Method for Determining Pressure Drop of Monatomic Gases Flowing in Turbulent Motion Through Constant-area Passages with Simultaneous Friction and Heat Addition
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FLOW OF GASES - TUBES↗
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Compressibility Effects on Heat Transfer and Pressure Drop in Smooth Cylindrical Tubes
An analysis is made to simplify pressure-drop calculations for nonadiabatic and adiabatic friction flow of air in smooth cylindrical tubes when the density changes due to heat transfer and pressure drop are appreciable. Solutions of the equation of motion are obtained by the use of Reynolds' analogy between heat transfer and skin friction. Charts of the solutions are presented for making pressure-drop calculations. A technique of using the charts to determine the position of a normal shock in a tube is described.
AIR FLOW - TUBES, CYLINDRICAL↗
Altitude-Wind-Tunnel Investigation of a 4000-Pound-Thrust Axial-Flow Turbojet Engine: Analysis of Turbine Performance - 5
Performance characteristics of the turbine of a 4000-pound-thrust axial-flow turbojet engine was determined in investigations of the complete engine in the NACA Cleveland altitude wind tunnel. Characteristics are presented as functions of the total-pressure ratio across the turbine and of turbine speed and gas flow corrected to sea-level conditions. Three turbine nozzles of different areas were used to determine the area that gave optimum performance. Inasmuch as tail-pipe nozzles of different diameters were investigated in combination with the standard turbine nozzle, the effect of varying discharge conditions on turbine operation could be observed. The investigations covered a range of pressure attitudes from 5000 to 40,000 feet. The engine was investigated over the entire operable range of speeds at each altitude. At pressure altitude of 30,000 feet, the effect on turbine operation of varying the ram pressure ration over a range from 1.10 to 1.77 was evaluated. An altitude effect was apparent when turbine pressure ratio was plotted against corrected turbine speed but it was so slight as to be negligible insofar as the turbine efficiencies were concerned. A maximum turbine efficiency of slightly more than 82 percent was obtained with the configuration using the standard turbine nozzle and the low-flow compressor. This efficiency, which is somewhat lower than the actual turbine efficiency, is uncorrected for accessories drive power, bearing friction, tail-pipe pressure drop, compressor thermal radiation, and introduction of turbine-disk cooling air into the gas stream. Changes in the ram pressure ratio had a negligible effect on the turbine efficiency.
Krebs, Richard P.↗
Dynamics of face and annular seals with two-phase flow
A detailed study was made of face and annular seals under conditions where boiling, i.e., phase change of the leaking fluid, occurs within the seal. Many seals operate in this mode because of flashing due to pressure drop and/or heat input from frictional heating. Some of the distinctive behavior characteristics of two phase seals are discussed, particularly their axial stability. The main conclusions are that seals with two phase flow may be unstable if improperly balanced. Detailed theoretical analyses of low (laminar) and high (turbulent) leakage seals are presented along with computer codes, parametric studies, and in particular a simplified PC based code that allows for rapid performance prediction: calculations of stiffness coefficients, temperature and pressure distributions, and leakage rates for parallel and coned face seals. A simplified combined computer code for the performance prediction over the laminar and turbulent ranges of a two phase flow is described and documented. The analyses, results, and computer codes are summarized.
Hughes, William F.↗
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↗
Investigation of Gas Turbine Internal Cooling Using Supercritical CO 2 —Effect of Surface Roughness and Channel Aspect Ratio
In this paper, an experimental and numerical investigation of internal cooling channels with rib turbulators is presented with sCO 2 as the working fluid at process conditions (pressure-20.7 MPa and temperature up to 150 °C). The effect of channel aspect ratio up to 2:1 on thermal-hydraulic performance is explored in additively manufactured rectangular channels and square channels, both with and without 60 deg ribs on the top and bottom sides. The Wilson-plot method is employed to experimentally measure channel-averaged Nusselt number over a Reynolds number range up to 370,000. The friction factor is calculated from pressure drop and mass flow rate and additionally, the overall thermal performance factor (TPF) is reported. A companion computational fluid dynamics (CFD) simulation is performed for the rib turbulated cooling configurations reported in the experiments using the Reynolds average Navier–Stokes-based turbulence model. The objective of the numerical study is to gain insight into the local heat transfer augmentation in the ribbed channels as a result of varying the aspect ratio, channel configuration (square versus rectangular), operating conditions (Reynolds number) and the surface roughness, an inherent outcome of the additive manufacturing process. Surface roughness is simulated using sand grain roughness height (K S ) calculated from the experimental data, and a comparison is presented with the corresponding channel configuration with varying surface roughness heights starting from smooth surfaces (K S = 0). Experimental results indicate that the heat transfer augmentation is negligible in the rectangular channels with ribs on the long side compared to the square channel. However, it is enhanced by 60% in comparison to placing ribs on the shorter side. The TPF remains constant at around 1 for the entire range of Reynolds numbers consistent with prior work at the National Energy Technology Laboratory (NETL). Here, the simulation results highlight that increased surface roughness can have a favorable considerable influence on Nusselt number and overall thermal performance enhancement.
