Turbulent flow seperation ahead of forward facing steps in supersonic two-dimensional and axisymmetric flows

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BIBLIOTHEEK

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IJ

van KARMAN INSTITUTE

·

FOR FLUID DYNAMICS

TECHNICAL NOTE 54

TURBULENT FLOW SEPARATION AHEAD OF FORWARD FACING STEPS . IN SUPERSONIC TWO - DIHENSIONAL AND AXISYMMETRIC FLOWS

b Y

H. T. UEBELI~ACK

RHODE-SAINT-GENESE, BELGIUM

Technica1 Note

54

TURBULENT FLOW SEPARATION AHEAD OF FORWARD FACING STEPS IN SUPERSONIC TWO - DIMENSIONAL AND AXISYMMETRIC FLOWS

by

H.T. UEBELHACK

Pressure distributions in the separated flow region ahead of forward facing steps and on the step face in super-sonic turbulent flows obtained at VKI are compared with those found by previous investigatorso The following geometries were investigated :

1. Flat plate step models which

(a) spanned the tunnel completely (b) spanned

75%

of the tunnel widtho 2. Cone-Cylinder-step modelso

30 Axisymmetric internal flow models

Ca) nozzles followed by a 900 _contraction

(b) ejectors with a 900 _{contraction of the supersonic} diffuser.

Parameters such as step height, unit Reynolds number and Mach number we re compared. It was intended, in particular, to relate the axisymmetric results to existing two-dimensional data.

A general law relating the variation of the step pressure integral with Mach number was found by analyzing pressure distributions on the step faceo

The influence of flow inclination, Mach number var~­ ation and three-dimensional effects on the characteristic pressures were discussedo The flow has been visualized by schlieren and schadow photographs and by the oil flow tech-nique.

TABLE OF CONTENTS

SUMMARY _{• • • • • • • •} i

LIST OF SYMBOLS. _{• • • • • •}

_•

. i i i 10 INTRODUCTION.

_•

_{• •}

_•

_•

_•

_{• • •}

_•

1 20 REVIEW OF RESULTS OF PREVIOUS INVEST IGATORS _• 3 3 .. EXPERIMENTAL PROGRAMME AND TEST CONDITIONS. _• 6

301 Facilities. _{• •}

_•

_{• •} 7

3.2 Models _{• • • • • • •}

_•

_{• •} 7

4.

EXPERIMENTAL RESULTS _{• • • •} 0 _• 0 0 9 4 01 Planar Model s.

_•

_•

_•

_{• • • • •} 9 4.2 Cone-Cylinder-Step Models _•

..

_{• •} 10 403 Axisymmetric Internal Flow t~odels _{• • •} 12 4.4 Flow Visua1izations. _{• • •} 0 0 • 0 13 4.5 The Pressure Distribution and the Pressure.

Integral Over the Step Face _{• •} 0 _• 0 14 4.6 Discussion. _{• • • • • • • • •} 16 50 CONCLUSIONS _{• • • • • • • • • • •} 0 19 REFERENCES _{• • • • • • • •} 0 20 FIGURES

A Cp d,D D Fi h L M P Re x y a

e

ó

o

00 1 ne P s HH LIST OF SYMBOLS cross-section pressure coefficient diameter

=!pdy p,res sure integral induced side force

step height model length Mach number pressure

Reynolds number

coordinate in flow direction step coordinate

angle of lncidence flow angle

boundary l~yer thickness Subscripts

free stream stagnation conditions before interaction nozzle exit first peak separation throat ~ection second throat

1. INTRODUCTION

The phenomenon of flow separation ahead of forward facing steps and similar obstacles has been studied experi-mentally during the past fifteen years mostly in the context of other types of separation induced by pressure gradients caused by shock waves, or ramps. (Refs.l,2). In aerodynamic designs, steps and sudden enlargements ' of the cross-section are usually avoided because of the high drag of these geometries. There are, however, a few cases where a sudden change of the flow direction and separation cannot be avoided such as the interaction between the outer flow and the bound-ary of an underexpanded jet at the exit of a rocket nozzle, gas or fuel injection into a supersonic stream (Refs.3,4) or three-dimensional obstacles at the surface of an aerodynamic body (Refs.5,6). In all those cases, the study of flow separ-at ion ahead of the obstacles becomes indispensable in order to predict the drag and the side forces caused by the pressure distribution in the separated flow region.

Other technical applications of a rather sudden change in cross-section are supersonic diffusers (second throats) in supersonic wind tunnels and in supersonic diff-users of ejectors. Here a high contraction angle is of ten desired because a long ramp would interfere with the shbck wave pattern of the central flow. The pressure distribution on the contract ion has to be known in order to predict the efficiency and the pressure recovery of a second throato

Experiments on second throat diffusers of ejectors have shown that a sudden contraction of the cross-section

(forward facing step) displays the same improvement in pressure recovery as a ramp type contraction (Ref.?). Para-meters like the ramp angle of the second throat, the axial

location of the ramp and the possible occurence of separation ahead of the ramp complicate the analysis of the problem. In the case of a sudden contraction (step) the flow forms its "natura! ~amp" by the process of separation.

