Free Compressible Jet Nozzle Investigation - ULisboaltces.dem.ist.utl.pt/lxlaser/lxlaser2012/upload/163_paper_ecvgbw.pdfcompressible flows require an accurate description of the large-

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 09-12 July, 2012

- 1 -

Free Compressible Jet Nozzle Investigation

Fabrizio De Gregorio 1,*

, Floriana Albano 1

1: Fluid Mechanics Department, Italian Aerospace Research Centre (CIRA), Capua (CE), Italy

* [email protected]

Abstract The compressibility effect on a supersonic turbulent jet was investigated. A new supersonic nozzle and a new flow feeding systems were designed and realized. A nozzle Mach exit of Mj=1.5 was selected in order to obtain a convective Mach number of Mc=0.6 where the compressibility effect becomes sensible. The density gradient (ρj/ρa) effect was also investigated using carbon dioxide as feeding gas in order to obtain a CO2 jet flowing in still air. The jet nozzle was investigated for the cases of over expanded, fully expanded and under expanded jet. Mach number, total temperature and flow field measurements were carried out in order to characterize the jet behaviour. The inlet condition of the jet flow were monitored in order to calculate the nozzle exit speed of sound and evaluate the mean Mach number distribution starting from the flow velocity data. A detailed analysis of the Mach results obtained by the staic Pitot probe and by the PIV measurement system was carried out. The mean flow velocity was investigated and the Mach decay phenomena and the spreading rate where correlated to the compressibility effects. The longitudinal and radial distribution of the total temperature was investigated, the temperature profiles were analysed and discussed. The total temperature behaviour correlated to the turbulent phenomena and to the compressibility effects. The self similarity condition encountered and discussed for the over expanded jet. Compressibility effect on the local turbulence, on the turbulent kinetic energy and on the Reynolds tensor is discussed.

1. Introduction There is a need to be able to predict and control high speed jet flows for optimal design of

aerospace vehicles. In this Mach number range, large variations in pressure, density or temperature

can take place that can have an impact on the dynamics of turbulence. The early work by Bradshaw

(1977) pointed out the need for models with significant compressibility corrections for reliable

predictions of free shear flows. Improving prediction capabilities and providing effective control of

compressible flows require an accurate description of the large- and small-scale dynamics as well as

the time-averaged statistical properties of the flow.

The most significant effect of compressibility on a free shear flow is the reduction in its growth

rate. Early reference of this behaviour can be found in Birch and Eggers (1972), Bogdanoff (1983)

and Papamoschou and Roshko (1988) who used the concept of convective Mach number (Mc) to

characterize the shear layer compressibility. The Mach convective number is defined as Mc=(Uex-

Uin)/(aex-ain) where U is the jet speed, a is the speed of sound, the subscripts ‘ex’ and ‘in’ indicate

the magnitudes related to the external and internal flows. It has been demonstrated by Bogdanoff

(1983) that the compressibility reduces the increment rate of the mixing layer thickness respects

incompressible flow at same speed ratio r=Uex/Uin. The compressibility effects become important

for values of the convective Mach larger than 0.5.

More detailed studies have shown a suppression of mixing-layer growth rate with increasing

compressibility (see Chinzei et al. 1986; Papamoschou and Roshko 1988; Elliott and Samimy 1990;

Clemens and Mungal 1992, 1995). The growth rate of incompressible mixing layers is always

associated with increased turbulent activities, and its suppression in compressible mixing layers is

accompanied by a reduction in turbulence production.

There have been several past investigations to provide proper scaling and characterization of the


- 2 -

self-similar region of axisymmetric turbulent jets. Richards and Pitts (1993) showed that regardless

of the initial conditions i.e. fully developed pipe flow or nozzle flow, axisymmetric free jets decay

at the same rate, spread at the same half-angle and both mean and fluctuating mass fraction values

collapse in a form consistent with self-preservation. Subsequently Papadopoulos and Pitts (1998)

demonstrated experimentally that in the case of constant density gases the initial turbulence

intensity is a significant source of excitation that feeds into the growing shear layer which is

responsible for breaking up the potential core and for transforming the jet into a fully developed

self-similar flow. The spreading rate of compressible jets varies with the jet exit Mach number

(Zaman 1998). Results for the far asymptotic region show that both spreading rate and centreline

velocity decay rates, when properly non-dimensionalized by parameters at the nozzle exit, decrease

with the jet Mach number. The work of Wang and Andreopoulos (2010) investigated the combined

effect of density and compressibility, testing different gases and different subsonic Mach numbers

up to Mj=0.9 and confirmed the reduction of the mixing layer increasing the jet Mach number for

each gas. Although many works have been carried out and many step forward have been performed

toward the understanding of the physics of turbulent jet (at limited Reynolds number of the order of

10.000-100.000), few experimental data are available at higher speed and higher Reynolds numbers

and still many aspects need to be investigated in order to optimize the space propulsion and

minimize the noise emission. For this scope in 2006 the Italian Space Agency launched the CAST

project aimed to investigate innovative theoretical chemical-physics models and advanced

numerical methodologies for building an integrated numerical/experimental system able to better

investigate fundamental aspects of the aerothermodynamics and of the aeroacoustic of the space

propulsion. The understanding of the physic/chemical laws regulating the mixing layer of two

coaxial flows characterised by different chemical composition, speed, temperature and pressure was

one of the aims of the project.

This work was aimed to fulfil the lack of experimental data to validate new models of turbulence

and turbulent dissipative transport in continuous development (Paciorri and Sabetta 2003). The

behaviour of compressible jets originated from a convergent/divergent nozzle issuing in still air was

investigated at supersonic speed. The experiment was designed in order to achieve significant effect

of the compressibility on the free shear flow. A dedicated convergent/divergent nozzle was

designed and built in order to obtain a jet Mach exit equal to Mj=1.5 in order to obtain a convective

Mach number of Mc=0.6. The nozzle jet was characterised for three different conditions: isentropic

expansion where the nozzle exit pressure (pj) is equivalent to the ambient pressure (pa) (pj=pa

adapted nozzle), over expanded nozzle characterised by nozzle exit pressure lower than the ambient

pressure (pj<pa) and under expanded nozzle with the nozzle exit pressure higher than the ambient

pressure (pj>pa). Carbon dioxide (CO2) was used to generate the jet flow in order to evaluate the

additional effect of the density ratio and of different chemical species on the flow structures.

