1 Introduction

Double bypass engine(DBE)is a potential future engine for mix-mission aircrafts and versatile applica-tions. It is able to adapt to the required mass flow, load and bypass ratios throughout the flight envelope to main-tain a high efficiency, thus to increase flight endurance and reduce running cost. Contributing most to the perfor-mance advantages, the compression system of a DBE, which is characterized by multiple bypasses and vari-able area valves^[1~4], is far different from traditional axi-al compressors. In a DBE compression system, three main components, i.e. fan, core-driven fan stage(CDFS)and high pressure compressor(HPC), are in-terconnected by two bypass ducts, which enhance and perplex the aerodynamic cooperation of the fan, CDFS and HPC. Obviously, there may be complicated compo-nents matching problems, which can be affected by the controlling rules of the variable area valves, i.e. mode se-lect valve(MSV), forward variable area bypass injector(VABI)and rearward VABI, and by the compressor throttling schemes. Reasonable component matching guarantees the performance superiority of DBEs and should be well considered during the preliminary design process.

The concept of DBE was firstly developed by Gen-eral Electric Co. in the middle of 1970s^[5]. The compres-sion system was designed with a throughflow procedure programmed for turbofan engines^[6], which is incapable in dealing with multiple bypass flows and lack of models for variable area valves and so is incompetent in match-ing the components appropriately at design phase. Vast experimental studies have been carried out to explore the matching of the components^[4], however, they cost a lot.

It is well known that, until very recently, the pre-liminary design procedures, such as one-dimensional design/analysis methods and throughflow design/analy-sis methods, are still the only way to design a variable cycle compression system^{[6, 7]}. Lots of one-dimensional methods based on component performance models have been developed for performance studies of DBEs ^[8~11] and other variable cycle engines^{[12, 13]}. The compressor performance models used in these one-dimensional methods are based on the compressors which have been designed and tested. The methods are well used to ex-plore the performance potential of candidate variable cy-cle engines and to define the target performance of each compression components. Zhang ^[7] introduced velocity triangle method into aerodynamic characteristics investi-gating of a CDFS in both single bypass and double by-pass modes. However, it can only provide flow informa-tion at the mean radius of the compressor and are inade-quate to determine the whole spanwise matching of com-ponents. Three-dimensional computational fluid dynam-ics(CFD)method can provide all the information that is necessary in designing a variable cycle compression system, but it is usually limited to be used in detailed design stage for the huge computational source and time consuming, despite of the up-to-date computer technol-ogy. Experimental study is long-periodic and is poor in economic. To realize a matching design and quick per-formance prediction of a variable cycle compression sys-tem in preliminary design stage, a cheap and fast twodimensional method is in need. However, based on the published literatures, no such procedure has been devel-oped.

In the present work, to make a deep understanding of the working principles of variable cycle compression systems and realize reasonably matched configurations for a high-performance DBE, a versatile integrated com-pressor throughflow calculation system(VICT)has been developed and validated. And then, VICT is used to analyze the component matching principles of a cus-tom-designed double bypass compression system. The baseline matching state and two throttling schemes, i.e. first bypass throttling and second bypass throttling, were investigated in detail and some tips for the design of a variable cycle compression system were summarized.

2 Throughflow analysis method 2.1 Versatile integrated compressor throughflow calculation system(VICT)

Versatile integrated compressor throughflow calcu-lation system(VICT)is a newly developed throughflow calculation platform for the design and analysis of axial compressor systems. It is particularly suitable for multibypass variable cycle compressors as well as traditional ones. VICT takes the compression system of adaptive cy-cle engine(ACE, see Fig. 1)as the model sample. Fig. 2 shows the ideal compression system construction built in VICT. It includes eight domains, which in order are intake, third bypass(TBP), fan, second bypass(SBP), core-driven fan stage(CDFS), first bypass(FBP), high pressure compressor(HPC), and HPC bypass. The domains can be flexibly combined to model kinds of axi-al compression systems. For example, domain 7 can be used alone for traditional axial compressors, domains 5~7 can be combined for turbofan compression sys-tems, domains 3~8 can be combined for DBE compres-sion systems and domains 1~8 can be combined for ACE compression systems.

The flow field of each domain are solved by stream-line curvature throughflow method, which is fully de-scribed by Smith^[14], Denton^[15], Cumpsty^[16], etc. and will not be repeated here. The inlet and outlet boundary conditions of each domain in calculation are determined from the flow fields of the upstream and downstream do-mains respectively. The calculation process of VICT is shown in Fig. 3.

