Numerical simulation and CFD-Based Correlation of Erosion Threshold Gas Velocity in Pipe Bends

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1 El-Behery et al. CF Letters Vl. 2(1) Vl. 2(1) March 2010 Numerical simulatin and CF-Based Crrelatin f Ersin Threshld Gas Velcity in Pie Bends Samy M. El-Behery 1c, Mfreh H. Hamed 2, M. A. El-Kadi 1 and K. A. Ibrahim 1 1 Mechanical Pwer Engineering eartment, Faculty f Engineering, Minufiya University, Shebin El-km, EGYPT 2 Mechanical Engineering eartment, Faculty f Engineering, Kafrelsheikh University, Kafrelsheikh, EGYPT Received: 12/08/2009 Revised 04/01/2010 Acceted 18/02/2010 Abstract This aer resents numerical simulatin f sand ersin henmena in curved ducts. The Eulerian-Lagrangian arach is used t simulate the gas-slid tw-hase flw while semi-emirical mdel is used t calculate the ersin rate. The effect f slid hase n the gas hase is included in the mdel. The mdel redictin is validated with the available exerimental data and gd agreement was btained. Based n many redictins f the maximum enetratin rate, a CF based crrelatin is develed t calculate the enetratin rate in bends. Frm this equatin a mdel t redict the ersinal velcity was develed. The resent results shwed that the flw velcity shuld be decreased as the mass lading rati, article size, ie diameter increase in rder t avid failure. Keywrds: Gas-slid, Ersin, Bend, Numerical simulatin, Tw-hase 1. Intrductin Ersin is a cmlex rcess that is affected by numerus factrs and small r subtle changes in eratinal cnditins can significantly affect the damage it causes. This can lead t the scenari in which high ersin rates ccur in ne rductin system, but very little ersin ccurs in ther seemingly very similar systems [1]. Metal lss was rimarily due t mechanical frces which are induced by slid articles, liquid drlet, r cavitatin. The current il and gas industries ractice fr sizing rcess iing, flw lines, ielines and tubing limits the flw velcity t the maximum ersinal velcity, V e as calculated by American Petrleum Institute Recmmended Practice 14E (API RP 14E) equatin [2]: C Ve (1) m Fr slids-free fluids values f cnstant, C are 100 and 125 fr cntinues service and intermittent service, resectively, are cnservative. The recmmended ractice adds: "If slids rductin is anticiated, fluid velcity shuld be significantly reduced. ifferent values f cnstant, C may be used where secific alicatin studies have shwn them t be arriate." It is bvius that Eq. (1) is very simle and easy t use, but the equatin des nt accunt fr many factrs cntributing t ersin such as article size and density, mass lading rati and c Crresnding Authr: Samy M. El-Behery s_elbehery@yah.cm Telehne: Fax: All rights reserved. ISSR Jurnals 39

