Robert A. Miller, Maria A. Kuczmarski, and Dongming Zhu

Glenn Research Center, Cleveland, Ohio

Burner Rig With an Unattached Duct for Evaluating 

the Erosion Resistance of Thermal Barrier Coatings

NASA/TM—2011-217008

June 2011
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Robert A. Miller, Maria A. Kuczmarski, and Dongming Zhu

Glenn Research Center, Cleveland, Ohio

Burner Rig With an Unattached Duct for Evaluating 

the Erosion Resistance of Thermal Barrier Coatings

NASA/TM—2011-217008

June 2011

National Aeronautics and

Space Administration

Glenn Research Center 

Cleveland, Ohio 44135
Available from

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7115 Standard Drive

Hanover, MD 21076–1320

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2011-217008 1

Burner Rig With an Unattached Duct for Evaluating the Erosion 

Resistance of Thermal Barrier Coatings

Robert A. Miller, Maria A. Kuczmarski, and Dongming Zhu

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

Extensive computational fluid dynamics (CFD) modeling backed by experimental observation has 

demonstrated the feasibility of using an unattached duct to increase the velocity and spatial spread of 

erodent particles exiting from a burner rig. It was shown that gas velocity and temperature are mostly 

retained if the inner diameter of the unattached duct equaled the exit diameter of the burner rig nozzle. 

For particles having a mean diameter of 550 μm, the modeled velocity attained at a distance 2.0 in.

(50.8 mm) beyond the exit of a 12 in. (305 mm) long duct was approximately twice as large as the 

velocity the same distance from the nozzle when the duct was not present. For finer particles, the relative 

enhancement was somewhat less—approximately 1.5 times greater. CFD modeling was also used to 

guide the construction of a device for slowing down the velocity of the particles being injected into the 

burner rig. This device used a simple 45° fitting to slow the particle velocity in the feed line from 20 m/s, 

which is in the range needed to convey the particles, to about 3 m/s just as they are injected into the 

burner. This lower injection velocity would lessen the severity of the collision of large particles with the 

wall of the burner liner opposite the injection port, thereby reducing potential damage to the burner liner 

by high-velocity particles.

Introduction

Projected performance goals for rotorcraft engines require a 30 percent efficiency improvement over 

the next decade and further improvements in subsequent decades (Ref. 1). Performance and efficiency 

improvements generally require higher gas temperatures, higher pressures, and lower cooling air flows.

This means that future thermal barrier-coated turbine section components will have to operate at increased 

surface temperatures, requiring the thermal barrier coatings (TBCs) to be more resistant to hightemperature sintering. In addition, TBC thermal conductivity will have to be reduced in order to minimize 

coating thickness. However, the reduced conductivity and improved sintering resistance of turbine blade 

coatings must not come at the expense of reduced erosion resistance. TBC compositions with combined 

high toughness, erosion resistance, and low thermal conductivity have to be used for turbine component 

applications in the harsher environments within the advanced rotorcraft engines. For example, it is known 

that zirconia-yttria-gadolinia-ytterbia TBCs having compositions from the cubic phase field have lower 

conductivity and reduced erosion resistance compared with tougher compositions taken from the 

tetragonal phase field (Refs. 2 and 3). Although the cubic compositions would be favored for combustor 

applications where erosion is not a concern, they would likely be ruled out in favor of tetragonal 

compositions for high-pressure turbine blade applications. For the same reason, another class of lower 

conductivity zirconia-based TBCs, known as pyrochlores, may not be the best choice for high-pressure 

turbine blades from the erosion standpoint (Ref. 3). Therefore, tetragonal phase, low conductivity/sinter 

resistant TBCs must be considered for future advanced rotorcraft turbine blade applications.

Solid particles interacting with TBCs may remove coating material by either of two types of 

processes, depending on particle size. Smaller particles having diameters of tens of microns cause 

erosion, which is characteristically gradual. Larger particles having diameters of hundreds of microns 

cause impact damage, which may be sudden. Coating damage that does not result in removal of the 
NASA/TM—2011-217008 2

coating can also occur. Prior to sudden failure, large particles can cause coating densification (Ref. 4). In 

addition, under certain combinations of particle compositions and temperatures, fine particles can melt, 

causing damage by corrosion (Ref. 5). Since this study will concentrate on damage resulting from particle 

impacts, the effects of corrosion will not be discussed further.

TBC removal by erosion and impact damage is especially likely at the leading and trailing edges of 

the turbine blades (Ref. 6). Rotorcraft engines are subject to greater loading of injected particulate matter

than other types of turbine engines because rotorcraft may operate at relatively low altitudes, take off and 

land from less improved landing sites, and their operation involves hovering that may stir up considerable 

amounts of particulates. While these factors can be especially true for certain military missions, they also 

apply for commercial missions that are the primary focus of NASA. Particle separators can remove large 

ingested particles, but particles with diameters on the order of tens of microns can reach the turbine 

section, especially during periods of heavy loading. Travel through the compressor tends to reduce 

particle size further (Refs. 7 and 8), insuring that ingested particulate sizes are in the range likely to 

causes erosion. However, particles of carbon, zirconia, or other debris hundreds of microns in diameter or 

larger may shed from the combustor and cause impact damage to the turbine blade TBC (Refs. 9 and 10).

Therefore, future TBCs must be resistant to both erosion and impact resistance.

Effective and affordable laboratory methods for evaluating and understanding erosion and impact 

resistance of TBCs are needed. Erosion rigs used for TBC research have tended to be one of two types. In

one type, erodent particulates are injected into a burner rig and accelerated through an exhaust nozzle

towards a test specimen, with the acceleration continuing for a short distance afterwards in the potential 

core of the flame. Examples of burner rig-based erosion rigs are a rig at General Electric (Ref. 11), a 

former rig at NASA (Ref. 12), and the current rig at NASA (Ref. 3). Alternatively, erosion rigs are

combustion-driven ducted rigs where the acceleration occurs throughout the length of a duct. Examples of 

the latter type of rig are the wind-tunnel rig at the University of Cincinnati (Refs. 13 and 14) and the 

ducted rig at Cranfield (Ref. 4). Erodent particles can be accelerated to higher velocities in ducted rigs 

than in burner rigs, but burner rigs are generally simpler and capable of achieving higher temperatures.

