Numerical simulation method of surge experiments on gas turbine engines

Xinqian ZHENG, Hanxuan ZENG, Baotong WANG, Mengyang WEN,Heli YANG, Zhenzhong SUN

a School of Vehicle and Mobility, Tsinghua University, Beijing 100084, China

b Institute for Aero Engine, Tsinghua University, Beijing 100084, China

KEYWORDS Air-injection;Body-force model;Gas turbine engine;Numerical method;Surge experiment

Abstract In order to obtain the surge margin of an aero-engine during its operation, an engine surge experiment is required.A multi-dimensional simulation method for an aero-engine is established in this paper.The simulation of a surge experiment using high-pressure air-injection is then carried out on a turbo-shaft engine to obtain the surge boundary using this method.More specifically,firstly,a body-force model is employed to calculate the compressor performance owing to its capability of capturing the main three-dimensional features of compressor surge and avoiding excessive simulation time required by the traditional fully-three-dimensional Reynolds Averaged Navier-Stokes (RANS) method.Then, a one-dimensional model combining a lumped-parameter plenum model is used for the combustor to account for the propagation of pressure waves and the heat-release process,and a zero-dimensional throttle model is used to mimic the choking effect at the turbine nozzle.Finally,the air-injection system is modeled by imposing an injection boundary condition, which can be used conveniently in changing injection parameters.Based on the established method,the influences of different test parameters,such as the air-injection location,the pressure, the orifice size, the number of injection orifices, and the injection time duration on the surge characteristics and boundary are further studied, which offer effective guidance to optimize an actual experimental design.

1.Introduction

Surge not only seriously degrades the aerodynamic performance of an aero-engine but also poses a considerable threat to the structural integrity.During surge,especially deep surge,due to the instantaneous collapse of the adverse pressure gradient, the reverse flow of the downstream high-pressure air propagates upstream, causing a transient high load on the blades and even leading to blade damage.1The transient axial force caused by surge also seriously threatens the structural safety of the shafting.2,3In order to avoid the occurrence of surge, it is necessary to keep the engine operating point away from the surge boundary with an appropriate surge margin.Therefore,evaluating the surge boundary is critical in avoiding surge in aero-engines.4

On a test rig of a compressor component, a method to obtain the surge boundary is to adjust the downstream valve step by step to move the compressor operating point approaching the surge line steadily with the compressor speed fixed.Then, the first operating point when surge occurs is recorded as the surge point of this speed line.After that, the same method is repeated and applied to other speed lines until the complete surge boundary is obtained by connecting the surge points at each speed line.It is comparatively easy to get the surge boundary on a test rig of a compressor component.However, this boundary is often not consistent with the one in an actual engine assembly.5Therefore,it is necessary to carry out surge tests on an engine test bench.

However,obtaining the surge boundary on an actual engine is more challenging.This is mainly due to the compressor and the turbine’s matching,which constraints the rotational speed,the mass flow rate, and the power balance.As a result, the engine operating point can only move along the engine working line instead of being adjusted arbitrarily along each speed line as in a test rig of a compressor component.Therefore, a different strategy for an engine surge experiment is required.At present, there are four main types of method for an engine surge experiment as follows:

(1) High-pressure air-injection method: high-pressure air is injected into the compressor, thus increasing the backpressure of the compressor and moving the engine operating point closer to the surge boundary.6–9

(2) Fuel-stepping method:this is achieved by over-fueling to increase the turbine inlet temperature and its subsequent effect of decreasing the turbine inlet mass flow rate.This is because of the general design choice of choking the high-pressure turbine guide vane which results in a constant corrected turbine mass flow rate.Then, the decreased engine mass flow rate pushes the operating point closer to the surge boundary (the rotational speed remains unchanged because of the inertia).10,11

(3) Variable geometry method: this is done by adjusting either the stagger angle of the turbine stator or the opening of the engine nozzle,which again increases the compressor back-pressure and drives the engine to surge.12,13

(4) Water-injection method: this method is similar to the air-injection method, and the physics behind it is the instantaneous vaporization of the injected water.7

No matter which method is adopted,the essence is to create a high back-pressure at the compressor outlet so that the engine operating point can be throttled to the surge boundary.

Each of the four methods has its pros and cons.The airinjection method requires an additional compressed air supply with a higher pressure than the compressor outlet pressure and an adequate mass flow rate for long periods of operation.This is not always available for turbojet/turbofan engines, and it is more suitable for medium- and small-sized engines like a turboshaft engine.6The fuel-stepping method does not require additional accessories and can directly throttle an engine to surge by over-fueling.Thus, this method is used in various types of engines.However, fuel stepping will create overtemperature at the turbine inlet, limiting its application at higher operating speeds.5,7The variable geometry method requires a reliable mechanical system that can withstand the harsh environment of high temperature, which makes the system complex and has a limited adjustment range.The waterinjection method also requires additional elements like a water filter system and an injection nozzle.Additionally, using this method alone may lead to engine flameout.7At present,small- and medium-sized aero-engines represented by turboshaft engines usually adopt the high-pressure air-injection method.In contrast,larger aero-engines represented by turbojet/turbofan engines usually adopt the fuel-stepping method.