Particular care was taken in measuring the mixing layer flow characteristics.

2. Experimental design set-up The test campaign and consequently the nozzle was designed taking in mind the following

requirements: reproduce the compressibility effect (Mc>0.5), investigate the density gradient effect,

achieve a Reynolds number of the order of 106, generate an axisymmetric turbulent jet characterised

by sizes compatible with the pressure and temperature intrusive probes, reduce the complexity of

the feeding system and the cost of the test experiment. The compressibility effect in the mixing

layer was obtained designing and manufacturing a dedicated convergent/divergent nozzle

characterised by a Mach exit equal to Mj=1.5 and a convective Mach number of Mc=0.6, value for


- 3 -

which the compressibility effect become sensible. The method of the characteristics (MOC) was

adopted for design the nozzle geometry. The density gradient effect was reproduced selecting the

carbon dioxide (CO2) for feeding the nozzle jet. The CO2 presented: density heavier than that of the

air and a smaller value of the specific heat ratio (Table 2), low hazard factor in term of operational

safety, easy to supply at low cost. For designing the test condition the assumption of Eulerian, one-

dimensional and isentropic flow was taken. The over expanded condition was selected taking into

account the Sommerfield principle to avoid flow separation in the nozzle divergent and a limitation

on the minimum temperature was imposed in order to avoid a variation of the flow status during the

flow expansion. The designed test matrix foresaw three different test conditions: an over expanded

jet (P0=2.1bar), a fully expanded jet (P0=3.6 bar) and an under expanded jet (P0=4.25 bar). In Table

1, the total pressure (P0), temperature (T0) and density (ρ0) in stilling chamber together with the

static pressure (pj), temperature (Tj) and density (ρj) in correspondence of the nozzle exit and the

mass flow (Q) and Reynolds number are summarised. These values were calculated on the

hypothesis of one-dimensional flow, of calorically perfect gas. The Reynolds number is calculated

on the speed of sound a, gas density and viscosity and the nozzle exit diameter Dj .

µ

γ

**

**Re

0

0

TR

Dp j

D = (1)

where µ indicates the viscosity in stilling chamber (µ=1.5∗10−5 Pa s); R is the specific gas constant

(R=188.92 J/kg K for the carbon dioxide).

Test condition MJ P0

[Pa]

T0

[K]

ρ0

[kg/m3]

pj

[Pa]

Tj

[K]

ρj

[kg/m3]

Q

[kg/s] ReD

Over expanded jet 1.5 210000 300 3.7 59559 224 1.41 0.17 1.4 106

Adapted jet nozzle 1.5 360000 300 6.35 102101 224 2.41 0.3 2.4 106

Under expanded jet 1.5 425000 300 7.49 120813 224 2.84 0.34 2.87 106

Table 1: Nozzle designed test conditions

2.1 Convergent-divergent supersonic nozzle and feeding flow facility

The Eulerian one-dimensional isentropic law for the selected Mach number and gas (CO2), fixed the

nozzle section ratio equal to Aj/At =1.189, where Aj is the nozzle exit section and At is the throat

section. Fixed the mass flow value of Q=0.3 kg/s the nozzle exit diameter of Dj=21.22mm and a

length of the divergent of Ld=21mm were obtained. The nozzle was equipped with 27 pressure port

(PTS), 24 PTS distributed long the nozzle longitudinal direction and 4 pressure ports in proximity

of the nozzle exit section equally spaced in azimuth (Figure 2 b). A complex flow supply system

was designed and realised in order to provide steady quantity of mass flow at the required values of

pressure and temperature. The feeding system was composed by a 12.000 litres tank car storing the

CO2 liquid at a pressure of 25barg and a temperature of 253,15k , followed by a dedicated vaporiser

system providing a maximum flow rate of 1000 Nm3/h and an heating system dedicated to increase

the gas temperature at TCO2≥293.15 k (Figure 1 a). Next the first stage pressure regulator was

installed allowing a gas pressure drop from 22barg to 14barg, the pressure regulator was followed

by 50 meters of pipe rake delivering the gas inside the hangar to the second pressure stage regulator.

The second pressure stage regulator was designed for fine regulation. It was composed by two

distinct lines that if used singularly provided the necessary pressure and mass flow to the test article

for reproducing the case of over expanded jet (P0=2.1 bar) and the fully expanded jet (P0=3.6bar).


- 4 -

Figure 1: Liquid tank, vaporizer and heating systems (a) and 2

nd stage pressure regulator, sensors and control

panel (b).

Using the two lines simultaneously the setting condition for the case of under expanded jet (P0=4.25

bar) were obtained. At the end of the flow supply system, ahead the test article inlet the measure

and control patch panel was located. The transducers measured the static pressure (pCO2) and

temperature (TCO2) and the mass flow (QCO2) of the gas before entering in the CIRA test article

(Figure 1 b). The transducers signals were delivered to the control panel digital displays and to the

PSI8400 data acquisition system (DAS) and continuously recorded.

2.2 Test article

The CIRA pneumatic calibrator was used for generate the free turbulent nozzle jet. The test article

was composed by different sections (Figure 2 a). The inlet section was equipped with a breaking

plate and the honeycomb screens, a second section was adapted for feeding the seeding particles in

the flow, a third section with different net screens for improving the flow quality and remove

eventual turbulent structures shedding from the seeding pipes, a fourth section was empty as stilling

chamber. On the first, third and fourth sections, two static pressure port for each section were

present. The sections have internal diameter of Dsc=174mm. The last component was the supersonic

nozzle (Figure 2 b).

