Y. Ito, K. Sawasaki, N. Tani, T. Nagasaki, T. Nagashima, “A Blowdown Cryogenic

Cavitation Tunnel and CFD Treatment for Flow Visualization around a Foil”, Journal

of Thermal Science, 14, pp.346-351 (Dec 2005) (Springer)

A Blowdown Cryogenic Cavitation Tunnel and CFD Treatment for Flow

Visualization around a Foil

Yu IT01 Kazuya SAWASAKI2 Naoki TANI3 Takao NAGASAKI1

Tosbio NAGASHIMA 4 1. Tokyo Institute of Technology, G3-33, 4259, Nagatsuta-cho, Midori-ku, Yokohama, 226-8502, Japan2. Honda Motor Co. Ltd., 2-1-1, Minami-Aoyama, Minato-ku, Tokyo, 107-8556, Japan3. Japan Aerospace Exploration Agency, 2-1-1, Sengen, Tsukuba, 305-8505, Japan4. University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

Cavitation is one of the major problems in the development of rocket engines. There have been few experimental studies to visualize cryogenic foil cavitation. Therefore a new cryogenic cavitation tunnel of blowdown type was built. The foil shape is "piano-convex". This profile was chosen because of simplicity, but also of being similar to the one for a rocket inducer impeller. Working fluids were water at room temperature, hot water and liquid nitrogen. In case of Angle of Attack (AOA)=8', periodical cavity departure was observed in the experiments of both water at 90'C and nitrogen at -190 ° C under the same velocity 10 m/sec and the same cavitation number 0.7. The frequencies were observed to be llO and 90 Hz, respectively, and almost coincided with those of vortex shedding from the foil. Temperature depression due to the thermodynamic effect was confirmed in both experiment and simulation especially in the cryogenic cavitation.

Keywords: cavitation, tunnel, cryogen, CFD, visualization, simulation, foil.

CLC number: V411 Document code: A Article ID: 1003-2169(2005)04-0346-06

Introduction

Cavitation is one of the difficult problems to overcome in the recent development of liquid fuel rocket engines, because high performance engines require the higher combustion pressure so that their turbo-pumps have to operate at the higher rotating speed. At present, it is difficult to accurately predict and control the phenomena of cavitation and its influence on the performance of the turbo-pumps. Especially, cryogenic cavitation is complex, wherein cryogens such as LH2, LOX and L凡have three thermodynamic features compared to ordinary fluids like比0. Firstly cryogens reveal small latent heat and nucleation of cavitation easily occurs. Secondly, cryogens are characterized by low specific heat, hence large temperature reduction can result from heat removal due to latent heat of evaporation. Finally, cryogens have steep gradient of the saturation curve, so that the saturation pressure rapidly decreases with the temperature depression, moderating cavitation growth. These are called'' thermodynamic effect." Therefore

Yu ITO: Ph. D.

it is not a good way to rely upon existing abundant empirical data base of the ordinary fluid pumps in the case of designing cryogenic ones. Consequently, visible investigation by means of both experiments and calculations that take into account the thermodynamic effect are required in order to understand the fundamental features and the structure of the cryogenic cavitation in more detail.

Hord111 carried out a visible experimental study on a cavitating flow around a 2 dimensional axisymmetric ogive body by using LN2 and LH2 in 1974. Thereafter, in order to investigate a faster chocked flow with cavitation in LN2, LOX and LC比，an experimental study of that in three different shape nozzles was carried out by Simoneau and Hendricks12l in 1979, who made no effort to visualize the flow patterns. Several U.S. groups [3~6]

reported on a subsonic flow of LHe, however measurements were only for pressure or mass flow rate, not elaborating flow visualization. There are very few studies to visualize cryogenic cavitation through a nozzle, because of difficulty in the experiments. Hori et. al. 171 carried out

Yutaka ITO et al. A Blowdown Cryogenic Cavitation Tunnel and CFD Treatment for Flow Visualization around a Foil 347

visualization experiments on the cavitating flow of LN2 by employing the same nozzle profile as Simoneau and Hendricks. Ishii and Murakami t81 studied the flow of He I and He II in a small nozzle incorporating successfully flow visualization. Meanwhile, for the cavitation around foils there are quite a few experiments in case of water flow, but very few in cryogenic flow except Hord. One of the objectives in the present study is therefore to investigate the cavitation around the foil in a comparative way of experimented flow visualization between the cryogen and the ordinary fluids to elucidate the distinction due to the thermodynamic effect.