42 ENGINEERING↗
Test of sodium boiling in a single tube-in- shell heat exchanger over the range 1720 deg to 1980 deg F /1211 to 1355 K/
Sodium was boiled in a vertical, 1/2-inch (1.27-cm) inside diameter by 4-fOOt (1.22-m) long tube. The columbium alloy boiler operated at flow rates of 75 to 380 lbm/hr (9.4 to 48 g/sec) and up to 0.93 quality. Boiling performance depended on whether the inlet flow was two-phase or liquid. Two-phase momentum pressure drops were 1(1/2) times frictional drops. Qualities over 0.9 were obtained at some critical (burnout) boiling conditions. Liquid superheats up to 250° F (139 K) existed before initiation of boiling.
James P. Lewis↗
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↗
Development of Flow and Heat Transfer Models for the Carbon Fiber Rope in Nozzle Joints of the Space Shuttle Reusable Solid Rocket Motor
Methodologies have been developed for modeling both gas dynamics and heat transfer inside the carbon fiber rope (CFR) for applications in the space shuttle reusable solid rocket motor joints. Specifically, the CFR is modeled using an equivalent rectangular duct with a cross-section area, friction factor and heat transfer coefficient such that this duct has the same amount of mass flow rate, pressure drop, and heat transfer rate as the CFR. An equation for the friction factor is derived based on the Darcy-Forschheimer law and the heat transfer coefficient is obtained from pipe flow correlations. The pressure, temperature and velocity of the gas inside the CFR are calculated using the one-dimensional Navier-Stokes equations. Various subscale tests, both cold flow and hot flow, have been carried out to validate and refine this CFR model. In particular, the following three types of testing were used: (1) cold flow in a RSRM nozzle-to-case joint geometry, (2) cold flow in a RSRM nozzle joint No. 2 geometry, and (3) hot flow in a RSRM nozzle joint environment simulator. The predicted pressure and temperature history are compared with experimental measurements. The effects of various input parameters for the model are discussed in detail.
Wang, Q.↗
Robust foil regenerator flow loss and heat transfer tests under oscillating flow condition
A regenerator works as an energy storage component in a Stirling engine. Thus, it is one of the most critical components that makes the Stirling engine highly efficient. Traditionally, the regenerators are made of wire media such as woven screens and random fibers. These wire regenerators experience considerably high flow losses through the regenerator due to the flow separation and the resulting vortices. The high flow losses associated with the flow separation and vortices result in a lower engine efficiency. This research is to test a new robust foil regenerator to investigate its feasibility for free-piston Stirling engine applications. The robust foil regenerator is configured with parallel flow channels and stiffening ribs. Comparing to complex flows patterns in woven screen and random fiber regenerators, the flows in the parallel plates are simple and the flow losses are considerably small, and the heat transfer coefficient is also relatively small. To test the regenerator experimentally, a regenerator test rig was manufactured. To verify the accuracy of the test rig, a woven screen regenerator was made and tested prior to the robust foil regenerator test. The friction factor correlation of the woven screen regenerator shows a good agreement with the published regenerator correlations. The robust foil regenerator tests were conducted under the oscillating flow condition with different Reynolds numbers. The flow losses were measured with dynamic pressure transducers and the friction coefficient was derived from measured pressure drop. The measured temperature difference over the regenerator was used to calculate the heat transfer coefficient and Nusselt number. The figure of merit with two methods of NPH/NTU ratio and j/f ratio was calculated to evaluate the suitability of the robust foil regenerator. The results show that the robust foil regenerator has considerably higher figure of merit and therefore, better performance than other types of regenerator.
