Quasi One Dimensional Analysis of the Effects of Pipe Friction, Cooling and Nozzle Geometry on Gas/Particle Flows in HVOF Thermal Spray Gun

(1)Materials Transactions, Vol. 47, No. 11 (2006) pp. 2791 to 2797 #2006 Japan Thermal Spraying Society. Quasi-One-Dimensional Analysis of the Effects of Pipe Friction, Cooling and Nozzle Geometry on Gas/Particle Flows in HVOF Thermal Spray Gun* Hiroshi Katanoda Department of Mechanical Engineering, Kagoshima University, Kagoshima 890-0065, Japan The High Velocity Oxy-Fuel (HVOF) thermal spraying can make highly tough and dense coatings on a solid surface. It is experimentally recognized that the quality of the coating largely depends on the particle velocity and temperature, which depend on the gas flow in the HVOF gun. The gas flow in the gun is affected by two factors; pipe friction and cooling along the inner wall of the long gun. This paper investigates the gas/particle flow in the HVOF gun by using quasi-one-dimensional analysis including the effects of pipe friction, cooling and nozzle geometry. The standard values of the parameters, to include the effects of pipe friction and cooling are selected based on the experimental result. The nozzle length is varied in the range of 110–330 mm. The calculated results show that (1) the pipe friction decreases the particle velocity and increases the particle temperature, (2) the cooling increases the particle velocity and decreases the particle temperature, (3) the maximum particle velocity is obtained when the length of the diverging part of the nozzle is approximately equal to the length of the following non-diverging straight part, (4) the longer nozzle results in larger particle velocity at the nozzle exit. These numerical results help understand the gasdynamics occurring in the HVOF gun, and assist in the design of the gun. [doi:10.2320/matertrans.47.2791] (Received March 6, 2006; Accepted August 28, 2006; Published November 15, 2006) Keywords: high velocity oxy-fuel (HVOF) thermal spray, numerical analysis, gasdynamics, supersonic flow, pipe friction, heat transfer. Among many types of thermal spraying techniques, only the high-velocity oxy-fuel (HVOF) thermal spraying process employs supersonic combustion gas-flow. The gas speed of the HVOF process is higher than any other thermal spraying techniques, resulting in higher particle velocity than those achieved in the conventional flame-spray process. Previous experimental work1) shows that the higher speed of the particle seems to give higher-quality coatings. Although the HVOF process is widely used as a wear-resistant coating for such things as automotive brake discs and piston rings, the design of the gun has been primarily empirical, and the understanding of gas/particle flow is based on engineering intuition. To advance the HVOF thermal spraying technology, for a corrosion-resistant coating2) against seawater, we require detailed information on the process. The understanding of the particle behavior, as well as gasdynamics of the HVOF gun, is one of the most important research areas, because the final coating-quality strongly depends on particle velocity and temperature at impact. References 3) and 4) numerically investigated particle behavior in HVOF gun by assuming isentropic gas flow. However, the assumption of isentropic flow will be impractical for the HVOF gun because the gas flow in the gun is affected by pipe friction and cooling along the barrel wall. Yang, et al.5) numerically studied gas/ particle flow in the HVOF gun by taking into account pipe friction and cooling. The analysis is, however, restricted to subsonic gas flow in a straight barrel attached to a converging nozzle, which is an early design of the HVOF gun. The latest HVOF gun has a supersonic nozzle followed by a straight barrel. The effects of pipe friction, cooling and gun-geometry. on the gas/particle flow in the latest gun are not well clarified yet. The present study systematically clarifies the effects of pipe friction, cooling and nozzle geometry on the gas/ particle flow in the latest gun by using a quasi-one-dimensional analysis. 2.. Analytical Method. 2.1 Nozzle geometry The geometry of the HVOF gun used in the present study is shown in Fig. 1. The geometry is axisymmetric. The throatto-exit part of the gun is called the nozzle in this paper. The nozzle consists of a diverging part followed by a straight barrel. The nozzle has a 7.9 mm throat diameter, and 11 mm exit diameter D. The nozzle length, Ln , varies in the range of 110 mm–330 mm. Diverging length ratio , defined as ¼ Ld =Ln , varies in the range of 0:04 < < 1:0. When Ln ¼ 230 mm and ¼ 0:04 (Ld ¼ 10 mm), the nozzle geometry is almost identical to the Praxair-Tafa JP-5000 attached 8-inch barrel. This nozzle geometry is referred to as the reference configuration in this paper.. Ln Ld 11. Introduction. 7.9. 1.. ψ = Ld /L n *This. Paper was Originally Published in Japanese in J. Japan Thermal Spraying Society 43 (2006) 79–85.. Fig. 1. Tested nozzle (unit: mm)..