The interest of the author in this field has lead to a study of flow separation ahead of forward facing steps in order to :

i compare axisymmetric internal and external flow data, particularly in the case of flows over cavities, with two-dimensional results;

ii explain the scatter of available experimental data and discuss the experimental difficulties;

iii ·predict the pressure distribution and the pressure integral over the step face;

iv visualize and examine the separated flow region; v find a suitable reattachment criteria for this

2. REVIEW OF RESULTS OF PREVIOUS INVESTIGATORS

Turbulent flow separation ahead of fOTward facing steps and comparable obstacles were studied in the past mainly on flat plate step models which spanned the wind tunnel or which had side fences and on similar models with free ends (about 75% of the available data) (Refs.l,2,8~9,10.11,12). Other data were obtained on models such as two- and three-dimensional flow injection into uniform flow (Refs03,4) and three-dimensional obstacle on flat plate models (Ref.5). A summary of the most important available data is given in Ref. 13. The main features of this type of flow and the essential phenomena should be briefly summarized here

The wal 1 pressure distribution in the separated flow region, including the step face, at sufficiently high Reynolds numbers always shows a similar variation. A Reynolds number range from Re

6

=

3.l0~.~.106 have been investigated so far :

The wall pressure rises in a steep gradient from the point where the interaction is feIt first up to a first peak value which is situated at about 50% of the separated length. The wall pressure then decays towàrds the step and rises again reaching about 1.4 times the value of the first peak pressure in the corner. On the step face towards the outer corner, i t decays again to a minimum of about 102 times the first peak value between 30 and 40% of the step height and then rises _, continuously reaching 2 ••• 3 times Pp at the outer edge of the step. In the outer 20% of the step height the pressure dis-tributions seems to be strongly influenced by the Mach number and the relative step height, Refs.4,5.

primary attent ion in the previous experiments has been paid to the value of the first peak pressure in the separated flow region and its dependence on Mach number and

Reyno1ds number. All the experimentations have found rising peak pressure ra.tios Pp

lp

1 wi th rising ini tia1 Mach numbers Ml o A Mach number range between 1.4 and

6

has been

invest-igate~ experimenta11y so faro The peak pressure r,tio pp/pl scatters around a mean va1ue by about + 10%. In Ref.8, the

mean value has been approximated by

=

3.2 (1 )

which represents the average value rather we11 particu1ar1y

at 10w supersonic Mach numbers and up to Ml=305o Beyond MI=5

there are on1y few data avai1able (Ref.10). In order to

re-present the mean va1ue a1so at high Mach numbers

Pl

is suggested in Ref.13.

An aerodynamica11y based method to predict the first

peak pressure wou1d be the pressure rise across an ob1ique

two-dimensiona1 shock wave, analogous to the separation

phe-nomenon at rearward facing steps where the base pressure is determined by the deviation of the outer flow in the expansion fan at the corner. The peak pressure ratio then is given by

It has been observed that the separation ang1e. 1oeo the angle between the wal1 and the straight dividing

stream-lines from separation to reattachment very close to the outer

dorner of the step, is rough1y constant and scatters around

MI

=

2 and

5.

As mentioned before there are not enough data available beyond MI

=

5 in order to speak of a mean valueo

The Reynolds number dependenee of the peak pressure has been examined particularly in Refs.2,8,9 . It was found that there was almost no dependence on Reynolds number in tur-bulent flow when the initial Reynolds number is sufficiently high. The data presented in Ref.2 show a small decrease of Pp with increasing Re. This however could be due to the still

transitional behavior of the tripped boundary layer.

The separation pressure Ps has been determined by different techniques such as pitot probes shadowgraphs and oil flow pictures. (Refs.l,2,lO). Only a few attempts were made in locating the separation point. As ~n average of those few measurements the separation pressure is suggested to be approximated (Ref.13) by

=

.73

PI

( 4 )

The pressure integral over the separated flow region ahead of the step has also been a subject of discussion in Refo 13. There, many separated pressure profil es were examined and a similarity was found in their normalized shape which permits an integration in a general form. For the normalized separ-ation induced side force the following linear dependence on Mach number was found

( 5 )

Pressure distributions on the step face itself are only presented in Refs.l and

4

with a sufficient number of points in order to speak of a pressure distribution.

30 EXPERIMENTAL PROGRAMME AND TEST CONDITIONS

The experimental programm presented here was carried out in two different facilities : a supersonic blowdown tunnel

(M=305) and an ejector test bench. In the blowdown tunnel

axi-symmetric cone-cylinder step models and flat plate ~tep models were examined.

In the ejector facility, tests were carried out on steps behind an axisymmetric nozzle, designed for parallel flow and on an

arrangement of nozzle and a diffuser with a sudden contraction

(cavity).

The experimental programmed consisted in a wall pressure survey in the separated flow reg ion ahead of the steps at stagnation pressures between 8 kg/cm2 and 17 kg/cm2

in tunnel

s4

and between 18 kg/cm2 and 30 kg/cm2 in the eject-or test facility.

All the tests in tunnel

s4

were carried out at step heights of 5 and 7.5 mm in or~er to check repeatability and

the influence of the step height. The boundary layer thickness was determined from schlieren photographs and was found to be 105 to 2 mmo The dependence of characteristic pressures on the angle of incidence of the model has been the subject of a

series of experiments on both the two-dimensional and the aX1-symmetric "models.

In the ejector facility the axial distance between nozzle exit and step was varied in order to check the

uniform-ity of the flow and the dependence of the pressure data on the boundary layer development length.

3.1 .. Faci1·i t i e s

i

The supersonic blowdown tunnel s4 at VKI was used in the first series of experiments. The wind tunnel was

designed for a Mach number of 3.5 in the test section of 100 mm height and 80 mm span. Ca1ibration tests disp1ayed a tota1

Mach number variation of 1

%

in vertica1 direction and 0.5

%

in lateral direction at a stagnation pressure of 8 kg/cm2 •

An ejector behind the tunnel allows a stagnation pressure

range between 1 kg/cm2 and 18 kg/cm2 • The tunnel is equipped

with a sch1ieren and a shadowgraph system.

