# Wide-Beam X-Ray Source Target Thermal Management Simulation Using Inner Jet Cooling

Authors: Chang H. Kim; J. Michael Doster; Mohamed A. Bourham
Journal: Scholarly Research Exchange
 (2009)

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## Abstract

A wide-beam area X-ray source has been proposed as a practical replacement for synchrotron sources in clinical DEI applications. Due to a wide X-ray illumination area, a decrease in X-ray flux is expected and thus high electron beam currents up to 3A are considered. To ensure the target performance without deterioration, melting, cracking, or even evaporation, an active cooling system is required for the target block in order to remove the heat and allow for sufficient scanning time. In this study, jet cooling of the target back is investigated for a prototype proof-of-principle target. The prototype target was simulated with the transient k-ɛ turbulence multiphysics model in ANSYS CFX. The simulations were conducted at a heat flux of 1.8×107 W/m2, consistent with values anticipated for a full scale target. The simulation results show that the target temperature exceeds the copper melting point in 2 seconds at inlet velocities below 2 m/s. Also, critical heat flux calculations show that a  1.5 m/s inlet velocity at atmospheric pressure is a lower limit for prevention of target burnout using water as a coolant. Inlet velocities in excess of 2 m/s allows for steady-state operation while satisfying all thermal design constraints.


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## Body

## 1. Introduction

In the proposed compact wide-beam X-ray source for diffraction
enhanced imaging applications, highly collimated, high intensity photon flux is
a major requirement [1–3]. Conventional X-ray
tubes cannot meet these requirements due to their relatively low X-ray flux and
the fan shape of the X-ray beam. To increase X-ray flux to compete with a
synchrotron radiation beam, a high electron beam current (up to 3A) is proposed
in conjunction with a large X-ray illumination area. Heat removal in a
conventional X-ray source is not a critical issue because lower electron beam
currents are used and a rotating target allows for spreading the heat flux over
a larger area of the target. Conventional X-ray tubes which use stationary
targets are passively cooled with air or oil [4]. The wide-beam X-ray source in
this study has a stationary target (anode) and hence heat removal at high beam
currents is essential. For a device expected to operate at the commercial
level, a 3A beam current would be required in order to generate the necessary
high X-ray flux. At 60 kV acceleration potential with 3A beam current, the
total power on the target is 180 kW that requires special thermal management
for target heat removal. The estimated scanning time of a DEI-based wide-beam X-ray
system is ~20 seconds during which time the beam energy will be converted to
heat energy on the target [5]. The cooling demands of such a target exceed the
heat removal capacity of a passive cooling system and necessitate an active
cooling system.Early research work on the wide-beam X-ray system considered
cryogenic cooling using liquid nitrogen through a contact or invaded cold
finger [1]. This study revealed that heat removal via conduction utilizing
liquid nitrogen could not obtain the required operating time before the target
reached its melting temperature. In addition, the large thermal gradients and
induced stresses in such a system would render it infeasible.In this study, an inner impinging jet cooling method was
employed for active cooling with water at atmospheric pressure and room
temperature. The prototype proof-of-principle design was simulated using the
ANSYS CFX finite element code [6].


## 2. General Considerations

Due to the high heat loads, target thermal management is an
important issue for the proposed wide-beam X-ray system. Impinging jet cooling
has been shown as an effective way to remove heat from the heated surface in
various devices, and is considered in this study for target cooling [7]. Design
of a jet cooling system requires maximizing the convective heat transfer from
the target back while satisfying thermal limits associated with maximum target
temperatures and critical heat flux. Convective heat transfer can be maximized
by optimizing the geometry of the jet nozzle. To maintain target integrity,
maximum target temperatures must remain well below the melt temperature. This
is dictated by the target materials, geometry, and the efficiency of the target
cooling system. If the heat flux at the coolant/target interface exceeds the
critical point, transition to film boiling can occur, which degrades heat transfer
and potentially leading to target failure [8].


