A Thermo-Hydraulic Investigation of the Unprecedented TMRS Upper Neutron Spallation Target

Los Alamos National Laboratory (LANL) operates a national user facility that provides the greater scientific community with an intense source of spallation-produced protons and neutrons; spallation being the method by which bombarding a nucleus with high energy proton particles resulting in disintegration of the nucleus and subsequent ejection of neutrons [1]. LANL’s reputation as a world-renowned establishment for basic and applied neutron science is predicated on the longstanding success of the target–moderator–reflector system (TMRS) and the capability to deliver a wide array of energy-spectral distributions along a multitude of flight paths.

Although the service life has grown incrementally over the TMRS iterations, the in-service TMRS Mk. III is due for replacement in 2021 due to the confluence of radiation damage and an outdated design. The lifetime of the TMRS is limited by radiation damage to the tungsten targets, as the targets can only withstand 2500 mA*h of proton delivery. Given the historical duty cycles, this threshold will be crossed sometime in 2021.

Further effectuating replacement is the increased demand for neutrons in the keV-MeV range; the keV-MeV regime is paramount for basic and applied nuclear science as related to neutron capture and resonance total cross-section measurements [2]. Recognizing such an improvement in neutronic performance is only possible with a redesign of the TMRS. The nascent water-cooled upper target represents the culmination of the analytical design procedure. While high-performance computing and finite element analysis (FEA) tools are indeed powerful, the reliability and robustness of a target inaccessible for up to a decade warranted empirical investigation.

Governing the design was the criteria that the beam is assumed in an off-normal, overpowered configuration. In essence, a dually worst-case scenario with the prescribed cooling of the tpper target is now of concern. The purpose of this effort was to assess whether the computational cooling results, around which the target housing was designed, agree with experimental results. By designing and instrumenting a flow loop capable of replicating flow conditions of the upper target, three aspects of the upper target are slated for definition: deformation under pressure, the magnitude of critical fluid velocities, and the characteristic heat transfer coefficient (HTC).

Assuming the deformation under pressure conforms to analysis, the absence of flow maldistribution can be concluded. Meanwhile, observation of paramount velocities insinuates satisfaction with cooling requirements. Finally, the nonexistence of flow boiling can be confirmed in explicitly determining the HTC in the vicinity of beam impingement.

Heavy metals are predominately utilized as the impinged-upon nuclei for spallation, as neutron yield increases with the mass of the targeted nucleus [3]. Thus, tungsten has been the target heavy metal of choice since the inception of the TMRS in 1985 [4]. The TMRS Mk. III houses two tungsten targets, six neutron moderators, and a composite reflector perforated with cooling water passages [5]. The positional stratification of the two targets delineates the system into an upper and a lower portion.

The fourth-generation TMRS, the Mk. IV, is currently targeting an installation date of the 2021 beam maintenance period. To a large degree, the Mk. IV mimics the Mk. III with slight moderator alterations to increase flexibility from an operational perspective. By far, the most discernable difference between the apparatuses is the incorporation of the new upper target, thereby propagating a downward shift of the previous generation targets (Fig. 1).

The new upper target was originally to comprise a single disk, turned on edge so that the proton beam struck the circumferential edge. Upon analysis, the heat deposition inherent to a single target prompted flow boiling; flow boiling is the evaporation of a working fluid in the presence of bulk fluid flow. Two additional disks, albeit slightly smaller in diameter (9.812 cm vs. 10.16 cm), were thus incorporated to straddle the original disk.

Inconel 718 was selected as the housing material, with the nickel-based superalloy demonstrating strength retainment at temperatures exceeding 650 °C. Examining the left-most image in Fig. 2, one can see the target possesses two independent channels denoted by “1” and “2.” Cooling water enters the first channel on the disk side through the elevated tube in the right-most image in Fig. 2. Water then flows horizontally across and over the tungsten targets and then loops back through the second channel and out the same manifold. The first and second channels are referred to as the target side and emission side, respectively. The emission side serves as an integral downstream water volume to effectively moderate the neutrons.