The ejector test banch consisted of a sett1ing chamber of 40 mm diameter which was fo11owed by a nozz1e

designed for uniform flow (15 mm throat diameter, 45, 60,

75 mm exit diameter). The step in this faci1ity was rea1ized by a sudden contraction, 90°, of the diffuser section (75 mm

di ameter) to a diameter of 62 mmo Thus the step height was

6.5 mm in all configurations. The boundary 1ayer thickness was estimated to be roughly 4 mm by comparing the flow

condi-t ion to other simi1ar arrangements, where the boundary 1ayer

thickness was measured. The stagnation pressure in this

faci1ity cou1d be varied between 18 and 30 kg/cm2o

3.2. Mode1s

The two-dimensiona1 mode1s used in tunnel s4 were flat p1ate step mode1s which spanned the tunnel comp1ete1y

and which were cut down to 75

%

of the tunn~l span in the

second series of tests (Fig.1). The geometry of the axi-symmetric cone cylinder step modeLs is a1so given in the same figure. All the mode1s were mounted on a sting and con-nected tQ a mechanica1 system which was used to vary the ang1e of incidence. The diameter of the pressure taps was

0.8 mm on all the modeIs. The spac~ng of the pressure taps was 2 mm in average on the two-dimensiona1 and the axisymmetric

modelso Step heights were, in both cases,"5 and 7.5 mme

The thickness of the turbulent boundary layer was in both cases about 1.5 to 2 mm according to the variation in

stag-nation pressure. All pressures were measured"through a scanning

valve system by a 15 psi transducer. The output signa1 was re-corded on "graphispot" recorders.

In the ejector test bench the spacing of the pressure

taps (0.8 mm) was 2 mme The pressure holes were located along

a meridian. On the step face (6.5 mm) there w.ere 7 pressure holes. The pressures were sensed over the same system of scanning valves and recorders described above.

40 'EXP~RIMENTAL RESULTS

4.1. P1anar Mode1s

The complete wa11 pressure distribution on the center-1ine of the two p1anar mode1s is shown in Figs.2a,2b,3a,3b for two step heights h = 5 and 7.5 mm and tunnel stagnation press-ures between 8 and 17 kg/cm2 • In all figures the sca1e of the step face coordinate is en1arged four times in order to show more details. The variation of the peak pressure ratio with stagnation pressure (unit Reyno1ds number) is shown in Fig.4 together with the resu1ts of other mode1s. The curves show c1ear1y a sma11 decay of the peak pressure ratio with ~n­

creasing tunnel stagnat~on pressure. The variation of Reyno1ds number at separation is rough1y from 4.8.107 to 1.1.1080 The peak pressure ratio seems to approach assymptotica11y a

constant va1ue at still higher Reyno1ds number. The change in the peak pressure ratio measured on p1anar mode1s is about 10

%

(mode1s which spanned the tunnel) and 3

%

(mode1s with free ends). Love (Ref.8) has a1ready observed a constant peak pressure in a Reyno1ds number range between 10 6 and 107 at Mach numbers between 1.5 and 2 05.

The peak pressures obtained at the highest Reyno1ds number emp10yed are shown in Fig05 together with the resu1ts from other mode1s and experimenta1 va1ues by other invest-igators which came to the a~thor's attention.

The step height had no inf1uence on the peak pressure ratio when the model spanned the tunnel. The peak pressure

ratios Pp/Pl are about 3

%

10wer for the 10wer step when they were measured on the mode1s spanning on1y 75

%

of the tunnel width. The peak pressure ratios obtained on the mode1s with

free ends are slight1y (3-5

%)

be10w those obtained on the mode1s which were sea1ed against the tunnel wa11s.

The statie to total pressure ratio before

interact-ion has also been recorded over,the range of stagnation press-ures employed (Fig06)0 A mean value of PI/POl ~ 0 0011 has been

found and the corresponding initial Mach number MI=3 062 has

been attributed to the peak pressure ratios in Figo5o

The influence of flow inclination on the peak press-ure ratio also was checked by varying the angle of incidence

of the model between ·2 and +2 degrees, Fig.

The peak pressure dependenee on the angle of attack can be

estimated to be p -p

a

( p I ) PI

=

-

_aa

( 6)

aa

p -p '.Th e n

a

(P I ) /

aM

PI I is taken from Eqo(3) for a separation angle of 6₈=13° _{and 3M I}

/aa

from isent~opic flow tables at MI=3062

then

= .052 deg-I

The measurements (Figo7) confirm the value ghowing th at only the variation in Mach number influences the peak pressure ratio.

4

02. 'Cone-Cylinder-Step Models

The wall pressure distributions on the axisymmetric models at tunnel stagnation pressures between 8 and 17 'kg/cm2

·and for two step heights 5 and 705 mm are shown in Figs o9a-p, the step face coordinate being enlarged four times. The vari-ation of the peak pressure with tunnel stagnvari-ation pressure is

plotted in Fig.4 and the peak pressure ratio obtained at the highest tested stagnation pressures~ are .also shown in Fig.5.

Here a stronger variation of the peak pressure with

Po was observed. At the highest tested Po the measured peak

~ ~

pressure ratio is within a few percent the same as the one obtained on the two-dimensional models at VKI and by other

investigators. At the lowest tested Po they are however by 00

about 30

%

higher. The variation seems to indicate a still transitional behaviour of the boundary layero

There was no influence of the step height observedo

The initial pressure ratio PI/POl also was recorded. It ri~es

from about .009 at PI=8 kg/cm2 to .010 at 15 kg/cm2 (Fig o6).

