Free Compressible Jet Nozzle Investigation

Transcription

1 Free Comressible Jet Nozzle Investigation Fabrizio De Gregorio 1,*, Floriana Albano 1 1: Fluid Mechanics Deartment, Italian Aerosace Research Centre (CIRA), Caua (CE), Italy * f.degregorio@cira.it Abstract The comressibility effect on a suersonic turbulent jet was investigated. A new suersonic nozzle and a new flow feeding systems were designed and realized. A nozzle Mach exit of M j =1.5 was selected in order to obtain a convective Mach number of M c =0.6 where the comressibility effect becomes sensible. The density gradient (ρ j /ρ a ) effect was also investigated using carbon dioxide as feeding gas in order to obtain a CO 2 jet flowing in still air. The jet nozzle was investigated for the cases of over exanded, fully exanded and under exanded jet. Mach number, total temerature 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 seed 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 robe and by the PIV measurement system was carried out. The mean flow velocity was investigated and the Mach decay henomena and the sreading rate where correlated to the comressibility effects. The longitudinal and radial distribution of the total temerature was investigated, the temerature rofiles were analysed and discussed. The total temerature behaviour correlated to the turbulent henomena and to the comressibility effects. The self similarity condition encountered and discussed for the over exanded jet. Comressibility 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 redict and control high seed jet flows for otimal design of aerosace vehicles. In this Mach number range, large variations in ressure, density or temerature can take lace that can have an imact on the dynamics of turbulence. The early work by Bradshaw (1977) ointed out the need for models with significant comressibility corrections for reliable redictions of free shear flows. Imroving rediction caabilities and roviding effective control of comressible flows require an accurate descrition of the large- and small-scale dynamics as well as the time-averaged statistical roerties of the flow. The most significant effect of comressibility 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 Paamoschou and Roshko (1988) who used the concet of convective Mach number (M c ) to characterize the shear layer comressibility. The Mach convective number is defined as M c =(U ex - U in )/(a ex -a in ) where U is the jet seed, a is the seed of sound, the subscrits ex and in indicate the magnitudes related to the external and internal flows. It has been demonstrated by Bogdanoff (1983) that the comressibility reduces the increment rate of the mixing layer thickness resects incomressible flow at same seed ratio r=u ex /U in. The comressibility effects become imortant for values of the convective Mach larger than 0.5. More detailed studies have shown a suression of mixing-layer growth rate with increasing comressibility (see Chinzei et al. 1986; Paamoschou and Roshko 1988; Elliott and Samimy 1990; Clemens and Mungal 1992, 1995). The growth rate of incomressible mixing layers is always associated with increased turbulent activities, and its suression in comressible mixing layers is accomanied by a reduction in turbulence roduction. There have been several ast investigations to rovide roer scaling and characterization of the - 1 -

2 self-similar region of axisymmetric turbulent jets. Richards and Pitts (1993) showed that regardless of the initial conditions i.e. fully develoed ie flow or nozzle flow, axisymmetric free jets decay at the same rate, sread at the same half-angle and both mean and fluctuating mass fraction values collase in a form consistent with self-reservation. Subsequently Paadooulos and Pitts (1998) demonstrated exerimentally 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 resonsible for breaking u the otential core and for transforming the jet into a fully develoed self-similar flow. The sreading rate of comressible jets varies with the jet exit Mach number (Zaman 1998). Results for the far asymtotic region show that both sreading rate and centreline velocity decay rates, when roerly non-dimensionalized by arameters at the nozzle exit, decrease with the jet Mach number. The work of Wang and Andreooulos (2010) investigated the combined effect of density and comressibility, testing different gases and different subsonic Mach numbers u to M j =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 ste forward have been erformed toward the understanding of the hysics of turbulent jet (at limited Reynolds number of the order of ), few exerimental data are available at higher seed and higher Reynolds numbers and still many asects need to be investigated in order to otimize the sace roulsion and minimize the noise emission. For this scoe in 2006 the Italian Sace Agency launched the CAST roject aimed to investigate innovative theoretical chemical-hysics models and advanced numerical methodologies for building an integrated numerical/exerimental system able to better investigate fundamental asects of the aerothermodynamics and of the aeroacoustic of the sace roulsion. The understanding of the hysic/chemical laws regulating the mixing layer of two coaxial flows characterised by different chemical comosition, seed, temerature and ressure was one of the aims of the roject. This work was aimed to fulfil the lack of exerimental data to validate new models of turbulence and turbulent dissiative transort in continuous develoment (Paciorri and Sabetta 2003). The behaviour of comressible jets originated from a convergent/divergent nozzle issuing in still air was investigated at suersonic seed. The exeriment was designed in order to achieve significant effect of the comressibility on the free shear flow. A dedicated convergent/divergent nozzle was designed and built in order to obtain a jet Mach exit equal to M j =1.5 in order to obtain a convective Mach number of M c =0.6. The nozzle jet was characterised for three different conditions: isentroic exansion where the nozzle exit ressure ( j ) is equivalent to the ambient ressure ( a ) ( j = a adated nozzle), over exanded nozzle characterised by nozzle exit ressure lower than the ambient ressure ( j < a ) and under exanded nozzle with the nozzle exit ressure higher than the ambient ressure ( j > a ). Carbon dioxide (CO 2 ) was used to generate the jet flow in order to evaluate the additional effect of the density ratio and of different chemical secies on the flow structures. Particular care was taken in measuring the mixing layer flow characteristics. 2. Exerimental design set-u The test camaign and consequently the nozzle was designed taking in mind the following requirements: reroduce the comressibility effect (M c >0.5), investigate the density gradient effect, achieve a Reynolds number of the order of 10 6, generate an axisymmetric turbulent jet characterised by sizes comatible with the ressure and temerature intrusive robes, reduce the comlexity of the feeding system and the cost of the test exeriment. The comressibility effect in the mixing layer was obtained designing and manufacturing a dedicated convergent/divergent nozzle characterised by a Mach exit equal to M j =1.5 and a convective Mach number of M c =0.6, value for - 2 -