Figure 2: Test article layout (a) and pressure ports distribution on the supersonic nozzle (b)

2.3 Instrumentation and data acquisition system

The jet Mach number and total temperature distribution long the jet symmetry axis up to x/D=7 and

long the jet radius at different distances from the nozzle exit were investigated by means of

dedicated miniaturised intrusive probes. The reduced dimension of the probes was mandatory in

order to get several measurement points inside the jet mixing layer. A conical static Pitot probe L

shaped with a diameter of 1mm and the static taps located at 8 probe head diameter behind the head

(a) (b)

(b)

(a)


- 5 -

base for minimise the probe interface was utilised for the Mach number measurements. The probe

was connected to the electronic pressure transducers for recording the mean total and static flow

pressure. The total temperature probe was L shaped as well, the diameter was 1.6 mm and the

venting holes were located 8mm behind the probe head. Inside the probe there was a J type

thermocouple. The temperature sensor was calibrated in the temperature range from 203.15 to

293.15 K. The probes were singularly mounted on a dedicated support connected to a 2D linear

traversing system and located in front the nozzle (Figure 3 a). The adopted reference system

foresaw the origin located on the centre of the nozzle exit section, the x-axis coincident with the

nozzle axis of symmetry oriented versus the flow direction, the z-axis along the vertical and upward

oriented and the y-axis is oriented following the rule of the right hand. Furthermore the jet flow

field was measured up to x/Dj=16 using a 2 components PIV system. The system was composed by

two Nd-Yag resonator heads providing a laser beam of about 300 mJ each at 532 nm. The free jet

was illuminated from above. The measurements were performed on the vertical symmetry plane of

nozzle jet. Two high resolution (2048x2048 px) double frame PIV cameras were simultaneously

used. The cameras were mounted side by side on the traversing system in order to cover a larger

region with higher spatial resolution. The cameras were mounted on the right side of the jet as

shown in Figure 3b. Each camera recorded a region of about 95x95mm2 with a spatial resolution of

0.56 mm/vector. The cameras were moved of about 70mm in x-direction up to cover a total region

of 350x95 mm2. The flow field recording regions together with the probe measurement path are

summarised in Figure 4.

The seeding selection was a critical point due to the possibility of the presence of shock wave trains

long the jet. A dedicated high pressure seeding generator was developed. The generator was

equipped with twenty four Laskin nozzles providing particles diameter of 1 µm. DEHS oil was

adopted as seeding material. The seeding generator was remotely controlled by the control room,

activating different sets of nozzles (from 3 to 24). The system was able to operate up an

overpressure of 5 barg in order to overcome the total pressure in the calibrator stilling chamber. The

seeding particles were insert in the test article trough the seeding pipes located in the second section

(Figure 2a).

Probe 2D traversing

system

Probe

Support Laser PIV

cameras

Light sheet

Figure 3: Over view of the Static Pitot probe set up (a) and of the PIV set up (b)

A PSI 8400 data acquisition system was used for recording: the pressure distribution long the

nozzle and at the three different stations of the pneumatic calibrator, the total and static pressure of

the static Pitot probe, the total temperature of the TAT probe, the imposed reference pressure to the

EPS modules and the CO2 supply system measurement sensors (pressure, temperature and mass

flow).

(a) (b)


- 6 -

Gas γ R

[J/kg K)]

a sound

speed [m/s]

ρ

[kg/m3]

µ

[10-6 Pa s]

ν=µ/ρ

[10-6 m2/s]

Cp

[J/kg K]

Cv

[J/kg*K]

CO2 1.3 188.92 266 1.87 15 8.02 815 626

Table 2: Carbon dioxide properties at ambient temperature k=288.15

Figure 4: Static Pitot and total temperature probes measurement regions.

3. Data Reduction

3.1 PIV data analysis and Accuracy Estimation

One hundred and fifty (150) PIV couples of images were acquired per each test condition. The

images were filtered by subtracting the minimum image calculated on the complete set of samples

of the correspondent test case. This pre-process function allowed reducing the background noise of

the PIV images and increases the signal to noise ratio. Moreover all the recordings acquired in

proximity of the nozzle exit were masked for increasing the results reliability otherwise affect by

strong light reflections. The pre-processed images were analysed by a multi-grid algorithm. The

algorithm uses a pyramid approach by starting off with larger interrogation windows on a coarse

grid and refining the windows and grid with each pass. From the u and v velocity components the

following quantities are extracted, the out of plane component of the vorticity and the enstrophy

that provide an information about the dissipation effect, the shear strain εij and the normal strain εii

and the velocity magnitude 22222 2vuwvuV +=++= assuming that the out of plane

component is equivalent to the radial component. Furthermore some statistical quantity are

evaluated as the ensemble average velocity field, and the RMS velocity components. Knowing the

flow density the Reynolds stresses components ρu’u’, ρv’v’ and ρu’v’ were calculated. Furthermore

being the jet axial symmetric we assumed that v’v’ was equivalent to w’w’, in this way the turbulent

kinetic energy was calculated k=TKE=1/2(u’u’+2v’v’). An estimation of the measurement accuracy

was performed. Following the work of Adrian (1991), the number of pixels/particle for the adopted

experimental set up was determined. First the image diameter of the focal spot produced by a zero

diameter particle was calculated, given by the following formula:

λ#**)1(*44.2 fMds += (2)

Where ds is the diameter of a particle on the CCD sensor, M the image magnification factor, and λ

the wave number of laser light. Using this result along with particle diameter, magnification and

resolution the image diameter of the particle on the CCD sensor was obtained being governed by:

2222

rspe dddMd ++= (3)


- 7 -

where dp is the actual particle diameter (1µm) and dr is the pixel resolution (7.4 µm). Carrying out

the calculations using the data summarise in Table 3 it was found a value of 1.124 pixels for

particle. The pixel particle ratio being larger than 1 assured minor effect due to the pixel locking

effect.

f# dr

(10-6 m)

dp

(10-6 m)

ds

(10-6 m)

de

(10-6 m) pixel/particle

2.8 7.4 1 3.8 8.32 1.124

Table 3: Calculation of the pixel particle ratio

The PIV data evaluation followed the standard procedures given by Raffel et al (2002). The random

noise of the displacement was considered smaller than 0.05px. Minor bias errors were expected,

including minor effects of peak-locking. However, based on the displacement histograms, the bias

error was estimated to fall below random noise, i.e. less than 0.05px. The resulting velocity error εu

was estimated as:

εεεεu = εεεεx / (∆∆∆∆t M) (4)

where ∆t is the pulse-separation time and M is the optical magnification. The velocity error was

calculated in εu=2.34 m/s and scaling with the maximum in-plane velocity component Umax

=350m/s the relative error εu,rel = εu/Umax was determined equal to εu, rel=0.6 %. Further

consideration about the PIV accuracy shall be performed in the following discussing the PIV

behavior through the shock waves.