Besides, a surge experiment on an actual engine is not only challenging and costly but also risky.During surge tests, the process of obtaining the surge boundary will inevitably lead to surge.Any delay in the surge control system will cause severe damage to the engine integrity.Therefore, it is crucial to reduce the number of surge experiments, as well as risks and costs.A higher standard for an efficient experimental parameters design is set because any redundant tests are undesirable.On the other hand,additional unneeded effects are introduced in a surge experiment,such as the transient effect caused by the fuel-stepping method and the distortion effect caused by the air-injection method.Evaluating these factors on the surge dynamics and boundary is essential to obtain accurate results.

Due to the aforementioned problems, it is necessary to establish a numerical method that can simulate the process of a surge experiment on an actual engine.Over previous years of research, methods of different simulation fidelities have been developed to predict surge characteristics.These methods can be grouped into two main categories: fully-threedimensional methods and reduced-order methods.Fullythree-dimensional methods like URANS (Unsteady Reynolds Averaged Navier-Stokes), LES (Large Eddy Simulation), or DES (Detached Eddy Simulation) can resolve the effects of complex blade geometries,viscosity,and turbulence.They provide most credible numerical results but consume considerable computational resources which are not currently acceptable during the design process.Shahin et al.simulated surge on a single-stage radial compressor using LES.14For a single surge cycle, the simulation took three months to finish running with 48 CPUs.Moreno simulated surge on a multi-stage compressor of a modern three-spool turbofan engine using URANS.1The mesh size reached 1 billion.By using 192 CPUs, the simulation time of a complete surge cycle still requires several months.By contrast, using reduced-order models seems more practical.However, overly simplified models like the lumpedparameter model and the actuator-disk model cannot resolve a three-dimensional flow field.Therefore,a model that can balance the computational efficiency and fidelity is required.The body-force model replaces the effects of compressor blades with a spatially distributed body-force field.15Besides, since this model features a three-dimensional grid resolution, it can provide more detailed flow field information.The bodyforce model is commonly used to simulate the effect of inlet distortion, but recently, it has started to be used in surge simulation.Past studies have shown its application in axial compressors,16but for radial and axial-radial compressors used in turboshaft engines, additional research works are needed.Furthermore, for simulation of engine surge experiments,how to include the effects of the downstream combustor and turbine appropriately and how to model the process of surge experiments that uses the air-injection method have not been well established.

Therefore, a multi-dimensional simulation method for an aero-engine is proposed in this paper.The simulation of a surge experiment using the high-pressure air-injection method is carried out on a turbo-shaft engine to obtain the surge boundary.Based on the established method, the influences of different test parameters, such as the air-injection location,pressure and orifice size, the number of injection orifices, and the injection time duration on the surge characteristics and boundary are further studied.A practical guideline to the design of experimental parameters is thus discussed.

2.Establishment of numerical method

In this section, an example of engine surge experiments using the air-injection method is briefly introduced first.Then, the modeling method is explained in detail for each engine component, including the air-injection system.Finally, a partial validation is presented to illustrate the capability of the method in surge prediction.

2.1.Example of engine surge experiments

The engine surge experiment to be modeled in this paper was conducted on a turboshaft engine and reported by Kuang et al.6The test rig has three main parts:the turboshaft engine,the control system, and the air-injection system, as shown in Fig.1.The engine features a front-output layout and is composed of an engine intake, an axial-radial compressor, a reverse-flow combustor, a multi-stage turbine including a free-turbine, an accessory gearbox, etc.The air-injection system consists of a compressed air tank, various throttle valves and control valves,which are used mainly to regulate the pressure level and avoid unnecessary over-pressure.The High-Pressure (HP) air delivered from the tank enters the compressor flow path through several injection orifices.These orifices were initially used as a bleeding port.They are located at the diffuser casing of the engine,which directs the air to the impeller inlet(outlet of the axial compressor stages)in the end.During the experiment,the engine started up to the idle speed first,and then the fuel flow was regulated to speed up the rotor until the target speed was met.After that,the engine speed was kept constant, and the Control valves 3 and 1 were gradually opened to raise the pressure of injected air until the engine entered into surge.

Fig.1 Sketch of test rig configuration6 (reproduced).

There are three main methods to identify the occurrence of surge during the experiment:

(1) Sound identification: when surge occurs, it takes the form of a sudden‘‘bang”along with a violent shake of the entire testbed, which can be used to infer the beginning of surge.

(2) Real-time monitoring of the pressure at the compressor outlet: the amplitude of the pulsating component (commonly referred to as A value) exceeds a pre-set threshold.

(3) Real-time monitoring of the engine operating point:this method requires measurement of the engine mass flow rate,and surge is identified simply by a sudden deviation of the operating point from the steady-state performance map.

