Transfer Enhancement using Weakly-Ionized,
Experimental measurements and computational analysis of heat transfer in atmospheric pressure, mid-temperature range (1200K-1600K) plasma flow over an aluminum cylinder have been carried out. A comparison of transient temperature measurements for the aluminum cylinder under convective unionized air flow and those with convective plasma flow shows significantly higher heat transfer from plasma flow compared to air flow under identical temperature and flow conditions. A heat transfer problem is computationally modeled by using available experimental measurements of temperature rise in the cylinder to determine the degree of ionization in the plasma flow. The continuity, momentum, and energy conservation equations as well as conservation equations for electrons and ions, and the Poisson’s equation for self-consistent electric field are solved in the plasma by a finite volume method. The conjugated transient heat transfer in the cylinder and in the plasma is obtained by simultaneous solution of the transient energy conservation equations. It is shown that the enhancement of heat transfer in plasma flow is due to the energy deposited by charged species during recombination reaction at the solid surface. An important finding is that even a small degree of ionization (< 1%) provides significant enhancement in heat transfer. This enhancement in heat transfer can lead to productivity increase in metallurgical applications.
Table of Symbols
Symbol Description Units
D Diffusivity m2/s
e Electron charge C
h Heat transfer coefficient w/m2K
k Boltzmann Constant J/K
m Mass kg
N Number Density 1/m3
p Pressure Pa
Pr Prandtl Number
q Heat Transfer Rate W
Heat Flux W/m2
r Radial coordinate m
R Radius m
Re Reynolds Number
Sc Schmidt Number
T Temperature K
t Time s
u velocity m/s
V Voltage V
x Axial coordinate m
a Thermal diffusivity m2/s
Flux of ions and electrons 1/m2
Ratio of ion to electron diffusivity
Viscosity Ns/ m2
Density kg/ m3
Thermal conductivity W/m K
w, s wall
Flow of plasma, or ionized gas, is used in a variety of materials processing and metallurgical applications including plasma spray coating, arc welding, near net-shape manufacturing, plasma vapor deposition, polymer deposition, and wire bonding in microelectronic chips [1, 2]. Based on the temperature and pressure range, the plasmas used in these applications can be divided in two primary types. First are the systems that use high temperature and atmospheric or near-atmospheric pressure ionized gas, also referred to as thermal plasmas. The condition of Local Thermodynamic Equilibrium (LTE) is reached in thermal Plasma with temperatures around 10000 K and electron densities ranging from 1021 to 1026 m-3. The high temperatures prevalent in thermal plasmas are useful for heating and melting of ceramic and metallic particles in coating and welding applications and in destruction of bio-hazardous materials. The second type of systems use the low pressure, low temperature plasmas. The operating pressure and gas density are very low. There is a significant difference in electron and heavy particles (neutral and ions) temperature due to weak collision coupling between them. The temperature of ions and neutral molecules is typically close to room temperature. The abundance of ionized species in this type of plasma is used to aid in chemical reactions in vapor deposition and polymer processing.
Heat transfer in plasma flow has received much attention in the literature, in the 1960s and 1970s mainly in the context of electrostatic probes and in aerospace applications, whereas in the last thirty years mainly in the context of plasma-aided manufacturing. Available reviews [3, 2] provide detail discussion of a number of factors that affect the heat transfer to a solid body from plasma. It is noted that the analysis of heat transfer from plasma to a solid surface is significantly more complicated as compared to unionized gas flow because it not only involves the hydrodynamic and thermal boundary layers encountered in unionized gas flows, but also electrical effects due to the presence of charged species. These electrical effects arise due to the difference in mobilities of ion and electron. The electrons having very high mobility travel faster towards the surface and give rise to a negative potential at the solid surface . This negative potential repels electrons and attracts ions. Subsequently the flow of ions and electrons towards the surface becomes equal and the surface potential remains constant thereafter. The surface potential when both the ion and electron fluxes become equal is called the floating potential . These charged species recombine at the surface and release energy equivalent to their ionization potential to the surface. Therefore the electric field and charged species transport play an important role in determining the heat transport to the surface [2, 3, 5, 6].
