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DOE OSTI2018

Thermal modeling and efficiency of a dual-stage sodium heat engine

In this paper, a thermal design of an axisymmetric dual-stage sodium thermal electrochemical converter (Na-TEC) is presented, where a reduced-order finite-element model is used in conjunction with a Na-TEC thermodynamic model to determine the total parasitic heat loss of this dual-stage design. A number of simplifications are applied in the reduced-order model to decrease the computational time while maintaining acceptable accuracy. These include the use of effective thermal conductivities to account for complex corrugated geometries and apparent surface emissivities to accommodate the effect of radiation shields. Furthermore, a simplified analytical model is developed to account for conduction bypass through the Na-TEC liquid-return path. An iterative procedure between the finite-element and thermodynamic models is described in detail, and the thermal performance of the design proposed herein is analyzed. According to this analysis, a maximum efficiency of 29% and a maximum power output of 125 W can be achieved.

14 SOLAR ENERGY↗

DOE OSTI2021

A Comparative Study of Layer Heating and Continuous Heating Methods on Prediction Accuracy of Residual Stresses in Selective Laser Melted Tube Samples

Thermal distortion and residual stresses are two important factors that affect the quality and reliability of steel parts manufactured by laser powder bed fusion (LPBF) processes. A cost-effective model for evaluation of those heat effects is needed to refine the manufacturing process and provides insights into the product design and heat treatment. In this study, the layer heating method and sophisticated track-layer scanning method were applied to simulate the thermo-mechanical response of IN625 tube parts built by LPBF. Based on the similarity of temperature field in each layer deposit, a swept mesh was constructed to perform the thermal analysis for top layer, with the rest of layers referring to the temperature by node number offsetting. A novel explicit finite element analysis code accelerated by graphics processing unit was used for the massive-element numerical analysis. The computational accuracy and efficiency of the layer heating and track-layer scanning methods were compared in detail. It is shown that layer heating method can efficiently capture the pattern of stress distribution with reasonable accuracy in stress magnitude. The grouped track-layer scanning method can predict the residual stress and strain more accurately at a higher cost (5 ~ 10×). The elastic strain distribution was compared with the measurement by X-ray diffraction, confirming the accuracy of residual stress prediction.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Thermomechanical design optimization for low metal footprint in hybrid metal-polymer heat exchanger

Material and maintenance costs of metal-based heat exchangers surpass profits in waste heat recovery (WHR) from ultra-low temperature (<100C) sources [1]. A low-cost alternative like polymer pipes suffer from poor thermal conductivity (~0.2 W/mK), and a low overall heat transfer coefficient. Polymers’ thermal conductivity have previously been enhanced through systematic molecular alignment by stretching [2], chemical vapor deposition of extended polymers [3], surface grating [4], etc. However, these approaches suffer from scalability issues for WHR heat exchangers in terms of cost [3], and thermomechanical considerations [5]. In this work, we propose novel hybrid metal-polymer heat exchangers that are made from polymer-copper strips. Through finite element method (FEM) simulations, we first optimize the placement of copper around polymer strips to enhance the transverse thermal conductivity of the strips. The copper cladded polymer strips are wound helically in a roll-to-roll system to form the pipes for a heat exchanger. We then optimize the design of helically wound pipes to reduce thermomechanical strains to < 0.2 % at 100C and 40 psi working conditions. At 25 % volume fraction of copper in the pipe, we predict up to 20 % enhancement in overall heat transfer from a base polymer with a thermal conductivity of 0.2 W/mK. We also compare and contrast the thermomechanical performance of the optimized metal-polymer strips to random metal matrix composites. Finally, we experimentally verify the thermal conductivity of the optimized strips through bulk thermal conductivity and thermal interface resistance measurement setup. By systematically improving the design through FEM and experimental measurements, we provide an optimized design of hybrid metal-polymer pipes that provides a low metal footprint and cost-effective means for harvesting waste heat from ultra-low temperature sources. Thekdi, Arvind, and Sachin U. Nimbalkar. Oak Ridge National Lab, 2015 Shen, Sheng, et al. Nature nanotechnology 5.4 (2010): 251. Xu, Yanfei, et al. Science advances 4.3 (2018): 3031. Smith, M. K., Singh, V., Kalaitzidou, K., & Cola, B. A. (2015). ACS nano, 9(2), 1080-1088. Aymonier, C., Bortzmeyer, D., Thomann, R., & Mülhaupt, R. (2003). Chemistry of Materials, 15(25), 4874-4878.