Figure 3 portrays the target and manifolds in an exploded view. While both manifolds direct flow and are eventually electron beam welded into place, the two manifolds are differentiated by the left-hand side manifold serving as the inlet and outlet; however, the right-hand manifold supports the tungsten-disk holder. One may notice the inlet/outlet manifold possesses a “tab” perpendicular to the body. This feature directs the incoming cooling water towards the highly heated upper portion of the disks.

As required by the physics design, the external Inconel walls on the target and emission side are extremely thin: 2.159 mm and 0.762 mm, respectively. Found within the  Appendix, Drawing 144Y620856 Section A-A illustrates this phenomenon. To compensate for the thermal-mechanical loading, 6.35-mm beryllium strong backs are employed to offset the deformation without overly deteriorating neutron transmission. Figure 3 portrays the beryllium strongbacks in grey on either side of the target housing body.

A closed-water flow loop was constructed, capable of reproducing the flow parameters intrinsic to the TMRS Mk. IV. To recreate the flow criteria and provide appropriate experimental diagnostics, a host of thermocouples, pressure transducers, and flowmeters were employed. Parameters in need of replication include maintaining water at 21.85 °C, a flowrate of 75.708 lpm, and a pressure of 0.689 MPa (Fig. 4).

An index of the flow loop instrumentation hardware is found in Table 1, with percentage accuracies relative to the magnitude of the measured value on a 95% confidence interval. All five thermocouples and the flowmeter relayed to a 16-channel, 24-bit National Instruments (NI) 9213 input module with 0.02 °C measurement sensitivity [6]. Meanwhile, a 24-bit NI 9208 input module processed pressure signals, differential or otherwise. These input modules populated the slots of an embedded National Instruments CompactRIO controller, featuring a field-programmable gate array managed by real-time, in-house control software known as Experimental Physics and Industrial Control System: EPICS.

To attain a circulating pressure of 0.689 MPa, a compressed nitrogen cylinder pressurized liquid water contained in a pressure vessel identified as the reservoir in the P&ID. Hypothesizing regulator failure and a subsequent flowrate of approximately 0.0533 m³/s, inclusion of a pressure relief valve (PRV) was warranted. Appropriately sizing the PRV required the development of a maximum allowable working pressure (MAWP) for the entire system. All of the Swagelok, Grainger fittings, and stainless-steel tubing incorporated into the flow loop possessed published pressure ratings, leaving only the working pressure of the target unknown.

An ANSYS analysis ascertained the volumetric heating behavior of the target. LANL performed independent testing to generate Inconel 718 strength curves at various temperatures. Conflating the volumetric heating behavior and the strength testing, one estimated the allowable stress for the target. Following the ASME Boiler and Pressure Vessel Code, Section II, Part D,  Appendix, the allowable stress is defined as the lesser of 2/3σ_y or σ_UTS/3.5; σ_y and σ_UTS are yield strength and ultimate tensile strength, respectively. The design allowable stress was 230 MPa at the ANSYS-determined peak temperature.

Proceeding to the FEA stress, the ASME Boiler and Pressure Vessel Code Section VIII, Part 5, details the design-by-analysis methodology: “When continuum elements are used in a structural analysis, the total stress distribution is obtained. Therefore, to produce membrane and bending stresses for comparison to allowable stresses, the total stress distribution will need to be linearized to arrive at equivalent membrane and bending stresses.” Linearized stress locations were identified based on the likelihood of failure, with E-1 realizing a maximum combined membrane and bending stress of 157.75 MPa as depicted in Fig. 5.

Considering the limits of equivalent stress, the ASME Boiler and Pressure Vessel code applies a coefficient of 1.5 to the design allowable stress. Therefore, the resultant membrane and bending stress were compared relative to the design allowable stress multiplied by 1.5, or 345 MPa in this instance. Exploiting the design allowable stresses adherence to the linear elastic regime, one extrapolated by formulating a ratio between the combined membrane and bending stress, the corresponding pressure, and the design allowable stress to estimate the MAWP. With a MAWP of approximately 1.551 MPa, the target itself represented the limiting component in the system. Pressure relief valves and an accompanying restricted flow orifice were sized and located accordingly.

