CALCULATION OF THE PARTICLE VELOCITY IN COLD SPRAY IN THE ONE-DIMENSIONAL NON-ISENTROPIC APPROACH

Transcription

1 VOL 10 NO 6 APRIL 015 ISSN ARPN Journal of Engineering and Alied Sciences Asian Research Publishing Network (ARPN) All rights reserved wwwarnjournalscom CALCULATION OF THE PARTICLE VELOCITY IN COL SPRAY IN THE ONE-IMENSIONAL NON-ISENTROPIC APPROACH A N Ryabinin Saint-Petersburg State University Faculty of Mathematics and Mechanics 8 University Ave Petersburg Russia aryabinin@sburu ABSTRACT The mathematical model of the motion of gas articles in e Laval nozzle in the one-dimensional non-isentroic aroximation is considered The model takes into account the exchange of momentum and energy between the gas and solid hases We obtained a system of ordinary differential equations for the arameters of the gas and article velocity and temerature For the articular case of air as a carrier gas and coer articles the system of equations is solved by the Runge-Kutta method Inlet ressure was equal to Pa inlet temerature was equal to 773 K For articles of different diameters the article velocity and the temerature were calculated at the nozzle exit both in the isentroic and non-isentroic aroximations The ratio of article and gas mass rates varied u to 0% For small article of 8 microns in diameter exit article velocity decreases from 691 m/s to 641 m/s exit article temerature increases from 113 K to 143 K while ratio of mass rates arises from 0 to 0 % For large articles velocity difference is less than for small ones Keywords: cold gas dynamic sray mathematical model two-hase flow de laval nozzle INTROUCTION Cold gas dynamic sraying (CGS or cold sray) is a rocess in which owder articles of sraying material are injected within suersonic gas flow Particles move at high seed in the gas stream and imact with the substrate material to form a coating [1 3] Proerties of the deosited coating and the deosition efficiency are determined by the seed and temerature of the articles at the time of imact [ ] and by substrate temerature [8 9] Carrier gases are accelerated u to suersonic velocities through converging-diverging e Laval nozzles Particles are injected in the carrier gas across either the nozzle inlet region or diverging art of the nozzle downstream the throat In the first case higher final velocities can be reached as they are entrained in the jet stream for a long eriod of time On the other hand when the articles are injected downstream the nozzle throat at low ressure zone it is a more ractical solution but the imact seed reduces Most researchers searates the calculations of article seed and temerature into two stages In the first ste arameters of the gas are calculated in the nozzle and in the sace between the nozzle and the substrate surface In the second stage the calculation of article velocity and temerature is erformed It is usually assumed that the article concentration is so low that articles have no influence on the characteristics of the gas flow [10-6] Calculation of gas flows is carried out either based on onedimensional isentroic aroximation [ ] or by Comutational Fluid ynamics (CF) methods [ ] Most of the CF calculations were erformed using the Fluent commercial software The Lagrangian iscrete Phase Modeling (PM) algorithm is imlemented in Fluent Thus the calculation of the gas motion and the calculation of article trajectory and article velocity can be carried out sequentially by Fluent [ ] Samareh et al [9] have studied the behavior of articles in e Laval nozzles and effects on gas velocity for high article loadings (60 to 180 g/min) and by imlementing aanced multile equations Reynolds Stress Model Such models can be accurate but are relatively difficult to consistently converge u to higher order schemes [1] Basics of one-dimensional isentroic method of gas velocity calculation in Laval nozzle are resented in aers [3 4 5] The alication of this method of calculation gives some overestimated values for