Design and performance of a high-pressure ratio turbocharger compressor Part 1 : design considerations

Transcription

1 115 Design and performance of a highpressure ratio turbocharger compressor Part 1 : design considerations A Whitfield, BSc, MSc, PhD, MMechE, M D C Doyle, BSc, CEng, MMechE School of Mechanical Engineering, University of Bath M R Firth, BSc, CEng, MMechE Holset Engineering Company, Huddersfield The compressor design requirement was for a pressure ratio of 3.6, with a peak pressure ratio of 4.3 at the maximum nondimensional speed of the impeller of Due to the stresslimited speed, an aluminium alloy impeller was specijied, the impeller discharge blade backsweep had to be restricted and the application of prewhirl was considered from the outset as a means of extending the operating range. A nondimensional conceptual design procedure, including the effect of inlet prewhirl, was applied to the design of three turbocharger impellers. An impeller, designated A, was designed with the inclusion of 25" of prewhirl. A second impeller, designated B, was designed with zero prewhirl for comparison purposes, but was not manufactured. A third impeller, C, was manufactured through the modijication of an existing design and the design study was applied to the assessment of this third design. a A b c Cslip d f h tit M M M" ns N P PR Q r R T TR U W M P Y Ahos v s % A P v P NOTATON speed of sound area blade or passage height absolute velocity slip velocity diameter function of ent halpy mass flowrate Mach number relative Mach number nondimensional tip speed of the impeller = UhOl specific speed rotational speed (r/min) pressure pressure ratio volume flowrate radius gas constant temperature temperature ratio blade velocity re1 ative velocity absolute flow angle, positive in direction of impeller rotation relative flow angle, positive in direction of impeller rotation ratio of specific heat isentropic stagnation enthalpy change stage efficiency nondimensional mass flowrate = ~ /(polao,m~) work input factor slip factor = 1 C,,,,/U, impeller inducer hubshroud radius ratio density The MS was received on 28 January 1993 and was accepted for publication on 30 April t,b o flow coefficient = tit/(pol U2 nr;) head or enthalpy coefficient rotational speed (rad/s) Subscripts B blade s shroud tip position % tangential component 0 stagnation condition 1 2 station position at stage inlet station position at impeller outer diameter 1 NTRODUCTON The automotive diesel engine continues to demand increased pressure ratio from the turbocharger. Proposed emissions legislation means that more air must be made available for combustion and hence higher boost pressures are necessary. These requirements, together with the need for fuel efficient engines that can operate over a wide speed range, lead to a turbocharger requirement not only for a highpressure ratio but also for a broad operating range between surge and choke and with good efficiency. Gas turbine experience and attempts to develop singlestage compressors with pressure ratios of up to 12: 1 have shown that operating range is inextricably reduced as the pressure ratio is increased (1,2). The design of a turbocharger is constrained by a number of nonaerodynamic considerations. These include cost, overall frame size, inertia of the rotating components and general durability (3, 4). To obtain an increased pressure ratio through increased impeller tip speeds will eventually mean that cast aluminium alloy impellers will have to be replaced with alternative metals such as titanium, with a consequent increase in cost. Current requirements, however, are for pressure ratios that can be achieved at rotational speeds suitable for aluminium impellers, and the need to switch to A00593/1 Q MechE S09/93 $ Proc nstn Mech Engrs Vol 207

2 116 A WHTFELD, M D C DOYLE AND M R FRTH alternative materials is not yet overwhelming. f impeller tip speed is considered to be limited by stress considerations then increased pressure ratio can only be achieved by reducing the magnitude of the impeller discharge blade backsweep. This will lead to a reduction in operating range which could possibly be recovered through the application of positive swirl at impeller inlet. This in turn, in the absence of the ability to increase blade tip speeds, will lead to the necessity to further reduce the discharge blade backsweep in order to achieve the desired pressure ratio. The alternative approach of increasing the blade speed through the application of alternative materials will lead to the design of a transonic inducer (4), and this, as shown by gas turbine design, will lead to a reduction in operating range. Again the application of inlet prewhirl can be considered in order to reduce the inlet relative Mach number and increase the operating range. The specific design requirements for the turbocharger compressor considered here were: (a) to provide a pressure ratio of 3.6 with a mass flowrate of 0.4 kg/s and with a target efficiency of 0.73 ; (b) to provide a peak pressure ratio of 4.3 at a maximum nondimensional impeller tip speed of 1.66; (c) to provide a broad operating range between the surge and choke flow conditions. From the outset the application of inlet swirl was considered as it is a wellestablished method of extending the operating range (although not yet widely adopted for turbocharging). Designs were developed nondimensionally as it provided a ready means of assessing both the design options and the effect of imposed design constraints. Three designs were considered : 1. mpeller A included the application of 25 degrees of prewhirl and was manufactured and tested. 