EP1834699A1 - Thermal spraying nozzle device and thermal spraying equipment - Google Patents

Abstract

[Subject]

A thermal spraying nozzle device and a thermal spraying system are to be provided which can supply a thermal spraying material constantly and can control the state of a film or deposit.

[Solution]

In a thermal spraying nozzle device wherein carrier gas is introduced into an inlet side of a nozzle to form a supersonic gas flow and a thermal spraying material is atomized and ejected by the gas flow, a storage section (4) for the storage of molten metal as the thermal spraying material is connected an end portion on the inlet side of the nozzle (2) through a connecting pipe, the nozzle has a throat portion (2a) for accelerating the introduced carrier gas to supersonic velocity and a divergent region (2b) formed downstream of the throat portion toward an outlet, the metal particles atomized by the supersonic gas being cooled to a solidified or semi-solidified state in the divergent region.

Description

FIELD OF ART
• The present invention relates to a thermal spraying nozzle device, as well as a thermal spraying system, wherein with use of gas a thermal spraying material is atomized and brought into collision with a base material to form a film or a deposition layer.
BACKGROUND ART
• Heretofore, a thermal spraying process has been known as a technique of heating a coating material and the resulting melted or half-melted fine particles are brought into collision at high speed with the surface of a base material to form a film.
• According to this thermal spraying process, since the base material and the film are joined together physically, a film can be formed on any material insofar as the material can be melted. The film formed can satisfy various conditions required in surface treatment, including abrasion resistance, corrosion resistance and heat insulating property, and is therefore utilized widely in various fields.
• According to a cold spraying method, a spraying material is brought into collision with a base material as a supersonic flow together with inert gas and as it is in a solid phase without being melted or gasified, to form a film. Thus, unlike other spraying methods, the cold spraying method is advantageous in that there occurs no thermal change in characteristics of the material and that it is possible to suppress oxidation in the resulting film.
• Fig. 32 shows a schematic construction of a cold spraying system.
• In the same figure, high pressure gas supplied from a gas source 30 is branched into two pipes 31 and 32. The gas as a main flow in the pipe 31 is heated by a gas heater 33, while the remaining gas flowing in the pipe 32 is introduced into a powder supply unit 34.
• The gas heated by the gas heater 33 is introduced into a chamber 36 through a pipe 35, while the powder supply unit 34 supplies powder particles to the chamber 36 through a pipe 37.
• The gas and the powder particles are mixed together within the chamber 36 and the resulting mixture passes through a convergent portion 38a and a diffusion portion 38b in a supersonic nozzle 38, whereby the mixture is accelerated and collides as a supersonic jet flow onto a base material 39 (see, for example, Japanese Patent Laid-Open No.2004-76157 , Patent Literature 1).
• On the other hand, there also has been proposed a method wherein molten metal is used as a thermal spraying material and is allowed to flow in the state of a thin film from a chamber having a slit-like outlet, then is atomized and sprayed by a supersonic gas flow which passes in the state of a laminar flow through a nozzle, the nozzle having a slit-like orifice formed in the vicinity of an outlet of the nozzle (see, for example, Japanese Patent Laid-Open No.2002-508441 , Patent Literature 2).
• Patent Literature 1:
  Japanese Patent Laid-Open No. 2004-76157
• Patent Literature 2:
  Japanese Patent Laid-Open No. 2002-508441
DISCLOSURE OF THE INVENTION
• However, in the former cold spraying system referred to above, since powder particles of a normal temperature are brought into collision with a base material and are heated locally to a temperature of not lower than the melting point thereof with heat resulting from plastic deformation and thereby adhered onto the base material, a gas pressure of 1.0 to 3.0 MPa is needed for attaining a particles velocity of, say, 600 m/s or more. Besides, it is necessary to pre-heat the gas up to 600°C. Thus, there is the problem that handling is difficult. Moreover, it is not easy to supply the powder particles at a constant rate.
• In the latter thermal spraying system referred to above, atomization is performed at a supersonic velocity, the nozzle is not designed for acceleration of particles and therefore it is impossible to obtain such high density film or deposit as permits omission of HIP (Hot Isostatic Pressing).
• The present invention has been accomplished in view of the above-mentioned problems involved in the conventional spraying systems and provides a thermal spraying nozzle device and a thermal spraying system both able to supply a thermal spraying material at a constant rate and control the state of a film or a deposit.
• The thermal spraying nozzle device according to the present invention is, in the gist thereof, a thermal spraying nozzle device wherein carrier gas is introduced from an inlet side of a nozzle to form a supersonic gas flow and a thermal spraying material is atomized and ejected by the gas flow, the thermal spraying nozzle device comprising, a storage section storing molten metal as the thermal spraying material connected to an end on the inlet side of the nozzle through a connecting pipe, and, the nozzle having a throat portion and a divergent region in a downstream of the throat portion toward an outlet side to form the supersonic gas flow, wherein the thermal spraying nozzle device is configured such that metal particles atomized by the supersonic gas flow are cooled to a solidified or semi-solidified state in the divergent region and then ejecting in a predetermined direction from the outlet side of the nozzle.
• Preferably, within the connecting pipe in the above thermal spraying nozzle device, a molten metal outlet pipe is extended from the storage section toward the center in the throat portion or the center on the downstream side of the throat portion and an outside portion of the molten metal outlet pipe constitutes a channel for the carrier gas to flow therethrough in an accelerated state.
• According to the gist of the nozzle used in the present invention, a divergent angle of the divergent region formed on the downstream side of the throat portion is not larger than 15° in terms of a half-cone angle.
• The length of the divergent region is a flight distance until solidification or semi-solidification of the atomized metal particles and is determined on the basis of a flight distance which is determined by modeling both flight distance of the atomized metal particles and the temperature of the metal particles. More specifically, the flight distance until solidification or semi-solidification of the atomized metal particles is determined by first determining a flight time until change of the atomized metal particles into a solidified or semi-solidified state and then substituting the said flight time into the following expression, and the length of the divergent region, in the gist thereof, is set to a length of not shorter than the said flight distance:
• $$I_f=u_g{t}_f-\frac{{u_{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}^2{\mathit{\rho }}_g{t}_f+{\mathit{\rho }}_s{d}_s{a}_g}{{u_{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}^2{\mathit{\rho }}_g}\sqrt{\frac{{u_{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}^2{\mathit{\rho }}_s{d}_s{a}_g}{{u_{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}^2{\mathit{\rho }}_g{t}_f+{\mathit{\rho }}_s{d}_s{a}_g}}+\frac{{\mathit{\rho }}_s{d}_s{a}_g}{u_g{\mathit{\rho }}_g}$$

  

  
  where l_f is the flight distance of the particles, t_f is the flight time until solidification or semi-solidification of the particles, u_g is flow velocity of gas, ρ_g is gas density, ρ_s is particle density, d_s is particle diameter, and a_g is sound velocity of gas.
• Preferably, given that an inlet pressure of the carrier gas is po and a nozzle outlet pressure thereof is P_B, the carrier gas is introduced into the nozzle in a state in which the inlet pressure Po satisfies the following expression:
• $${\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">p</figure-callout>}}_0\ge p_B(1+\frac{\mathit{\kappa }-1}{2}{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}^2{)}^{\frac{\mathit{\kappa }}{\mathit{\kappa }-1}}$$

