Metal particles in solid propellants enhance rocket engines performance. An interaction of particles with a high Reynolds number turbulent gas ow acceler- ating to a nozzle, has not been characterized thoroughly. We study the particle- turbulence interactions in a two-dimensional model of a rocket engine. Two- phase particle image/tracking velocimetry provides the ow velocity simultane- ously with the velocities of irregularly shaped inertial particles ( dp320m, StokesSt70, particle Reynolds number Rep300). We reveal the local augmentation of turbulent uctuations in the particle wakes (up to 5 particle diameters downstream the particle). Despite the low mass fraction, the large response time of the particles leads to an increase of turbulent kinetic energy (TKE) everywhere in the chamber. The increase of local particle mass frac- tion near the nozzle, due to the mass conservation and converging streamlines, compensates for the dampening e ect of the strong mean ow acceleration and further augments TKE at the nozzle inlet. Furthermore, this is accompanied by unexpectedly isotropic uctuations in the proximity of the nozzle. The phe- nomenon of the isotropic, strongly enhanced turbulence in the proximity of the engine nozzle achievable with the low mass fraction of high St;Re pparticles, can be used to improve the design of solid propellant rocket engines. Keywords: Particle laden turbulent ow, Rocket engine, Turbulence modu- lation, Spatial acceleration 1. Introduction 1 Despite a vast body of research on the dynamics of dispersed particles in 2 turbulence, we cannot predict whether TKE will be augmented or attenuated 3 in complex ow cases (Balachndar and Eaton, 2010). For instance, appar- 4 ently similar ow cases were reported to have contradicting trends in studies 5 of particle-turbulence interaction in fully developed channel ows for di erent 6 sizes and densities of particles Kulick et al. (1994); Kussin and Sommerfeld 7 (2002); Kiger and Pan (2002); Li et al. (2012). Kulick et al. (1994) investigated 8 Preprint submitted to Elsevier August 26, 2020 turbulent ow in a vertical channel and found turbulence attenuation that in- 9 creased with mass loading and Stokes number. Kiger and Pan (2002) showed 10 turbulence augmentation far from the wall and negligible e ect near the wall. 11 Kussin and Sommerfeld (2002) found signi cant turbulence augmentation near 12 the channel center plane for particles larger than with particle Reynolds num- 13 bers above 350, and turbulence attenuation near the wall. Conversely,Li et al. 14 (2012) found increased uctuations near the wall and reduced uctuations in the 15 outer region of the boundary layer. Cisse et al. (2013) developed a fully resolved 16 direct numerical simulation around a relatively large particle at moderate parti- 17 cle Reynolds numbers, and using conditional analysis in the coordinate system 18 relative to the particle position, have shown that particles reduce uctuations 19 in their wake. The authors presented particle uid coupling at distances of one 20 particle diameter and that a particle essentially creates a \shadow in its wake". 21 At larger particle Reynolds numbers, Hetsroni (1989) found an augmentation 22 of TKE. The authors explained this by the vortex shedding mechanism in the 23 wake of the particle. These examples are by no means a comprehensive review 24 of the existing literature. It is a small sample emphasizing that a small vari- 25 ation of parameters, along with the carrier phase ow and particle properties, 26 can produce substantially di erent e ects of particles on the TKE. 27 Particle- uid ow interaction is characterized by the ratios of a) length 28 scales, namely, the size of the particle relative to the relevant ow length scale, 29 b) time scales, i.e., particle response time relative to the relevant ow time scale, 30 or the Stokes number, c) particle Reynolds number, Rep, based on the relative 31 (sometimes called slip) velocity (Hetsroni, 1989; Tanaka and Eaton, 2008): 32 Rep=jUVpjdp ; (1) wheredpis the particle diameter, Vpis the particle velocity (bold symbols de- note vectors), is the uid kinematic viscosity, and Uis a so-called \undisturbed uid velocity at the position of the particle", which is practically estimated as an interpolation of the surrounding uid velocity to the position of the parti- cle (e.g. Meller and Liberzon, 2015). The particle relaxation time pfor small and relatively heavy particles, p fandRep<1 is de ned as: p;s=pd2 p 18(2) However, for higher Repa non-linear drag force correction is required (Crowe et al., 2011): p= p;s 1 + 0:15Re0:687p(3) The Stokes number is the time scales ratio (Crowe et al., 2011): St= p f: (4) 2 Large Stokes number St 1 means that particles response time is longer 33 than the ow time scale. In this work, the particles are larger than the Kol- 34 mogorov length scale ( dp> ), and heavier than the surrounding uid ( p 35 f). Therefore, an appropriate ow time scale is that of the mean ow, i.e., 36 f=L=U, whereLis a turbulent integral scale. 