All three methods are applicable, but only Method (3) is used during the above introduced engine experiment.Correspondingly, in order to mimic this process of surge identification, a parameter named Surge Mass Flow (SMF) is defined to track the rate of change of the mass flow rate as follows:

where the mass flow rate is measured at the inlet plane.The variation of the SMF directly shows the moving speed of the engine operating point.Therefore, by monitoring this parameter,the surge point is identified by its deviation from the value of zero with a threshold of–5×10-3.Fig.2 illustrates how the SMF is used in identifying the surge boundary during experiments by high-pressure air-injection.In Fig.2, Jec1, Jec2,and Jec3 represent different air-injection locations; te represents injection time duration.The presented data are simulation results obtained using the method established in this paper.In Fig.2(a), surge points are clearly identified and marked by points a, b, and c, respectively, for the cases with a low air-injection rate.However,for those cases with a higher air-injection rate (see Fig.2(b)), the SMF changes violently,thus it is unable to identify surge.Detailed discussion about the effects of injection parameters on engine surge characteristics will be provided in Section 3.

Two more things are worthy of note concerning the choice of the surge indicator during the simulation:

(1) For large civil and military engines, Method (2) is the most commonly used one.In this method, the pressure signal should contain high-frequency components, and the surge indicator is often calculated by the ratio of the time-averaged dynamic head to its pulsating component.However, the pulsating component is not obtainable in reduced-order models and even in URANS simulations, as the grid resolution is insufficient, which will bypass the high-frequency components.Therefore,only parameters representing the overall performance of the compressor can be used.Since the time interval between the inception of local high-frequency instabilities that finally leads to surge and the beginning of overall performance variation should be extremely small,this simplified treatment is reasonable.

Fig.2 Variation of SMF during surge.

(2) The investigated engine is a turboshaft engine, so the measurement of the mass flow rate of the core-engine is feasible,which subsequently makes real-time monitoring of the compressor operating point possible.This is how the surge point was identified during the actual engine surge experiment.Since the process of pressure ratio drop upon surge is relatively slow, especially when the downstream plenum is large,only the rate of change of the mass flow rate is used.

The study in this paper is based on a virtual turboshaft engine with a configuration similar to that of Kuang, et al.6The compressor is a multi-stage axial-radial compressor (a three-stage axial compressor and a single-stage radial compressor) with a design pressure ratio of 10.0, and the turbine inlet temperature is 1300 K.The numerical method established in this paper is to reproduce the engine surge experiment as depicted above and obtain the engine surge boundary.

2.2.Modeling of compressor

For simulation of compressor surge, as discussed in the Introduction section, the most commonly used URANS method requires massive computing resources, which is undesirable in the design process.Therefore, related studies based on this method mainly focus on single-stage or single-passage simulations for simplicity.1,17–19Different from high-fidelity methods,the body-force method is a more efficient alternative for engineering application with the premise of retaining key threedimensional flow features of surge, and its capacity of surge prediction has been validated on multi-stage axial compressors.16

A three-dimensional body-force solver TSCQ (Tsinghua Compressor Quasi-3d) developed by Tsinghua University is used in this paper.Since this code was initially built for axial compressors and validated on single- and three-stage axial compressors,16only the modifications related to the application on radial compressors and a brief introduction of the main solver are presented here.Detailed model derivation can be found in the Ref.16

The governing equations to be solved are the unsteady Euler equations with body-force source terms in the absolute frame of reference as follows:

where V, p, ρ, ht, and t are the velocity, static pressure, static density, total enthalpy, and time; U is the blade velocity, and f is the body-force per unit mass of fluid;b is the local blockage factor accounting for the blockage caused by the blade thickness and boundary layer growth, which can be further rearranged into source terms.In the body-force model, the work input of the blade is achieved by a body-force field.Fig.3 shows the real blade geometry and the computational domain of the body-force model.The modeled compressor is composed of an Inlet Guide Vane (IGV), a three-stage axial compressor (R1, S1, R2, S2, R3, S3), and a single-stage radial compressor which includes an impeller(IMP),a radial diffuser(DIF_R), and an axial diffuser (DIF_A).The dark regions in Fig.3(a) and Fig.3 (b) represent the blade geometry and the body-force field acting to substitute the effect of the blade.The key to a correct simulation of compressor characteristics is an appropriate formulation of the body-force field.

The calculation of the body-force field is based on local flow conditions.Firstly, the entire computational domain is divided into forward- and reverse-flow regions.The criterion is the streamwise flow direction at each mesh point.Then,for each region, a target velocity field is predicted, and the body-force field acts to minimize the differences between the actual velocity field and the target velocity field.

In order to achieve this,the solver borrows the idea of feedback control, which yields a general form of

Fig.3 Compressor computational domain.

where W is the relative velocity,n is the normal component of the target velocity, and Kpis the feedback factor.The idea of Eq.(5) is that the difference between the actual flow field and the target velocity field (represented by W ?n) is taken as an error signal.The body-force is always in the direction of reducing this difference and thus completing the feedback control process.