the article velocities because there is thick boundary layer near the nozzle wall so the one-dimensional aroximation is not valid However the correction roosed in aers [ ] leads to the fact that the estimation of the article velocity becomes accurate The flow in e Laval nozzle in the case of high concentration of articles is not adiabatic and isentroic because there is heat and momentum transfer between the gas and articles In this aer we roosed onedimensional non-isentroic method of calculation of gas arameters in e Laval nozzle MATHEMATICAL MOEL The equations of energy momentum mass and equation of state for ideal comressed gas are resented below: d u u i Fu q du 1 d u F ua const RT where x is coordinate along axis of the nozzle; i is gas enthaly; u is gas velocity; F is the secific force acting on the gas from the accelerating articles; q is the heat received from articles by unit of gas mass; ρ and T are (1) 435

2 VOL 10 NO 6 APRIL 015 ISSN ARPN Journal of Engineering and Alied Sciences Asian Research Publishing Network (ARPN) All rights reserved wwwarnjournalscom ressure density and temerature of the gas; A is area of the nozzle cross section; R is gas constant Let take into account that i RT a = γ R Here γ is the ratio of 1 gas secific heats a is a seed of sound After transformation equations (1) could be resented in the next form: du q( 1) Fu ua a u Fa q u a u da 1 a u a u 1 da A a The system of equations () should consider together with the equations of motion of the articles under the acting of aerodynamic force Equations of motion of a single article (3) is taken from the [6 7] d 3 C dt 4 dt dt 6 Nu k ( T T ) dt d c u u d where v ρ T d c are velocity density temerature diameter and secific heat of article Nu is Nusselt number which deends on Reynolds number Re Prandtl number Pr and Mach number M [7] C is drag coefficient k is thermal conductivity Re u v d M u v a Variable t in equations (3) can be relaced by variable x: d 3 u u C 4 dt 6 Nu k a T d cv R Thus two systems of equations (3) and (4) are combined into one system (5): () (3) (4) du fu ucg( 1) ua a u da 1 gucu / a a / u fau u a u f dt g 1 da A 6 Nu k g d cv 3 f C 4 a T R u u a Combining the two systems we use the relationshis between F q and f g: F uf q ucg Here δ is the ratio of article and gas mass rates Exression for Nusselt number was taken from [7]: Nu 044 Re Pr ex01 087M This exression is only valid for M > 04 and T > T In all other cases the Nusselt number does not deend on Mach number: 1 3 Nu 044 Re Pr 1 Exressions for drag coefficient C were taken from Henderson aer [3] For isentroic flow (δ = 0) at the nozzle throat (θ = 0) gas velocity u is equal to the seed of sound a For non-isentroic flow oint of sonic conditions (u = a) is shifted from the throat If δ << 1 in the vicinity of sonic condition du a0 da a 0 1 d d 1 and shift Δx is given by fu cg( 1) u x (7) a d / (5) (6) The system of ordinary differential equations (5) can be solved numerically 436

3 VOL 10 NO 6 APRIL 015 ISSN ARPN Journal of Engineering and Alied Sciences Asian Research Publishing Network (ARPN) All rights reserved wwwarnjournalscom CALCULATIONS If articles are injected downstream the throat the initial conditions should be set at oint of article injection The initial article velocity must be greater than zero The flow ustream the oint of injection can be determined in isentroic aroach The case of article injection across the nozzle inlet region is more comlex In this case initial conditions should be set at sonic oint near the nozzle throat Aroximately gas arameters and article velocity and article temerature can be determined in isentroic aroach We considered the second case The nozzle had a circular cross-section the length of the converging art was equal to 50 mm and length of diverging art was equal to 10 mm The nozzle had the throat of 67 mm in diameter Exit diameter of diverging art was equal to 53 mm We calculated the flight of coer articles injected across