# Structure of unsteady flow in system of rows stator-rotor-stator of the axial compressor

Rotor blade fbw

The R flow analysis is based on measurements of static pressure pulsations on the R case with the help of 6 high-response sensors, uniformly distributed along an axis of the compressor within of an axial projection of the R blade from a leading (the sensor No.1) up to trailing (the sensor No.6) edges of R (see Fig.1).

On Fig.6 as illustration distributions on a R blade pitch (the sensor No.4, X = 0,6) of values AP(y, t) = P(y, t) — ((P)t )y, where P(y, t) is static pressure in a point of measurement are presented. Static pressure is expressed in the R system of reference and thus, corresponds to its blade to blade distribution at the various moments of time at fixed mutual circumferential position of the IGV and S (v = 0). Axis Oy is directed opposite to R rotation. The difference of the maximal and minimal values of AP reflects difference of static pressure on pressure and suction surfaces of the R blade, a little bit distinguished (to reduction) from true owing to leakages in a radial clearance.

The analysis of results of measurements has shown, that time-averaged values of static pressure difference A(P)t = (P)t — ((P)t)y practically do not depend on v for all investigated compressor assemblies 1, 2 and 3. Thus, averaged on time parameters of relative ft>w in the R do not depend on unsteady interaction of rows. The unsteady part of static pressure thus rather essentially depends on axial gaps, numbers of vanes in stators and their mutual circumferential position. Fluctuations of AP (y, t) on time for various sensors make 10 — 20% from it time-averaged value A(P)t. These fhctuations characterize unsteady interaction in system of rows stator-rotor-stator.

For an estimation of influence of v on an unsteady part of static pressure distribution and, hence, on aerodynamic loading on the R blades the value was used

m = Ry{t]v [Ry)t ■ ioo%,

(Ry )t

where Ry (t) is instant value of the linear circumferential aerodynamic load, acting on the R blade, and (Ry )t is it averaged on time value. Necessary for definition Ry (t) the difference of static pressure on the R blade was determined on measurements of static pressure on the case by sensors No.1-6. Examples of such measurements are submitted on Fig.6. Further, after project of the local loading determined thus on a circumferential direction, total loading was calculated as result of integration on 6 values of the local loading, received on each of sensors.

As illustrations on Fig.7 dependences of Г = r(t) for compressor assemblies 1 and 3 are presented at values v = 0 and 0,6. The similar data, received for all assemblies and various values v show, that the circumferential aerodynamic loading, acting on the R blade, has on the period significant fluctuation from 5 up to 10% from its averaged on time loading. Thus the amplitude of fluctuations of loading is essentially various for various values v, in particular for assembly 1. Thus, overall aerodynamic interaction of the R with IGV and S at their mutual circumferential shift is changed significantly.

Velocity fi elds behind the rotor

Research of a velocity field behind R is based on laser flow anemometry in an axial gap between R and S and calculation of viscous flow by the numerical simulation of averaged on Reynolds 2-D unsteady Navier-Stokes equations.

Influence of mutual circumferential shift of the IGV and S on time-averaged and unsteady parameters of a vortical wake is illustrated on Fig.8, where for three compressor assemblies the measured distributions on the R pitch of time – averaged relative velocities behind R |(W)t | /Wav and their RMS deviations on time < W >t for two values of v = 0; 0,5 are presented. It is visible

that distributions of |(W)t | /Wav practically coincide at v = 0 and v = 0,5. Thus, averaged on time fl>w parameters of the R blades do not depend from unsteady aerodynamic interactions of R with IGV and S.

Apparently on Fig.8 that unsteadiness of a velocity vector in a vortical wake behind R, estimated in the value < W >t, first, it is rather significant especial in the field of a vortical wake where it achieves 25% and more, and, second, essentially changes at mutual circumferential shift of the IGV and S. As one would expect, for assembly 1 of the compressor stronger inflience of circumferential shift of stators on structure of unsteady vortical wakes behind R, than for assemblies 2 and 3, is observed. Besides assembly 3 differs more a high level of unsteadiness in a flow core and less expressed clocking effect, that is connected to strong potential inflience of the S upwards on a stream owing to small (Д23 = 0,05) an axial gap between R and S.