C Rajagopal, Manjunath↗

DOE OSTI2016

High-order solution methods for grey discrete ordinates thermal radiative transfer

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Assessing the Impact of a Novel TBC Material on Heat Transfer in a Spark Ignition Engine through 3D CFD-FEA Co-Simulation Routine

Thermal barrier coatings (TBCs) have been of interest since the 1970s for application in internal combustion (IC) engines. Thin TBCs exhibit a temperature swing phenomenon wherein wall temperatures dynamically respond to the transient working-gas temperature throughout the engine cycle, thus reducing the temperature difference driving the heat transfer. Determining these varying wall temperatures is necessary to evaluate and study the effect of coatings on wall heat transfer. This study focuses on developing a 3D computational fluid dynamics (CFD)-finite element analysis (FEA) coupled simulation, or co-simulation, routine to determine the wall temperatures of a piston coated with a thin TBC layer subject to spark ignition combustion heat flux. A CONVERGE 3D-CFD model was used to simulate the combustion process in a single-cylinder, light-duty experimental spark ignition (SI) engine. Transient piston heat transfer analysis was conducted using ABAQUS, a FEA package, under the simulated combustion heat flux load. The effect of the temperature swing phenomenon due to this TBC layer was observed in a CFD simulation by implementing the FEA results as the piston thermal boundary conditions. The boundary conditions were passed between the CFD and FEA tools until a quasi-steady state solution was achieved. Furthermore, a reduction in wall heat transfer was observed due to a reduced temperature difference between the wall and the working gas.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

ADDITIVELY MANUFACTURED SURFACE HEAT TRANSFER ENHANCEMENTS FOR THE TRANSFORMATIONAL CHALLENGE REACTOR

The Transformational Challenge Reactor (TCR) is a high-temperature gas-cooled reactor design that uses additively manufactured fuel elements. TCR fuel elements have walls made of silicon carbide and are filled with tristructural-isotropic fuel particles. These fuel elements can have radically different shapes and integrated features than existing designs due to the reduced cost for complex structures in binder jet additive manufacturing. As such, binder jet additive manufacturing enables wall surface features to be embedded that can deliver superior heat transfer performance than smooth wall designs. In this work, the authors conducted a computational fluid dynamics study to evaluate selected wall features integrated into TCR fuel elements. Results show that surface features can outperform smooth wall designs; however, there are unique challenges for gas-cooled reactor core designs that have not been fully explored by previous research. For example, the rough surface finish and process variability of ceramics additive manufacturing make it challenging to predict surface roughness effects before fabrication. Additionally, the small hydraulic diameters of coolant channels in reactor cores make it difficult to engineer surface features that do not significantly increase the pressure drop. Engineers must carefully size surface features for heat transfer enhancement in additive fuel elements to operate above the base material's surface roughness effects and below the coolant channel size.

Weinmeister, Justin↗

NASA NTRS1992

Modeling of the WSTF frictional heating apparatus in high pressure systems

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

Skowlund, Christopher T.↗

DOE OSTI2015

Electric Motor Thermal Management R&D; NREL (National Renewable Energy Laboratory)