42 ENGINEERING↗
Review of heat transfer enhancement techniques in two-phase flows for highly efficient and sustainable cooling
We show that two-phase internal flow is ubiquitous to many systems due to its ability to transfer large amounts of heat effectively. Recent advances motivated by sustainability have pushed towards augmenting the heat transfer between the tube and the two-phase working fluid. Augmenting heat transfer in two-phase flows enables process intensification, and compactness leading to reduced cost and material consumption. This review investigates the effect of heat transfer enhancement techniques on different fluids including R134a, R407C, R22, etc … The techniques are categorized into passive and active and focus on durable enhancement methods which do not include surface structuring or coating. Passive techniques utilize geometrical and surface modifications to induce better mixing. Several passive techniques are analyzed including fins, inserts, and more. In analyzing these techniques, the effect of changing geometric parameters is studied, and the limitations are highlighted. Further, active techniques that enable heat transfer enhancement through applying power are also investigated. Electrohydrodynamic approaches are analyzed and compared to passive techniques. Additionally, the implications of heat exchange enhancement in the context of global energy are discussed. An energy analysis discretized by the use sector is conducted, with an emphasis on predicting the future potential for renewable and sustainable development. Moreover, although active approaches provide the highest heat transfer enhancement, due to implementation difficulties, passive techniques are more frequently adopted. The review ends with discussion of next-generation heat exchangers which will rely more on additive manufacturing due to its flexibility and reduced cost per part as the technology matures.
Nusselt number↗
Particle bed reactor modeling
The topics are presented in viewgraph form and include the following: particle bed reactor (PBR) core cross section; PBR bleed cycle; fuel and moderator flow paths; PBR modeling requirements; characteristics of PBR and nuclear thermal propulsion (NTP) modeling; challenges for PBR and NTP modeling; thermal hydraulic computer codes; capabilities for PBR/reactor application; thermal/hydralic codes; limitations; physical correlations; comparison of predicted friction factor and experimental data; frit pressure drop testing; cold frit mask factor; decay heat flow rate; startup transient simulation; and philosophy of systems modeling.
Sapyta, Joe↗
Two-Phase Flow in Filters and Orifices: In preparation for Measurements on ISS Packed Bed Reactor Experiment-Water Recovery Series (PBRE-WRS)
Understanding the hydrodynamics of adiabatic two-phase flows in packed bed reactors offers numerous benefits. It enables the optimization of chemical reactions rates and products, crucial for pharmaceuticals and energy production industries. Additionally, this understanding aids in designing more efficient and compact reactors, reducing space and resource requirements. Insights gained from studying such flows in microgravity contribute to advancements of space technologies and the enhancement of our capabilities for undertaking future long duration safe, and sustainable space exploration missions. The Packed Bed Reactor Experiment-Water Recovery Series (PBRE-WRS) is a flight experiment planned for operation on the Microgravity Science Glove box (MSG) facility of the International Space Station (ISS). The objective of the experiment is to validate hydrodynamic models at a range of gas and liquid flow rates. The microgravity environment allows for measurement and observation of aspects of fluid dynamics that are unique when compared to observations made in full or partial gravity environments. The experiment consists of testing two-phase flow hydrodynamics in three different filters, four (4) orifices and one check valve test articles. The experiment utilizes the hardware of the previously flown PBRE and PBRE-2 with packed beds of different packings materials and sizes. The fluid system of the PBRE-WRS consists of a nitrogen gas delivery and water delivery subsystems. The gas delivery subsystem can accommodate two ranges of gas flow rates, just as for the water delivery system. The nitrogen gas loop is open whereas the water loop is closed. Gas is separated from the water using a gas-liquid phase separator which is located in the water delivery module. Preliminary results from ground testing show the pressure drop increasing at different rates with the liquid and gas flow rates in the Brine filter. In this work, a detailed system description is presented along with a summary of results from ground performance testing of different test sections in an end-to-end preflight testing campaign.
Packed Bed Reactor Experiment↗
Enhanced internal condensation of R1233zd(E) on micro- and nanostructured copper and aluminum surfaces
In-tube condensation of refrigerants is an important process which affects thermal efficiency in many applications, ranging from refrigeration and air conditioning to electronics thermal management. In-tube heat transfer and pressure drop are important to heat exchanger sizing and design. Here, in this work, micro- and nanostructured surfaces are applied to the internal wetted areas of copper and aluminum mini-channels to enhance the condensation heat transfer coefficient of hydrofluorocarbon R1233zd(E) refrigerant. To achieve scalable nanomanufacturing, surfaces were uniformly structured by relying on hydrochloric acid etching of aluminum and chemical oxidation of copper. The etched aluminum surfaces exhibited a 150% increase in heat transfer coefficient compared to smooth aluminum channels at specific qualities, with a 66% heat transfer coefficient improvement for complete phase change from saturated vapor to saturated liquid. Copper oxide structures showed no discernable difference in thermal-hydraulic performance when compared to smooth copper channels. Critical dimensionless parameters governing the heat transfer enhancement were identified by varying the tube internal diameter (2.3 mm to 4.7 mm), refrigerant mass flux (50 to 300 kg/(m 2 ·s)), and refrigerant quality (0 to 1). The dimensionless parameters include the Bond number normalized to the condensate film thickness, and the Weber number modified by the vapor friction factor. The relatively small increase in pressure drop (< 10%) associated with these surface enhancements further supports the promise of this method. The scalable and cost-effective techniques used to create these aluminum microstructures may reduce manufacturing cost when compared with current enhancement approaches such as extrusion, drawing, and welding.
