Flow pulsations on the rotor blades and intensity of free vortexes

Flow pulsations on the R blades were estimated by change in time of instant value of velocity circulation in peripheral sections of blades

r(i)= Tke2wk^ , і = , T0 = hs/u, (2)

к=—ж

where u is linear speed of moving of the given section; t is time.

Putting that y=v+-v- is difference of velocities on a pressure and suction blade surfaces, it is easily to receive the equation, connecting value у with pressure difference AP on blade

s

1 Of

-AP (s, t) = — I 7 (s, t) ds + t>o7 (s, t), (3)

0

where p is density of gas, vo = v+is a half-sum of velocities on a pressure and suction blade surfaces; s is length of airfoil camber line, counted from a leading edge. In assumptions of linearity (p=const, v0=const) the decision of the equation (3) gives expression for factors Гк of decomposition (2)

So

Г k = f —A Pk{s)e-lP^{So~s)ds, (4)

J pv0 0

^ h

E d ґ І2ттк-Рп APk (s) e ь*

к=-те

where S0 is full length of airfoil camber line, pressure difference for n-th R blade is expressed by the formula

and hR is a pitch of the R blades.

Thus, the formula (4) reduces calculation of a pulsation of velocity circula­tion on the R blade to definition of instant difference of static pressure in the system of coordinates connected with R.

The specified pressure difference was measured for assembly 2 of the com­pressor by six sensors of static pressure pulsations D, in regular intervals dis­tributed along an axis of the compressor above R blade on the external R case. The data from each sensor were registered with frequency of discretization

19,2kHz during 1 second, then from the received time series it was allocated a periodic component with the basic frequency equal to the R blade passing fre­quency. Thus phase-locked for all sensors was provided by synchronous data recording with the R speed sensor.

After similar data processing for various values of coordinate Y, determining simultaneous circumferential shift of the IGV and S for each fixed value v it is easy to receive experimental factors of the Fourier series of a kind

к=—<x l=-<x

where T = is the R blade passing period, P (s, Y. и, I ) is the instant static pressure, measured by the sensor to which arc coordinate s of airfoil camber corresponds.

For transition to the rotor (y, t) system of reference it is enough in decom­position (6) to make replacement of variables

Y = TP У ~ =t.

hs. g*27Tfcy

Then the Fourier series of a kind turns out

к = — <X l = -<X

determined for each coordinate y, counted along R blade to blade at the fixed time t. Instant difference of static pressure on the blade, determined as a dif­ference of maximal (on a pressure surface) and minimal (on a suction surface) values P for the fixed time obviously gives the series (5) with known factors APk (s, v).

At fixed number N=10 of various circumferential positions of the IGV and S the number of determined harmonics of series (7) obviously does not exceed 2 (k=0, ±1, ±2). Besides the integral (4) for six used sensors may be calcu­lated only approximately. Using linear interpolation AP к (s) between the next sensors for factor Гк the formula turns out

< Г >t — (< Г >t)v

(<r>t)„

is presented, where < Г >t and ((< Г >t)v are, accordingly, RMS deviation of Г from its time-average value and average value Г on v. For comparison on Fig. 5 values є0 = є0 (v) for 1/3 octava band with average frequency 1250Hz and total noise (see Fig.4b and 4e) are represented also. Comparison of de­pendences h (v) and є0 (v) allows to see that area of mutual positioning of the IGV and S, appropriate to the increased and lowered acoustic disturbances in the plenum coincide with areas of the increased and lowered periodic pulsa­tions on the R blades.

For an experimental estimation of intensity of sweeped by a fhw the peri­odic vortexes descending with the R blades it was used laser anemometry of fhw along a line LL parallel to exit front of the R on 8,75mm from it on mean radius of a flawing path [5]. The velocity pulsations was estimated by value

wi(v) =<< w(v, y,t) >t>y, w(v, y,t) = (W — Wo)n,

where W and W0, accordingly, are instant and time-averaged values of relative velocity in a point y of line LL, and (W — W0)n is a projection of a differ­ence (W — W0) on a direction of time-averaged and circle-averaged of relative velocity behind R.

On Fig.6 dependence

Wl И – (wi)„

Mv

is presented for the measurements, executed on a line LL for assembly 2. The received dependence is compared to value є о = є0 (v), received for 1/3 octava band of frequencies with the basic frequency 1000Hz (see Fig.4a). Apparently, dependences ^ (v) and є0 (v) are correlated, that allows to assume, that change of intensity of radiated noise in the specified band of frequencies is connected to its generation by the periodic vortexes, descending with the R blades.

Comparing the data on Fig.5 and Fig.6, it is possible to notice that areas v, providing lowered and increased noise radiation, are various for the noise, generated by fbw pulsations on the R blades and periodic vortexes behind them. It is possible to explain this circumstance to that, according to Thomson theorem, intensity of free vortexes is proportional to value дГ/dt, that as it is easy to see from elementary calculations, displaces values v, appropriate to extreme values of intensity of free vortexes, including for 1-st harmonic.

1. Conclusion

Measurement of noise, radiated system of the blade rows IGV-R-S of the axial compressor and appreciated on a reverberation chamber method, at equal number of vanes IGV and S has shown the following:

-radiated noise essentially depends on mutual circumferential shift of sta­tors;

relative change of total intensity of radiated noise in a frequency range of 25-20000Hz for not optimum and optimum values of stators clocking achieves 80% (~3,7dB).

Comparison of results of measurement of noise and fbw pulsations on the R blades and in vortical wakes behind R allows to assume that:

specified in item 3.1 clocking effects are caused by change, at mutual circumferential shift of stators, the tone noise, generated by pressure pulsations on the R blades (~5dB) and vortical wakes behind R (~1,7dB);

decrease of effect on total noise in a wide range of frequencies in compar­ison with effects of tone noise is caused by displacement of optimum mutual positioning of stators for various sources of tone noise.

The received results testify that optimization of a mutual circumferential position of stators in system of rows stator-rotor-stator an axial turbomachine may be used as effective practical means of decrease of the tone noise, caused by a rotor-stator interaction.