Since the body-force field is calculated based on the target velocity field, a prediction of the target velocity field is essential.For forward-flow regions in the axial-flow compressor,the classic deviation model is used to predict the deviation angle δ2at the exit of each blade row.Combining the exit blade metal angle β′2, the predicted outflow angle β2of the target velocity field is calculated by

The inflow angle β1is set to be the same as the actual inflow angle.The target velocity field is obtained by further including a prescribed angle distribution(typically linear)from the blade row inlet to the outlet.It is worth noting that only the direction of the target velocity field matters in the body-force formulation, and its magnitude is calculated during the simulation.

For radial compressors, traditionally, the slip factor σ is commonly used to calculate the trailing edge flow quantities instead of the deviation model.Therefore,σ is used in the formulation.Fig.4 shows the velocity diagram at the impeller outlet to illustrate the slip effect.The slip factor is defined by

where U2and Cm2are the blade velocity and the meridional flow velocity at the impeller outlet, respectively, and the expression of β2can be obtained by rearranging Eq.(7) as follows:

where φ2=Cm2/U2is the outlet flow coefficient, which means that the outlet airflow angle can be estimated using Eq.(8)and the flow parameters at the impeller outlet.Then, the target velocity field can be obtained similar to the treatment for axial compressors.

The slip factor σ is estimated using Qiu’s model,20which can predict the slip effect of radial- and mixed-flow impellers.The final expression of Qiu’s formulation is as follows:

where Z2and s2are the blade number and the blade pitch at the impeller outlet,respectively,and F is a shape factor,which can be calculated from geometric parameters.

For reverse-flow regions,the same treatments are applied to both the axial and radial compressors.Fig.5 illustrates the flow field under reverse-flow conditions with a comparison to high-fidelity URANS results.1It can be seen that the incidence angle to the rotor blade at Station 2 is over 90°,which creates large separations at the rotor’s trailing edge.While at Station 1, the flow attaches to the pressure side of the blade surface again.Therefore, the deviation angle of the outflow (e.g., the rotor inlet and the stator inlet) is set to zero for reverse-flow modeling.Admittedly, the flow conditions at both sides of the blade should be different.However,the current model cannot differentiate the blade-to-blade flow.Therefore, only the pressure-side flow is modeled, as the flow momentum on the pressure side is dominant.

Based on the above procedures, the target velocity field is obtained for each flow region.The body-force field is then calculated.Thus,the body-force model for a compressor component is established.Since only a small mesh size is required,the computing efficiency is well-improved by two orders of magnitude.21

Fig.4 Slip effect at the outlet of a back-sweep impeller.

Fig.5 Velocity diagram for reverse-flow conditions(last stage).1

2.3.Modeling of combustor

In aero-engine combustors, complex cooling holes and flow paths are designed to effectively organize the airflow for combustion reactions.The turbulent combustion process requires and produces vortex structures of various length scales.In order to accurately capture these geometric boundaries,as well as delicate flow structures, extremely fine grids plus highfidelity methods of RANS or Large-Eddy Simulation (LES)are used in general,which is overly time-consuming.However,for the surge simulation studied in this paper, relatively largescale and one-dimensional flow features are dominant.As a result, the importance of a detailed flow field solution inside the combustion chamber is significantly weakened.Thus, the propagation of one-dimensional pressure waves in the connecting channel (to the compressor), the cavity effect of the combustion chamber itself as an‘‘a(chǎn)ir reservoir”, and the heating effect are crucial to the combustor simulation.

Corresponding to the above discussions, the connectingchannel flow is solved using the method of characteristics.The data transfer at the interface with the compressor model outlet is solved using the one-dimensional/three-dimensional coupled method.22The combustor itself is simplified to a homogeneous plenum with a heat source.The governing equations are the continuity equation and the energy equation as follows:

where ρ0,cmb,T0,cmb,and T0,care the total density and total temperature of the combustor (also turbine inlet) and the total temperature at the compressor outlet, respectively.˙mcand ˙mtare the mass flow rates at the compressor outlet and turbine inlet, respectively.Vcmbis the volume of the combustor.˙Q is the heat release,and γ is the heat capacity ratio.The above formulation forms the combustor model of the engine.Again,the simulation time is greatly reduced with the influences of system parameters on the surge behaviors included.

2.4.Modeling of turbine

For the turbine components in most aero-engines, a highpressure stage is commonly designed at the choking condition.This is partly due to the extremely high turbine inlet temperature, and the other reason is that it can fix the location of the engine working line.In that case,the strong shock wave at the throat of the high-pressure turbine blocks downstream flow formation from propagating upstream to the combustor and the compressor.