On Fig.9 the data on measurements (W)t, shown on Fig.8 for the assemble 1, are compared to results of direct numerical simulation (see item 2). Apparently, calculation well is coordinated to experiment in a flow core and considerably differs in the zone of vortical wake.

As a whole the received data testify that at a rotor-stator interaction flow velocity pulsations appear behind the R, especially significant in the zones of vortical wakes. From here it is necessary to expect that stators clocking most essentially may affect on value << w >t>y, which determines RMS deviation on the R pitch of RMS deviation on time of a velocity vector. Really, dependence from v value << w >t>y, presented on Fig.10 for various compressor assemblies, shows essential influence of stators clocking on velocity pulsations in vortical wakes, in particular for assembly 1. The detailed description of structure of vortical wakes behind R blades is given in [15, 16].

Pressure pulsations behind R

Measurements of stagnation pressure pulsations were made by the insert probes, equipped with high-response sensors, on mean radius in an axial gap behind R and on an exit from the compressor. By results of static and dynamic calibrations receivers of probes are insensitive to a fl>w angles ±15° and have the uniform amplitude-freauency characteristic up to frequency 20kHz.

For an estimation of influence of the R and stators interaction on a level of stagnation pressure pulsations Pt2 (behind R) and Pt3 (behind S) values were used

[< (Pt2)t >y? + [«Pt2 >t>y]2 – 12 (< Pt2 >t )y

where Pt2 and Pt3 are expressed in the stator system of reference. It is easy to notice, that for isolated R and S values SPt2 and SPt3 are equal to zero and are nonzero for interactive rows. SPt2 and SPt3 were determined both for periodic (SPt2,3 )p and for random (SPt2,3)r pressure pulsations. Thus in expressions for SPt2 and SPt3 denominators are determined in both cases by a periodic part of pressure pulsations.

Dependences of values SPt2p, SPt2r and also SPt3p, SPt3c from parameter v are presented on Fig.11 for assembly 1. Apparently, behind R the periodic part of stagnation pressure pulsations, caused by vortical wakes, considerably surpasses random component and essentially depends from v. On an exit from the compressor, on the contrary, random component has essentially increased concerning periodic component, which poorly depends from v. The similar result is received also for assembly 2.

Undoubtedly the received data testify to evolution of vortical wakes behind R, which dissipate during mixture.

The increase of random pulsations concerning periodic pulsations on all compressor assemblies is shown also for static pressure p, which pulsations were measured on mean radius on the S vanes. Measurements were carried out by 12 high-response sensors, which were allocated in regular intervals along suction and pressure surfaces of the next S vanes (on 6 sensors on one vane) from leading up to trailing edges.

As an illustration on Fig.12 dependence from v value is presented

< P>t

A (p)t for the sensors No. 4, located on middle of a S vane chord from the suction and pressure sides. Here Ap = (pp. s.)t — (Ps. s.)t is difference of time-averaged static pressure. The value A is presented for assembly 1 both for periodic (Ap), and for random (Ar) components of pressure pulsations of p.

Apparently from Fig.12, both on suction and pressure sides of the S vanes random pressure pulsations practically do not depend from v and surpass periodic pulsations, for which dependence from v remains appreciable.

The important conclusion follows from results of measurement of value A(p)t for various mutual circumferential positions of stators. Dependences from v of A(p)t are presented on Fig.13 (assembly 1) for 5 pairs of sensors, where sensor No.1 and No.6, accordingly, concern to vicinities of leading and trailing edges of the S vanes. The received data show that as distributed and

overall averaged on time aerodynamic loading on the S vanes practically does not depend on a mutual circumferential positions of the IGV and S vanes.

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