(2) 2792. H. Katanoda. 2.2 Basic equations of gas flow In this paper, the following assumptions are used for the gas flow in the nozzle to simplify the analysis. (1) The gas flow is steady and quasi-one-dimensional, including the effects of pipe friction and cooling. (2) The fuel (kerosene) injected into a combustion chamber is burned completely with oxidizer (oxygen gas). (3) The mole fractions of the gas species remain constant in the nozzle. (4) The combustion gas consists of CO2 , H2 O and excess O2 . (5) All the gas species follow the equation of state of a perfect gas. (6) The velocity and temperature of the gas flow are not affected by the particles traveling in the nozzle. (7) The Mach number at the throat is unity. (8) The shock wave generated in the nozzle is a normal shock wave. (9) The gas flow is isentropic from the combustion chamber to the throat. (10) The gas flow is uniformly cooled in the nozzle from the throat to the exit. (11) The value of equivalent relative roughness,6) ke =r, described later is constant in the nozzle. Due to the assumptions made above, equations (1)–(3) are derived from the conservation equations of mass, momentum, and energy, including the effects of pipe friction and cooling.   dg 1 dug 1 dA ð1Þ ¼ g þ ug dx A dx dx ! Mg2 4 f dug ug dA ug 1 q   ¼ cp Tg dx dx ðMg2  1ÞA dx ðMg2  1Þ 2 d . dTg   1 q dug þ ug ¼ Rg dx dx dx. . ð2Þ ð3Þ. where x is the axial distance from the throat, d the inner diameter of the nozzle, A the cross-sectional area of the nozzle, g the gas density, ug the gas velocity, Tg the static temperature of gas, Mg the Mach number of gas flow,  the specific heat ratio, cp the specific heat at constant pressure, Rg the gas constant, f the Fanning friction factor, q the removed heat value (positive value) by cooling during dx per unit mass of the gas, respectively. The value of q=dx in eqs. (1) and (3) is constant in the nozzle by the assumption (10). The value of cp was calculated by the function proposed in Ref. 7). The value of the Fanning friction factor, f , was calculated as f ¼ =4 after obtaining Darcy friction factor, , by the following equation,8) which can be applied to turbulent pipe flows.   1 ke 18:7 pffiffiffi pffiffiffi ¼ 1:74  2 log þ ð4Þ r  Red  where ke the equivalent roughness of the inner nozzle-wall, r the radius of the nozzle, respectively. The value of ke is, for example, 1.35–1.52 mm6) for the drawn virgin copper-pipe. The larger value of equivalent relative roughness, ke =r, gives a larger value of f , causing a larger effect of pipe friction on. the gas flow. The present analysis employs ke =r as a parameter to study the effect of pipe friction. The Reynolds number, Red , in eq. (4) is defined as; Red ¼. g ug d g. ð5Þ. where g is the viscosity of the combustion gas. The viscosity for each gas species forming the combustion gas was calculated by the Sutherland formula.9) Then, the average value, g , was calculated by the equation proposed in Ref. 10). Another important parameter, in addition to ke =r, in eqs. (1)–(3) is q=dx which expresses the effect of cooling. In terms of cooling, the author define a non-dimensional parameter (cooling rate), , by eq. (6); ¼. qm_ g Hl m_ f. ð6Þ. where q is the heating value removed from the gas flow in the nozzle by cooling, m_ g the mass flow rate of the gas, m_ f the mass flow rate of the fuel, Hl the lower heating value of the fuel (Hl ¼ 44 MJ/kg for kerosene). Equation (6) gives the value of the rate of heating loss from the gas flow in the nozzle, against the heating value released through the complete combustion upstream of the throat. The present analysis employs  as a parameter to study the effect of cooling. From the assumption (10) and eq. (6), q=dx in eqs. (1) and (3) can be expressed as; q q Hl m_ f  ¼ ¼ dx Ln Ln m_ g. ð7Þ. The static pressure of the gas flow was calculated by the equation of state of a perfect gas. Equations (1)–(3) were numerically integrated from the throat to the nozzle exit by using three-step Runge-Kutta method. 