To compensate for the pressure losses within the loop, an in-line pump was included. Attempting to repurpose a pump already in possession, a Grundfos CM5-3 centrifugal pump was integrated. Valves V-101, V-106, and V-107 provided the necessary refinement via bypass to emulate the exact pressure and flowrate parameters of the TMRS Mk. IV. An external Neslab HX-200 series chiller connected the supply and return lines associated with the plate heat exchanger and instrumentation labeled in the 200s.

Static pressure testing of the housing assembly with beryllium strongbacks was undertaken to assure conformity with the ANSYS FEA, as structural behavior is intrinsic to the cooling design. Without a well-defined coefficient of friction for the beryllium and Inconel interface, a value identical to that of steel on steel, 0.85, was assumed. A press-fit condition was enforced across the same interface, consistent with geometric dimensioning and tolerancing.

Exposed to a purely mechanical load of 1.034 MPa, the FEA model predicted a maximum deformation of approximately 0.203 mm. This maximum deformation was predicted on the emission side, at the geometric center of the beryllium strongback as seen in Fig. 6. Note 1.034 MPa is the pressure of interest as the ASME Boiler and Pressure Vessel Code Section VIII Division 1 dictate a proof pressure check of 150% of operating pressure. Recall drawing 144Y620856 Section A-A found within the  Appendix; the 0.762 mm wall on the emission side transitions to 1.499 mm at the final point of tangency between the Inconel housing and beryllium strongback. This transition affected the displacement of the beryllium, as the Inconel super-imposed the pressure distribution upon the beryllium.

Peak deformation at the geometric center of the emission side was recorded at 1.499 mm, 7.4 times larger than expected. To holistically characterize the deformation on the emission and target side, individual measurements were made uniformly across the surface of the beryllium strongbacks. The recorded displacements on the emission and target side are depicted as contour plots in Figs. 7 and 8, respectively. Continuity was maintained in the numbering system, with 1 being closest to the inlet/outlet manifold for both the emission and target sides.

The permanent set was confirmed in both the Inconel and beryllium by juxtaposition of pre- and post-measurement of said components. The absence of a press fit was evident as the deformation of the Inconel exceeded that of the beryllium by 0.737 mm at the point of maximum deformation. In essence, the beryllium inhibited advance of the thin Inconel wall, but only after the Inconel had displaced sufficiently to meet the beryllium.

In subjecting the target to 1.034 MPa, the FEA failed to forecast the true deformation. The FEA methodology was incorrect as Figs. 7 and 8 demonstrate iso-surfaces more vertical in nature than elliptical. That is not to say that elliptical deformation on the housing is completely non-existent, but rather simple beam behavior dominated. The press-fit constraint was unsubstantiated, and the Inconel housing accommodated pivoting of beryllium strongbacks at the extremes.

To provide resolve, the ansys structural analysis was revisited. By manipulating the frictional contact formulation, the detection method, and the low friction coefficient, the measured displacement was recreated. As mentioned, the coefficient of friction between beryllium and Inconel 718 is not well documented. A parametric study on the coefficient of friction revealed that a value of 0.2 mirrored physical behavior. Examining the updated analysis in Fig. 9, the deformation contour plot is now elliptical on the housing and principally vertically oriented on the beryllium, in agreement with empirical behavior.

There are significant ramifications of the unforeseen magnitude of deformation. Permanent distortion in the target side affected the geometry of the cooling channels nearest the targets. Recall the upper portion of the disks experience elevated volumetric heating due to greater beam incidence, with water flowing adequately over the top of the disks for cooling purposes under preliminary FEA deflection results. However, the cooling capacity in this localized area is now suspect due to geometry alteration. Finally, the behavior of the distortion suggests that the Inconel and beryllium never achieved a press fit, thereby further delegitimizing the simulated cooling results which surmised thermal contact.

Another objective of this experimental investigation was flow visualization, implicitly satisfying cooling requirements by confirming adherence to the computational fluid dynamics (CFD) velocimetry. Recollect that the flow is parametrized by a pressure of 0.689 MPa and a mass and volumetric flowrate of 1.258 kg/s and 75.708 lpm, respectively. The primary concern was to avoid flow boiling in the vicinity of the targets, especially where subject to initial contact by the beam. Temperature attenuation is achieved by the inclusion of the aforementioned “flow tab” on the inlet/outlet manifold, which modulates velocity in that area.