Numerical simulations on the cavitating flow in nozzles and around foils have been reported, which, however, mostly treat water cavitation, whereas there are again very few studies on the cryogenic one. Ito and Nagashima t91 conducted CFD simulation of cryogenic cavitating flow using Lagrangian-Eulerian coupling model, which was based on rather strict modeling, thus require large computational time. Ito and Nagasaki I~°1 improved this method and tested a new code by using "Bubble Size Distribution model," which reduced computational time with a reasonable degree of accuracy. Tani and Nagashima Ilu developed a numerical code based on homogeneous two-phase formulation by employing "Bubble Two-phase Flow model "112~, in which the energy equation was incorporated in order to accurately take into account the thermodynamic effect. Ishimoto and Kamijo t131 carried out CFD simulation on the cavitation in LHe pump. The other objective of the present study is therefore to perform a numerical simulation, by employing Tani and Nagashima's method that can treat the thermodynamic effect, in order to compare the results against the experimental observation.

Experimental Arrangements

A new cryogenic cavitation tunnel of the blowdown type was developed in order to observe the flow around a foil. As shown in Fig. 1, this apparatus consists of upper and lower tanks of 100 and 120 liter capacity, respectively, and an intermediate module of a visible test section of 200 mm length installing a 2 inches bore ball valve at its lower end. To prevent the failure due to thermal stress, the test section is made of polycarbonate, whilst the rest parts are of stainless steel. The whole assembly except the valve is insulated by dry nitrogen, therefore it is possible to operate with not only water at room temperature but also hot water and even LN2. The maximum withstanding pressure is 0.5 MPa. Fig.2 shows the test section and the foil geometry. The test section has 20 mm square cross sectional shape, wherein the foil is set at the center. The foil size is 20 mm in both chord and span lengths with its shape of "piano-convex", that is, one surface being plane

and the other convex with a radius of 26 mm. This profile was chosen because of simplicity, but also of being similar to an inducer impeller in the turbo-pump of rocket engines, which is the primary target of the present study. One of the particular features of this facility is the access to flow visualization at the foil from all the directions except the side supporting the foil, i.e. the pressure and suction surfaces as well as the side section. Monitoring the static pressure under operation is provided by a pressure-tap: P~ at 60 mm upstream of the

-5-7-

1 N2 gas cylinder 2 Lower tank 3 Valve 4 Visible test section installing the foil inside

5 Upper tank 6 Pressure transducer 7 RTD 8 High speed video camera

9 A/D converter unit 10 PC

Fig.1 Experimental apparatus

Fig.2 Visible test section and foil geometry

348 Journal of Thermal Science, Vol. 14, No.4, 2005

foil center and two pressure-taps: P2, P3 set directly upon the convex surface of the foil, whilst two platinum RTDs (resistance-thermal-devices): T1, T2 are also installed at 60 mm upstream and downstream of the foil.

Experimental procedure is the following (Fig.l). Firstly working fluid is pumped into the upper tank5 and pressurized by high pressure gaseous nitrogen1. Secondly the valve3 is instantaneously opened and the fluid flows down into the lower tank2 through the visible test section4 wherein the cavitating flow pattern is observed by the high speed video camera8. Pressure6 and temperature7 are recorded and analyzed by the PC10.

Working fluids as already described are water at room temperature, hot water and LNz. Experimental conditions are set by inlet velocity and cavitation number,

, / 1 2 O" = ( P1 -- Psa, ) / ~ pLUinte, (1)

where, Psat, PL and Uinle t are saturation pressure, liquid density and inlet velocity, respectively. Ui,tet is calculated from temporal change of liquid level in the upper tank measured by a electrostatic capacitance level meter. Two kinds of experimental conditions were arranged to clarify, in the first, the effect of cavitation number by varying the water temperature under a constant flow velocity, and secondly, the effect of physical (thermodynamic) properties by replacing hot water by LN2 under a constant flow velocity and cavitation number. Flow velocity was varied between 0 and 15 m/sec.