Placing a short duct after a burner rig nozzle exit and before a test specimen could combine positive 

features of both by allowing further acceleration of the ingested particles without losing excessive heat. A 

photograph of the unducted burner rig at NASA, adapted from Figure 1 of Reference 3, is shown in 

Figure 1. The burner in the lower portion of this figure has pivoted to the cooling position away from the 

specimen. The specimen in this portion of the figure is 50.8 mm in diameter and it has been spot-welded 

to the fixture. A 25.4 mm specimen held in a spring-loaded clam-shell fixture is shown in the insert. This

specimen is being heated by the burner rig flame that is operated using jet fuel and preheated air. Erodent 

powder, usually alumina grit, is injected into the burner using a feeder of the type used in plasma

spraying. Alumina is chosen because it is readily available and it produces damage in rig tests that 

matches the damage seen in engine experience (Ref. 11).

The current rig at the NASA Glenn Research Center is a modified jet-fuel/preheated air fired burner 

rig typically referred to as a “Mach 0.3 burner rig.” It has been modified for operation up to Mach 1 by 

increasing the air flow and switching from a nozzle that was 1.00 in. (25.4 mm) in diameter to one that is 

0.75 in. (19.05 mm) in diameter using design concepts suggested for ASTM flow nozzles (Ref. 15). This 

rig has been described elsewhere for erosion testing involving particles tens of microns in diameter

(Ref. 3) and is quite similar to a former rig at NASA described by Handschuh (Ref. 12). Although this rig 

accelerates the small particles to adequately high velocities, the burner rig approach does not accelerate 

large particles to high velocities (Ref. 11). Unfortunately, the NASA burner rig does not readily lend itself 

to attaching a duct for increasing particle velocities because specimen temperature cycling is 

accomplished by rather forceful pivoting of the burner using pneumatic actuators. This pivoting, even if 

redesigned for more gentle motion, would soon cause misalignment of a duct.
NASA/TM—2011-217008 3

Figure 1.—Photograph of the unducted erosion burner rig at NASA.

The goal of this study is to determine whether a new erosion rig design, having an unattached stationary 

duct and a pivoting burner rig, would be feasible for conducting erosion burner rig exposure of advanced 

coatings. This approach would allow the burner rig to pivot in front of the unattached duct in the heating 

position and away from the duct in the cooling position. This paper presents the results of extensive CFD 

modeling backed by laboratory experiments that demonstrate the feasibility of such a design, along with an 

experimental examination of the effect of such a duct on the behavior of small particles.

Model Description

The computational fluid dynamics code FLUENT (Ref. 1) was used to model the experimental 

apparatus. The code uses a finite volume method to discretize the continuity, momentum, and energy 

equations. An axisymmetric model was used; various regions and boundary conditions are shown on 

Figure 2. In this figure, the dimensions represent cases having the 12 in. (305 mm) long, 0.75 in.

(19.05 mm) diameter duct. Other duct diameters and lengths, as well as cases having no duct, were 

modeled and will be discussed. The spacing between the nozzle exit and the duct entrance was set to

0.50 in. (12.7 mm). For the cases examined in this paper, gas enters at the pressure inlet on the far left of 

the drawing, passes through the nozzle and exits at the pressure outlet at the far right. A relatively small 

amount of air enters though the two pressure inlets at the top and left side of the box that bounds the 

region of the model after the nozzle exit. The air entering through the pressure inlets in the box results 

from air that aspirates into the gas jet.
NASA/TM—2011-217008 4

Figure 2.—Schematic drawing of burner rig and duct as used for the CFD 

model. The same geometry was used for all cases, except that the length 

and vertical position (radius) of the duct was varied.

A standard k-epsilon turbulence model with the C1-epsilon changed from the standard value of 1.44 

to 1.56 was used as a starting point for a numerical study of this apparatus because of the successful use 

of this turbulence model by Senesh and Babu (Ref. 16) to describe the potential core and other 

characteristics of similar jets. Strictly speaking, this model is only applicable for fully-developed 

turbulent flow. The range of flows used in this study yielded Mach numbers at the nozzle exit from 0.3 to 

1.0. Reynolds numbers at these Mach numbers were about 8,300 and 21,000, respectively, which is in the 

range for turbulent flow. However it is likely fully developed turbulent flow is not actually established in 

this problem because of the relatively short axial length. Nonetheless, because the model with the 

modified C1 constant predicted a potential core having a length matching that observed experimentally—

both in our case and with the work of Senesh and Babu—it was felt that the k-epsilon model would be 

fully adequate for the needs of this study. Standard wall functions were used and viscous heating was 

enabled. The discrete phase model was activated to allow solid particles to be injected into the gas flow 

and their paths tracked. These particles were allowed to interact with the gas phase. A spherical particle 

drag law from Morsi and Alexander (Ref. 17) was used:

( )

2 3

1 Re 2 Re

d

a a C a =+ + (1)

where Cd is the drag coefficient, Re is the Reynolds number, and the values of the constant are described 

in Morsi and Alexander. This drag law was further modified using a high Mach number drag law

(Ref. 18). This modification affects the drag law for relative Mach numbers greater than 0.4. 

Injections were defined as inert alumina particles released across the surface of the particle inlet. 

Three particle injection velocities were employed for each case—a minimum, a maximum, and a velocity 

midway between the two.

A second-order upwind scheme was used for both the momentum and energy equations, with an 

under-relaxation factor set to 0.3 for the momentum equation and 1 for the energy equation. The 

convergence criteria for the solutions were defined as scaled residuals below 1×10–5 for the momentum 

equation, 1×10–6 for the energy equation, and 1×10–3 for both the turbulent kinetic energy and dissipation 

rate. Decreasing these values did not result in a change in the model predictions.