Midplane vector plots of the steady-state CFD solutions can be seen in Fig. 10. The commercial CFD tool used to model the turbulent flow was ansys cfx 2019 R1, running a Reynolds average Navier–Stokes simulation with a shear stress transport (SST) turbulence closure model inherent. The SST turbulence closure model not only overcomes the shortfalls of the k–ɛ, and k–ω models but also models near-wall vorticity/turbulence exceptionally well.

To further demarcate flow characteristics such as pressure drop, separation, recirculation, shear effects, and heat transfer, one had to elucidate the velocity profile near the wall. With wall conditions often predictable, wall functions were employed to determine near-wall profiles in favor of computationally intensive mesh resolution.

An aluminum mock-up was designed and machined, replicating the internal geometry of the upper target with windows on the target side for perspective. With specific areas and velocities of interest, a high-speed, monochromatic, 1.3-megapixel Mini UX50 Photron camera was coupled with a 55-mm Nikon microlens. At a full resolution of 1280 × 1040, the Mini UX50 is capable of capturing images at 2000 frames per second (fps). Compromising the horizontal resolution, one can increase the frame rate to a maximum of 160,000 fps [11]. A light-emitting diode (LED) assembly featuring a fiber light sheet was repurposed to provide volume illumination.

The camera came integrated with Photron Fastcam Analysis (PFA) software, capable of mapping component-specific velocities. Devoid of any filtering, PFA calculates velocities by tracking particles frame by frame in the presence of a fiducial marker and a known fps rate. The template matching method was the tracking technique of choice as this method permits inter-frame prediction to more accurately follow the particle. This method is only permissible assuming the particle’s shape remains unchanged as the initial shape constitutes the template. Conscious of parallax error, the camera lens was oriented perpendicular to the image plane and depth of field was minimized.

Difficulties in forming a uniform particulate solution led to entrapped bubbles replacing more traditional particle media. There are a number of foreseeable issues with entrapped air that can inadvertently affect dynamics and quantitative results if left unaccounted for. Volume fractions were kept moderately low to avoid phenomenon such as coalescence and breakup [12]. Bubble size was minimized to achieve a Stokes number in the vicinity of unity, whereby the time scale of the particle pales in comparison to that of the flow; bubbles thus behaving as particles and mostly following fluid streamlines [13]. Conversely, bubbles were tracked that possessed a Froude number in excess of unity. By exceeding unity, inertial forces dominate buoyant forces and ensure particle-like behavior [14]. Finally, velocities were derived from the average of a number of individual particles for the sake of thoroughness (Fig. 11).

The primary objective was to qualitatively confirm the ansys CFD results, with a secondary emphasis on quantitative results. These results initially deemed target cooling adequate when coupled with the Monte Carlo N-Particle Transport Code (MCNP) heating loads. In summary, empirical results were in excellent agreement with the FEA solution. Proceeding right to left across the target, Fig. 12 portrays the inlet with the flow tab directing cooling water toward the upper portion of the disks. Note that individual bubble resolution, or lack thereof, is indicative of velocity. Hence, one recognizes dead zones above and below the flow tab consonant with the CFD solution.

Immediately below the disk holder framework, the flow behaves as seen in Fig. 13. This behavior is mirrored precisely in ansys. On the right-hand side of Fig. 13, one sees the extension of the diffuse dead zone existing beneath the flow tab. Following initial contact with the disks and holder framework, a portion of the high-velocity fluid is diverted vertically downward and delimits the dead zone. Still possessing momentum following separation from the disk holder framework, the fluid contacts the bottom of the target and separates into opposing horizontal flows. Note the emanation of a small-scale turbulent eddy on the bottom left-hand side of the figure, directly beneath the disk holder structure.