37 The length scales ratio, dp=L, whereLis the integral length scale of turbu- 38 lence, was proposed by Gore and Crowe (1989) to distinguish between attenua- 39 tion fordp=L< 0:1 and augmentation for dp=L> 0:1. 40 Separately, the aforementioned ratios of time/length scales could not predict reliably the augmentation or attenuation e ect for di erent ow cases. Tanaka and Eaton (2008) suggested another dimensionless parameter that combines the Stokes number with the ow Reynolds number ReL=UL= and turbulence scale separation =L: Pa=StRe2 L(=L)3(5) The authors (Tanaka and Eaton, 2008) combined empirical data from 80 ex- 41 periments and demonstrated that in the range 103< Pa < 105there is an 42 attenuation of TKE, while for all other cases (below 103or above 105) there is 43 an increase in TKE due to particles. 44 Gany et al. (1978) photographed aluminized solid propellants under cross- 45 ow conditions forming and burning in the form of agglomerates of Al/Al 2O3. 46 The primary particles of the order of 10 m behaved like ow tracers and did 47 not exhibit two-way coupling. However, the irregularly shaped agglomerates, 48 in the range of 40 to 800 m, that formed primarily on the surface during the 49 burning process, afterwards were detached and carried by the turbulent ow. 50 Caveny and Gany (1979) studied the breakup of agglomerates in aluminized 51 propellants when the agglomerates burn slowly compared to the residence time 52 in the rocket motor. They found that the agglomerates velocity lags in the 53 nozzle, cause breakup of suciently large agglomerates, and thereby permit 54 reasonable combustion eciency to be achieved. The motion of large irregular 55 particles resembling the agglomerates in the turbulent ow and their contribu- 56 tion to the TKE balance (augmentation vs attenuation) is the central question 57 of this study. 58 In this work, we study experimentally the e ect of large, heavy, and irreg- 59 ularly shaped particles on the TKE in a simpli ed model of a rocket engine. 60 We reproduce the key features of the mean ow: a) acceleration towards the 61 nozzle; b) the shape of the chamber and the converging type of ow through a 62 small nozzle throat; and c) particle sizes that correspond to metal agglomerates 63 reported in the literature. In this ow, there are competing e ects of acceler- 64 ation, particle-turbulence interaction, and monotonically increasing local mass 65 fraction due to the contracting ow through the nozzle. To what extent various 66 mechanisms contribute to the overall increase or decrease of turbulent kinetic 67 energy is not yet clear. 68 This two-phase ow case is somewhat di erent from the aforementioned ones 69 also in the sense that the particle residence time in the ow is rather short as 70 compared to the particle response time. Due to uid acceleration towards the 71 3 nozzle, all the key parameters, the relative velocity, Stokes number, particle 72 Reynolds number, the uid Reynolds number, all vary in the Lagrangian sense, 73 or inhomogeneous in the Eulerian sense. The case is to some extent analogous 74 to the interaction of large Stokes particles with the near to far- eld of the 75 jets (Prevost et al., 1996), but all the changes occur on time scales shorter than 76 the particle residence or response time. 77 We used particle image/tracking velocimetry (PIV/PTV) to measure simul- 78 taneously the velocities of the uid and particulate phases in two dimensions. 79 In the most general case, a two-wavelength illumination and imaging would be 80 necessary to distinguish between the two phases (Elhimer et al., 2017; Poelma 81 et al., 2006). However, in this case the particles are much larger as compared 82 to the ow tracers, and a simple PIV system is sucient to separate the parti- 83 cles and uid tracers (Khalitov and Longmire, 2002; Hwang and Eaton, 2006). 84 Simultaneous measurements allow to estimate the instantaneous slip velocity 85 using local ow interpolation and to measure TKE, as well as its change in 86 respect to the location of particles. 87 2. Experimental details 88 We created a quasi-two-dimensional experimental chamber (500 mm long, 89 245 mm wide, and 35 mm front-to-back wall distance, nozzle throat width is 90 35 mm) which resembles a cross-section of a generic solid-propellant rocket 91 motor with round symmetrical cavities (Volkov et al., 2012; Ciucci and Iaccarino, 92 2012), shown in Fig. 1. The cavities are characteristic of solid rocket motors 93 with a thrust vectoring system. The back and front walls of the channel were 94 made from glass for particle imaging and the side walls have optical windows to 95 enable optical access for the laser sheet. The purpose is to create a quasi-two- 96 dimensional velocity eld as a proxy of the two-dimensional axisymmetric ow 97 eld in a cylindrically shaped rocket engine. 