3 which the comressibility effect become sensible. The method of the characteristics (MOC) was adoted for design the nozzle geometry. The density gradient effect was reroduced selecting the carbon dioxide (CO 2 ) for feeding the nozzle jet. The CO 2 resented: density heavier than that of the air and a smaller value of the secific heat ratio (Table 2), low hazard factor in term of oerational safety, easy to suly at low cost. For designing the test condition the assumtion of Eulerian, onedimensional and isentroic flow was taken. The over exanded condition was selected taking into account the Sommerfield rincile to avoid flow searation in the nozzle divergent and a limitation on the minimum temerature was imosed in order to avoid a variation of the flow status during the flow exansion. The designed test matrix foresaw three different test conditions: an over exanded jet (P 0 =2.1bar), a fully exanded jet (P 0 =3.6 bar) and an under exanded jet (P 0 =4.25 bar). In Table 1, the total ressure (P 0 ), temerature (T 0 ) and density (ρ 0 ) in stilling chamber together with the static ressure ( j ), temerature (T j ) and density (ρ j ) in corresondence of the nozzle exit and the mass flow (Q) and Reynolds number are summarised. These values were calculated on the hyothesis of one-dimensional flow, of calorically erfect gas. The Reynolds number is calculated on the seed of sound a, gas density and viscosity and the nozzle exit diameter D j. γ * * Re = 0 D j D R * T * µ (1) 0 where µ indicates the viscosity in stilling chamber (µ= Pa s); R is the secific gas constant (R= J/kg K for the carbon dioxide). Test condition M J P 0 [Pa] T 0 [K] ρ 0 [kg/m 3 ] j [Pa] T j [K] ρ j [kg/m 3 ] Q [kg/s] Re D Over exanded jet Adated jet nozzle Under exanded jet Table 1: Nozzle designed test conditions 2.1 Convergent-divergent suersonic nozzle and feeding flow facility The Eulerian one-dimensional isentroic law for the selected Mach number and gas (CO 2 ), fixed the nozzle section ratio equal to A j /A t =1.189, where A j is the nozzle exit section and A t is the throat section. Fixed the mass flow value of Q=0.3 kg/s the nozzle exit diameter of D j =21.22mm and a length of the divergent of L d =21mm were obtained. The nozzle was equied with 27 ressure ort (PTS), 24 PTS distributed long the nozzle longitudinal direction and 4 ressure orts in roximity of the nozzle exit section equally saced in azimuth (Figure 2 b). A comlex flow suly system was designed and realised in order to rovide steady quantity of mass flow at the required values of ressure and temerature. The feeding system was comosed by a litres tank car storing the CO 2 liquid at a ressure of 25barg and a temerature of 253,15k, followed by a dedicated vaoriser system roviding a maximum flow rate of 1000 Nm 3 /h and an heating system dedicated to increase the gas temerature at T CO k (Figure 1 a). Next the first stage ressure regulator was installed allowing a gas ressure dro from 22barg to 14barg, the ressure regulator was followed by 50 meters of ie rake delivering the gas inside the hangar to the second ressure stage regulator. The second ressure stage regulator was designed for fine regulation. It was comosed by two distinct lines that if used singularly rovided the necessary ressure and mass flow to the test article for reroducing the case of over exanded jet (P 0 =2.1 bar) and the fully exanded jet (P 0 =3.6bar)