### 2.1. Convective Heat Transfer Coefficient

Impinging jet cooling has been studied as a function of both
the fluid characteristics and the shape of the jet [9–12].
Correlations for the convective heat transfer coefficient are a function of the
ratio of the exit-to-impingement distance to the jet exit diameter (S/d) and the ratio of the diameter of
the impingement surface to the jet exit diameter (D/d) [13]. For 2≤S/d≤12, 5≤D/d≤15, and 2000≤Red≤400000, the convective heat transfer
coefficient for a submerged, single jet water nozzle can be expressed in terms
of the Nusselt number through the empirical equation by Martin [7],
(1)Nu=dD[2−4.4(d/D)][1+0.2((S/d)−6)(d/D)]F(Red)Pr0.42,
where F(Red) is a power function of Reynolds number and Pr represents the Prandtl number. The
power function, F(Red), is
shown in (2)
(2)F(Red)=2Red0.5[1+Red0.55200]0.5.
The Prandtl number satisfies the
general definition of viscous diffusion rate over thermal diffusion rate.


### 2.2. Critical Heat Flux

Generally an impinging jet causes a stagnation point on the
surface, and therefore, the critical heat fluxqc″ will occur at the stagnation point. A
generalized critical heat flux correlation for forced convective cooling with
impinging jets was proposed by Monde et al. [13]. The correlation between the
critical heat flux of a subcooled impinging jet qc″,
and the predicted critical heat flux of a saturated impinging jet qco″,
is given by (3), (3)qc″qco″=1+1+4CJa2, where Ja is the Jacob number and C is a constant given by (4).
The applicable ranges of the given equation for subcooled impinging jet cooling
are a density ratio ρl/ρg
of 8.8~1605, a jet velocity u of 5~34 m/s, and subcooling ΔTsub of 0~115 K. Mitsutake and Monde
have
shown that (3) fits the data well for D/d ratios less than 5 [14],
(4)C=0.95(d/D)2(1+D/d)0.364(ρl/ρg)0.43(2σ/ρlu2(D−d))0.343. The predicted critical heat flux
with a saturated impinging jet is given in (5), (5)qcoρvhhgu=0.221(ρl/ρv)0.645(2σρlu2(D−d))0.343(1+D/d)−0.364, where ρv and ρl represent vapor and water density, hhg is the latent heat of vaporization, u is the jet velocity, and σ is the
surface tension of water.


## 2.1. Convective Heat Transfer Coefficient

Impinging jet cooling has been studied as a function of both
the fluid characteristics and the shape of the jet [9–12].
Correlations for the convective heat transfer coefficient are a function of the
ratio of the exit-to-impingement distance to the jet exit diameter (S/d) and the ratio of the diameter of
the impingement surface to the jet exit diameter (D/d) [13]. For 2≤S/d≤12, 5≤D/d≤15, and 2000≤Red≤400000, the convective heat transfer
coefficient for a submerged, single jet water nozzle can be expressed in terms
of the Nusselt number through the empirical equation by Martin [7],
(1)Nu=dD[2−4.4(d/D)][1+0.2((S/d)−6)(d/D)]F(Red)Pr0.42,
where F(Red) is a power function of Reynolds number and Pr represents the Prandtl number. The
power function, F(Red), is
shown in (2)
(2)F(Red)=2Red0.5[1+Red0.55200]0.5.
The Prandtl number satisfies the
general definition of viscous diffusion rate over thermal diffusion rate.


## 2.2. Critical Heat Flux

Generally an impinging jet causes a stagnation point on the
surface, and therefore, the critical heat fluxqc″ will occur at the stagnation point. A
generalized critical heat flux correlation for forced convective cooling with
impinging jets was proposed by Monde et al. [13]. The correlation between the
critical heat flux of a subcooled impinging jet qc″,
and the predicted critical heat flux of a saturated impinging jet qco″,
is given by (3), (3)qc″qco″=1+1+4CJa2, where Ja is the Jacob number and C is a constant given by (4).
The applicable ranges of the given equation for subcooled impinging jet cooling
are a density ratio ρl/ρg
of 8.8~1605, a jet velocity u of 5~34 m/s, and subcooling ΔTsub of 0~115 K. Mitsutake and Monde
have
shown that (3) fits the data well for D/d ratios less than 5 [14],
(4)C=0.95(d/D)2(1+D/d)0.364(ρl/ρg)0.43(2σ/ρlu2(D−d))0.343. The predicted critical heat flux
with a saturated impinging jet is given in (5), (5)qcoρvhhgu=0.221(ρl/ρv)0.645(2σρlu2(D−d))0.343(1+D/d)−0.364, where ρv and ρl represent vapor and water density, hhg is the latent heat of vaporization, u is the jet velocity, and σ is the
surface tension of water.