2. mpeller B was designed with no inlet swirl, but has not been manufactured. 3. mpeller C was manufactured by modifying an existing zero prewhirl design, and unlike impeller B was not designed for the specific design requirements. The nondimensional design procedure was used to assess this design alongside impellers A and B. The principal constraints imposed on the design were : 1. Stage eflciency. A target stage totaltototal efficiency of 73 per cent was specified and maintained constant. Failure to achieve the target efficiency, or the specification of a lower magnitude, will lead to the necessity to reduce the discharge blade backsweep or, if possible, increase the impeller tip speed in order to achieve the target pressure ratio. While the efficiency was specified a primary objective of the design was to maximize the efficiency, and the design was developed with a view to minimizing the energy dissipation due to the main loss generating mechanisms such as impeller incidence, passage friction, impeller shroud tip clearance and separation due to diffusion in the impeller passage. Part A: Journal of Power and Energy 2. Nondimensional impeller tip speed. A nondimensional impeller tip speed of 1.5 was adopted. This was derived from the imposed maximum nondimensional speed of 1.66 where a peak pressure ratio of 4.3 was specified together with a target efficiency of 70 per cent. Alternative nondimensional speeds were considered in order to assess the consequences of the imposed restraint. 3. mpeller rotational speed. An impeller rotational speed of r/min was imposed on the design in order to meet the requirements of a parallel design study associated with a mixedflow turbine. This imposition, together with the nondimensional speed, effectively fixed the outer diameter of the impeller, and as a consequence the nondimensional mass flowrate was effectively fixed. The effect of this constraint was investigated and found not to be detrimental. 4. The application of an existing difuserluolute housing: The designed impeller had to be tested as part of an existing turbocharger design, and as a consequence the vaneless diffuser and collecting volute were not designed in parallel with the impeller. As part of the experimental investigation (see Part 2), the passage depth of the vaneless space was systematically increased in order to maximize the overall efficiency ; it was not possible, however, to change the outer diameter of the vaneless diffuser or modify the collecting volute. 2 NONDMENSONAL DESGN Dimensional analysis is a classical technique used to identify the basic nondimensional parameters that influence the behaviour of a turbomachine. This method reduces the number of parameters involved by the number of primary dimensions. f, in addition, the application is restricted to a single working fluid and for an initial design study the effect of Reynolds number can be considered a secondary influence, the number of nondimensional groups can be further reduced to give the functional relationship [see reference (5)] as These basic groups are often combined to yield alternative parameters; for example the temperature ratio is usually combined with the pressure ratio and replaced by the more useful totaltototal isentropic efficiency through the relationship ppl)/y 1 " = TR 1 The appropriate nondimensional relationship is then This relationship is widely used for the presentation of compressor performance. These nondimensional groups, however, are not usually adopted for design purposes. When designing an impeller the pressure ratio is specified and is not a variable. However, the compressor geometry cannot be represented by a single characteristic dimension (usually the impeller diameter) as a (3) 0 MechE 1993

3 DESGN AND PERFORMANCE OF A HGHPRESSURE RATO TURBOCHARGER COMPRESSOR. PART series of design options must be studied; that is geometrically similar machines are not being considered. Consequently, the major impeller dimensions must be included and equation (3) expanded to?s =f(e, Mu 2 rls/r2 3 rlh/r2 2 b2/r s) (4) The design objective is to find the combination of nondimensional parameters that will either maximize the efficiency or provide a satisfactory compromise with any other restraints, such as impeller size and speed limitations. The nondimensional impeller tip speed Mu is fixed through stress considerations and it remains for the designer to select the nondimensional mass flowrate 8 from which the most appropriate design must be developed. The additional specification of the desired mass flowrate and inlet stagnation conditions enables the impeller outer diameter to be derived from the nondimensional mass flowrate. t should be noted that the additional specification of any dimensional parameter, for example the rotational speed as specified for this design, will restrict the design options available. Some designers make extensive use of the alternative parameters of specific speed and specific diameter (69). Specific speed is not used directly here, however; it is presented for comparison purposes through the definition n, = OJQ Here the volume flowrate Q is defined at the inlet stagnation conditions, that is Q = m/pol. The expression for specific speed can be developed to As the pressure ratio P, and nondimensional speed Mu are fixed by the design requirements the specific speed is directly proportional to the nondimensional mass flowrate 8. 