UNIVERSITY OF MICHIGAN DEPARTMENT OF MECHANICAL ENGINEERING CAVITATION AND MULTIPHASE FLOW LABORATORY Report No. UMICH 014571-1-T INVESTIGATIONS OF SECONDARY LIQUID PHASE STRUCTURE IN STEAM WAKE (submitted to ASME) by S. Krzeczkowski W. Kim F. G. Hammitt J-B. Hwang Supported by: National Science Foundation Grant Nos. ENG 75-2315 and GK-40130 and National Academy of Sciences (with cooperative program with the Polish Academy of Science) June, 1976

INTRODUCTION Wet steam flow has been studied for the break-up of liquid films on flat plates inserted parallel to flow at the trailing edge, as well as liquid droplet stability and disintegration. Some results are shown in this paper. Moving rotor blading erosion of steam turbine final stages is considered to be still an important problem from the technical and economic point of view. Because of this fact, there is a reason to investigate the liquid phase behavior inside the turbine. In particular, several problems are particularly interesting: 1. condensation of the steam in state downstream of the Wilson line 2. small (A 0.05 pm) primary droplets settling upon blades surfaces and liquid film motion due to aerodynamic and centrifugal forces 3. large secondary drop motion and structure 4. erosion of turbine blading and methods useful in avoiding erosion damage The matter under consideration here concerns the third group of problems. A thin liquid film flowing upon a fixed blade disintegrates at the trailing edge, due to aerodynamic forces. The droplets thus formed are believed to be about four orders of magnitude larger than the primary droplets in the wet steam due to condensation. The maximum droplet size which has been estimated based on theoretical approach (1) for the last stage

-2of the turbine was around 300 pm, and other authors have expected droplets to be larger than 1 mm (2),(3), using experimental turbines for their research. The main purpose of the work hereby presented is to measure the relationship between droplet stream structure and the flow conditions. This has been done according to the suggested procedure of J. Kryzanowski (4) in his work at the University of Michigan. EXPERIMENTAL EQUIPMENT USED Figure 1 is a schematic representation of our experimental facility and the pertinent flow parameters are as below: (P3 )ax = 3.75 psia = 0.258. 105 N/ 2 (saturated steam) P4 = 2.55 psia = 0.17S.10 m N2m Maximum Mach Number is - 0.75. The test section is located after a stilling tank which is supplied with low pressure steam from the laboratory heating supply ("'5 psig, 0.9 quality). A diffuser then guides the steam to a jet-cooled condenser. The test section is of plexiglas, so that the liquid droplets downstream,as well astlh liquid film upon the inserted flat plate,can be easily observed This plate, which replaces a turbine fixed blade, is located inside the test section (Fig. 2). A thin liquid film was obtained upon the blade by means of a slot placed near the leading edge (Fig. 3). Water flow-rate was measured by a flow meter, and liquid film thickness by means of the residencd

-3gage method (5), (6), using four gages in the plate surface. The flow rate and liquid film thickness were as follows: c = 2.5,10 cm3/(cm.min) h = 50'. 250 Pm The liquid film on the plate appeared first to disintegrate into liquid filaments, and next into "secondary" droplets (Fig. 4 ). These then pass downstream in the aerodynamic wake, still being disintegrated due to the increasing aerodynamic forces, since the velocity of the wake increases with distance downstream from the trailing edge. This liquid-phase behavior was studied photographically. The camera was located as close as possible to the test section, producing a magnification of 2 2.4x. A light flash duration of 1 us has been used, with light source perpendicular to camera axis (Fig. 2). This was most suitable,as pictures so taken were sharp and with good contrast. Several typical pictures are included in this report (Fig. 4-9). Droplet size measurement capability was, however, limited to droplets above r' 50 pm diameter because of limited optical resolution of the camera and film. Smaller droplets had too great velocity to be recorded with the available flash duration. These limitations proved most significant at high Mach number (M - 0.75), and relatively long distances downstream of trailing edge. We hope to develop another method for small droplets well downstream and at high Mach number. This method will be based