42 ENGINEERING↗
An improved pressure drop correlation for modeling localized effects in a pebble bed reactor
Advances in the development of pebble bed reactors (PBRs) has created a desire for accurate and cost-effective simulation tools for design scoping studies and safety analysis. The current state-of-the-art for these simulations is the use of porous media models, although these models rely on correlations to capture the effects of flow features that are not explicitly modeled. One of the areas where correlation accuracy is currently lacking is in the near-wall region of the bed. In this region, the presence of the wall causes the pebbles to pack more orderly, drastically changing the geometry and flow behavior in this region. This work presents a new generalized pressure drop correlation for PBRs based on the KTA equation. A high-to-low methodology is applied, where large eddy simulation (LES) is performed on two beds of 1568 and 1700 pebbles to generate a high-fidelity dataset. The flow fields are then averaged in time and separated into concentric rings of 0.05 D peb width. Average porosity, velocity, and pressure drop are extracted for each ring and the friction and form losses are calculated. The Reynolds number range for this study is 625–10,000, and thus the form losses are dominant over the friction losses. The form losses across the rings are investigated, and a correction term for the form loss calculation is determined and applied to the KTA equation to drastically improve the capability of modeling localized porosity effects in a porous media code. Finally, the improved correlation reduces near-wall velocity prediction error from over 50% with the KTA correlation to around 5%. Agreement in pressure drop prediction between LES and porous media simulations is also improved.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
CFD Analysis of an Installation Used to Measure the Skin-Friction Penalty of Acoustic Treatments
There is a drive to devise acoustic treatments with reduced skin-friction and therefore fuel-burn penalty for engine nacelles on commercial airplanes. The studies have been experimental, and the effects on skin-friction are deduced from measurements of the pressure drop along a duct. We conduct a detailed CFD analysis of the installation, for two purposes. The first is to predict the effects of the finite size of the rig, including its near-square cross-section and the moderate length of the treated patch; this introduces transient and blockage effects, which have not been included so far in the analysis. In addition, the flow is compressible, so that even with homogeneous surface conditions, it is not homogeneous in the streamwise direction. The second purpose is to extract an effective sand-grain roughness size for a particular liner, which in turn can be used in a CFD analysis of the aircraft, leading to actual predictions of the effect of acoustic treatments on fuel burn in service. The study is entirely based on classical turbulence models, with an appropriate modification for effective roughness effects, rather than directly modeling the liners.
Spalart, Philippe R.↗
Thermal-Hydraulic Performance of a Zeotropic Refrigerant in a Brazed Plate Evaporator
In this work we report the results of a preliminary investigation focused on evaluating the thermal-hydraulic performance of R455A (CO2, R32, R1234yf – 3/21.5/75.5) in a commercial brazed plate heat exchanger. Three key parameters were measured which were refrigerant flow maldistribution, overall refrigerant side heat transfer coefficient, and total refrigerant side pressure drop. These same parameters were also measured for R134a which served as a base-line refrigerant for comparison. The experimental test matrix was set up to investigate the influence of refrigerant mass flux (3 ≤ Gref ≤ 5 kg m-2 s-1), refrigerant inlet vapor quality (0.1 ≤ xin ≤ 0.4), and refrigerant exit superheat (5 ≤ Tsh ≤ 10 K) on the above mentioned thermal-hydraulic parameters. For these experimental conditions, on average, the overall refrigerant side heat transfer coefficients for R455A were 45.2% lower than those of R134a. Refrigerant flow maldistribution for R455A, on average, was observed to be 62.6 % higher than that measured for R134a, and the total pressure drop across the heat exchanger (minor and frictional losses) for R455A was on average 26.5% higher than that measured for R134a. These initial results set the stage for a comprehensive investigation focused on further investigating the thermal-hydraulic performance of zeotropic refrigerants in brazed plate heat exchangers.
Jajja, Saad [ORNL]↗
Critical Reynolds number for sinusoidal flow of water in rigid tubes.
Experimental friction factor for pulsatile water flow, obtaining empirically pressure drop and flow rate data
Hershey, D.↗