The sensitivity of the results to the grid density was studied using three different grid densities based on 

the number of cells used across the nozzle. A non-uniform grid was used over parts of the model to 

minimize the total number of computational cells. The maximum aspect ratio for the cells was 5:1. Using

10 cells across the nozzle yielded 15,393 total cells in the computational domain, 15 cells across the nozzle 

yielded 34,251 total cells, and 20 cells across the nozzle yielded 61,257 total cells. Comparisons were made 
NASA/TM—2011-217008 5

among the grids for both temperature and velocity magnitude at a number of points that spanned the radius 

of the nozzle and a distance of 0.1016 m from the nozzle exit. Comparisons of temperature among the grids 

at identical points yielded differences of generally less than 1 percent, with the maximum difference being

3 percent. Similar comparisons of velocity magnitude yielded differences generally less than

2 percent, with the maximum difference being 6 percent. This shows that the grid with 15,393 total cells is 

sufficient to achieve grid-independent results. This grid was used for the rest of the study.

Values for normal and tangential restitution coefficients, which are required by FLUENT, were based 

on room temperature measurements of the velocity- and directional-restitution coefficients reported in the 

literature (Refs. 7 and 19). The literature values show that the angle of impact of particles colliding with a 

wall is very similar to the angle of reflection. For the purposes of this paper, it is sufficient to allow the 

angle of incidence to equal the angle of reflection. After making this simplifying assumption, the normal 

and tangential restitution coefficients must be equal to each other and their value will be equal to the 

velocity restitution coefficient, where the velocity restitution coefficient is the ratio of the particle velocity

after striking a surface to the velocity before the collision. At least for the case of smaller particles in the

range that causes erosion damage, the value reported for the velocity restitution coefficient appears to be

close to 0.5 at essentially all collision angles. A lack of angular dependence may imply a balanced 

combination of the effects of friction (whose effect is strongest at lower angles) and plastic deformation

(whose effect is strongest at higher angles). Friction is related to surface roughness and particle size. 

Plasticity may be related to the hardness of the particle and the surface with which it collides.

The velocity restitution coefficient, measured at room temperature for large particles, is near 1.0

(near elastic) for low angle collisions falling off at higher angles (Ref. 19). The data from Swar (Ref. 19)

was approximated by two polynomials. One segment of the polynomial gave a restitution coefficient 

between 0.96 and 0.97 between 0° and 15°, and the other segment allowed the restitution coefficient to 

drop to 0.25 at 90°. This will be referred to as “near-elastic-forward restitution” in the paper. For our 

experimental case of a high temperature mullite duct, the surface may be relatively soft, which could 

lower the forward restitution coefficient. Because of the uncertainty, two types of velocity restitution 

coefficients were used for the large particle calculations. For one group, the particle dynamics were 

calculated using restitution coefficients that matched the results reported; another set of cases used the 

value of 0.5 at all angles. The directional restitution coefficient for all cases was simply allowed to

equal 1.0, making the angle of reflection equal to the angle of incidence.

Modeling Results

Modeling of Unattached Ducted Rig

Extensive CFD modeling was conducted to investigate the new unattached ducted rig concept. Initial

runs focused on the behavior of the gas phase when the rig was operated at Mach 0.5. Gas temperature 

and velocity plots are shown in Figure 3. For all cases, the distance between the nozzle exit and the duct 

entrance was set to 0.5 in. (12.7 mm). The case with the largest duct diameter—1.94 in. (49.3 mm)—

behaved essentially the same as a rig not having a duct. Practically speaking, it could be viewed as a 

windscreen rather than a duct. The figures for the corresponding unducted case are not shown because 

they are visually nearly identical to this case. Decreasing duct diameter to 1.0 in. (25.4 mm) showed a 

similarly short potential core (as approximated by the red-colored region of the figure). Decreasing the 

duct further to equal the duct diameter of 0.75 in. (1.905 mm) resulted in a flame having an extended

potential core whose length was several inches longer than the length of the 4.5 in. (44.5 mm) duct. 

Extending the duct length to 12 in. (305 mm), the approximate maximum length available in the test cell, 

produced a potential core several inches longer than the length of the longer duct.
NASA/TM—2011-217008 6

Gas Temperature Gas Velocity

Duct Diameter: 1.94 in. 

(49.3 mm)

Duct Length: 4.5 in. 

(114 mm)

Duct Diameter: 1.00 in. 

(25.4 mm)

Duct Length: 4.5 in. 

(114 mm)

Duct Diameter: 0.75 in. 

(19.05 mm)

Duct Length: 4.5 in. 

(114 mm)

Duct Diameter: 0.75 in. 

(19.05 mm)

Duct Length: 12 in. 

(305 mm)

Figure 3.—Gas total temperature and velocity magnitude plots for a burner rig operated at 2500 °F (1371 °C, 1644 K) 

and Mach 0.5.Showing duct diameter of 19.05 mm and length of 114 and 305 mm. Geometric dimensions of the

12 in. (305 mm) case are given in Figure 2.
NASA/TM—2011-217008 7

Figure 4.—Centerline (a) total temperatures and (b) velocity magnitudes corresponding to Figure 3.

The centerline total temperatures and velocities taken from the text data corresponding to the above 

plots for the four ducts are shown in Figures 4(a) and (b), respectively. Note that for the 1.94 in.

(49.3 mm) diameter duct and the 1.00 in. (25.4 mm) duct, the total temperature of the gas falls off quickly 

after a few inches from the nozzle (i.e., it quickly drops off after exiting the relatively short potential core 

of the jet). For the 4.5 in. (49.3 mm) long, 0.75 in. (1.905 mm) diameter duct, the temperature is largely 

maintained throughout the length of the duct and a few inches beyond. For the 12 in. (305 mm) long,

0.75 in. (1.905 mm) diameter duct, the temperature is again maintained up to a few inches beyond duct 

exit. Gas velocity falls off more quickly initially but then recovers and increases throughout the length of 

the 0.75 in. diameter duct, and continues to increase to a few inches beyond duct exit. These results show 

that an appreciable fraction of the gas exit velocity and temperature is retained throughout the length of 

the unattached duct as long as the duct diameter is equal to the nozzle diameter.