3 DESGN CONSDERATONS The design procedure derives the overall dimensions of the impeller in terms of the appropriate diameter ratios and inlet and discharge blade angles. To achieve this objective the designer must specify other parameters to develop the design analysis, and must also derive additional parameters in order to assess the likely success of the design proposals. For the design procedure described here the following parameters were specified : 1. Absolute $ow angle at impeller discharge. The optimum absolute flow angle at impeller discharge is often quoted to lie between 60 and 70" (8, 10). A magnitude of 65" is generally adopted here, with the effect of alternative magnitudes assessed. A large magnitude for the absolute flow angle will lead to a long flow path through the following vaneless diffuser, with a consequent increase in losses and possibly stall and separation leading to surge. 2. mpeller efficiency. t is necessary to specify a magnitude for the impeller efficiency so that the fluid density can be established at impeller discharge MechE 1993 through which the discharge flow area and hence blade height can be established. A magnitude of 80 per cent was applied. 3. nducer hubshroud radius ratio. As the inducer hub imposes a blockage to the flow it is desirable to minimize its size. The diameter of the hub is controlled by mechanical considerations and the necessity to provide sufficient circumferential space to accommodate the desired number of blades. Based on current turbocharger designs a magnitude of 0.35 was applied. 4. Optimum incidence angle. The inlet design conditions are considered in terms of the relative flow angle and it is necessary to specify an optimum incidence angle in order to derive the blade angle. 5. Slip factor. For the initial design analysis it is not necessary to specify a slip factor. The design can be developed in terms of the relative flow angle at impeller discharge and the slip factor introduced at a later stage to transform the relative flow angle to the actual blade angle (5). The uncertainties associated with the slip factor can, therefore, be left to a later stage in the design process. t is, however, the blade backsweep that is important mechanically and in order to transform the relative flow angle into the blade angle a slip factor of 0.8 was adopted; this is a conservative magnitude and the application of a larger value, for example 0.85, would have led to an increase in the blade backsweep that could have been adopted. 4 DESGN PROCEDURE The impeller inlet and discharge velocity triangles were developed for a series of specified impeller radius ratios, rljrz, for any given nondimensional mass flowrate 8. As the design procedure was developed fully nondimensionally it was not necessary to utilize the specified mass flowrate and inlet stagnation conditions to derive the inlet geometry. Velocities were established in terms of the Mach number and the impeller geometry in a form nondimensionalized by the discharge radius. 4.1 nducer conditions Application of the continuity condition at impeller inlet leads to the nondimensional mass flowrate at impeller inlet [see references (11) and (12)] as el = m Po1 a01 A, cos Uls = M,( Y1 M:,) (Y + 1)/(2(Y 1)) t should be noted that with the application of inlet prewhirl the continuity equation as applied in equation (7) assumes that the axial component of velocity does not vary with the radius. This is only true if the prewhirl is of the free vortex type. For other prewhirl vortices it is necessary to apply an integration from inducer hub to tip in order to derive the mass flowrate in terms of the absolute Mach number. This has been done for both a solid body and constant angle prewhirl and yielded very similar results to those presented here. (7) Proc nstn Mech Engrs Vol 207

4 118 A WHTFELD, M D C DOYLE AND M R FRTH The impeller nondimensional mass flowrate 8 is related to that at inlet, 8,, through D E c P > 2? Bart = O1zr:,(l v2) cos als and equation (7) can be developed to 8 = (1 v2) cos a,, M,, t2 Y (Y+1)/{2(Y,)) x ( 1+ y; M:,) (8) This expression was solved for the absolute Mach number through the specification of a range of nondimensional mass flowrates and impeller radius ratios. The inducer hub tip radius ratio v was maintained constant at 0.35, and the effect of inlet swirl, a,,, investigated. t is, however, the inlet relative Mach number that is the critical parameter and this can be derived through A4tre = (Ms cos ~1,)' + M,, sin a,, where the inducer tip blade Mach number is related to the nondimensional speed of the impeller through Design with inlet swirl A specific objective of this study was to include the effects of inlet swirl, and consequently the initial design, impeller A, was developed with the