2 Numerical simulatin and CF-Based Crrelatin f Ersin Threshld Gas Velcity in Pie Bends tye f gemetry. The nly hysical variable accunted fr in Eq. (1) is the fluid density. The equatin suggests that the limiting velcity culd be higher when the fluid density is lwer. This des nt agree with exerimental bservatin fr sand ersin, because sand in gases with lwer densities will cause higher ersin rates than liquids with higher densities [2-8]. Therefre, the frm f Eq. (1) des nt seem t be arriate fr situatin invlving sand rductin. Recgnizing the limitatins f API RP 14E in the resence f sand, several investigatrs have develed mdels fr ersin redictin r ersinal velcities. Mst f these mdels are fr ersin in bends, since bends are esecially suscetible t ersin. Many f these mdels are based n an imact damage mdel f the frm: n ER AW F( 1 ) (2) 1 where, ER is the ersin rate (kg f material remved/kg f sand hitting it). W 1 is the article imact velcity n the metal surfaces. This velcity deends n the flw cnditin, the gemetry f the cmnent and sand rerties. A and n are exerimentally determined cnstant deending n the material being erded and ther factrs. α 1 is the article imact angle and F(α 1 ) is a material deendent functin f the imact angle between 0 and 1. Furthermre, the Tulsa mdel [5, 7] relies n emirical frmula t accunt fr article tracking while the Huser and Kvernvld [8] mdel allws actual calculatin and the values f A, n and F(α 1 ) are derived frm sand-blasting tests n small material samles [9]. The main bjective f the wrk resented herein is t adt a numerical rcedure t redict sand ersin henmena in curved duct. Then the data generated frm numerical redictin is t be used t devel a CF based crrelatin that can be used t calculate the ersinal velcity in ie cntains bends. 2. Mathematical mdel The Euler-Lagrange arach was alied in the calculatin f gas-slid flw in bends by slving the Reynlds-averaged Navier-Stkes (RANS) equatins tgether with a turbulence mdel. The revius study by the resent authrs [10] shwed that the RNG based k-ε turbulence mdel f [11] redicts the flw within the bend better than the standard k-ε mdel, lw Re k-ε mdel f [12] and the extended k-ε mdel f [13]. Therefre, the RNG based k-ε is recmmended in the resent study. Mvements f articles are simulated by accunting fr all the imrtant frces. The culing effect f slid articles n the gas hase is described thrugh mdificatins f gas hase equatins. This is achieved by intrducing the vid fractin which is defined as the vlume f a hase divided by the vlume f the tw hases, and mmentum exchange surce term in the gas hase equatins. The gas hase is cnsidered as a cntinuus hase, and the slid hase is accunted fr as a disersed hase. Sme simlifying assumtins are made t rvide a reasnable slutin fr engineering bjectives Mdel Assumtins 1. The flw mdel is fr a tw-dimensinal bend therefre, the influence f san-wise velcity n the article mtin is nt included. 2. The articles are sherical in the article tracking rcedure. Hwever, the ersin rati mdel in the resent study is based n the exerimental data fr sand articles (the ersin rati is defined as the rati f mass lss f the target material by the mass f articles iminging n the target material). 3. The effect f inter-article cllisins is ignred since inertial effects revail. 4. The effects f turbulent flw velcity fluctuatins n the articles are nt cnsidered. This assumtin reduces the alicability f the mdel t gemetries that redirect the flw such as elbws. There situatins, hwever, where the effects f turbulent fluctuatins n the article mtin can nt be ignred such as flw with articles in a straight ies [6]. 40

3 El-Behery et al. CF Letters Vl. 2(1) The rati between article density and gas density is very high s the effects f added mass frce, ressure gradient frce n the article are neglected in the resent study Gas Flw Mdeling The general frm f ellitic differential equatins gverning tw-dimensinal, turbulent, steady, incmressible and isthermal tw-hase flw thrugh curved duct with ustream and dwnstream straight ducts is given by j 1 1 j 1 y v u y S S g 1 (3) j j j j j S y y y y y y y y y where, j = 1, y = r fr curved duct, while fr straight ducts j = 0, θ = x. and the S Ф and S are surce terms f gas and disersed hases resectively. Cnstants f the used turbulence mdel are are taken as in [11]. The effective and eddy viscsities are taken and calculated as in [11], 2 C k eff 1, t eff (4) The effect f articulate hase n the turbulent structure can be written as rerted in [11] fr k and ε equatins, resectively, as fllws, k S S 2k 1 ex( k ) l (5) S S 2 1 ex( ) l (6) 2.3. Particulate Phase Mdeling The slid hase is simulated using the Lagrangian arach. A few thusands f cmutatinal articles ((i.e. arcels)) were traced thrugh the flwfield fr each culed iteratin. After each given time ste the new sitin f the arcels and the new transitinal and angular velcities are calculated frm the equatins f mtin as in [14] thrugh, d X dt m I du dt U (7) d dt F F F F (8) T LS LR 3 T 0. 5 U g where, X is the article sitin vectr, U, U are the gas and article velcity vectrs, is the article angular velcity vectr, T is the trque acting n the article, article mment f inertia and m is the article mass, LS LR g 2 0.1m S (9) (10) I is the F, F, F ana d F are the cmnents f the frce arising frm drag, shear lift, Magnus lift due t article rtatin and gravity, resectively. etailed descritin f these frces can be fund in [10] Fr the calculatin f article mtin, the equatins f article mtin are integrated using furth rder Runge Kutta methd. T achieve this, the lcal values fr the linear and 41