Figures 5(a) and (b) show total temperature and velocity magnitude, respectively, of the gas for the

12 in. (305 mm) long, 0.75 in. (1.905 mm) diameter duct as a function of distance from the nozzle for 

Mach numbers from 0.3 to 1.0. The curves for Mach 0.5 are the same as those in Figure 4(a) and (b), 

except that the temperature axis scale is expanded. Figure 5(a) shows that the gas temperature falls 

somewhat less for higher Mach number. Figure 5(b) shows that there is a greater drop in velocity at the 

duct entrance for higher Mach number flow, but the gas velocity recovers nearly to the exit velocity for 

each case.

Figure 6(a) and (b) shows the absolute gas pressure versus distance from the nozzle exit for the 4 

different ducts and for 5 values of the Mach number for the 12 in. (305 mm) duct. For each plot, the 

pressure begins at the burner pressure appropriate for the particular Mach number of interest. The 

pressure drops to near atmospheric pressure at the nozzle exit. For the 0.75 in. (19.05 mm) diameter ducts, 

the pressure rises at the duct entrance and falls back to atmospheric pressure at the duct exit.
NASA/TM—2011-217008 8

Figure 5.—Plots of gas (a) total temperatures and (b) velocity magnitudes for the 12 in. (305 mm) long, 0.75 in.

(19.05 mm) diameter duct as a function of distance from the nozzle exit for Mach numbers from 0.3 to 1.0.

Figure 6.—Absolute gas pressure versus distance from the nozzle exit for (a) the 4 different ducts and (b) for 5 values 

of the Mach number for the 12 in. (305 mm) long, 0.75 in. (19.05 mm) diameter duct.
NASA/TM—2011-217008 9

Of the large number of particle-track calculations that were made for fine 20 to 32 μm alumina 

particles, only the 20 m/s injection cases are shown in Figure 7. This conveys the general trends using a 

more manageable number of figures. Each plot shows the two-dimensional most probable particle tracks 

on the upper part of the plot and the modeled velocity at the lower part. Note the increase in particle 

velocity with increasing Mach number. Also note that the velocity drops in half, due to the 0.5 restitution 

coefficient, whenever the particles strike a wall.

 

Figure 7.—Most probable particle tracks and velocity magnitudes as a function of distance from the nozzle for 20 to

32 μm alumina particulate fed at 20 m/s into burner rigs operated at Mach numbers from 0.3 to 1.0 for a 12 in.

(305 mm) long, 0.75 in. (19.05 mm) diameter duct.
NASA/TM—2011-217008 10

Figure 8.—Median velocity of 20, 26, and 32 μm diameter particulates 

(26 μm mean diameter) at 2 in. (50.8 mm) from the exit of the nozzle 

or from the 12 in. (305 mm) duct for Mach numbers ranging from 0.3 

to 1.0 for a 12 in. (305 mm) long, 0.75 in. (19.05 mm) diameter.

Because three injection velocities were modeled for each Mach number for the 20-to-32 μm powder, 

the total number of particle tracks was nine. The velocity attained by each of these tracks is a function of 

factors such as the particle size, the number and location of wall strikes, and the nearness of the particle 

tracks to the centerline. In the future, modeling involving a large number of particle tracks accurately 

replicating a statistical distribution of particle velocities may be conducted. For the current set of 

calculations, it would be instructive to examine representative particle velocities as a function of Mach 

number. Among the choices for representative particle velocities is the maximum, mean, or median 

velocity. Since very high or very low particle velocities will not affect the median value, the median 

particle velocity was used in Figure 8. Each bar in Figure 8 represents the median of nine velocities

(3 injection velocities times 3 particle sizes) at 2.0 in. (50.8 mm) from the duct exit for Mach numbers 

ranging from 0.3 to 1.0 for the 20 to 32 μm powder (mean particle size 26 μm). The distance of 2.0 in.

(50.8 mm) from the duct exit to the specimen was selected as a representative testing distance. The 

median velocities are plotted in Figure 8, along with the velocity at 2.0 in. (50.8 mm) from the nozzle. 

This velocity provides an estimate of the velocity that would have been achieved at the specimen if no 

duct were used. As a check of this assumption, the value at a distance of 2.0 in. (50.8 mm) from the 

nozzle exit for the 1.94 in. (49.3 mm) diameter duct is plotted on Figure 8 for the Mach 0.5 case. The 

large diameter 1.94 in. (49.3 mm) duct behaves essentially as an unducted burner rig. Inspection of the 

figure shows that the median velocity at 2 in. (50.8 mm) from the nozzle is very similar whether the 12 in.

(305 mm) duct is present or not. Therefore, the paired bars in the figure may be interpreted as an estimate 

of the predicted improvement in velocity that these relatively small particles achieved using the 

unattached duct. The figure shows that the improvement in velocity for these small particles is 47 percent 

for Mach 0.3, rising to 58 percent for Mach 1.0. 
NASA/TM—2011-217008 11

The lower portions of Figure 9(a) through (j) show plots of particle velocity versus distance through 

the rig for the case of three large diameter particles: 500, 550, and 600 μm. The upper portions of the 

figures shows the corresponding most probable particle tracks, which are modeled for Mach 0.3 to 1.0. 

All of the plots shown are for 3 m/s injection, which assumes that the injected particles have been slowed

from the faster speed required for conveying through the feed line to a slower speed using, for example, a 

45° elbow in the feed line just before injection. Such a device, which will be described later in the report,

would prevent possible damage of the burner liner when large particles were used. The plots on the left 

hand side of the page are calculated assuming a 0.5 restitution coefficient. The plots on the right were for 

a restitution expression that displayed near-elastic forward scattering (which was especially true for less 

than 15° incidence). The angle of incidence was allowed to equal the angle of reflectance in all cases.

Note that even with the slowed injection velocity, it was not possible to avoid striking the burner liner on 

the side opposite the injection.