In order to use the streamline curvature through-flow method in a variable cycle compression system inte-grally, the flows around the mode select valve, forward VABI and rearward VABI, which can be seen clearly in Fig. 1 and will not be encountered in a traditional com-pressor, should be well modeled.

Mode select valve is installed at the entrance of second bypass duct, as shown in Fig. 1. The state of MSV, open or closed, determines the operating modes of the compression system, i.e. in double bypass mode or single bypass mode. This is modeled in VICT by adding domain 4 or not to the compression system under simula-tion. Rearward VABI, positioned at the exit of HPC by-pass(see Fig. 1), is adjusted to control the mixing pres-sure of HPC bypass flow and the primary gas flow ex-hausted from low pressure turbines in the engine. It can be directly modeled by adopting pressure boundary con-dition at HPC bypass outlet instead of the mass flow boundary condition.

Forward VABI is placed at the exit of first bypass duct, as shown in Fig. 1. It is adjusted to tune the flow of first bypass and second bypass via varying the outlet ar-eas of them. A new model must be constructed for for-ward VABI for that the pressure at the trailing edge of forward VABI can hardly be known before the flow field is solved. Forward VABI is modeled as hinged wing(see Fig. 4)in VICT^[17]. In calculation, either the posi-tion of VABI or the mass flow rates of both the two by-passes should be assigned. The pressure at the trailing edge of forward VABI is calculated by imposing Kutta condition at the edge.

Downstream of forward VABI, the flows of first by-pass and second bypass mix out gradually with each oth-er in the HPC bypass duct. The flow properties of each flow in the mixing process are calculated by Casey' s span-wise mixing model but with enhanced mixing factors around the stagnation streamline(see Fig. 4). The flow field of HPC bypass is divided into two parts by the stag-nation streamline and is solved part by part.

2.2 Calibration of VICT

Basically, streamline curvature throughflow meth-od takes the flow in turbomachinery as axisymmetric, compressible and inviscid. The effects of viscous and three-dimensional flow are taken into account by empir-ical models including deviation model, flow loss model and blockage model. The accuracy of streamline curva-ture throughflow method relies heavily on the reliability of these models, which should be carefully calibrated be-fore using based on experimental data. The calibrations of VICT on NASA rotor 67, NASA stage 37 and an ex-perimental investigated low-speed four-stage repeating compressor have been accomplished previously. In or-der to apply VICT to the DBE compression system, fur-ther calibrations are needed. However, considering that no detailed experimental data for a DBE compression system could be achieved, the numerical simulation re-sults by using computational fluid dynamics(CFD)will be employed in the present work.

The CFD tool used here is the code originally de-veloped by Denton^[18] for turbomachines. This code has been widely used in both university researches and in-dustry applications in the world wide^{[19, 20]}. The version of the code employed in the present work has been im-proved by Liu et al^[21~23]. The new version code has also been widely used in turbomachinery designs and flow mechanism researches^[24~27]. Steady flow method was ad-opted to calculate the characteristics and also detailed flow fields inside the fan, the CDFS and the HPC sepa-rately. And then, the empirical models mentioned above in VICT were calibrated based on the numerical results to make sure it can predict the performance of all the components in DBE compression system well with the same empirical model parameters.

The double bypass compression system considered in this paper consists of a single stage fan, a core-driv-en fan stage(CDFS), a five-stage high pressure com-pressor(HPC)and bypass ducts, as shown in Fig. 5. The design specifications of the fan, CDFS and HPC are listed in Table 1, in which the corrected mass flow rates and pressure ratios are normalized by the corresponding values of fan. The fan and CDFS are typical transonic ax-ial compressors whose loading coefficients, based on the tip speed of the rotor blade, are both at the level of 0.23(for reference, the loading coefficient of NASA rotor 67 is 0.25). The loading coefficients of the HPC stages are in the range of 0.31~0.34(for reference, the loading coefficient of NASA stage 37 is 0.36).

During the calibration procedure, the secondary flow loss level, the deviation increments in the region near endwall and the blockage effects of the leakage flow were adjusted based on the CFD results. Mean-while, the profile losses and shock losses predicted by VICT were examined against the values calculated by the CFD codes. The ultimately calculated spanwise dis-tributions of rotor efficiencies, flow coefficients and load-ing coefficients of the fan, CDFS and the first and fifth stages of HPC at the corresponding design conditions are shown in Fig. 6(a)~(c). It can be seen in the fig-ures that the VICT results agree well with the CFD re-sults except some departures in the near endwall re-gions. Fig. 6(d) shows the spanwise profile of the loss co-efficients of the fan stator and the first stator of HPC.For clarity, the results of other stators, which are very similar to the results of the first stator of HPC, are not plotted in the figure. Good agreements between the CFD results and VICT results were acquired for the stator loss coefficients.