2.3 Basic equations of particle flow The following assumptions are used for the particle flow in the nozzle to simplify the analysis. (1) The particles are spherical in shape. (2) The particles travel along the nozzle axis. (3) The interaction between the particles is negligible. (4) The acceleration of particles in the gas flow is caused by gasdynamic drag force. (5) The particle is heated by the gas flow through heat transfer. (6) The temperature distribution inside of a particle is uniform. (7) The material properties of the particle are constant. The equation of particle motion is written as; m p up. dup 1 ¼ cd g ðug  up Þ  jug  up jAp 2 dx. ð8Þ. where mp is the mass of the particle, up the particle velocity, Ap the projected area of the particle, cd the drag coefficient of the particle, respectively. The value of cd was calculated from a database made from the experimental data11) obtained by using solid spheres of room temperature, along with a correction given by eq. (9) due to high temperature of the gas.12).

(3) Quasi-One-Dimensional Analysis of the Effects of Pipe Friction, Cooling and Nozzle Geometry on Gas/Particle Flows 0:45 cd ¼ cd;exp fprop. where cd;exp is the drag coefficient based on the experimental data, fprop is the correction factor given by eq. (16) later in this section. The particle temperature can be calculated by the following equation. mp cup. dTp ¼   ðTg  Tp Þ  As dx. Table 1. ð9Þ. kg; f Nu dp. Case 214Þ. Combustion pressure. 670 kPa [abs]. 670 kPa [abs]. Combustion temperature. 3190 K15Þ. 3030 K. Flow rate of kerosene. 0.0051 kg/s. 0.0037 kg/s. Equivalence ratio. 1.0. 0.6. ð10Þ. Table 2. ð11Þ. ð12Þ. The Nusselt number, Nu, in eq. (11) was computed by RanzMarshall correlation along with correction factors:12)   cp 0:38 0:6 1=3 Nu ¼ ð2 þ 0:6R1=2 P Þ  fprop fKn ð13Þ ep r cp;w where the subscript w indicates surface of particle. In eq. (13), the particle Reynolds number Rep and Prandtl number of the gas Pr are defined as g; f dp jug  up j ð14Þ Rep  g; f g; f cp; f Pr  ð15Þ kg; f The factors fprop and fKn in eq. (13) represent the effect of variation in gas temperature in the boundary layer on the particle surface and noncontinuum effect, respectively. They are given by the following equations.12) g g fprop ¼ ð16Þ g;w g;w      2a w 4  1 fKn ¼ 1 þ Kn ð17Þ a 1 þ w Prw where a is the thermal accommodation coefficient which is set as 0.8 in this study, Kn is the Knudsen number based on an effective mean free path and is given by Kn ¼. Prw kg; f g;w vw dp =2 cp; f. Powder conditions.. Material. Inconel 718. Density Specific heat. 9000 kg/m3 462 J/(kg K). Melting point. 1648 K. Heat of fusion. 312  103 J/kg. Diameter. Here, Nu is the Nusselt number, kg the thermal conductivity of the gas. The subscript f in eq. (11) means the value at the film temperature, Tf , defined as Tf ¼ ðTg þ Tp Þ=2. Gas conditions. Case 113Þ. where Tp is the particle temperature, c the specific heat of the particle, As the surface area of the particle,  the heat transfer coefficient which can be calculated by ¼. ð18Þ. where vw is the mean molecular speed which is dependent on the average molecular weight W of the gas mixture and gas temperature on particle surface, Tg;w , and is given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 R vw ¼ Tg;w ð19Þ W where R is the universal gas constant. Equation (10) does not take into account the effect heat radiation, which will be included in our future work. When the particle is partly melted, the melted mass fraction to the mass of the single particle is called Melting. 