  

  
  where κ: specific heat ratio of compressed gas, M: Mach number in the expanded nozzle portion on the downstream side of the throat portion.
• The thermal spraying system according to the present invention, in the gist thereof, comprises the thermal spraying nozzle device constructed as above, a carrier gas supply unit connected to the nozzle through a conduit to introduce the carrier gas under pressure into the nozzle, a sealed chamber accommodating the nozzle and a base material for collision therewith of the ejected particles, and pressure reducing means for reducing the internal pressure of the sealed chamber.
• The thermal spraying system according to the present invention, in the gist thereof, comprises the thermal spraying nozzle device constructed as above, a molten metal supply unit connected to the storage section through a connecting pipe to supply molten metal under pressure continuously to the molten metal in the storage section, and a base material supply unit for continuous supply of the base material.
• The present invention is advantageous in that the thermal spraying material can be supplied constantly and that it is possible to control the state of a film or a deposit.
BRIEF DESCRIPTION OF THE DRAWINGS
• Fig. 1 is a perspective view showing the construction of a thermal spraying device according to the present invention;
• Figs. 2(a) and 2(b) are explanatory diagrams showing the definition of an expanded portion of a nozzle.
• Fig. 3 is a graph explaining a relation between Mach number and drag coefficient.
• Fig. 4 is a graph showing nozzle lengths according to particle diameters.
• Fig. 5 is an explanatory diagram showing a conventional nozzle divergent angle.
• Fig. 6 is an explanatory diagram showing a case where a shock wave is generated within the nozzle.
• Fig. 7 is an explanatory diagram showing a case where a supersonic flow is formed throughout the entire region of the nozzle.
• Fig. 8 is a graph showing a typical example of a nozzle shape.
• Fig. 9 is a graph showing a nozzle outlet diameter providing an appropriate expansion.
• Fig. 10 is a graph showing nozzle length vs. Mach number at a particle diameter of 20 µm and a throat diameter of 25 mm.
• Fig. 11 is a graph showing nozzle length vs. gas temperature/velocity distribution at a particle diameter of 20 µm and a throat diameter of 25 mm.
• Fig. 12 is a graph showing nozzle length vs. particle temperature/velocity distribution at a particle diameter of 20 µm and a throat diameter of 25 mm.
• Fig. 13 is a graph showing nozzle length vs. Mach number at a particle diameter of 20 µm and a throat diameter of 35 mm.
• Fig. 14 is a graph showing nozzle length vs. gas temperature/velocity distribution at a particle diameter of 20 µm and a throat diameter of 35 mm.
• Fig. 15 is a graph showing nozzle length vs. particle temperature/velocity distribution at a particle diameter of 20 µm and a throat diameter of 35 mm.
• Fig. 16 is a graph showing nozzle length vs. Mach number at a particle diameter of 50 µm and a throat diameter of 25 mm.
• Fig. 17 is a graph showing nozzle length vs. gas temperature/velocity distribution at a particle diameter of 50 µm and a throat diameter of 25 mm.
• Fig. 18 is a graph showing nozzle length vs. particle temperature/velocity distribution at a particle diameter of 50 µm and a throat diameter of 25 mm.
• Fig. 19 is a graph showing nozzle length vs. Mach number at a particle diameter of 50 µm and a throat diameter of 35 mm.
• Fig. 20 is a graph showing nozzle length vs. gas temperature/velocity at a particle diameter of 50 µm and a throat diameter of 35 mm.
• Fig. 21 is a graph showing nozzle length vs. particle temperature/velocity distribution at a particle diameter of 50 µm and a throat diameter of 35 mm.
• Fig. 22 is a graph showing nozzle length vs. Mach number at a particle diameter of 100 µm.
• Fig. 23 is a graph showing nozzle length vs. gas temperature/velocity distribution at a particle diameter of 100 µm.
• Fig. 24 is a graph showing nozzle length vs. particle temperature/velocity distribution at a particle diameter of 100 µm.
• Fig. 25 is an explanatory diagram showing the construction of a thermal spraying system to be applied to a batch process.
• Fig. 26 is an explanatory diagram showing the construction of a thermal spraying system to be applied to a continuous molding process.
• Fig. 27 is a diagram corresponding to Fig. 1, showing a nozzle of a second embodiment according to the present invention.
• Fig. 28 is a diagram corresponding to Fig. 1, showing a nozzle of a third embodiment according to the present invention.
• Fig. 29 is a diagram corresponding to Fig. 1, showing a nozzle of a fourth embodiment according to the present invention.
• Fig. 30 is a diagram corresponding to Fig. 1, showing a nozzle of a fifth embodiment according to the present invention.
• Fig. 31 is a diagram corresponding to Fig. 1, showing a nozzle of a sixth embodiment according to the present invention.
• Fig. 32 is an explanatory diagram showing the construction of a conventional cold spraying system.
BEST MODE FOR CARRYING OUT THE INVENTION
• The present invention will be described in detail hereinunder by way of embodiments thereof illustrated in the drawings.
• Fig. 1 illustrates a basic construction of a thermal spraying nozzle device according to the present invention.
1. Principle of the thermal spraying nozzle device
• The thermal spraying nozzle device shown in the same figure and indicated at 1 supplies molten metal M directly into a supersonic nozzle (hereinafter referred to simply as "nozzle") 2.
• Within the nozzle 2, gas flows at a supersonic velocity, while the molten metal supplied into the nozzle 2 flows at low speed. A shearing force acts between the two and so does a surface tension of the molten metal, whereby the molten metal is atomized downstream of a throat portion 2a of the nozzle 2.
• Atomized metal particles (hereinafter referred to simply as "particles") are accelerated within the nozzle 2 and are cooled rapidly into a solidified state. Thus, in the thermal spraying nozzle device 1 according to the present invention, the throat portion 2a wherein the atomizing process is performed and a divergent region 2b wherein a flying/cooling process follows the atomizing process are formed integrally with each other.
• The particles ejected from the nozzle 2 just after solidification come into collision with a base material 3 at a velocity of about 450 m/s. The particles generate heat due to deformation caused by the collision and a portion thereof rise in temperature up to a level of the melting point thereof or higher, whereby the particles adhere to the base material 3 (see the impact depositing process in the figure).
• The numeral 4 in the figure denotes a storage section for storing the molten metal M, the storage section 4 having a connecting pipe 4a communicating with the nozzle 2.
• A front end portion of the connecting pipe 4a is extended as a molten metal outlet pipe 4b toward the center of a cylindrical hole of the throat portion 2a and accelerated carrier gas flows over the outer periphery of the molten metal outlet pipe 4b.
• The principle of collision of solidified particles against the base material 3 is the same as in the conventional cold spraying. That is, collided particles undergo a marked plastic deformation and are depressed like a crater, affording a compact void-free structure within a film (or a deposit layer). Therefore, a molding material thus formed with the film need not be subjected to HIP (Hot Isostatic Pressing) as a post-treatment, i.e., application of pressure to remove remaining voids.
• In case of using nitrogen gas as carrier gas (hereinafter referred to simply as "gas") for generating a supersonic gas flow, it is possible to obtain a molding material having a low oxygen content because oxidation does not proceed after collision therewith of the particles. Moreover, since the particles are solidified within only 1 ms as a flight time thereof through the nozzle 2, it is possible to prevent the progress of nitriding.
• Besides, molten metal is used as the thermal spraying material and the particles thereof are brought into collision with the base material 3 at a temperature slightly lower than the solidifying point thereof. Therefore, in comparison with cold spraying, even when the collision is performed at a low Mach number (e.g., a Mach number of 2 or so), the surface temperature of the base material 3 reaches a level of not lower than the melting point and thus the particles can be adhered positively to the base material 3. The Mach number means gas velocity/sound velocity.
• The nozzle 2 has a nozzle length of the expanded portion set at 100 mm or more and is configured so as to operate in a state in which a total carrier gas pressure po satisfies the following expression (1):
• $${\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="imgf0003.png,imgf0005.png"\; state="\{\{state\}\}">p</figure-callout>}}_0\ge p_B(1+\frac{\mathit{\kappa }-1}{2}{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}^2{)}^{\frac{\mathit{\kappa }}{\mathit{\kappa }-1}}$$