Numerical Formulation

In the present calculation, cavitation is considered as a cluster of many tiny bubbles, and this is named as the Bubble Two-phase Flow model. The original model II21 applied for water cavitation, thus, temperature was assumed to be constant. Since the present objective is cryogenic cavitation, energy equation has to be properly incorporated, so that the governing 2D Navier-Stokes equations may be written as,

p pu pv I 0 - - + - - " + - - " 2

0

r . (2) Z'y~

where, p, u, v, e, P, r and /3 are density, x and y component of velocity, specific total energy, pressure, stress tensor and energy diffusion term, respectively. The formulation takes the same as that for the single-phase Navier-Stokes equations, however, density, energy, viscosity and heat conductivity for two-phase flow, herein derived by averaging gas and liquid, need to be treated as follows.

p = a. PG + (1 - a) 'PL (3)

e = [ z C ~ + (1 - Z ) C~L ]" T +--~ lul 2 + [ zE~ + (1 - Z ) EL J (4)

g = a-/z G + (l-a).AzL (5)

t¢ = 2"- ~¢c + (I - Z)' tel (6)

where, o4 Z, Cv, E, T, u , / t and t¢ are gas phase volume fraction (void fraction), mass fraction (quality), specific heat at constant volume, intemal energy at the reference temperature, temperature, velocity vector, viscosity and heat conductivity, respectively, and subscript G and L mean gas (vapor) and liquid phase. Equation (3), (5), (6) and the first and second term on the right hand side of equation (4) constitute the ordinary homogeneous two- phase flow formulation, whilst the third term of the latter represents the latent heat absorption. The relationship between void fraction and quality is described as,

a : P Z = 4xR3N (7) Pa 3

where, R and N are bubble radius and number density per unit volume, respectively. Bubble number density and initial bubble radius are set to 1.6xl09114] and nil, respectively, while the subsequent bubble radius is obtained by solving Rayleigh-Plesset equation.

where,

RDZR+3(DR]2_P~._~-P -b-?- 7t.~-7-t .) pL

(8)

D 0 0 . . . . ~ u - - + v - - (9) Dt - 3t ~x ~v

The above set of equations has to be closed by applying the state equation. Presently, a two-phase averaged state equation described by Okuda et al. I151 is employed.

1 _ K(T+T~) 1 R ,T (10) p P+~ (-x)+--F-z

where, K, Tc, Pc and Rot are liquid constant coefficient, temperature constant, pressure constant and gas constant, respectively.

TCUP numerical scheme [16] was employed to solve the above set of N.S. and energy equations.

Results and Discussion

Experimental results The foil angle of attack (AOA) is set at 8 degree in

all cases. Firstly the flow pattern of water at 20.7 °C is shown in Fig.3(a). There occurred no cavitation at ff=1.84. Secondly Fig.3(b) shows the temporal change in

Yutaka ITO et al. A Blowdown Cryogenic Cavitation Tunnel and CFD Treatment for Flow Visualization around a Foil 349

cavity profiles of water at 88.5 ° C. The inlet velocity was set to be nearly the same as that at 20.7°C, therefore

cavitation number became 0-= 0.66. The cavity was

formed out of the cavitation cloud, then grew and

departed from the foil surface periodically at f = 111 Hz. Finally, Fig.3(c) shows cavitating flow of LNe at -1910

C. The condition of velocity and cavitation number was nearly the same as that of water at 88.5°C. The cavity

again grew and departed periodically, but frequency was

f = 89.7 Hz. Here, let f and L be the frequency of cavity departure and the foil chord length, respectively. Strouhal

number can be defined as follows,

S t = f L , (11) Uinla

which is calculated to be 0.216 and 0.191 in cases of water at 88.6°C and nitrogen at -191°C, respectively.

These values of St indicate that the cavity departure coincides with a vortex shedding from the foil surface,

furthermore, suggesting the cavity is formed in the low

pressure region associated with the vortex.