2793. 27{54 mm. Initial speed. 10 m/s. Initial temperature. 293 K. Fraction of Particle (MFP) in this paper. The MFP is defined by the following equation. Zt  ðTg  Tmp ÞAs dt tmp ð20Þ MFP ¼ Hm mp where Hm is the latent heat of fusion of the particle, Tmp the melting point of the particle, tmp the time when Tp became equal to Tmp . The value of MFP lies in the range 0  MFP  1; fully solid at MFP ¼ 0, fully liquid at MFP ¼ 1. Equations (1)–(3), (8) and (10) were numerically integrated by using three-step Runge-Kutta method for the mesh size in the x-direction x ¼ 0:05 mm. The dependency of x on the numerical results of the gas/particle behavior was negligible for x smaller than 0.05 mm. Normal shock wave in the nozzle was resolved by one mesh when choking occurred at the nozzle exit. 2.4 Numerical conditions The input conditions of the analysis are the same as the experimental data of Refs. 13) and 14). The gas conditions are listed in Table 1. The combustion temperature, which is too high to measure, for Case 1 in the table is taken from the estimation in Ref. 15). The input values of Case 1 are used in this paper except for Sec. 3.2. The values of Case 2 are used later in only Sec. 3.2. The combustion temperature for Case 2 in Table 1 is estimated from Ref. 13). The particle conditions are listed in Table 2. The spray particle is Inconel 718. The particles are injected along the centerline at 25 mm downstream of the nozzle throat. 3. 3.1. Results and Discussion. Reference values of cooling rate and equivalent relative roughness In order to numerically integrate eqs. (1)–(3), the values of equivalent relative roughness, ke =r, and cooling rate, , need to be specified before starting the computation. For this purpose, it is important to know the standard values (reference values hereafter) of ke =r and  for HVOF thermal.

(4) H. Katanoda. spraying. In this section, the reference values of ke =r and  for the JP-5000 are estimated from the experimental data.13) 3.1.1 Cooling rate According to Ref. 13), the gas temperature of the JP-5000 with 8-inch barrel measures 2366 K at the nozzle exit. The temperature is measured by inserting a thermocouple with blunt head in the flame jet. Therefore, 2366 K is expected to be almost equal to the stagnation temperature of the gas flow at the barrel exit. The mass flow rate of kerosene and the equivalence ratio used in Ref. 13) are listed in Table 1 as Case 1. According to thermodynamics, the stagnation temperature at the nozzle exit depends on the cooling rate , not on the equivalent relative roughness ke =r. The author calculated the stagnation temperature at the nozzle exit Tgo;e for JP-5000 with 8-inch barrel (Ln ¼ 230 mm, ¼ 0:04) for a wide range of values of . Then, it was found that when  ¼ 0:159, the temperature Tgo;e is 2365 K, which is very close to the experimental value 2366 K. According to the measurement,15) the cooling rate through the barrel of JP-5000 is 1.7% per inch. Therefore, the cooling rate of the present 220-mm-barrel case is expected to be 14.7%, which is close to the estimated  ¼ 0:159 (15.9%). Although the value of  will somewhat vary depending on input parameters in the practical operation, 0.159 is used as the reference value of . The author determined the range of  used in the present analysis as 0 <  < 0:30, which includes the reference value 0.159. 