Therefore, for simulation of engine surge, the variations of turbine characteristics can be modeled by a zero-dimensional choking throttle function.The mass flow rate through the throat is calculated by

where p0,cmbis the total pressure.Atis a constant calculated from the area of the turbine throat.The above equation essentially represents the fact that the corrected mass flow rate is constant at the throat.Combining Eq.(12)with the combustor model, the engine boundary condition for the compressor is fully defined.

In the actual surge experiment, the power consumption of the compressor increased as its operating point moved to the surge boundary.As a result, to keep the rotational speed constant, the fuel injection of the combustion chamber needed to be increased slightly to increase the turbine power output.Meanwhile, as additional high-pressure air was injected into the compressor, the mass flow rate of the combustor also increased.Therefore,the combustor temperature stayed nearly constant during the entire surging process (before the engine entered surge).This phenomenon was shown in the Ref.6that the measured engine exit temperature stayed constant before surge and even for a short time duration after surge.In the model proposed in this paper, it is achieved by adjusting the value of ˙Q to fix T0,cmbin Eq.(11), and the compressor speed is set to a constant value.

2.5.Modeling of air-injection system

The air-injection system is the foundation of the engine surge experiment.The purpose of a complex air-injection system design is to achieve a stable and continuously adjustable injection pressure control.In this engine model, the air-injection system is simulated by an injection boundary condition.More specifically, the injection orifice is represented by a newly defined patch located between the IMP inlet and the S3outlet,as shown in Fig.6(denoted by Jec2).Recalling the experiment shown in Fig.1, multiple air tanks are used to ensure a stable injection pressure (i.e., one throttle opening position matches only one injection pressure).Thus,the total pressure and total temperature condition is used for that boundary patch.The flow angle is set normal to the injection boundary.Reasons for this angle setting are: (A) in the actual engine surge experiment described in Section 2.1, a bleeding port was used to inject the high-pressure air into the flow path.Detailed design of the bleeding port is unknown, and thus a simplified treatment is applied; (B) setting the flow angle normal to the boundary will have minimal effects on the flow field inside the blade row, which is always desirable since the subsequent effects on the surge boundary will also be minimized.A change of the throttle opening position is realized by setting the total pressure to be time-dependent.Besides, the air temperature delivered from the tank is close to the ambient temperature,which means the heat transfer on the pipe wall is negligible(i.e., adiabatic wall).Therefore, the total temperature is set to a constant equal to the room temperature.To study the effect of different injection locations, two more patches are defined at the R3inlet and the compressor outlet, denoted by Jec3 and Jec1, respectively, as shown in Fig.6.

Fig.6 Boundary condition setup for air-injection.

In order to investigate the effects of different injection locations, injection pressure, size and number of injection orifices,and injection time duration (more specifically, the injection pressure is defined by the maximum pressure or the pressure in the air tank; the orifice size is defined by the equivalent diameter; the injection time duration is defined by the time required for the current injection pressure increasing to twice of its initial value), the corresponding non-dimensional values are defined for each parameter: the size of injection orifices is nondimensionalized by their circumferential spacing;the injection time duration is nondimensionalized by the surge cycle;the injection pressure is nondimensionalized by the compressor outlet static pressure.The above definitions are summarized in Table 1.

It is worth noting that even in a situation of the flow angle normal to the injection boundary, the injected highmomentum flow may still have a non-negligible impact on the performance of the downstream blade row.However, aswill be shown in Section 3.1, the injection location should always be set at the compressor outlet (Jec1) to ensure that a correct surge boundary is obtained with unchanged compressor matching.In this case,settings with different injecting flow angles have no effects on the compressor performance.Thus,the effects of injection angles are not analyzed in this paper.

Table 1 List of injection parameters.

2.6.Validation of modeling method

The computational domain is shown in Fig.7.The compressor component is solved using three-dimensional grids,while other engine components are solved in a reduced-order manner.By using the cyclic boundary condition, the governing equation is solved on only one quarter of the full-annulus mesh grid,which further improves the computing efficiency.The mesh has 15, 261, and 40 mesh layers in the radial, streamwise,and circumferential directions, respectively.The total temperature and total pressure boundary condition is set at the domain inlet, and if reverse flow occurs during surge, it is changed to a given static pressure condition.The domain outlet boundary is set according to the discussions in Sections 2.3 and 2.4 for the simulations of the combustor and the turbine characteristics.The adiabatic slip boundary condition is set at the compressor hub and shroud.For the temporal settings,the maximum Courant number is limited below 0.1, resulting in a physical time step smaller than 1 × 10-6s.The reason for a relatively conservative setting of the maximum Courant number is that the current solver uses an explicit timemarching scheme.Larger time steps may cause divergence.

The above-established engine model can be used to simulate the compressor component surge experiment by setting the value of ˙Q to zero and substituting the turbine function with a parabolic throttle function.In order to validate the capability of the proposed method in surge prediction, the highfidelity URANS method is used to simulate the same compressor geometry.By comparing the results produced by the two methods, to what extend the established model can reproduce the surge characteristics predicted by the URANS method can be confirmed.