-4on laser light scattering from small particles, and should be useful for the measurement of 1 -.r 20 pm droplets. RESULTS OF THE EXPERIMENT Because of the erosion threat to turbine blading, informatio of maximum droplet size is important. Many photographs ( - 300) have been made at three Mach numbers; M = 0.35; 0.55; 0.75 and at three values of the flow rate: q= 2.5; 5.0; 10.0 cm Acm. min). Several relationships have been obtained. These are presented in Fig. 10-12. All large droplets provide data points on these graphs according to their distance downstream in aerodynamic wake (x-coordinate). The relationship between maximum droplet size and distance downstream,D = f(x), is established as a max limiting line above the area of the data points. This function has been shown as a belt because the process of liquid phase disintegration is very non-uniform. The function Da= f(x) decreases with distance x until max x e 20 cm and then remains essentially constant. It is independent of liquid flow rate for this experiment. However, the shape of the curves depends very strongly on the Mach number (Fig. 13 ). To allow application of these results for other conditions, a more universal relationship has been generated. Using the results of Fig. 13, and transforming them into a dimensionless function of Weber number, We = f (M), max

the relationship of Fig. 14 was obtained. Here We = D = maximum droplet size, from center of data scatter, at distance x = 22 cm, assuming maximum droplet size to be approximately constant for distances longer than x = 22 cm Vc:, = the velocity of the steam outside of the aerodynamic value Results obtained by other authors are also presented, i.e., Weigle and Severin (7), using an air tunnel, and Valha from a steam tunnel (8). To obtain further information on liquid droplet stream structure, still another approach was applied. Based on several droplet pictures (Fig. 4-9 ), a droplet size distribution function has been established. This function is defined as follows: d N(d) 1 N Ad whe re: d = droplet size Ad = droplet size interval (Ad = 200 Em for presented experiment) N(d)= average number of droplets of the size enclosed in the region (d A d d + 2 2 N = average total number of the droplets visible in the test area. In order to obtain the above function, droplets visible on the picture were counted according to their sizes (using a magnifying glass with scale). Consequently, the droplet size distribution

-6function was used to establish a droplet mass distribution function: N(d) d. F(d.) m(d) 1 i di) 1 i F(di) R(m) m Ad ==n Ad i=n d i=n Ad d3 N(d.) di F(di) i=l i=l where: m'(d) = average mass of droplets of the size enclosed in the region (d n, d + ) 2 2 m = average total mass of the droplets visible in the test area. d max n Ad Both functions were normalized in order that the integral is equal to one. The results'of the experiment reduced to size and mass distribution functions are shown on Figs. 15-18 for the following values of the Mach number: M = 0.35 M = 0.55 To be sure, both functicns are being changed according to the distance x; the ratio of large droplets decreases, and the ratio of small droplets increases. The same effect takes place as Mach number increases. The highest probability of droplets occurring (the maximum of the function of probability density) is shown below in the conclusions. WUnfortunately it was impossible to obtain any droplet size mass distribution function at Ma = 0.75. The cause has been dis cussed above. The same difficulty appeared for long distances (x) between the trailing edge and the test area.

-7CONCLUS IONS 1. The maximum droplet size function D = (x,M), decreases with the distance x and Mach number M. D becomes max constant for distance x - 22 cm. In this region, maximum droplet size varies with Mach number. M = 0.35; max = 750 pm 0.55; 500 pm 0.75; 250 pm The variation of D with respect to x and M proved to be max different than had been estimated theoretically based on the steam velocity distribution in the aerodynamic wake and assumed critical Weber number, (We = 13) (1). Droplet diameter here measured is at least twice that estimated before. 2. The critical value of the Weber number We V Dmax has been estimated as follows: M = 0. 35 We = 30 M = 0.5; 0.75; We - 45 (Fig. 14) 3. The most probable droplet size to appear in the aerodynamic wake, in the vicinity of the trailing edge (x = 2.5 to 4 mm), according to the size distribution function is: M = 0.35; d= 250 M M = 0.55; d - 133 V and according to the mass distribution function: M = 0.35; d - 500AW* M = 0.55; d 475 it 4. There is no significant influence of (water) liquid film ~ 3 flow rate (up to q = 10 cm /cm.s) on the maximum droplet size D max and on the droplet size and mass distribution function F (d), Rmm or