  

  
  where p₀: total carrier gas pressure (throat upstream-side inlet pressure), p_B: throat outlet back pressure, M: Mach number in the thermal spraying material melting section, κ: specific heat ratio of the carrier gas.
• In accordance with the expression (2) the Mach number M is associated with a sectional area A* of the throat portion 6 and an intra-nozzle enlarged sectional area A.
• The enlarged sectional area includes a conical enlarged portion of a gradually increasing diameter from the narrowest portion A* as the throat portion toward the downstream side, as shown in Fig. 2(a), and an enlarged portion whose diameter suddenly increases from the narrowest portion A* toward the downstream side and then becomes nearly constant, as shown in Fig. 2(b).
• $$\frac{A}{A^{*}}=\frac{1}{M}[\frac{(\mathit{\kappa }-1){\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">M</figure-callout>}}^2+2}{\mathit{\kappa }+1}{]}^{\frac{\mathit{\kappa }+1}{2\left(\mathit{\kappa }-1\right)}}$$

  
• It is known that if compressed gas having a pressure represented by the expressions (1) and (2) is supplied to a convergent-divergent (Laval) nozzle, there is formed a supersonic flow up to the expanded portion of the nozzle. In the narrowest portion the high-speed gas flow becomes Mach 1 (about 340 m/s). Molten metal exposed to such a high-speed gas flow is atomized into fine particles. By Hinze (Honze, J.O., Fundamentals of the Hydrodynamic Machanism of Splitting in Dispersion Processes, AIChEJ., Vol, No.3, 1955, pp.289-295) it has empirically been made clear that this is represented by the following expression (3):
• $$\frac{{\mathit{\rho }}_G(V_G-V_L{)}^2{D}_L}{\mathit{\sigma }}\approx 13$$

  

  where ρ_G: gas density, V_G: gas velocity in nozzle inlet, V_L: liquid velocity, D_L: droplet diameter after division, σ: liquid surface tension.
• If reference is made to aluminum alloy as an example of molten metal and nitrogen gas is supplied at a pressure of 0.8 MPa to the nozzle, a particle diameter of the aluminum alloy after atomization, which is determined from the expression (3), is about 20 µm.
• The particles after atomization undergo both accelerating and cooling actions by a supersonic gas flow and are eventually ejected from the nozzle 2 while having a supersonic velocity.
• The said acceleration and cooling can be estimated by numerical analysis. More particularly, a mass, momentum and energy conservation expression as a quasi-one-dimensional compressive fluid conservation type representation is solved by making an expression (4) simultaneous with a particles motion equation (6).
2. Method of Numerical Analysis (1) First, symbols used in a numerical analysis method to be described later are shown below.

A:

sectional area of the nozzle

C_D:

particle drag coefficient

C_P:

specific heat

D:

nozzle diameter

d:

particle diameter

f:

wall surface friction coefficient

g:

gravitational acceleration

h:

specific enthalpy

m:

mass flow rate

Nu:

Nusselt number

p;

gas pressure

Pr:

Prandtl number

Q:

energy per unit time necessary for heating the nozzle

R:

gas constant

Re:

Reynolds number

T:

temperature

u:

flow velocity

x:

distance in nozzle flow direction

α:

Stefan-Boltzmann constant

ε:

emissivity

κ:

specific heat ratio

λ:

thermal conductivity

µ:

viscosity coefficient

ρ:

density

• The following are the meanings of subscripts:

g:

gas

s:

second phase (droplet, particle, powder)

x:

distance from the nozzle throat portion

W:

nozzle wall surface

(2) Dominance Equation of Gas Phase
• A mass, momentum and energy conservation expression as a quasi-one-dimensional compressive fluid conservation type representation is shown below as an expression (4). $$\frac{\partial \mathbf{U}}{\partial t}+\frac{\partial \mathbf{F}}{\partial x}=\mathbf{S}$$

  

  Provided, however, that the following equation (5) of Johnson-Rubeshin is used in connection with turbulent flow heat transfer of the nozzle wall: $$\begin{array}{l}\mathbf{U}=\left(\begin{array}{c}{\mathit{\rho }}_{g}A\\ {\mathit{\rho }}_g{\mathit{Au}}_g\\ {\mathit{\rho }}_g\mathit{AE}\end{array}\right),\mathbf{F}=\left(\begin{array}{c}{\mathit{\rho }}_g{\mathit{Au}}_g\\ {\mathit{\rho }}_g<figure-callout\; id="2"\; label="\; Au\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}"></figure-callout>{{\mathit{Au}}_g}^{}{{}_{}}^2+\mathit{pA}\\ {\mathit{\rho }}_g{\mathit{Au}}_{g}H\end{array}\right),\mathbf{S}=\left(\begin{array}{c}0\\ p=\frac{\partial A}{\partial x}-\mathit{\pi Df}\frac{1}{2}{\mathit{\rho }}_g{{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2+s\\ {\mathit{\pi D}\mathrm{Nu}}_x\frac{\lambda }{x}\left(T_W-T_g\right)+e\end{array}\right)\\ E=\frac{1}{2}{{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2+\frac{1}{\mathit{\kappa }-1}\frac{p}{{\mathit{\rho }}_g},H=E+\frac{p}{{\mathit{\rho }}_g}\\ {\mathrm{Nu}}_x=0.0296{\mathrm{<figure-callout\; id="2"\; label="Pr"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Pr</figure-callout>}}^{\frac{2}{3}}{\mathrm{<figure-callout\; id="4"\; label="Re\; x"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">Re</figure-callout>}}_{x^{}}\end{array}$$

  

  In the above expression, s and e stands for a momentum generation term and an energy generation term, respectively, which represent an interaction between gas phase and second phase.
• In actual solution of the expression (1), an advection term is made discrete using Roe's Flux difference Splitting method which has been made into MUSCL (Monotone Upstream-centred Schemes for Conversion laws), and time integral is performed using a four-stage Runge-Kutta method.
(3) Dominance equation of the second phase (droplet, particle, powder)
• Particles' velocity can be obtained by solving the following particle motion equation (6): $$\frac{\partial u_s}{\partial t}+u_s\frac{\partial u_s}{\partial x}=\frac{{\mathit{\rho }}_s-{\mathit{\rho }}_g}{{\mathit{\rho }}_s}g-\frac{u_s}{{\dot{m}}_s}s$$

  

  Provided, however: $$s=\frac{3}{2}\frac{{\dot{m}}_s{C}_D}{d_s{\mathit{\rho }}_s{u}_s}\frac{1}{2}{\mathit{\rho }}_g\left(u_s-u_g\right)\left|u_s-u_g\right|$$

