NASA研究：Zante揭示高速轴流压缩机叶栅恢复机制

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本文主要探讨了Zante在NASA Lewis Research Center进行的一项关于高速轴流压缩机叶片涡后恢复机制的研究工作。这项研究由Dale E. Van Zante博士，来自爱荷华州立大学的专家，在1998年完成，得到了国家航空和航天局（NASA）的资助（NAG3-1302）。研究的焦点在于理解高速流动条件下，轴流压缩机叶片工作后的涡流如何重新组织并恢复正常性能，这对于航空航天工业的气动设计和效率提升具有重要意义。该研究项目得以开展，首先要感谢Ted Okiishi博士，他为Zante提供了在NASA进行研究的宝贵机会，并作为导师和朋友给予了极大的支持。同时，研究的成功离不开众多NASA Lewis中心的同仁们的贡献。Tony Strazisar和John Adamczyk博士提供了指导和专业建议，他们在技术层面给予Zante关键的支持；Jerry Wood先生在数据分析阶段提供了深入的洞察和建议；Ken Suder博士在激光测速系统方面提供了宝贵的协助；Mark Celestina和Richard Mulac则在数值模拟方面提供了援助。此外，文中特别提到了Mike McGhee、Mike Goin、Dave Williams、Bob Gronski、Glenn Christman和Rob Bruckner等人的辛勤工作，他们确保了实验设备的正常运行以及电子系统的维护，这些都是研究顺利进行不可或缺的基础。这篇研究文章揭示了高速轴流压缩机涡后恢复机制的关键发现，对推进航空发动机设计优化、提高能源利用效率及减少涡损失具有深远的影响。通过深入解析涡流行为，研究人员能够更好地理解和控制这种复杂现象，从而推动整个航空工程领域的科技进步。

dict rotor wake decay and its associated mixing loss with the assumption that the mixing loss

can be determined by treating the rotor as an isolated blade row. In a stage environment, it is

known that the rotor wakes are chopped and transported through the downstream blade row.

Early research efforts assumed that the rotor wake transport which occurs in this downstream

blade row only redistributes losses and does not have any influence on the rotor wake mixing

loss. A more recent concept is that the rotor wake stretching which occurs due to the wake

transport within a stator does lead to a reversible reduction of velocity gradients and thus mix-

ing losses, known as recovery. The focus of the current research effort is the study of rotor

wake recovery for a viscous compressible flow in a high-speed compressor stage.

1.1 Interaction Effects

The effects of bladerow interactions on compressor performance were noted in early com-

pressor measurements. Smith (1970) in a study of the performance of a four-stage low-speed

compressor found that, for a series of tests with different aspect ratio blades, peak pressure

rise correlated with tip clearance/staggered spacing ratio and axial gap/spacing ratio. He sug-

gested that more information on the effects of axial gaps is needed to establish why deviation

angles and loss coefficients are apparently lower when axial gaps are small. He speculated that

the cause was the circumferential variation of total pressure caused by the downstream blade

row imposing non-uniform back pressure on the upstream rotor.

In compressor design, interaction effects are dealt with by empirical means often without a

clear knowledge of underlying mechanisms. Koch and Smith (1976) again mention blade row

interaction as having a performance impact. A downstream blade row moving relative to an

upstream row was thought to reduce static pressure in regions of low axial velocity such as

thick wakes in the casing boundary layer. This increases the velocity for the same total pres-

sure, but also increases total pressure by reducing losses thus enhancing the velocity increase

and reducing the boundary layer thickness. Although the mechanisms were not understood,

the importance of the interactions to accurate performance predictions was considered impor-

tant enough to attempt a correlation. The report contains an empirically generated curve which

relates the change in boundary layer displacement thickness to axial gap/tangential spacing

ratio. Additionally the report authors speculate that higher unsteadiness, which impacts wake

NASA/CR-- 1998-206594

growth, could be totally/partly responsible for the performance improvement instead of the

boundary layer thinning arguments. The important mechanism for the performance impact is

unclear.

