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DOE OSTI2026

Modeling Flow in a Microreactor Core: From High-Fidelity CFD to Subchannel Analysis

The accurate prediction of pressure drop in tightly packed, low–Reynolds number (Re) bare rod bundles is essential for the thermal-hydraulic design of the Microreactor Applications Research Validation and EvaLuation (MARVEL) reactor and other microreactor concepts. However, existing friction factor correlations, particularly the upgraded Cheng-Todreas (UCTD) correlation, have limited validation for the small pitch-to-diameter ratios (P/Ds) and transitional flow conditions characteristic of these systems. In this work, we perform high-fidelity large-eddy simulations (LESs) of both an infinite bare rod bundle and a finite bare 37-pin scalloped rod bundle across the range 1000≤ 𝑅𝑒 ≤5500. The simulations reveal strong gap vortex–driven transitional behavior and indicate that the UCTD may underpredict the friction factor by up to 28% at 𝑃/𝐷 = 1.05. Using the LES-calculated pressure drops, we formulate a new friction factor correlation that follows the Cheng-Todreas functional form but is calibrated for low-Re and tightly packed geometries representative of a MARVEL-like reactor. The correlation is implemented in the MOOSE (Multiphysics Object-Oriented Simulation Environment) subchannel module and compared against both the LES and UCTD predictions. Across all subchannel types, the proposed model reduces the streamwise velocity differences from as high as 44% (UCTD) to below 9%, and decreases the pressure gradient differences from 13% to 25% (UCTD) to 0.7% to 7% relative to the LES results. These results suggest that the new correlation has the potential to improve the pressure drop and flow field predictions for such geometries, highlighting the importance of high-fidelity simulations in supporting microreactor thermal-hydraulic model development and motivating future pressure drop experiments for compact rod bundles to further validate these findings.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2023

Optimization of Dimensions of Smooth and Twisted-Tape-Inserted Tubes for Heat Transfer with NaCl/KCl/MgCl 2 Molten Salts by Principle of Entropy Generation Minimization

The entropy generation minimization principle is used as the criterion to optimize the flow and heat transfer of solar collectors and heat exchangers that use molten salts NaCl–KCl–MgCl 2 and KCl–MgCl 2 . The Gnielinski correlation for the Nusselt number versus Reynolds number, as well as the Moody friction factor given by Petukhov, was used for the calculation of the convective heat transfer coefficient and pressure loss due to friction in smooth tubes. For twisted-tap-inserted tube, equations of Nu and friction factor provided by Manglik and Bergles were used. The objective function, the entropy generation rate of the heat transfer system, was expressed as the function of Reynolds number, Prandtl number, heating flux, tube diameter, etc. As a result of the analysis, the optimum Reynolds number was determined and thereby to determine the optimum Nusselt number, convective heat transfer coefficient, friction factor, and tube diameter, which also allows the calculation of optimum flow velocity. The analysis was conducted in the fluid temperature range of 500–700 °C, which covers the operation temperature for supercritical CO 2 power cycles in concentrated solar power (CSP) system. Here, optimized results from the smooth tube and twisted-tap-inserted tube are compared, which is important to the design of solar receivers for CSP systems.

14 SOLAR ENERGY↗

DOE OSTI2022

Measurement of Convective Heat Transfer Coefficients with Supercritical CO2 in Novel Additively Manufactured Helically Patterned Pin Fin Tubes Using the Wilson Plot Technique

This paper describes the measurement of convective heat transfer coefficients and friction factors for sCO2 flowing in pin-fin patterned pipes in the Heat Exchange and Experimental Testing (HEET) facility at the US DoE’s National Energy Technology Laboratory (NETL) in Morgantown, WV. The measurement procedures in the HEET rig were validated by conducting benchmark tests with smooth stainless-steel tube and comparing the results with published correlations for Nusselt number (Nu) and friction factor. Over typical Reynolds number range in sCO2, the measured Nu and friction factors were within 7% of classical correlations for smooth tube flow.The candidate pin fin patterned pipes were additively manufactured (AM) at the Oak Ridge National Laboratory. The pins were circular or elliptical in cross-section. Pin length to diameter aspect ratios were 1.33 and 2, while the pin diameter to tube diameter ratio was 0.188 and 0.125. Tests were performed for ReD varying from 6.9×104 to 2.2×105 and at conditions equivalent to the low pressure outlet (8.69 MPa, 361 K) of the low temperature recuperator (LTR) in an indirect sCO2 power cycle. The Wilson plot technique was utilized to measure the bulk heat transfer coefficients.For the better performing design (tube A, pin length to tube diameter ratio: 1.33, pin diameter to tube diameter ratio: 0.188), the local heat transfer coefficient increased by 112% relative to the Dittus-Boelter correlation at the LTR low pressure outlet. This corresponded to a 282% increase in the product of the heat transfer coefficient and the surface area. Large pressure drops across the test articles were observed.