inclusion of 25" of prewhirl. Equations (8) and (9) can be solved for the absolute and relative Mach numbers for a range of nondimensional mass flowrates and impeller radius ratios. The result of such an analysis is presented in Fig. 1 for an assumed inlet swirl angle of 25". Also shown, from the geometry of the velocity triangle, are the straight line contours of the relative flow angle, pis. n order to minimize impeller incidence and passage friction loss, Mu = 1.5 a, = o o Design point PS, 1, "s and ensure an adequate flow range to the chocked flow condition, it is desirable to minimize the inlet relative Mach number. rrespective of the nondimensional mass flowrate this is shown to occur at a relative flow angle of approximately 50". With an assumed optimum incidence angle of 6" this gives a corresponding inlet blade angle of 440much smaller than that usually adopted with a conventional zero prewhirl design. Each plotted point on a nondimensional flow contour represents a radius ratio specified in 0.02 decrements from an initial value of 0.8. Clearly, for any nondimensional mass flowrate and specific speed, a wide range of impeller geometries are available. A desire to minimize the relative Mach number reduces the options, while the selection of the magnitude of the nondimensional mass flowrate is a compromise between the desire to minimize the relative Mach number and the impeller outer diameter. ncreasing the nondimensional mass flowrate leads to an increase in the impeller radius ratio at the minimum Mach number condition; for example the radius ratio increases from approximately 0.52 to 0.68 as the nondimensional mass flowrate increases from 0.1 to 0.2. Either extreme, a low or a high radius ratio, is likely to lead to an increase in the impeller passage loss. With the imposed design constraint of an impeller rotational speed of r/min, together with the imposed nondimensional impeller speed, the impeller outer diameter and consequently the nondimensional mass flowrate are effectively prescribed. The nondimensional mass flowrate is shown in Fig. 1 as the contour, together with the selected design point. The design point was selected slightly away from the minimum relative Mach number condition as this reduced the inlet Mach number and increased the impeller radius ratio without significantly increasing the relative Mach number Design with no inlet swirl A consequence of the application of prewhirl to an impeller design with a specified nondimensional speed is that a relative low amount of discharge blade backsweep can be adopted. By designing for no inlet prewhirl, impeller B, the discharge blade backsweep can be increased from 7 to 22" (see Section 4.2). The inducer design conditions are shown in Fig. 2. n this case the minimum relative Mach number condition occurs at an inlet relative flow angle of approximately 60", as shown by Stanitz (13). Again the nondimensional mass flowrate is effectively fixed by the design constraints and a proposed, but not used, design point is indicated at the minimum relative Mach number condition. The removal of inlet swirl has led to an increase in the relative Mach number from 0.84 to f it were essential to reduce this relative Mach number it would be necessary to design with a lower nondimensional mass flowrate; this would lead to a larger impeller diameter and a reduced rotational speed. The design indicated above was not manufactured ; an existing impeller design was modified to match the inducer requirements only, thereby eliminating the need to carry out a detailed passage design and manufacture. This modified impeller, impeller C, had a smaller discharge diameter than that required by the above MechE 1993

5 (Y DESGN AND PERFORMANCE OF A HGHPRESSURE RATO TURBOCHARGER COMPRESSOR. PART b 1.1 a : 1.0 s. ; 0.9 > 0.8 = P S Fig. 2 nlet Mach number U Design point nlet Mach numbers for impeller B conditions and a discharge blade backsweep of 30. Consequently, this design would not meet the performance requirements set for impellers A and B. The inducer design dimensions were the same as those developed for impeller B, and in order to compare it with the above designs it was assessed at the same rotational speed, r/min, that is at a nondimensional tip speed of As a consequence of the reduced impeller diameter the nondimensional mass flowrate increased to The inducer Mach numbers are shown in Fig. 3. The modified impeller design, with a reduced outer diameter, leads to the design point shown, coincident with the 0.66 radius ratio point. This is slightly away from the minimum Mach number condition and leads to an inducer relative Mach number of mpeller discharge conditions While the nondimensional speed of the impeller is effectively fixed by the imposed design requirements the effect of alternative magnitudes was investigated together with alternative rotational speeds. The stage stagnation pressure ratio is given by pg VY = 1 + ~ 21)qs ( ~ 2 a0 1 which can be developed to pfl)/v 1 p tan a2 (y 1)qS ~, 2 tan a2 tan Be2 ~ 0 2 Uic01,) r:, tan als r: tan als tan Bls By systematically varying /?2B and rls/r2 the above expression can be solved for the nondimensional speed Mu. The inlet relative and discharge absolute Mach numbers can then be derived and presented as shown in Fig. 4 for impeller A; the assumed parameters are shown on the figure. An ability to increase the impeller tip speed leads to an increase in the magnitude of the blade backsweep that can be adopted, assuming that stage efficiency and slip factor remain unchanged. However, the inlet relative Mach number increases unless the impeller radius ratio is reduced. f the designer is free to select the nondimensional impeller speed then a range of impeller radius ratios and blade 98k _ 0.55 = 0.8 1, = , = 56 = 65 ~& Nondimensional impeller speed Mu n 0. c 21.0, s $ 0.9 >. $ TJ Design point 0 Design point , i nlet Mach number Fig. 3 nlet Mach numbers for impeller MechE Nondimensional impeller speed Mu Fig. 4 mpeller Mach numbers for uls = 25 Proc nstn Mech Engrs Vol 207