3.1.2 Equivalent relative roughness Since the reference value of  is fixed, the reference value of ke =r for JP-5000 can be estimated in the next step. According to the experimental result,13) the Mach number of the gas flow at the nozzle exit, Mg;e , is 1.64. The value of Mg;e depends on  and ke =r. The author calculated Mg;e for a wide range of values of ke =r with fixed  ¼ 0:159, the reference value. Then, it was found that when ke =r ¼ 0:005, the Mach number Mg;e is 1.648, which is almost equal to the experimental value 1.64. Although the value of ke =r will increase during the process, 0.005 is used as the reference value of ke =r. The author determined the range of ke =r used in the present analysis as 0 < ke =r < 0:010, which includes the reference value 0.005. 3.2 Code validation To validate the analytical method, calculated particle velocity and temperature are compared to the experimental data.14) The nozzle has the reference configuration (Ln ¼ 230 mm, ¼ 0:04). The Case 2 in Table 1 is used as numerical conditions for the gas, along with the reference values of  ¼ 0:159, ke =r ¼ 0:005. The calculated particle velocities and temperatures at the nozzle exit are compared to the experimental value in Table 3 and Table 4, respectively. In the tables, the R.P.D.D. means the ratio of particle diameter distribution. The calculated particle velocity and temperature averaged by the R.P.D.D. reasonably agree with the experimental values. 3.3 Gas flow in nozzle The effects of pipe friction and cooling on the gas flow are investigated in this section. The nozzle has the reference configuration.. Table 3 Particle velocity at barrel exit. Dia.. R.P.D.D.. Exp.14Þ. Cal.. 27 mm. 60%. 577 m/s. 42 mm. 18%. 475 m/s. 54 mm. 22%. 431 m/s. Average 527 m/s. 497  5 m/s. Table 4. Particle temperature at barrel exit.. Dia.. R.P.D.D.. Cal.. 27 mm. 60%. 1426 K. 42 mm. 18%. 1140 K. 54 mm. 22%. 997 K. Exp.14Þ Average 1280 K. 1333  67 K. 2.5. Mach number of gas, Mg. 2794. Isentropic flow. 2.0. Fanno & Rayleigh flow. 1.5 1.0. Barrel inlet. Fanno flow. 0.5. Normal shock wave 0. 50. 100 150 Axial distance, x/mm. Fig. 2 Mach number of gas flow for for non-isentropic flows).. Barrel exit 200. 250. ¼ 0:004 (ke =r ¼ 0:005,  ¼ 0:159. The calculated Mach number of the gas flow, Mg , is shown in Fig. 2. The vertical axis shows the Mach number Mg , and the horizontal axis shows the axial distance, x, measured from the throat. The values of  and ke =r in eqs. (1) and (3) are set to their reference values for non-isentropic calculations. For the isentropic flow (curve ‹) the Mach number is constant at 2.0 from the inlet to the exit of the barrel. By adding the effect of pipe friction (Fanno flow,16) curve ›) to the isentropic flow, the Mach number at the barrel inlet is Mg ¼ 1:96. Then, it decreases in the downstream direction until Mg ¼ 1:51 at x ¼ 106 mm where a normal shock wave exists. And then, the gas flow is abruptly decelerated to subsonic speed, Mg ¼ 0:68, through the normal shock wave. After that, the flow is accelerated to reach the speed of sound at the nozzle exit. By adding the effects of pipe friction and cooling (Fanno flow along with Rayleigh flow,16) curve fi) to the isentropic flow, we can expect to obtain a numerical result closer to the real HVOF gun. The Mach number of curve fi at the barrel inlet is Mg ¼ 1:98, decreasing gradually in the downstream direction, but still supersonic, Mg ¼ 1:65, at the nozzle exit. This is because, the supersonic flow is accelerated by cooling according to the theory of Rayleigh flow. That is, the starting supersonic flow of curve › is kept accelerating due to cooling, making the frictional deceleration alleviate till the nozzle exit. If the effect of cooling was larger to that of pipe.