Numerical results Two dimensional calculations were carried out using

the grid as shown in Fig.4. A O A was also set at 8 degree

in all cases. Boundary conditions were nonslip walls, a fixed velocity at inlet and a fixed pressure at outlet. Inlet t empera tu re and ve loc i ty are 77 K and 8.5 m/sec, respectively. Outlet pressure is determined by corresponding

cavitation number in experiments. Fig.5 shows the numerical

results. There was no cavitation at o-=1.35. The cavity

was formed in the downs t ream half on the suct ion surface of the foil at cr=1.08, and grew at 0-= 0.81. At 0- = 0.67, the cavity region and temperature depression

t = 0.00 msec 2.25 msec 4.50 msec 6.75 msec 9.00 msec

(a) Water at a = 1.84, blinle t -~ 10.4 m/sec, T1 = 20.7°C = 293.9 K, PI = 102 KPa. Non cavitation

, r z

ii!:!il

i~ ~i ~

t = 0.00 msec 2.25 msec 4.50 msec 6.75 msec 9.00 msec (b) Water at or= 0.66, Ui~l~t = 10.3 m/sec, Tl = 88.5°C = 361.7 K, P1 = 101 KPa.f= 111 Hz, St = 0.216

Q iiiiiiil

t = 0.00 msec 2.79 msec 5.57 msec 8.36 msec 11.1 msec

(c) Nitrogen at or= 0.67, uinlet =9.4 m/sec, Tl = -191 °C = 82 K, P1 = 79 KPa.f= 89.7 fHz), St = 0.191

Fig.3 Temporal change of cavity profiles

350 Journal of Thermal Science, Vol. 14, No.4, 2005

became much larger. Void fraction and pressure profiles showed a correlation that void fraction is large in the low pressure region. Velocity profiles indicated the boundary layer gradually became thicker along the foil surface in cases of negligible cavitation. However, it was found to become rapidly thicker in the cavity region to such an extent that separation occurred in cases of cavitating flow. Fig.6 shows the streamlines around the leading edge at o" =0.81. The separation occurred on the suction surface near the leading edge and a small cavity was formed as shown in the void fraction profile of Fig.5. Fig.7 shows

the static pressure distributions on the foil upper and lower surfaces corresponding to 4 different cavitation numbers, and white circle symbol shows P3 pressure on the foil surface (Fig.2) measured experimentally at o" = 0.67. The pressure on the suction surface became lower than the saturation pressure corresponding to the inlet temperature. Generally speaking, pressure inside the cavity is nearly equal to the local saturation pressure, therefore the present data indicate that both local temperature and pressure in the cavity region progressively decreased downstream due to thermodynamic effect.

Fixed velocity condition inflow 4 . &

0 0 • ~ - ~

O O

.~ .%

Z Z

outflow Fixed Pressure condition

Fig. 4 Grid of calculation (400 x 55 x 2 zones)

Void fraction 1 Temperature

Pressure

Velocity

/ ' J

/ / ;

/ / / / / / , ~ L . . . . .

I I l i ' \ L C::,

i:+i ~r= 0.67

Pouaet = 111

s

¢ g

....... 2--,% ,5 7z: : : 7 - ~3)",

/ I i / - - .....

/

!: ; J f / /

.".L, ...... " / ' : i l q ~\

/ ; ] I " -, 0.81 121

, / , , ' ; , j / ..

t (,,?/{! ......

i t, ~,,

, . , ' /

1.08 132

[/./,,:;Tt -;;;77 > / , "ttt L . . . . . . .

I - / / I ,

1.35 140 KPa

Fig. 5 Numerical results at T/,,t~; = 77 K and uintet = 8.5 m/sec

Fig. 6 Streamlines near the leading edge at o'= 0.81

100

~ 50

0

' o - ' 1 . 3 5 - - ' - - ' 0 .81 ' ' 1 . 0 8 . . . . . 0 . 6 7

~_~'- - -, ---Z ~ . . . . . . -_---_- - - - ---, - ~ = - - _ _ _ _ . . . . - . . . . . . . : . ~ : = . . . . . . . . . . . . it: "¢-,

o

' 0~.2 ' ' ' 0~.6 ' 018 ' ~" 0 0.4 1.0

(L.E) Position x//chord (T.E)

Fig.7 Numerical pressure profiles on the foil surfaces and experimental pressure at Xllchord = 0.65, (7"= 0.67 on the suction surface of the foil

Yutaka ITO et al. A Blowdown Cryogenic Cavitation Tunnel and CFD Treatment for Flow Visualization around a Foil 351

~ 1.2

1.1

"~ I.o

o 0.9

0.8 0.6 018 112

Cavitation number cr

o

1.4

Fig. 8 Lift coefficient

Fig.8 shows Lift coefficient

~f~il ~ 1 2 CL = P(x)ndxl-~pLUinletlchor d (12)

where, fi, g chord are normal vector to the chord and chord length, respectively. Lift coefficient diminished as cavitation number was reduced, because the suction side pressure in the cavity region was controlled by the saturation pressure. Fig.9 shows a comparison between the experimental photo and the numerical void fraction profile at o-=0.67. The cavity in the experiment grew more remarkably than the numerical one because the experimental velocity is larger. Since the larger velocity leads to the larger temperature depression, the difference was raised between the numerical solid line and the experimental white circle symbol in Fig.7.