Fig.7 Computational domain and setups (Body-force method,1/4 annulus).

The computational domain for the URANS model is shown in Fig.8,where a single-passage computational domain is used.All the boundary conditions are kept consistent with those of the engine model, except that the wall boundary is set to a non-slip wall where the viscosity is fully resolved.The sliding mesh method is used for the interfaces at the inlet and outlet of each rotating domain,while in the engine model,since the flow field is solved in the absolute frame of reference,no special treatments are required.The k-ε turbulence model is used.A mesh independence analysis is conducted and yields a total number of meshes around 5 million, which ensures that the variations of the choking mass flow rate and the maximum efficiency are within 0.5%by further refining the mesh grids.A temporal resolution of at least 7 timesteps per rotor passage is chosen, resulting in a physical timestep of 1 × 10-5s.

Fig.9 compares the results of surge simulations triggered by closing the downstream throttle (increasing the throttle coefficient in the outlet boundary condition).All the data shown in the plot are nondimensionalized based on the design point data.Typical stages of surge are labeled by blowdown,flow reversal, and recovery in Fig.9(a).Overall, the dynamic surge cycles and the transient pressure variations from the two methods match quite well,especially during the surge process from point N to point S.A discrepancy occurs after the surge inception of point S where the compressor operating point switches from a forward-flow condition to a reverseflow condition.The engine model under-estimated the strength of the back-flow resulting in a smaller negative mass flow rate at point N compared to the URANS results.This effect also led to an over-prediction of the period of surge cycles:the process from point S to point P lasted for 27.8 shaft revolutions in the engine model simulation, while it lasted for 23.1 shaft revolutions in the URANS simulation.

In Fig.9(b), pressure spikes caused by the back-flow and the shut-off head at zero mass flow rate are captured and marked by point A and point B, respectively.These distinct flow phenomena are typical surge flow features that have been observed in various engine tests, compressor component tests,and high-fidelity simulation results.11,23,24Furthermore, to show the capability of the proposed model in predicting the surge boundary,simulations with different throttle coefficients are conducted to find the surge points at 100% and 90%design speeds.Surge points are identified by the last stable operating point before consecutive surge cycles begin for both methods.The loss coefficients and the deviation model are calibrated at 100%design speed according to the URANS results to produce correct steady-state overall and stage performances.The resultant model coefficients are used for surge simulations at 100%speed and both the steady and surge simulations at 90% speed.

Fig.10 shows the overall performances and the surge boundaries obtained by the two methods.To evaluate the accuracy in surge boundary prediction, the predicting error is quantified by the parameter σ and defined by

where ^π and ^˙m are the pressure ratio and the mass flow rate at the surge point obtained by the URANS method,respectively,while π and ˙m by the engine model, respectively.It is shown from the figure that the deviations are less than 5%.Thus,the established method is proven to be capable of producing reasonable surge simulation results.

It should be noted that the phenomenon of surge is primarily dominated by the development and evolution of onedimensional streamwise flow features.This is the main reason that the proposed model can produce comparable results to those of the URANS method.Detail discussions about the potential and shortcoming of the proposed body-force-based model can be referred to past literature.16,21

Fig.8 Computational domain and setups (URANS method, single-passage).

Fig.9 Simulation results of compressor surge.

Fig.10 Comparison of surge boundary prediction.

3.Results and discussion

Based on the established numerical simulation method, the effects of different injection parameters on the surge transients and boundary are analyzed in this section.Besides, a preliminary guide on the optimization of experimental design is discussed.Meanwhile, simulation results are discussed in combination with theoretical analysis, which further verifies the correctness of the proposed engine simulation method.

3.1.Influence of injection location

Three different injection locations (Jec1, Jec2, and Jec3, as shown in Fig.6) are studied in this section.The transient trajectories of the compressor operating point are compared and shown in Fig.11,denoted by"Transient".A steady-state compressor map is also presented and denoted by"Steady",which is obtained by using the throttle function to mimic the compressor component tests (The corresponding surge boundary is denoted by"Surge line").It can be seen from the figure that as the injection location shifts upstream, the transient compressor pressure ratio decreases significantly, resulting in the transient trajectory being lower than the steady-state characteristic curve.To further evaluate the influence on the engine surge boundary, the surge identification method introduced in Section 2.1 is used, and the corresponding surge points are marked in the figure by a, b, and c.The predicted surge margins for the three cases are 20.9%, 16.6%, and 14.5%,respectively.It is clear that different injection locations affect both the surge transients and the surge boundary.

Fig.11 Influences of injection locations on the surge transient and the boundary (te = 10.0).

To find the reason behind the above differences, Fig.12 shows the time traces of the mass flow rate on several streamwise planes for each case (normalized by the mass flow rate at the design point).This model captured an increase of the mass flow rate downstream from the injection plane and a gradual decrease of the mass flow rate on the upstream planes due to the choking effects.Taking Jec3 as an example (see Fig.12(c)), the mass flow rate increased on the downstream planes of the IMP inlet and the DIF_A inlet, while it decreased on the upstream planes of the axial compressor stages (R1and R2).