4 Figure 1: Liquid tank, vaorizer and heating systems and 2 nd stage ressure regulator, sensors and control anel. Using the two lines simultaneously the setting condition for the case of under exanded jet (P 0 =4.25 bar) were obtained. At the end of the flow suly system, ahead the test article inlet the measure and control atch anel was located. The transducers measured the static ressure ( CO2 ) and temerature (T CO2 ) and the mass flow (Q CO2 ) of the gas before entering in the CIRA test article (Figure 1 b). The transducers signals were delivered to the control anel digital dislays and to the PSI8400 data acquisition system (DAS) and continuously recorded. 2.2 Test article The CIRA neumatic calibrator was used for generate the free turbulent nozzle jet. The test article was comosed by different sections (Figure 2 a). The inlet section was equied with a breaking late and the honeycomb screens, a second section was adated for feeding the seeding articles in the flow, a third section with different net screens for imroving the flow quality and remove eventual turbulent structures shedding from the seeding ies, a fourth section was emty as stilling chamber. On the first, third and fourth sections, two static ressure ort for each section were resent. The sections have internal diameter of D sc =174mm. The last comonent was the suersonic nozzle (Figure 2 b). Figure 2: Test article layout and ressure orts distribution on the suersonic nozzle 2.3 Instrumentation and data acquisition system The jet Mach number and total temerature distribution long the jet symmetry axis u to x/d=7 and long the jet radius at different distances from the nozzle exit were investigated by means of dedicated miniaturised intrusive robes. The reduced dimension of the robes was mandatory in order to get several measurement oints inside the jet mixing layer. A conical static Pitot robe L shaed with a diameter of 1mm and the static tas located at 8 robe head diameter behind the head - 4 -

5 base for minimise the robe interface was utilised for the Mach number measurements. The robe was connected to the electronic ressure transducers for recording the mean total and static flow ressure. The total temerature robe was L shaed as well, the diameter was 1.6 mm and the venting holes were located 8mm behind the robe head. Inside the robe there was a J tye thermocoule. The temerature sensor was calibrated in the temerature range from to K. The robes were singularly mounted on a dedicated suort connected to a 2D linear traversing system and located in front the nozzle (Figure 3 a). The adoted 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 uward oriented and the y-axis is oriented following the rule of the right hand. Furthermore the jet flow field was measured u to x/d j =16 using a 2 comonents PIV system. The system was comosed by two Nd-Yag resonator heads roviding a laser beam of about 300 mj each at 532 nm. The free jet was illuminated from above. The measurements were erformed on the vertical symmetry lane of nozzle jet. Two high resolution (2048x2048 x) 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 satial resolution. The cameras were mounted on the right side of the jet as shown in Figure 3b. Each camera recorded a region of about 95x95mm 2 with a satial resolution of 0.56 mm/vector. The cameras were moved of about 70mm in x-direction u to cover a total region of 350x95 mm 2. The flow field recording regions together with the robe measurement ath are summarised in Figure 4. The seeding selection was a critical oint due to the ossibility of the resence of shock wave trains long the jet. A dedicated high ressure seeding generator was develoed. The generator was equied with twenty four Laskin nozzles roviding articles diameter of 1 µm. DEHS oil was adoted 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 oerate u an overressure of 5 barg in order to overcome the total ressure in the calibrator stilling chamber. The seeding articles were insert in the test article trough the seeding ies located in the second section (Figure 2a). Light sheet Probe Suort PIV cameras Laser 2D traversing system Probe Figure 3: Over view of the Static Pitot robe set u and of the PIV set u A PSI 8400 data acquisition system was used for recording: the ressure distribution long the nozzle and at the three different stations of the neumatic calibrator, the total and static ressure of the static Pitot robe, the total temerature of the TAT robe, the imosed reference ressure to the EPS modules and the CO 2 suly system measurement sensors (ressure, temerature and mass flow)

6 Gas γ R [J/kg K)] a sound seed [m/s] ρ [kg/m 3 ] µ [10-6 Pa s] ν=µ/ρ [10-6 m 2 /s] C [J/kg K] Cv [J/kg*K] CO Table 2: Carbon dioxide roerties at ambient temerature k= Data Reduction Figure 4: Static Pitot and total temerature robes measurement regions. 3.1 PIV data analysis and Accuracy Estimation One hundred and fifty (150) PIV coules of images were acquired er each test condition. The images were filtered by subtracting the minimum image calculated on the comlete set of samles of the corresondent test case. This re-rocess function allowed reducing the background noise of the PIV images and increases the signal to noise ratio. Moreover all the recordings acquired in roximity of the nozzle exit were masked for increasing the results reliability otherwise affect by strong light reflections. The re-rocessed images were analysed by a multi-grid algorithm. The algorithm uses a yramid aroach by starting off with larger interrogation windows on a coarse grid and refining the windows and grid with each ass. From the u and v velocity comonents the following quantities are extracted, the out of lane comonent of the vorticity and the enstrohy that rovide an information about the dissiation effect, the shear strain ε ij and the normal strain ε ii and the velocity magnitude V = u + v + w = u + 2v assuming that the out of lane comonent is equivalent to the radial comonent. Furthermore some statistical quantity are evaluated as the ensemble average velocity field, and the RMS velocity comonents. Knowing the flow density the Reynolds stresses comonents 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 erformed. Following the work of Adrian (1991), the number of ixels/article for the adoted exerimental set u was determined. First the image diameter of the focal sot roduced by a zero diameter article was calculated, given by the following formula: d s 2.44*(1 + M )* f #*λ = (2) Where d s is the diameter of a article on the CCD sensor, M the image magnification factor, and λ the wave number of laser light. Using this result along with article diameter, magnification and resolution the image diameter of the article on the CCD sensor was obtained being governed by: d e M d + ds + = d (3) 2 r - 6 -