  
• The following equation (8) of Kurten is used for drag coefficient: $$\begin{array}{l}{C}_D=0.28+6{\mathrm{Re}}^{-0.5}+21{\mathrm{Re}}^{-1}\\ \mathrm{Re}=\frac{{\rho }_g|u_s-u_g|d_s}{\mathit{\mu }}\end{array}$$

  
• The particle temperature can be obtained by solving the following particle energy equation (9): $$\frac{\partial h_s}{\partial t}+u_s\frac{\partial h_s}{\partial x}=-\frac{u_s}{{\dot{m}}_s}\left(q+e\right)$$

  

  However, in the case of a heat insulating wall with nozzle wall temperature equal to the gas temperature: $$e=\frac{6{\dot{m}}_s}{{\mathit{\rho }}_s{u}_s{d}_s}\left\{\mathrm{Nu}\frac{\mathit{\lambda }}{d_s}\left(T_s-T_g\right)+\mathit{\alpha }\mathit{\epsilon }\left(T_s^4-{\mathrm{<figure-callout\; id="4"\; label="T\; W"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">T</figure-callout>}}_W^{}\right)\right\},q=0$$

  

  In case of the nozzle wall 1b being a heated isothermal wall: $$e=\frac{6{\dot{m}}_s}{{\mathit{\rho }}_s{u}_s{d}_s}\mathrm{Nu}\frac{\mathit{\lambda }}{d_s}\left(T_s-T_g\right),q=\frac{6{\dot{m}}_s}{{\mathit{\rho }}_s{u}_s{d}_s}\mathit{\alpha }\mathit{\epsilon }\left(T_s^4-{\mathrm{<figure-callout\; id="4"\; label="T\; W"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">T</figure-callout>}}_W^{}\right)$$

  
• The following expression (12) of Ranz-Marshall is used for Nusselt number: $$\mathrm{Nu}=2+0.6{\mathrm{<figure-callout\; id="1"\; label="Pr"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Pr</figure-callout>}}^{\frac{1}{3}}{\mathrm{<figure-callout\; id="1"\; label="Re"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Re</figure-callout>}}^{\frac{1}{2}}$$

  
• In actual solution of the expressions (6) and (9), QUICK method is used for making the advection term discrete and time integral is performed using a four-stage Runge-Kutta method.
(4) Quantity of heat required for heating the nozzle
• The quantity of heat necessary for maintaining the isothermal condition can be estimated by the following expression (13): $$Q={\int }_0^L\left[\mathit{\pi D}{\mathrm{Nu}}_{\mathrm{x}}\frac{\mathit{\lambda }}{x}\left(T_W-T_g\right)-q\right]\mathrm{dx}$$

  
(5) Nozzle Length
• In operation using the thermal spraying nozzle device according to the present invention, the distance from the nozzle outlet to the deposit is set extremely short because the device is configured so that the atomized particles collide with the deposit before deceleration of the particles' velocity. Therefore, it is approximately presumed that the particle velocity and enthalpy in the nozzle output are substantially maintained, allowing the particles to be deposited.
• The state of the deposit depends much on the state of the particles being deposited, but in case of the particles being brought into collision and deposited at a subsonic velocity as in the conventional thermal spraying nozzle device, the particles cannot be adhered to the base material or the deposit if the particles are in a solidified state.
• On the other hand, the thermal spraying nozzle device according to the present invention defines as an operating condition that semi-solidified or solidified particles with a greater solid phase ratio so far not utilized should be brought into collision and deposited at a supersonic velocity. In this connection, it is presumed that molten metal changes into a semi-solidified state while being atomized and flying, and a minimum flight distance required until that time-point is determined. This flight distance is presumed to be a minimum nozzle length required for the device.
• As noted earlier, a motion equation which represents acceleration of the particles is the following equation (6): $$\frac{\partial u_s}{\partial t}+u_s\frac{\partial u_s}{\partial x}=\frac{{\mathit{\rho }}_s-{\mathit{\rho }}_g}{{\mathit{\rho }}_s}g-\frac{u_s}{{\dot{m}}_s}s$$

  
• The expression (6) is convenient for numerical calculation using a fixed calculation lattice because it is described from the Euler's coordinate system which stands still together with the nozzle.
• However, the expression in question is inconvenient for tracing the state of the particles one by one to check both particle velocity and particle enthalpy. Therefore, if it is expressed in terms of an equation described from the Lagrangian coordinate system which moves together with flying particles, the following equation (14) is obtained.
  However, for the purpose of simplification, a gravitational term which exerts little influence is ignored. Further, it is presumed that in a section where the flight distance is still short the particles are in the course of acceleration and are pushed from behind like a fair wind by the gas flow and that there always exists the relationship of gas flow velocity u_g > particle velocity u_s.
• $$\frac{\mathrm{d}{u}_s}{\mathrm{d}t}=\frac{3}{2}\frac{C_D}{d_s{\mathit{\rho }}_s}\frac{1}{2}{\mathit{\rho }}_g(u_g-u_s{)}^2$$

  

  By taking a relative velocity between the gas flow velocity u_g and the particle velocity u_s to obtain U = u_g - u_s and by assuming that the gas flow velocity as a supersonic velocity is approximately constant within the nozzle, the expression (14) can be transformed into the following expression (15):
• $$\frac{\mathrm{d}\mathit{U}}{\mathrm{d}t}=\frac{3}{2}\frac{C_D}{d_s{\mathit{\rho }}_s}\frac{1}{2}{\mathit{\rho }}_g{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">U</figure-callout>}}^2$$

  

  In the expression (15), the drag coefficient C_D can be expressed by a function of Reynolds number in the case where the relative velocity U is a subsonic velocity, as shown in the expression (12), but in the state just after atomization the relative velocity U is very likely to be a supersonic velocity. Therefore, in the graph of Fig. 3 (an explanatory diagram of a sphere obtained from bullet route measurement, as well as drag coefficient of cone-cylinder and Mach number dependence), the drag coefficient in question is approximated by the following expression (16) from an experimental result on drag coefficient of Mach number and the sphere (see an approximate line E in the figure).
• Fig. 3 was quoted from "2nd edition McGraw-Hill Series in Aeronautical and Aerospace Engineering, Modern Compressible Flow with historical Perspective." $$C_D=\frac{2}{3}M=\frac{2}{3}\frac{U}{a_g}$$

  

  where a_g stands for the sound velocity of gas and M stands for Mach number.
• From the expressions (16) and (15) there is obtained the following expression (17) which expresses a relation between the particle flight time, t, and the relative velocity U: $$U=\sqrt{\frac{{{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2{\mathit{\rho }}_s{d}_s{a}_{\mathrm{<figure-callout\; id="2"\; label="g\; u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}{{u_g}^{}}}$$

  

  where the particle velocity u_s is assumed equal to zero at t = 0.
• The relation between the flight time t_f and the flight distance l_f is obtained from the following expression (18): $$I_f=u_g{t}_f-\frac{{{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2{\mathit{\rho }}_g{t}_f+{\mathit{\rho }}_s{d}_s{a}_{\mathrm{<figure-callout\; id="2"\; label="g\; u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}{{u_g}^{}}\sqrt{\frac{{{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2{\mathit{\rho }}_s{d}_s{a}_{\mathrm{<figure-callout\; id="2"\; label="g\; u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}{{u_g}^{}}}+\frac{{\mathit{\rho }}_s{d}_s{a}_g}{u_g{\mathit{\rho }}_g}$$