Searle, Matthew↗

NASA NTRS2005

Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation turbulence model is an effective approach for turbulence modeling in the near solid wall surface region of flow over a concave wall.

Wang, Chi R.↗

DOE OSTI2020

Measuring Heat Transfer Coefficients for Supercritical Carbon Dioxide Cycle Recuperators

This paper describes the measurement of convective heat transfer coefficients and friction factors for sCO 2 flowing in pin-fin patterned pipes at the US DoE’s National Energy Technology Laboratory (NETL) in Morgantown, WV. The measurement procedures were validated by conducting benchmark tests with smooth stainless-steel tube and comparing the results with published correlations for Nusselt number (𝑁𝑢) and friction factor. Over Reynolds numbers (Re D ) ranging from 5×104 to 2.5×105 , measured 𝑁𝑢 was within 5% of the Dittus-Boelter correlation and measured friction factors were within 5% of the McAdams correlation for smooth tube flow.

42 ENGINEERING↗

DOE OSTI2024

Optimization-Inspired Pin-Fin Array for Supercritical Carbon Dioxide Recuperator

Additively manufactured heat exchangers are one possible route to cost-effective sCO 2 power cycles. In this paper, experimental results are obtained for two helical pin fin tubes that were designed following parametric optimization of the fin array. Neither the numerical optimization nor the experimental testing have been previously reported in the literature. The two tube designs were, (1) the optimization inspired design, and (2) the optimization-inspired design with a fin diameter increased by a factor of 2. To characterize the print, the designs were scanned using X-ray computed tomography to measure feature sizes and heat transfer area. The optimization was conducted in a commercial, computational fluid dynamics code. The code solved the Reynolds Averaged Navier-Stokes (RANS) and energy equations with turbulence closure provided by the shear stress transport (SST) k-ω model. In the experiments, the Nusselt number augmentation was measured using the Wilson plot technique and the friction factor was determined with mass flow and pressure drop measurements. The experimental testing indicated that the optimization-inspired design had a friction factor that was four times less than the baseline tube design at equal Nusselt number. Additionally, the optimization-inspired design had a 14% improvement in Nusselt number, at equal friction factor, relative to the best performing computational fluid dynamics (CFD) trial points. Tube design (2), with the larger diameter pin fins, had similar performance, within experimental error, as the tube with the smaller diameter pin fins (1). Both tubes achieved overall fin array efficiencies near 1. A performance factor, V/V 0 , equal to the volume of the enhanced heat exchanger divided by the volume of the baseline (no-fins) heat exchanger, is recommended to quantify internal cooling performance. In conclusion, the experimental shell and tube heat exchanger, using the additively manufactured tube, is competitive with printed circuit heat exchangers in its pressure drop class and could be further improved by optimizing a shell-and-tube heat exchanger utilizing this heat transfer enhancement feature.

42 ENGINEERING↗

DOE OSTI2018

Universal scaling-law for flow resistance over canopies with complex morphology

Flow resistance caused by vegetation is a key parameter to properly assess flood management and river restoration. However, quantifying the friction factor or any of its alternative metrics, e.g. the drag coefficient, in canopies with complex geometry has proven elusive. We explore the effect of canopy morphology on vegetated channels flow structure and resistance by treating the canopy as a porous medium characterized by an effective permeability, a property that describes the ease with which water can flow through the canopy layer. We employ a two-domain model for flow over and within the canopy, which couples the log-law in the free layer to the Darcy-Brinkman equation in the vegetated layer. We validate the model analytical solutions for the average velocity profile within and above the canopy, the volumetric discharge and the friction factor against data collected across a wide range of canopy morphologies encountered in riverine systems. Results indicate agreement between model predictions and data for both simple and complex plant morphologies. For low submergence canopies, we find a universal scaling law that relates friction factor with canopy permeability and a rescaled bulk Reynolds number. This provides a valuable tool to assess habitats sustainability associated with hydro-dynamical conditions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Measurement of Convective Heat Transfer Coefficients With Supercritical CO 2 Using the Wilson-Plot Technique