Lens focal

length

(mm)

f-

number

M

[10-2 mm/px]

CCD

resolution

Recording

region size

[mm2]

Interrogation

Window size Step size

Interrogation

method

εx

[px]

εu

[m/s]

∆t

[10-6 s]

100 2.8 4.4/4.7 2048x2048 96x96 24x24/32x32 12x12 /

24x24 Multi grid 0.05 2.34 1

Table 4: Summary of main PIV recording and data processing settings and error estimation.

3.2 CO2 inlet data monitoring and recording and total temperature data correction

The carbon dioxide inlet conditions to the supersonic nozzle were continuously monitored and

recorded. The pressure and mass flow inlet maintained a constant value during the test run time

(Figure 5a and b), whereas the values of the static temperature presented always a slight increment

that was possible to interpolate for the case of over expanded and adapted jet with a linear curve and

for the under expanded jet case the temperature behavior was approximate by a quadratic curve

(Figure 5c). The Carbon dioxide inlet temperature increment influenced the jet total temperature

measurements. For the under expanded jet, the total temperature distribution long the jet symmetry

axis showed a fluctuating profile characterized by a positive mean value increment (Figure 5d

indicated by the blue line), increment corresponding to the inlet temperature increment (Figure 5d

red line). The total temperature increment was not justified by the flow conditions it was due by the

positive gradient of the inlet gas. The total temperature data were corrected subtracting the

temperature component due to the inlet gradient (black curve in Figure 5d).


- 8 -

Figure 5: CO2 static temperature (a) static pressure (b) and mass flow (c) inlet data versus the recording time,

total temperature raw data and correct data long the jet axis of symmetry.

3.3 Sound speed calculation

Starting from the static temperature and the mass flow measured by the CO2 supply system was

possible to evaluate the CO2 sound speed, static pressure and temperature and gas density to the

nozzle exit. Taking into account the dioxide carbon magnitudes reported in Table 2. Starting from

the measured mass flow rate, calculating the CO2 density from the equation of the ideal gas

TR

p

*=ρ (5)

and knowing section area of the pipe it is possible to obtain the CO2 speed in the sensor section

pipe Vpipe. In the same way knowing the section of the stilling chamber is possible to calculate the

gas speed in the stilling chamber Vsc. Once that the speed in the pipe is known and the static

temperature is measured, it is possible using the equation under the assumption of isentropic flow

below indicated to calculate the total temperature in the Pipe T0 CO2.

2

2

0

uTcTc pp += (6)

Once that the total temperature is calculated, knowing the ratio between the total temperature and

the static temperature to the exit due to the nozzle geometry (T0/Texit =1.3375), it is possible to

calculate the static temperature to the nozzle exit. At this point using the equation (7), the speed of

sound at nozzle exit aj for the different conditions is obtained.

TRa **γ= (7)

Where vp cc /=γ is the specific heat ratio, R is the gas universal constant and T is the static

temperature. The static pressure and the gas density to the nozzle exit were calculated using the

formulas (8). Table 5 the CO2 speed of sound to the nozzle exit for the three conditions of correct

expanded nozzle, over expanded and under expanded are reported.

(a) (b)

(c) (d)


- 9 -

( )120

2

11

−

−+=

γγ

γM

p

p and ( )1

1

20

2

11

−

−+=

γγ

ρ

ρM (8)

P0 PCO2 TCO2 QCO2 ρρρρCO2 VPipe Psc ρρρρ sc V sc T0 CO2 a CO2 Tj aj Pj ρρρρj

[bar] [bar] [k] [kg/s] [kg/m3] [m/s] [Pa] [kg/m3] [m/s] [k] [m/s] [k] [m/s] [Pa] [kg/m3]

2.1 2.2 288.7 0.167 4.03 17.9 211912 3.88 1.81 288.9 266.3 216.0 230.3 60103 1.47

3.6 3.7 301.7 0.301 6.58 19.7 362834 6.37 1.99 301.9 272.2 225.7 235.5 101189 2.46

4.25 4.4 290.7 0.337 8.00 18.1 426343 7.76 1.82 290.9 267.2 217.5 231.1 120920 2.94

Table 5: Measured CO2 inlet quantities and calculated speed of sound, p, T and ρρρρ to the nozzle exit.

3.4 Mach number calculation (Static Pitot and PIV)

Considering the static Pitot probe in a compressible flow the equation (8) that relates the total

pressure with the static pressure is valid. Solving for M the following equation is obtained:

( )

−

−=

−

11

21

1

1,0

γγ

γ p

pM

(9)

Hence knowing the total and static pressure the Mach number was calculated. The Mach number

results successively were corrected taking into account the calibration matrix provided by the probe

producer. The Mach number distribution was calculated also starting from the PIV data. Once that

the sound of speed (a) was calculated to the jet nozzle exit for each test condition, the flow velocity

field was divided by the sound of speed providing the Mach number distribution. The Mach number

was obtained assuming that the speed of sound of the CO2 was constant for the full flow field,

assumption that can not be considered valid for all the test conditions. We shall see in the following

that the under expanded jet condition presented a substantial oscillation of the static temperature

with the consequent variation of the speed of sound that induced a substantial effect on the Mach

number distribution. The Mach number measurements, obtained with both techniques, provided

results in good agreement between them. The Pitot probe data was corrected for taking into account

the probe deformation due to the aerodynamic loads. The probe deflection ranged between 6.7mm

to 17 mm for the different jet conditions. Mach number radial distribution showed a fair good

agreement between the Pitot and PIV results both qualitatively that quantitatively (Figure 6 a, b and

c). The Mach longitudinal distribution for the case of under expanded jet presented some

discrepancy between the raw PIV data and the Pitot results (Figure 6 d). The PIV and Pitot

behaviours were qualitative similar, a large expansion was encountered immediately downstream

the nozzle exit followed by a train of oblique shocks and expansion waves resulting in an accentuate