Figure 9.—Most probable particle tracks and velocity magnitudes versus distance from the nozzle for 500, 550, and

600 μm alumina particulate fed at 3 m/s into burner rigs operated at Mach numbers from 0.3 to 0.7; Figures (a),(c) 

for restitution coefficient, e, of 0.5; Figures (b),(d) for near-elastic forward restitution.
NASA/TM—2011-217008 12

Figure 9.—Concluded. Most probable particle tracks and velocity magnitudes vs. distance from the nozzle for 500, 

550, and 600 μm alumina particulate fed at 3 m/s into burner rigs operated at Mach numbers from 0.7 to 1.0; 

Figures (e),(g),(i) for restitution coefficient, e, of 0.5; Figures (f),(h),( j) for near-elastic forward restitution.
NASA/TM—2011-217008 13

Figure 10 represents the effect of the unattached duct on the velocity of larger 500, 550, and 600 μm

diameter particles. As above, the median velocity from a range of injection velocities was plotted at

2.0 in. (50.8 mm) from the nozzle and from the duct exit, respectively. However, for these large particles, 

this is the middle of only three velocities because only one injection velocity per case was modeled. Also, 

the results of an unducted case are presented for Mach 0.5 operation. Inspection of the figure shows that 

the velocity plotted for the unducted case is very similar to the velocity at 2.0 in. (50.8 mm) from the 

burner nozzle for the ducted cases when compared at the same Mach number. As with the small particles, 

the ratio of these two velocities is taken to be essentially equal to the enhancement in velocity achievable 

using the duct. The enhancement was found to be greater for larger Mach numbers and somewhat greater 

for the cases where near-elastic forward restitution was assumed. Velocity enhancements were found to 

range from 91 to 114 percent for the near-elastic forward scattering cases. For the cases having the 0.5 

restitution coefficient, the velocity enhancement decreased with increasing Mach number from 95 percent

at Mach 0.3 to 70 percent at Mach 1.0. For the Mach 0.7 cases, the velocity using the duct was predicted 

to be increased by 85 or 101 percent, respectively, for the restitution coefficient of 0.5 or the near-elastic 

forward scattering case. For reference, the enhancement at Mach 0.7 for the small 26 μm particle case 

was 52 percent.

Figure 10.—Median velocity of 500, 500, and 600 μm diameter particulates (550 μm mean diameter) at 2 in.

(50.8 mm) from the exit of the nozzle or from the 12 in. (305 mm) duct for Mach numbers from 0.3 to 1.0 for 

constant 0.5 and near elastic restitution coefficients.
NASA/TM—2011-217008 14

Modeling of Elbow Injector

A related CFD study was conducted to determine whether a device employing a simple 45° elbow 

fitting followed by a short length of a wider tube could be used to slow down the injection velocity of 

large particles sufficiently to avoid damage to the burner liner opposite the injection location. For this 

study, the modeled carrier gas velocity and pressure upstream of the elbow were adjusted so that 500 to

600 μm particles would be conveyed at about 20 m/s. The exit pressure was adjusted to represent the 

burner pressure for Mach 0.7 burner rig operation. The gas pressure and velocity are shown in

Figure 11(a) and (b), respectively. Two different sets of restitution coefficients were employed: in

Figure 11(c), constant restitution coefficient of 0.5 and, in Figure 11(d), restitution coefficient near one 

for angles less than about 15° but falling off at higher angles (i.e., near-elastic forward restitution).

Figures representing the results of the modeling are shown below.

From inspection of Figures 11(c) and (d), the injector is shown to slow the particles down considerably 

for either case. Figures 12(a) and (b) show the velocities of the 12 particle tracks are plotted versus time for 

the two cases. In these figures, the Y-axis is the velocity in meters per second and the X-axis is the transit 

time in seconds of the particles. The exit velocity of the particles from injector (which would also be the 

entrance velocity of the particles into a Mach 0.7 burner) is seen to vary from about 1 to 4 m/s.

Figure 11.—(a) Gas pressure from 136804 (blue) to 138536 (red) pascals and (b) gas velocity for carrier gas flowing 

through an elbow injector from 0 (blue) to 44.1 m/s (red), and particle tracks for 12 particles in the range of 500 to 

600 μm (550 μm mean) prior to injection into a burner rig operated at Mach 0.7 assuming (c) a restitution 

coefficient of 0.5 with tracks colored by velocity from 0.45 (blue) to 20.44 (red) m/s and (d) near-elastic forward 

restitution with tracks colored by velocity from 1.17 (blue) to 20.44 (red) m/s. Arrows refers to the direction of flow.
NASA/TM—2011-217008 15

Figure 12.—Particle velocity versus time for 500 to 600 μm (550 μm mean) particles in a 45° elbow injector assuming

(a) restitution coefficient of 0.5 or (b) near-elastic forward restitution.

Figure 13.—Photograph of particle injector employing a 45° fitting.

For the assumption of near-elastic forward restitution, shown in the lower set of figures, the exit 

velocities of the particles are seen to range from a little above 2 m/s to a little above 3 m/s. The particle 

tracks may be seen to straighten more for the near-elastic case than for the case where the restitution 

coefficient was assumed to equal a constant value of 0.5. In either case, the particle velocities are slowed 

to comparable values of generally 2 to 3 m/s. A photograph of an injector employing a 45° fitting 

constructed from simple fittings is shown in Figure 13. This has been tested and shown to work well.
NASA/TM—2011-217008 16

Experimental Results

An early version of the unattached duct was constructed that had insulation wrapped around the 

center 10 in. (254 mm) of a 12 in. (305 mm) long, 0.75 in. (19.05 mm) inner diameter, 1.0 in. (25.4 mm) 

outer diameter mullite tube (Ref. 3). While it initially functioned well from an aerodynamic viewpoint, it 

suffered from post-test cracking of the mullite tube at the burner end of the duct. A second version, shown 

in Figures 14(a) and (b), placed the mullite tube inside of a Schedule 40 stainless steel pipe. A specimen 

temperature of 1800 °F (980 °C) could be achieved, while the temperature of the metal pipe near the 

nozzle could be kept as low as 1650 °F (900 °C). Ideally, specimen temperatures of 2000 °F (1090 °C) or 

higher are needed. However, use of this stainless steel pipe prevented testing at temperatures that high. 

