Steel slag can emerge from steelmaking at temperatures as high as 1,600 °C, but recovering its heat is difficult because the material is highly viscous and difficult to handle. In the roller-crushing and hot-disintegration process examined by the researchers, molten slag is first crushed and cooled in a semi-open roller-crushing area and then transferred to a closed hot-disintegration tank. Intermittent water spraying triggers exothermic hydration of free calcium and magnesium oxides, promoting internal cracking, particle-size reduction and stabilization of the slag for later use. This treatment produces saturated steam, but the study noted that a substantial portion of the high-temperature sensible heat released during crushing was not recovered.

The proposed configuration attempts to connect two stages that operate at different heat levels. Radiative heating surfaces positioned around and above the roller-crushing region recover high-temperature heat, while hot disintegration supplies saturated steam. Part of the recovered heat preheats feedwater in a water-wall economizer, and the remainder superheats the steam before it enters the turbine. A steam drum provides steam-water separation and a location for chemical dosing and bottom blowdown. The researchers modeled a direct-steam Rankine cycle because the recovered steam can serve as the cycle working fluid; this avoided the additional heat-transfer stage and separate organic-fluid loop that would be required if an organic Rankine cycle were supplied with the steam.

To evaluate the enclosure geometry, the team built a MATLAB model of diffuse-gray surfaces exchanging radiation. The radiation network represented the slag, top surface and aggregated side walls, with slag emissivity set at 0.90 and receiver emissivity at 0.80. The top and side temperatures were prescribed at 120 °C and 25 °C in the main comparison, while convection, radiation involving participating gases or particles, and direct contact heat transfer were excluded. The rectangular enclosure measured 16 by 5 by 4 metres, whereas the cylindrical design had a radius of 5.744 metres and a height of 4 metres. Both provided about 248 m² of combined top-plus-side receiver area, but they did not have identical slag footprints: the idealized slag-emitting area increased from 80 m² in the rectangle to 103.64 m² in the cylinder.

For an idealized 30,000-kilogram slag batch with a constant heat capacity of 1.2 kJ per kilogram per kelvin, the rectangular configuration had a modeled cooling-time mean radiative heat-transfer rate of 13.83 MW, compared with 17.54 MW for the cylindrical configuration. The cylinder’s result was approximately 27% higher under the prescribed surface-radiation conditions. Because the slag-emitting area and view factors changed along with the enclosure shape, this was a comparison of the selected geometries rather than an isolated view-factor gain or a matched-footprint comparison. Sensitivity calculations also showed that lowering slag emissivity from 0.90 to 0.75 reduced the mean rates to 11.66 MW for the rectangle and 14.84 MW for the cylinder. Lowering receiver emissivity from 0.80 to 0.60 changed the modeled cylinder-to-rectangle difference from 26.85% to 23.43%. These calculations describe model sensitivity, not measured uncertainty, and the effects of evolving slag surfaces, enclosure gases, dust, deposits and fouling were not quantified.

The integrated-cycle analysis used Aspen Plus V11 with IAPWS-IF97 water properties and represented the superheater, economizer, steam drum, condenser, pump and turbine. In the selected case, 10,400 kg/h of feedwater entered the flowsheet: 2,400 kg/h passed through the economizer and 8,000 kg/h entered the hot-disintegration heat-recovery section. Their modeled heat duties were 7.247 MW for hot disintegration, 0.267 MW for feedwater preheating and 2.613 MW for steam superheating, giving a total cycle heat input of 10.127 MW. Saturated steam from the drum reached 556.8 °C at 0.2 MPa before entering the expander. The model then calculated 2.068 MW of expander shaft output and a cycle thermal efficiency of 20.4%. The reported cycle power subtracts the represented feed-pump demand from expander shaft output; it is not net exported electricity because generator losses and plant auxiliaries were outside the model boundary.

A literature benchmark tested the baseline calculation without heat supplied by the crushing enclosure. At a hot-disintegration steam pressure of 0.2 MPa and a flow of 2,600 kg/h, the model generated 291.5 kW of expander shaft output, close to the reference value of approximately 300 kW and representing a deviation of about −2.8%. Its modeled efficiency was 15.5%, however, above the literature-reported range of 10–12%, a difference attributed to calculations that did not share fully equivalent component assumptions or efficiency boundaries. The comparison therefore served as a numerical benchmark rather than experimental validation of the integrated design.