Thermal constraints place significant limitations on how electric motors ultimately perform. Without the ability to remove heat, the motor cannot operate without sacrificing performance, efficiency, and reliability. Finite element analysis and computational fluid dynamics modeling approaches are being increasingly utilized in the design and analysis of electric motors. As the models become more sophisticated, it is important to have detailed and accurate knowledge of both the passive thermal performance and the active cooling performance. In this work, we provide an overview of research characterizing both passive and active thermal elements related to electric motor thermal management. To better characterize the passive thermal performance, work is being performed to measure motor material thermal properties and thermal contact resistances. The active cooling performance of automatic transmission fluid (ATF) jets is also being measured to better understand the heat transfer coefficients of ATF impinging on motor copper windings.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Design Optimization of A-Type Heat Exchangers based on High Performance, Non-Round Tubes

Air-to-refrigerant heat exchangers (HXs) have been the topic of considerable research as they are the fundamental heat transfer components of HVAC&R systems. For residential and commercial applications, indoor heat exchangers are often in A-type configurations to reduce air-conditioner system footprint while still delivering the required cooling or heating. Classical HX design practices typically assume a uniform frontal air velocity profile to facilitate the use of conventional tube-fin airside heat transfer and pressure drop correlations for performance prediction. However, it is well-reported throughout the literature that A-type HXs experience significant airflow maldistribution which can severely degrade HX performance. Additionally, recent advancements in simulation software such as Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA) and optimization algorithms have led researchers to consider primary heat transfer surface optimization to achieve highly compact HXs which do not require fins. In this paper, an A-type HX which utilizes shape-optimized non-round tubes is optimized for minimum duct size and airside pressure drop. This is achieved through coupling of an experimentally validated finite volume HX model with automated 2D CFD simulations of airflow through the HX for airside thermal-hydraulic performance evaluation. Preliminary results show that the optimal designs deliver similar capacity while achieving 20% reductions in airside pressure drop and duct cross-section area. Additionally, the optimal design apex angles in this study were similar to those from previous A-Type HX optimization studies for conventional tube-fin HX geometries, suggesting that the apex angle for optimal A-Type configuration performance may be independent of tube geometry.

42 ENGINEERING↗

NASA NTRS1984

Testing and evaluation of Vespel up to 450 deg F when used in nuts and bolts as a self-locking element

The object of this investigation was to evaluate Vespel for potential application on the Solid Rocket Booster to replace all-metal deformed self-locking nuts and anchor nuts and be used as self-locking elements for bolts and screws. The Vespel self-locking elements were tested for prevailing torque retention at room temperature, after heating to 450 F and exposure for 3 hr, breakaway torque at 450 F and for vibration at a level consistent with the maximum expected on the SRB at lift-off and reentry. The investigation revealed Vespel has properties that can provide a self-locking capability for threaded fasteners up to 450 F and it can be used in nuts and anchor nuts for installation on the SRB. Vespel elements in bolts did not meet all our SRB requirements for reuse, however, we have defined a design for Vespel elements in nuts/anchor nuts that fully meets all requirements. It is recommended that No. 1, 1/4 in. and 5/16 in. nuts/anchor nuts be procured for use on the SRB. This system will eliminate the galling problems now encountered and achieve a much higher reuse life than the present deformed nut design.

Wood, C. M.↗

DOE OSTI2024

Operation and Security Considerations for Heat Pipe Cooled Microreactors

Microreactors and small modular reactors (SMRs) are anticipated to be key elements in the United States' carbon-free energy portfolio, serving as reliable power sources for remote communities, disaster relief zones, extraterrestrial deployments, and backup power needs. Microreactors employ technologies that are substantially more advanced and recent compared to conventional reactors. Furthermore, they are of a drastically smaller scale and are designed to be operated in a diverse set of locations, offering operational flexibility and mobility. In addition, the autonomous or semi-autonomous operation of microreactors with minimal or no on-site staff is anticipated. These factors give rise to specific challenges with regards to their safety and security. The present work investigates considerations related to heat pipe operation, reactor transport, and cyber/cyberphysical security to ensure the indirect and direct consequences of nefarious actors’ actions are understood and can be mitigated by design or through physical security measures. In addition, future directions are proposed for consideration by both HPMR designers and for regulators.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Single-Bubble Flow Boiling Phenomena - Interface Tracking Simulation