6 1 20 A WHTFELD, M D C DOYLE AND M R FRTH backsweep are available. ncreasing the blade backsweep has a beneficial effect on the impeller discharge Mach number (see Fig. 4). The ability to adopt 30" of backsweep leads to a significant reduction in the discharge Mach number, and if a radius ratio less than 0.55 is considered acceptable the discharge Mach number is reduced to just below unity while the inlet relative Mach number remains approximately the same as that for the actual design point. The array of design options shown in Fig. 4 are not available to the designer if the rotational speed of the impeller is prescribed. The broken lines present contours of rotational speed; for this design the rotational speed was fixed at 98 OOO r/min. A similar set of results is shown in Fig. 5 for the case of no inlet swirl, impeller C. For this example the actual impeller manufactured was selected, and as it was a modification of an existing design it had a discharge blade angle of approximately 30". Consequently, in order to achieve the desired pressure ratio at a nondimensional impeller speed of 1.433, commensurate with a rotational speed of r/min, it was necessary to increase the assumed slip factor from 0.8 to 0.85 and the assumed stage efficiency from 0.73 to 0.8. n other words, if this modified impeller is to attain the desired pressure ratio at the desired rotational speed it must achieve an improved eficiency and/or slip factor. While the inlet relative Mach number exceeds unity, as indicated in Fig. 3, the adoption of 30" of blade backsweep leads to a discharge Mach number of approximately The magnitude of blade backsweep that can be p = 0.85 = 0.8 /31s = 68 0 adopted is directly related to the nondimensional speed of the impeller: the greater the impeller speed the larger the degree of backsweep possible and the more significant is the reduction of the discharge Mach number. This, of course, must be applied within the bounds of stress limitations and the impeller rotational speed contours are again shown as broken lines. mprovements in stage eficiency also make it possible to increase the magnitude of blade backsweep for any given impeller speed; the results shown in Figs 4 and 5 are a function of the anticipated efficiencies for the proposed designs. A major design parameter at the impeller discharge is the magnitude of the discharge blade angle. This has been dealt with above, and is generally fixed by the impeller speed limitations. For the design with 25" of prewhirl a discharge blade angle of 7" is possible, while repeating the design with no prewhirl leads to a discharge blade angle of 22". This latter design proposal was not manufactured and the modified impeller used had a discharge blade angle of 30". The impeller discharge flow area and associated nondimensional passage height, b2/r2, is the remaining geometric parameter to be established. The analysis can be developed in exactly the same manner as that given for the inlet in Section 4.1. n this case it is necessary to specify the absolute flow angle a,; this has generally been assumed to be 65", but the effect of alternative assumptions is assessed in the next section. A flow angle between 60 and 70" is generally recommended in the literature. A large flow angle will lead to a long flow path through the following vaneless diffuser with consequent high friction losses and an increased potential for the boundary layer to stall. The discharge flow area must be established through the application of the continuity condition. The nondimensional mass flowrate at impeller discharge is given by qt L. J Nondimensional impeller speed M, 0 Design point 0.70 = M, (1 + 2 Y 1 Mi) (Y+l)/{z(Yl)) (10) The impeller nondimensional mass flowrate 8 is related to that at discharge, Q2, through m Polaol Po2 a02 0zr; = e2 cos a2 A2 Polaol This can be rearranged with A, = 2zr2 b2 to give 0 = 20, cos a2 Replacing the discharge nondimensional flow with the Mach number from equation (10) gives 0 = 2 cos cl2 b2 p, 12 Po Nondimensional impeller speed Mu Fig. 5 mpeller Mach numbers for a, = 0 Part A: Journal of Power and Energy With the impeller nondimensional mass flowrate selected from the inducer conditions, or imposed by the Q MechE 1993