In the composite diagramme (Fig.5) the initial Mach number

MI=3070 has been attributed to the peak pressure ratios ob-tained at bhe highest Po •

00

The Reynolds number at the interaction point was not evaluated in this case since the boundary layer was undergoing

the change from conical to axisymmetric flow in the expansion

fan at the shoulder of the model. The boundary layer develop-ment length down to the point of interaction was long er than the one on the planar modeis. The peak pressure ratio observed

at the highest Po again corresponds weIl to the two-dimensiona~

00

results and to the values given by Eqs.(2) and (3).

The influence of the angle of attack has also been

checked on this configurationo The results are presented in

Figo8o The peak pressure shows a much stronger dependenc~ on

the angle of attack due to·,the three-dimensionality of the flow than Eq.(6) would predict.

4030 Axisymmetric Internal Flow Models

The wa11 pressure distribution on those models was measured at vari~~s positions of the step with respect to the nozzle exit plane (Figs.lO.11,12) and in two cases the position was kept constant (x/D=2 00) and the stagnation pressure was varied (Figs.13,14). The initial Mach numbers were determined by the statie to total pressure ratios when the 75 mm nozzle was used. It was found te be 4.83 for the step location at x/D=2000 In the ejector set-up the jet boundary Mach number was first determined by the base pressure to tot~l pressure ratio and then the shroud wal1 Mach number was determined by the two-dimensional oblique shock relation for the measured pres sure rise 0 The ini tial Mach numbers MI were .thus determin-ed to be 4.0 (45 mm nozzle) and 4.15 (60 mm nozzle).

The diffuser wa11 pressure behind the 75 mm nozzle showed a small pressure drop. A gradient of a(p/po)/a(x/D) ~

.65°10 3 can be estimated from the pressure readings. The other nozzles produced a remarkab1y constant diffuser wall pressure confirming that the flow in the nozzle exit is uniform.

Practically no dependence of the peak pressure on unit Reynolds number was observed (Figs.13,14). The axial location of the step also had only a small and random influ-ence on the pressure distribution in the separated flow regiono

The peak pressure ratio as a function of initial Mach number compares weIl with other data taken in the same Mach number range and with Eqs.(2.3) (Fig05).

404.

Flow Visua1izations

The flow around the mode1s in tunnel

s4

was examined by the sch1ieren and the shadowgraph techniques {Figo18)o At tunnel stagnation pressures of 12 and 13 kg/cm 2 , the photo-graphs show a similar flow pattern for all geometries :

A slight1y wavy shock wave at separation indicating un-steady flow - a rough1y straight 1ine between the

approx-imate location of separation and a point slight1y above the

out er corner of the step which indicates the upper mixing regiono

- A second shock wave near the reattachment at the outer corner which intereferes with the expansion fan issuing from the corner.

The ratio step height to boundary 1ayer thickness h /ó can be estimated from those photographs to be 3 to

40

An oil flow technique. ~as been used to visualise the surface flow pattern on the mode1s in tunnel

s4

and in the ejector facility. On the planar models which were sealed against the tunnel wall, the fol1owing oil motion was observed during the tests :

An irregular but symmetric separation line was formed as shown in Fig.19.

Two rather important vortices were situated close together on the tunnel wal1 and on the model surfaceo

Severa1 other vortices were located behind the separation line as indicated in Fig.19.

A very straight separation 1ine was observed at about 20

%

of the step height indicating a small vortex which is

located in the corner. At this oi1 accumulation line sma11 irregu1arly distributed vortices were also observedo

The two-dimensional model with free ends The bil accumulation line at separation on this model showed smaller disturbances than the one described beforeo Similar but

small-er vortices were observed behind the separation lineo In total

the separation line looked more "two-dimensional" having less

disturbances and approaching more a straight lineo

Cone-cylinder step models : Here the separation

line was rather straight over about 70% of the circumferenceo Two rather large vortices were observed on either side of the

model and were spaced at 1800 _{{Figs o20a-b)0 A regular}

separ-ation line on the step face (y/h ~ 20 %) with small vortices

on ithas also been observed o During the visualization test the angle of incidence of the model was alteredo The oil pattern and the oil motion was only little influenced herebyo The same oil flow pattern was obtained when the axial location of the model in the test section was changedo

Axisymmetric internal flow models : Here essentially

the same phenomena have been observedo A regular separation

line on about 20 % ~f the step heighto A rather regular

separ-ation line (compared to the above-mentioned models) and small-er vortices behind that separation lineo The separation es angle here was smaller ( 10 000 11 degrees) when determined from oil accumulation at separation and the step heighto

405.

The Pressure Distribution and the Pressure

Integral Over the Step Face

One of the major objectives of the experiments pre-sented here was to find a general rule for the step pressure

integral as afunction of the main parameters - relative step

height and Mach"number. The measured pressure distribution in

the ejector facility is plotted versus the cross sectioned

All cases show a similar behaviour at different pressure

levels. The integration has been carried out graphically and the resulting values are shown in Fig.17 under the di-mensionless form

. ·D

J

PIt:.A

=

step

The pressure distribution obtained from the two-dimensional and axisymmetric models in tunnel s-4 are

present-ed in Figo16~ For the planar models a mean value can be defined around which the measured ~ta scatter by about ~ 5%0 The

pressure variation is in general the same as' observed by

Bogdonoff (Ref.l) and Sterret {Ref.4)0

The integration

J

~

~

h ( 8 )

has been carried out graphically and the result is also in-di cated in Fig.17.