## 3. Nozzle Design in the X-Ray Target

The wide-beam X-ray target is a cylindrical stationary target
made of oxygen-free copper with a thin layer of molybdenum which acts as the X-ray-generating
material [1]. Figure 1 illustrates the target design and its dimensions for a
prototype proof-of-principle system fabricated by Brand X-Ray, LLC, Wood Dale,
Ill, USA. Figure 2 shows the initial configuration of the jet nozzle.Figure 1
Wide-beam X-ray oxygen-free target with a layer of
molybdenum [1].Figure 2
Configuration of the impinging jet nozzle.The convective heat transfer coefficient can be found from
the Martin correlation (1). Based on the Reynolds number range for the
correlation, the fluid velocity is between 0.2 m/sec and 33 m/sec, which is
adequate for the proposed application. For a 1 m/sec inlet velocity, the
Reynolds number varies from about 2 300 to 5 300 for values of d between 2.4 mm and 5.6 mm. The convective heat transfer
coefficient as a function of S/d and D/d is shown in Figure 3. The convective
heat transfer coefficient increases with the decrease in the S/d ratio. At any given S/d, the heat transfer coefficient also
increases with the decrease in the D/d ratio. The diameter of the impingement surface D is fixed as the target diameter. As the Martin correlation has a
lower limit on the D/d ratio of 5,
this sets the optimum nozzle diameter, which in turn sets the optimum nozzle to
target spacing. The optimized design is shown in Figure 4 with dimensions that
correspond to an S/d ratio of 1.8 and D/d ratio of 5.15.Figure 3
Convective heat transfer coefficient as a function
ofS/d for various values of D/d.Figure 4
Optimized jet nozzle design (units: mm).


### 3.1. Equivalent Beam Current

The proof of principle target is designed to operate at the
same heat flux as the industrial scale target. To provide the necessary photon
flux for practical clinical or industrial screening applications, it has been
shown to require power levels of 180 kW on the target for beam currents at 3A
and an accelerating potential of −60 kVp [15]. For an industrial scale target area
of 100 cm2, this implies an inward heat flux on the target of 1.8×107 W/m2. As the proof of principle target is designed to
have a surface area of 10 cm2, the target heat flux can be obtained
using an order of magnitude less beam current of 300 mA.


## 3.1. Equivalent Beam Current

The proof of principle target is designed to operate at the
same heat flux as the industrial scale target. To provide the necessary photon
flux for practical clinical or industrial screening applications, it has been
shown to require power levels of 180 kW on the target for beam currents at 3A
and an accelerating potential of −60 kVp [15]. For an industrial scale target area
of 100 cm2, this implies an inward heat flux on the target of 1.8×107 W/m2. As the proof of principle target is designed to
have a surface area of 10 cm2, the target heat flux can be obtained
using an order of magnitude less beam current of 300 mA.