The corresponding position on the upper half of the target is depicted in Fig. 14. Observation once again concurs with simulated results. An analogous quiescent zone consumes the right-most area of the figure. Phenomena such as the separation streamline and recirculating wake are much more pronounced in Fig. 14 relative to Fig. 13, due to the elevated Reynolds number of the former. Finally, while separation can occur from a stream-wise pressure increase, the target’s behavior is due to a radius of curvature effect whereby the fluid is unable to follow the drastic change in the contour of the disk holder [15].

Quantitative validity of the analysis was verified between the disks due to the integral nature, with the CFD velocity in the vicinity of 3–4 m/s. Congruently, experimentally observed velocities average 3.4 m/s between the disks as seen in the latter half of Fig. 15. Three particles were tracked, with mean Stokes and Froude numbers of 4.3 and 2400, respectively. While the Stokes number does exceed unity, the margin is small such that the particle is still representative of the flow; there is also no evidence of detachment from the flow as is associated with elevated Stokes numbers. From the Froude number, one is certain inertial forces are predominant.

The software consistently lost the trajectory of the particles at each’s left-most extent, as adduced by the erratic trace lines. Ensuing dissonance in velocity was omitted from the aggregate.

With flow boiling directly beneath beam incidence of primary concern, elevated velocities in this region were a design requirement. Referring to the ansys analysis, velocities of approximately 5–6 m/s are present in the domain between the top of the disks and housing. Tabulated in the lower half of Fig. 16, empirical data indicate velocities in excess of 6 m/s. Two particles were tracked, with a mean Stokes and Froude number of 6.9 and 7500, respectively. Once again, the Stokes number exceeds unity but not significantly so as the order of magnitude is invariant.

Averaging the data across both particles to combat uncertainty, one arrives at a velocity consilient with the ANSYS solution: 5.9 m/s. While averaging allows for singular comparison to CFD results, the concave nature of the velocity profile is indicative of velocity and acceleration fluctuations in this region and is not to be ignored.

Internal flow correlations were utilized in conjunction with the flow visualization velocity results to estimate the HTC. Due to geometric complexity, a number of simplifying assumptions were necessary. Therefore, the goal was to glean the order of magnitude of the HTC as opposed to the true solution.

Calculating the target-side Reynolds number, one concludes the flow is likely turbulent with a Reynolds number of approximately 6000. A Reynolds number of 12,000 will also be carried through the succeeding calculations to bound the HTC as if the entire hydraulic diameter is at the elevated velocities atop the disks.

The flow was qualified as simultaneously developing. In the absence of a sufficient hydrodynamic entry length, the turbulent flow remains non-developed from a momentum standpoint as evidenced by transient velocities in Fig. 16. From a thermal perspective, the flow is also non-developed as the thermal boundary layer is subjected to inconsistent thermal boundary conditions in the form of beam heating.

To further characterize the turbulent flow regime for correlation-matching purposes, the influence of roughness was taken into account [16]. Based on the calculation of the roughness Reynolds number, Re_ɛ, the flow can be classified into one of three regimes depending on the variation of f with Re_ɛ and the relative roughness (ɛ/a)

(1) hydraulically smooth regime 0 ≤ Re_ɛ ≤ 5: f = f(Re)

(2) transition regime 5 ≤ Re_ɛ ≤ 70: f = f(ɛ/a,Re)

(3) completely rough regime Re_ɛ > 70: f = f(ɛ/a)

In calculating Eq. (2), a non-physical friction factor of 0.36 was required to exit the hydraulically smooth regime with a surface-roughness element height and a mean velocity based on empirical observation. Thus, one concludes the flow is within the hydraulically smooth regime without explicitly solving for the friction factor.

Recognizing that the friction factor in a turbulent flow is unrelated to the shape of the channel, the following analysis exploits correlations for circular ducts with the adjusted hydraulic diameter. Furthermore, the turbulent flow was assumed fully developed to produce an estimate of the HTC that is conservative in nature.

The lower limit of the HTC, resultant from operational volumetric flow conditions, is approximately 4000 W/m²-K. The upper limit of the HTC, based on the application of peak disk velocities found from observation, is approximately 10,500 W/m²-K.

Notwithstanding the inexactitudes from the simplifying assumptions, conclusions regarding the order of magnitude of the HTC were drawn. First, recollect that the assumption of a fully developed flow translates to an in-situ HTC greater than that calculated. The conclusion is straightforward; a HTC exceeding 4000 W/m²-K and, in all likelihood, on the order of 10⁴ was to be expected.