7 DESGN AND PERFORMANCE OF A HGHPRESSURE RATO TURBOCHARGER COMPRESSOR. PART design constraints, equation (12) can be solved for the nondimensional passage height for a specified range of Mach numbers and flow angles, provided the impeller stagnation temperature ratio and pressure ratio can be quantified. The stagnation temperature ratio is a function of the stage pressure ratio and assumed efficiency [see equation (2)], while it is necessary to provide an estimate for the impeller efficiency in order to obtain the impeller stagnation pressure ratio, which is then given by Equation (12) is shown graphically, for a range of assumed discharge flow angles, in Fig. 6. The assumed parameters are also shown in the figure. Clearly, increasing the assumed discharge flow angle leads to an increase in the nondimensional passage height; this will be beneficial in terms of impeller clearance loss as the fixed clearance gap will become a smaller proportion of the passage height. This, however, will have to be assessed along with the downstream diffuser losses and the consequences on the overall diffusion attempted in the impeller. Modifying the discharge Mach number has a small effect on the calculated discharge blade height; however, this range of discharge Mach number is not available to the designer. There is only a single Mach number that will satisfy the design requirements and constraints for any assumed flow angle, and this is shown as a contour in Fig. 6 for the designs considered. The stage pressure ratio is given by (p R )(Y 1)lY 1 Vs(Y 1) = M: tan c1, tan a, tan& Having selected rls/r2 from the inducer design conditions the only unknown in equation (14) is 8, for any specified a,. For the zero prewhirl option the inducer design conditions are not relevant. Equation (14) can be solved for /3, for any known a, = qc = 0.73 q1 = 80 With a, and p, known the absolute Mach number is given by U2la2 M, = sin a2 tan 8, cos ci2 where Equations (15) and (16) can be combined and solved for the impeller discharge Mach number, and the possible design points can then be located on Fig. 6. The zero and 25" swirl designs are shown together with the design actually adopted for the case with no inlet swirl. nlet prewhirl has little affect on the nondimensional discharge passage height for any selected absolute flow angle. The uncertainties associated with the estimated stage and impeller efficiencies do not carry across to the calculated passage height. The effect of increasing the stage and impeller efficiency on the passage height is shown to be small (see Fig. 6). The effect on the constant flow angle contours was too small to illustrate. 5 DESGN ASSESSMENT The objective of any design is to maximize the efficiency within any imposed constraints. For example, it may be considered appropriate to sacrifice efficiency for an appropriate gain in operating range. The assessment of the design in terms of its ability to meet the efficiency requirements was based on the minimizing of the inlet relative and discharge absolute Mach numbers. The inlet conditions have been fully assessed, within the bounds of an initial onedimensional design ; the discharge conditions, however, have been based on an assumed discharge flow angle of 65". t can be seen from Fig. 6 that increasing the flow angle leads to a reduction in the absolute Mach number and an increase in the discharge passage height, both of which should lead to a reduction in losses. Repeating the designs with a range of absolute flow angles from 55 to 80" leads to a modification of the relative flow angle and consequently the discharge blade angle. The resultant blade backsweep increases as the absolute flow angle increases (see Fig. 7). The high angles shown for the zero prewhirl cases would probably be unacceptable due to high stress levels. Nonetheless, the increased blade backsweep for the 25" prewhirl case would be acceptable. The consequent reduction in the discharge absolute Mach number has been shown in Fig. 6 where it can be seen that there is very little further reduction in Mach number as the absolute flow angle is increased beyond 75". n order to assess further the effect of modifying the absolute flow angle the impeller diffusion factor, defined by Rodgers (14,15), was derived as Discharge Mach number Fig. 6 Nondimensional discharge passage height Q MechE 1993 (17) Proc nstn Mech Engrs Vol 207

8 122 A WHTFELD, M D C DOYLE AND M R FRTH Absolute flow angle a , " Fig. 7 Effects of absolute flow angle on discharge blade angle This was stated to be applicable for zero prewhirl; however, with the work factor q defined as it has been applied with the inclusion of prewhirl. As the impeller design is considered fully nondimensionally it was necessary to develop equation (17) in terms of known or readily derived geometric parameters. For the third term of equation (17), which represents the bladetoblade loading, L is the blade length along the mean streamline and has been considered here to be the quadrant of a circle of radius rz rlrms and the bladetoblade loading parameter derived through For the final term of equation (17), which represents additional diffusion due to meridional curvature, b is the average passage height and rs is the shroud radius given by r2 rls. The ratio b/rs can then be derived in terms of the nondimensional parameters through Each of the terms in the diffusion factor [equation (17)] can be derived and used to assess any proposed design. From his study Rodgers (15) concluded that optimum impeller designs would have stall point diffusion