7 where d is the actual article diameter (1µm) and d r is the ixel resolution (7.4 µm). Carrying out the calculations using the data summarise in Table 3 it was found a value of ixels for article. The ixel article ratio being larger than 1 assured minor effect due to the ixel locking effect. f# d r (10-6 m) d (10-6 m) d s (10-6 m) d e (10-6 m) ixel/article Table 3: Calculation of the ixel article ratio The PIV data evaluation followed the standard rocedures given by Raffel et al (2002). The random noise of the dislacement was considered smaller than 0.05x. Minor bias errors were exected, including minor effects of eak-locking. However, based on the dislacement histograms, the bias error was estimated to fall below random noise, i.e. less than 0.05x. The resulting velocity error ε u was estimated as: ε u = ε x / ( t M) (4) where t is the ulse-searation time and M is the otical magnification. The velocity error was calculated in ε u =2.34 m/s and scaling with the maximum in-lane velocity comonent U max =350m/s the relative error ε u,rel = ε u /U max was determined equal to ε u, rel =0.6 %. Further consideration about the PIV accuracy shall be erformed in the following discussing the PIV behavior through the shock waves. Lens focal Recording f- M CCD Interrogation length region size number [10-2 mm/x] resolution Window size (mm) [mm 2 ] / x x96 24x24/32x32 Ste size 12x12 / 24x24 Interrogation method ε x ε u t [x] [m/s] [10-6 s] Multi grid Table 4: Summary of main PIV recording and data rocessing settings and error estimation. 3.2 CO 2 inlet data monitoring and recording and total temerature data correction The carbon dioxide inlet conditions to the suersonic nozzle were continuously monitored and recorded. The ressure and mass flow inlet maintained a constant value during the test run time (Figure 5a and b), whereas the values of the static temerature resented always a slight increment that was ossible to interolate for the case of over exanded and adated jet with a linear curve and for the under exanded jet case the temerature behavior was aroximate by a quadratic curve (Figure 5c). The Carbon dioxide inlet temerature increment influenced the jet total temerature measurements. For the under exanded jet, the total temerature distribution long the jet symmetry axis showed a fluctuating rofile characterized by a ositive mean value increment (Figure 5d indicated by the blue line), increment corresonding to the inlet temerature increment (Figure 5d red line). The total temerature increment was not justified by the flow conditions it was due by the ositive gradient of the inlet gas. The total temerature data were corrected subtracting the temerature comonent due to the inlet gradient (black curve in Figure 5d)

8 (c) (d) Figure 5: CO 2 static temerature static ressure and mass flow (c) inlet data versus the recording time, total temerature raw data and correct data long the jet axis of symmetry. 3.3 Sound seed calculation Starting from the static temerature and the mass flow measured by the CO2 suly system was ossible to evaluate the CO 2 sound seed, static ressure and temerature and gas density to the nozzle exit. Taking into account the dioxide carbon magnitudes reorted in Table 2. Starting from the measured mass flow rate, calculating the CO 2 density from the equation of the ideal gas = R* T ρ (5) and knowing section area of the ie it is ossible to obtain the CO2 seed in the sensor section ie V ie. In the same way knowing the section of the stilling chamber is ossible to calculate the gas seed in the stilling chamber V sc. Once that the seed in the ie is known and the static temerature is measured, it is ossible using the equation under the assumtion of isentroic flow below indicated to calculate the total temerature in the Pie T 0 CO2. c 2 u = c T (6) 2 T0 + Once that the total temerature is calculated, knowing the ratio between the total temerature and the static temerature to the exit due to the nozzle geometry (T 0 /T exit =1.3375), it is ossible to calculate the static temerature to the nozzle exit. At this oint using the equation (7), the seed of sound at nozzle exit a j for the different conditions is obtained. Where v a = γ * R * T (7) γ = c / c is the secific heat ratio, R is the gas universal constant and T is the static temerature. The static ressure and the gas density to the nozzle exit were calculated using the formulas (8). Table 5 the CO2 seed of sound to the nozzle exit for the three conditions of correct exanded nozzle, over exanded and under exanded are reorted