98 The chamber was positioned vertically with the main ow direction and the 99 particle motion aligned with the gravitational acceleration (Fig. 1a). The air 100 was supplied by a blower through a converging channel (750 mm above the 101 measurement region). The measurement volume is 1 Lt1.8Lt, the lowest edge 102 is 40 mm above the nozzle throat, as shown in Fig. 1c. Above this measure- 103 ment location, the ow resembles the fully developed channel ow with constant 104 streamwise velocity. Mean streamwise velocity pro les are shown for the two 105 Reynolds number cases in Fig. 1b. Within the measurement region, the ow 106 is inhomogeneous in both streamwise and spanwise directions, accelerating and 107 converging into the nozzle, as shown in Fig. 1d. 108 Olive oil aerosol (1 m droplets) produced by a Laskin nozzle seeder, and 109 alumina particles supplied by a custom-made particle seeder (both manufac- 110 tured by I.T.E.S Engineering LLC, Israel) were mixed into the air stream before 111 entering the chamber. 112 We measured turbulent ow and particle motion for two ow rates (low/high). 113 The Reynolds number at the throat is based on the characteristic velocity de- 114 ned by the volumetric ow rate through the chamber and the cross-sectional 115 4 � � B C particles aerosol air Lt7Lt 14Lt 21 0.0 1.841.380.920.46 1.2 1.0 0.8 0.6 0.4 0.218 16 14 12 10V (m/s) 35x/L t y/L ta) b) d) c)Figure 1: a) Schematic drawing of the rocket engine model setup and PIV region of interest. The coordinate system is de ned with xin the streamwise direction of the mean ow through the nozzle and yin the transverse direction. The origin is de ned on the centerline of the chamber 2.8 Ltabove the nozzle throat, b) Mean streamwise velocity distribution U(y=Lt) at 4Ltabove the nozzle throat for both ow rates, c) Zoom in view of the measurement region of 1Lt1.8Lt, d) Mean ow velocity eld and streamlines in the measurement region. 5 area of the nozzle. The Reynolds number at the throat is ReL= 185;000 and 116 260;000, for the low and high ow rates, respectively. In our setup, Ltis the 117 size of the nozzle throat, and the smallest dimension of the chamber determines 118 the integral scale of the turbulent ow. Additional relevant parameters for the 119 two experiments are given in table 1. 120 The PIV setup consists of the double-head pulsed Nd:YAG laser (120 mJ/pulse, 121 532 nm, 15 Hz, New Wave Solo), with laser optics creating a light sheet with 122 approximately 1 mm wide, and a 2672 4008 pixel double exposure 12 bit CCD 123 camera (TSI Inc. Shoreview, MN), equipped with a 100 mm Nikon macro-lens 124 at f/2.8, resulting in a spatial resolution of 42 m/pixel. 125 For the PIV analysis, we used Insight 3G software (TSI Inc.) and compared 126 it to the open source software (OpenPIV, 2019). We used a multi-pass algorithm 127 from 6464 to 3232 pixel interrogation windows, with 50% overlap. The 128 multi-pass method increases the dynamic range, which is especially important 129 for the particle-laden ow cases, due to the high relative (slip) velocity. At 130 each iteration, the outliers vectors were rejected and replaced by the mean of 131 the ve nearest neighbors. The experiments consist of 4 runs at two ow rates 132 with/without particles. Every experimental run consists of 5 sets (repetitions), 133 125 pairs of images each. 134 The mean ow in the region of interest is shown qualitatively in Fig. 1d 135 as color-coded vector plot and streamlines. The spatial coordinates xandy 136 are normalized by the nozzle width Lt. Note that the position of the region 137 of interest is shown in Fig. 1c. The bottom side is 40 mm away from the 138 nozzle throat. The streamlines of the ow eld for both Reynolds numbers are 139 practically identical, except for the representative velocity scale at the nozzle 140 throat of 96 m/s for the low ow rate and 135 m/s for the high ow rate 141 experiments. 142 2.1. Particles 143 We used non-spherical alumina particles that are common in solid propel- 144 lants for rocket engines and other industrial applications. An e ective particle 145 diameterdpwas measured with a laser di raction device (Malvern Analytical) 146 and presented in Fig. 2a. In Fig. 2b, we present the reciprocal of the inscribed 147 circle sphericity of the particles (Wadell, 1935; Riley, 1941), the square root of 148 the ratio of the inscribed and circumscribed circles of the particle. The particle 149 distribution cut o below 250 m because the particle was separated from ner 150 particles with a 250 m sieve. We sieved small batches (about 10 gram) in a 151 controlled manner to verify ne particles were removed after sieving. The mean 152 sphericity of 56 particles, examined under a microscope, is m= 0:810:1. 153 The microscopic images are shown in Fig. 2c, emphasizing random shapes, sharp 154 edges, rough surfaces, cavities, and protrusions. 