LANL chose to motivate the upper target design based on off-normal, unprecedented beam conditions. These conditions are characterized by a non-uniform, Gaussian beam with a 200 micro-amp apex-current and full-width half-max in the x and y directions of 10.148 mm and 24.308 mm, respectively. This particular beam configuration is truly a worst-case scenario, as neither the beam power nor the beam profile has ever been realized.

Mapping the MCNP housing heating loads back to the CFD model and solving, a depiction of the housing volumetric heating is generated as seen on the left side of Fig. 17. Integrating across the target, total housing power deposition tallies roughly 3.69 kW. Differentiating between volumetric heating and heat fluxes, a peak heat flux of 1.69e⁴ W/m² is attained atop the target side housing where the beam initially impinges. The volumetric heating manifests in a housing thermal profile as seen on the right side of Fig. 17. By reproducing the beam geometry and peak heat flux of the focused beam, derivation of an empirical HTC was achieved.

An induction heating assembly was purchased from GH Induction Atmospheres, featuring a 30-kW power supply designed to operate at either 50 or 150 kHz resonant frequency [19]. The user defines heating parameters through a programmable logical controller (PLC) on the power supply. One can operate the power supply in two different fashions via the PLC, either open-loop or closed-loop control. A pyrometer focused on the workpiece forms the closed-loop feedback control. Closed-loop control was utilized exclusively throughout the experimental procedure.

To monitor the power deposition of the induction coil onto the upper target, calorimetry of the internal cooling water was performed via two specialized thermistors that measure 3.175 mm in diameter by 228.6 mm long. These GEC S2TH Precision Thermistors were selected based on their meritorious accuracy and resolution, as collated in Table 2. Note that the listed system response times represent the respective maximum and minimum recording rates, with resolution sacrificed for response time. With the intention of recording data at steady-state conditions, the resolution was favored over response time.

Recalling from Fig. 17 that heat deposition is concentrated on the target side of the housing, the thermistors were positioned in the flow to measure the temperature difference over the length of the target chamber. One thermistor was instrumented in the influent piping, while the other was embedded at the delineation between the target and emission chambers. The target was encased with high-temperature insulation for adiabatic purposes.

A susceptor acts as an intermediate material, readily heated by induction while subsequently heating the actual workpiece by conduction. With high efficiencies and a synergistic concentration of flux lines inside the coil, a solenoid was chosen to encompass a cylindrical graphite susceptor. The inception of the susceptor design is portrayed in Fig. 18. In the right-most image of Fig. 18, one can visualize the characteristic filleted ellipse with the curvature of the housing imparted. The ellipse was truncated to account for the behavior in which the beam “spills” onto the housing wall as in Fig. 17. To establish the temperature of the housing, a slot measuring 0.508 mm in depth and width was machined along the highlighted blue line. This slot was to accommodate a 0.508-mm type-K thermocouple possessing specifications as listed in Table 1.

A parametric study was performed on a two-dimensional (2D) axisymmetric COMSOL model to ascertain the optimal coil/susceptor gap and number of windings. Scrutinizing the COMSOL model, one notices the development of a significant temperature gradient along the face of the boss. To more accurately evaluate this behavior, a SolidWorks model of the assembly was devised for thermal study. Arbitrary heat powers, resulting in arbitrary temperatures, were assigned to the longitudinal midplane of the susceptor to represent the effects of the induction coil. Most salient, the temperature stratification between the extremes of the susceptor ellipse and the location of the thermocouple became more pronounced at elevated levels of power.

Locating the susceptor was achieved by means of a stainless-steel plate affixed to the target via a threaded rod. Furthermore, a 0.127-mm sheet of Indium was placed between the susceptor boss and target. Melting at 156.6 °C, boiling at 2080 °C, and possessing a thermal conductivity of 81.8 W/m-K at room temperature, Indium becomes molten without boiling under operational conditions and offsets contact resistance (Fig. 19).