REFERENCES 1. Puzyrewski, R. and Krzeczkowski, S., "Some Results of Investigations on Water-Film Break-Up and Motion of Water Drops in Aerodynamic Trail," IFFM Trans., 29-31, 1966, Gdansk, Poland. 2. Christie, D. G., and Haywood, G. W., "Observation of Events Leading to the Formation of Water Drops Which Cause Turbine Blade Erosion," Phil. Trans. Roy Soc., 260 SA, No.l1 London, 1966. 3. J. P. Faddeev, Proceedings of the III Conference on Steam Turbine of Great Output, Prace IMP-PAN, Gdansk, Poland, 197q 4. Krzyzanowski, J., "Wet-Steam Tunnel Facility-Design and Program of Investigations", ORA Report No. UMICH 03371-18-T) Univ. of Mich, Ann Arbor, Mich., 1972. 5. Puzyrewski, R. and Jasinski, R., "Measurement of the Thicknd of Thin Water Films by Resistance Method," IFFM - Trans. Noi 1965, Gdansk, Poland. 6. Mikielewicz, J., Hammitt, F. G., "Generalized Characteristid of Electrical Conductance Film Thickness Gauges," Proc. 6th Steam Turbines Large Output, Pilsen, Czech. 16-19, Sept. 191 ACKNOWLEDGMENTS The financial support of this investigation is provided by National Science Foundation Grants No. ENG 75-2315 and GK-40130. The authors are indebted to Professor Jerzy Krzyzanowski, Institj of Fluid Machibiery, Polish Academy of Science, Gdansk, for the Dreillninary design of the facility and constant helpful suggestid

List of Figures Figure 1 - Schematic Diagram of the University of Michigan Steam Tunnel (4) Figure 2 - Schematic of Test Section and the Position of Camera and Flash (4) Figure 3 - Schematic of Blade with Gases Figure 4 - Photographs of Liquid Film Disintegration into 3 Droplets at the Trailing Edge, M = 0.-, q = 5 cm /cm.min. Figure 5 - Photographs of Liquid Film Disintm-ration into Droplets at the Trailing Edgqc, iv = 0.55, q. = 25 cm3/cm.min. Figure 6 - Photographs of Liquid Film Disintegration into Droplets at the Trailing Edge, M = 0.75, q. = 5 cm3/cm.min. Figure 7 - Photographs of Liquid Droplets Distribution in Downstream Flow, M = 0.35, q = 10 cm3/cm*min., X = 14 cm Figure 8 - Photographs of Liquid Droplets Distribution in Downstream Flow, M = 0.55, q = 10 cm /cm-min., X = 14 cm Figure 9 - Photographs of Liquid Droplets Distribution in Downstream Flow, M = 0.75, q = 10 cm3/cm-min, X = 5 cm Figure 10 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge, M = 0.35 Figure 11 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge, M = 0.55 Figure 12 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge, M = 0.75 Figure 13 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge at three Mach Numbers Figure 14 - The Weber Number of Maximum Droplets for Downstream From the Trailing Edge Figure 15 - Droplet Size Distribution Function at M = 0.35, X = 2.5 cm and X = 4.0 cm. Figure 16 - Droplet Size Distribution Function at M = 0.55, X = 2.5 cm and X = 4.0 cm. Figure 17 - Droplet Mass Distribution Function at M = 0.35, X = 2.5 cm and X = 4.0 cm Figure 18 - Droplet Mass Distribution Function at M = 0.55, X = 2.5 cm and X = 4.0 cm.

The Scheme of the Facilit.. GST t2 P r'Ti V SILENCER EST DIFFUZER I I! GG'P4C jGp FLOAT VALVE Gcw MIXING CONDENSER 3502 /<h 4 5_ _./ Figure 1 - Schematic Diagram of the University of Michigan Steam Tunnel (4) A..h_ ~~

ADA PTOR ABOUT 100+1 50 _ ~ FI DIM SCREEN _ ~ ~ FLASH 836 Figure 2 - Schematic of Test Section and the Position of Camera and Flash (4)

I I U. M. Gage IFFM Gage U. M. Gage U. M. Gage Ii j Mod.]I Mod. 3 Mod. 2 Mod. 2 7-7/8 Water - Inlett. — 3/4 -1-1/2' - - /2 1-3/i 0.A52 1 I 1 625c Figure 3 - Schematic of'Blade with Gases