9 0 γ 1 = 1+ M 2 2 γ ( γ 1) and ρ0 γ 1 = 1+ ρ 2 1 ( γ 1) 2 M (8) P 0 P CO2 T CO2 Q CO2 ρ CO2 V Pie P sc ρ sc V sc T 0 CO2 a CO2 T j a j P j ρ j [bar] [bar] [k] [kg/s] [kg/m 3 ] [m/s] [Pa] [kg/m 3 ] [m/s] [k] [m/s] [k] [m/s] [Pa] [kg/m 3 ] Table 5: Measured CO 2 inlet quantities and calculated seed of sound,, T and ρ to the nozzle exit. 3.4 Mach number calculation (Static Pitot and PIV) Considering the static Pitot robe in a comressible flow the equation (8) that relates the total ressure with the static ressure is valid. Solving for M the following equation is obtained: M = 2 γ 1 ( γ 1) γ 0,1 Hence knowing the total and static ressure the Mach number was calculated. The Mach number results successively were corrected taking into account the calibration matrix rovided by the robe roducer. The Mach number distribution was calculated also starting from the PIV data. Once that the sound of seed was calculated to the jet nozzle exit for each test condition, the flow velocity field was divided by the sound of seed roviding the Mach number distribution. The Mach number was obtained assuming that the seed of sound of the CO 2 was constant for the full flow field, assumtion that can not be considered valid for all the test conditions. We shall see in the following that the under exanded jet condition resented a substantial oscillation of the static temerature with the consequent variation of the seed of sound that induced a substantial effect on the Mach number distribution. The Mach number measurements, obtained with both techniques, rovided results in good agreement between them. The Pitot robe data was corrected for taking into account the robe deformation due to the aerodynamic loads. The robe 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 exanded jet resented some discreancy between the raw PIV data and the Pitot results (Figure 6 d). The PIV and Pitot behaviours were qualitative similar, a large exansion was encountered immediately downstream the nozzle exit followed by a train of oblique shocks and exansion waves resulting in an accentuate Mach number oscillation long the jet symmetry axis. The Pitot data resented larger Mach number oscillation amlitude than PIV raw data and a better satial resolution detecting some sudden deceleration and acceleration that the PIV data smoothed. For examle at about x/d=1 the Pitot data indicated a dro 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 sike at x/d=1 showing a lateau in the mach curve. The reason is ascribable to the article velocity lag. Although the limited size of the article (d =1 µm) the resonse time calculated using equation (10) was τ s =3.41*10-6 s, corresonding to a article dislacement of about 1 1 (9) - 9 -

10 1.5mm. The seeding articles were not able to following the sudden flow deceleration, just sensed the flow exansion showed by the lateau during the descending sloe. τ s ρ d 2 = (10) 18µ The under exanded jet was interested by a large fluctuation of the total temerature, knowing the flow velocity was ossible to evaluate using the equation (6) the static temerature distribution long the jet symmetry axis and consequently calculate the sound of seed. The PIV Mach distribution corrected using the aroriated seed of sound resented results closer to the Pitot robe (Figure 6 d red curve), the value of the oscillation amlitude increased becoming of the order of the Pitot results. The PIV data resented a mean value slightly higher than the Pitot results. Hereinafter the PIV data shall be adoted for investigate the jet behaviour. (c) (d) Figure 6: Pitot and PIV Mach radial distribution comarison in over exanded jet, fully exanded and under exanded (c). Pitot and PIV Mach longitudinal distribution. 4. Results 4.1 Free turbulent Jet discussion Tyical flow visualization images that are used to determine the sreading rate are shown in Figure 7. These images were obtained combining three PIV recording regions covering from the jet exit u to x/d=10, and they are indicative of concentrations of the articles used to seed the flow. Their Stokes number defined as the ratio of the article resonse time scale τ s = ρ d 2 /18µ (where ρ and d are resectively the article density and diameter and µ is the flow viscosity) to that of the flow time D/U J (where D is the jet exit diameter and U j is the exit jet seed), i.e. the equation St ρ d 2 = (11) D / U /18µ j

11 reached values of St=0.055 for the case of over exanded jet and St=0.056 for the case of adated and under exanded jet. It has been found that article disersion correlates closely with the Stokes number. Longmire and Eaton (1992) showed exerimentally in a round jet that articles with St near unity tend largely to low-vorticity/low-seed 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 article disersion only when St is close to 1 and that the article closely follow the vortical motion and diserse uniformly in the flow for St = Most articles 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 lace the disersion atterns adjust to the new time scales of the flow, while the time resonse of the article remains the same. (d) (e) (f) Figure 7: Pressure ratio effect on the sreading rate, flow visualization and ensemble average Mach number colour ma distribution, over exanded jet (a and b), fully exanded jet (c and d ), under exanded jet (e and f). This change increases the effective Stokes number, and therefore the articles 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 article distribution as a whole looks uniform. The resent flows were already turbulent (Re> ) and as shown by the ictures of over exanded and adated jet the article concentration aears to be reasonably uniform immediately after the exit of the nozzle. Then, mixing with ambient fluid taken lace which leaded to sreading and entrainment and ockets of low article concentration aear in the images which indicate a fish bone like structure in the flow. The under exanded jet resented the same structure and Stokes number of the other test conditions but it was characterised by an aarent higher article concentration in the shear layer region. This was due to the further jet exansion with consequent further cooling downstream the nozzle exit, inducing in the mixing layer region the vaour condensation of the external air. This high concentration of water articles in the mixing layer regions, indicated by an higher light brightness, addressed a decrement of the PIV image otical quality starting from x/d=5 for