(5) 3500. Normal shock wave. Isentropic flow. 2500 2000. Fanno & Rayleigh flow. 1500 Barrel inlet. Barrel exit 1000 0. 50. Fig. 3 Gas temperature for isentropic flows).. 100 150 Axial distance, x/mm. 200. 250. ¼ 0:004 (ke =r ¼ 0:005,  ¼ 0:159 for non-. friction, the Mach number Mg would increase along the barrel. In Fig. 2, however, the Mach number of curve fi decreases in the downstream direction, indicating the larger effect of pipe friction to that of cooling in terms of the Mach number of gas flow. The gas velocity, not shown here, also shows the same trend as the Mach number in Fig. 2. The gas temperatures obtained for the same input conditions as Fig. 2 are shown in Fig. 3. The vertical axis shows the gas temperature Tg , and the horizontal axis and curves ‹–fi mean the same as Fig. 2. For the isentropic flow (curve ‹), the Tg is kept constant in the barrel. By taking into account the pipe friction (curve ›), Tg gradually increases in the downstream direction until x ¼ 106 mm due to the supersonic deceleration caused by friction. Then, Tg jumps to 3080 K from 2690 K through the normal shock wave generated at x ¼ 106 mm. And then, Tg decreases slightly toward the exit due to the subsonic acceleration. By taking into account pipe friction and cooling (curve fi), Tg steadily decreases along the barrel. This is because, the decrease in gas temperature by cooling exceeds the increase in gas temperature due to the deceleration of the flow caused by friction. Therefore, the effect of cooling is greater to that of pipe friction in terms of the gas temperature. 3.4 Particle velocity, temperature and melting fraction The effect of pipe friction, cooling rate and nozzle geometry on the particle behavior is investigated in this section. The nozzle length Ln is 230 mm, the same value as the reference configuration, in subsections 3.4.1 and 3.4.2 to investigate the effects of pipe friction and cooling. While, Ln ¼ 110 mm{330 mm in 3.4.3 to focus on the effect of nozzle length. 3.4.1 Effect of pipe friction The effect of pipe friction on the particle velocity at the nozzle exit, up;e , is shown in Fig. 4(a). The cooling rate is set as  ¼ 0:159, the reference value. In the figure, the reference value of ke =r is also indicated by a dotted line. The calculated results show that the larger the value of ke =r becomes, the smaller up;e becomes. This tendency implies that the larger the roughness of the inner barrel-wall becomes by use, the smaller up;e becomes for the same operating conditions.. 2795. 600. ψ = 0.04 0.5 1.0. 580 560 540 520 500 0. Reference value of ke / r 2 4 6 8 Equivalent relative roughness, ke / r. 10x10. -3. (a) Particle temperature at nozzle exit, Tp,e /K. Gas temperature, Tg /K. Fanno flow 3000. Particle velocity at nozzle exit, up,e /ms. -1. Quasi-One-Dimensional Analysis of the Effects of Pipe Friction, Cooling and Nozzle Geometry on Gas/Particle Flows. 1600 1550 1500 1450. ψ = 1.0 0.5 1400 0.04. Reference value of ke / r. 1350 1300 0. 2 4 6 8 Equivalent relative roughness, ke / r. 10x10. -3. (b) Fig. 4 Effects of equivalent relative roughness and diverging length ratio on velocity (a), temperature (b) of 30 mm-particle at nozzle exit ( ¼ 0:159).. Figure 4(a) also shows that ¼ 0:5 gives the largest up;e among ¼ 0:04; 0:5; 1:0, showing the existence of the optimum value of to maximize up;e . In fact, the detailed parametric study for 0:04 < < 1:0 shows that  ¼ 0:5 gives the maximum up;e for the present numerical conditions. The particle temperature at the nozzle exit, Tp;e , is shown in Fig. 4(b) for the same numerical conditions as Fig. 4(a). The particle temperature Tp;e increases by the increase in ke =r. This tendency implies that the larger the roughness of the inner barrel-wall becomes by use, the larger Tp;e becomes for the same operating conditions. The particle temperature Tp;e is smaller for < 0:5 because of the higher particle velocity as can be seen in Fig. 4(a). 3.4.2 Effect of cooling rate The effect of the cooling rate on the particle velocity, up;e , is shown in Fig. 5(a). The equivalent relative roughness is set as ke =r ¼ 0:005, the reference value. In the figure, the reference value of  is also indicated by a dotted line. The ‘‘N.S.’’ in the figure means normal shock wave. The calculated results show that the larger the value of  becomes, the larger up;e becomes. However, it is also seen from the slope of the three solid lines that the effect of  on the particle acceleration becomes small for  larger than the.