In the same figure finally the step pressure integrals from measurements by Bogdonoff (Refol) and Sterret (Refo4) are

included. Heyser et alo (Ref.14) measured the force acting on the step with a strain gauge balanceo Allthe data indicate a

linear variation of the step pressure integral in the Mach

num-ber range between 2 and 6 having the approximate form

Step pressure data obtained from another

test programme carried out independently at VKI at MI

=

2 on planar models which completely spanned the wind

tunnel with a beundary layer trip near the 1eading edge are

inc1uded in Figs.

5,

16 and 17. The step pressure

distrib-ution has the expected level and the step pressure integral agrees with Eq.(9).

4.6.

Discussion

The variation of the peak pressure ratio, induced side force and induced drag c1ear1y shows a linear variation

with Mach rtumber. A 10

%

scatter of the experimental resu1ts about the mean values has been found to be typica1. Test results obtained at VKI were repeatable. An eventual

inf1u-ence of the unsteadiness of the flow, therefore, can be

eliminated as a possib1e reason for the scatter of the

results.

Other parameters must be considered to exp1ain the scatter of all the experimenta1 data; e.g., three-dimensiona1

effects in dimensional and axisymmetric flows. A rea1 two-dimensiona1 situation has not been achieved in all the experi-ments conducted so faro Side fences as we11 as free ends on two-dimensional mode1s have disp1ayed three-dimensiona1

effects. A1so axisymmetric internal and external flow mode1s

have irregularly distributed vortices behind the a1so ~regu1ar

separation 1ine. Those fl~w irregularities which seem to be

independent of the model geometry and strong1y connected to the separation process itself a1ready cou1d be the reason for

a non-uniform lateral pressure distribution and lateral flows o

They wou1d explain a certain scatter of the measured pressureso Experiments on high1y three-dimensional mode1s have shown that

lateral f10ws affect the pressure distribution on the axis of

symmetry on1y te a certain degree but nev'er dominate the Mach

Other sources of errors in correlating peak pressure and induced forces with Mach number are the uncertainties in the tunnel Mach number and the relative flow inclinationo The tunnel free stream Mach number changes over larger stagnation pressure ranges due to the change in nozzle boundary layer displacement thickness and the resulting effective nozzle contour o In two-dimensional flows the effect of flow inclin-ation can be related to a corresponding Mach number variinclin-ation o On axisymmetric models the cross flow ~aused a bigger effect of the angle of attack infue pressure variationo

Reynolds number effects on the characteristic

pressure were found to be present at higher values of Reynolds number than previously reportedo However, different conditions in wind tunnels and on the tested models can produce the slight Reynolds number influence which was found in some parts of the present research. Tripped boundary layers, finally~ are known to introduce additional effects into the flow and cannot be compared directly to boundary layer which have undergone a

"natural" transition.

Previous inv~stigations as weIl as the present one have shown that the relative step height has no influence on the characteristics pressures in the separated flow region if h/ö is larger than one and below a certain limit which depends on Mach number. Three regimes of relative step height can be roughly separated so faro When the step height is smaller than the boundary layer thickness the pressure level of the charac-teristic pressures depends strongly on the step height as

Bogdonoff (Ref.l) has showno A similarity in the pressure dis-tribution exists in the second regime when h/ö lies between one and the upper limit. Here the pressure level is linearly related to the Mach number. For larger step heights the pressure on the outer portion of the step, particularly at hypersonic

Mach numbers, is strongly influenced by the step height and

the Mach number (Refso4-5)o

The linear variatîon of characteristic pressures and forces with Mach number for the second step height regime

and for Mach numbers between 2 and

6

has been confirmed by

many investigators. A suitable physical model describing the experimental results is s t i l l locking. The oblique shock

relations which could be used to determine the pressure level

in the separated flow region imply the separation angle as a

parameter. The separation angle has been found to be approx

-imately 13° and roughly constant. There are, however,

indi-cations that the separation angle decreases with higher Mach

numbers (oil flow pictures in the internal flow facility

indi cated 8_{s =110 at M=4.8).} A decreasing separation angle

woul d explain the linear variation of the pressure with Mach

number together with the quadratic oblique shock relationso

Difficulties in determining experimentally the

separation point and the correct inclination of the shear

l ayer are still the main problem to a correct answer to

50

CONCLUSIONS

The results of the present experimental program

m

conjunction with the work of previous investigators lead to the following conclusions

1 there is no essential difference in the pressure

distribution in the separated flow reg ion ahead of steps in axisymmetric internal and external flow and on two-dimensional and three-dimensional con-figurations.

i i A similarity exists in the pressure distribution throughout the whole separated flow region for turbulent flow and within a certain limit of the relative step heights.

i i i Above a certain Reynolds number and for step height ratios h/ó>l at Mach numbers between 2 and

6,

the peak pressure ratio Pp/Pl' the induced side force and the step pressure integral were found empiric-ally to be linear functions of the Mach numbero

iv A step-type contraction in supersonic diffusers of ejectors (second throat) can be used in order to improve pressure recoveryo The law for the step pressure integral allows one to predict the pressure recoveryo

REFERENCES

~o BOGDONOFF, SoM., and KEPLER, CoE., Interaction of a turbulent boundary layer with a step at M=3, Princeton Univo Report 238, 19530

20 CHAPMAN, DoR., KUEHN, D.Mo, LARSON, HoKo, Investigation of separated flows in supersonic and subsonic

streams with emphasis on the effect of transition 5 NACA TN 3869, 1957.

