Effects of S-shaped Duct on Fan Blade Vibration

Yun Zheng Ning Wang

(School of Energy and Power Engineering,BeiHang University;Collaborative Innovation Center for Advance Aero-Engine,Beijing,China)

Abstract：S-shaped intakes are commonly used in modern aero-engine designs.The flow distortion induced by flow turning and duct effects could lead to the blade vibration problems,such as blade flutter and forced response.This paper analyzes the vibration characteristics of fan blades with the effects of a S-shaped intake interaction.Using a coupled CFD/CSD numerical code，aeroelasticity analysis of the rotor67 fan with an S-shaped duct is conducted.The in-house numerical code featured a three-dimensional unstructured finite-volume compressible flow solver in the fluid domain and a structure dynamic solver with the modal superimposition method for blade vibration.A mixing-plane model is used at the interface between intake domain and fan domain in order to model the blade vibration without interaction with the duct.A sliding-plane model is used at same condition to include the flow distortion and duct effects on the fan blade motion.The overall aerodynamic damping of the rotor blade is presented for both cases.The transient response of the fan with the intake is analyzed.This study proves the S-shaped duct intake interaction has significant impact on the blade vibration by increasing forced response and causing flutter.

Keywords： Fan/Intake Interaction, Flutter, Aeroelasticity, Blade Vibration, Fluid-structured Interaction,Aerodynamic Damping

0 Introduction

In recent years, the design of modern aviation propulsion system have moved toward high thrust weight ratio,light weight[1].This leads to the result that fan and compressor blades are lighter and thinner than ever. Due to combination of low stiffness and increasingly higher aerodynamic loads, lighter and thinner blades are prone to fluid-induced aeroelastic problems [2]. The intake is responsible for transferring the kinetic energy of incoming airflow into pressure and supplying the uniform high pressure airflow to the compression system[3], thus it plays an important role to the overall efficiency and stability of jet engines. One important characteristic of a modern aircraft is its wide operation range. However, at high flow angles of attack or during aircraft maneuvering the performance of intakes is significantly deteriorated.Typical flow phenomena such as large flow separation,shock-wave and boundary layer interaction appear at supersonic speed, and vortex convection is conveyed to downstream rotor blade passages. There are often time-variant and spatial flow distortion at intake/engine interface plane (AIP), including total pressure, total temperature, swirl and static pressure distortion[4]. Most of the research on intake flow distortion in the last several decades are focused on the engine stability and compatibility aspect. However,the aero-mechanical issue, especially the intake flow distortion effects on flutter characteristics of downstream rotor blades,has received much less attention.

It is well known that aeroelasticity is an important consideration in the fan and compressor blade designs[5]. There are two main aeroelastic problems for fan/compressor blades, namely forced response and flutter. The most common excitation source is a non-uniform flow field generated by intake distortion,wake,etc.[6].The blades are affected by large unsteady loads, when blades pass through the non-uniform flow[7]. When the frequency of these unsteady forces match one of the blade natural frequencies, fan blades will experience forced response, which can lead to severe vibration, and more than that, blade breaks down due to the high cycle fatigue[8].Flutter is defined as an unstable and self-excited vibration of blades in an airstream and results from a continuous interaction between the fluid and the structure[9]. Flutter is a particularly difficult problem in fans and compressors because there are many additional features with not fully-understood consequences: flow distortions due to upstream and downstream blade-rows,acoustic wave interactions between blade-rows, blade/disk modes coupling, and loss of spatial periodicity of vibration due to aerodynamic effects and blade mistuning.

S-shaped duct intakes are widely used in military aircraft and unmanned aerial vehicles. There are three key parameters to evaluate an intake: overall aerodynamic layout,the invisibility and total pressure recovery coefficient[10].Sshaped duct intakes have wide application on account of the excellent performance in these aspects[11].However,a problem with S-shaped intake is flow distortion induced by high turning angle. Intake is located before the fan stage, thus the flow distortions and unsteadiness could lead to serious aeroelastic problems in the fan stage.

Most studies of the intake design are focused on two main aspects: the effects on the aerodynamic performance and stability. In the first aspect, James et al.[12] performed whole-annulus calculations on a candidate attached to the inlet, which forms a coupled inlet/fan system. The unsteady simulations show that boundary-layer ingesting (BLI) generates a complex total pressure inlet distortion, which has significant effects on the blade aeromechanics and dynamic stall. Sun et al.[13-14] studied the influences of total pressure distortion on the flow field in a fan using a three-dimensional unsteady numerical method. The study indicates that the main loss is the mixing loss in the root segment and midsection of rotor blades and vortices and backflow are formed below the midsection of stator, which has major contribution to the aerodynamic loss.