(6) Particle velocity at nozzle exit, up,e /ms. -1. 2796. H. Katanoda. 600. N.S. in nozzle 550. ψ = 0.04 0.5 1.0. 500. Reference value of σ. 450. N.S. in nozzle 400 0. 0.05. 0.10 0.15 0.20 Cooling rate, σ. 0.25. 0.30. Particle temperature at nozzle exit, T p,e /K. (a) 1700. ψ = 0.04 0.5 1.0. 1600 1500 1400 1300. Reference value of σ. 1200 0. 0.05. 0.10 0.15 0.20 Cooling rate, σ. 0.25. 0.30. (b). MFP at nozzle exit, MFPe. 1.0 0.8. ψ = 0.04 0.5 1.0. 0.6 0.4. Reference value of σ. 0.2. 0. 0.05. 0.10 0.15 0.20 Cooling rate, σ. 0.25. The particle temperature at the nozzle exit, Tp;e , is shown in Fig. 5(b) for the same numerical conditions as Fig. 5(a). Figure 5(b) shows that Tp;e decreases almost linearly for  exceeding a certain value. The values of < 0:5 gives the smaller Tp;e due to larger particle velocity. The horizontal part of the solid lines mean that the particle is partly or fully molten as shown in the next figure. The MFP at the nozzle exit, MFPe , is shown in Fig. 5(c) for the same numerical conditions as Fig. 5(a). Figure 5(c) shows that the value of MFPe decreases by increasing  until it reaches zero. The value of ¼ 0:5 gives the smallest MFPe among ¼ 0:04; 0:5; 1:0. 3.4.3 Effect of nozzle length The calculation in subsections 3.4.1 and 3.4.2 shows that the nozzle configuration of ¼ 0:5 gives the maximum particle velocity up;e for the fixed nozzle length Ln ¼ 230 mm. In this subsection, the effect of nozzle length Ln on the particle velocity up;e as well as particle temperature Tp;e is investigated by using ¼ 0:5. The reference value of ke =r ¼ 0:005 is used in the calculations. As for the cooling rate , it is linearly dependent on the nozzle length Ln , and its reference value was found as  ¼ 0:159 for Ln ¼ 230 mm. Therefore, the rate of  ¼ 0:159 per 230 mm is used for the range of Ln ¼ 110 mm{330 mm in this subsection. Figure 6(a) shows the effect of nozzle length on the particle velocity for 20, 30, 40 mm diameter dp . The horizontal axis of the figure shows the nozzle length divided by the nozzle exit diameter D (11 mm). Figure 6(a) indicates that the longer nozzle is preferable for the acceleration of the particle. We need to keep in mind, however, that the longer nozzle will experience trouble from clogging or spitting. In the previous subsections, the maximum up;e was obtained  0:5 for the value of the horizontal axis Ln =D ¼ at ¼  21. The dependency of on up;e for Ln =D ¼ 30, 230=11 ¼ the maximum horizontal value of Fig. 6(a), was calculated for confirmation. The result, not shown here, indicated again  that ¼ 0:5 gives the maximum up;e . Therefore, nozzle geometry of  ¼ 0:5 is the optimum condition to obtain the maximum up;e for the longer nozzle; 21 < Ln =D < 30. The particle temperature at the nozzle exit, Tp;e , is shown in Fig. 6(b) for the same numerical conditions as Fig. 6(a). The figure shows that Tp;e of the 20 mm particle is equal to the melting point for a wide range of Ln =D > 12:8. The temperature of particles for dp 30 mm increases by increasing Ln =D, but Tp;e doesn’t reach the melting point for Ln =D  30.. 0.30. (c) Fig. 5 Effects of cooling rate and diverging length ratio on velocity (a), temperature (b), melting fraction (c) of 30 mm-particle at nozzle exit (ke =r ¼ 0:005).. reference value. The normal shock wave appears in the nozzle for small values of  < 0:05 and < 0:5, decelerating the particle due to subsonic gas-flow downstream of the normal shock wave. In addition, Fig. 5(a) shows that ¼ 0:5 gives the largest up;e among ¼ 0:04; 0:5; 1:0.. 4.. Conclusions. The effects of pipe friction, cooling and nozzle geometry on the particle behavior as well as supersonic gas flow in the HVOF gun were investigated by using the quasi-one-dimensional analysis. The particle material is Inconel 718. The tested nozzle had a 7.9 mm throat diameter, and 11 mm exit diameter. The nozzle length was varied in the range of 110– 330 mm. Results of the present study are summarized as follows. (1) By the effect of pipe friction, the gas/particle velocity decreases and the gas/particle temperature increases in the downstream direction..