Atmospheric pressure, high temperature thermal Plasmas have been studied extensively. Review  and a monograph  provide detailed discussion of the work published in literature. Heat and momentum transfer to spherical particles in thermal plasma has been studied extensively for the application of plasma spray coating [7 and references therein]. A unified treatment of heat transfer under continuum and non-continuum conditions has been developed . Correlations for Nusselt number have been proposed for thermal plasma flow over spherical particles . These correlations have been employed by several researchers in computational analysis of plasma spray systems (see for example, Proulx et al., ). However these correlations ignore the electrical effects. For plasmas at low pressure, heat transfer to a solid has been investigated applying results from kinetic theory of rarefied gases [11, 12].
Unfortunately, these two extremes (very hot plasmas at atmospheric pressure or cold plasmas at low pressures) are not best suited for common metallurgical work. For example, most of the aluminum melting or steel heat treatment is carried out between 900 K and 1500 K. The low pressure plasma possesses very low energy density and can not be used for aluminum melting. The very high temperature thermal plasmas result in significant heat losses and may result in poor efficiencies. Only recently, atmospheric pressure convective plasma torches have become available that provide mid-temperature range plasma (1200 K – 1600 K) at atmospheric pressure. These plasma torches are being considered for aluminum melting, continuous flow plasma chemical reactors, surface heat treatment and remediation of biohazards and toxic wastes. However, plasma flows under these conditions are not yet well characterized. To design and improve mid-temperature plasma devices, the ability to predict the plasma flow over a solid body and the concomitant heat transfer, is highly desirable.
In this paper, we report experimental measurements of temperature rise in an aluminum cylinder exposed to air flow and plasma flow under identical temperature and flow conditions. The results show significant increase in heat transfer with plasma flow. Computational modeling for air flow and plasma flow have been carried out to determine the degree of ionization in the plasma and to analyze the heat transfer phenomena in the two cases.
A schematic of the experimental setup is shown in Figure 1. The setup consists of an insulated cylindrical chamber. An Airtorch [a] or a Plasmatorcha is connected to the chamber on the left and the high temperature gas enters the chamber through the opening along the centerline of the chamber. A thermocouple is placed at the entrance of the chamber to measure the temperature at the exit of the torch. An aluminum sprue is placed in the chamber with a thermocouple attached to the sprue through a hole drilled from the back of the sprue along its centerline. The thermocouple is at a location, 12mm from the front surface, along the centerline. The K type thermocouple was used which can record temperatures up to 1500 K. The air torch exit temperature was measured with a B type thermocouple. Both thermocouples were connected to a data acquisition system for transient temperature measurements. An MHI DACs data acquisition system was employed for the thermal measurements and the sampling rate was 1 Hz. The mass flow rate was measured at the inlet and the average velocity at the inlet of the insulated chamber was calculated based on the measured temperature.
measurements were carried out with two identical aluminum sprues of
38.7mm diameter and 39mm length. In
the first case, an air torch was used to provide the gas at 1573 K
for convectively heating the sprue.
Transient temperature measurements were recorded.
In the second case, a plasma torch was used.
In this case, a weakly ionized gas from the torch provided
the convective heating of the sprue.
Once again, transient temperature change was measured for the
sprue interior. The sprue heated with the plasma torch resulted
in substantially higher heating rate compared to one heated with the
air torch. The experimental
measurements are discussed later in detail with the computational
A flow of weakly ionized gas consisting of neutrals, ions and electrons over a cylindrical aluminum sprue is considered. The far field pressure is atmospheric and the flow Reynolds number based on the inlet velocity and sprue diameter is in the laminar range. As the degree of ionization is expected to be small, the overall velocity field can be found from the solution of the continuity, momentum, and energy equations for the neutral gas flow field . The flow was considered to be steady and axisymmetric, however the temperature field was considered transient due to heating of the sprue. Gas thermophysical properties were evaluated at the far field temperature. The neutral gas flow in the chamber and conduction in the sprue were computationally modeled by using FLUENT 6.2.1 commercial flow/thermal solver. Using GAMBIT 2.1, a 2-D axisymmetric mesh was generated using the dimensions given in the experimental setup. The mesh generated was highly refined in order to facilitate greater accuracy in the numerical solution and to account for steep gradients near the sprue.
Using the velocity field, a computational model was developed to evaluate the electron and ion flux and the self-consistent electric field. A separate program was developed to determine the number density of charged species and the electric field as described below. The charged species flux to the surface was then evaluated and the contribution to heat transfer due to recombination of electron and ions was determined.