155 In table 1, we present the ow and particle parameters (some are given as 156 the range of values in the chamber) for the two experiments. Using PIV data 157 and the aforementioned de nitions in Eqs. (2) { (4), we estimated the particle 158 response time scales and the Stokes number. The residence times of the particles, 159 estimated from r=H=V pwhenHis the height of the chamber and Vpin the 160 6 c)Figure 2: a) Probability density function (PDF) of particle e ective diameters dpde ned as a diameter of an equivalent sphere and normalized by the e ective mean diameter dp;mof 320 m b) PDF of reciprocal of sphericity 1normalized by the mean shericity 1 mc) alumina particle's picture under a microscope. mean particle velocity, were 30 to 40 ms. The ratio of particle response time to 161 the residence time, p= r, is between 2 and 4, for the two Reynolds number runs. 162 This ratio explains that particles leave the chamber before they can respond to 163 the air streamwise velocity. 164 Furthermore, we estimate the response of the particles to the spatial accel- eration of streamwise velocity using the acceleration time scale, a: a= (dUc=dx)1(6) and the ratio of scales, a= p. Mean slip due to acceleration of the ow is 165 expected when a= p>1. In our ow, however, a= p 1 is everywhere in 166 the chamber (table 1). Thus, these particles can be characterized in general as 167 \unresponsive" (Hardalupas et al., 1989). It is also important to mention that 168 when a= p= 1, there is a mean slip for nite-size particles due to the shear 169 across the particle diameter. 170 The time scale ratios do not mean that there is insigni cant local particle- 171 turbulence interaction. Conversely, there is a substantial transfer of momentum 172 between the particulate phase and the turbulent uctuations of the carrier ow, 173 as will be explained in the following. 174 Table 1: Particle and ow parameters: ReLbased on ow rate, pis the particle response time, Eq (3), ais the ow acceleration time scale, Eq. (6), ris the particle residence time estimated from r=H=VpwhenHis the height of the chamber, tfis the integral time scale, tf=Lt=Uf,Stis the Stokes number, Eq. (4), ais the acceleration time scale, Eq. (6), particle Reynolds number, Eq. (1), Lis the integral length scale based on the autocorrelation function and is the Kolmogorov length scale = (3=)1=4, whenis the dissipation derived from the structure function. Exp.ReL p(ms) a(ms) r(ms)tf(ms)St p= r a= pRepL(mm)(m) 1 260000 75-90 0.1-1 30 9-11 85 2-3 0.0013- 0.011 300-450 9 62 2 185000 95-121 0.2-3.4 40 13-15 75 2-4 0.0021-0.028 450-650 9 76 7 12 1.25 1.31.15 0.4 0.5 0.3 a)b) 0.4 0.5 0.3Figure 3: Instantaneous ow eld of the carrier phase in the green vectors and particulate phase in the red vectors; a) for instantaneous ow eld; and b) for the uctuations, overlapped on the original PIV image. The ow eld was taken from the dashed square in Fig. 1. 2.2. Two-phase PIV/PTV velocity analysis 175 We follow the procedure previously reported by Khalitov and Longmire 176 (2002), among others. We lter PIV images based on the size and intensity 177 of objects, (above 15 pixels in diameter and intensity level of 200/255) to create 178 particle-free PIV images from which we obtain turbulent velocity elds. The 179 separated images of large particles processed with particle tracking velocimetry 180 (PTV) analysis, using the nearest neighbor algorithm are written in Matlab 181 (Mathworks Inc.). In Fig. 3, we present an example of a small region in an 182 instantaneous ow eld (green arrows overlaying the original image) of the car- 183 rier phase and particulate phase on the left panel, and the uctuating ow eld 184 in the right panel (after subtracting the ensemble averaged ow eld, shown in 185 Fig. 1c.) 186 3. Results 187 In this section we will summarize the main results obtained from the two- 188 phase PIV/PTV measurements. We present rst the de nition of the local mass 189 loading ratio, describing the ratio of particles mass to the mass of air, varying 190 with the distance to the nozzle. The mass distribution is not uniform in the 191 ow eld and this fact is re ected in the the ow eld results. We proceed 192 to the comparison of the mean and turbulent ow pro les for unladen versus 193 particle-laden ows and conclude the results section with the local analysis of 194 particle-turbulence interactions. 195 3.1. Local mass loading ratio 196 The mass fraction or mass loading ratio, , is de ned as the ratio of particle 197 mass in respect to that of the uid. We estimate the local mass loading at 198 8 various distances from the beginning of the measurement volume based on the 199 number of particles, N, extracted from PIV images, and their size distribution, 200 shown in Fig. 2a. The mass of particles is divided by the mass of air in the 201 measurement volume. This volume is calculated as the area of interest in the 202 PIV image times the laser sheet thickness, excluding the volume of particles 203 within the measurement volume. The thickness of the laser, obtained from the 204 re ection of the laser from a calibration target inside the measurement section. 