Mach number oscillation long the jet symmetry axis. The Pitot data presented larger Mach number

oscillation amplitude than PIV raw data and a better spatial resolution detecting some sudden

deceleration and acceleration that the PIV data smoothed. For example at about x/D=1 the Pitot data

indicated a drop of Mach number followed by a sudden acceleration at x/D=1.15 and followed by a

smoother deceleration until reaching the first minimum. The PIV data was not able to detect the

negative spike at x/D=1 showing a plateau in the mach curve. The reason is ascribable to the

particle velocity lag. Although the limited size of the particle (dp=1 µm) the response time

calculated using equation (10) was τs=3.41*10-6

s, corresponding to a particle displacement of about


- 10 -

1.5mm. The seeding particles were not able to following the sudden flow deceleration, just sensed

the flow expansion showed by the plateau during the descending slope.

µ

ρτ

18

2

pp

s

d= (10)

The under expanded jet was interested by a large fluctuation of the total temperature, knowing the

flow velocity was possible to evaluate using the equation (6) the static temperature distribution long

the jet symmetry axis and consequently calculate the sound of speed. The PIV Mach distribution

corrected using the appropriated speed of sound presented results closer to the Pitot probe (Figure 6

d red curve), the value of the oscillation amplitude increased becoming of the order of the Pitot

results. The PIV data presented a mean value slightly higher than the Pitot results. Hereinafter the

PIV data shall be adopted for investigate the jet behaviour.

Figure 6: Pitot and PIV Mach radial distribution comparison in over expanded jet (a), fully expanded (b) and

under expanded (c). Pitot and PIV Mach longitudinal distribution.

4. Results

4.1 Free turbulent Jet discussion

Typical flow visualization images that are used to determine the spreading rate are shown in Figure

7. These images were obtained combining three PIV recording regions covering from the jet exit up

to x/D=10, and they are indicative of concentrations of the particles used to seed the flow. Their

Stokes number defined as the ratio of the particle response time scale τs= ρpd2

p/18µ (where ρp and

dp are respectively the particle density and diameter and µ is the flow viscosity) to that of the flow

time D/UJ (where D is the jet exit diameter and Uj is the exit jet speed), i.e. the equation

j

pp

UD

dSt

/

18/2 µρ= (11)

(b)

(d) (c)

(a)


- 11 -

reached values of St=0.055 for the case of over expanded jet and St=0.056 for the case of adapted

and under expanded jet. It has been found that particle dispersion correlates closely with the Stokes

number. Longmire and Eaton (1992) showed experimentally in a round jet that particles with St

near unity tend largely to low-vorticity/low-speed streaks and high-straining regions of large-scale

structures. The direct numerical simulations of Luo et al. (2006) have shown similar results for the

effects of large scale structures on particle dispersion only when St is close to 1 and that the particle

closely follow the vortical motion and disperse uniformly in the flow for St = 0.01. Most particles

also distribute uniformly in the case of St = 0.1, but some of them concentrate in the inner

boundaries of the large-scale structures. When transition to turbulence takes place the dispersion

patterns adjust to the new time scales of the flow, while the time response of the particle remains

the same.

Figure 7: Pressure ratio effect on the spreading rate, flow visualization and ensemble average Mach number

colour map distribution, over expanded jet (a and b), fully expanded jet (c and d ), under expanded jet (e and f) .

This change increases the effective Stokes number, and therefore the particles accumulate in the

low vorticity and high strain-rate regions of the turbulent eddies that are very smaller in size than

before, and therefore the particle distribution as a whole looks uniform. The present flows were

already turbulent (Re>300.000) and as shown by the pictures of over expanded and adapted jet the

particle concentration appears to be reasonably uniform immediately after the exit of the nozzle.

Then, mixing with ambient fluid taken place which leaded to spreading and entrainment and

pockets of low particle concentration appear in the images which indicate a fish bone like structure

in the flow. The under expanded jet presented the same structure and Stokes number of the other

test conditions but it was characterised by an apparent higher particle concentration in the shear

layer region. This was due to the further jet expansion with consequent further cooling downstream

the nozzle exit, inducing in the mixing layer region the vapour condensation of the external air. This

high concentration of water particles in the mixing layer regions, indicated by an higher light

brightness, addressed a decrement of the PIV image optical quality starting from x/D=5 for

(a)

(b)

(d)

(f) (e)

(b)


- 12 -

completely precluding the analysis at a nozzle exit distance x/D larger than 11. A visual inspection

of the images of Figure 7 a, c and d indicates that the spreading rate is larger for the case of over

expanded jet for becoming smaller for the case of adapted jet and further smaller for the case of

under expanded flow. PIV images were processed and the ensemble average Mach number was

evaluated. The spreading rate S defined as the gradient coefficient (S=dr1/2/dx) of the jet half-width

distance, i.e. r1/2 is the jet half-width distance defined as the radial position where the U(x, r1/2) is

equal to half of the axial speed (U0). The Mach number radial behaviour long the jet axis was

processed, and the spreading rates were estimated to be about 0.094 for the over expanded jet,

0.0249 for the adapted jet and 0.0209 for the under expanded jet (Figure 8). These values suggest

substantial larger mixing in the case of over expanded jet and considerable less mixing in the case

of under expanded jet. It is, therefore, expected that the over expanded jets entrain considerable

more ambient fluid than fully expanded jet or under expanded jet which are characterized by

reduced entrainment.