This paper describes the measurement of convective heat transfer coefficients and friction factors for sCO 2 flowing in a smooth tube and compares the results with published correlations for validation. The paper also describes the Heat Exchange and Experimental Testing (HEET) rig recently designed and built at the U.S. Department of Energy’s (DoE’s) National Energy Technology Laboratory (NETL) in Morgantown, WV. Here, the Wilson-plot technique used for measuring the heat transfer coefficients is described along with the data reduction process. The Wilson-plot technique was chosen as the basis for the design of NETL’s HEET rig. Advantages of the Wilson-plot technique include the (1) ability to measure high convective heat transfer coefficients accurately, (2) ability to measure average heat transfer coefficient for complicated heat exchange geometries like those produced using additive manufacturing, (3) ability to measure heat transfer coefficients on both sides of a heat exchanger independently, and (4) simplicity of experimental setup. Capabilities of the HEET rig include pressure to 24 MPa (3500 psig), temperature to 538 °C (1000 °F), mass flow rate to 1.5 kg/s (3 lb/s), and Re to 500,000. The rig is designed to operate with pure CO 2 or a mixture of CO 2 and up to 10% N2 by volume to study the impact of gas mixtures typical of direct-fired sCO 2 power cycles on the convective heat transfer and pressure drop. Preliminary tests in the HEET rig were performed with smooth stainless-steel tube and pure CO 2 , and the results were compared with published correlations for Nusselt number (Nu) and friction factor. Over a Reynolds number (Re) range from 58,000 to 228,000, measured Nu was compared to predictions using the Dittus and Boelter equation (Kreith and Bohn, 1993, “Principles of Heat Transfer, West Publishing Company”) within 5% and measured friction factors were compared to predictions using the McAdams correlation (“McAdams, 1954, “Heat Transmission,” 3rd ed., McGraw Hill, New York)” for smooth tube to be within 5%.

42 ENGINEERING↗

DOE OSTI2025

A Colebrook equation for impinging radial wall jets

Here, in this study, we evaluate the skin coefficient of friction for steady turbulent radial wall jets across smooth and rough surfaces. Although the Colebrook equation has been used successfully for many decades to evaluate friction factors for flows through smooth and rough pipes, how roughness affects the skin friction coefficient for steady turbulent radial wall jets remains unclear. Here we explore a Colebrook-type equation for skin friction coefficients associated with single-phase turbulent radial wall jets arising from orthogonally impinging circular jets. The fully iterative solution, based on well-established concepts of turbulent wall-bounded flow, is presented along with a power-law approximation and a non-iterative approximation for the friction coefficient derived therefrom. We find the skin coefficient of friction defined on the peak radial velocity to be a function of position over rough but not smooth surfaces in contrast to pipe friction factors that remain independent of axial position. These results follow expected trends, explain prior heterogeneity in power-law expressions for the skin friction coefficient and have significant implications for the industrial use of jets in mixing vessels.

friction losses↗

DOE OSTI2024

Thermal and hydraulic performance of volumetrically heated triply periodic minimal surface heaters

Advanced heat transfer surfaces, mainly Triply Periodic Minimal Surfaces (TPMSs) have great potential to increase heat transfer performance over traditional heat transfer surfaces due to their tortuous flow path and higher surface area-volume ratio. The emergence of additive manufacturing of nuclear fuel motivates experimental investigation of such advanced geometries in the context of a nuclear reactor core. Here, this study employed a novel method to explore the performance of gyroid and diamond TPMS geometries. Volumetrically heated heaters were additively manufactured from conductive polymer filament, and airflow was used to simulate the convective heat transfer from the core within a nuclear reactor. The mass flow and volumetric generation rates were varied, local Nusselt number correlations were obtained using embedded thermocouples to measure the solid and fluid temperature, and friction factor correlations were developed using differential pressure measurements. The gyroid TPMS presented a friction factor 1.5 times higher than the diamond TPMS and 90 times that of the rod bundle. TPMS geometries showed Nusselt numbers 8–10 times higher than that of the rod bundle, also maintaining colder internal temperatures, which suggested that they could sustain 250–275 % higher power density than the rod bundle for a given centerline temperature. Hence, having the potential to greatly increase the safety margins and power output of a nuclear reactor core with similar volume.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRSDate not supplied

Comparison of Convective Heat Transfer Correlations and Their Application to NTP Reactors

This study analyzes various Nusselt number and friction factor correlations and applies them to a Small Nuclear Rocket Engine model with a Sinusoidal power distribution profile to understand their effects on the temperatures and pressures inside the reactor. A nodal thermal hydraulic solver was used to determine the fluid and channel surface temperatures while also incorporating variable fluid properties and channel roughness. The results showed that the considered friction factors could essentially be used interchangeably given that their difference affected the pressure by less than 1%. However, large variations in the tube surface temperature were obtained for the different Nusselt numbers while the fluid temperature distribution was forced to remain the same. Supersonic flow conditions presented by Maynard Taylor are investigated to serve as a baseline for how experimental errors can lead to uncertainties in the reported empirical correlations. Detailed experimental investigation is necessary to determine the Nusselt number correlation that will provide the best prediction of the thermal hydraulic performance inside the reactor fluid flow channels.