205 The re ection was recorded with the high magni cation PIV camera and es- 206 timated to be approximately 1 mm. The volume of the particles we estimate 207 using their equivalent diameter of 320 m, obtained as the weighted mean from 208 the probability distribution in Fig 2a. We estimate the errors due to spatial 209 inhomogeneity, laser sheet thickness non-uniformity, and particle size distribu- 210 tion approximations to sum up to 10%. The corresponding volume fractions 211 areh vi= 3:77:4105for the low ow rate and 0 :10:3105for the 212 high ow rate, respectively. The volume loading range corresponds to the two- 213 way coupling regime, (Elghobashi and Trusedell, 1993), far from the four-way 214 coupling regimeh vi>102. Although recent computational studies (Esmaily 215 and Horwitz, 2017) have shown that even at low volume fractions there is a 216 possibility of inter-particle interactions, we could not nd any evidence of such 217 interactions in the results. 218 We present the local mass loading ratio, averaged from the ensemble of PIV 219 images, and horizontally across the measurement volume, h i, in Fig. 4a. Note 220 that the streamwise ow direction is from small x=Ltto largex=Lt, and the 221 mass loading ratio increases as the ow with particles approaches the nozzle. 222 The particles trajectories converge with the ow towards the nozzle and the 223 mass loading increases because of the conservation of mass. The mass loading 224 of the particles could not be precisely controlled in the present setup, as the 225 particles enter the air ow from a pneumatic seeder that was kept at constant 226 pressure and ow rate. This experimental artifact leads to a higher particle 227 entrainment rate and the higher on average mass loading, mass loading for the 228 lower air ow case. Accordingly, a larger number of particles in the chamber 229 lead to a steeper mass loading increase rate as the ow accelerates towards the 230 nozzle. 231 It should be noted that due to the two round cavities on both sides of the 232 chamber from which particles rebound at high speed, few particles arriving at 233 a large angle to the streamwise direction were excluded from the present data. 234 3.2. Mean air and particle velocities 235 In Fig. 4b, we plot the variation of the average streamwise velocity along the 236 centerline,Uc(hereinafter capital letters denote the ensemble averaged quanti- 237 ties, lower case letters for turbulent quantities) for the particle unladen ( lled 238 triangles) and laden cases (open circles) for the two Reynolds numbers (di er- 239 ent colors). In addition, we plot the average velocity of particles (squares). In 240 the lower panel, Fig. 4c-d, we present the mean velocity pro les (unladen and 241 laden ow cases) at several distances from the nozzle for a more quantitative 242 9 a) b) c) d) =0.2 1.1 1.5Figure 4: a) Averaged mass loading h ialong the centerline. Superscriptdenotes the particle laden cases. x=Ltb) Air mean air ow velocity along the centerline of the chamber, Ucand particles average streamwise velocity Up. Triangles are for the unladen cases, open circles for the particle laden cases (in both panels). Square markers are for the particle velocity Up. c-d) Mean velocity pro les, U(y) andV(y), respectively, for the un-laden ( lled) and laden cases (open symbols) at ReL1, at di erent distances from the nozzle, x=Lt= 0:2;1:1;1:5 (diamonds, squares and circles, respectively). 10 presentation of the ow eld. The summary of the key ow features visible in 243 Fig. 4b-d is: 244 the mean streamwise velocity rapidly increases towards the nozzle (Fig. 4b- 245 c) with spatial acceleration values of @U=@x2;00010;000 s1); 246 The ow accelerates spatially also in the transverse direction, from the 247 sides of the measurement volume towards the centerline, with @U=@y 248 5003;000 s1(Fig. 4d); 249 average particle velocities, Vpare practically constant during the time 250 particles cross the measurement volume (squares at the bottom of Fig. 4b); 251 the average air velocity distribution and amplitude have not changed in 252 particle-laden cases as compared to the unladen ones (the lled and open 253 symbols in Fig. 4b-d) ; 254 the high Stokes/Reynolds number irregular inertial particles move signif- 255 icantly slower than the air ow and preserve their velocity (squares in 256 Fig. 4b), despite substantial ow acceleration. 257 The particles do not have enough time to respond to a spatial streamwise ve- 258 locity gradients, despite a strongly accelerating ow. This result is in agreement 259 with the experiments of Gilbert et al. (1955) and Gany et al. (1978); Caveny 260 and Gany (1979), where agglomerates of 200 1000m were found to move 261 slower as compared to the carrier ow everywhere in a two dimensional rocket 262 motor chamber. 263 3.2.1. Turbulent kinetic energy, Reynolds stresses and production 264 In Fig 5a-c we present the pro les of turbulent kinetic energy (TKE) com- 265 ponents: streamwise hu2i, transversehv2iand the Reynolds stress component 266 huvifor theReL1unladen ow case. We present pro les at the same distances 267 from the nozzle as for the mean ow pro les in Fig. 4c-d. 268 First, we observe from the spatial distributions that the uctuations are 269 stronger at the sides (large y=Lt), far from the centerline. The strong reduc- 270 tion of turbulent kinetic energy at the centerline is due to the acceleration. 