The effects of intakes on aerodynamic stability have received much attention in recent years. Shaw et al. [15] published their research on the effects of the distortion with variable inlet guide vanes (VIGVs). Their results show that the inlet distortion significantly reduced stall margin and some of the reduction could be recovered by using VIGVs. James et al. [16] used three-dimensional unsteady CFD method to model the flow stalling mechanisms of a transonic fan rotor with inlet distortions induced by curved ducts, and assessed the importance of each distortion pattern with regards to stall margin loss. Liu et al. [17] investigated impact of the inlet distortion on the fan performance using the prototype and an optimized flush-mounted S-shaped inlet and a fan stage.The results show that the stable operation range is improved after optimization of the intake and overall aerodynamic performance in terms of the mass flow rate and efficiency is also improved.

There are also few reports focused on the aeroelasticity aspect of the intake. Vahdati et al. conducted investigations on the influence of inlet on the fan blade flutter [18-23].They pointed out that steady flow state is one of most critical requirements for flutter analysis [18]. They also compared seven different methods, which shows nonlinear method and linearized viscous method can accurately capture the flutter boundary and aerodynamic damping.Two independent mechanisms causing flutter are shown in their studies[19-20] :1)Flow and mode shape driven; 2) Acoustic flutter. For the flow driven flutter, the results suggest that shock induced boundary layer separation is the key aerodynamic driver.Furthermore, the mechanism of the‘flutter bite’is presented.For the acoustic flutter, it is demonstrated that acoustic reflections from the intake is a crucial factor in fan flutter and should be considered when designing new engines. Vahdati[21] further explained the fan‘flutter bite’due to acoustic reflections from the intake. They conducted a flutter analysis of a civil aero-engine fan assembly with two different intake ducts using an integrated three-dimensional aeroelasticity model[22]. The results show that blade flutter appears when the pressure perturbation caused by fan rotation and blade vibration matches in frequency and shape. Furthermore, they pointed out that a full description of the flutter needs to include an intake model. Breard et al.[23]conducted a flutter analysis of a full CFD analysis of an intake duct,together with a fan model.The results indicate that the areoelastics stability is sensitive to the type of the intake.The results indicate strong unsteady aerodynamics interactions between the fan blades and flows in the intake.Rabe et al.[24]investigated the unsteady aerodynamic loads on blade surface and vibration response under circumferential distortions.Zhang et al.[25]discussed two key parameters of inlet unsteady distortion, turbulence intensity and frequency in blade vibration analysis.

In this paper, the vibration characteristic of rotor67 fan with an S-shaped duct intake is studied with a fluid structure interaction method. Flutter analysis is conducted at 80% of the design speed of the Rotor67 fan stage with an S-shaped intake. The fluid/structure interaction method is adopted in the unsteady solution of the flow field and the response of the blade under unsteady aerodynamic loads. Blade vibration, blade motion and aerodynamic damping with and without intake are presented. Interaction between the S-shaped duct and the blade vibration is analyzed.A detailed areoelastic analysis of fan blades with an S-shaped duct intake is conducted in this study.

1 Numerical Method

1.1 Flow Model

The computations are based on the in-house HGAE[26](hybrid grid aeroelasticity and flow solver) code, a three-dimensional unstructured finite- volume compressible flow solver for turbomachinery applications. In the flow domain,unsteady Reynolds-averaged Navier-Stokes equations are solved with dynamic deforming grids in order to model the effects of blade motions.The system of equations, written in an arbitrary Lagrangian-Eulerian (ALE) conservative form,taking the form:

where Ω is the control volume, ?Ω is the boundary of the control volume, n? represents the outward pointing vector of the boundary, q→is the vector form of the conservative variables, F→is the convective and viscous flux vector, vector S→contains the terms due to the rotation of the reference frame, and ω is the grid surface velocity. The numerical fluxes are evaluated using Roe’s upwind scheme.A standard version one-equation Spalart-Allmaras turbulence model is used in all calculations presented in this paper. The validation of the HGAE code in various aeroelasticity cases has been reported in Ref[27，28].

1.2 Structural Model

The aeroelasticity equations of a structural motion can be written as

where M, K, C and Q are respectively the mass, damping matrices, stiffness and the unsteady aerodynamic forces on the blade surface, x is the displacement vector. Detailed derivation is shown in Ref[29].

The structural dynamic equation is transformed into m non-coupling equations by using modal superposition method. Each modal equation is advanced in time with a second order integration scheme[30].