The transient operating point of each compressor stage is presented and compared from Figs.13 to 15.The corresponding steady-state characteristic curves are shown by dash lines.Five distinct operating points marked by s1-s5are also labeled in the figure showing the process from steady to surge (s1represents the initial condition of the numerical surge experiment and the beginning of air-injection).For the case of air-injection at the compressor outlet(Jec1,Fig.13),the operating points of all four stages were steadily pushed to smaller mass flow rate conditions along the steady-state characteristic curves, which resembled the process of surge tests in a compressor component test rig by closing the downstream valve.

Fig.12 Time traces of mass flow rate during surge.

However,for the case of inter-stage air-injection,things are different, such as at the IMP inlet (Jec2, Fig.14) and the R3inlet(Jec3,Fig.15).It can be seen that the transient trajectory of the compressor stages downstream from the injection location deviated from the steady-state characteristic curves significantly (the last stage in Fig.14 and the last two stages in Fig.15).However, the upstream stages remained as a quasi-steady process approaching the surge limit.Apparently,this led to a mismatch of the studied multi-stage compressor and thus engine performance deterioration.Therefore, the injection location should always be set at the compressor outlet(Jec1) to ensure a correct surge boundary obtained with unchanged compressor matching.

Normally, a mismatch of the multi-stage compressor may also lead to a change of the surge inception location.For the studied compressor, surge points a, b, and c shown in Fig.11 are also labeled on the stage characteristic curves in Figs.13–15.It can be seen that a surge point occurs right after the stalling point of the first stage (R1+ S1, s4) for all three cases with different injection locations.As discussed above,the injected high-pressure air increases the mass flow rate of the downstream compressor stages and stabilizes these stages,while the upstream stages are still throttled into surge as usual.Therefore, the surge inception location can only migrate upstream under the effect of air-injection, and for the current compressor, surge is always triggered by stalling of the first stage.

It is worth noting that the engine surge point b for the case of Jec2 is located exactly on the compressor component surge boundary, as shown in Fig.11.However, the outlet boundary conditions used in the engine and compressor component surge simulations were different.In addition, the engine surge simulation involved strong transient effects.Therefore, the compressor component surge boundary is only a reference here and cannot be used as a benchmark for the judgment of accuracy.In contrast, it is concluded from the above analysis that the surge point obtained by air-injection at the compressor outlet (Jec1, point a) is the most accurate one.

Fig.13 Matching of each compressor stage during surge (Jec1).

Fig.14 Matching of each compressor stage during surge (Jec2).

Fig.15 Matching of each compressor stage during surge (Jec3).

3.2.Influences of injection pressure and injection orifice size

The influences of the injection pressure and the injection orifice size on surge are further investigated in this section.The selection of these two parameters directly determine the success of the engine surge experiment (that is, whether engine surge can be achieved under a given injection pressure and orifice size).Meanwhile,its impact on the surge boundary needs to be evaluated.Since the engine surge experiment is of high risk and high cost, it is always expected to use a lower air pressure and a smaller injection size under the premise that surge can be achieved.Therefore,the selection of these two parameters is of great importance in terms of both cost and accuracy.

Fig.16 compares the trajectories of the simulation cases under different air-injection pressures.It can be seen that cases with low injection pressures (mag = 2.0 and mag = 2.5) did not enter into surge cycles.Instead, the compressor stabilized at operating points e and d, respectively.However, the case with a higher injection pressure (mag = 3.0) finally entered into surge, and the corresponding surge point was identified as point a.This difference shows that the injection pressure has a decisive impact on the success of a surge test.In addition,it can be seen that the transient trajectories of the three simulation cases coincide with each other.Thus, the transient process is not affected.

Fig.17 shows the surge trajectories with different injection orifice sizes.It is noted that the trajectory is slightly different between the two cases.Besides, since the mass flow rate of the injected air is proportional to the size of the injection orifice, the transient effect on the simulation case with a larger injection orifice (sz = 0.068) is much more significant, which makes the surge point almost impossible to identify.Therefore,only the surge point of the case with a small injection orifice is marked in the figure (sz = 0.017, point a).

In summary, the injection pressure determines whether surge can be achieved during the engine experiment but does not affect the location of the surge boundary.As for the orifice size, larger orifices will cause excessive transient effects, making it difficult to identify the surge boundary during the test.