The overall performance of the fan, CDFS and HPC are shown in Fig. 7. The VICT results agree well with CFD results both qualitatively and quantitatively for the fan and CDFS. For the HPC, it is convinced by the expe-riences acquired from another multi-stage compressors that the CFD codes predict larger pressure ratios from design condition to near stall condition, where the VICT results are more realistic. On the contrary, the CFD codes predict the performances well at lager mass flow rate conditions while the VICT results are a little ideal. Despite these, it is convinced that the calibrated VICT is accurate enough for component matching study of the DBE compression system at preliminary design phase.

3 Components matching analysis for DBE compression system

As shown in Fig. 8, a DBE compression system con-sists of fan, CDFS, HPC, first bypass(FBP), second by-pass(SBP), HPC bypass, mode select valve(MSV), forward VABI and rearward VABI. It may work in dou-ble bypass model(DBM, with MSV opened)or in sin-gle bypass model(SBM, with MSV closed). In this work, only double bypass mode is considered for con-cise and for it is the most complex case that may be en-countered in service.

3.1 Baseline matching state 3.1.1 Characteristics of the BM state

At baseline matching state, the fan works at its de-sign conditions. The corrected mass flow rate and the corrected rotating speed of the CDFS are maintained at their design values. Extra flows from fan are guided to the second bypass duct. The physical rotating speed of HPC is the same with that of the CDFS since that they are assembled on the same shaft. HPC works at its de-sign mass flow rate. The first bypass duct swallows the extra mass flow from the CDFS. The work points of the fan, CDFS and HPC are indicated by open stars named 'BM state' in Fig. 7(a)~(c), respectively. At the BM state, the first bypass ratio(the mass flow rate of first by-pass divided by that of the HPC)is 0.167 and the sec-ond bypass ratio(the mass flow rate of second bypass di-vided by that of the CDFS)is 0.586.

3.1.2 Matching state of fan in DBE compression system

See Fig. 7(a), the work point of the fan at BM state is coincident with that at design conditions. It is be-cause that the inlet flow conditions of fan at BM state are maintained at the same values of the design state and the variations in fan outlet flow conditions have lit-tle effects on the flow upstream and even in the fan blade rows.

3.1.3 Matching state of CDFS in DBE compression system

In the DBE compression system, the CDFS inlet flow conditions are determined by the upstream compo-nents, i.e. by the work state of fan and the matching state of CDFS and second bypass. So, the inlet flow con-ditions of the CDFS at baseline matching state are some different from its design state. The profiles of CDFS in-let flow coefficient at both design and baseline matching states are shown in Fig. 9(a). The variations in flow co-efficient profile are the net effects of the variations in the profiles of inlet total pressure (Fig. 9(b)) and tem-perature (Fig. 9(c)), which are resulted by the work state of fan, and the changes in streamline curvature, which are caused by the matching state of the CDFS and the second bypass. The variations in the inlet flow coeffi-cient profiles indicate variations in the spanwise match-ing state of CDFS, thus variations in the performance of the CDFS.

Compared to the design values, the flow coeffi-cients below about 0.7 blade span at baseline matching state are some larger, which indicate lower work inci-dence angles, i.e. nearer to the choke state, of these blade sections. Both the pressure ratios and the efficien-cies of the blade sections are lower at baseline matching state that at the design conditions. The flow coefficients in the upper 30% span region at baseline matching state are lower than that at design state, which means the blade sections working at larger incidence angles. Thus, the pressure ratios and work efficiencies are promoted for these blade sections. The overall variations in the pressure ratio and efficiency of the CDFS are shown in Fig. 7(b). The efficiency and total pressure ratio of the CDFS at the baseline matching state is a little lower than the design value.

3.1.4 Matching state of HPC in DBE compression system

The inlet flow conditions of HPC are determined by the work state of CDFS and the matching state of HPC and first bypass. At baseline matching state, the profiles of total pressure (Fig. 10(a)) and total temperature (Fig. 10(b)) at the HPC inlet are different from those at the design conditions, which should be determined by the work state of CDFS. Besides, the matching of HPC and first bypass induces an enhanced radial flow at the leading edge of the first bypass splitter. The resulted in-let flow coefficient profile of HPC is different from that of the design state, as shown in Fig. 10(C).

