and negative incidence angles. At the negative incidence angle, separation bubble takes place on both cascades; the position of the bubble is moving downstream with the cascade VD17. At higher positive incidence angles,

6 the turbulent boundary layer separates near T.E. The position of separation moves upstream with increasing incidence angle for both cascades, although this movement is more progressive with cascade RK3. RK3 I Dusek, (1990) and causes an increase of loss and deviation angle. Therefore, a more safe choice is just to avoid this separation. The particular shape of such a velocity distribution (VDss) has already been determined from the distribution of shape factor H=const, e.g. SpaLek (1956), Papailiou (1969), Citavy (1974), etc. The cascades have been denoted as PVD or later as CDA. Still higher loading is proposed here as a maximum permissible, namely such that gives the separation point TS a small distance, say 10 per cent of the chord, upstream of the trailing edge. Such a VDss is schematically shown in Fig. 1 and is denoted as (VD)ss II. II r o it xlc i P essure surface a 0,5 )i RK3 VD17 l il Design ^ L.E ' -40' -30' a 1-20' Fig. 7: Flow visualisation on suction and pressure surface of cascades RK3 and VD17 Pressure surface. At the design incidence angle, there is a closed separated region near the leading edge on the cascade RK3, while the boundary layer is purely laminar with the cascade VD17. This is the main difference in the boundary development for the two cascades. At negative incidence angles the extent of the closed separated region increases and approaches nearly mid-chord position at the lowest inlet flow angles (-25 deg.). At positive incidence angles the boundary layer remains laminar up to the trailing edge. MAXIMUM PERMISSIBLE LOADING From the qualitative relation between the boundary layer development and the chosen velocity distribution (CVD) as well as from the experiments on cascades RK3 and VD17, the maximum permissible loading (MPL) can be specified as follows: i) suction surface: most important factor is the turbulent boundary layer separation (TS) near the trailing edge. This separated region is closed in the near-wake, e.g. Citavy and Fig. 8: Summary of surface flow visualisation at various incidence angles on suction and pressure surface ii) pressure surface: the most important role plays a flow deceleration near the leading edge which takes place often on a very short length of blade surface. It is influenced by the minimum value of VDps, radius of the L.E., position of the stagnation point, etc. Although this is a typical situation in boundary layer development at low negative incidence angles for any cascade, there appears little data about it so far. From visualisation on cascade RK3 it appears that turbulent separation bubble (TSB) is formed near the L.E. However, a transitional SB (which should occur in front of the TSB) was not possible to detect apparently due to a very small radius of L.E. Neglecting this detail, it has been suggested (Citavy, 1986) to use the minimum relative velocity in the form of the diffusion factor as it has been common for the suction surface. From experiment on RK3, it is proposed that a maximum permissible loading (MPL) on the pressure surface is such a VDps which gives a closed separated region near the L.E. of an extent of 10 per cent of blade chord. Schematically such a VDps is illustrated in Fig. 1 where it is denoted as (VD)ps II.