Boiling, as one of the most efficient heat transfer mechanisms, is widely used in various engineering systems. Better understanding and modeling of this process remains a major challenge in multiphase flow research. The distribution of vapor in boiling system affects the heat transfer rate and may cause unfavorable conditions, such as heater burn-out. A number of flow regimes have been observed experimentally. In general, there are three regimes under boiling conditions: nucleate boiling, transition boiling, and film boiling. The nucleate boiling regime is categorized into partial boiling regime and fully developed nucleate boiling, according to behavior of bubble dynamics and heat transfer characteristics. In the first region, as the wall temperature increases, the fraction of the wall surface subject to nucleate boiling increases until bubble formation occupies the entire heated surface. Heat transfer in this region is a complex mixture of single-phase forced convection and nucleate boiling. As bubble density increases, bubbles turn to coalesce and form insulating vapor patches, which impedes liquid flow back to the surface. The heat transfer rate under this condition reduces dramatically. This point is called Critical Heat Flux (CHF), which leads to boiling crisis. The behavior of boiling crisis is dependent on local fluid conditions due to bubble growth and departure. Experiments are the ultimate tool for boiling model development and verification, but they still lack some capabilities needed for better understanding of the local mechanism of this phenomena. It's difficult to capture many important details at the pressure/temperature conditions of interest using experimental techniques, such as full three dimensional measurements of velocity and temperature distribution and estimates of heat flux partitioning during the boiling process. The interface tracking simulation (ITS) is one of the promising approaches to describe heat transfer of boiling phenomena and their underlying mechanisms. The advances of high performance computing (HPC) in recent years made it possible to apply DNS to a wide variety of adiabatic flows. Some work has been done to implement evaporation / condensation models as well. Lee and Nydahl performed a numerical simulation of bubble growth and departure assuming that the bubble has the shape of a truncated sphere and a micro-layer exists during bubble growth. A 2-D cylindrical bubbles simulation has been done by Son with a simplified model to predict the heat flux in a thin liquid micro-layer. A direct simulation of 2D film boiling is conducted by Juric and Tryggvason. The film boiling, below critical pressure with a modified Level Set Method, is studied by Son and Dhir. Ose and Kunugi have developed a boiling and condensation model on subcooled boiling phenomena. Fuchs performed numerical simulations of bubble growth and departure considering wall conduction effects. Fully transient heat and fluid flow is modeled with a free surface of a rising bubble and a periodic calculation of the whole cycling of a growing, detaching, and rising bubble. Mukherjee and Kandikar have done a numerical simulation of an evaporating meniscus on a moving heated surface with level set method. The heat transfer associated with the advancing and receding contact angle has been studied. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate single-bubble growth scenarios. For a single bubble simulation in infinite liquid, the analytical solution exists and can be compared with the numerical results for verification purposes. The presented capabilities will be utilized in the large scale DNS of boiling flows in the future. The finite-element based code, PHASTA is used for the simulation. It is a parallel, hierarchic, higher-order accurate, adaptive, stabilized, transient analysis flow solver, which has been shown to be an effective tool for a wide range of single and two-phase flow problems. It has been shown to be highly scalable on top supercomputers ({approx}85% scaling on up to 3 million mesh partitions using a 92 billion element mesh . PHASTA has been shown to reliably predict the details of adiabatic bubbly flows as well as single-phase flows with heat transfer. To develop the capability of physics-based boiling process, in the presented work the energy and momentum equations are coupled to simulate a single-bubble growth scenario. For a single bubble growth in superheated water, the analytical solution exists and can be compared with the numerical results for verification purposes. The second-order accurate spatial and time discretization is used for the flow solver in the presented work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