At baseline matching state, the lower 50% blade sections of the HPC first rotor tend to work at lower inci-dence angles while the upper 50% blade sections tend to work at larger incidence angles. Consequently, the performance of the first stage is changed and the work points of the following stages are altered accordingly, which can be seen in Fig. 11. The overall pressure ratio and efficiency of HPC at baseline matching state are a little lower than those at design condition, indicated in Fig. 7(c).

In double bypass compression system, the inlet flow conditions of CDFS and HPC are determined by the work state of the upstream components. If the matching principles are not well considered at design phase, the component performances and the overall performances of the compression system will drop significantly. In this study, the overall pressure ratio at baseline matching state is 0.98 times of the design value and the overall efficiency is 0.2% lower than the design target.

The capabilities to adapt to large extent changes of the mass flow rate, loading level and bypass ratio of the engine are the standout characters of DBE compression systems. The adaptions are realized by adjusting mode select valve, forward VABI and rearward VABI. In dou-ble bypass mode, mode select valve is fully opened; for-ward VABI and rearward VABI are adjusted to optimize the performance of each component. The effects of ad-justing forward VABI and rearward VABI are explored separately in the following parts.

3.2 First bypass throttling analysis 3.2.1 Characteristics of the first bypass throttling

In the process of first bypass throttling, the fan work point is maintained at the design condition. The corrected rotating speed of the CDFS and the static pres-sure at the outlet plane of the HPC are set to the same values as in baseline matching condition. Forward VABI is then turned down gradually to change the work point of the CDFS. The controlled and calculated variables in the process of first bypass throttling are listed in Table 2.

3.2.2 Matching state of CDFS for first bypass throttling

With the turning down of the forward VABI, the outlet pressure of the CDFS increases and the mass flow rate decreases. The work point of the CDFS moves to the left along the characteristic line, as indicated in Fig. 12. In the figure, 'Design' represents the characteristics of the CDFS at design inlet flow condition, for which the values and profiles of total pressure, total temperature and flow angles of the inlet flow are kept at the same val-ues with those at the design point.

In the process of first bypass throttling, the work state of fan stays unchanged, thus the profiles of total pressure and total temperature at the inlet of CDFS are the same as those at baseline matching state. The mass flow rate of the CDFS decreases with the mass flow rate of the second bypass increasing in the throttling pro-cess. Therefore, the matching state of the CDFS and sec-ond bypass is changed, which leads to the variations in the profile of flow coefficient at the inlet of CDFS. Fig. 13 shows the flow coefficient profiles of the CDFS at four different matching states in the process of first by-pass throttling. The same work points are indicated by P1~P4 in Fig. 12. It can be seen in Fig. 13 that the pro-file shape of the flow coefficient at the inlet of CDFS stays almost unchanged from P1 to P4, which means the changes in the matching state of CDFS and second by-pass has little effect on the flow coefficient profile shape of the CDFS in this case. It is because the second by-pass ratio of the DBE compression system studied in this paper is large and the reduced mass flow from the CDFS just slightly altered the flow at the leading edge of the second bypass splitter, which makes an increase of the second bypass ratio of about 0.05.

In Fig. 12, the first bypass throttling characteristic line displays some departure from the design character-istic line. As discussed previously, it is the consequence of the changes in the matching state of the CDFS in the DBE system. As the lower 70% blade sections of the CDFS are more prone to choke in the DBE compression system, the choked mass flow rate of the CDFS in dou-ble bypass mode is smaller than the designed value.

3.2.3 Matching state of HPC for FBP throttling

The shift of the CDFS work point in the process of FBP throttling significantly changes the profiles of total pressure and total temperature at HPC inlet, as shown in Fig. 14(a) and (b). Besides, the throttling of the first by-pass greatly altered the matching state of HPC and first bypass(the first bypass ratio decreases from 0.214 to 0.074). Consequently, the inlet flow coefficient profiles of HPC first rotor changed remarkably, as shown in Fig. 14(c). With the turning down of the forward VABI(the work state shifts from P1 to P4), the flow coeffi-cient in the lower 60% span region decreases, while it increases in the upper 40% region. The upper blade sec-tions tend to be choked while the lower blade sections tend to work more efficiently. Fig. 15 shows the inlet flow coefficient profiles of the second rotor. The shapes of the spanwise profiles are almost unchanged from P1 to P4. Comparing with Fig. 14(c) and Fig. 15, it can be inferred that it is the first stage that experiences signifi-cant variations in work conditions, which should be care-fully considered at the design phase.