12 comletely recluding the analysis at a nozzle exit distance x/d larger than 11. A visual insection of the images of Figure 7 a, c and d indicates that the sreading rate is larger for the case of over exanded jet for becoming smaller for the case of adated jet and further smaller for the case of under exanded flow. PIV images were rocessed and the ensemble average Mach number was evaluated. The sreading rate S defined as the gradient coefficient (S=dr 1/2 /dx) of the jet half-width distance, i.e. r 1/2 is the jet half-width distance defined as the radial osition where the U(x, r 1/2 ) is equal to half of the axial seed (U 0 ). The Mach number radial behaviour long the jet axis was rocessed, and the sreading rates were estimated to be about for the over exanded jet, for the adated jet and for the under exanded jet (Figure 8). These values suggest substantial larger mixing in the case of over exanded jet and considerable less mixing in the case of under exanded jet. It is, therefore, exected that the over exanded jets entrain considerable more ambient fluid than fully exanded jet or under exanded jet which are characterized by reduced entrainment. Figure 8: Jet half width r 1/2 vs axial distance The Mach number distribution along the Jet centreline M 0 for the three different jet conditions is comared (Figure 9). The over exanded jet shows a strong shock to the exit, not detected by the PIV but illustrated by the CFD simulation (Figure 9 a green rofile) followed by a small exansion and comression for stabilizing in a constant value of M 0 =1.1 u to 4 nozzle diameter distance followed by a linear Mach decay. The fully exanded jet condition was characterized by a nozzle exit static ressure slightly higher (Table 5) than the ressure ambient resenting a series of weak trains of exansion and comression waves, resulting in a M 0 oscillating behaviour. The mean Mach number was almost constant down to x/d=10 for then starting to decay. The under exanded jet resented marked oscillation of M 0, starting with a large flow exansion to the jet exit, followed by a series of oblique shock and exansion waves. The tyical under exanded jet behaviour characterised by a continuous divergent/convergent behaviour is shown in the Mach colour ma distribution (Figure 7 f). The mean value of M 0 remain constant u to x/d=11. The Mach number radial distribution was investigated. For all the jet conditions the Mach rofile changed in the jet core region, the influence of the oblique shocks and of the exansion waves are evident in the double eaks rofiles. As the jet decays and sreads, the mean Mach radial rofile change as shown in Figure 9 b, c and d but the shaes of the rofiles do not change. The jet self similarity was verified by lotting the Mach number distribution in self similarity variables ( i.e. M/M 0 vs r/r 1/2 Figure 10b). The over exanded jet case showed that for x/d larger than 7 the curves collase onto one singular curve, confirming the self similarity flow condition although still in the develoing region x/d<30. The self similarity was also confirmed by the values of the sreading rate S= and by the value of the velocity-decay constant B found equal to B=5.8 in agreement with the data resented by Hussein et al in 1994 and by Panchaakesan and Lumley in 1993 (Table 6)

13 (c) (d) Figure 9: Mach radial distribution at different x/d locations in over exanded jet, adated flow and in under exanded jet (c). (c) (d) Figure 10: Mach number (M/M 0 ) radial distribution in similarity coordinates (r/r 1/2 ); over-exanded jet, adated nozzle, under-exanded jet (c). Mean axial velocity decay long the symmetry jet axis for the different three cases (d). The self similarity of the over exanded jet was verified comaring the radial distribution at different distance from the nozzle of the Reynolds stress tensor comonents u u, v v and u v dimensionless resect the square of the centreline velocity U 0 2 with the data resented by Hussein et al in 1994 (Figure 11 a). Analogous comarison was carried out on the radial distribution of the local turbulence intensity dimensionless resect the mean velocity with the Hussein results (Figure 11 b). The calculated Reynolds stress tensor comonents showed similar rofiles characterised by

14 slightly smaller values, for examle the u u /U 0 2 comonent reached a maximum value of almost 0.06 instead of 0.08, v v /U 0 2 reached 0.03 instead of 0.05 whereas u v /U 0 2 reached a value of 0.02 as exected (Figure 11 c). The radial distribution of the non dimensional local turbulence intensity u /<U> resented a similar rofile and slightly smaller values (Figure 11 d). Panchaakesan and Hussein et al. (1994), Hussein et al. (1994), Present work, Present work, Present work, Lumely (1993a) hot wire data laser-doler data over exanded jet adated nozzle under exanded jet Re S B N.A. Table 6: The sreading rate S and the velocity-decay constant B for turbulent round jet (from Poe 2000) The fully exanded jet condition showed for x/d larger than 15 the Mach rofiles collase onto a single curve (Figure 10c), but the sreading rate equal to S= 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 exanded jet condition where the radial Mach rofiles do not converge each other (Figure 10d), the sreading rate S was further smaller S= and the lack of decay do not allowed to measure the decay constant B. (c) (d) Figure 11: Profile of Reynolds stresses and local turbulence intensity in the self-similar round jet (LDA data of Hussein et al 1994), Reynolds stresses (c) and local turbulence intensity (d) at different ositions long the jet in over exanded condition. 4.2 Total temerature behaviour Some further insight into the structure of the jet can be obtained by considering the thermal field and in articular the total temerature measurements. Longitudinal and radial total temerature measurements were erformed. The T 0 distribution long the jet centreline (Figure 12 a) resents for the case over exanded a constant behaviour u to a distance of about 5 nozzle diameter where a