Steady-state data was taken at 50-deg intervals from 500 to 850 °C based on pyrometer measurement. Three data sets were recorded on the intervals from 500 to 700 °C, two back-to-back and the final point after each temperature interval had two sets of data documented. By recording data in such a manner, the validity of the experiment was assessed based on time-independent, repeatable results, or lack thereof. Two data sets were then recorded in succession on 50-deg intervals from 750 to 850 °C. By delaying measurements at elevated temperatures, the potential for graphite oxidation to confound recorded measurements was ameliorated.

Data relevant to the determination of the HTC are listed in Table 3. Note that the interface temperature is indicative of the thermocouple embedded in the boss and that data sets at a particular pyrometer temperature have been averaged. Flux represents the lone calculated values in Table 3. Power deduced from calorimetry was divided by the surface area of the radial susceptor boss (2.26 cm²) to calculate the flux. Observe that the peak heat flux was met and exceeded when the pyrometer set point was 850 °C.

To better calculate the HTC, three extraneous variables needed to be quantified: system power offset, apparent interface temperature, and the effects of radiation on power. To quantify the steady-state power offset, the flow loop was started and run uninterrupted by induction heating for approximately an hour. With a transient time of approximately 2 min, averaging nominal power output thereafter resulted in a value of −40.17 W. In recording steady-state data after 2 min has passed, one can apply the −40.17 W offset to the powers listed in Table 3.

To assure the interface thermocouple remained in place during experiment, the slot depth was cut to 0.508 mm. Ideally, the depth would have been 0.254 mm to better record the temperature of the Inconel/graphite interface. By rearranging the linear conduction model to solve for temperature, the true interface temperature is estimated by accounting for the temperature difference across the 0.254 mm too deep slot. Henceforth, this calculated temperature will be referred to as the adjusted interface temperature.

To quantify radiations effects on measured power, a piece of high-temperature insulation was situated between the susceptor boss and Inconel housing. Leaving the interface thermocouple embedded in the solidified Indium following from the previous induction heating, two sets of data were recorded and averaged on each pyrometer interval from 500 to 850 °C.

Assuming the outer wall temperature to be the interface thermocouple reading, and the inner wall temperature to be the bulk fluid temperature, the power conducted through the Inconel wall based on the linear conduction model was subtracted from the measured total power. The difference between these values is thus the approximate radiative heating at a given pyrometer temperature and is to be subtracted from the listed powers in Table 4. The exponential relationship demonstrated between radiative power and pyrometer temperature lent credence to this approach to refine the data.

Applying all three corrections to the data, an updated and condensed version of Table 3 is presented in Table 4.

Using the adjusted interface temperature, adjusted power, temperature-dependent conductivity, area of the susceptor, and Inconel wall thickness, one can calculate the internal wall temperature immediately below the susceptor by rearranging the equation for linear conduction. Proceeding from the internal wall temperature, one can then solve for the HTC by manipulation of the convective heat transfer formula.

These calculated results are presented in Table 5. The arithmetic mean of the HTCs found at every pyrometer temperature is 13,726.44 W/m²-K, with a standard deviation of 2730.

The calculated HTCs all exceed 4000 W/m²-K, and all instances are on the order of 10⁴ as predicted in the preceding flow visualization section. Furthermore, the internal wall temperature provided no indication of flow boiling as the saturation temperature of water at 0.689 MPa is 170 °C. Examining the adjusted fluxes, incorporation of the steady-state offset and heating due to radiation attenuates the empirical peak heat flux below the desired 169 W/cm². With a percentage difference of approximately 3%, failure to meet the peak heat flux is not especially concerning due to the relatively infinitesimal point nature of the MCNP-derived peak heat flux. While the peak heat flux is indeed 169 W/cm², this flux over the entire beam area is quixotic. As illustrated in Fig. 20, the actual beam is Gaussian such that averaging the power deposition across the susceptor boss results in the empirical power far exceeding the actual beam.

Plotting the power versus the interface temperature as in Fig. 21, one would expect a proportional relationship as a single-phase HTC is proportional to power over temperature. While the relationship is indeed proportional, the constant of proportionality is not equal to one. This departure from intuition is exacerbated by considering the HTC relative to the power, as the HTC decreases as the power increases.