On a somewhat different line of thinking, Smith (1966) proposed an interaction mecha-

nism which would reduce wake mixing loss in a reversible way and thus improve perfor-

mance. This mechanism occurs due to a wake being stretched in the downstream blade row

due to the relative motion and loading of the downstream row. This work is mentioned here in

the context of interaction effects and will be discussed in more detail later.

Advances in measurement and computational methods now allow more direct observation

of interactions. Early laser anemometer measurements by Ding (1982) suggested that there is

a high level of unsteadiness in the rotor/stator gap. He noted violent flow accelerations and

deflections in a short axial distance in the rotor/stator gap of a high speed compressor. Only

two axial positions were measured with three circumferential points at each position so the

data were too sparse to draw any further conclusions. These measurements hinted at the strong

wake/blade interactions present in high-speed closely-coupled machines.

Williams (1988) acquired laser anemometer measurements in a high speed multistage

compressor. The measured velocity downstream of a stator row showed the influence of the

downstream rotor and the upstream rotor which had a different blade count. Using FFT tech-

niques Williams extracted additional information about hardware related periodicities in the

flow. Performance impact was not assessed in the paper, but the measurements clearly show

the extent of bladerow interactions in a multistage machine.

Adamczyk et al. (1996b) used steady and unsteady numerical simulations to study the

effects of wake induced unsteady flows on blade row performance and the wake rectification

process. Wake rectification refers to the attenuation of a wake velocity deficit by mechanisms

other than viscosity. Major performance differences were found between a rotor operating in

isolation and a rotor operating downstream of a stator when the rotor had the same time aver-

age inlet flow condition. Use of a mixing plane in the stator/rotor gap improved agreement

between the steady rotor simulation and the unsteady rotor simulation. Adamczyk's average

passage model which includes the deterministic stress fields of surrounding blade rows pro-

vided far better agreement with the full unsteady rotor calculation. A dynamic wake rectifica-

NASA/CR--1998-206594

tion process was also identified which occurs as the wake convects past the leading edge of the

downstream rotor. This numerical study showed that interactions are important to predicting

compressor performance and need to be correctly modeled.

The above investigations all show either directly or indirectly the presence and possible

impact of interaction effects. In general most of the thinking about wake mixing losses consid-

ered the wakes of isolated blade rows. Along that line of thinking a brief summary of turbo-

machinery wake decay research is presented next.

1.2 Wake Decay

Wake decay by viscous dissipation results in the accrual of mixing loss and is therefore an

important contributor to loss production. However, all of the wake decay work discussed

below deals with wake decay in the absence of a downstream blade row moving relative to the

wake generating row.

Several studies have considered the decay of wakes downstream of rotors or cascades of

cambered airfoils. Kool and Hirsch (1982) developed a scheme for rotor wake decay predic-

tion. They postulated the presence of a separation bubble at the trailing edge creating a free

stagnation point that induces a pressure gradient which effects wake decay. The decay of axial

and tangential velocity is based on an assumed profile shape and an eddy viscosity concept.

The agreement of the model with available experimental data was fair.

Raj and Lakshminarayana (1973) measured the far and near wake of a plane cascade of

airfoils to determine the mean velocity, turbulence intensity, and Reynold's stress profiles of

the wakes. They found that the wake is asymmetrical past 3/4 of a blade cord downstream and

that the decay of the defect is strongly dependent on the wake edge velocity. The decay rate of

the wake defect was slower than that of a fiat plate wake at zero incidence.

Hobbs et al. (1982) measured a plane cascade of airfoils and used the data to improve the

computation of airfoil wakes with the intent of better loss predictions. A displacement surface

determined from experimental measurements was added to the trailing edge of the airfoil in

the computation to alter the trailing edge conditions of the computation. This was an attempt

to adjust the computation to achieve a more accurate wake profile shape prediction. Again, the

airfoil trailing edge conditions were important to predicting the wake shape and thus the loss

NASA/CR-- !998-206594

predicted due to wake mixing.