3.3.Influence of number of injection orifices

The existence of injection orifices inevitably creates pressure distortion in the upstream and downstream flow fields of the injection plane.Two different configurations are simulated,i.e.,4-orifice and 8-orifice.The pressure distortion is quantified by a distortion magnitude D defined by

where pθis the static pressure at a circumferential position θ and a certain time t, and pmeanis the circumferentiallyaveraged static pressure.Clearly, D indicates the magnitude of the local distortion.Fig.18 shows the distribution of the pressure distortion from the axial diffuser outlet to the injection location.D is further normalized by the maximum value of D in the 4-orifice case.It can be seen that in the 4-orifice case,there is distinct pressure distortion at the compressor outlet that gradually decays along the flow path,while this distortion is much weaker for the 8-orifice case.

Fig.16 Influence of injection pressure on the surge transient and boundary (pos = Jec1, te = 10.0, sz = 0.017).

Fig.17 Influence of injection orifice size on the surge transient and boundary (pos = Jec1, te = 10.0, mag = 3.0).

To evaluate the influence of the number of injection orifices on surge, Fig.19 shows the trajectories of the compressor operating point for the above two cases.The identified surge point for the 4-orifice case is marked by point a.The difference between the two trajectories is marginal.However, the transient effect of the 8-orifice case is much stronger, and the surge point can hardly be identified.This is similar to the case with a larger orifice size.Furthermore,to show the effects on the surge boundary, an additional case with the 8-orifice configuration is simulated with a shorter air-injection time duration to weaken the transient effect.The corresponding surge point is marked by point g.It can be seen that point g nearly coincides with point a, which indicates that the surge boundary is not affected by the pressure distortion by using the 4-orifice configuration when the transient effect is negligible.

In summary, more injection orifices can substantially suppress the pressure distortion caused by the air-injection.However,they may lead to a highly dynamic surge process,making it hard to identify the surge boundary.For the studied engine model,it is no longer necessary to consider the effect of distortion on the surge boundary by using the 4-orifice configuration, so all other simulations mentioned in this paper are conducted with four injection orifices.

Fig.18 Streamwise dissipation of injection-induced distortion.

Fig.19 Influence of the number of injection orifices on the surge transient and boundary (pos = Jec1, te = 10.0,sz = 0.017,mag = 3.0).

3.4.Influence of injection time duration

The discussions in the previous three sections mainly focus on the parameters that need to be determined before the experiment.In this section, the injection time duration representing the speed of the injection process is studied,and this parameter is free to be adjusted during the experiment.

Results obtained using different injection time durations are compared in Fig.20.It is noted that for the case with the shortest injection time duration (i.e., the fastest injection rate, te = 0.25), the compressor exhibits a sudden pressure ratio spike, and the transient operating point deviates from the steady-state characteristic curve.This mainly results from the delayed response of the compressor mass flow rate to the overly fast injection rate.As the injection rate is reduced(te = 10, te = 50, te = 100, and the corresponding surge points are identified as points a, j, and k), the transient trajectories coincide entirely with the steady-state curves.In addition, the overly fast injection process makes the surge point hard to identify.As the injection time duration increases, the surge point is clearly identified and gradually shifts closer to the compressor component surge boundary.

To summarize, if the high-pressure air supply is sufficient,the injection time duration should be set as long as possible to ensure the accuracy of the obtained engine surge boundary.

From the discussion, the effects of different injection parameters are closely coupled together.For example, using a larger orifice size and more injection orifices results in uncertainties in the surge point identification,as also reported in this section by using a faster injection rate.This coupling effect further illustrates the importance of using the numerical method to comprehensively evaluate each test parameter before an actual engine surge experiment.

Fig.20 Influence of injection time on the surge transient and boundary (pos = Jec1, sz = 0.017, mag = 3.0).

4.Conclusions

In this paper, a numerical method for simulation of aeroengine surge experiments using a high-pressure air-injection method is established.Models of different fidelities are used for each engine component, including the air-injection system:a three-dimensional body-force model is used for the compressor; a one-dimensional model combined with a lumpedparameter plenum model is used for the combustor; a zerodimensional throttle model is used for the turbine; finally,the air-injection system is modeled by an injection boundary condition, which can be used conveniently in changing injection parameters.Based on the established method, the surge boundary of a turbo-shaft engine is obtained.

Simulations with different injection parameters are further carried out using the established method to investigate their effects on a surge experiment.It is found that: (A) interstage air-injection may change the original matching of the multi-stage compressor, resulting in false prediction or measurement of the surge boundary.Therefore,the injection location should be set at the compressor outlet; (B) the injection pressure determines whether surge can be achieved during the experiment and has little effect on the boundary.Larger injection orifices may cause excessive transient effects, making it hard to identify the surge boundary.Therefore, larger injection pressure and smaller injection orifice are always desirable;(C) more injection orifices can substantially suppress the pressure distortion caused by the air-injection.For the studied engine model,the 4-orifice configuration is adequate to exclude the distortion effect; (D) when the air supply is sufficient, the injection time duration should be set as long as possible,which can increase the accuracy in measuring the engine surge boundary.For the studied engine model, a non-dimensional injection time of 50 is acceptable.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported by the National Science and Technology Major Project (Nos.J2019-I-0011 and 2017-II-0004-0016).