While non-physical, these results are readily explained by the increased temperature gradient across the susceptor boss at elevated powers. As the temperature gradient increased, the interface thermocouple became decreasingly indicative of the average temperature over the entire area of conduction. Effectively, the interface thermocouple recorded apex temperatures as opposed to average temperatures. This discrepancy then propagates through the calculation of the HTC as one assumes the susceptor area is at a uniform temperature, culminating in a HTC that is artificially low at elevated powers. Therefore, stronger weight is to be attributed to the higher HTCs computed at lower powers; even further is the possibility of flow boiling avoided.

Error in the computation of the HTC arises due to propagation of uncertainty. At a pyrometer temperature of 850 °C, computing the HTC with uncertainty yields 11,775 ± 1931 W/m²-K. In conducting said computation, one realizes 93% of that uncertainty arises from the thermistors. Synoptically, predominate power determinations are resolved from minute temperature differences sensitive to the 0.002 °C accuracy of the thermistors. Hence, the magnitude of the HTC uncertainty increases as the temperature differential being resolved decreases.

For over three decades, the TMRS has been delivering neutrons via spallation to advance science in the national interest. The current in-service iteration of the TMRS is the TMRS Mk. III, which is scheduled for decommissioning in 2021 in favor of the TMRS Mk. IV. Underlying the ensuing evolution of the TMRS is the innovative and unprecedented water-cooled upper target, designed completely by analysis under a worst-case scenario: an incident beam off-normal in profile and overpowered. With the cooling of the target housing thus of concern, a complementary empirical investigation was undertaken to validate the computational cooling results. Three aspects were highlighted for quantification specifically: deformation under operational flow conditions, magnitude of critical fluid velocities, and the characteristic HTC.

Performing a static pressure test according to the ASME Boiler and Pressure Vessel Code Section VIII Division 1, a maximum displacement of 0.203 mm was expected on the emission side beryllium. Not only was the observed displacement an order of magnitude larger, 1.499 mm, but the contour of deformation was unforeseen. Revisiting the ansys analysis, the primary culprit proved to be the coefficient of friction was assumed in the absence of a well-documented Inconel-beryllium coefficient of friction. In permanently deforming the housing, the conclusion of ample cooling was uncertain due to altered geometry/flow.

A closed flow loop was fabricated with instrumentation to reproduce operational flow conditions in the TMRS Mk. IV. Qualitatively, the observed fluid dynamics agreed with the computational results. Quantitatively, critical fluid velocities such as exist directly below beam incidence exceeded expectations. Internal flow correlations in conjunction with the flow visualization velocimetry were then employed to estimate a HTC eclipsing 4000 W/m²-K in the aforementioned location.

A graphite susceptor with a boss analogous to the beam geometry was coupled to a solenoid coil to replicate a peak heat flux of 169 W/cm² to within 3%. On average over experimentation, the HTC at the point of beam impingement was 13,726.44 W/m²-K with a standard deviation of 2730. Even considering the individual HTCs intrinsic to the average, the conditions for the onset of flow boiling were never satisfied, in agreement with analysis. This empirical investigation affirmed the validity of the upper target design, adduced by sufficient cooling despite the focused beam and unforeseen displacements.

Prior to the TMRS Mk. IV’s installation in 2021, structural contingencies must be enacted in response to permanent deformations seen in the upper target upon static pressure testing. Moreover, explicit disk/target heating is necessary to experimentally verify if the tantalum-clad tungsten disks avoid thermal erosion given the current flow parameters.

The entirety of this work was financially supported by the National Nuclear Security Administration.

There are no conflicts of interest.

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.

f =

friction factor

T =

temperature

$f¯$ =

apparent friction factor

Nu =

Nusselt number

u_m =

mean velocity

u_t =

friction velocity

Re =

Reynolds number

Re_ɛ =

roughness Reynolds number

α =

thermal diffusivity

ΔT =

temperature differential

ɛ =

surface-roughness element height

µ =

dynamic viscosity

ν =

kinematic viscosity

σ_y =

yield strength

σ_UTS =

ultimate tensile strength