Figure 8: Jet half width r1/2 vs axial distance

The Mach number distribution along the Jet centreline M0 for the three different jet conditions is

compared (Figure 9). The over expanded jet shows a strong shock to the exit, not detected by the

PIV but illustrated by the CFD simulation (Figure 9 a green profile) followed by a small expansion

and compression for stabilizing in a constant value of M0 =1.1 up to 4 nozzle diameter distance

followed by a linear Mach decay. The fully expanded jet condition was characterized by a nozzle

exit static pressure slightly higher (Table 5) than the pressure ambient presenting a series of weak

trains of expansion and compression waves, resulting in a M0 oscillating behaviour. The mean

Mach number was almost constant down to x/D=10 for then starting to decay. The under expanded

jet presented marked oscillation of M0, starting with a large flow expansion to the jet exit, followed

by a series of oblique shock and expansion waves. The typical under expanded jet behaviour

characterised by a continuous divergent/convergent behaviour is shown in the Mach colour map

distribution (Figure 7 f). The mean value of M0 remain constant up to x/D=11. The Mach number

radial distribution was investigated. For all the jet conditions the Mach profile changed in the jet

core region, the influence of the oblique shocks and of the expansion waves are evident in the

double peaks profiles. As the jet decays and spreads, the mean Mach radial profile change as shown

in Figure 9 b, c and d but the shapes of the profiles do not change. The jet self similarity was

verified by plotting the Mach number distribution in self similarity variables ( i.e. M/M0 vs r/r1/2

Figure 10b). The over expanded jet case showed that for x/D larger than 7 the curves collapse onto

one singular curve, confirming the self similarity flow condition although still in the developing

region x/D<30. The self similarity was also confirmed by the values of the spreading rate S=0.0938

and by the value of the velocity-decay constant B found equal to B=5.8 in agreement with the data

presented by Hussein et al in 1994 and by Panchapakesan and Lumley in 1993 (Table 6).


- 13 -

Figure 9: Mach radial distribution at different x/D locations in over expanded jet (a), adapted flow (b) and in

under expanded jet (c).

Figure 10: Mach number (M/M0) radial distribution in similarity coordinates (r/r1/2); over-expanded jet (a),

adapted nozzle (b), under-expanded jet (c). Mean axial velocity decay long the symmetry jet axis for the different

three cases (d).

The self similarity of the over expanded jet was verified comparing the radial distribution at

different distance from the nozzle of the Reynolds stress tensor components u’u’, v’v’ and u’v’

dimensionless respect the square of the centreline velocity U02 with the data presented by Hussein et

al in 1994 (Figure 11 a). Analogous comparison was carried out on the radial distribution of the

local turbulence intensity dimensionless respect the mean velocity with the Hussein results (Figure

11 b). The calculated Reynolds stress tensor components showed similar profiles characterised by

(a)

(b)

(c) (d)

(a) (b)

(c) (d)


- 14 -

slightly smaller values, for example the u’u’/U02 component reached a maximum value of almost

0.06 instead of 0.08, v’v’/U02 reached 0.03 instead of 0.05 whereas u’v’/U0

2 reached a value of 0.02

as expected (Figure 11 c). The radial distribution of the non dimensional local turbulence intensity

u’/<U> presented a similar profile and slightly smaller values (Figure 11 d).

Panchapakesan and

Lumely (1993a)

Hussein et al. (1994),

hot wire data

Hussein et al. (1994),

laser-Doppler data

Present work,

over expanded jet

Present work,

adapted nozzle

Present work,

under expanded jet

Re 11.000 95.500 95.500 720.000 1.210.000 1.400.000

S 0.096 0.102 0.094 0.0938 0.0249 0.0209

B 6.06 5.9 5.8 5.8 12 N.A.

Table 6: The spreading rate S and the velocity-decay constant B for turbulent round jet (from Pope 2000)

The fully expanded jet condition showed for x/D larger than 15 the Mach profiles collapse onto a

single curve (Figure 10c), but the spreading rate equal to S=0.0249 and the velocity decay constant

equal to B=12, indicated that the core region was still too close and the self similarity was not

reached, Analogous for the under expanded jet condition where the radial Mach profiles do not

converge each other (Figure 10d), the spreading rate S was further smaller S=0.0209 and the lack of

decay do not allowed to measure the decay constant B.

Figure 11: Profile of Reynolds stresses (a) and local turbulence intensity (b) in the self-similar round jet (LDA

data of Hussein et al 1994), Reynolds stresses (c) and local turbulence intensity (d) at different positions long the

jet in over expanded condition.

4.2 Total temperature behaviour

Some further insight into the structure of the jet can be obtained by considering the thermal field

and in particular the total temperature measurements. Longitudinal and radial total temperature

measurements were performed. The T0 distribution long the jet centreline (Figure 12 a) presents for

the case over expanded a constant behaviour up to a distance of about 5 nozzle diameter where a

(a) (b)

(c) (d)


- 15 -

linear positive gradient occurs indicating a substantial growth of the mixing layer with consequent

gas entrainment from the warmer external flow toward the colder inner jet and by an increment of

the flow fluctuation and of the stress tensor. The case of fully expanded jet shows a constant

behaviour characterised by limited oscillations due by the weak trains of expansion and shock

waves presents in the jet. T0 remains constant confirming the lack of flow mixing being the jet still

in potential core conditions. The total temperature for the under expanded jet case presents a

substantial oscillating behaviour around an initial constant value up to 3 nozzle diameters followed

by a reduction of the mean value. The large fluctuations are due by the marked trains of expansion

and shock waves occurring along the jet core. The radial total temperature measurements were

performed traversing vertically the jet flow moving the probe from the undisturbed flow trough the

full jet sizes to the outer undisturbed air. Both directions (upward and downward) were carried out

having encountered an hysterisis in the probe measurements, probably due to the probe deflection

or to a delay in the thermocouple response in following steep temperature gradients. The radial

measurements were carried out at x/D= 2.4, 4.7 and 7.1. Figure 12 b, c and d shows the radial

temperature distribution respectively for the over expanded jet, fully expanded and under expanded

flow. In the jet core region the total temperature showed a T0 decrement entering from the

undisturbed flow in the mixing layer for reaching a maximum peak still in the mixing layer and for

after decreasing to a lower a constant value in the jet core. Moving on the other side of the jet radius

the total temperature presented a symmetric behaviour. For better understand the jet behaviour, the

radial distribution of the non dimensional total temperature respect the inlet temperature condition

TCO2 is plotted together with the radial Mach ratio M/M0 (Figure 13a, b and c). Let note that the T0

cooling starts with the Mach slope, reach a maximum and decreases for reaching a constant value

coincident with the constant front of the Mach radial distribution.