271 Furthermore, the acceleration a ects di erently the streamwise component (de- 272 creasing) and the transverse component (increasing on the sides and constant at 273 the centerline shown by the order of the pro les from diamonds to circles (from 274 0:2Ltto 1:5Lt, respectively). We also observe that the Reynolds stress values 275 are large far from the centerline. At the centerline, partially due to symme- 276 try and partially due to acceleration, the Reynolds stresses are practically zero. 277 These results are in agreement with the modi cation of the turbulence structure 278 observed in converging channels, see, for instance Shah and Tachie (2008). 279 We combine the results from the ensemble averaged ow elds and the tur- 280 bulent properties to estimate the terms of turbulent kinetic energy production 281 in Fig 6a-d. We plot the pro les of turbulent production terms huvi@U @y,huvi@V @x, 282 11 Figure 5: Turbulent kinetic energy component pro les a) hu2i, b)hv2iand c)huvi, respectively, forReL1and the un-laden case ( lled symbols) and laden case (empty symbols). The symbols and colors legend are the same as in Fig. 4. hu2i@U @x, andhv2i@V @y, for the unladen and laden cases ( lled and open symbols, 283 respectively) at ReL1(at the same distances from the nozzle as in Fig 5). 284 The e ects of acceleration on the TKE production Fig 6a-d are visible in 285 the termshuvi@U @yandhuvi@V @x. The terms contribute positively to the TKE 286 production far from the centerline with the peak at about x=Lt0:5, and 287 decrease towards the centerline. This is partially due to symmetry of the ow 288 and diminishing derivatives @U=@y and partially due to the decorrelation of 289 the velocity components. Along the centerline ( y= 0), the intense spatial 290 acceleration towards the nozzle and TKE components u2andv2contribute to 291 a sort of \negative TKE production". It is noteworthy that the two terms 292 hu2i@U @xandhv2i@V @yin Fig 6c-d are also stronger as compared to the production 293 terms stemming from the Reynolds stresses in Fig 6a-b. On the overall, it 294 can be summarized that the strong spatial acceleration in the streamwise and 295 transverse directions due to the convergent type of the ow diminishes TKE 296 production terms, therefore the turbulent uctuations in the unladen ow case 297 decrease towards the nozzle. 298 3.3. Particle-turbulence interaction mechanism 299 Figures 4b-d, 5a-c, and 6a-d present the e ects of particles on the mean 300 ow, TKE components and the TKE production terms, respectively. We noted 301 that the mean ow in the chamber has unchanged insigni cantly and the small 302 variations of a few percents appear closer to the nozzle. The centerline velocity 303 pro les along xand the transverse pro le (e.g., U(y)) all show that the ow 304 velocity eld is practically unchanged at the same locations with only a slight 305 reduction of the mean velocity in the particle-laden case (the results for the 306 lower Reynolds case are similar and not shown here for the sake of brevity). We 307 observe somewhat increasing uctuating components in Fig. 5a-b, however, the 308 most prominent change is in the eld of Reynolds stresses in FIg. 5c. Clearly, this 309 increase also a ects the production terms shown in Fig. 6a-b. However, because 310 of the strong acceleration, the negative TKE production terms are dominant 311 and increase towards the nozzle entrance. 312 12 Figure 6: Pro les of turbulent production terms: a) huvi@U @y, b)huvi@V @x, c)hu2i@U @x, and d) hv2i@V @y, respectively, for the un-laden case ( lled symbols) and laden case (empty symbols) and forReL1, at di erent distances from the nozzle. The symbols and colors legend is the same as in Fig. 4. 13 We also recall that the ow is in the dilute two-way coupling regime, with 313 a relatively small number of heavy particles. Therefore, in the following we 314 present a more insightful, local analysis around the particles and as a function 315 of distance from the particles. 316 To reveal the local e ects of particles on the turbulent ow, we use condi- 317 tional sampling in the following form: we divide the instantaneous PIV/PTV 318 elds in the particle-laden cases, along the centerline, into small control volumes 319 of 2020 mm. From each sub-volume, we conditionally sample the turbulent 320 uctuations depending on whether the sub-volume in a given ow realization 321 contains particle(s) and marked it as a region B (particles) or C (no particles) 322 (as schematically marked in Fig. 1c). For the sake of reference we compare with 323 the distributions of properties in case A that is the clear air ow case at the 324 same Reynolds number and at the same sub-volume locations. 