High temperature ceramic heat exchanger for solid oxide fuel cell

A ceramic heat exchanger with high effectiveness and low-pressure drop has been developed for application as a cathode air preheater for a Solid Oxide Fuel Cell (SOFC). At the operating conditions of SOFCs, typical metallic alloys as those used in commercial heat exchangers may undergo chromium volatilization, which is a known cathode degradation mechanism that reduces SOFC performance and life. Use of ceramics such as alumina or alumina-silicate instead of chromium-containing metal is one approach to eliminate the effects of chromium on the SOFC cathode. This project leverages the geometric design of a heat exchanger previously prototyped and tested [1] to fabricate a novel heat exchanger made from a ceramic material. All calculations of heat exchanger performance requirements are based on state of the art SOFC operating conditions. The alumina-silicate material selected to fabricate the modular prototype heat exchanger was made via a heat transfer based trade-off analysis that shows that for low pressure-drop devices, flow convection is the limiting heat transfer mechanism, and therefore wall conductivity becomes less relevant to heat transfer effectiveness. The modular design presented allows for incremental aggregation of modules to target a broad range of operating conditions typical of present and upcoming SOFC applications (e.g., 25 to 400 kWe). The completed prototype was subjected to a series of static leak/pressure tests, dynamic pressure drop tests both at ambient and realistic service temperature conditions, and finally to a matrix of heat transfer experiments to fully characterize its heat transfer effectiveness (including tests at hot gas temperatures up to 1033 K or 1400oF). The stand-alone system was demonstrated in the laboratory to successfully satisfy the design criteria at realistic operating conditions, showing a total pressure drop at the design flow of 8 g/sec of 6 kPa (vs. 3.45 kPa approximate requirement). It was also shown to have heat transfer effectiveness of 76% (with 73% being the design requirement). Moreover, the unit was shown to operate leak-free, and the ceramic elements and seals were capable of withstanding the thermal cycling resulting from the testing procedure. The heat exchanger was then integrated into a modified fuel cell test stand and tested at steady state operation. Unfortunately, the level of performance achieved was lower than expected based on laboratory performance tests. This appears to have been the result of an unforeseen loosening of a heat exchanger structural component, which resulted into a leak that prevented proper supply of hot gas to the heat exchanger. However, in general terms, the heat exchanger/fuel cell integration process provides confidence that a future application of the unit with a SOFC is feasible, assuming structural issues are addressed. It is considered that the difficulties encountered at the last stage of the program provided invaluable input in locating shortcomings of the mechanical design and integration approach. A portion of this work was presented at the ASME Power & Energy Conference, in Charlotte, NC, on June 28th 2016 in a paper entitled “Development of a Ceramic Heat Exchanger for Application as Solid Oxide Fuel Cell Cathode Air Preheater” and the corresponding paper was published in the Proceedings of the ASME 2016 Power & Energy Conference, Paper No.: PowerEnergy2016-59333 [8].

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2016

THE UBIQUITOUS PRESENCE OF LOOPLIKE FINE STRUCTURE INSIDE SOLAR ACTIVE REGIONS

Although most of the solar surface outside active regions (ARs) is pervaded by small-scale fields of mixed polarity, this magnetic “carpet” or “junkyard” is thought to be largely absent inside AR plages and strong network. However, using extreme-ultraviolet images and line-of-sight magnetograms from the Solar Dynamics Observatory, we find that unipolar flux concentrations, both inside and outside ARs, often have small, loop-shaped Fe ix 17.1 and Fe xii 19.3 nm features embedded within them, even though no minority-polarity flux is visible in the corresponding magnetograms. Such looplike structures, characterized by horizontal sizes of ∼3–5 Mm and varying on timescales of minutes or less, are seen inside bright 17.1 nm moss, as well as in fainter moss-like regions associated with weaker network outside ARs. We also note a tendency for bright coronal loops to show compact, looplike features at their footpoints. Based on these observations, we suggest that present-day magnetograms may be substantially underrepresenting the amount of minority-polarity flux inside plages and strong network, and that reconnection between small bipoles and the overlying large-scale field could be a major source of coronal heating both in ARs and in the quiet Sun.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Microstructural and hardness investigations on a dissimilar metal weld between low alloy steel and Alloy 82 weld metal