the inlet art of the nozzle The diameter of articles was in the range from 8 μm to 15 μm The inlet ressure o = Pa inlet temerature T o = 773 K The ratio of article and gas mass rates 0 < δ < 0 The carrier gas was air System of equations (5) was solved by fourthorder Runge-Kutta method Code was written in Pascal Initial conditions were set at sonic oint ustream the throat of the nozzle In the small vicinity of the sonic oint first two equation of system (5) were relaced by equations (6) We erformed calculation downstream and ustream the oint of sonic condition Figure-1 shows the deendence of gas velocity on the distance x from lace of article injection for article loading 0% The deendence of article velocity on distance x is resented in Figure- ifference between results of isentroic and non-isentroic calculations for small articles is greater than for large articles Figure- Particle velocity as a function of a distance from article feeding (δ = 0) ash line - isentroic aroach solid line - non-isentroic aroach 1 - d = 8 μm - d = 7 μm 3 - d = 64 μm 4 - d = 15 μm Figure-3 demonstrates deendence of exit article velocity on the ratio of article and gas mass rates One can see that this deendence is close to a linear one Figure-3 Exit article velocity as a function of a ratio of mass rates δ 1 - d = 8 μm - d = 7 μm 3 - d = 64 μm Similar deendences are found for exit article temerature Figure-4 illustrates the exit article temerature as function of a ratio of mass rates Figure-1 Gas velocity as a function of a distance from article feeding (δ = 0) 1 - isentroic aroach - nonisentroic aroach article diameter d = 15 μm 3 - nonisentroic aroach article diameter d = 8 μm At the nozzle exit for articles d = 8 μm velocity difference is equal to 50 m/s while for article d = 15 μm this difference reduces down to 15 m/s 437

4 VOL 10 NO 6 APRIL 015 ISSN ARPN Journal of Engineering and Alied Sciences Asian Research Publishing Network (ARPN) All rights reserved wwwarnjournalscom [6] Wong W Irissou E Ryabinin AN Legoux J-G Yue S 011 Influence of helium and nitrogen gases on the roerties of cold gas dynamic srayed ure titanium coatings Journal of Thermal Sray Technology 0(1-): 13-6 [7] Wong W VO P Irissou E Ryabinin AN Legoux J-G Yue S 013 Effect of article morhology and size distribution on cold-srayed ure titanium coatings Journal of Thermal Sray Technology (7): Figure-4 Exit article temerature as a function of a ratio of mass rates δ 1 - d = 64 μm - d = 7 μm 3 - d = 8 μm At the nozzle exit for articles d = 8 μm article temerature increases with arising of ratio of mass rates from 113 K to 143 K for article d = 64 μm the temerature increases from 37 K to 380 K only CONCLUSIONS Basing on a one-dimension non-isentroic mathematical model of two-hase flow we analyzed the gas and article velocities and article temeratures The momentum and energy transfer from the articles to gas leads the reducing of gas and article velocities and arising of article temerature REFERENCES [1] Payrin A Kosarev V Klinkov S Alkhimov A Fomin V 007 Cold sray technology Elsevier Science Amsterdam 336 [] Irissou E Legoux J-G Moreau C Ryabinin AN Jodoin B 008 Review on cold sray rocess and technology: Part I Intellectual roerty Journal of Thermal Sray Technology 17(4): [3] ykhuizen RC Smith MF 1998 Gas dynamic rinciles of cold sray Journal of Thermal Sray Technology 7(): 05-1 [4] Assadi H Schmidt T Richter H Kliemann J-O Binder K Gärtner F Klassen T Kreye H 011 On arameter selection in cold sraying Journal of Thermal Sray Technology 0(6): [5] Schmidt T Assadi H Gartner F Richter H Stoltenhoff T Kreye H Klassen T 009 From article acceleration to imact and bonding in cold sraying Journal of Thermal Sray Technology 18(5-6): [8] Mconald M G Ryabinin A N Irissou E Legoux J-G 013 Gas-substrate heat exchange during coldgas dynamic sraying Journal of Thermal Sray Technology (-3): [9] Ryabinin AN Irissou E Mconald A Legoux J- G 01 Simulation of gas-substrate heat exchange