THE PHYSICAL MODELLING OF FLOWS AFTER MOVING OBSTRUCTIONS E.Ya. Epik, T.T. Suprun Institute of Engineering Thermophysics of National Academy of Sciences

THE PHYSICAL MODELLING OF FLOWS AFTER MOVING OBSTRUCTIONS

E.Ya. Epik, T.T. Suprun

Institute of Engineering Thermophysics of National Academy of Sciences of Ukraine

(IET NASU), Kyiv, Ukrainee-mail: [email protected]

NATOAdvanced Study Institute

PST.ASI.980064

Flow and Transport Processesin Complex Obstructed Geometries:

from cities and vegetative canopies to industrial problems

Kyiv, Ukraine, May 4 - 15, 2004

Organized by:Institute of Hydromechanics

of National Academy of Sciences of Ukraine

CONTENTS

1. INTRODUCTION

2. EXPERIMENTAL INSTALLATIONS

3. RESULTS OF MEASUREMENTS

3.1 Distribution of external flow velocity

3.2 Distribution of external flow longitudinal fluctuations

3.3 Total characteristics of external flow

3.4 Separation of total fluctuations into turbulent and nonstationary components

4. CONCLUSION

1. INTRODUCTION

Unsteady flows after moving obstructions are widely spread in various technical applications. It is necessary to distinguish unsteadiness of two types: specially organised for intensification of working processes; caused by principle of operation of heat power and technological

equipment.

Despite the intensive growth of computer technique and successful development of new progressive numerical approaches, the results of physical experiments are the main basis for verification of different models in CFD.

The modelling of flows with velocity periodic nonstationarity is often realised by means of moving cylinders or “squirrel cage”. The latter reproduces the peculiarities of flow after working blades in turbomachines.

1. INTRODUCTION

During two last decades in IET NASU and IFFM PAS (Institute of Fluid-Flow Machinery of Polish Academy of Sciences) experimental investigations of laminar-turbulent transition are carried out under conditions of interaction of different disturbances (turbulence, separation, periodic velocity unsteadiness, etc.).

Taking into account the joint scientific interests of both organisations (IET NASU and IFFM PAN), namely comparison of flow characteristics with periodic velocity unsteadiness generated by “squirrel” cages is the object of given presentation.


Fig. 1 Squirrel cage wake generator and flat plate arrangement in IFFM (workingsection 0.60x0.46x1.5 m3)

Fig. 2 Squirrel cage wake generator and flat plate arrangement in IET (workingsection 0.12x0.12x0.80 m3)


Parameter IFFM PAS IET NASU

Distance between axis of rotation and leading edge of the plate

yo=0 mm yo=35 mm

Distance from the nearest rods to the leading edges of plate

xo=124 mm xo=15 mm

Diameter of „SC” D=200 mm D=70 mm

Diameter of rods d=3 mm d=3 mm

Spreading of wakes over the plate surface Y=D/2+d=103 mm Y=D+d=73 mm

Rotation frequency f=4 Hz f=5 Hz

Flow velocity U=20 m/s U=9 m/s

Natural level of turbulence Tu=0.08% Tu=0.3%


Principal differences in constructions: The clearances between the top walls of working

sections and the treads of squirrel cages are ~128mm (IFFM) and only 20 mm (IET).

In IFFM at D=200 mm the axis of rotationcoincides with the horizontal axis of the leadingedge of the plate. In IET at D=70 mm the distancebetween axises of rotation and leading edge of theplate is 35 mm.

3. RESULTS OF MEASUREMENTS

The standard hot-wire technique DISA-55M was used


Fig. 3 Mean velocity distribution U/Uo behind the wake generator in IFFM

In IFFM defect of velocity manifests itself in appearance of theminimum in the velocity distribution (at y/R~0.8 Umin/Uo=0.84) withconsequent recovery of uniformity near the outer edge of the boundarylayer (at y/R<0.5 Ue/Uo=0.9=const).

The formation of boundary layer happens under conditions ofshearless external flow (Ue=const) despite the presence of velocityunsteadiness induced by wakes.

The thickness of boundary layer is determined as usually byconditions U=0.99Ue.


20 600 40 80

1

0.8

0.9

1

1

1

1

U/ Ue

y, mm

Z

Z

Z

Z

x=600 mm

400

200

100

50

Fig. 4 Velocity distribution behind the squirrel cage wake generator in IET

In IET the boundary layer formation happens in shear flow at U/Ue=var. The velocity minimum caused by wake takes place near the outer edge of

the boundary layer. The thickness of boundary layer is determined as the extreme point in

which dU/dy=0.


Fig. 5 Velocity fluctuation distribution behind the squirrel cage in IFFM

Fig. 6 Velocity fluctuation distribution behind the squirrel cage in IET


The distributions of total fluctuations ( eu)including turbulent ( tu) and nonstationary ( nu)components differ by peaks, amplitude of whichdecreases downflow.

In IFFM the mean level of u’/Uo changes from~6% to 3.5% at x=112-622 mm (fig.5).

In IET it reaches to ~ 12% and decreases to4.5% at x=100-600 mm (fig.6).

