University of Michigan Department of Mechanical Engineering Cavitation and Multiphase Flow Laboratory Report No. UMICH 012449-20-I-a DATA REDUCTION PROCEDURES -STEAM TUNNEL FILM THICKNESS TESTS by A. Mancuso F. G. Hammitt S. Blome J. B. Hwang (Submitted by A. Mancuso in partial fulfillment of ME 600) Supported by: NSF Grant GK-40130 June 1975

SUMMA RY A low pressure steam tunnel has been constructed and is currently in operation at the University of Michigan. The steam tunnel is being utilized to study droplet erosion on turbine blades caused by low pressure moisture formation. The purpose of this report is to describe the procedures involved in reducing the data obtained from the steam tunnel and comparing it to theoretical predictions. Presented in the Appendices are the experimental results and the theoretical predictions. The theoretical predictions for the liquid film are based on a one-dimensional Couette-flow model. For the steam flow calculations, the velocity profile is assumed to be fully developed.

LIST OF FIGURES 1. Forces Acting on the Steam Flow 2. Friction Factor as a Function of Reynolds Number 3. Liquid Film Velocity Profile 4. Dimensionless Minimum Film Thickness as a Function of Contact Angle 5. Product of Characteristic Factor and Specific Conductivity vs. Temperature 6. Generalized Characteristics of Electrical Conductivity Gauges 7. Electrical Conductivity Gauge Calibration Curve

I. INTRODUCTION Under National Science Foundation grant GK-40130, the University of Michigan is researching droplet erosion on turbine blades caused by low pressure moisture formation. Therefore a low pressure steam tunnel and two blading profiles have been designed and constructed. This equipment has been described previously (1-3 e.g.). One particular area of concern in this research program is the formation and break-up of the liquid film created on a stationary blading profile within the steam tunnel test section. The thickness of the liquid film under various steam flow conditions is determined experimentally and then compared to theoretical predictions. I have been involved in reducing the data obtained from the steam tunnel and comparing it to theoretical predictions. This report describes the procedures involved in reducing the data obtained from the steam tunnel and comparing it to theoretical results, The theoretical predictions of the liquid film thickness under various flow conditions are based on the work of Drs. F,G. Hammitt, J. Mikielewicz and J.B. Hwang. The experimental data obtained from the steam tunnel includes measurements of the steam line and test section pressures and temperatures; and the temperature and flow rate of the liquid film. The liquid film is formed on the stationary blading profile by injecting a salt water solution on the upstream surface of the blade. This procedure has been described previously ( 3 eg.).

The steam velocity is determined by orifice and pitot tube pressure difference measurements. The liquid film thickness under various flow conditions is determined from the resistivity readings of four guages installed in the stationary blading profile. The electrical conductivity guages used in determining the film thickness have been described previously ( 4 e.g,) II. PREDICTED SURFACE STRESS OF THE LIQUID FILM AS A FUNCTION OF STEAM VELOCITY blade 2 Fig. 1 Forces Acting on Steam Flow

Applying force equilibrium in Fig. 1, we obtain, tP(ac) = steam2(ab) + Ywall2(bc) steam wall If we assume that Csteam = rwall = film' then (ac) AP Tfilm 2(ab) + 2(bc) whe re, ~= surface stress (lb/in2) AP = pressure difference (lb/in2) For our particular steam tunnel configuration, a = 3.15 in b = 4.5 in c = 1.575 in there fore, (3.It5)(1.575) p fim = 2(3.5)(4.5) + 2(4.5)(1.575) Tfilm =.1167 AP (1) Equation 1 is a fixed relation between T andLPfor our particular steam tunnel configuration. The pressure drop,&P, can be determined from the relation) EL,, a v, 4A P~~~~~~

where, = friction factor L= characteristic length (in) DHY~O hydraulic diameter (in) -Swh.= density of the steam (lbm/ft3) VS+t= velocity of the steam (ft/sec) 4aP= pressure drop (lb/in2) for our configuration, L =4.5 in DHYD = Wetted Perimeter 2= 3 15) + 2( 2575) therefore, AP = 2.3X10O4f7LJStm Stk The friction factor,;, can be gotten from the Moody chart, Fig. 2, as a function of Reynolds Number and pipe roughness. For our calculations we assumed a smooth pipe. The Reynolds Number can be calculated using; Re = Js+m DUYD V5+ where, /5f,~= viscosity of the steam (lbm/ft-sec)