325 In Fig. 7, we present a comparison of probability distribution functions 326 (PDF) of the streamwise uctuations in the case of a unladen ow case (red 327 triangles) with these at two conditional samples: the regions with at least one 328 particle (B) and the regions in the particle-laden case that do not contain iner- 329 tial particles (C). Both PDFs of the particle-laden cases have wider tails, cor- 330 responding to higher u0values (up to 3 times higher values, as seen in Fig. 7b.) 331 The turbulent ow in the proximity of the inertial particles (case B) is sig- 332 ni cantly di erent from the unladen case (case A). It is noteworthy that the 333 turbulent uctuations are stronger also far from the particles (case C), as if the 334 ow is \contaminated" with the velocity uctuations stemming from the local 335 particle-turbulence interactions. The result are a di erent view on the increase 336 of uctuations in particle-laden case, shown above in Fig. 5. 337 Re ecting on the introductory section, we can attribute these local e ects 338 with negative uctuations to the \vortex shedding" regime and infer that the 339 wakes are transported and a ect the ow for a substantially longer time scale as 340 compared to the particle residence time. To quantify the region of in uence of 341 particles on turbulent uctuations, we present in Fig. 7b the r.m.s of streamwise 342 uctuations (denoted by u0) in particle-laden cases normalized by the value of 343 the unladen cases for the two Reynolds numbers. For this plot, we sample PIV 344 ow realizations in respect to the particle centroids in the streamwise direction 345 (i.e., in the Lagrangian frame of reference attached to the particle center). The 346 normalized r.m.s. of streamwise uctuations in the particle wake is plotted 347 versus the streamwise distance from the particle, normalized by the particle 348 average diameter, dp(downstream, in the direction of motion of the particle). 349 We observe signi cantly higher turbulent uctuation within a region of at least 350 5 diameters and the e ect of slightly increased turbulent uctuations far from 351 the particle, supporting the aforementioned results in terms of distributions in 352 Fig. 7a or pro les in Fig. 5a-c. 353 We are also interested in the local analysis of the e ect of decorrelation on 354 the streamwise and transverse uctuations observed in Fig. 5c. The results of 355 the conditional sampling analysis along the centerline are shown in Fig. 8. We 356 present the values of u0andv0of the local/non-local conditional samples and 357 of the unladen case together to emphasize the di erent rate of decrease of the 358 14 Figure 7: a) PDF of streamwise velocity uctuations at x=Lt1 along the centerline, y= 0, where the red triangles denote the unladen case (A), blue squares denote the particle-laden ow with instantaneous accumulation of particles (B) and the green circles denote the particle- laden ow with locally clear air (C). Skewness values are 0.25, -0.11 and 0.48, respectively. b) Root-mean-square of streamwise uctuations u0for the particle laden cases at two Reynolds numbers as a function of distance from the particle, normalized by the corresponding r.m.s of the unladen ow case. The distance is measured along streamwise direction from the origin attached to the particle, xp, normalized by the mean particle diameter. uctuations in the direction of mean ow acceleration. The ratio of r.m.s. of the 359 uctuations v0=u0which is in some sense a measure of anisotropy (a horizontal 360 line atv0=u0;= 1 means the isotropic ratio of uctuations) is shown in Fig. 8b. 361 The local analysis reveals very peculiar phenomena arising due to the com- 362 petition between the e ect of strong acceleration (namely, a strong decrease of 363 streamwise uctuations and an increase of spanwise uctuations), and the e ect 364 of the particles, which increase the uctuations locally in the downstream wake 365 of the particle. The peculiarity is that the two counteracting e ects lead to an 366 isotropic ratio of turbulent uctuations. We recall that the e ects are linked to 367 the local mass fraction increasing towards the nozzle, as was shown in Fig. 4a. 368 4. Summary and conclusions 369 In this work, we created the experimental setup of a two dimensional model 370 of a rocket engine and studied the particle-turbulence interaction when the 371 particulate phase consists of dispersed alumina particles of irregular shape in 372 the size range of 250 550m. We focused on the pre-nozzle region in which 373 the carrier phase ow spatially accelerates towards the nozzle. We applied a 374 two-phase PIV/PTV algorithm and quanti ed the carrier and particulate phase 375 velocity elds. 376 The alumina irregularly shaped particles are strongly inertial with relatively 377 high Stokes and particle Reynolds numbers. The particles pass the nite size 378 15 AB C { A BCisotropicFigure 8: a) Root-mean-square of uctuation components, v0andu0along the centerline x=Lt (same legend as in Fig. 7). Filled markers denote u0and open markers are for v0. b) anisotropy measure,v0=u0for the three cases A-C, a horizontal line at v0=u0= 1 emphasizes the isotropic ratio. ow chamber quickly, as compared to their response time scale. As a conse- 379 quence, the interactions are abrupt and strong, but the residence time is