The corrected mass flow rate of the HPC decreases in the process of FBP throttling and also does the over pressure ratio and efficiency of the HPC, as shown in Fig. 16. The corrected rotating speed of the HPC decreas-es from 1.0 to 0.984 times the design value when the work state moves from P1 to P4, for the CDFS work point is promoted (see Fig. 12) while the physical rotat-ing speed staying unchanged. With the turning down of forward VABI, the work point of the HPC approaches its choke boundary, which is partially because of the reduc-tion of rotating speed and partially because of the span-wise mismatches in HPC.

3.3 Second bypass throttling analysis 3.3.1 Characteristics of the second bypass throttling

Second bypass throttling is performed on the dou-ble bypass compression system by gradually turning down the rearward VABI with the corrected rotating speeds of the fan and CDFS being kept at their design values. Forward VABI is adjusted to let the CDFS and HPC work at a reasonably matched state. The controlled and calculated variables in the process of second bypass throttling are listed in Table 3.

3.3.2 Matching state of fan for second bypass throttling

With the turning down of rearward VABI, the mass flow rate of fan decreases while the pressure ratio in-creases. The work point moves to the left along the char-acteristic line, as shown in Fig. 17. The spanwise match-ing state of the fan is not changed in the process. Thus, the throttling characteristic line coincides with the de-sign one.

3.3.3 Matching state of CDFS for second bypass throttling

In the process of second bypass throttling, the movement of the fan work point changes the spanwise profile of total pressure and total temperature at the in-let CDFS, as shown in Fig. 18(a) and (b). Besides, with turning down the rearward VABI, the second bypass ra-tio decreases from 0.601 to 0.544, which means the matching state of the CDFS and the second bypass is changed. As a result, the inlet flow profiles of the CDFS are changed, as shown in Fig. 18(c). It can be inferred from the figure that the lower 70% blade sections of CDFS tend to work at larger incidence conditions while the upper 30% blade sections tend to work at near choke conditions in the process of second bypass throt-tling. The overall performances of the CDFS are shown in Fig. 19. Since the corrected rotating speed of the CDFS at matching states of P5~P7 are all the same as that in design conditions, the divergence among the con-stant speed characteristic lines is the result of the mis-matching of the CDFS. The stable work range of CDFS is cut down a lot in the throttling process.

3.3.4 Matching state of HPC for second bypass throt-tling

Since the work state of the CDFS changes slightly in the process of second bypass throttling, the variations of the total pressure and total temperature are tender, as shown in Fig. 20(a)~(b). Besides, the first bypass ra-tio decreases from 0.125 to 0.093 in the process, which means a tender variation in the matching state of HPC and first bypass. Consequently, the HPC inlet flow coef-ficient varies slightly in the process of SBP throttling, as shown in Fig. 20(c). Fig. 21 shows the characteristics of the HPC in the process of second bypass throttling. With the work point moving from P5 to P7, the corrected rotating speed of the HPC reduces from 0.990 to 0.987 times the design value. The pressure ratio drops from 0.981 to 0.966 times design value while the effi-ciencies staying almost unchanged.

4 Conclusion

Based on the above analyses, the following conclu-sions can be drawn:

(1) For the compression system studied in this pa-per, the spanwise mismatches in CDFS and HPC at baseline matching state incurred a decrease of 2% in the total pressure ratio and a decrease of 0.002 in the work efficiency.

(2) Throttling of first bypass has significant influ-ence on the spanwise matching state of HPC while does not affect the spanwise matching state of CDFS.

(3) Throttling of second bypass affects the span-wise matching state of CDFS remarkably while has weak effect on the spanwise matching state of HPC.

(4) In the process of first bypass throttling, the matching state of the first stage of HPC is remarkably changed while the matching state of the following stages are weakly affected.

(5) In the process of second bypass throttling, the spanwise mismatches of CDFS substantially cut down the stable work range of CDFS, which may be a critical consideration for the design of a CDFS.

In this work, the versatile integrated compressor throughflow calculation system(VICT)was calibrated based on the CFD codes predicted flow field of fan, CDFS and HPC, separately. Further calibrations of VICT based on integrated CFD results and experimental results are to be conducted to improve the accuracy of VICT in analyzing such a DBE compression system.