4 Numerical simulatin and CF-Based Crrelatin f Ersin Threshld Gas Velcity in Pie Bends angular velcities cmnents, the liquid viscsity, turbulent kinetic energy and its dissiatin rate at the lcatin f the article are required. These lcal values at the article center are linearly interlated frm values at the clsest grid ndes f the fluid finite-difference scheme enclsing the article Culing between the Tw Phases The articles ccuy the cmutatinal cell and reduce the gas vlume fractin. They als exert interactin frces n the surrunding gas hase. Thus, the tw hases are culed thrugh the gas vlume fractin and thrugh the ttal surce term, S s that accunts fr the mmentum exchange between slid articles and the gas hase (tw-way culing). The vid fractin fr disersed hase, β and fr gas hase, α are calculated using trajectry methd, as given in [18] as, nk t kv, 1 (11) traj VC here, n k is the number f actual articles in the cmutatinal article (arcel) k, V P is the vlume f the article, V c is the vlume f cmutatinal cell and means summing ver all traj trajectries assing thrugh the cmutatinal cell. It was assumed that each arcel cntains several articles with the same rerties and the number f actual articles in each arcel is btained by dividing the ttal number f flwing articles by the number f simulated arcels. The surce term f disersed hase in the gas mmentum equatin is calculated as in [14] by, n u, v S s F FLR FLS (12) k k k m n k 1 where, n is the number f trajectries assing thrugh the cmutatinal cell Ersin Mdel T cmute the ersin rate, ER, a semi emirical relatin fr sand ersin given by [19] is used, n ER AF W F( 1 ) (13) s 1 where, F(α 1 ) is a functin deends n imact angle and material being erded and is given by; a1 b1 1 F( 1) (14) 2 2 cs 1 sin( 1) sin 1 1 The values f the emirical cnstants based n W 1 in ft/sec are taken as in [19]. W 1 and α 1 are the imact velcity and imact angle, resectively, as shwn in Fig. 1. The F S cefficient accunts fr sand sharness. If the ersin in kg/kg is multilied by the sand flw rate the ersin rate in kg/sec will be btained. The enetratin rate is btained by dividing the ersin rate by the lcal cell area and by the density f the wall material Bundary Cnditins At the inlet, the axial velcity rfile fr gas hase is assumed fully develed turbulent velcity rfile, where the radial velcity is assumed t be zer. At utlet, the gradient f flw variables in the flw directin is set equal zer; / x 0. 0 (Neumann cnditins), and the radial velcity v is set t zer. At the slid wall bundaries, hwever, u = v =0.0, n-sli cnditins. Because the k and ε equatins are nt slved at the grid int adjacent t the wall, a 42

5 El-Behery et al. CF Letters Vl. 2(1) 2010 mdeling scheme is required t simulate the variatin f eddy viscsity, μ t. Fr this urse the mixing length arach is adted where the eddy viscsity is mdeled as a functin f mixing length as in [20] Particle Wall Interactin The article-wall cllisin ccurs when the distance between the article centre and the wall is less than the article radius. The cnditin f rebund is achieved if the article velcity befre cllisin, w 1 is greater than the critical article velcity, w,cr as in [21]. The slutin f the mmentum equatins with Culmbs law f frictin yields a set f equatins fr sliding and nn-sliding cllisin rcess [22]. 3. Slutin Prcedure A hybrid discretizatin scheme is used fr the mmentum, turbulent kinetic energy and dissiatin rate equatins f the gas hase while the equatins f article mtin are integrated using furth rder Runge Kutta methd. The mathematical mdel using Eulerian-Lagrangian arach as well as wall ersin sub-mdel was imlemented in a FORTRAN rgram in which the equatins f mtin are reetitively slved fr each reresentative article. The bundary cnditins and article-wall interactin are als incrrated. The cntinuus hase flw is btained using the SIMPLE arach described by Patankar [23]. The mtin f each arcel is then fllwed in a Lagrangian frame using the frces generated by fluid mtin and gravity. The effect f articles n the lcal flwfield must then be mdeled and fed back int the flwfield fr the next iteratin f gas calculatins. The rcedure is reeated until the maximum errr in the axial gas velcity between tw successive culed iteratins is less than 0.5% f the inlet mean velcity. Fig. 2 shws the histry f the axial mmentum residuals. The mmentum residuals fluctuate during the tw-way culing rcess, even thugh the gas hase slutin cnverges t a rescribed tlerance (0.001) fr every culing. Residuals f radial mmentum and cntinuity shw a similar kind f fluctuatins. uring the calculatin the imact lcatin, angle and velcity are stred and used in the ersin sub-mdel after the verall cnvergence is achieved. The selectin f the grid size influences the btained slutin and its selectin reresents a cmrmise between the accuracy and cmuter time. Therefre, at the beginning f each run, the cmuter rgram erfrms the calculatin fr gas hase nly fr different grid sizes. The axial gas velcity at bend exit is cmared fr different grid sizes. If the difference in axial gas velcity at bend exit in case f fine grid and carse grid is less than 0.5% f the mean inlet velcity, the carse grid was chsen. Unifrm grid in bth directins is used, and the value f the dimensinless wall distance, y+ fr the cell adjacent t the wall, is in the range f fr all simulatins. Figure 1. efinitin f velcities and angles befre imact and after rebund. Figure 2. Cnvergence histry fr tw-way culing (δ = 0.33, U = 20 m/s, = 100 µm and = 0.1 m). 43