  

  
  where u_g is the flow velocity of gas, ρ_g is the density of gas, ρ_s is the density of particles, and d_s is particle diameter.
• Once the flight time t_f until the particles reach a semi-solidified state is known, the particle flight distance l_f in the past is calculated, corresponding to the required minimum nozzle length. For this reason, the flight time t_f until the particles become semi-solidified is determined. Cooling of the particles is given in terms of the foregoing expression (9): $$\frac{\partial h_s}{\partial t}+u_s\frac{\partial h_s}{\partial x}=-\frac{u_s}{{\dot{m}}_s}\left(q+e\right)$$

  
• Like the expression (14), this can be expressed in terms of the Lagrangian coordinate system as follows (19): $$\frac{{\mathit{dh}}_s}{\mathit{dt}}=\frac{6}{{\mathit{\rho }}_s{d}_s}\left\{\mathrm{Nu}\frac{\mathit{\lambda }}{d_s}\left(T_s-T_g\right)+\mathit{\alpha }\mathit{\epsilon }\left(T_W^4-{\mathrm{<figure-callout\; id="4"\; label="T\; s"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">T</figure-callout>}}_s^{}\right)\right\}$$

  

  Initial molten metal temperature, liquidus temperature and solidus temperature are almost equal approximately and if the value there of is represented by the material melting point T_m, T_s= T_m. The gas temperature T_s and the nozzle wall surface temperature T_w are also assumed equal approximately.
• Nusselt number Nu, which represents the degree of heat transfer, is represented by the expression (12), but can be rewritten into the following expression (20) using the relative velocity U: $$\mathrm{Nu}=2+0.6{\mathrm{<figure-callout\; id="1"\; label="Pr"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Pr</figure-callout>}}^{\frac{1}{3}}{\left(\frac{{\mathit{\rho }}_g{d}_s}{{\mathit{\mu }}_{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">g</figure-callout>}}}\right)}^{\frac{1}{2}}{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}^{\frac{1}{2}}$$

  
• If latent heat of solidification of the molten metal is assumed to be L, the following expression (21) is valid in order to attain a semi-solidified state with a larger solid phase ratio: $${\int }_0^{t_1}-\frac{\mathit{dh}}{\mathit{dt}}\mathit{dt}\ge \frac{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">L</figure-callout>}}{2}$$

  

  In the above expression there is written L/2 because a nearly intermediate point of transition from liquid phase to solid phase corresponds to a semi-solidified state.
• In this case there is established an equal sign in the expression (21) because determining a minimum nozzle length means determining the shortest flight time t_f until the particles becomes semi-solidified.
• If Nusselt number Nu is eliminated from the expressions (19) and (20) and the relative velocity U is also eliminated using the expression (17) and if an equal sign expression in the expression (21) is used, there is obtained the following relationship (22) of the shortest flight time t_f until the particles reaches a semi-solidified state: $$\begin{array}{l}0.6{\mathrm{<figure-callout\; id="1"\; label="Pr"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">Pr</figure-callout>}}^{\frac{1}{3}}\mathit{\lambda }\left(T_m-T_g\right)\sqrt{\frac{{\mathit{\rho }}_g}{{\mu }_g{d}_s}}\left\{\frac{4\left({{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2{\mathit{\rho }}_s{t}_f+{\mathit{\rho }}_s{d}_s{a}_{\mathrm{<figure-callout\; id="3"\; label="g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}\right)}{3{{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2{\mathit{\rho }}_s}(\frac{{{\mathrm{<figure-callout\; id="2"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^2{\mathit{\rho }}_s{d}_s{a}_{\mathrm{<figure-callout\; id="2"\; label="g\; u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}{{u_g}^{}}{)}^{0.25}-\frac{4{\mathit{\rho }}_s{d}_s{a}_{\mathrm{<figure-callout\; id="3"\; label="g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">g</figure-callout>}}}{3{{\mathrm{<figure-callout\; id="3"\; label="u\; g"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">u</figure-callout>}}_g}^{\frac{3}{2}}{\mathit{\rho }}_g}\right\}\\ +\left\{\frac{2\mathit{\lambda }}{d_s}\left(T_m-T_g\right)+\mathit{\alpha }\mathit{\epsilon }\left({T_m}^4-{{\mathrm{<figure-callout\; id="4"\; label="T\; W"\; filenames="imgf0001.png,imgf0003.png"\; state="\{\{state\}\}">T</figure-callout>}}_W}^4\right)\right\}{t}_f=\frac{{\mathit{\rho }}_s{d}_{s}L}{12}\end{array}$$

  

  
  where Pr is Prandtl number of gas, λ is the thermal conductivity of gas, T_m is the material melting point, T_g is the temperature of gas, and µ_g is the viscosity coefficient of gas.
• The above expression (22) cannot be solved for t_f, but can be solved numerically using the Newton's method.
• Thus, by determining the shortest flight time t_f from the expression (22) and substituting it into the expression (18) there is determined the shortest flight time, i.e., minimum nozzle length l_f.
• The thermal spraying nozzle device according to the present invention is characterized by being a device using a nozzle with a length of not smaller than the above nozzle length l_f, and by accelerating the particles up to a supersonic velocity the particles even in a solidified state adhere to the base material or deposit. Thus, the nozzle length has no upper limit theoretically.
• Fig. 4 is a graph of having determined minimum nozzle lengths concretely with use of aluminum and copper. The nozzle lengths shown therein are considered necessary when particles of various diameters assume a semi-solidified state with a solid phase ratio exceeding 0.5. In the same graph, the particle diameter is plotted along the axis of abscissa and the nozzle length along the axis of ordinate.
  Carrier gas conditions are the same as in Table 1 which will be described later.
• As a result of atomization, when an average particle diameter in terms of volume occupancy for example is 50 µm, a required nozzle length is 0.17 m in case of aluminum and 0.12 m in case of copper.
• Heretofore, when flowing molten metal into a supersonic nozzle for the purpose of atomization, there is used a nozzle having a larger divergent angle (a divergent angle of the divergent region on the downstream side of the throat portion) of θ > 15° in terms of a half-cone angle as shown in Fig. 5 in order to avoid adhesion of the particles to the inner wall surface of the nozzle. The said half-cone angle means the angle between the central nozzle axis and the nozzle inner wall.
• In this case, the sectional area ratio A/A* increases abruptly and so does Mach number (see the expression (2)), but a shock wave front appears upon arrival at Mach number M₁ which is determined from the isentropic change expression (23) and the vertical shock wave relationship (24), and with this as a boundary the gas flow on the downstream side becomes a subsonic flow and the divergent angle of the nozzle inner wall is large, so that the gas flow near the inner wall surface peels off the inner wall surface.
• At this time, the Mach number M₁ is determined from the expression (25) and the sectional area ratio A/A* at the position where the shock wave front appears is determined from the expression (26).
• Such a nozzle has heretofore been suitable for atomization, but the intra-nozzle gas flow immediately becomes a subsonic flow and the concept of accelerating particles is not existent. On the other hand, in the construction of the nozzle according to the present invention, the particles after atomization are accelerated up to a supersonic velocity while setting the divergent angle of the nozzle at 15° or less to prevent separation of the gas flow and so that the particles even in a semi-solidified state can be adhered to the base material or deposit. In other words, in the nozzle according to the present invention, the distance from the narrowest portion of the nozzle up to the shock wave front generating position is extended long until the particles reach a solidified or semi-solidified state.
• $$\frac{p_0}{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}=(1+\frac{\mathit{\kappa }-1}{2}{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}^2{)}^{\frac{\mathit{\kappa }}{\mathit{\kappa }-1}}$$