The modeled superheating increased the physical exergy carried by the steam entering the expander. Specific physical exergy rose from 586 kJ/kg at 120 °C to 1,031 kJ/kg at 557 °C, an increase of 76%. As steam flow increased from 2,600 to 10,400 kg/h, the inlet-steam physical-exergy rate rose from 0.42 to 2.98 MW and modeled cycle power increased from 291.3 to 2,067.7 kW. The ratio of modeled cycle power to inlet-steam physical exergy remained near 69% in the two cases. This ratio describes conversion within the modeled cycle, not the exergy efficiency of the complete slag-recovery system, because losses in individual recovery sections, slag exergy, generator losses and auxiliary inputs were not included.

Intermittent steam production remains unresolved. Hot disintegration depends on periodic spraying and hydration reactions, whereas the thermodynamic model assumes a steady, time-averaged supply and does not resolve batch-scale transients or water accumulation in the drum. A simplified estimate for a drum containing 20,000 kg of water at 0.2 MPa suggested a characteristic buffering time of approximately 118 seconds, or about two minutes, during an allowable transient pressure decrease to 0.15 MPa. That estimate does not demonstrate that one drum could smooth a complete batch of intermittent production. Staggered operation of multiple hot-disintegration tanks was proposed as a possible way to reduce aggregate flow fluctuations, but measured single-tank steam profiles and plant scheduling records were unavailable, so the arrangement remains an operating assumption. A preliminary cost screen estimated the added equipment at RMB 4.5 million and compared it with an indicative annual electricity value of about RMB 5.33 million at 6,000 operating hours and RMB 0.50/kWh. The resulting ratio of roughly one year is not a definitive payback because installation, civil work, generator and auxiliary consumption, maintenance, downtime, financing, taxation and electricity-price changes were excluded.

Water chemistry presents a separate constraint. Condensate collected from hot-disintegration steam at Henan Jiyuan Iron and Steel Group in China initially contained total calcium and magnesium concentrations of 1.18 and 0.80 mmol/L. In the proof-of-concept dosage series, adding sodium phosphate caused calcium and magnesium to decline sharply before varying non-monotonically. At a sodium phosphate dosage of 5.53 mmol/L, total calcium and magnesium measured 0.009 and 0.085 mmol/L, and equivalent hardness reached 0.188 ± 0.011 mmol/L, 95.2% below the untreated value of 3.944 mmol/L. Visual MINTEQ equilibrium simulations at 15 °C reproduced the general concentration trend and identified hydroxyapatite and magnesium phosphate as possible precipitating solids, but the calculations assumed chemical equilibrium and did not resolve nucleation or precipitation kinetics. Together, the radiation and cycle models and the preliminary water tests support the feasibility of the proposed integration under the studied conditions. They do not establish continuous turbine operation, industrial-scale hardness compliance or long-term chemical stability, which require dynamic pilot testing, independent treatment replicates, long-term scaling studies and validation of turbine control, blowdown, steam purity and auxiliary power.

Subject of Research: Modeled steel-slag waste-heat recovery and preliminary phosphate treatment for Rankine-cycle power generation

Article Title: An integrated waste heat recovery system for Rankine cycle power generation from the steel slag hot disintegration process

Article References: Wu, H., Zhou, T., Bai, R., Xu, Z., Li, Y., Xia, B., Zhang, M., & Yang, H. (2026). An integrated waste heat recovery system for Rankine cycle power generation from the steel slag hot disintegration process. Frontiers in Energy Research, 14, Article 1965673. https://doi.org/10.3389/fenrg.2026.1965673

Image Credits: AI Generated

DOI: 10.3389/fenrg.2026.1965673

Keywords: steel slag, waste-heat recovery, Rankine cycle, hot disintegration, radiative heat transfer, steam superheating, power generation, water hardness, phosphate treatment, steel industry, integrated, waste

The problem the researchers tackled is known as base heating. As a rocket ascends, the hot exhaust plume radiates energy toward the aft structures of the vehicle, including the base region between clustered nozzles and the surfaces surrounding them. At sea level, the surrounding air constrains the plume and much of the heat is convected away, but at high altitudes the plume expands freely into the rarefied environment. Under these vacuum-like conditions the gas cools rapidly as it diffuses, yet the condensed particles suspended in the flow remain hot and continue to radiate. Understanding how much of that particle-driven radiation strikes the rocket base is critical for thermal protection design, particularly for solid rocket motors, whose propellants typically contain substantial amounts of aluminum powder to boost performance.