Using the following dimensionless quantities: , , , and , , , , , , , , , , .
The governing equations in dimensionless form are:
Energy conservation in the plasma
Energy conservation in the sprue
Neglecting production and recombination of the charged species in the bulk of the flow, the conservation equations for the charged species number densities and the governing equation of the self-consistent electric field can be written as follows.
Continuity Equations for electrons
Continuity Equations for ions
Poisson equation for electric field
The ion and electron fluxes are given by
The plasma and air are considered optically thin and the radiation transport is considered between sprue surface and the container wall. Since the gas is at atmospheric pressure, the difference in temperature between the neutral gas and the charged species was assumed to be small throughout the flow domain ( ).
The flow field for the computational domain is obtained first by solving equations (1) and (2) in FLUENT flow/thermal solver. The SIMPLE algorithm for pressure correction was employed and discretization was carried out using the Power-law method as described in Patankar . An under relaxation technique was used for the momentum equation. The solution of these equations provides the flow field in the entire domain. The equations (3) - (7) are solved to obtain the number density distribution of the ions and electrons and the electric potential in the plasma as well as temperature distributions in the plasma and the sprue. A finite difference method was employed to discretize equations (3) – (7) based on the Alternate Direction Implicit Scheme . A computer program was developed to iteratively solve the resulting tri-diagonal systems of equations using the Thomas algorithm. We expect to have steep gradients in velocity and temperature near the sprue surface. To resolve these steep variations a very fine grid was taken. The convergence criterion was set at 1x 10-6 of relative error between successive iterations at all points. Thermophysical properties for charged species were obtained from Refs.  and . For the case of heating from unionized air flow, the methodology is similar to the one described above, however equations (5) – (7) are not needed.
The governing equations were solved with the following boundary conditions. The sprue surface was considered as a perfect sink for the charged species . The sprue surface was considered at the floating potential so that . The velocity was zero due to the no-slip condition at all solid surfaces. The heat balance at the surface is . The heat flux deposited at the surface due to charged species recombination is given by . At the inlet and the inlet velocity is specified. At the walls of the outer chamber, temperature and electric potential gradients are zero and velocity is zero. At the outlet, the outflow condition of zero gradient of temperature in the axial direction is considered. Zero gage pressure is prescribed at the outlet.
Results and Discussion
In a computational study, it is important to evaluate the effect of grid spacing on the solutions to make sure that the results are grid-independent. The computations were carried with different grid sizes until the solution was insensitive to the grid size. The node points were doubled until the computed heat transfer coefficient at the sprue surface changed by less than 0.1%. The final grid had 721 points in the axial direction and 193 points in the radial direction.
Heat transfer in air flow
Using this grid, we first considered the flow from an air torch in the analysis. The streamlines for the flow are shown in Figure 2. It is clear from the figure that as the flow goes around the sprue, a re-circulating flow pattern is obtained. Due to the decrease in the cross-sectional area due to the presence of the sprue, the velocity increases as the gas moves along the container walls.
The temperature contours obtained for the flow domain are shown in Figure 3. Most of the region in the upstream of the sprue the temperature is nearly uniform. Due to the re-circulating vortex patterns on the downstream region from the sprue, colder fluid from the sprue mixes with the hotter fluid away from the sprue. This is evident from the temperature contours. The temperature contours show that the heat transfer rate is maximum at the front surface of the sprue and as there is a sharp change in gas temperature near the surface. As the flow proceeds toward the outlet there is a decrease in the heat transfer rate on the top surface of the sprue. This is evident from the temperature contours showing temperature drop over a larger distance compared to the front surface. The heat transfer coefficient was obtained at all points along the surface of the sprue by equating the net heat transfer to the surface from gas flow to the product of heat transfer coefficient and the temperature difference between the inlet temperature and the surface temperature as . Then the overall heat transfer coefficient was obtained by an area weighted average taken over the surface of the sprue. The temperature contours in the interior of the sprue showed only a small variation. This is to be expected due to the high thermal conductivity of aluminum ( = 227 W/m K). The Biot number is very low and temperature distribution is nearly uniform.