6 Numerical simulatin and CF-Based Crrelatin f Ersin Threshld Gas Velcity in Pie Bends 4. Results and discussin The value f time ste, Δt and the number f cmutatinal articles are chsen t ensure indeendent results. T reach this cnditin, several simulatins are erfrmed using different time stes and deferent number f arcels fr each cnditin. The effect f time ste n the enetratin rate rfiles is shwn in Fig. 3. It can be seen that, after a certain value f Δt, the results is indeendent f the time ste. Similar results are rerted in Fig. 4 fr the effect f number f arcels. Based n these results, the time ste is selected t be 10-6 sec. and the number f arcels was chsen t be arcels. Figure 3. Effect f Lagrangian time ste, Δt n the enetratin rate rfile (cnditins as in Fig. 2). Figure 4. Effect f number f arcels n the enetratin rate rfile (cnditin as in Fig. 2). T validate the resent flw mdel, the redicted radial and axial velcities fr bth hases and the article cncentratin are cmared with the measured nes f [24 and 25] and resented in [10]. The cmarisns with the exerimental and numerical results f Wadke et al. [26] are resented in the resent aer. Single article trajectry was traced numerically and exerimentally in a 90 hrizntal-t-vertical curved duct. The time required fr the article t travel frm feeding int t the end f hrizntal ie and the time required fr the article t travel frm the feed int t end f the bend were measured. In the resent redictin the article is released at the feed int at zer transitinal and rtatinal velcities. The article after that is transrted under the effect f gravity and aerdynamic frces. The tested bend dimensins and flw cnditins were taken as in [26]. The trajectry f such article is shwn in Fig. 5. Figure 5. Particle trajectry at a velcity f 20 m/sec (the hrizntal and vertical scales are nt the same). 44

7 El-Behery et al. CF Letters Vl. 2(1) 2010 Figure 6 shws cmarisns between the resent redicted time (the time required fr the article t travel frm feed int t the end f hrizntal ie and t the end f the bend) and the measured and redicted results f [26]. A very gd agreement between the resent redictins and measured data is btained. The resent mdel redicts the time required fr the article t travel t the end f the bend at higher values than thse f [26] as shwn in Fig. 6.b. This may be due t the assumtin, f fully develed velcity rfile at every sectin, given in [26]. The ersin mdel is validated by cmaring the resent redictins with exerimental data rerted in [4, 6-7] and with the exerimental data f Bikbaev et al. [27]. Figure 7 resents a cmarisn between resent redictins and exerimental results rerted in [4, 6-7]. The sand flw rate is 1.02 ft 3 /day ( m 3 /hr) and the flw velcity changes frm 9.15 t 30.5 m/sec. It can be seen frm Fig. 7 that the mdel redictin agrees very well with the exerimental data. Figure 8 shws cmarisns between resent redicted and measured enetratin rates given by [27] at different mass lading ratis. It can be seen frm the figure that the resent mdel redicts the maximum enetratin rate fr smaller lading rati (Mr =0.57) fairly well, as the mass lading rati increase the mdel ver-redict the maximum enetratin rate. The majr cntributin t the discreancy between redicted values and data f [27] may be due t the interactin between sand articles where the resent mdel neglects this effect. a- Time required fr article t travel frm the b- Time required fr article t travel frm the feed int t the end f the hrizntal ie. feed int t the end f the bend. Figure 6. Cmarisns between redicted time and the ublished data f [26]. Figure 7. Cmarisn between redicted maximum enetratin rate and Ex. data rerted in [4, 6-7] Figure 8. Cmarisn between the redicted enetratin rate and the exerimental data f [27]. 45