15 linear ositive 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 exanded jet shows a constant behaviour characterised by limited oscillations due by the weak trains of exansion and shock waves resents in the jet. T 0 remains constant confirming the lack of flow mixing being the jet still in otential core conditions. The total temerature for the under exanded jet case resents a substantial oscillating behaviour around an initial constant value u to 3 nozzle diameters followed by a reduction of the mean value. The large fluctuations are due by the marked trains of exansion and shock waves occurring along the jet core. The radial total temerature measurements were erformed traversing vertically the jet flow moving the robe from the undisturbed flow trough the full jet sizes to the outer undisturbed air. Both directions (uward and downward) were carried out having encountered an hysterisis in the robe measurements, robably due to the robe deflection or to a delay in the thermocoule resonse in following stee temerature 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 temerature distribution resectively for the over exanded jet, fully exanded and under exanded flow. In the jet core region the total temerature showed a T 0 decrement entering from the undisturbed flow in the mixing layer for reaching a maximum eak 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 temerature resented a symmetric behaviour. For better understand the jet behaviour, the radial distribution of the non dimensional total temerature resect the inlet temerature condition T CO2 is lotted together with the radial Mach ratio M/M 0 (Figure 13a, b and c). Let note that the T 0 cooling starts with the Mach sloe, reach a maximum and decreases for reaching a constant value coincident with the constant front of the Mach radial distribution. This articular shae, characterised by a double eak in corresondence of the inner zone of the mixing layer and by two minimum regions off the centreline, was characteristics for all the measurements excet that for the over exanded jet at x/d=7.1. At that distances, the over exanded jet that is characterized by the larger sreading rate, is already mixed and as discussed earlier can be considered in self-similarity conditions. The total temerature radial distribution still resent the two minimum values but the eaks are disaeared showing a more uniform shae (Figure 12a and Figure 13a) similar to the T 0 data resented by Wang and Andreooulos (2010). Some understanding of this behaviour can be obtained by considering the total enthaly transort equation: DT Dt 0 1 = ρc d k dt ρc T x i x + 1 i ρc ( τ u ) where τ ij is the deviatoric stress tensor defined as: u u i j 2 uk τ = + ij µ δ ij x j xi 3 xk The last term on the right-hand side reresents the dissiation rate of kinetic energy. It is the negative sign in front of the heat conduction term that rovides an oosite contribution to the DT 0 /Dt and in addition, the diffusivity k/ρc which controls its magnitude. Thus, higher diffusivity or temerature gradient will result higher changes in T 0. The rocesses involve large unsteady mixing due to high turbulence level that is resent there, while molecular mixing aears to be slower in time. The jet static temerature is always below the ambient temerature, which initiates an unsteady heat exchange between the ambient air and the jet flows. The high stress tensor values ij x j i (12)

16 (Figure 14 a,c,e) and high turbulence level (Figure 14 b,d,f) in the mixing layer induced the two maximum eaks out side the centreline. As a result, total T 0 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 T a at the edges of the jet due to high conductivity losses. (c) (d) Figure 12: Total temerature distribution long the centerline at different jet conditions.radial total temerature distribution measured at different axial distance in over exanded jet, fully exanded jet (c) and under exanded jet (d). Further considerations arise from the total temerature behaviour. The centreline T 0 value is directly connected to the jet seed and to the inlet temerature conditions. For the same test case, the difference of the inlet temerature is equivalent to the ste of the total temerature measured in the centreline, whereas the T 0 ste of the maximum eaks in the inner mixing layer are related to the turbulent distribution in the mixing layer, so the over exanded jet resents first an increment followed by a decrement, whereas for the adated jet and under exanded jet conditions the eak ste shows a continuous increment still being in the jet core region. The T 0 eaks ste behaviour is fully in agreement with the turbulent flow distribution (Figure 14 b, d f). The comarison of T 0 radial distribution at the same distance from the nozzle exit for the different jet nozzle conditions (Figure 13 d) shows as the over exanded jet is characterised by larger sreading rate with the mixing layer starting at r=40mm. followed by the fully exanded jet with mixing layer border at about r=30mm and by the under exanded jet with the closer aerture with r= 27mm