Heat Transfer in Plasma Flow
With plasma flow, number densities of charged species and the induced electric field are determined. Figure 4 (a) and (b) show the dimensionless ion and electron density contours, respectively with degree of ionization at the inlet as 0.64%. The motion of the charged species is the net effect of convection, diffusion, and drift under the influence of electric field. Both ion and electron are convected with the same neutral flow. However, electric field has opposite effect on the motion of ions as compared to that of electrons. As the electric potential at the surface is negative, it results in repelling electrons and attracting ions. Not surprisingly, the number densities of electrons are low closer to the surface whereas ion densities are higher near the sprue surface. The recombination reaction of charged species at the surface gives energy equal to the ionization potential to the surface.
Figure 5 shows the transient temperature measurement with the thermocouple placed in the sprue interior. The significant increase in the rate of temperature rise indicates higher heat transfer with plasma heating as compared to heating with air flow. To validate our model, we first compared the computational results of temperature rise with the experimental measurements. As seen in the figure, the computational results match well with experimental measurements. Next, to determine the degree of ionization in plasma, a parametric study was conducted by considering different values of inlet ion and electron number densities. The predicted values of the temperature rise with different degree of gas ionization were compared with the experimental measurements of temperature change in the sprue interior with plasma heating. This gave the degree of ionization as 0.64% for the case considered here. The predicted results for 0.64% ionization are shown in Figure 5.
The influence of ionization on heat transfer enhancement is plotted in Figure 6. The figure shows the area weighted average heat transfer coefficient as a function of the degree of ionization at the inlet. With increase in the degree of ionization the number densities of charged species and hence the flux of charged species to the sprue surface increases. This leads to higher heat transfer to the sprue surface and the enhancement of heat transfer is seen to increase nearly linearly with degree of ionization. For the first case with no ionization, the average heat transfer coefficient was 28.2 W/m2K, whereas with plasma flow with 0.64% ionization the heat transfer coefficient was 39.2 W/m2K. A change in the gas ionization from 0 to 0.64% resulted in approximately 40% increase in the average heat transfer coefficient. It may be noted that the model presented here is restricted to weakly ionized gas and as such the results should not be directly extrapolated beyond 1% ionization unless field effects are incorporated.
Summary and Conclusions
Transient temperature measurements and computational simulation of convective heating of an aluminum sprue was carried out. Two cases were considered, one with heating by unionized air flow and the other with plasma flow. Transient temperature rise in the sprue interior was measured and it showed significant increase in heat transfer with plasma flow compared to air flow under identical temperature and flow conditions. To computationally simulate the process, the flow of continuum, axisymmetric, laminar, mid-temperature range (1200K – 1600K) plasma flow over a cylinder was modeled using a finite volume method. The continuity and the momentum conservation equations for the flow were solved using commercially available FLUENT flow/thermal solver. Using the flow field, a computational model was developed to solve the governing equations for the conservation of electrons and ions and the self-consistent electric field as well as the energy conservation in the gas flow and the sprue interior. The governing equations were discretized using a finite volume method and the resulting system of equations was solved by Alternating Direction Implicit scheme. Transient heat transfer to the cylinder was evaluated by considering convective heat transfer from the neutral flow, the energy transport by radiation between the sprue surface and the wall, and the energy deposited by recombination of charged species at the cylinder surface. Results for transient temperature rise in the cylinder with air heating were used to validate the computational model. The degree of ionization present in the plasma flow was determined. The following conclusions can be drawn from this part of the study.
Figure 1. A schematic of the experimental setup
Figure 2. Flow stream lines
Figure 3. Temperature contours with air torch heating (K).
Figure 4. (a) Dimensionless ion number density contours and (b) Dimensionless electron number density contours
Figure 5. Comparison of computational predictions and experimental measurements of temperature increase in the sprue
Figure 6. Variation of heat transfer coefficient with the degree of ionization
Figure 1. A schematic of the experimental setup
Figure 2. Flow stream lines
Figure 3. Temperature contours
with air torch heating (K).
(a) Dimensionless ion number density contours and (b) Dimensionless
electron number density contours
Comparison of computational predictions and experimental measurements
of temperature increase in the sprue.
Figure 6. Variation of heat transfer coefficient with the degree of ionization
[a] Airtorch and Plasma Airtorch are Trademarks of MHI-Inc.
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