30 MAURER, F., Three-dimensional effects in shock separated flow regions ahead of lateral control jets issuing from slot nozzles of finite lengtho Separated Flows Part 2, Proc. of a Specialists' Meeting, AGARD Fluid Dynamics Panel (AGARD, Paris, France, 1966).

40 STERRET, JoRo, and BARBER, JoBo, A theoretical and experi-mental investigation of secondary jets in a Mach 6 free stream with emphasis on the structure of the jet and separation ahead of the jet,

Separated Flows Part 25 Proc o of a SpecialistsV

Meeting, AGARD Fluid Dynamics Panel (AGARD, Paris, France, 1966)0

50 WESTKAEMPER, J.C., Turbulant boundary layer separation ahead of cylinders, AIAA Jo 6, 19680

60 BERNSTEINE, Ho, and BRUNK, WoEo, Explorating investigation of the flow in the separated region ahead of two

blunt bodies at Mach number 2, NACA RM E55 D076 5 June 1955.

70 JOHNSTON, S.C., Experimental investigation of a supersonic air-air ejector operating with a se60nd throat o

VKI TN 45, von Karman Institute, Rhode-Saint-Genèse, Belgium.

80 LOVE, EoS., Pressure rise associated with shock induced boundary layer separation, NACA TN 3601, 19550 90 LAUGE, R.H., Present status of information relative to

the prediction of shock-induced boundary layer separation, NACA TN 3055, 19540

100 STERRETT,J.K., and EMERY, JoC., Extension of boundary layer separation criteria to a Mach number of 6 05 by utilizing flat plates with forward facing steps. NASA TN D-618, 1960.

11. BOGDONOFF, S.M., Some experimental studies of the separ-ation of supersonic turbulent boundary layers, Princeton Univ. Report 336, ~955.

12. ABBOTT, I.H., Some factors contributing to scale effect at supersonic speeds, AGARD Memorandum AG8/M4, 1953.

130 ZUKOSKI, E.E., Turbulent boundary layer separation in front of a forward facing step, AIAA Jo Vol 5, No. 10, 1967.

140 HEYSER, A. and MAURER, Fo, Experimentelle Untersuchungen an festen Spoilern und Strahlspoilern bei Machschen Zahlen von 0.6 bis 2.8,

J I

~~ ______________ ~J

modczl span: tunnczl span h modczl span:: 60 m m h

: 80mm

L::120mm h: 5 and 7,S mm

Fig, 1 a TWO - DIMENSIONAl MODELS,

d

L

L: 85 m m h:: Sand 7,5 mm Fig, 1 b AXI- SYMMETRIC MODEL

D ~ . dcz h d:: 30 mm x h x o h d*=15mm dcz:45and 60mm D::75mm d~*:62mm h:6,Smm x:: O,S, , • 2,0 D

Fig, 1 c INTERNAL FLOW AND EJECTOR FACILITY Fig, MODELS AND FACllITIES,

Mco

=

3,5 _M1

=

3.62 3,2 Re

6

t'

k9':m:i]

f . - Poco

=

588.10 - - . 4 • cm h= 5 mm

~

2 f--o Po

-=

17 kg lcm

~

'il _Po

=

15 kg/cm2

~

r---à Po

=

13kg/cm2

....

~

_-"

1<

, 1 kg Icm 2 0 _Po

=

~,

2,8 2,4 f--X P ₀

=

9 kg/cm2 J"ll~

,

•

Po :: 7 kg Icm 2

1,6 Model spanning wind tunnel. :,

•

)

1,2

-y(mm)

-0,8 0 2,5 5,0 1

1

step - -I--- _face X(mm) _y

J

80 60 40 ... 20 ~

-

J.

'I

1--

I

~

!I

i

~.

JI~lIeilr

0,4

o

"

MOl) = 3,5 M₁ :: 3,62 3,2 Re 6 [1 kQ/:mJ

l

- p - ::.588.10 cm • _~ f - - _{0 00}

~,

J

h:: 7,5mm r - - 0 _{Po = 17 kg /cm}2 v P :: 15 kg/ cm2

rJ

0 1--1::. P = ₀ 13 kg/cm 2

..

~

,~

_~

0 _{Po= 11 kQ/cm}2 I - - X Po = 9 kg/cm 2 ~ 2,8 2,4 2,0

•

P :: 7 kg/cm 2

&

0

Model spanning wind tunnel, v

-1,6 v 1,2

-v Y (mm) -0,8 ~ 0 2,5 5;0 7\5 step face

"

_Yf

X(mm)20 60 40 20

,I

~

_o~

'"

l "

I

o

~ ~ 9J'

v#Jlê3f}

~.

3,2

_{- P o}

Re

=.588.10

6 [ 1

- .

_cm

kg,:

ma

00

h:: 5 mm

_I

-

Span

=

75-/. of tunnel width

~

0 _Po

_{=16 kg /cm}

2

~~

-kg /cm 2

~

v

_Po

=

15

2,4

·

1,6

6. _Po

=

_{13 kg /cm}

2

-kg/cm2

f\

D _{P - 11} 0 -X _Po

=

9

kg

lcm 2

2,0

,

1,2

c Y(mm)

0,8

,

~

2

i

S

5,

/

o

~ / / /

_step

face

-0,4

~

4 Y y v _

... III.Q

_AA ~A •

.J

I

A- A J:!. .6.