This particular shape, characterised by a double peak in correspondence of the inner zone of the

mixing layer and by two minimum regions off the centreline, was characteristics for all the

measurements except that for the over expanded jet at x/D=7.1. At that distances, the over expanded

jet that is characterized by the larger spreading rate, is already mixed and as discussed earlier can be

considered in self-similarity conditions. The total temperature radial distribution still present the

two minimum values but the peaks are disappeared showing a more uniform shape (Figure 12a and

Figure 13a) similar to the T0 data presented by Wang and Andreopoulos (2010).

Some understanding of this behaviour can be obtained by considering the total enthalpy transport

equation:

( )j

iij

piipp x

u

Cx

T

xC

k

dt

dp

CDt

DT

∂

∂+

∂

∂

∂

∂−=

τ

ρρρ

110 (12)

where τij is the deviatoric stress tensor defined as:

∂

∂−

∂

∂+

∂

∂= ij

k

k

i

j

j

i

ijx

u

x

u

x

uδµτ

3

2

The last term on the right-hand side represents the dissipation rate of kinetic energy. It is the

negative sign in front of the heat conduction term that provides an opposite contribution to the

DT0/Dt and in addition, the diffusivity k/ρCp which controls its magnitude. Thus, higher diffusivity

or temperature gradient will result higher changes in T0. The processes involve large unsteady

mixing due to high turbulence level that is present there, while molecular mixing appears to be

slower in time. The jet static temperature is always below the ambient temperature, which initiates

an unsteady heat exchange between the ambient air and the jet flows. The high stress tensor values


- 16 -

(Figure 14 a,c,e) and high turbulence level (Figure 14 b,d,f) in the mixing layer induced the two

maximum peaks out side the centreline. As a result, total T0 is higher at the inner mixing layer than

in the centreline of the jet where the flow velocity stress tensor and the turbulence level is almost

negligible and lower than the Ta at the edges of the jet due to high conductivity losses.

Figure 12: Total temperature distribution long the centerline at different jet conditions (a).Radial total

temperature distribution measured at different axial distance in over expanded jet (b), fully expanded jet (c) and

under expanded jet (d).

Further considerations arise from the total temperature behaviour. The centreline T0 value is directly

connected to the jet speed and to the inlet temperature conditions. For the same test case, the

difference of the inlet temperature is equivalent to the step of the total temperature measured in the

centreline, whereas the T0 step of the maximum peaks in the inner mixing layer are related to the

turbulent distribution in the mixing layer, so the over expanded jet presents first an increment

followed by a decrement, whereas for the adapted jet and under expanded jet conditions the peak

step shows a continuous increment still being in the jet core region. The T0 peaks step behaviour is

fully in agreement with the turbulent flow distribution (Figure 14 b, d f). The comparison of T0

radial distribution at the same distance from the nozzle exit for the different jet nozzle conditions

(Figure 13 d) shows as the over expanded jet is characterised by larger spreading rate with the

mixing layer starting at r=40mm. followed by the fully expanded jet with mixing layer border at

about r=30mm and by the under expanded jet with the closer aperture with r= 27mm.

(a)

(c) (d)

(b)


- 17 -

Figure 13: Mach number and total temperature distribution at about x/D=8 in over expanded jet (a), fully

expanded jet (b) and under expanded jet distribution. Radial Total temperature comparison at x/D=8 in different

jet conditions (d)

4.3 Compressibility effects

The compressibility effect due to the different jet conditions has been already encountered

discussing the mean velocity field and the total temperature distribution. The mean velocity field

showed that increasing the inlet pressure the spreading rate value decreased showing smaller mixing

layer thickness and Mach decay was delayed. The total temperature radial behaviour also presented

the influence of the compressibility in the centreline behaviour and on the radial distribution related

to the flow turbulence level strictly connected to the compressibility effect. Another consideration

can be drawn about the shear strain, increasing the jet compressibility the shear strain in the mixing

layer increases as well (Figure 14 a, c, e). The compressibility effect on the flow turbulent level and

on turbulent kinetic energy (Figure 14 c, d and f) showed a decrement of the kinetic turbulent

energy. The over expanded jet was characterised by an intense value of the turbulent kinetic energy

(TKE) immediately starting from the nozzle exit, reaching a maximum for later decreasing beyond

the core region. The fully expanded jet, characterised by a reduction of the mixing layer, showed

also a reduction in the TKE close to the nozzle exit with negligible values up to a distance of

x/D=4.7 (about x=100mm), for distance larger than 4.7 diameters the turbulent kinetic energy value

become intense along the full measured mixing layer. The under expanded jet also followed the

already discussed trend, the mixing layer growth was the smallest and the TKE becomes

appreciable at larger nozzle distance of x/D= 5.9. The effects of the compressibility was

investigated also on the local turbulence intensity along the axisymmetry and on the radial

distribution of the Reynolds stress components u’u’, v’v’ and u’v’. The local turbulence distribution

long the symmetry axis showed that increasing the compressibility effect the local turbulence

decreases (Figure 15 a). The Reynolds stress radial distribution at the nozzle distance of x/D=7 for

the different jet conditions were compared (Figure 15 b, c and d). The non dimensional Reynolds

stress components presented similar trend, the value decreases as the compressibility of the jet

increases.

(c) (d)

(a) (b)


- 18 -

Figure 14: Shear strain contours for over expanded jet (a), fully expanded jet (c) and under expanded jet.

Turbulent kinetic energy in over expanded jet (b) fully expanded jet (d) and under expanded jet (f).