factors below With this in view the diffusion factor was calculated for the design options, with an assumed blade number, ZB, of 16. The resultant diffusion factors are presented in Figs 8 to 10 as a function of inlet Mach number and can be referenced back to Figs 1 to 3. The 25" prewhirl design, impeller A, is shown in Fig. 8. Each plotted point represents an impeller radius ratio, decreasing from 0.8 in steps of 0.02 as the Mach number is increased. Reducing the radius ratio leads to a clear reduction in the diffusion factor. This is due to the reduction in relative Mach number shown in Fig. 1 and selection of the minimum inlet relative Mach number condition as the Part A : Journal of Power and Energy $ 0.7.a '\ Bladetoblade loading Qii nlet Mach number Fig. 8 Diffusion factors with 25" prewhirl design point has led to the minimum diffusion factor. The disadvantage of increasing the absolute flow angle is shown through a sharp increase in the diffusion factor. For a flow angle of 70" the diffusion factor is close to the 0.75 limit suggested by Rodgers, and if a broad operating range is important, as is usually the case in turbocharger applications, a flow angle below 70" is required. Also shown on Fig. 8 is the bladetoblade loading factor, the third term in equation (17). This represents the inverse of the relative Mach number plot of Fig. 1. For the design considered with zero prewhirl, impeller B, there is an increase in the diffusion factor at the assumed design flow angle of 65" (Fig. 9). However, removing prewhirl actually reduces the diffusion at the higher absolute flow angles, and the bladetoblade loading factor is reduced. This parameter, however [equation (19)], is inversely proportional to the inlet relative Mach number, as the relative Mach number increases the loading factor decreases. For impeller C, with a blade backsweep of 30", the diffusion factor increases further (Fig. lo), but only by a small amount from that of Fig. 9. The diffusion factor illustrates the disadvantage of designing with a large ' 1.O ~no~oo ' Q Bladetoblade loading !,, nlet Mach number Fig. 9 Diffusion factors with zero prewhirl, impeller MechE 1993

9 ~ 0.6 DESGN AND PERFORMANCE OF A HGHPRESSURE RATO TURBOCHARGER COMPRESSOR. PART r 1.1 Q B v) r1sifz g 0.5 a oa 0.3 \ Bladetoblade loading "." ~ nlet Mach number Fig. 10 Diffusion factors with zero prewhirl, impeller C discharge flow angle. Additional losses would also be developed in the long flow path of the vaneless diffuser. The final term of equation (17) represents the passage curvature in the meridional plane, and, as can be seen L h * E "" Bend radius ratio b/r, Fig. 11 Effect of bend radius ratio, impeller A E! 1.4. x d > & o C Bend radius ratio b/r. Fig. 12 Effect of bend radius ritio, impeller B Q MechE 1993 kn g h 1.6 ' 1.5.s 1.4 L x. > 0. U m 1.2 e z & 1.1 DF Mu = L. 9 d C. v) a Bend radius ratio b/r, Fig. 13 Effect of bend radius ratio, impeller C from equation (20), encompasses all of the linear nondimensional parameters of the impeller. The diffusion factor and the impeller relative velocity ratio are presented as a function of the bend radius ratio in Figs 11 to 13 for each of the impeller designs considered. n each case the minimum diffusion factor and relative velocity ratio occurs at a nondimensional bend radius ratio between 0.5 and 0.6. As the bend radius ratio is increased both the diffusion factor and relative velocity ratio increase. Rodgers (15) showed from experimental data that the stall point velocity ratio decreased as the bend radius ratio increased. Consequently, increasing the bend radius ratio not only leads to an increase in the relative velocity ratio but also to a reduction in the velocity ratio at stall. t can, therefore, be anticipated that increasing the bend radius ratio will lead to a reduction in the operating range, as the design point relative velocity ratio will increase while the stall point velocity ratio will decrease, thereby narrowing the range between them. 6 CONCLUSONS A fully nondimensional conceptual design procedure for centrifugal compressor impellers with or without inlet swirl has been developed and applied to the design and assessment of three impellers. The first design, impeller A, considered the inducer design in association with the application of inlet swirl. The main feature of this design was the modified inducer required to accept the inlet swirl. The second design excluded prewhirl at the design stage and was carried out in order to provide comparisons with impeller A. This design was not manufactured ; instead a third impeller, impeller C, was adapted from an existing one. As this third design was a modification of an existing impeller it would not meet the specified design requirements (at the specified speed of r/min a pressure ratio of only 3.1 was anticipated, with an assumed efficiency and slip factor of 0.73 and 0.8 respectively). The design procedure was applied to this third impeller to assess the design in parallel with impellers A and B. mpellers A and C have been manufactured and tested and the resultant performance is described in Part 2. Proc lnstn Mech Engrs Vol 207