~

V " " IS ... v

-o

3,6 M 00 = 3,5 M1 = 3,62

"

Re 6 [ 1 kg/:m

iJ

- - = 588,10 - _ . - P o o o ' cm \ h= 7,5mm

r

I

l~

'l I - - Span =

75·,.

of tunnel wldth kg/cm 2 I~

~ï

0 _p.

=

₁₆ 0 I - -v p = 15 kg /cm2 0

V

A _{P = 13} kgl cm 2 0

-IN

1 - - 0 _P

=

11 kg Icm 2 0 X P -_0- 9 kg/cm2 3,2 2,4 2,0 1,6 1,2 V(mm) 0,8 2,5 5,.0 7,5 • step face

_I

0,4 V

o

..

.. ..

... I.~~ll ,

~

~ fT etflJ

1:1"

y 'ti ~

P1

_,"J

IJ f-2 M1

=

4, M 00

=

3.5 _ _

1 ___

1

___

+

__

-'-+---t==~1=~...:::.=r==~-1----~-- 6 1

~

=.5875 x 10 ( cm Po CD __ 1 ) kg/cm 2 1- 0 step height l:l

_"

ft 5mm} 7.5 "

<

0

Axisymmetric \I IJ _"

re

"

"

x

..

IJ

•

"

"

5 .. } 7.5 IJ 5 Ol } 7.5 "

... ..., Flat plate (tunnel span)

... ..., Flat plate(75%of tunnel span)

I

5 10 15 20 25

Po CD (kg /cm 2) 30

P,

_ _ _ C - 3.2 r f P -8+CM,-1)2 e . (8 ) Pp -P1 1

---p;-

=2

_{M1 ref. (13)} equ (2.3 ) o o present data

10,8

1

~~.

1-0-

two-dimcznsionol, tunnczl span

o

two-dlmensionol I 75 ",. tunnczl span

IY'~ I~ axlsym me trie utczrnol flow

EB oxlsymmetric infernol flow

o

1,4 \8 2,2 2,6 3.0 3,4 3,8 4,2 4,6 5,0 5,4 M1 5,8

~~

~-~

~-~

~

..

0 I> .009

>---

0 0 0 oxisymmetric h:7,Smm 6 oxlsymmetric h= S mm V flat plate h:7,Smm .007 c flat plate h: Smm_

I

p (kg/cm2) OCD ,005 5 7 9

"

13 1 S 17 , 9 Fig,6 INFlUENCE OF P. ON PRESSURE RATIO BEFOR E INTERACTION

000

T _{1 I}

flat plate(tunnel span) equ (4,1> Po: 15 kg/cm2

--

_---+--2:

step height 5 m m_ ~ M 00

=

3,S 2,2 f--a~oE; ~

I

I

a

(deg) 1,8 ',4 -6 -4

-f-

0 2 4 6 8

Fig, 7 INFlUENCE OF ANGlE OF ATTACK ON PEAK PRESSURE RATIO

2,2r---r---~----_r---~----~---~----~ Pp-P, P, axisymmetric model step height 7,5 mm Moo :3,S

',8

t---+---It---+---""'~t__----_+---t__----~

1,41-IÏnT===:::::$~=====f) --+----+---~.Ir--__I

a( deg)

,

-

6

-4 -2

o

2

6

8

Moo = 3.5 _{M1 =3.73} 3,6

~

= 588.10 6

[~.

1

J

I - -Po 00 • cm kg/cm 2 h

=

5mm

~

1 - -0 POoo = 17 kg/cm 2 ~ \

~ ri~

A P. = 15 kg/cm 2 000 t - -D Pooo

=

13 kg/cm 2

~ I~

r

l\j

•

POoo = 11,5 kg/cm 2

-~

t - -X Poco

=

10 kg/cm 2

rE:

V POco = 8 kg/cm 2 3,2 2,8 2,4 2,0 1,6

r~

Y (mm) 1,2 0 2,5 c;~ step face 0,8 Y r - - - -

-~

0,4 _~. ._~.

-I

~ X (mm)

J

..

o 100 80 60 40 -""'" 20

o

fig. 9 a WALL PRESSURE DIS1RIBUT ION

.

3,6

Moo

=

3.5 M,

=

3.73 11

V

li Re 6

f

1

k9,:mJ

- Po ₀₀ =.588.10 - - . . cm _p

Z

h = 7,Smm = 15 kg /cm2

~

_ 6 _Poco

3,2

0

Po

00

=

13 kg /cm 2 _I r - - •

'beo

= 11,5 kg/cm2 '9

R,

~ ~

l

~'t

X POoo

=

10 kg/cm2 r--'il _POco = 8 kg/cm2

~

~

_~

~

~~

fi ~ ~

r

~~

~

2,8

2.4

2

,

0

'.6

Y(mm) 0 2,5

~Io

7, J _Istep J 1,2 S face V 7

-0,8

~

w

.

ct

.-

w

.-I

t _ X (mm) . ~

o

--100 80

60

40

20

o

•

~l

= 2.0

~xl03

1

Po

_.L=1.5

0 • .!..= 1.0

-•

0 d*=15 mm .

•

•

• L= 0.5 0 O:75mm

•

1--,

•

d,Q=62mm

•

-••

_•

•

20 16 r#

•

•

••

12 st(lp fac(l

'"

_~

-

•

••

•

.'

_..

r # - •

...

•

,

,Y'f'

1& ...

-~---

...

-..

_•

_--

-•

_~

..

, ~ ~A ~

..

.4

8

•

A

•

4 11

o

o

20 16 12 8 4

o

o

"' • •

1

• t··

_.A.