Nuclear Thermal Propulsion↗

DOE OSTI2026

Predicting roughness effects in additively manufactured coolant channels with helical enhancements

Additive manufacturing (AM) is a promising technique for fabrication of complex geometries such as those expected to be utilized in the blanket, first wall, and divertor. In the case of cooling, metallic AM may be exploited to embed geometric enhancements (ribs, rifling, etc.) to improve cooling performance. However, due to the roughness of these unfinished internal AM surfaces, prediction of thermal hydraulic performance in such channels is difficult. In this work, we consider a methodology for predicting pressure drop and heat transfer in AM channels containing helical enhancements (e.g. helical ribs, twisted tapes) that allows the incorporation of roughness data through conventional pipe flow correlations. This methodology is tested using experimental friction factor and heat transfer coefficient data from high-pressure helium coolant flow measurements in AM stainless steel tubes fabricated by laser powder bed fusion. Both a featureless AM tube and one containing helical ribs were considered alongside a conventionally manufactured smooth tube. The AM surface roughness is obtained by profilometry and used to predict an equivalent sand-grain roughness, with this equivalent roughness confirmed through AM featureless tube measurements. Under the proposed methodology, this roughness information is incorporated into predictions of friction factor and Nusselt number for the rifled tube. Furthermore, these predictions agree well with experimental data across a large range of Reynolds numbers, encouraging the use of this methodology for thermal hydraulic analysis of similar systems and design of future coolant channel geometries.

Additive manufacturing↗

NASA NTRS1971

Optimization of conical hydrostatic bearing for minimum friction.

Equations for the flow rate, load capacity, and friction torque for a conical hydrostatic bearing were developed. These equations were solved by a digital computer program to determine bearing configurations for minimum friction torque. Design curves are presented that show optimal bearing dimensions for minimum friction torque as a function of dimensionless flow rate for a range of dimensionless load capacity. Results are shown for both laminar and turbulent flow conditions. The results indicate that hydrostatic pocket friction is a significant portion of the total friction torque. However, the bearing dimensions for a minimum friction design are affected very little by inclusion of pocket friction in the analysis. For laminar flow the values of the outer-land radius ratio X3 and outer bearing radius ratio X4 did not change significantly with increasing friction factor. For turbulent flow, the outer bearing radius ratio X4 did not change with increasing friction factor; therefore the value determined for X4 in the laminar flow case is valid for all turbulent flows.

Nypan, L. J.↗

NASA NTRS1993

Oscillating flow and heat transfer in a channel with sudden cross section change

We have computationally examined oscillating flow (zero mean) between two parallel plates with a sudden change in cross section. The flow was assumed to be laminar incompressible with the inflow velocity uniform over the channel cross section but varying sinusoidally with time. The cases studied cover wide ranges of Re(sub max) (from 187.5 to 2000), Va (from 1 to 10.66), the expansion ratio (1:2 and 1:4) and A(sub r) (2 and 4). Also, three different geometric cases were discussed: (1) asymmetric expansion/contraction; (2) symmetric expansion/contraction; and (3) symmetric blunt body. For these oscillating flow conditions, the fluid undergoes sudden expansion in one-half of the cycle and sudden contraction inthe other half. The instantaneous friction factor, for some ranges of Re(sub max) and Va, deviated substantially from the steady-state friction factor for the same flow parameters. A region has been identified below which the flow is laminar quasi-steady. A videotape showing computer simulations of the oscillating flow demonstrates the usefulness of the current analyses in providing information on the transient hydraulic phenomena.