10 124 A WHTFELD, M D C DOYLE AND M R FRTH The main criterion used to aim for maximum efficiency was the minimization of the inlet relative and absolute discharge Mach numbers. Due to the imposed speed limitations the maximum discharge blade backsweep possible was effectively fixed and there was no scope to minimize the discharge Mach number. However, the deliberate selection of 25" of prewhirl for the first impeller design meant that the maximum blade backsweep possible was only 7"; without the inclusion of prewhirl the backsweep possible was 22" (these are for an assumed slip factor of 0.8 and a target stage efficiency of 0.73). The inlet relative Mach number was minimized through the appropriate selection of the inlet relative flow angle, as the nondimensional mass flowrate was effectively fixed by the design requirements. Further design assessment through the application of the diffusion factor is dominated by the initial selection of the minimum inlet relative Mach number. The diffusion factor increases if the design is selected away from the minimum Mach number condition. The diffusion factor establishes an order of magnitude for the impeller discharge absolute flow angle and confirms the oftenquoted range to be between 60 and 70". Once the basic nondimensional parameters have been selected the impeller geometry in the form of inlet and discharge blade angles, radius ratio rls/r2 and discharge blade height b, /r2 can be developed. Selection of the minimum relative Mach number condition, or otherwise, at inlet leads to the impeller radius ratio and to the inlet relative flow angle from which the blade angle can be derived. Selection of the absolute flow angle at discharge, based on diffusion factor considerations, leads to the discharge blade height bjr2 and to the discharge relative flow angle from which the blade angle can be derived through the specification of an appropriate slip factor. The proposed design was further assessed through the application of empirical loss models and correlations in order to calculate the efficiency and offdesign performance. However, with the restraints imposed through nonaerodynamic considerations the main parameters could only be varied through a very limited range. Selection of the inlet conditions is not dependent on the assumed efficiency, and it has been shown (Fig. 6) that the discharge passage height is not sensitive to the specified efficiency. At inlet the main uncertainties lie in the estimation of the optimum incidence angle and the blockage factor required to translate the flow area into a geometric area. The uncertainty associated with the discharge blockage factor translates to the determination of the geometric area at discharge and the consequent blade height. At discharge the assumed slip factor and efficiency play an essential part in the determination of the degree of blade backsweep that can be adopted. t was felt, however, that the uncertainties associated with the empirical loss models and correlations were such that the blade backsweep could not be based, with confidence, on the predicted efficiency. REFERENCES 1 Morris, R. E. and Kenny, D. P. High pressure ratio centrifugal compressors for small gas turbine engines. AGARD Conference Proceedings 31, Schorr, P. C., Welliver, A. D. and Winslow, L. J. Design and development of small high pressure ratio single stage centrifugal compressors. ASME Conference on Advanced centrifugal compressors, McCutcheon, A. R. S. Aerodynamic design and development of a high pressure ratio turbocharger compressor. MechE Conference on Turbocharging and turbochargers, 1978, paper C73/78 (Mechanical Engineering Publications, London). 4 Flaxington, D. and Mahbod, B. Turbocharger compressor developments for broad range and high pressure ratio applications. MechE Conference on Turbocharging and turbochargers, 1990, paper C405/024, pp (Mechanical Engineering Publications, London). 5 Whitfield, A. Nondimensional aerodynamic design of a centrifugal compressor impeller. Proc. nstn Mech. Engrs, Part A, 1991, 205(A4), Balje, 0. E. A study on design criteria and matching of turbomachines: part A similarity relations and design criteria of turbomachines. Trans. ASME, J. Engng Power, January 1962, 84, Balje, 0. E. Turbomachines: a guide to design selection and theory, 1981 (John Wiley, Chichester). 8 Rodgers, C. and Langworthy, R. A. Design and test of a small two stage high pressure ratio centrifugal compressor. ASME paper 74GT137, Rodgers, C. Efficiency of centrifugal compressor impellers. AGARD CPP 282, Brussels, May Osborne, C., Runstadler, P. W. and Stacy, W. D. Aerodynamic and mechanical design of an 8 : 1 pressure ratio centrifugal compressor. NASA CR134782, Whitfield, A. and Baines, N. C. Design of radial turbomachines, 1990 (Longman Scientific and Technical, London, and John Wiley, New York). 12 Whitfield, A. Conceptual design of a centrifugal compressor including consideration of the effect of inlet prewhirl. ASME paper 92GT11, Stanitz, J. D. Design considerations for mixed flow compressors with high flow rates per unit frontal area. NACA RM E53A15, Rodgers, C. mpeller stalling as influenced by diffusion limitations. Trans. ASME, J. Fluids Engng, 1977,99, Rodgers, C. A diffusion factor correlation for centrifugal impeller stalling. ASME paper 78GT61, 1978; also Trans. ASME, J. Engng Power, October 1978,100,592. Part A: Journal of Power and MechE 1993