8 Numerical simulatin and CF-Based Crrelatin f Ersin Threshld Gas Velcity in Pie Bends In the resent wrk, based n many CF redictins f ersin rate and n the curve fitting f maximum enetratin rate results, a new CF based crrelatin is develed and is recmmended as an arximate engineering calculatins used fr calculating the effect f different arameters n the maximum enetratin rate in 90 bends. The fllwing crrelatins are recmmended; where, P n max Fs. BH.. U, / cr ( m / kg). Mr. e (15) Fs. BH. U, / cr. Mr. e U.. Mr cr 126 (16) / e In the abve crrelatin cr is defined as the article size in µm at which the enetratin des nt be affected by article diameter. This behavir, frm the authrs' int f view, is due t that, as the article diameter increases the article inertia increase, which leads t an increase in the enetratin rate. On the ther hand, fr cnstant mass lading rati the number f articles within the flwfield decreases, this leads t a decrease in the enetratin rate. Thus, at a certain article diameter, cr, deending n the flw and gemetric arameters, the tw effects cancel each thers. Fr a wide range f erating cnditin, the critical article, cr is fund t vary between 100 and 200 µm. It shuld be nted that the abve crrelatin is based n the cnditin that the sand article density is arund 2650 kg/m 3 and the carrier fluid is air at standard cnditin (ρ = 1.22 kg/m 3 and µ = a.s). If the article density r fluid rerties deviate significantly frm abve values, it is recmmended that the flw mdeling and article tracking rcedure be used instead f this simlified mdel. Furthermre, the crrelatin was based n simulatin with article diameter ranging frm 40 t 500 µm, curvature rati between 0.05 and 0.65, ie diameter ranging between and 0.4 m. The accuracy f Eq. (15) is demnstrated by cmaring its redictins with measured and redicted enetratin rates in ie bends by different investigatrs under different cnditins. The results f this cmarisn are given in table 1 (see aendix). The errr f the redicted enetratin rates against the number f data ints (as a histgram) is resented in Fig. 9. The redictins f Salama [4] were based n the fllwing Equatin: P n max m 2 1 m s Vm (17) 2 S m In the abve equatin S m is a gemetry deendent cnstant, secified by Salama [4]. Figure 9 indicates that mre than 75% f the redicted enetratin rate is in the errr range ±50%. Althugh this errr is high, it is quite accetable fr cmlex mixture and ersin redictin where a large number f uncntrlled arameters act. T btain the ersinal velcity limits fr air-slid flws at standard ressure and 2 temerature, multilying Eq. (15) by m s ( ms U Mr ) and rearranging fr the flw 4 velcity in terms f enetratin rate in µm/sec and erating arameters as fllw: 46

9 El-Behery et al. CF Letters Vl. 2(1) 2010 V e Pn BH e Mr Fs Pn BH e Mr Fs / / ,, The ersinal velcity mdel rsed by Salama [4] has the fllwing frm: cr cr (18) 1/ 3 20P n V e (19) Mr where, P n = Penetratin rate in mm/year and a limiting value f = 400 µm shuld be used if > 400 µm. Figure 9. The errr f the redicted enetratin rates using the rsed crrelatin against the number f data ints. Figure 10 resents a cmarisn between the redicted ersinal velcity limits by the resent mdel, equatin (18), and Salama's mdel, equatin (19), in terms f mass lading rati. It can be seen frm the figure that bth mdels have the same trend and the resent mdel accunts fr the effect f bend gemetry. The figure shws als that the flw velcity shuld be decreased as the mass lading rati increases in rder t avid failure. This is due t that, as the mass lading rati increases the enetratin rate in µm/sec increases. The resent mdel redictins indicate that the ersinal velcity increases as the curvature rati decreases. This is due t the decrease in enetratin as the curvature decreases. The figure shws als that, as the ie diameter increases the ersinal velcity decreases. This may be due t that, as the ie diameter increases the sand flw rate increases fr a certain mass lading rati which resulting in an increase in the enetratin rate. Equatins (18) and (19) can be rewritten t redict the ersinal velcity limits in terms f sand flw rate, m s as fllw: 47