during cold-gas dynamic sraying International Journal of Thermal Sciences 56: 1-18 [10] Jen T-C Li L Cui W Chen O Zhang X 005 Numerical investigations on cold gas dynamic sray rocess with nano- and microsize articles International Journal of Heat and Mass Transfer 48: [11] Marrocco T McCartney G Shiway PH Sturgeon AJ 006 Production of titanium deosits by cold-gas dynamic sray: numerical modeling and exerimental characterization Journal of Thermal Sray Technology 15(): 63-7 [1] Jodoin B Raletz F Vardelle M 006 Cold sray modeling and validation using an otical diagnostic method Surface and Coatings Technology 00: [13] Li W-Y Li C-J Wang H-T Li C-X Bang H-S 006 Measurement and numerical simulation of article velocity in cold sraying Journal of Thermal Sray Technology 15(4): [14] Karimi M Fartaj A Rankin G Vanderzwet Birtch W Villafuerte J 006 Numerical simulation of the cold gas dynamic sray rocess Journal of Thermal Sray Technology 15(4): [15] Li W-H Liao H ouchy G Coddet C 007 Otimal design of a cold sray nozzle by numerical analysis of article velocity and exerimental validation with 316L stainless steel owder Materials and esign 8: [16] Katanoda H Fukuhara M Iino N 007 Numerical study of combination arameters for article imact velocity and temerature in cold sray Journal of Thermal Sray Technology 16(5-6):

5 VOL 10 NO 6 APRIL 015 ISSN ARPN Journal of Engineering and Alied Sciences Asian Research Publishing Network (ARPN) All rights reserved wwwarnjournalscom [17] Samareh B olatabadi A A 007 Threedimensional analysis of the cold sray rocess: the effects of substrate location and shae Journal of Thermal Sray Technology 16(5-6): [18] Schmidt T Assadi H Gartner F Richter H Stoltenhoff T Kreye H Klassen T 009 From article acceleration to imact and bonding in cold sraying Journal of Thermal Sray Technology 18(5-6): [19] Klinkov SV Kosarev VF Sova AA Smurov I 009 Calculation of article arameters for cold sraying of metal-ceramic mixtures Journal of Thermal Sray Technology 18(5-6): [0] Ning X-J Wang Q-S Ma Z Kim H-J 010 Numerical study of in-flight article arameters in low-ressure cold sray rocess Journal of Thermal Sray Technology 19(6): [1] Luoi R O'Neill W 011 Powder stream characteristics in cold sray nozzles Surface and Coatings Technology 06: [8] Fukumoto M Terada H Mashiko M Sato K Yamada M Yamaguchi E 009 eosition of coer fine article by cold sray rocess Materials Transactions 50(6): [9] Samareh B Stier O Lüthen V olatabadi A 009 Assessment of CF modeling via flow visualization in cold sray rocess Journal of Thermal Sray Technology 18(5-6): [30] Alkhimov AP Kosarev VF Klinkov SV 001 The features of cold sray nozzle design Journal of Thermal Sray Technology 10(): [31] Kosarev VF Klinkov SV Alkhimov AP Payrin AN 003 On some asects of gas dynamics of the cold sray rocess Journal of Thermal Sray Technology 1(): [3] Henderson CB 1976 rag coefficients of sheres in continuum and rarefied flows AIAA Journal 14(6): [] Sova A Okunkova A Grigoriev S Smurov I 013 Velocity of the articles accelerated by a cold sray micronozzle: exerimental measurements and numerical simulation Journal of Thermal Sray Technology (1): [3] Yin S Liu Q Liao H Wang X 014 Effect of injection ressure on article acceleration disersion and deosition in cold sray Comutational Materials Science 90: 7-15 [4] Sova A Grigoriev S Kochetkova A Smurov I 014 Influence of owder injection oint osition on efficiency of owder reheating in cold sray: numerical study Surface and Coatings Technology 4: 6-31 [5] Chamagne VK Helfritch J inavahi SPG Leyman PF 011 Theoretical and exerimental article velocity in cold sray Journal of Thermal Sray Technology 0(3): [6] Suo XK Liu TK Li WY Suo QL Planche MP Liao HL 013 Numerical study on the effect of nozzle dimension on article distribution in cold sraying Surface and Coatings Technology 0: [7] Stoltenhoff T Kreye H Richter HJ 00 An analysis of the cold sray rocess and its coatings Journal of Thermal Sray Technology 11(4):