0.07I 0.09 - Lom.no,... _.... _, ] f!.LnP - -- o omp/lee turbulence, rou1 ptp-' ~ 1 - 0 07, ii i -eloveuohness -CI/D= 0.05 _i j_.L-J-~.?~ I I i~ l-iI --- i I I I i i I -''oo. — 6= 0-0 0.0-' 0O CIDl = 0'03 Fheynois number p =,VD/, McGra"-Hi. lnc. Ui.d wih pcrmision of McGrt'w-Hui- Book Company. Adapied I,.m: L.F. Mood'. iwn'. _ == 00 0' 0.05 7I oS8J. c:671. 0l9; I, I ~ I r~ = i I iii ~ t I ~ "~~~~~-00, 0.03 ~..,..: Fioure -2. ) 5 0 2 4605' 2AeO 5 4 56 RO(GH 680 0 F(.02 It 0\ARI~yoU= nube 000 O'F-rom' ENGINEERING EXPERIMENTATION by G.L. l u%' and L.C. Dornholdt Copyrip.~: r l'9t h% McGTrau -Hill. inc. [3~d w,,th permission of McGraw-Hill Book Company. Adapied from: L.F. Mood%.;7rton /SS4f. $ 6:671. 19,44 Figyure -2, FRICTION FACTOR BASED ON RELATIVE ROUGHNESS FOR V'ARIOUS KINDS AND SIZES OF PIPE'

III. PREDICTED LIQUID FILM THICKNESS CALCULATIONS V * max l'iSd~,,,,,, _ h Fig. 3 Liquid Film Velocity Profile The liquid film thickness, h, can be estimated in the following manner, Tfilm I V.V (2) whe re, /,.Aliq= viscosity of the liquid film (lbm/ft-sec) Vmax = maximum liquid film velocity r = volumetric flow rate of the liquid film Rearranging equation (2), we obtain. h = / -- — Xand if, and V a max hL

then hrFILM hAR A, or h2= 0.038 /lLq rrs i For our configuration h=.375 ft in the above equations. IV. CALCULATION OF STEAM VELOCITY FROM THE ORIFICE READING The velocity of the steam can be calculated from the pressure difference measured in inches of Hg. by an upstream orifice. The derivation of the relation to be used is as follows; Vsteam = Ww / 3600 A where, Ww = mass flow rate of the steam (lbm/hr) /M = specific volume of the steam (ft3/lbm) A = area of the test section (ft2) 2 (for our configuration A =.069 ft ) Vsteam = steam velocity (ft/sec) and (Reference No. 8.) W = 2781,72 Pf

where, HHg inches of mercury manometer head f = steam line temperature (OR) Pf = saturation pressure at the steam line temp. (lb/in2) V. CALCULATIONS INVOLVED IN DETERMINING THE CRITICAL FILM. THICKNESS — (Ref. 5) The relations used to determine critical film thickness as a function of contact angle are from Fig. 4, tcrit - ii i ir i Ci' (,~['/ a - (C then, kCelt-' Cc2. n24 where, o0 = liquid droplet contact angle = viscosity = density = surface tension

D~~ ~~ ~ 0 _ _ _ _ _ 0 0_. S ~ ~ ~ ~ ~ ~ ~:-.... ~......... (b~~~~~~~~~~~~~.

The derivation of these relations are described by Mikielewicz and Moszynski in a report for the Polish Institute of FluidFlow Machinery entitled "Shear Driven Liquid Film" (5 e.g.). VI. CALCULATIONS INVOLVED IN DETERMINING THE LIQUID FILM THICKNESS AS A FUNCTION OF RESISTIVITY The liquid film thickness, h, is measured. experimentally in the steam tunnel in terms of resistivity, R,-by four electrical conductivity guages. The film thickness is determined from Figs. 12 and 14, which contain plots of film thickness versus resistivity reading for a liquid film temperature of 130~F and 70~F respectively. The procedure required to obtain these curves, together with sample calculations will be outlined in the following discussion. This procedure has been discussed previously (2-4,6 e.g). In obtaining a curve of liquid film thickness versus resistivi reading, Figs. 5, 6 and 7 are used. Figs. 5 and 6 concern the generalized characteristics of the four electrical conductivity guages and Fig. 7 concerns the calibration, of the bridge used in measuring resistivity. The first step in obtaining curves for the film thickness as a function of resistivity is to obtain an average value for the product of the characteristic factor and specific conductivity, Cg0, at the specified temperature. C is a guage constant which depends upon the guage geometry and materials used in its construction. is specific liquid conductivity. Cg as a function of temperature is plotted