## 4. Simulation Results and Discussion

Simulation of target performance was performed using the
finite element code ANSYS CFX. The initial designs for the target, the jet
nozzle, and the fluid volumes were created with the CAD tool Solidworks [16].
The input mesh file for ANSYS CFX was generated by the meshing tool ICEM CFD [17].
The transient k-ϵ turbulent flow model was used to model the fluid behavior.
Room temperature water was chosen as the coolant.Room temperature water with a uniform velocity distribution
was assumed at the inlet to the back of the nozzle. The initial target
temperature was also assumed to be at room temperature. The target face is
assumed to be subject to a uniform inward heat flux of1.8×107 W/m2.
In reality, the inward heat flux resulting from the incident electron
distribution on the target is not uniform. However, studies have shown that the
electron trajectories can be controlled to produce a near uniform distribution
[18]. The target's outer surface is considered thermally insulated and
radiative losses are neglected. Solid-to-fluid and fluid-to-solid interface
boundary conditions were applied to the target body-coolant interface and the
coolant-jet nozzle interface in this simulation. The coolant channel is assumed
to operate at atmospheric pressure. Inlet velocities were examined between 1 m/sec and 9 m/sec. Figure 5 shows the ANSYS CFX simulation results for an inlet
velocity of 5 m/sec at 20 seconds, and a 300 mA electron beam current.ANSYS CFX results at 20 seconds (inlet velocity: 5 m/sec, beam current 300 mA).
(a)
Velocity streamline(b)
Total temperature of coolant(c)
Pressure of coolant(d)
Temperature of coolant and bodyFigure5(a) shows the fluid velocity stream lines. The inlet
fluid velocity is 5 m/sec and increases up to 27 m/sec at the nozzle exit.
Figure 5(b) shows the fluid temperature. The fluid temperature remains constant
at the inlet value until impinging upon the target surface. After hitting the
target surface, the fluid temperature increases and exits the rear of the target.
A single jet nozzle produces a stagnation point at the impinging surface. The
stagnation point is shown as bright green in Figure 5(c). The temperature
distribution through the target body and the fluid is shown in Figure 5(d). The
maximum temperature at the heated surface is 717 K.The design of the impinging jet cooling system must satisfy
two conditions: the maximum target temperature must be below the melting point,
and the inward heat flux must be below the critical heat flux. In this target
design, the target body is made of oxygen-free copper with a thin layer of
molybdenum serving as the X-ray source. The melting points of molybdenum and copper are 2896 K and 1356 K, respectively, and hence the copper melting point
is considered as the temperature limit. Figure6 shows the maximum target
temperature as a function of time for inlet water velocities of 3, 5, and 7 m/s. It is clear that increasing the coolant velocity decreases the target
temperature. For example, increasing the coolant velocity from 3 to 7 m/s drops
the maximum target temperature from 820 K to 650 K. But, the maximum target
temperature exceeds the melting point of copper in 2 seconds at the inlet
velocity of 2 m/sec. Figure 7 shows the coolant temperature at the stagnation
point for the same three inlet velocities. Increasing the coolant inlet
velocity also decreases the coolant temperature. For example, increasing the
velocity from 3 to 7 m/s reduces the maximum coolant temperature from 318 K to
305 K. The critical heat flux depends on the coolant velocity at the nozzle and
the temperature at the stagnation point. Figure 8 shows the predicted critical
heat flux as a function of the coolant inlet velocity, where it is obvious that
the critical heat flux increases with increased velocity.Figure 6
Maximum target temperature as a function of time for 3 different coolant
inlet velocities (300 mA beam current).Figure 7
Coolant temperature at the stagnation point as a function of time for 3
different coolant inlet velocities (300 mA beam current).Figure 8
Critical heat flux as a function of the coolant inlet velocity.As seen from Figures6, 7, and 8, the maximum target body
temperature is reached in 2 seconds for all tested inlet velocities. In case of
the 3 m/sec inlet velocity, the maximum temperature is 829.17 K. The critical
heat flux at the same inlet velocity is computed to be 3.78×107 W/m2.
For an incident heat flux of 1.8×107 W/m2, it can be
inferred that boiling transition will not occur for a coolant inlet velocity of
3 m/sec. The calculations show that the minimum inlet velocity should be higher
then 1.5 m/s to avoid boiling transition, but the inlet velocity should be
higher than 2 m/sec
to keep the target temperature below the melting point of copper.


## 5. Conclusion

Target cooling in the wide-beam X-ray source is a major
design consideration due to the use of high beam current as compared to
conventional X-ray sources. Passive cooling or rotating target geometry is not
feasible for this wide-beam source design, and therefore, an active cooling
system is required to satisfy the minimum operation time of about 20 seconds
for a successful DEI scan. Previous studies of target cooling by liquid
nitrogen-cooled cold fingers determined that cooling by conduction cannot
provide better than 4 seconds operation with a 300 mA beam current [15], which
is not sufficient to obtain the required DEI scan.In this study, an active cooling system is proposed based
upon an impinging water jet at atmospheric pressure. The prototype target design
has been simulated using the finite element code ANSYS CFX. The simulations
were performed with uniform inward heat flux and varying nozzle inlet velocity.
Simulation results have shown that impinging jet cooling, with coolant inlet
velocities in excess of 2 m/sec, allows for steady-state operation while
satisfying all thermal design constraints.



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*Source: 797068-2009-02-08.xml*