  

  $$\frac{p_1}{p_B}=\frac{2{{\mathit{\kappa M}}_1}^2-\left(\mathit{\kappa }-1\right)}{\mathit{\kappa }-1}$$

  

  $$\frac{p_0}{p_B}=\frac{2{{\mathit{\kappa M}}_1}^2-\left(\mathit{\kappa }-1\right)}{\mathit{\kappa }+1}(1+\frac{\mathit{\kappa }-1}{2}{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}^2{)}^{\frac{\mathit{\kappa }}{\mathit{\kappa }-1}}$$

  

  $$\frac{A_1}{A^{*}}=\frac{1}{M_1}[\frac{(\mathit{\kappa }-1){{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}^2+2}{\mathit{\kappa }+1}{]}^{\frac{\mathit{\kappa }+1}{2\left(\mathit{\kappa }-1\right)}}$$

  

  In accordance with the above description, conditions for the supersonic nozzle in the present invention can be defined by the following (a) to (c):
1. (a) The divergent angle of the nozzle should be θ ≤ 15° in terms of a half-cone angle.
• (b) The divergent angle of the nozzle should be θ ≤15° in terms of a half-cone angle, and when a shock wave upstream Mach number M₁ is determined by the expression (25) on the basis of the total carrier gas pressure po and the nozzle outlet back pressure p_B and is substituted into the expression (26) to determine the sectional area A₁ of the nozzle, the nozzle length l_f up to the position corresponding to the sectional area A₁ of the nozzle should be not shorter than a minimum nozzle length l_f determined from both the expression (18) and the relationship (22) which defines the shortest flight time until the particles become semi-solidified.
• Fig. 6 shows a case where a shock wave is generated within the nozzle.
• (c) The divergent angle of the nozzle should be θ ≤ 15° in terms of a half-cone angle, the nozzle length l_f should be not shorter than the shortest nozzle length l_f determined from both the expression (18) and the relationship (22) which defines the shortest flight time until the particles become semi-solidified, and when a shock wave upstream Mach number M₁ is determined by the expression (25) on the basis of the total carrier gas pressure po and the nozzle outlet back pressure p_B and is substituted into the expression (26) to determine the sectional area A₁ of the nozzle, the sectional area A₁ should be larger than the nozzle outlet sectional area A_e.
• In this case, since a supersonic flow is generated in the whole region of the nozzle as shown in Fig. 7, a shock wave front is generated on the downstream side of the nozzle outlet.
3. Designing an actual nozzle 3-1) Physical property values of materials and Restraint conditions
• Physical property values of materials and restraint conditions used calculating an actual nozzle are shown in Table 1.
• [Table 1]

  Physical property values of materials and restraint conditions used in calculating an actual nozzle
  Kind	Material/Shape	Physical Properties & Conditions	Value	Unit
  Carrier Gas	Nitrogen	Specific heat	297	J/KgK
  		Specific heat ratio	1.4
  		Thermal conductivity	2.5x10-3	W/mK
  		Viscosity coefficient	18x10-6	Pas
  		Prandtl number	0.72
  		Initial total temperature	293	K
  		Total pressure	0.8	Mpa
  		Back pressure	0.1	MPa
  Particles	Aluminum alloy	Density	2700	kg/m3
  		emissivity	0.5
  		Specific heat in liquid phase	902	J/kgK
  		Specific heat in solid phase	951	J/kgK
  		Latent heat of solidification	398x103	J/Kg
  		Liquefaction start point temperature	934	K
  		Solidification start point temperature	773	K
  		Initial temperature	1173	K
  		Initial flow velocity	6	m/s
  Nozzle	Axisymmetric specific heat	Maximum half-cone angle	5	deg

  By the maximum half-cone angle in the above table is meant a maximum angle between the nozzle axis and the nozzle inner wall.
3-2) Conditions for study
• Molten metal (particles) mass flow rate [kg/s],
  four conditions: 0.025, 0.050, 0.075, 0.100
  Particle diameter [µm], three conditions: 20, 50, 100
  Nozzle throat portion dia. [mm], two conditions: 25, 35
  The mass flow rate of gas at the throat diameter of 25 mm and that at the throat diameter of 35 mm correspond to 0.9 [kg/s] and 1.8 [kg/s], respectively.
• Under the above conditions, a nozzle shape in case of an appropriate expansion (static pressure in nozzle outlet =back pressure = atmospheric pressure) being obtained was determined and the relation between particle temperature and particle velocity was checked. At a supersonic flow there is no influence exerted on the upstream side from the downstream side and therefore, for example, the result of calculation at the position of 300 mm in a nozzle 500 mm long can be regarded as it is as the state in the outlet of a 300 mm long nozzle. This is a different point from a subsonic nozzle.
3-3) Construction of the actual nozzle 3-3-1) Entire Construction
• A typical example of a nozzle shape designed for spray acceleration is shown in the graph of Fig. 8.
• In the illustrated example the maximum half-cone angle of the nozzle is set at 5° (see Table 1).
• This nozzle is configured with a view to (a) expanding dispersed droplets after atomization quickly up to the maximum diameter so as not to adhere to the nozzle wall and (b) taking long a straight pipe portion at the maximum diameter at which the velocity becomes maximum so as to accelerate the particles.
• However, in comparison with a conical nozzle used commonly in cold spray, the nozzle of this embodiment is inconvenient in that the whole of a straight pipe portion which occupies most of the nozzle becomes subsonic in the case where a pressure ratio is lower than a design value or when a lot of cold particles are supplied. Thus, the nozzle of this embodiment is unsuitable for operation in a deviated state from the design value, but is suitable for production equipment in which operation is repeated under the same conditions. In this connection, the graph of Fig. 9 shows nozzle outlet diameters affording an appropriate expansion on the premise that operation is performed under the same conditions as just referred to above.
• In the same graph, the reason why the nozzle outlet diameter increases with an increase in flow rate of molten metal no matter which of 25 mm and 35 mm of the nozzle throat diameter may be is that the gas receives the heat carried in by the molten metal, creating an expandable state.
• An interesting point is that if a nozzle is designed under the condition of a small mass flow rate of molten metal, even if the molten metal is supplied to the nozzle at a flow rate exceeding the design value, operation can be done up to a limitation based on a momentum delivered to the particles although the acceleration efficiency decreases due to deficient expansion. Conversely, it is seen that at a mass flow rate of molten material smaller than the design value it is impossible to effect acceleration up to a supersonic velocity.
• Next, Table 2 shows a relation between nozzle throat diameters resulting from design calculation in the actual nozzle and mass flow rate of gas in case of heating being not performed.
• [Table 2]