Droplets atance f the T railing Edge, M =.35, q = 5 cm/cmi - a n,,,,,,,,* >,..>.,.&..,....,.......,.X= Ace.:v..ssz:.e<XD Z i.z. ax X >... 8...... %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......... I cm 2 cm 3 em Figure 5 - Photographs of Liquid Film Disintegration into Droplets at the Trailing Edge, M = 0.55, q. = 25 cm3/cm- hin i ki.:iii::i~ii~ii R-7l:i~i l:::::::::::l:''::'''':'::i::::: i;~::-:ii::i:ii-iiii I 4 - A:'i'"'~iici~i:i:'::: i::;iii,

8 Distance from trailitng edge I cm Z cm 3 cm Figure 6 Photographs of Liquid Film Disintegration into Droplets at the Trailing Edge, M = 0o75, qo = 5 cm3/cm -min, Distance fro tafinedge, Figure 7 ~ Photographs of Liquid Droplets Distribution in Dow0Mnstream. Flow, M = cm35 D = = 14 cm 4'~~"<~~8 b

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f12t0.35 p 2.5paia O.1V bar O X - ro /,cm -min fo %'-5.o crr/-m'mir 3.0 E 2 X Li, * X * X*@o Xo.o 0 o o o 0 0 0 0 ~ Z 4 It )1 18 10 Z 8400 Figure 10 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge, M = 0.35

M/Wa 0.55;' Z.55 psa Y o.Io,/ baOr -2.5 c/m.cvenrntn g-5.0 cm1/cmvmi.m 0.0 to0.O cr /c. lr 3.0-' ~!E X~X [W //' " Figure 11 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge, M =.55 0 )c ),X KI:K e 2 t 4 6 8 io lz 14 I( LB 20 2Z 841 Figure 11 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge, M = 0.55

[1~ ~~~~~~~~ ~~Ma,,D o.; 75 p. scia o.18 bar t ~~~~~~~~~~~~~X 9,25cm3/cmflmaii o 0 cP/cern-rain 3.0 40.0 cr~ /m. rn/ln ~2.o -o L..J I X'~~.O o' 4.o.~~~ O~~ O e~ o oxo T 00y x~-~ 0 0 00 o 2 4 G 4O 12 14 I 20 2Z o 842 X rcm] Figure 12 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge, M = 0.75

p. 2.s5'p55 o.a 18 bar 3. o2 2.5 40. 0 cm /em. mn 2.0 750 z 4 6 8 /i IZ 14 1b 08 20 22 843 Figure 13 - Maximum Droplet Size as a Function of the Distance From the Trailing Edge at three Mach Numbers

Ev Perrnle ts: * - lrzerezkowskiS.+ kinW.'74,4, _ Valhk, 1q70 WcOb| p= Z55psaia- O.:r -. Valha, I147Z e| X t'leB. S5eve'rin,H.'71 60 \ so X // - 30 20 /0 0.1 O.Z 0.3 O.4 0 0.$ 0.t, 0.7 O. 0.9 /.O 844 Figure 14 - The Weber Number of Maximum Droplets for Downstream From the Trailing Edge

Mat 0.55 p-2.55 psrf a o. 8 kr z2.5 1 0.0 cr/,V'm mmnn X =.25 cm 1.0i,II \\< / X- t rn i' Zc200 400 600 800 1000oo 4200 4400 MI M'J 845 Figure 15 - Droplet Size Distribution Function at M = 0.35, X = 2.5 cm and X = 4.0 cm.

MOI= 0.55 p z.5 ps ia 0 o. 18 bar - 2.5'4o0.0 I / eOn min z — 2. 5~n I' I.o~i I I,: i; o 200 400 600 800 40oo 2oo 4400 d[ 846 Figure 16 - Droplet Size Distribution Function at M = 0.55, X = 2.5 cm and X 4.0 cm.

Mcr 0.35 ~1 p3 15ssi a"'cO. Is bar 4'2.3 *1O.O cvn%nm~rnn ui 1.0 -~~~~~~~~~~ V 500 1000 4oo 5 2000 25C'O 847 Figure 17 Droplet Mass Distribution Function at M = 0.35, X = 2.5 cm and X = 4.0 cm

MaA; 0.55 2.55 p5iCa a0. o1 ar ~~1 5 k / /6~ ~ ~ ~~g 2..5 — 1o.o cm/rn aMin X/ 2.5 cni Io0 Os 500 t L 4500. 2 ~500 tro 42000 2500 848 Figure 18 - Droplet Mass Distribution Function at M = 0.55, X = 2.5 cm and X = 4.0 cm.