2 Case Study

2.1 Preliminaries

The effects of the intake on aeroelasticity have been known for some time through rig tests of aero-engines.However,detailed study of aeroelasticity effects of S-shaped duck intakes on rotor blades is rarely carried out. Mixing-plane model and sliding-plane model are used at the interface between the intake and the rotor blades.The sliding-plane interface models the interaction correctly and all waves are propagated without any simplified assumptions, where the actual effect of intake on the aeroelasticity of the blades can be obtained. The mixing-plane interface taken here, the information can only be exchanged in an average sense. Due to this averaging process,the correct circumferential wave is not allowed to propagate. However, it can still be used to capture global unsteadiness characteristics such as the variation of mass flow, which can assure that the operating condition is same with sliding-plane model.

2.2 Computational Grids

A transonic fan,NASA Rotor67,was used as the benchmark geometry for this study. There are 22 blades and the hub-tip ratio at inlet to the rotor is 0.375. Details of the fan stage design are summarized in Tab.1.

Tab.1 Fan Design Parameters

The computation domain is shown in Fig. 1. It includes the complete fan assembly, with an S-shaped intake upstream of the fan.A complete analysis of the whole compressor is computationally very expensive because of the number of grid points required for the model in order to resolve the non-linear flow phenomenon.However due to loss of the circular symmetry, strong three-dimensional effects of the flows, and potentially non-linear interaction between unsteady flows and the blade vibration, a whole annulus analysis of the model are conducted in current study. Number of grid points in each domain is shown in Tab.2.

Fig.1 Domain used for flutter computations

Tab.2 Number of grid points in fluid domains

2.3 Blade Vibration Mode Analysis

The structural mesh of the rotor blade for the mode analysis is composed of hexahedral element, shown in Fig.2.There are 40 and 65 in chord-wise and span-wide,respectively.2 layers of elements are used in the direction of blade thickness.

The structural modes of vibration obtained from a commercial finite element solver-ANSYS. The rotor blades are made of TC4,which material properties are listed in Tab.3.

Fig.2 Structure mesh of rotor blade

Tab.3 Material properties of rotor blades

There is a fixed constraint applied at the blade root,and a small initial angular velocity is prescribed.The natural frequencies of the first six modes at 80% rotational speed are displayed in the Tab.4. The assembly modes corresponding to the first blade mode(1F mode)were included in the flutter analysis.The twist to plunge ratio parameter(α)can be computed from

where Xland Xtare the displacement of leading edge and trailing edge, respectively. The αparameter is very important in fan flutter [31-32].For this mode, α=0.56, which means this mode is necessary to performed flutter analysis.

The first flap mode at 80%engine rotational speed is illustrated in Fig.3. The contour levels indicate the amplitude of vibratory motion, with the tip section exhibiting the largest response.The modal integration function of the HGAE is used to obtain the integral modes of the full annuluses blades. The sixth nodal diameter (ND) forward traveling wave for the first flap mode is shown in Fig.4.

Fig.3 Contour of blade first flap(1F)mode shape

Tab.4 Natural frequency at 80%rotational speed

Fig.4 Expanded 1F/6ND mode shape for whole-annulus

3 Aerodynamic Performance

The steady-state flow is used as the initial solution for a flutter calculation. The steady-state flow simulation is carried out with a single passage calculation. A uniform total conditions were applied at the inlet of the intake domain,where total pressure and total temperature were specified.An average static pressure was imposed at the outflow of the fan. A mass averaged mixing-plane is used at the interface between the intake and the rotor domain for steady calculations. The total pressure ratio and isentropic efficiency characteristic maps of the fan with S-shaped duct is plotted in Fig.5.CFD computational results agree well with experimental data for the rotor alone configuration [33]. With the Sducted intake,the efficiency and choking mass flow are lower than the measured data, which is due to the aerodynamic loss of the intake. The point selected for the blade vibration study is near the maximum efficiency point at 80%speed,labeled“A”in Fig.5.

Fig.5 Total pressure ratio and isentropic efficiency characteristics of the fan with S-shaped duct

4 Flutter Analysis

In a whole-annulus aeroelastic calculation, the rotor domain is constructed by copying and rotating the single passage grid and a steady flow solution multiple times.The aeroelastic calculation is started by applying a small modal velocity as initial condition to each mode under consideration, the computational process is analogous to hitting a blade and monitoring whether the response is decaying or growing in time.

For each calculation, all 22 nodal-diameters were considered, and several typical modal time histories are plotted in Fig. 5. The first-nodal-diameter (ND) mode, second-ND,seventh-ND and eighth-ND are respectively shown in Fig.6a to Fig. 6d. The unstable modes have growing time histories,whereas the stable ones have decaying ones. The time histories of seventh-ND mode and eighth-ND mode are stable for both mixing-plane and sliding-plane.The first-ND mode and second-ND mode are stable for the mixing-plane. However,the time histories of first-ND mode and second-ND mode for sliding-plane show a beating on the blade.