More recently, a Haynes 230 superalloy pipe has been acquired. This alloy is suitable for prolonged use 

up to 2100 °F (1150 °C) (Ref. 20). Therefore, long duration exposure of specimens to temperatures of 

2000 °F or higher is expected to be easily achievable using the superalloy pipe. 

A high-speed camera was used to visualize the particle streaks and measure their velocity for both 

ducted and unducted runs that were conducted in the absence of specimens. Figure 15 for the unducted

case, repeated from Reference 3. These images, although necessarily lower resolution that the originals, 

serve to define the measurement approach. The lines drawn on the figure represent the particle streaks at 

1/8000 sec shutter speed of the nominally 27 μm alumina particle size. In Figure 8, the predicted median 

velocity was 120 m/s at the nozzle exit and 170 m/s at 50.8 mm from the exit. The modeled velocities are 

quite consistent with the range of experimental velocities shown in Figure 15.

Figure 14(a).—12 in. (305 mm) long, 0.75 (10.05 mm) I.D. duct formed from a ceramic mullite tube within a 

temporary stainless steel pipe. For later versions, a Haynes 230 superalloy pipe is used; (b) End view of duct.

Figure 15.—Tracks of nominally 27 μm particles in the flame exiting from an unducted burner rig operating at

Mach 0.5 photographed using 1/8000 sec exposure.
NASA/TM—2011-217008 17

Figure 16 shows particles exiting from the initial ducted rig design. The Mach number for this 

example was 0.5. The velocity of particles after exiting from the duct was predicted to be about 250 m/s 

from Figure 8, which is similar to, but somewhat lower than, the velocities of over 300 m/s observed in 

the streak photograph. This result suggests that the restitution coefficient for small particles within the 

duct could possibly be higher than the modeled value of 0.5.

Figure 17 shows erosion recession in terms of both thickness and weight loss for a vendor-prepared 

ZrO2-7wt%Y2O3 baseline EB-PVD TBC on 1 in. (25.4 mm) diameter superalloy specimens, which were 

eroded in the prototype unattached ducted rig. These were tested using the nominally 27 μm alumina 

powder at 1800 °F (980 °C) in a Mach 0.5 flame. For the case where recession is expressed in terms of 

thickness, an error bar representing the 0.0127 mm readability of the micrometer is included on the plot.

Figure 16.—Tracks of nominally 27 μm particles in the flame exiting from a

12 in. (305 mm) long unattached duct placed in front of a burner rig operating 

at Mach 0.5 photographed using 1/8000 sec exposure.

Figure 17.—Recession in terms of thickness and weight loss for a 

vendor-prepared ZrO2-7wt%Y2O3 baseline EB-PVD TBC on

1 in. (25.4 mm) diameter superalloy specimens eroded in the 

unattached ducted rig. Tests used the nominally 27 μm powder 

at 1800 °F (980 °C) using a Mach 0.5 burner rig.
NASA/TM—2011-217008 18

Photos of tested specimens are shown below. Figure 18(a) shows a specimen tested in the unducted 

rig. Figure 18(b) shows a specimen tested in a ducted rig corresponding to the data in Figure 17. The 

eroded spot in Figure 18(b) was aligned somewhat below the center of the specimen and it is larger than 

the eroded spot attained in the unducted test. There are small satellite failures which are believed to be 

impact in nature from larger particles in the erodent powder. The erosion pattern is much larger than 

observed from the unducted rig. 

Figures 19(a) and (b) are images of the same 1.0 in. (25.4 mm) diameter specimens as in

Figure 18(a) and (b). However, the images in Figure 19 were obtained using a contour profiler and 

processing the data through software written by the first author. These figures show clearly that the 

specimens are dished from the erosion and that the final 25 μm or so of damage displays a steep uneroded 

edge that appears to indicate that the final portion of the damage had occurred suddenly.

Figure 18.—Photographs of 1.0 in. (25.4 mm) diameter specimens

tested in burner rig operated at Mach 0.5; (a) without and (b) with the 

12 in. (305 mm) long duct, showing a much larger eroded diameter 

when the duct was used.

Figure 19.—3D plot of the data obtained from contour profiler of post test specimens tested in 

burner rig operated at Mach 0.5; (a) without and (b) with the 12 in. (305 mm) long duct,

showing a much larger eroded diameter when the duct was used.
NASA/TM—2011-217008 19

Summary and Conclusions

The CFD modeling and experiments discussed in this paper have shown the feasibility of using an 

unattached duct with a burner rig for increasing injected particle velocity for burner erosion rig exposure 

of coated specimens as long as the duct has an internal diameter equal to the diameter of the burner rig 

nozzle. A 12 in. (305 mm) long, 0.75 in. (19.05 mm) diameter duct was found to lead to increased particle 

velocity, with the velocities of the larger 550 μm particles increasing by a factor of about 1.7 to 2.0

depending on Mach number and restitution coefficient. This compares with a smaller fractional benefit of 

about 1.5 to 1.6 for the velocities of the smaller 26 μm particles. Another potential benefit of the duct,

demonstrated experimentally, is that the particle distribution was observed to spread to a greater diameter 

at the specimen location when the duct was used, thus increasing the eroded region of the specimen and

allowing for more precise determination of average erosion rates. Further experimental work is required 

to assess the durability of the proposed unattached duct design and to investigate the use of unattached 

ducts with nozzles having diameters other than the one used in this study.

It has also been shown that an injector made from a simple 45° elbow fitting can be used to slow the 

particle velocities before injection from the relatively fast velocities needed to convey the powder through 

the feed line to much slower velocities that are less likely to damage the burner liner.

NASA/TM—2011-217008 21

Appendix.—Analytical Expressions for Particles Having

Non-Zero Initial Velocity in a Flowing Gas Stream

The analytical expressions for the velocity of particles in a parallel flowing gas stream may be

re-derived to include non-zero initial particle velocity. This will allow examination of the expressions 

describing the acceleration of particles in a duct after initial acceleration in the burner rig nozzle. 

Simplifying assumptions include constant gas temperature, velocity, and pressure, as well as spherical 

particles. 