  Results of nozzle design calculation of this time and mass flow rate of gas
  Mass Flow Rate of Molten Metal	Throat Dia.	Nozzle Outlet Dia.	Mass Flow Rate of Gas, kg/s
  			Particle Dia., µm
  kg/s	mm	mm		20	50	100
  0	25	32	0.91
  	35	45	1.79
  0.025	25	34	0.91	0.91
  	35	47	1.79	1.79
  0.05	25	36	0.90	0.91	0.92
  	35	48	1.78	1.79
  0.075	25	38	0.88	Subsonic
  	35	49	1.76	1.79	1.79
  0.1	25		Decelerate to subsonic immediately influx
  	35	50	1.76	1.79	1.79

3-3-2) In case of the particle diameter after atomization being 20 µm :
• In Figs. 10 to 12 there are shown intra-nozzle Mach number distributions, gas temperature/velocity distributions, and particle temperature/velocity distributions, respectively, assuming that the particle diameter after atomization is 20 µm and the nozzle throat diameter is 25 mm. In the graphs to be described below, Distance plotted along the axis of abscissa represents the nozzle length, while in the axis of ordinate, Mach number, Gas temp, Gas Velc, Solid temp, and Solid Velc, represent Mach number, gas temperature, gas velocity, particle temperature, and particle velocity, respectively.
• In Figs. 13 to 15 there are shown intra-nozzle Mach number distributions, gas temperature/velocity distributions, and particle temperature/velocity distributions, respectively, assuming that the particle diameter after atomization is 20 µm and the nozzle throat diameter is 35 mm.
• Because of a heated Rayleigh flow which receives heat from molten metal, Mach number decreases, gas temperature rises, and gas velocity decreases.
• Since in this embodiment the nozzle outlet diameter is determined so as to give an appropriate expansion after heating, the static pressure of gas is almost equal to the atmospheric pressure and gas velocities are all 510 m/s or so.
• It is interesting to note that if the nozzle outlet diameter is determined so as to give an appropriate expansion after heating with respect to each of such conditions, the state on the particles side now affords almost equal results in both particle velocity and particle temperature.
• This is because intra-nozzle gas velocity distributions are almost equal and the gas temperature difference is small in comparison with the difference in temperature from molten metal.
• The difference between the throat diameters 25 mm and 35 mm appears in the gas temperature, but does not appear in the gas velocity, as shown in Figs. 11 and 14. Therefore, as to the particles influenced by the gas temperature, a difference appears in the particle temperature, but does not appear in the particle velocity.
• In the case where the particle diameter is 20 µm, solidification is completed at a nozzle length of about 160 mm, but the particle velocity is only about 400 m/s. In this case, if the nozzle length is extended to 500 mm, it is possible to accelerate the particle velocity to 480 m/s, but the particles are cooled to a temperature of 400K.
• Thus, in case of the particle diameter being 20 µm, there is a tendency that the particles are cooled too much in comparison with acceleration, so it is necessary to determine the nozzle length prudently.
3-3-3) In case of the particle diameter after atomization being 50 µm:
• In Figs. 16 to 18 there are shown intra-nozzle Mach number distributions, gas temperature/velocity distributions, and particle temperature/velocity distributions, respectively, assuming that the particle diameter after atomization is 50 µm and the nozzle throat diameter is 25 mm.
• Likewise, in Figs. 19 to 21 there are shown intra-nozzle Mach number distributions, gas temperature/velocity distributions, and particle temperature/velocity distributions, respectively, assuming that the particle diameter after atomization is 50 µm and the nozzle throat diameter is 35 mm.
• Mach number, gas temperature and particle velocity show a tendency not greatly different from that in the case of the particle diameter being 20 µm, but a conclusive different point resides in the particle temperature cooling velocity shown in Figs. 18 and 21.
• In the case where the particle diameter is 50 µm, a flight distance of about 1.2 m is needed within the nozzle until completion of solidification. If the nozzle length is extended to 1.2 m accordingly, an asymptotic line of particle acceleration is fairly approached conveniently.
• In this condition the particles are ejected from the nozzle at a particle temperature of 750K and a particle velocity of 470 m/s and thus this condition is most preferred as an impact depositing condition for the base material.
3-3-4) In case of the particle diameter after atomization being 100 µm :
• In Figs. 22 to 24 there are shown intra-nozzle Mach number distributions, gas temperature/velocity distributions, and particle temperature/velocity distributions, respectively, in case of the particle diameter after atomization being 100 µm.
• This calculation result shows that a nozzle length of 5 m is needed until solidification after a lowering of the cooling velocity in case of the particle diameter being 100 µm. Since particle acceleration has already ended at the time point corresponding to the nozzle length of 3 m and the particle velocity now reaches about 450 m/s, cooling becomes later. Such a situation occurs when atomization cannot be done to a satisfactory extent.
• Fig. 25 shows a construction in case of a thermal spraying system according to the present invention being applied to a batch process.
• In the same figure, the same constituent elements as in Fig. 1 are identified by the same reference numerals, and explanations thereof will be omitted.
• As carrier gas, helium gas of a low molecular weight, which is preferred in point of a sound velocity becoming high when accelerating particles, is used in place of nitrogen gas.
• Carrier gas supplied from a helium gas cylinder 10 is branched into two pipes 11 and 12. The carrier gas flowing in the pipe 11 imparts a head pressure to molten metal stored in a storage section 4, while the carrier gas flowing in the pipe 12 is introduced into a nozzle 2 and passes through a throat portion 2a of the nozzle 2, whereby it is accelerated to a supersonic velocity. The helium gas cylinder 10 and the pipes 11, 12 function as a carrier gas supply unit for the supply of carrier gas under pressure.
• The molten metal flowing down from the storage section 4 is atomized by the supersonic gas flow in the nozzle 2, then the atomized particles are cooled in the nozzle 2 and ejected from a front end of the nozzle 2.
• The ejected particles collide with and adhere to the surface of a base material 3. The nozzle 2 and the base material 3 are accommodated within a chamber 13 which is a sealed chamber. The chamber 13 is connected to a gas storage tank 16 via a cyclone unit 14 as an exhaust unit and an exhaust vacuum pump (pressure reducing means) 15. The cyclone unit 14 recovers particles suspended in exhaust air and supplies only gas to the exhaust vacuum pump 15.
• The exhaust unit is provided for increasing the Mach number of carrier gas and thereby increasing the particle velocity. The helium gas recovered into the gas storage tank 16 is compressed by a compressor 17 and is re-utilized.
• Fig. 26 shows a basic construction in case of applying a thermal spraying system according to the present invention to a continuous molding process.
• In the continuous molding process shown in the same figure, a continuous melting furnace 20 is connected to a storage section 4 and the storage section 4 and the continuous melting furnace 20 are in communication with each other through a connecting pipe 21. The height of the continuous melting furnace 20 is set so that the inner pressure of the storage section 4 is held at 0.8 MPa by a head pressure. The continuous melting furnace 20 disposed at the above predetermined height functions as a molten metal supply unit for continuous supply of molten metal under pressure.
• Thus, molten metal can be supplied to a nozzle 2 continuously from the storage section 4.
• While a base material 22 rotates also in the direction of arrow A, it is drawn out in the direction of arrow B by rotation of take-off rollers (base material supply unit) 23a and 23b, whereby particles can be sprayed continuously onto the base material 22 to effect molding.
• Figs. 27 to 31 show other embodiments of nozzles 2 according to the present invention. In each of the nozzles, the nozzle itself is fabricated using a non-metal such as a ceramic material or carbon to deteriorate the surface affinity, whereby metal particles adhered to the inner surface of the nozzle can be blown off easily by a supersonic gas flow. In those figures, the same constituent elements as in Fig. 1 are identified by the same reference numerals, and explanations thereof will be omitted.
• In the case of a nozzle 40 shown in Fig. 27, a nozzle 41 is fabricated using zirconium for thermal spraying of aluminum alloy, the outside of the nozzle 41 being covered with a ceramic cylinder 42, and a nozzle heater 43 capable of raising temperature up to a maximum of 900°C is wound plural turns round the cylinder 42. As the material of the nozzle 41 it is preferable to use a material called partially stabilized zirconium with for example yttria (Y₂O₃) added as a stabilizing agent, which material possesses high strength, high abrasion resistance and high corrosion resistance.
• As to a nozzle 44 shown in Fig. 28, the nozzle itself is constituted by a ceramic fiber heater 45. More specifically, a material consisting principally of alumina and silica is made into a high temperature insulating ceramic fiber, followed by embedding a heating element into the ceramic fiber and subsequent integral molding. Numerals 46a and 46b in the figure denote electrode connecting portions of the heater.
• According to the construction of a nozzle 47 shown in Fig. 29, a carbon heater 49 is disposed around an outer wall of a body portion of a ceramic nozzle 48 and heating is performed by radiation.
• The carbon heater 49 is divided into plural portions by slits 51d and 51e which are formed a predetermined length alternately from both upper and lower sides of a cylindrical nozzle 48. Numerals 49a and 49b denote electrode connecting portions of the carbon heater 49. Numeral 50 denotes a cylindrical reflection case having a specular-finished inner wall and it is provided for enhancing the radiation efficiency.
• In the nozzle 47 constructed as above, when electric power is fed from a power supply (not shown) to the carbon heater 49 via the electrode connecting portions 49a and 49b, the carbon heater 49 generates heat from the interior thereof due to Joule heat induced by the supply of electric power. As a result, the ceramic nozzle 48 is heated by radiation heat transfer from the carbon heater 49 and the metal adhered to the inner wall of the nozzle 37 is melted.
• As to a nozzle 51 shown in Fig. 30, the nozzle itself is fabricated by a carbon heater 52. Numerals 52a and 52b denote electrode connecting portions of the carbon heater. By replacing a ceramic nozzle with a carbon or carbon composite nozzle, the radiation rate of the nozzle surface is further enhanced and it is possible to further improve the heating efficiency of the nozzle 51.
• In Figs. 29 and 30, the presence of oxygen causes an oxidation reaction of carbon itself, so for avoiding such an inconvenience, the whole of the system is covered with a chamber and gas such as argon or nitrogen gas is used as high pressure gas to purge the interior of the chamber with an inert atmosphere.
• Also by fabricating a nozzle with a metallic material superior in thermal conductivity, e.g., copper, and thermal spraying of a ceramic material to the inner wall of the nozzle thus fabricated to form a ceramic film, it is possible to deteriorate the surface affinity as is the case with each of the foregoing nozzles.
• In the case of a nozzle 53 shown in Fig. 31, a zirconium film (the portion indicated by a thick broken line in the figure) 55 is formed on an inner surface of a copper nozzle 54 and a nozzle heater 43 is wound plural turns round an outer periphery surface of the nozzle.
INDUSTRIAL APPLICABILITY
• The thermal spraying nozzle device and the thermal spraying system according to the present invention are suitable in a field in which it is required to supply a thermal spraying material constantly onto a base material and control the state of a film or deposit formed on the base material.