10 Numerical simulatin and CF-Based Crrelatin f Ersin Threshld Gas Velcity in Pie Bends V e Pn BH e 0.9 Mr Fs P n BH e 0.91 Mr F / / s ,, cr cr (18) e 19Pn m s 1/ 2 V (19) a- Large article. b- Small article. Figure 10. Effect f mass lading rati n the ersinal velcity limits, (allwable enetratin rate = 0.1mm/year, BH = 120 and shar article). Figure 11 resents a cmarisn between the redictins f the resent mdel, equatin (18), and that f Salama's mdel, equatin (19), in terms f ie diameter. It can be seen frm the figure that the ersinal velcity limits increases as the ie diameter increases. This is due t that, the enetratin rate decreases as the ie diameter increases at cnstant sand flw rate. Furthermre, the tw mdels are cmared in terms f sand flw rate in Fig. 12. It can be seen frm the figure that, as the sand flw rate increases the ersinal velcity limits decreases. This is due t the increase in enetratin rate as the sand flw rate increases. The figures als indicate that the mass lading rati increases as the ersinal velcity decreases. Figures 11.b and 12.b shw that the redictins f Salam's mdel give higher values f V e than the resent redictins. This may be due t that, the effects f secndary flw and turbulence disersin n the articles mtin, which are neglected in the resent study. Therefre, further wrk including the effects f turbulence disersin and secndary flw (3- simulatins) is needed t assess the resent mdel. 48

11 El-Behery et al. CF Letters Vl. 2(1) 2010 a- Large article. b- Small article. Figure 11. Effect f ie diameter n the ersinal velcity limits, (allwable enetratin rate = 0.1 mm/year, BH = 120, shar article and sand flw rate 5 kg/day). a- Large article. b- Small article. Figure 12. Effect f slid mass flw rate n the ersinal velcity limits, (allwable enetratin rate = 0.1 mm/year, BH = 120, shar article and = 0.2 m). 5. Cnclusin Ersin f bends cnveying sand articles entrained in air flw was numerically simulated. Based n the btained results, a new CF based crrelatin was develed. The resent results shw an accetable agreement with the available exerimental data. It is cncluded that the maximum allwable velcity shuld be decreased as the ie diameter, article size r mass lading rati increase. The effect f fluid rerties (density and viscsity), turbulent flw fluctuatins and secndary flws may lay imrtant rle in ersin redictin. These effects need t be further investigated. Nmenclature (Units are as stated here, unless nted therwise in the text f the aer) iameter f bend, m Particle diameter, μm ER Ersin rate, kg wall material/kg slid articles S Mr Mass lading rati, ( m / m g ) 49

12 Numerical simulatin and CF-Based Crrelatin f Ersin Threshld Gas Velcity in Pie Bends P n Penetratin rate, µm/kg r µm/sec R C Mean bend radius f curvature, m R Radius f bend uter wall, m t Time, sec v Mean radial velcity, m/s V e Ersinal velcity, m/s v Mean radial article velcity, m/s u Mean axial gas velcity, m/s U Mean-bulk lngitudinal velcity, m/sec u Mean axial article velcity, m/s Greek symbls Curvature rati (/2R C ) θ Axial crdinate alng the bend, degree Particle angular velcity, rad/s ω Aendix TABLE 1. COMPARISONS BETWEEN THE PREICTE PENETRATION RATES BY THE PRESENT SIMPLIFIE CORRELATION AN PUBLISHE ATA. U m/sec δ Mr Predicted maximum enetratin rate, m/sec Measured P n, m/sec Wang and McLaury et Salama [4] Present Shirazi [6] al. [7] ata based n Burgyne [3] ( = 350 µm, = m, articles are semi-runded, BH = 120 and 140, ρ = 2650 kg/ m 3 and ρ w = 7800 kg/m 3, redictin f Salama based n S m = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 50

13 El-Behery et al. CF Letters Vl. 2(1) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 ata based n Burgyne [29] ( = 350 µm, = m, article are semi-runded, BH = 120, ρ = 2650 kg/ m 3 and ρ w = 7800 kg/m E E E E E E E E E E E E E E E E E E E E E E E E-05 ata rerted in [4, 6 and 7] (data f Tlle and Greenwd), = 300 µm, = m, articles are shar, BH = 109, ρ = 2650 kg/ m 3 and ρ w = 7800 kg/m 3, redictin f Salama based n S m = E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-08 ata rerted in [4 and 7] (data f Weiner and Tlle), = 300 µm, = m, articles are shar, BH = 109, ρ = 2650 kg/ m 3 and ρ w = 7800 kg/m 3, redictin f Salama based n S m = E E E E E E E E-08 ata based n Bikbaev et al. [27], = 295 µm, = 0.05 m, article are semi-runded, BH = 120, ρ = 2580 kg/ m 3 and ρ w = 7800 kg/m E E E E E E E E E E E E E E E E-06 ata based n Bikbaev et al. [28], = 295 µm, = 0.05 m, article are semi-runded, BH = 120 ρ = 2580 kg/ m 3 and ρ w = 7800 kg/m E E E E E E E E-06 51

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