Figure 15: Non dimensional local turbulence intensity long the jet axis (a) and radial Reynolds stresses (u’u’ (b),

v’v’ (c) and u’v’ (d)) at x/D=7 for over expanded jet (P0=2.1 bar), fully expanded jet (P0=3.6 bar) and under

expanded jet (P0=4.25 bar).

5. Conclusion and Future activities In the present work, the behaviour of compressible supersonic jet issuing in calm air was

investigated. A new flow feeding system and a new supersonic jet were designed and realised for

reaching a jet exit Mach number of Mj=1.5 and obtain a convective Mach number of Mc=0.6, where

the compressible effect become sensible. The effect of the density gradient was investigated using

(b) (a)

(c) (d)

(a) (b)

(f)

(d) (c)

(e)


- 19 -

carbon dioxide as jet flow. The supersonic jet was investigated in over expanded, fully expanded

and under expanded conditions. Higher values of Mach and Reynolds number were reached respect

most of the values available in the literature. The Jet Mach number, the total temperature and the

flow field velocity were measured. The Mach longitudinal and radial distribution was investigated.

The compressibility effects were detected on the spreading rate behaviour of the different test

conditions, the over expanded jet presented the larger spreading rate respect to the other conditions.

The results indicated that increasing the inlet pressure the mixing growth decreases. The over

expanded jet was characterised by a strong shock immediately downstream the nozzle exit that

induced a speed deceleration to M0=1.1, followed for about four jet diameters by a constant value

for later starting to linearly decay. The over expanded jet for distance larger that 7 nozzle diameters

showed to be in self similarity flow conditions, substantiated by the values of the spreading rate and

of the velocity decay constant, by the collapsing of the radial velocity profiles onto a single curve

and by the behaviour of the local turbulent flow and of the Reynolds stress tensor components. The

fully expanded condition was characterised by a slightly over pressure value respect the ambient

conditions, presenting a train of weak expansion and oblique shock waves. The mean Mach number

distribution along the axisymmetric jet presented an almost constant value up to a distance of

x/D=11, where the Mach decay started. The under expended jet showed intense Mach fluctuation

due to stronger train of expansion and shock waves around a constant value, Mach decay in not

encountered because delayed by the compressibility effect. The reduction of the mixing layer was

evident also by the total temperature data showing the maximum growth of the mixing layer for the

over expanded case followed by the adapted jet and by the under expanded jet. The total

temperature radial distribution correlated the compressibility effect with the flow turbulence in the

mixing layer. The radial local turbulence intensity and the Reynolds tensor components showed that

increasing the compressibility effect together with the spreading rate reduction a turbulence

intensity reduction was encountered or would be better to say a delay. The data analysis is still

under process and the comparison with the numerical results shall be the next step of the activity.

Acknowledgements The authors would like to thank dr. Emanuele Martelli for supporting in designing the test matrix

and the supersonic nozzle. The work has been partially funded by the Italian Space Agency in the

framework of the project CAST.

References Adrian RJ (1991) Particle Imaging Techniques for Experimental Fluid Mechanics. Annual Review

of Fluid Mechanics, vol 23 pp 261-304.

Birch SL, Eggers JM (1972) A critical review of the experimental data on turbulent shear layers.

NASA SP 321

Bogdanoff DW (1983) Compressibility effects in turbulent shear layers. AIAA J 21:926–927

Chinzei N, Masuya G, Komuro T, Murakami A, Kudou K (1986) Spreading of two-stream

supersonic turbulent mixing layers. Phys Fluid 29:1345–1347

Clemens NT, Mungal MG (1992) Two- and three-dimensional effects in the supersonic mixing

layer. AIAA J 30:973–981

Clemens NT, Mungal MG (1995) Large-scale structure and entrainment in the supersonic turbulent

mixing layer. J Fluid Mech 284:171–216

Elliott GS, Samimy M (1990) Compressibility effects in free shear layers. Phys Fluid A 2(7):1231–

1240

Hussein HJ, Capp S and George WK (1994) Velocity measurements in a high-Reynolds-number,


- 20 -

momentum-conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 31-75.

Longmire EK, Eaton J (1992) Structure of a particle laden round jet. J Fluid Mech 236:217–243

Luo K, Klein M, Fan RJ, Cen KF (2006) Effects on particle dispersion by turbulent transition in a

jet. Phys Lett A 357:345–350

Maxey MR (1987) The gravitational settling of aerosol particles in homogeneous turbulence and

random flow fields. J Fluid Mech 174:441–453

Paciorri R and Sabetta F, (2003) Compressibility correction for spallart-allmaras model in free

shear flows. Journal of spacecraft and rokets, 40(3):326-331.

Panchapakesan NR and Lumley JL (1993a) Turbulence measurements in axisymmetric jets of air

and helium. Part 1. Air Jet. J. Fluid Mech. 246, 197-223.

Panchapakesan NR and Lumley JL (1993b) Turbulence measurements in axisymmetric jets of air

and helium. Part 2. Air Jet. J. Fluid Mech. 246, 225-247

Papadopoulos G and Pitts WM (1998) Scaling the near-field centreline mixing behaviour of

axisymmetric turbulent jets. AIAA J 36(9):1635–1642

Papamoschou D and Roshko A (1988) The compressible turbulent shear layer: an experimental

study. J Fluid Mech 197:453–477

Papamoschou D and Roshko A (1988) The compressible turbulent shear layer: an experimental

study. J Fluid Mech 197:453–477

Pope S B (2000) Turbulent Flows. Cambridge University Press, ISBN 0 521 59125 2

Raffel M, Willert C and Kompenhans J, (2002) Particle Image Velocimetry: A Practical Guide,

Springer,

Richards CD, Pitts WM (1993) Global density effects on the self preservation behaviour of

turbulent free jets. J Fluid Mech 254:417–435.

Wang Z and Andreopoulos Y (2010) Density and compressibility effects in turbulent subsonic jets

part 1 mean velocity fields. Exp Fluids 48 327-343

Documents

Free Compressible Jet Nozzle Investigation - ULisboaltces.dem.ist.utl.pt/lxlaser/lxlaser2012/upload/163_paper_ecvgbw.pdfcompressible flows require an accurate description of the large-