Fig.7 Interaction of wakes behind the rotating cylinders

Mechanism of peaks origin is connected withinteraction of wakes after rotating obstructions(cylinders) what causes the growth of energy ofdisturbances in points of intersections of wakes.

The number of peaks corresponds N-1 where N isnumber of cylinders.


For using the hydrodynamic characteristics after moving obstructions in further calculations, the shear external flow was replaced by its shearless equivalent. For this purpose in the every cross section the distributions of velocity and fluctuations were averaged in the range of y=D+d what corresponded the width of wakes spreading.

100 300 5000 200 400 600x , м м

2

6

10

14

0

4

8

12

16

u'/

Ue,

%

/u' / Ue

/

u' / Un e

/

u' / Ut e

Fig. 8 Distributions of fluctuations after the “squirrel cage” in IET



T h e decay law o f to ta l lo n g itu d in a l flu c tu a tio n o feq u iv a len t sh earless flo w w as p resen ted in u su a l fo rm :

me )XX(Au

U02

2

w h ere A = 96 5 .7 , X o= 0 .06 0 9 m , m = 1 .4 .

D ecay law p erm its to ca lcu la te th e v a lu es o f d iss ip a tiv esca le an d tu rb u len t v isco sity o n th e b asis o f “en erg y -d iss ip a tio n ” tu rb u len ce m o d e l

x, mm ee U/u ,

%

uL ,

mm

/te

50 15 12 180

600 4.3 20 88


F o r d i v i d i n g t u r b u l e n t a n d n o n s t a t i o n a r y c o m p o n e n t st h e a d d i t i o n a l m e a s u r e m e n t w e r e c o n d u c t e d a f t e r s t i l l“ s q u i r r e l c a g e ” i n I E T .T h e m e t h o d w a s b a s e d o n t w o f o l l o w i n ga s s u m p t i o n s : t h e r o t a t i o n d o e s n o t s u b s t a n t i a l l y i n f l u e n c e o n

t u r b u l e n t c o m p o n e n t ; t h e e n e r g i e s o f d i s t u r b a n c e s o f d i f f e r e n t n a t u r e a r e

n o t c o r r e l a t e d , i . e . 222nte uuu .


The results of separation demostrate that values ofturbulent and nonstationary components and rate oftheir decrease after “squirrel cage” are different:

The fluctuations of turbulent component measuredafter still cylinders changed slower than calculatedfluctuations of nonstationary component.

Immediately near the rotating cylinders the role ofnonstationarity was dominant.

Downflow after rotating cylinders turbulentcomponent became prevailing.

3.5 Brief comments about features of boundary layerDespite the development of boundary layer happens underdifferent external conditions, wake-induced laminar-turbulenttransition takes place in both installations.

Transformation of velocity profiles from pseudolaminar toturbulent is the same as in case of bypass transition.

The distributions of fluctuations are different.

Fig. 9 Velocity fluctuation distribution in the boundary layer inIFFM

In IFFM there are two peaks in distributions of totallongitudinal fluctuations.

Fig. 10 Velocity fluctuation distribution in the boundary layerin IET

In IET there is only one peak in distributions of totallongitudinal fluctuations.

3.5 Brief comments about features of boundary layer

3.5 Brief comments about features of boundary layer

Although the details of peaks mechanism are inneed of the further understanding; an existence oflongitudinal fluctuation minimum between peaks aty/0.3 in experiments in IFFM may be partlyexplained by many reasons.For example one could point the change of thekinetic energy phase in critical boundary layer, aswell as the redistribution of energy betweenlongitudinal and normal components, effects ofintermittency, etc.

4. CONCLUSION

On the basis of physical modelling of flow structure afterrotating obstructions in the form of “squirrel” cage it is shown: Velocity distributions are characterized by presence of two

regions: the shearless core broadening downflow and shearzone near the wheel tread of “squirrel” cage.

Fluctuation distributions demonstrate an origin of peaks inpoints of wake intersections as well as the different levels oftotal turbulence decreasing downflow.

For using in calculations the characteristics of shear flowthe latter can be replaced by shearless equivalent.

The rate of decay of nonstationary and turbulentcomponents are different.

The presented data emphasize the important role of physicalexperiment for numerical modelling. As it is confirmed byresults of given investigation every insignificant detail ofexperimental arrangement may cause the substantial changesof flow structure and characteristics of boundary layer.

Comparison of heat transfer and friction

Distributions of heat transfer and friction coefficients in wake-induced transition in IFFM

Comparison of heat transfer and friction

Cf ,

St

хRe104

105

-3

-2

St =0 .036(R ex) -0.2tur

St =0.55(R ex)lam

-0.5

C = 0.0595(R ex)flam tur

-0.2C =0 .664(R ex)f

-0.5

- S t

- C (U )f

- C (U )f e

Distributions of heat transfer and friction coefficients in wake-induced transition in IET

Documents

THE PHYSICAL MODELLING OF FLOWS AFTER MOVING OBSTRUCTIONS E.Ya. Epik, T.T. Suprun Institute of Engineering Thermophysics of National Academy of Sciences