much 380 shorter as compared to the particle response time. Therefore, in this peculiar 381 situation, the particles move at almost constant average velocity, despite the 382 fact that the carrier phase ow rapidly accelerates towards the nozzle. This 383 leads to the high and monotonically increasing relative (slip) velocity between 384 the particulate phase and carrier ow. 385 The combination of the high particle- uid relative velocity, slow response 386 time, and rapid acceleration of the air mean ow leads to substantial turbu- 387 lence argumentation, mostly in the streamwise component. The particle-related 388 mechanism for these Stokes numbers range from St > 75 and the particle 389 Reynolds numbers Rep>300 were termed in the literature as \vortex shedding" 390 mechanism Hetsroni (1989); Balachndar and Eaton (2010). In the present case, 391 in particular, the particles move slower than the carrier uid ow. Thus, a tur- 392 bulent wake, a region where the ow slows down, is in the direction of relative 393 velocity, which de ned as ~Vr=~Uf~Vp. The wake region \downstream" in 394 respect to the particle. It means that the next particle position will be inside 395 the wake of the particle itself at the previous time instant. More detailed local 396 ow around the particles analysis shows that on average, a local reduction of 397 the air ow velocity in the particle wake is pronounced up to ve particle diam- 398 eters downstream from the particle. We presented the comparison of the local 399 turbulence augmentation in the proximity of the particles and compared it to 400 the turbulence augmentation in the entire region of interest. We also demon- 401 strated the peculiar situation of streamline convergence leading to an increase of 402 the local mass fraction, streamwise acceleration, and particle-turbulence inter- 403 actions. First, the streamwise average velocity acceleration signi cantly reduces 404 16 the streamwise turbulent uctuations. Second, inertial particles of irregular 405 shape create streamwise uctuations in their wakes due to the vortex shed- 406 ding and compensate the mean ow acceleration e ect. In addition to the dra- 407 matic increase of TKE, the particle wakes are unexpectedly more isotropic than 408 the surrounding turbulence. Furthermore, the particle wakes are much more 409 isotropic as compared to the unladen ow case with the mean ow acceleration. 410 In our experiment, the particle mass fraction is monotonically increasing 411 towards the nozzle due to mass conservation and streamlines convergence (see 412 4). Nevertheless, in the measurement region of interest, the mass fraction is in 413 the two-way coupling regime and we did not observe any clustering of particles. 414 Our conclusions are therefore, limited to the dilute two-way coupling regime. 415 In respect to the aforementioned particle- ow dimensionless parameters, we 416 have estimated that Pa>105in the entire measurement region. As suggested 417 by Tanaka and Eaton (2008), it falls in the range that predicts an increase in 418 turbulence. The length scales ratio, dp=L(Gore and Crowe, 1989) is lower than 419 0.1 and predicts attenuation, however our particles lead to augmentation. This 420 discrepancy is likely to re ect the fact that the main e ect is due to the particle 421 wakes that are ve times larger than the particle e ective diameter. 422 This empirical work does not improve signi cantly our ability to predict the 423 e ects of particle-turbulence interactions in a general case, because it is lim- 424 ited to two Reynolds number cases, the nite range of mass loading and the 425 speci c type of particles studied. However, it adds a few important observa- 426 tions relevant for the case of particle-laden ows with high Stokes/Reynolds 427 numbers irregularly shaped particles, especially in the case of accelerating and 428 converging incompressible ows. We demonstrate the mechanism by which a 429 small mass fraction of particles in the accelerating and converging ow leads to 430 up to 20% increase of turbulent kinetic energy (at x=Lt= 1:3 in Fig. 8.a)). It 431 could lead to a comprehensive choice of the particle shape and density ( St;Re p) 432 and the mass fraction (number of particles per volume of solid propellant) that 433 can compensate the decrease of TKE by the ow acceleration. Furthermore, 434 we demonstrate that irregularly shaped particles, moving more slowly than the 435 surrounding uid, will create streamwise uctuations that lead to isotropic tur- 436 bulence regions with important consequences for mixing and transport ux. 437 We can infer that both the turbulent mixing and combustion rates could be 438 enhanced using these mechanisms. The right choice of turbulence enhancing 439 particles with the focus on the near-nozzle region shall a ect the overall perfor- 440 mance of the rocket engine and modify its exhaust content. The two-way global 441 and local coupling mechanisms could not be neglected in numerical simulations 442 and analytical models of multi-phase rocket engines. 443