The investigation on microstructure and hardness at the fusion boundary (FB) region of a dissimilar metal weld (DMW) between low alloy steel (LAS) A508-III and Alloy 82 weld metal (WM) was carried out. The results indicated that there were two kinds of FBs, martensite FB and sharp FB, with obvious different microstructures, alternately distributed in the same FB. The martensite FB region had a gradual change of elemental concentration across FB, columnar WM grains with high length/width ratios, a thick martensite layer and a wide heat affected zone (HAZ) with large prior austenite grains. By comparison, the sharp FB region had a relatively sharp change of elemental concentration across the FB, WM grains with low length/width ratios and a narrow HAZ with smaller prior austenite grains. The martensite possessed a K-S orientation relationship with WM grains, while no orientation relationship was found between the HAZ grains and WM grains at the sharp FB. Compared with sharp FB there were much more Σ3 boundaries in the HAZ beside martensite FB. The hardness maximum of the martensite FB was much higher than that of the sharp FB, which was attributed to the martensite layer at the martensite FB. - Highlights: •Martensite and sharp FBs with different microstructures were found in the same FB. •There were high length/width-ratio WM grains and a wide HAZ beside martensite FB. •There were low length/width-ratio WM grains and a narrow HAZ beside sharp FB. •Compared with sharp FB, there were much more Σ3 boundaries in HAZ of martensite FB. •Hardness maximium of martensite FB was much higher than that of sharp FB.

36 MATERIALS SCIENCE↗

NASA NTRS1982

Application of the Hughes-LIU algorithm to the 2-dimensional heat equation

An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.

Malkus, D. S.↗

DOE OSTI2017

Experimental Studies of Coolant Temperature and Velocity on an Integrated Water Model of a Fast Reactor in Different Operating Regimes

The results of experimental studies of a next-generation fast reactor performed using an integrated water model (scale 1:10) are presented: local velocity over height and radius of the top chamber in a plane in a direction from core center to the intermediate heat exchangers and coolant temperature in the top chamber and other elements of the circulation loop with forced circulation and emergency cool-down by natural convection. The data were obtained using a specially designed system for performing measurements which is incorporated in the bench and provides high accuracy and rate of acquisition. Stable temperature stratification of the coolant is observed in the top, cold, and pressure chambers of the reactor, elevator enclosure, and reactor vessel cooling system as well as at the exit from the intermediate and autonomous heat exchangers in different operating regimes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1993

Small hydrogen/oxygen rocket flowfield behavior from heat flux measurements

The mixing and heat transfer phenomena in small rocket flow fields with fuel film cooling is not well understood. An instrumented, water-cooled chamber with a gaseous hydrogen/gaseous oxygen injector was used to gather steady-state inner and outer wall temperature profiles. The chamber was tested at 414 kPa (60 psia) chamber pressure, from mixture ratios of 3.41 to 8.36. Sixty percent of the fuel was used for film cooling. These temperature profiles were used as boundary conditions in a finite element analysis program, MSC/NASTRAN, to calculate the local radial and axial heat fluxes in the chamber wall. The normal heat fluxes were then calculated and used as a diagnostic of the rocket's flow field behavior. The normal heat fluxes determined were on the order of 1.0 to 3.0 MW/meters squared (0.6 to 1.8 Btu/sec-inches squared). In the cases where mixture ratio was 5 or above, there was a sharp local heat flux maximum in the barrel section of the chamber. This local maximum seems to indicate a reduction or breakdown of the fuel film cooling layer, possibly due to increased mixing in the shear layer between the film and core flows. However, the flow was thought to be completely laminar, as the throat Reynolds numbers were below 50,000 for all the cases. The increased mixing in the shear layer in the higher mixture ratio cases appeared not to be due to the transition of the flow from laminar to turbulent, but rather due to increased reactions between the hydrogen film and oxidizer-rich core flows.

Reed, Brian D.↗