Claims (8)

1. A thermal spraying nozzle device wherein carrier gas is introduced from an inlet side of a nozzle to form a supersonic gas flow and a thermal spraying material is atomized and ejected by said gas flow, said thermal spraying nozzle device comprising,
   a storage section storing molten metal as said thermal spraying material connected to an end on the inlet side of said nozzle through a connecting pipe, and,
   said nozzle having a throat portion and a divergent region in a downstream of said throat portion toward an outlet side to form the supersonic gas flow,
   wherein said thermal spraying nozzle device is configured such that metal particles atomized by the supersonic gas flow are cooled to a solidified or semi-solidified state in said divergent region and then ejecting in a predetermined direction from the outlet side of said nozzle.
2. The thermal spraying nozzle device according to claim 1, wherein, within said connecting pipe, a molten metal outlet pipe is extended from said storage section toward the center in said throat portion or the center on the downstream side of the throat portion and an outside portion of said molten metal outlet pipe constitutes a channel for the carrier gas to flow therethrough in an accelerated state.
3. The thermal spraying nozzle device according to claim 1 or claim 2,
   wherein a divergent angle of said divergent region formed on the downstream side of said throat portion is not larger than 15° in terms of a half-cone angle.
4. The thermal spraying nozzle device according to claim 3, wherein the length of said divergent region is a flight distance until solidification or semi-solidification of the atomized metal particles and is determined on the basis of a flight distance which is determined modeling both flight distance of the atomized metal particles and the temperature of the metal particles.
5. A thermal spraying nozzle device according to claim 4, wherein the flight distance until solidification or semi-solidification of said atomized metal particles is determined by first determining a flight time until change of the atomized metal particles into a solidified or semi-solidified state and then substituting said flight time into the following expression, and the length of said divergent region is set to a length of not shorter than said flight distance: $$I_f=u_g{t}_f-\frac{{u_g}^2{\mathit{\rho }}_g{t}_f+{\mathit{\rho }}_s{d}_s{a}_g}{{u_g}^2{\mathit{\rho }}_g}\sqrt{\frac{{u_g}^2{\mathit{\rho }}_s{d}_s{a}_g}{{u_g}^2{\mathit{\rho }}_g{t}_f+{\mathit{\rho }}_s{d}_s{a}_g}}+\frac{{\mathit{\rho }}_s{d}_s{a}_g}{u_g{\mathit{\rho }}_g}$$

   

   
   where l_f is the flight distance of the particles, t_f is the flight time until solidification or semi-solidification of the particles, u_g is flow velocity of gas, ρ_g is gas density, ρ_s is particle density, d_s is particle diameter, and a_g is sound velocity of gas.
6. The thermal spraying nozzle device according to claim 1 or claim 2,
   wherein, given that an inlet pressure of the carrier gas is po and a nozzle outlet pressure thereof is P_B, the carrier gas is introduced into said nozzle in a state in which the inlet pressure po satisfies the following expression: $$p_0\ge p_B(1+\frac{\mathit{\kappa }-1}{2}{M}^2{)}^{\frac{\mathit{\kappa }}{\mathit{\kappa }-1}}$$

   

   
   where κ: specific heat ratio of compressed gas, M: Mach number in the expanded nozzle portion on the downstream side of the throat portion.
7. A thermal spraying system comprising:

   the thermal spraying nozzle device described in any of claims 1 to 6;

   a carrier gas supply unit connected to said nozzle through a conduit to introduce the carrier gas under pressure into the nozzle;

   a sealed chamber accommodating said nozzle and a base material for collision therewith of the ejected particles; and

   pressure reducing means for reducing the internal pressure of said sealed chamber.
8. A thermal spraying system comprising:

   the thermal spraying nozzle device described in any of claims 1 to 6;

   a molten metal supply unit connected to said storage section through a connecting pipe to supply molten metal under pressure continuously to the molten metal in the storage section; and

   a base material supply unit for continuous supply of said base material.

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