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in Fig. 5. The next step is to arbitrarily select a resistivity value and assume a value for the film. thickness at that resistivity. Then using Figs. 6 and 7 respectively, the values for the thickness function, f(h), and the proportionality constant, K, are obtained at the assumed film thickness. The next step is to determine the conductivity, C, utilizing the relation C = K/R. The thickness function can now be calculated using the relation f(h) = C/CgC. The calculated value for f(h) is compared to the value of f(h) obtained earlier from Fig. 6 for our assumed film thickness. If the two values of f(h) agree, then the assumed film thickness is the correct value corresponding to the selected resistivity. If the two values of f(h) do not agree, then the assumed film thickness at the selected resistivity is incorrect. Therefore a different value of film thickness is assumed. The procedure continues until the calculated value of the thickness function agrees with the value obtained from Fig. 6 at the assumed film thickness. To further clarify the procedure involved in determining the film thickness from the resistivity reading a sample calculation is provided below. If the temperature of the liquid film is 126.07 OF the average value of C t is 322(ohm-cm)-1 from Fig. 5. g We then select a resistivity of 1.Q and want to determine the film thickness to which this resistivity corresponds. We assume that at R = 1.0 the film thickness is 0.984 mils. Referrinr to Fig. 6, we find that at h =.984 mils the thickness function, f(h), is.984 ohm2 cm 1 Referring to Fig. 7, we find that 14

K = 316.8 at h =.984 mils. Therefore C = K/R = 316.8/1.0 = 316,8. We can now calculate the thickness function. f(h) = C/C 6= 316.8/322 =.984 ohm2 cm g The calculated thickness function value is equal to the value obtained earlier from Fig. 6 at the assumed film thickness of.984 mils. Therefore a film thickness of.984 mils corresponds to a resistivity of 1.0. -15

References 1. J. Krzyzanowski, "Wet-Steam Tunnel Facility - Design and Program of Investigations," ORA Report No. UMICH 03371-18-T, June, 1972. 2. J. Mikielewicz, F. G. Harnmitt, "Generalized Characteristics of Electrical Conductance Film Thickness Guages," ORA Report No. UMICH 012449-7-I, December, 1974. 3. F. G. Hammitt, J. Mikielewicz, G. Ernst, D. Krause, L. Rockwell, "Steam Tunnel Program and LiQuid Film Thickness Guage Develomentrs at.-e University of Michigan, " ORA Report N o. UMI CH 01 244 9-6-T, Jan. 1975 4. F.G. Hammitt, D.N. Linh, J.E. Tully, G.C. Ernst, J.B. H-jwang, D.A. K, N.R. Bhatt,'"Film Thickness Electrical Conductivitv Gages - Detailed -U zati on Procedure for the U-M Wet Steam Tunnel," OR~A Report No. UM' C 16-1, April 1!75. 5. J. Mikielewicz, J.R. Moszynski, "Shear Driven Liquid Film," Transactions of the Institute of Fluid-Flow Machinery, 66, 1975, p. 3-10. 6. F.G. Hammitt, J.B. HI-wang, A. Mancuso, D. Krause, S. Blome, " iicuid Fi.: Thickness Tests - Wet Steam Tunnel, " ORA Report No. UMICH C0li z- 9, 1c75. 7. G. B. Wallis, "One-Dimensional Two-Phase Flow,'McGraw-Hill, 1969. 8. L. K. Spink, "Principles of Flow Meter Engineering, " Foxborough Co., Foxbort Massachusetts, 1958.

Appendix A - List of Tables 1. Critical Film Thickness and Steam Velocity at Various Wetting Angles 2. Film Thickness for Various Resistivities, Gauges 1 and 3 Tiq= 126.070F 3. Film Thickness for Various Resistivitiec, Gauges 2 and 4 T= 126.070F liq 4. Film Thickness for Various Resistivities, Gauges 1 and 3 Ti 700F liq 5. Film Thickness for Various Resistivities, Gauges 2 and 4 Ti=700F 6. Predicted Film Thickness at Various Flow Rates, T = 126. 070F 7. Experimental Film Thickness at Various Flow Rates, T = 126. 07 F 8. Predicted Film Thickness at Various Flow Rates, T = 70 0F 9. Film Thickness vs. Axial Position -17

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Table 2 - Film Thickness (h) for Different Resistivities at Tq = 126.07 F GcLUges 1 and37 Blade 1, Mixture 4/22/75 cg= 322Z I C 4LC u AT FA --! 4 c/c | k, | — C 1C/ T — h,3 17 q9 53 183'3 53 73I tS - I - 1 - I - -- -- I -- --- ------- --- # qS — -82 6 J,- 7 -. fJ~_ —_; _ -- - 1- I_ 11170 -S- jI 4 - - — 2..@ I?_ ~-... - ID.. - - ~ ~ ~ -, - — I- -1 — -I -—.. -- ---— lX13 -~ — 1.-2 —7 [ _ 38.L l_:~e7,g~l —- /t 3 _21, I -*1-* # — — 1- w 4-E q - --- 1-; —- 3/6'8 1 —;3/48. [~~~~~~~~~~~~~~~~~~.8 X7... -S - ---- ~ _' I.. -. - -..- 1 "'..'.''.' ~~ "1 —'-,.::. — --; 1'.- - I' A, ik I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"