Accurate prediction of turbomachine near wake decay is difficult because wake decay is

highly dependent on the boundary layer condition near the blade trailing edge and this in itself

is difficult to measure or predict (see also Denton (1993)). Investigators have concentrated on

predicting the correct wake profile so that an accurate mixing loss could be calculated and

charged to that blade row.

All of the above studies considered wake decay without the presence of a downstream

blade row. This assumes that the presence of a downstream blade row does not have an effect

on the wake mixing loss. Although the research efforts discussed next still deal with wakes in

the absence of a downstream blade row, they do consider the effects of pressure gradients and/

or curvature which begin to mimic some of the effects that a downstream blade row may have

on an upstream blade row wake.

The effects of curvature and pressure gradient on a small defect wake were measured by

Nakayama (1987) in a low speed wind tunnel. Small perturbations to the potential flow were

found to significantly change the strain field of the small defect wake so that shear strain was

no longer dominant. This occurred because viscous wake decay is dictated by shear stress

which is proportional to the velocity defect squared and can be overcome by pressure or iner-

tia forces which are proportional to the absolute velocity squared. The findings suggest that

processes such as flow turning and pressure gradients in the stator could have large impacts on

rotor wake decay.

Denton and Cumpsty (1987) considered the effect of downstream conditions on the mix-

ing loss of a wake. It is shown that entropy generation during mixing greatly depends on the

velocity at the point of mixing and entropy generation is greatly reduced by accelerating the

wake prior to mixing. The trends of this process are not highly influenced by compressibility.

The relevance to unsteady mixing in a downstream blade row was not clear but the authors

suggest that the decelerating flow in a compressor might result in increased losses. The pro-

cess of wake stretching in a stator passage was not considered by the authors in making this

statement.

Denton (1993) revisits the topic of wake mixing more extensively. The loss associated

with wake mixing is dependent on the velocity and conditions at which the wake mixes.

NASA/CR--1998-206594

Accelerating a wake isentropically and then mixing it is shown to decrease the mixing loss

coefficient while an isentropic deceleration and then mixing increases loss. The overall benefit

of accelerating a wake prior to mixing will be affected by viscous dissipation of the wake

which is occurring concurrently with the pressure gradient effects.

For a control volume approach to mixing the exact mechanisms of mixing need not be

known to calculate the correct loss. Denton (1993) performed a viscous numerical calculation

of a compressor cascade for three cases for which the blade boundary layer and trailing edge

conditions were held constant, but the area downstream of the cascade was changed by 0%

and +/- 25%. The calculation showed about one third of the total loss occurred downstream of

the trailing edge. The change in area during mixing only affected losses by +/- 5%. A decrease

in area would correspond to an accelerating flow and stretching of the wake before mixing and

thus yields a decrease in losses. However, the current study will show that the wake stretching

in real machines is larger than the amount implied by Denton's study, thus the reduction in

mixing loss due to wake stretching is potentially greater, depending on viscous effects, than

the 5% considered here.

Hill et al. (1963) studied the effect of pressure gradient on the decay of turbulent wakes.

Wakes in adverse pressure gradients decay more slowly and there is a critical adverse pressure

gradient above which the wake grows instead of decaying. Wakes in favorable pressure gradi-

ents decay more rapidly. The work of Hill et al. is used extensively in the development of the

wake decay model in the present effort and will be discussed in detail later.

Wake transport in the stator is discussed next in the context that wake transport only redis-

tributes losses.

1.3 Wake Transport

Kerrebrock and Mikolajczak (1970) used a kinematic analysis to look at the influence of

upstream rotor wakes on the flow field of a downstream stator row in a compressor stage. The

rotor wake fluid has a lower relative velocity than the surrounding free stream fluid. From

velocity triangle arguments it can be shown that in the stator passage the rotor wake fluid will

have a drift velocity toward the stator pressure surface relative to the free stream fluid. As the

rotor wakes are chopped by the stator row, the higher total temperature rotor wake fluid drifts

NASAJCR-- i 998-206594

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