7 t ^ Higher loading R SB S LS TR Suction surface Design R Pressure surface Higher loadi ng TSB a, o ^f f + L Design az a, Higher loading T.E. Fig. 9: Model of aerodynamic loading at design incidence angle in relation to boundary development and to off-design incidence angles The proposed definition of maximum permissible loading for both suction and pressure surfaces are schematically illustrated in Fig. 9 where the length of separated regions of 10 per cent of chord are indicated at the design incidence angle (full line). A possible development of boundary layers at off-design incidence angles in relation to loss and outlet flow angle is also included. It is clear from the boundary layer development that increased loading at the design incidence angle causes a larger extent of separated regions (either near T.E. on SS or near L.E. on PS). Thus, the extent of working range at off-design incidence angles decreases. CONCLUSIONS From low speed experiments with two linear compressor cascades RK3 and VD17 having a chosen velocity distribution (CVD) at the design incidence angle, the main conclusions are as follows: i) High aerodynamic loading of blade pressure surface makes it possible to achieve a high flow deflection and acceptably low loss coefficient in incompressible flow. It has been accomplished by choosing a low velocities on both blade surfaces and solving an indirect problem. Using this procedure the cascades RK3 and VD17 have been designed. Both cascades have rather similar velocity distribution on the suction surface (VD)ss, but different (VD)ps (i.e. lower loading) on the pressure surface. As a result, a higher loss is obtained with the cascade RK3, but also higher flow deflection than with cascade VD17. This is caused by a closed separation region on pressure surface near the leading edge on cascade RK3. a, L.E. T.E. L.E. ii) The chosen velocity distribution (CVD) at the design incidence angle has also an affect on the off-design performance characteristics of a cascade. The increase of loss at positive (i.e. higher than the design) incidence angles is caused by an upstream movement of the turbulent separation point TS on suction surface for both cascades, Fig. 8. At negative incidence angles, the loss increases due to increasing the length of the closed separated region near the L.E. on the pressure surface for both cascades. iii) A definition of maximum permissible aerodynamic loading (MPL) has been proposed for both suction and pressure surfaces as follows: it is such a velocity distribution VDss for which the turbulent separation occurs at the relative distance 90 per cent of chord on the suction surface (i.e. near the T.E.); further on, it is such a velocity distribution VDps which gives a small separated region (the extend of which is 10 per cent of chord) on the pressure surface near the L.E. Higher aerodynamic loading is achieved by increasing and decreasing the blade surface velocity on the suction and pressure surfaces, respectively. This, in turn, causes a larger extend of the separated regions (a 'shift' in Fig. 9) on both the suction (near T.E.) and pressure (near L.E.) surface. iv) Further research should be aimed to resolve the details of the boundary layer development on the pressure surface near the leading edge. REFERENCES Beknev, V.S., Vasilenko, S.E., Kooftov, A.F., Tumashev, R.Z., 1990, "Designing the Compressor Blading Using the Aerodynamic Loading Concept", Proceedings of First International Symposium on Experimental and Computational Aerothermodynamics on Internal Flow (1st ISAIF). Chen Naixing, Jiang Hongde (Eds.), World Publishing House, Beijing, China, pp Citavy, J., 1974, "Two-Dimensional Compressor Cascades With Optimum Velocity Distribution Over the Blade", ASME Journal of Engineering for Power, Vol. 97, pp Citavy, J., 1986, "Performance Prediction of Straight Compressor Cascades Having an Arbitrary Profile Shape", ASME Journal of Turbomachinery, Vol. 109, pp Citavy, J., Dusek, M., 1990, "Separated Flow in a Straight Compressor Cascade", In: V. V. Kozlov, A.V. Dorgal (Eds.), Separated Flows and Jets, IUTAM Symposium Novosibirsk, Springer- -Verlag, Berlin, pp Howell, A.R., 1942, "The Present Basis of Axial Flow Compressors Design", A.R.C. Reports & Memoranda, No Lieblein, S., 1965, In: "Aerodynamic Design of Axial flow Compressors, " NASA SP 36 Liu, G., 1983, "Aerodynamic Optimization Theory of 3D Axial-Flow Rotor Blading via Optimal Control", Sixth International Symposium on Air Breathing Engines, ISABE, Paris, pp. 313 Papailiou, K., 1967, "Blade Optimization Based on Boundary Layer Concept", VKI CN 60 Sanger, N.L., 1983, "The Use of Optimization Technique to Design Controlled Diffusion Con-

8 pressor Blading", Journal of Engineering for Power, Vol. 105, pp Sanger, N.L., Shreeve, R.P., 1986, "Comparison of Calculated and Experimental Cascade Performance for Controlled-Diffusion Compressor Stator Blading", ASME Paper 86-GT-35 SpaL'ek, L., 1958, "Optimum Choice of Surface Velocity in the Design of Aerodynamic Devices", (in Czech, Proceedings Fluid Flow in Turbomachines, NCSAV, Prague, pp APPENDIX: Coordinates of profiles in cascades RK3 VD17 (x/c)ss (y/c)ss (x/c)ps (y/c)ps (x/c)ss (y/c)ss (x/c)ps (y/c)ps L.E. radius = L.E. radius = Note: The origin of Cartesian cordinate system is at mid-chord position.