,

_'.~

• 4

•

•

•

•

_{• •}

Fig _• 10 _I INFLUENCE OF _, ~TEP PO~ITJON O~ WALL fRESSUR~

20 40 60 80 100 120 140

~}C'03

_•

P.' ₀

•

d* = 15mm ~ de

=

60mm

~

&1

st.p~ac~.

0 =75mm d** =62 mm }C

.'"

• 0=2.0

•

...

I-}C

_A·

. - =1,5

••

0 1~4 Ie' ~

=

0

•

Ii"

,.-•

•

A ~.A--I- • • • I- - • t • A~ ~ A •

.,..

20 40 60 80 100 120 140

Fig. 11 INFLUENCE OF STEP POSIT JON ON WALL PR ES SU RE

, 160 180 x(mm)

•

•

•

~

•

..

~

I

160 180 (mm)

24

I

p' 0

d*=

15mm

de =

45mm

J

o

= 75mm I

d**=

62 mm 20

~

=

2.0

~

If

J..L=O

_·

_{step face}

.I'

...

_6,5mm

-./

.

16

12

Fig, 12 DIFFUSER WAll PRESSURE

(

DIST RIBUTJON •

8

J

.... .... 4

_~.""

V

• Je (mm) I

o

~IO

40 60 80 100 1?0 -140 160 11

o

80

~x103

I

_in

_lp"

Po variation

•

0

•

•

p' .: 30 kg

Icm

2 step tocation

•

0 .: 26 kg/cm2

Z·

..

p' 0

I-•

P~ = 22 kg/cm2

•

p.' .: 18 kg/cm2

•

•

0

lil

x _

d*=15mm

"

i

- - 2 0

o

•

16 12 8

_o

.:75mm

-

-,

45

5,0~ • .!.-d**=62mm y(mm) 4 · step face

111

IJ

"Sa.

_••••

_{• • • J}

•

•

·

o

I

o

20 40 60 80 100 120 140 160 mm 180

Fig, 13 WALL PRESSURE DISTRIBUTION, INFlUENCE OF STAGNATION PRESSURE • 20 ~x103 --I

I

step llocation

"

P.' variation in p'

.-0 0 Je

I

• p' 0 = 30 kg Icm2 1-1=0 -=20

o

.

...

•

.. p' : 26 kg/cm2 ₀ dtf = 15 mm

~

y p'

=

_{22 kg/cm 2} d e

=

60mm

t

_~ 0

=

18 kg/cm2 • p' ₀

o

= 75mm 16 12 8 d**= 62mm

_f

12,~~ ~6:;

i&..~

_.~

,

_{· y(mm)} step face 4

, i

t'

I '

t •

• • • t

••••

•

•

o

~

o

20 40 60 80 100 120 140 160 mm 180

P1 6 5 4 3 2 1

o

0/

/ I

~

/

I

"

M,

=

4,83

i"

I.

7

~

_c""~

M1=4,0 / ' I

-,---

.;f

I

1-

---+---::'III""~~;.,tI.~,..~~

-415 - t t -

I - ___

~~~.... ""1- I I

~

r

':::='-"'-'

I

I

I

I

I

I outer edge

I

J - - . - - - - + - 0 f st e p - - t 1 r t - - - I oxisymmetric

~

internol floW ~I

I

I ___

~

I---.J 25 23 21 1 9 1 7 ~ 1 5

A*

Fig. 15 PRESSURE DISTRIBUTION ON THE

STEP FAC E

P,

c

h=" 5mm

6 h=7,Smm 2-dim _ tunnel span

6 • h= 5mm • M1- 3,62 • h= 7.5mm 2-dlm 75% tunnel span .0 h= 5mm axisym. M,= 3,73

5.

/ /

4 L, < I ~7/ I

3 1

... 1

17"7/1

2

₁

_=T-

--#

h::7mm 1

1

*

h:5mm _I 2-dim _I M,=2.05 o~.

______

~

______

~

____

~

______

~

____ __

o

.2 ,4 .6 .~ Y 1.0

---n-Fig.

16

PRESSURE DISTRIBUTION ON THE

Fr 0 Pp p,h

,

P,h

,

P, L-

~

'2

. /

l /

v

8

V~

-~

. /

P;h =2.'M,

,-;,1'3)

l Á

" 0 1 , ( 4 )

... p',osont data .

.!!...=

',oe

V

axt-sym and 2d' Ö

~

V

ligl'6).!L",4 Im

~

'I . '01(1) Ö

~~

h 2

~~ ~

- - ' 1 M "" ... ,oIC,4)

1I

1V _

~

- - n

P,h - , ,

~ ~,",,"'"

...

J

~

/ /

~

,.

'" *"

_...

c~

;V

P p ,

.. __ -... 'I

=,.

M

.... _ _ ,1::-""- ___ .,.

prosont data p,osont data P,

2 '

t...~~

... - -

-R

rv 2 lig,C'6)

Z

axi-sym Into,nal Ilow ,of,(13)

-T

lig

I 15)

h

IV

2

Ö

I "I

4

o

1 2 3 4 5 M1 6

PLANAR MODEL,FREE ENDS'P_o=13kg/cm2JSHADOWGRAPH

PLANAR MODEL SEALE D TO TUNNEL SIDE WALLSJ

P.

=

12 kg/cm 2 SHADOWGRAPH

o

FLOW TECHNIQUE PLAN AR MODEL SJ SEAlED AGAINsT TUNNEL SIDE WAlls (ABOVEIAND FREE ENDS.