Fig.6 Modal displacement of blade varying with different nodal diameters

Two Fourier transforms of the blade motion, first-ND mode and second-ND mode, respectively, are plotted in Fig.7. The Fourier transform reveals the frequency of the blade motion. For first-ND mode, the main influence frequency is 486Hz, which is 1F modal frequency, and the secondary frequency is 219Hz, which is close to the rotational frequency.This indicates that the rotor suffered forced response due to the intake.For second-ND mode,the main influence frequency is also 486Hz, and the secondary frequency is 425Hz,which is close to the second order of harmonic components of rotational frequency. The same thing as the above situation is that the blades are affected by the intake.Fig.8 shows total pressure contours at the inlet of rotor and Fig. 9 shows relative Mach number at the inlet plane, where we can see the high pressure in the top semicircle, which is caused by the curved intake.The rotor blade is affected by the flow distortion from the intake. It is a problem of off-resonance forced response,and we will discuss it later.

Fig.7 FFT amplitude spectra of modal displacement

Fig.8 Total pressure at the inlet of fan blade

Fig.9 Relative Mach number at the inlet of fan blade

In flutter calculations, it is possible to calculate a logarithmic decrement value for each history time;hence,the logarithmic decrement value is representative of the aerodynamic damping only. However, the history time used to calculate the damping is affected by a single vibration frequency. The effects of other disturbances should be excluded. The processed modal displacements are plotted in Fig. 10. And the Fourier transforms of blade motion are plotted in Fig. 11, in which each order of harmonic components of rotational frequency is excluded.The blade vibration amplitude in slidingplane interface is greater than the mixing-plane. This suggests the effects of S-shaped intake induces large amplitude blade motion.

Fig.10 Processed modal displacement of blade varying with different nodal diameters

Fig.11 FFT amplitude spectra of processed modal displacement

After processing the time histories, the aerodynamic damping was plotted as a function of NDs for both slidingplane and mixing-plane in Fig. 12. It is seen that the aerodynamic damping of sliding-plane for 0ND is negative and is less than the one of mixing-plane. It indicates that the flutter stability is greatly reduced by the intake, and the flutter can occur in this condition.

Fig.12 Aerodynamic damping of blade using sliding-plane and mixing-plane

5 Blade Vibration Analysis

Campbell diagram of the rotor blade is plotted in Fig.13.At 100% rotation speed, the 2EO excitation line has one intersection point with the natural frequency of first flap mode.At 80%speed,these is not crossing between the blade vibration and 2EO excitation, thus forced response related resonance is not in play.

The blade vibration problem shown in Fig.7 is discussed in this section.Fig.7 illustrates two peaks of frequency amplitude for each nodal-diameter, which is gained by Fourier transform of the blade motion displacement. One is the natural frequency of the 1F blade mode (486Hz), and the other two are the first order harmonic components of rotational frequency (219Hz) and the second order harmonic components of rotational frequency (425Hz) respectively.For first-ND, a beating frequency of 267Hz (486-219=267),which gives period of 0.0037s, is shown in Fig. 6a. For second-ND, there are a beating frequency of 61Hz (486-425=61) and the displacement curve is beating with a period of 0.016s as shown in Fig.6b.

Fig.13 Campbell diagram

Fig.14 FFT amplitude spectra of different nodal diameters

As shown in Fig.14a to Fig.14d,each harmonic components of rotational frequency are discovered in the Fourier transform of blade displacement correspondingly. The influence of the inlet distortion decreases with the increasing nodal- diameter, and disappears when the nodal- diameter is above 4. These plots illustrate that off-resonance forced response exists in the first three NDs.

6 Conclusion

A time domain fluid/structure interaction method for aeroelastic analysis is presented in this paper, based on coupled CFD/CSD numerical approach. Consequently, fan blade vibration due to an S-shaped duct intake is studied. The results indicate that:

1)The aerodynamic damping of the fan stage due to the interaction of the intake and blade vibration is significantly different from the aerodynamic damping without intake.When the intake is included for unsteady solution, the blade vibration mode with 0ND becomes unstable. This indicates that blade flutter may occur at this condition.

2) According to the time histories of blade displacement,off-resonance forced response exists during fan operating,which should be treated with caution.

3) Fourier analysis shows that blade motion contains the lower band (＜4) of harmonic components of rotational frequency, which correspond to 0,1,2,3,4 nodal-diameters.Furthermore, the influence of the intake decreases with the nodal-diameter increasing.