C o n c l u s i o n

In case of AOA = 8 degree, periodical cavity departure was observed in the experiments of water at 90°C and of nitrogen at -190 ° C, wherein these experimental conditions were nearly the same at velocity 10 m/sec and cavitation number 0.7. The frequencies were measured to be 110 and 90 Hz, respectively, and almost agreed with those of vortex shedding from the foil. Meanwhile, temperature depression due to the thermo- dynamic effect was measured in the cavity region in both experiment and simulation. Especially, the thermo- dynamic effect appeared significantly in the cavitation region of cryogenic flow.

A c k n o w l e d g e m e n t s

This work was supported by the Grant-in-Aid for Scientific Research of MEXT, Japan. Mr. K. Seto, who was a postgraduate student of Tokyo Institute of Technology, was carried out additional experiments.

References

[1] Hord, J. Cavitation in Liquid Cryogens II - Hydrofoil. NASA CR 2156, 1974

[2] Simoneau, R J, Hendricks, R C. Two-phase Choked Flow of Cryogenic Fluids in Converging-diverging Nozzle. NASA TP 1484, 1979

[3] Ludtk, P R, Daney, D E. Cavitation Characteristics of a

Fig. 9 Comparison between the experimental photo and the numerical void fraction profile at if= 0.67

Small Centrifugal Pump in He I and He II. Cryogenics, 1988, 28:96--100

[4] Walstrom, P L, Weisend II, J G~ Maddocks, J R, et al. Turbulent Flow Pressure Drop in Various He 1I Transfer System Components. Cryogenics, 1988, 28:101--109

[5] Daney, D E. Cavitation in Flowing Superfluid Helium. Cryogenics, 1988, 28:132--136

[6] Pettersen, M S, Naud, C, Baliba, S, et al. Experimental Observations of Cavitation in Superfluid Helium-4. Physica B, 1994, 194-196:575--576

[7] Hori, S, Ito, Y, Yamaguchi, K. Observation of Cavitation Bubbles in Cryogenic 2D Nozzle Flows (in Japanese). In: Proc. of 40th Aerospace Propulsion Conference, Chofu, Tokyo, 2000. 169--174

[8] Ishii, T, Murakami, M. Comparison of Cavitating Flows in He I and He II. Cryogenics, 2003, 43:507--514

[9] Ito, Y, Nagashima, T. Numerical Simulation of Sub- cooled LN2 Nozzle Flow with Cavitation. In: Proc. of 5th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows, Gdansk, 2001, 2: 715-- 722

[10] Ito, Y, Nagasaki, T. Numerical Simulation of Sub-cooled Cavitating Flow by Using Bubble Size Distribution. Journal of Thermal Science, 2003, 12(4): 350--356

[11] Tani, N, Nagashima, T. Numerical Simulation Model for Cryogenic Pump Cavitation. In: Proc. of Asian Joint Conference on Propulsion and Power 2004, Seoul, 2004. 313--318

[12] Kubota, A, Kato, H, Yamaguchi, H. A new Modeling of Cavitation Flows- a Numerical Study of Unsteady Cavitation on Hydrofoil Section. Journal of Fluid Mechanics, 1992, 240:59--96

[13] Ishimoto, J, Kamijo, K. Numerical Simulation Model for Cryogenic Pump Cavitation. Advances in Cryogenic Eng., 2002, 47:1413--1420

[14] Wang, Y. Effect of Nuclei Size Distribution on the Dynamics of a Spherical Clouds of Cavitation Bubbles. Journal of Fluids Engineering, 19998, 121:881--886

[15] Okuda, K, Ikohagi, T. Numerical Simulation of Collapsing Behavior of Bubble Clouds. Transaction of JSME Series (B), 1996, (62): 3792--3793

[16] Himeno, T, Watanabe, T.:Numerical Analysis for Propellant Management in Liquid Rocket Tank, AIAA-3822, 2001

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