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Appendix B - List of Figures 8. Shear Stress of the Liquid Film vs. Film Thickness/(flow rate)l/2 9. Shear Stress of the Liquid Film vs. Steam Velocity 10. Critical Film Thickness vs. Steam Velocity, Tliq 130 F 11. Critical Film Thickness vs. Steam Velocity, Tliq- 700F 12. Film Thickness Function vs. Resistivity, T1 = 126.070F liq 13. Film Thickness vs. Resistivity, Tiq 126.070F 14. Film Thickness Function vs. Resistivity, T 70 F liq 15. Film Thickness vs. Resistivity, Tli 70 F liq 16. Film Thickness vs. Steam Velocity for Various Liquid Film Flow Rates, Tliq =126.07 0 17. Film Thickness vs. Steam Velocity, Flow Rate = 5 cc/min. 18. Film Thickness vs. Steam Velocity, Flow Rate = 10 cc/min. 19. Film Thickness vs. Steam Velocity, Flow Rate = 20 cc/min. 20. Film Thickness vs. Steam Velocity, Flow Rate = 30 cc/min. 21. Film Thickness vs. Steam Velocity, Flow Rate = 40 cc/min. 22. Film Thickness vs. Steam Velocity, Flow Rate = 50 cc/min. 23. Film Thickness vs. Steam Velocity for Various Liquid Film Flow Rates, Tiq=70 F liq 24. Film Thickness vs. Blade Position, V = 200 f/s steam 25. Film Thickness vs. Blade Position, V = 252 f/s steam 26. Film Thickness vs. Blade Position, V = 505 f/s steam 27. Film Thickness vs. Blade Position, V = 840 f/s steam 28. Film Thickness vs. Blade Position, V = 1042 f/s steam 29. Film Thickness vs. Blade Position, V = 1288 f/s steam -33

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i~~~~~~~~~r I ~~~~~~~~~ ~ $~~~~~~~~~~~~~~~~~~~~~~~~ o -~'"'1 o; \ ~~~~~~~~~~~~~~ —-- o o o. ~ ~ ~ ~ ~ ~ ~ ~ ( ca ~ —~~~~~~~~~~~~~~~~~~~~~ V~~~~~~~~~~~~~~~~~ o _ ~,) ~~~~~~~ ---- T ~ -....'. Y:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -c i -l ~ -. i, T r~~~~~~~~~~~~~~~~~.-~:'"'!'i~"': —:':-::........... ~... i-' 11 ~ 41~~~ ~ ~~~~~~ ~~~,-._ - ~ --.~. ~...- -_C — " — ~~~~~~~~~~~~~~ — ~- ~~~~~~-~- ~........ i;~. —.-...'-~~~~...1. -- ~~~~~~~i-~ ~- tr --— ~ ~-'...... -...............~C ~_.o —..... ~rrrr~rr~-...~C o~............

:' I' t'' ~ ~ ~ ~ ~,: ~LI. I ~ i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~'-I ]li I~~ ~ i.I.....'I i~r! i' i l i t;S1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~....-I..:..-:i... 31i'6!:1 i....'.........."':": 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'' I' i~~~~ i,, I., "~' -'!''2.0 1'':.... 1:~" "'...., 4'0..!. I i I i, I~~~~~~~~~~~, ",.i....!" i,1.~~~~~~~~~~~~-:..,-,,-.,!: I ~~~~~~~~~~~~~~~~-' /- I' 3C I 7d CP b 1 "' b rd C /0 f /1.... 1,' iI!j. ".il I 1 I i;.I i I i I I I j I i~~~E~~1.i. ~T~~iSEF~F~ j.1, I. ~!~~~~~~~~~~~~~~i. LZ -M _Fg!I:il~6li~7 Tt?;~ ~ ~ ~,~ns s eoiyo tn o rrosri~ ~iiE~~~~~~ilm ~~~~~~~~~~~~~~`L:~~~~~~~~~~~~~~/ ~~~~~~~~~~~~ates~~~~~~~~~~

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I t I Ili~,liiiii~~~iiiii IIi1ililti; iti i~!!'i il i! iiil!!i tl!~!t~Iiil Fig. l1. Film thickness vs. Velocity. of Steam; Liquid Film Flow Rate =!0 cc./min.

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