17 (c) (d) Figure 13: Mach number and total temerature distribution at about x/d=8 in over exanded jet, fully exanded jet and under exanded jet distribution. Radial Total temerature comarison at x/d=8 in different jet conditions (d) 4.3 Comressibility effects The comressibility effect due to the different jet conditions has been already encountered discussing the mean velocity field and the total temerature distribution. The mean velocity field showed that increasing the inlet ressure the sreading rate value decreased showing smaller mixing layer thickness and Mach decay was delayed. The total temerature radial behaviour also resented the influence of the comressibility in the centreline behaviour and on the radial distribution related to the flow turbulence level strictly connected to the comressibility effect. Another consideration can be drawn about the shear strain, increasing the jet comressibility the shear strain in the mixing layer increases as well (Figure 14 a, c, e). The comressibility 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 exanded 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 exanded jet, characterised by a reduction of the mixing layer, showed also a reduction in the TKE close to the nozzle exit with negligible values u 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 exanded jet also followed the already discussed trend, the mixing layer growth was the smallest and the TKE becomes areciable at larger nozzle distance of x/d= 5.9. The effects of the comressibility was investigated also on the local turbulence intensity along the axisymmetry and on the radial distribution of the Reynolds stress comonents u u, v v and u v. The local turbulence distribution long the symmetry axis showed that increasing the comressibility 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 comared (Figure 15 b, c and d). The non dimensional Reynolds stress comonents resented similar trend, the value decreases as the comressibility of the jet increases

18 (c) (d) (e) (f) Figure 14: Shear strain contours for over exanded jet, fully exanded jet (c) and under exanded jet. Turbulent kinetic energy in over exanded jet fully exanded jet (d) and under exanded jet (f). (c) (d) Figure 15: Non dimensional local turbulence intensity long the jet axis and radial Reynolds stresses (u u, v v (c) and u v (d)) at x/d=7 for over exanded jet (P 0 =2.1 bar), fully exanded jet (P 0 =3.6 bar) and under exanded jet (P 0 =4.25 bar). 5. Conclusion and Future activities In the resent work, the behaviour of comressible suersonic jet issuing in calm air was investigated. A new flow feeding system and a new suersonic jet were designed and realised for reaching a jet exit Mach number of M j =1.5 and obtain a convective Mach number of M c =0.6, where the comressible effect become sensible. The effect of the density gradient was investigated using

19 carbon dioxide as jet flow. The suersonic jet was investigated in over exanded, fully exanded and under exanded conditions. Higher values of Mach and Reynolds number were reached resect most of the values available in the literature. The Jet Mach number, the total temerature and the flow field velocity were measured. The Mach longitudinal and radial distribution was investigated. The comressibility effects were detected on the sreading rate behaviour of the different test conditions, the over exanded jet resented the larger sreading rate resect to the other conditions. The results indicated that increasing the inlet ressure the mixing growth decreases. The over exanded jet was characterised by a strong shock immediately downstream the nozzle exit that induced a seed deceleration to M 0 =1.1, followed for about four jet diameters by a constant value for later starting to linearly decay. The over exanded jet for distance larger that 7 nozzle diameters showed to be in self similarity flow conditions, substantiated by the values of the sreading rate and of the velocity decay constant, by the collasing of the radial velocity rofiles onto a single curve and by the behaviour of the local turbulent flow and of the Reynolds stress tensor comonents. The fully exanded condition was characterised by a slightly over ressure value resect the ambient conditions, resenting a train of weak exansion and oblique shock waves. The mean Mach number distribution along the axisymmetric jet resented an almost constant value u to a distance of x/d=11, where the Mach decay started. The under exended jet showed intense Mach fluctuation due to stronger train of exansion and shock waves around a constant value, Mach decay in not encountered because delayed by the comressibility effect. The reduction of the mixing layer was evident also by the total temerature data showing the maximum growth of the mixing layer for the over exanded case followed by the adated jet and by the under exanded jet. The total temerature radial distribution correlated the comressibility effect with the flow turbulence in the mixing layer. The radial local turbulence intensity and the Reynolds tensor comonents showed that increasing the comressibility effect together with the sreading rate reduction a turbulence intensity reduction was encountered or would be better to say a delay. The data analysis is still under rocess and the comarison with the numerical results shall be the next ste of the activity. Acknowledgements The authors would like to thank dr. Emanuele Martelli for suorting in designing the test matrix and the suersonic nozzle. The work has been artially funded by the Italian Sace Agency in the framework of the roject CAST. References Adrian RJ (1991) Particle Imaging Techniques for Exerimental Fluid Mechanics. Annual Review of Fluid Mechanics, vol Birch SL, Eggers JM (1972) A critical review of the exerimental data on turbulent shear layers. NASA SP 321 Bogdanoff DW (1983) Comressibility effects in turbulent shear layers. AIAA J 21: Chinzei N, Masuya G, Komuro T, Murakami A, Kudou K (1986) Sreading of two-stream suersonic turbulent mixing layers. Phys Fluid 29: Clemens NT, Mungal MG (1992) Two- and three-dimensional effects in the suersonic mixing layer. AIAA J 30: Clemens NT, Mungal MG (1995) Large-scale structure and entrainment in the suersonic turbulent mixing layer. J Fluid Mech 284: Elliott GS, Samimy M (1990) Comressibility effects in free shear layers. Phys Fluid A 2(7): Hussein HJ, Ca S and George WK (1994) Velocity measurements in a high-reynolds-number,

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