Assuming drag forces predominate, particle dynamics are governed by the following expression

(Ref. 21)

( ) 2

p p

p dp p p

dV dV

m mV C A V V V V

dT dx

ρ = = −− (2)

where the parameters referring to the particle are mass m, velocity Vp, and cross sectional area Ap. The gas 

parameters are velocity V, which is assumed to be constant, and density ρ; Cd is the drag coefficient.

The above expression may be rearranged to give

( )

2 p p

d p p p

m V dV

dx

c A VV VV = ρ − − (3)

For spheres of diameter D and density ρp:

3

6

m D p

π

= ρ (4)

2

4

A D p

π = (5)

Therefore, we may write:

( )

4

3

p pp

d p p

D V dV

dx

C VV VV

ρ = ρ − − (6)

For the greatly simplifying assumption of constant Cd and with accelerating particles:

( )

4

3

f

i i

x V p pp

x V d p p

D V dV

dx

C VV VV

ρ = ρ − − ∫ ∫ (7)

4 ln

3

p p

f i

d i pi

D VV V V

x x

C VV VV VV

ρ −   − =   + −

ρ− − −  

(8)
NASA/TM—2011-217008 22

The above expression is the same as the expression in the literature, except that the literature equation was 

derived for zero initial velocity. If the initial particle velocity Vi is set to zero, the equation for the 

literature is obtained. In our case, the initial velocity may represent the velocity of the particle as it exits 

the nozzle.

A somewhat less simplifying assumption of Cd proportional to the square root of the Reynolds 

number can also lead to an equation for particle velocity versus distance that may be integrated in closed 

form. The simplified square-root drag law is:

1/2 Re C B d = (9)

Re / =ρ − μ DV Vp (10)

where μ is the dynamic viscosity of the gas, and B is an arbitrary constant. This leads to the following 

expressions:

( )

1/2

3/2

4

3

p V p p

f i Vi

p

D V dV

x x B

V V

ρ   μ − =   ρ ρ   − ∫ (11)

( ) ( ) ( ) ( ) ( ) 1/2 1/2 1/2

3/2 1/2 1/2

4

3

p

f i p i

p i

V V x x D B V V V V

V V V V

 

ρ   −= μ −− − −− ρ − −  

(12)

The above equation is useful for visualizing the approximate influence of the various parameters. It may 

also be used to check closed-form solutions to solutions from numerical integration where the constant B

can be selected to give the best match in the range of interest of the Reynolds number to the drag 

coefficient calculated using a more accurate drag law. For a more accurate drag law, such as the Abraham 

equation (Ref. 22) that is sufficiently accurate for Re <5000, an expression may be obtained that must be 

numerically integrated. The Abraham equation is:

2

1/2 1/2

9.06 5.291 24.00 0.2924 1 0.2924

Re Re Re

Cd

  = + = ++     (13)

The expanded version clearly shows that Cd goes from the Stoke’s Law equation (24/Re) for very small 

Re towards 0.2924 for very large Re (at Re = 5000, Cd = 0.2972). This leads to the following expression 

that must be integrated numerically:

( )

4

3

f

i i

x V p p p

x V

p p

V dV

dx D

Cd V V V V

ρ = ρ − − ∫ ∫ (14)

( )

2

1/2

4

3 9.06 0.2924 1

Re

i

p V p p

f i V

p p

V dV

xx D

VV VV

ρ − = ρ   + −−    

∫ (15)
NASA/TM—2011-217008 23

The Abraham equation covers the entire range of Reynolds numbers of interest to this study. 

However, the CFD code FLUENT used the Morsi and Alexander equation (Ref. 17), as discussed in the 

Model Description section. The expanded version of the Abraham drag law is similar in form to the 

equation of Morsi and Alexander. However, with the Morsi and Alexander equation, the Re1/2 term is 

replaced by Re and the Re term is replaced by Re2

. The constant terms for the Abraham and the Morsi 

and Alexander equations are different from each other. In fact, the Morsi and Alexander equation uses 

different constants for different ranges of the Reynolds number, which allows either equation to predict 

similar values of Cd. This leads to the following relationship between particle velocity and distance:

( ) ( ) 2

12 3

4

3 / Re / Re i

p V p p

f i V

p p

V dV

xx D

a a a VV VV

ρ − = ρ   + + −−    

∫ (16)

The above analytical expression, which uses the same drag law that is used for the CFD analysis, may 

be numerically integrated to obtain estimates of the particle velocity versus distance from the nozzle exit.

During the numerical integration, care must be taken to use the constants in the Morsi and Alexander 

equation that are appropriate for the Reynolds number range of interest. An example of the results of such 

a numerical integration is shown in Figure 20, where curves for 26 and 550 μm particles being 

accelerated under Mach 0.5 conditions are plotted, along with the corresponding results from the CFD 

analyses, which had previously been presented in Figures 7 and 9. Mean values of the gas temperature, 

pressure and velocity (1573K, 1.034 MPa, and 310 m/s, respectively), that are needed for the analytical 

expression, were taken from the CFD calculations. Even with the simplification of using mean values for 

these gas properties, the results from the analytical expression matches the CFD modeled results very 

well. For the 550 μm case, the velocities drop somewhat beyond approximately 0.1 m because the 

particles strike the duct wall. The analytical expression initially matches very well, but after the wall 

strike the analytical expression somewhat over predicts because the analytical expression cannot account 

for the drop in velocity due to a wall strike.

Figure 20.—Predicted velocities of 26 and 550 μm particles 

for the ducted Mach 0.5 case as predicted by the CFD 

analysis and by the analytical expression. The CFD 

analysis is used to provide the initial particle velocity (i.e.,

the particle velocity and the nozzle exit) and the mean 

values of the gas velocity, temperature, and pressure.
NASA/TM—2011-217008 24

References

1. Yamamuchi, G.K., and L.A. Young, A Status of NASA Rotorcraft Research. NASA Technical Paper 

NASA/TP—2009-215369; Sept 2009.