Ibrahim, Mounir↗

NASA NTRS1995

Numerical thermal analyses of heat exchangers for the stirling engine application

The Regenerator, Cooler and Heater for the NASA Space Power Research Engine (SPRE) have been analyzed in detail for laminar, incompressible and oscillatory flow conditions. Each component has been analyzed independently and in detail with the regenerator being modeled as two-parallel-plates channel with a solid wall. The ends of the channel are exposed to two reservoir maintained at different temperature thus providing an axial temperature gradient along the channel. The cooler and heater components have been modeled as circular pipes with isothermal walls. Two different types of thermal boundary conditions have been investigated for the cooler and heater, namely, symmetric and asymmetric temperature inflow. In symmetric temperature inflow the flow enters the channel with the same temperature in throughout the velocity cycle whereas, in asymmetric temperature inflow the flow enters with a different temperature in each half cycle. The study was conducted over a wide range of Maximum Reynolds number (RE(max) varying from 75 to 60000, Valensi number (Va) from 2.5 to 800, and relative amplitude of fluid displacement (A(sub r) from 0.357 to 1.34. A two dimensional Finite volume method based on the SIMPLE algorithm was used to solve the governing partial differential equations. Post processing programs were developed to effectively describe the heat transfer mechanism under oscillatory flows. The computer code was validated by comparing with existing analytical solutions for oscillating flows. The thermal field have been studied with the help of temperature contour and three dimensional plots. The instantaneous friction factor, wall heat flux and heat transfer coefficient have been examined. It has been concluded that in general, the frictional factor and heat transfer coefficient are higher under oscillatory flow conditions when the Valensi number is high. Also, the thermal efficiency decreases for lower A(r) values. Further, the usual steady state definition for the heat transfer coefficient does not seem to be valid.

Kannapareddy, Mohan Raj↗

DOE OSTI2022

Exploring the Effects of Guide Vane on Dimpled Cooling Channel of Gas Turbine Blade

Abstract The purpose of the current study is to find out the heat transfer and pressure drop phenomena of the cooling channel with dimples and guide vane and compare the results with the no guide vane dimpled cooling channel. The first leg of the cooling channel is 490 mm, and the second leg is 460 mm. The two legs relate to the 180 deg turn region. The guide vane was inserted at the bend region of the dimpled cooling channel. The study was conducted with two different guide vanes geometry at two different orientations, i.e., U-guide vane with protrusion and depression orientation and curve-guide vane with protrusion and depression orientations both experimentally and numerically. The numerical study was performed with the large eddy simulation method. The result shows that for both stationary and rotational motion, the U-guide vane with depression experiences the highest thermal performance. The friction factor is comparatively higher for curve-guide vane with protrusion under stationary motion. However, under rotation, the curve-protrusion guide encounters the highest friction factor, which is higher compared to the no guide vane cooling channel.

Energy & Fuels↗

NASA NTRS1993

Supersonic boundary-layer flow turbulence modeling

Baldwin-Lomax and kappa-epsilon turbulence models were modified for use in Navier-Stokes numerical computations of Mach 2.9 supersonic turbulent boundary layer flows along compression ramps. The computational results of Reynolds shear stress profiles were compared with experimental data. The Baldwin-Lomax model was modified to account for the Reynolds shear stress amplification within the flow field. A hybrid kappa-epsilon model with viscous sublayer turbulence treatment was constructed to predict the Reynolds shear stress profiles within the entire flow field. These modified turbulence models were effective for the computations of the surface pressure and the skin friction factor variations along an 8 deg ramp surface. The hybrid kappa-epsilon model could improve the predictions of the Reynolds shear stress profile and the skin friction factor near the corner of a 16 deg ramp.

Wang, Chi-Rong↗

NASA NTRS1987

SSME seal test program: Test results for smooth, hole-pattern and helically-grooved stators

All of the listed seals were tested in a liquid Halon test facility at high Reynolds numbers. In addition, a helically-grooved-stator seal was tested in an air seal facility. An analysis of the test results with comparisons to theoretical predictions supports the following conclusions: (1) For small seals, the Hirs' friction-factor model is more restricted than had been thought; (2) For smooth seals, predictions of stiffness and damping improve markedly as the radical clearance is reduced; (3) Friction-factor data for hole-pattern-seal stators frequently deviates from the Hirs model; (4) Predictions of stiffness and damping coefficients for hole-pattern-stator seals is generally reasonable; (5) Tests for the hole-pattern stators at reduced clearances show no clear optimum for hole-pattern seals with respect to either hole-area ratio or hole depth to minimum clearance ratios; (6) Tests of these hole-pattern stators show no significant advantage in net damping over smooth seals; (7) Tests of helically-grooved seal stators in Halon show reasonable agreement between theory and prediction for leakage and direct stiffness but poor agreement for the net damping coefficient.

Childs, Dara W.↗