(7) 800 700. dp = 20 µm dp = 30 µm. 600 500. dp = 40 µm. 400 300 10. 15. 20 Ln / D. 25. 30. (a) Fig. 6. Particle Temperature at nozzle exit, Tp,e /K. Particle velocity at nozzle exit, up,e /ms. -1. Quasi-One-Dimensional Analysis of the Effects of Pipe Friction, Cooling and Nozzle Geometry on Gas/Particle Flows. 2797. 1700. dp = 20 µm. 1600 1500. dp = 30 µm. 1400 1300. dp = 40 µm. 1200 1100 1000 10. 15. 20 Ln / D. 25. 30. (b). Effect of nozzle length on velocity (a), temperature (b) of particle at nozzle exit ( ¼ 0:5,  ¼ 0:159 per 230 mm, ke =r ¼ 0:005).. (2) By the effect of cooling, the gas/particle velocity increases and the gas/particle temperature decreases in the downstream direction. (3) The pipe friction has a larger effect on the gas/particle velocity than cooling, causing a decrease in gas/ particle velocity. On the other hand, the cooling has a larger effect on the gas/particle temperature than pipe friction, causing a decrease in gas/particle temperature. (4) When the axial length of the diverging part of the nozzle is approximately equal to that of the following non-diverging straight part, the particle velocity at the nozzle exit becomes maximum. (5) The longer nozzle results in larger particle velocity at the nozzle exit. REFERENCES 1) J.-G. Legoux, B. Arsenault, V. Bouyer, C. Moreau and L. Leblanc: J. Thermal Spray Technol. 11 (2002) 86–94. 2) S. Kuroda, T. Fukushima, J. Kawakita and T. Kodama: Proc. Int. Thermal Spray Conf. 2002, ed. by E. Lugscheider (2002) pp. 819–824. 3) C. M. Hackett and G. S. Settles: Proc. 8th Nat. Thermal Spray Conf., ed. by C. C. Berndt and S. Sampath (1995) pp. 135–140.. 4) K. Sakaki, Y. Shimizu, N. Saito and Y. Gouda: J. Japan Thermal Spraying Soc. 34 (1997) 1–9. 5) Y. M. Yang, H. Liao and C. Coddet: Proc. Int. Thermal Spray Conf. 1995, ed. by A. Ohmori (1995) pp. 399–404. 6) JSME: Hydraulic Losses in Pipes and Ducts, (Maruzen, Tokyo, 1979) p. 32. 7) B. J. McBride, S. Gordon and M. A. Reno: NASA TM-4513, 1993, 89 pages. 8) H. Schlichting: Boundary-Layer Theory, 7th ed., (McGraw-Hill, NY, 1979) p. 621. 9) F. M. White: Viscous Fluid Flow, 2nd ed., (McGraw-Hill, NY, 1991) pp. 28–29. 10) S. Gordon and B. J. McBride: NASA Reference Publications 1311, 1994, 55 pages. 11) A. B. Bailey and J. Hiatt: AIAA J. 10 (1972) 1436–1440. 12) Y. P. Wan, V. Prasad, G.-X. Wang, S. Sampath and J. R. Fincke: J. Heat Transfer 121 (1999) 691–699. 13) W. D. Swank, J. R. Fincke, D. C. Haggard and G. Irons: Proc. 7th Nat. Thermal Spray Conf., ed. by C. C. Berndt and S. Sampath (1994) pp. 313–318. 14) W. D. Swank, J. R. Fincke, D. C. Haggard, G. Irons and R. Bullock: Proc. 7th Nat. Thermal Spray Conf., ed. by C. C. Berndt and S. Sampath (1994) pp. 319–324. 15) M. L. Thorpe and H. J. Richter: Proc. Int. Thermal Spray Conf. 1992, ed. by C. C. Berndt (1992) pp. 137–147. 16) M. J. Zucrow and J. D. Hoffman: Gas Dynamics, (John Wiley & Sons, NY, 1976) pp. 244–326..

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