2. Dongming Zhu and Robert A. Miller; Development of Advanced Low Conductivity Thermal Barrier 

Coatings. Int. Journal of Applied Ceram Technol, 2005, 1(1): pp. 86–94.

3. Zhu, D., R.A. Miller, and M.A. Kuczmarski. Development and Life Prediction of Erosion Resistant 

Turbine Low Conductivity Thermal Barrier Coatings NASA/TM—2010-215669; Feb 2010.

4. Wellman, R.G., M.J. Deakin, and J.R. Nicholls, The effect of TBC morphology on the erosion rate of 

EB PVD TBCs, Wear, 2005. 258: pp. 349–356.

5. Borom, M.P., C.A. Johnson, and L.A. Peluso, Role of environmental deposits and operating surface 

temperature in spallation of air plasma sprayed thermal barrier coatings, Surf Coatings Technol.,

1996. 86–87: pp. 116–126.

6. Roberts, G.D., R.T. Bhatt, P.J. Bonacuse, R.G. Bryant, M.C. Halbig, K.E. Jackson, W.C. Jackson, 

J.C. Johnston, M.A. Kuczmarski, R.A. Miller, T.K. O’Brien , Chapter 8, Structures and Materials in 

G.K. Yamamuchi and L.A. Young, A Status of NASA Rotorcraft Research. NASA Technical Paper 

NASA/TP—2009-215369; Sept 2009, pp. 325–376.

7. Hamed, A., Y.D. Jun, and J.J. Yeuan, Particle dynamics simulations in inlet separator with an 

experimentally based bounce model, J Propulsion Power, 1995. 11(2): pp. 230–235.

8. Zedan, M., P. Hartman, A. Mostafa, A. Sehra, Viscous flow analysis for advanced inlet particle 

separators, AIAA-90-2136 (1990).

9. Strangman, T.E., D. Narasimhan, J.P. Armstrong, K.R. Karesek, Carbon Deposit Inhibiting Thermal 

Barrier Coating for Combustors, Patent No. US 6.656,600 B2, Dec 2, 2003.

10. Mariocchi, A., A. Bartz, and D. Wortman, PVD Experience on GE Aircraft Engines, J Thermal Spray 

Technology, (1997). 6(2): pp. 193–198.

11. Bruce, R.W., “Development of 1232 °C (2250 °F), Erosion and Impact Tests for Thermal Barrier 

Coatings, Tribology Transactions, (1998). 41(4): pp. 399–410.

12. Handschuh, R.F., High Temperature Erosion of Plasma-Sprayed Yttria-Stabilized Zirconia in a 

Simulated Turbine Environment, NASA TP 2406; AVSCOM TR-84-C-17, December 1984. Also 

AIAA–85–1219.

13. Hamed, A.A., W. Tabakoff, R.B. Rivir, K. Das, P. Arora, Turbine blade surface deterioration by 

erosion, J. Turbomachinery, (2005). 127: pp. 445–452.

14. Hamed, A., W. Tabakoff, and R. Wenglarz, Erosion and Deposition in Turbomachinery, J Prop 

Power, (2006). 22(2): pp. 350–360.

15. ANSI/ASME MFC-3M-2004, Measurement of Fluid Flow in Pipes Using Orifice, Nozzle, and 

Venturi, Includes Addenda A, American Society of Mechanical Engineers / 01-Jan-2004 / 92 pages.

16. Senesh, K., and V. Babu, Numerical Simulation of Subsonic and Supersonic Jets, 11th AIAA/CEAS 

Aeroacoustics Conference (26th AIAA Aeroacoustics Conference) 23–25 May 2005, Monterey, 

California AIAA–2005–3095.

17. Morsi S.A. and A.J. Alexander, An Investigation of Particle Trajectories in Two-Phase Flow Systems, 

J. Fluid Mech., (1972). 55: pp. 193–208.

18. Clift, R., J. Grace, J.R. and M.E. Weber. Bubbles, Drops, and Particles, 1978, Academic Press,

p. 276. (Dover Pub Inc. 2005 reproduction).

19. Swar, R., Particle Erosion of Gas Turbine Thermal Barrier Coatings; A thesis submitted to the 

University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science 

(M.S.) in the Department of Aerospace Engineering and Engineering Mechanics of the College of 

Engineering, 2009.
NASA/TM—2011-217008 25

20. Haynes International, High temperature Tech Brief, Hanes® 230® Alloy, H-3024E, Haynes 

International Inc. 2009.

21. Dykhuizen, R.C., and M.F. Smith, Gas Dynamic Principles of Cold Spray, J Thermal Spray Technol.,

1998. 7(2): pp. 205–212.

22. Abraham, F.F., Functional dependence of drag coefficient of a sphere on Reynolds number. Phys. 

Fluids, 1970. 13: pp. 2194–2195.
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Burner Rig With an Unattached Duct for Evaluating the Erosion Resistance of Thermal 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

Extensive computational fluid dynamics (CFD) modeling backed by experimental observation has demonstrated the feasibility of using an 

unattached duct to increase the velocity and spatial spread of erodent particles exiting from a burner rig. It was shown that gas velocity and 

temperature are mostly retained if the inner diameter of the unattached duct equaled the exit diameter of the burner rig nozzle. For particles 

having a mean diameter of 550 mm, the modeled velocity attained at a distance 2.0 in. (50.8 mm) beyond the exit of a 12 in. (305 mm) long 

duct was approximately twice as large as the velocity the same distance from the nozzle when the duct was not present. For finer particles, 

the relative enhancement was somewhat less-approximately 1.5 times greater. CFD modeling was also used to guide the construction of a 

device for slowing down the velocity of the particles being injected into the burner rig. This device used a simple 45° fitting to slow the 

particle velocity in the feed line from 20 m/s, which is in the range needed to convey the particles, to about 3 m/s just as they are injected 

into the burner. This lower injection velocity would lessen the severity of the collision of large particles with the wall of the burner liner 

opposite the injection port, thereby reducing potential damage to the burner liner by high-velocity particles. 

15. SUBJECT TERMS

Computational fluid dynamics (CFD); Erosion; Thermal control coatings 

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