Simulating such a flow is notoriously difficult because the physics spans two very different regimes. The gas in a high-altitude plume is so rarefied that the continuum assumptions underlying ordinary computational fluid dynamics break down; molecular collisions become infrequent and the flow must be treated statistically. The research team therefore employed the direct simulation Monte Carlo method, using the SPARTA code, to model the rarefied plume field particle by particle, or more precisely molecule by simulated molecule. This approach, rooted in the molecular gas dynamics framework pioneered by Graham Bird, tracks representative molecules and their collisions to build up a statistical picture of the flow without solving the continuum equations at all.

The alumina particles, however, demanded a different treatment. Because they are far more massive than gas molecules and travel on largely ballistic trajectories punctuated by drag interactions with the thin gas, the team modeled them with Lagrangian particle tracking implemented in the open-source OpenFOAM toolkit. The two solvers were then coupled to an in-house radiative base-heating solver based on the discrete ordinates method, which computes how thermal radiation propagates through the particle-laden plume and how much of it is intercepted by the base region. This integrated computational framework, combining DSMC gas dynamics, Lagrangian particle dynamics, and radiative transfer, is one of the study’s central technical contributions, allowing each physical ingredient to be resolved with the method best suited to it.

The first major finding concerns what happens to the gas itself. The exhaust plume analysis revealed substantial diffusion and backflow under vacuum conditions: instead of forming a narrow, directed jet, the exhaust spreads laterally and a portion of it reverses direction, flowing back toward the vehicle. This expansion causes a pronounced drop in gas temperature. That cooling has a welcome simplifying consequence for the modelers, because the reduced gas temperature justified neglecting radiative heat transfer from the gas phase altogether. In other words, at high altitude the radiative threat to the rocket base comes almost entirely from the hot alumina particles, not from the glowing exhaust gases, a conclusion that sharply focuses where design attention should be directed.

With the gas-phase radiation set aside, the researchers systematically explored how particle characteristics shape base heating. Holding the propellant composition fixed, they varied the size of the alumina particles and computed the resulting radiative flux. The results reveal a strikingly nonlinear relationship. Radiative base heating increases rapidly as particle diameters move from the submicron range into the micron range, but beyond that transition the rate of increase diminishes markedly for larger particles. The physical explanation lies in the interplay between how much thermal radiation a particle emits, which scales strongly with its surface area and temperature, and how those particles are distributed and transported through the expanding plume. Small particles cool quickly and radiate inefficiently in aggregate, while the largest particles contribute less per unit mass than the intermediate sizes where the effect peaks.

The second axis of the study examined propellant composition. For a fixed particle size, the team varied the aluminum mass fraction in the propellant and found that base heating rises steadily as more aluminum is added. This makes intuitive sense once the chemistry is considered: aluminum powder burns in the motor to form aluminum oxide, so a propellant richer in aluminum produces a greater loading of radiating oxide particles in the exhaust. The finding carries a practical tension for rocket designers, because aluminum is added to solid propellants precisely to raise performance, yet every additional percentage point of aluminum buys a hotter radiative environment at the vehicle base. The new results quantify that trade-off in a form that thermal engineers can use during early design studies.

The authors are careful to frame the reliability of their numbers. Because formal benchmark validation of the modified radiation coupling procedure has not yet been completed, they caution that the predicted radiative-heating levels should be interpreted as engineering-level comparative sensitivity indicators for particle-driven base heating, rather than as fully validated absolute local heat-flux predictions. In practical terms, the study tells designers with confidence how base heating changes when particle size or aluminum content is changed, but the absolute magnitudes await experimental or high-fidelity benchmark confirmation. That honesty about validation status is a valuable feature of the work, distinguishing robust trends from numbers that should still be treated as provisional.

The study builds on a long lineage of plume radiation research stretching back decades, from early analyses of large solid propellant rocket plumes using DSMC in the 1980s, through finite-volume radiation analyses of rocket plume base heating in the 1990s, to more recent investigations of how the optical properties of alumina particles influence radiative base heating. What distinguishes the new effort is the tight coupling of three state-of-the-art tools, SPARTA for rarefied gas dynamics, OpenFOAM for particle tracking, and a dedicated radiation solver, into a single pipeline capable of answering parametric questions about particle size and propellant formulation. The work was supported by the National University Development Project of Jeonbuk National University, and the corresponding author, Man Young Kim, has previously published related predictions of radiative base heating from solid rocket exhaust plumes.

For the aerospace community, the implications extend across launch vehicles, upper stages, and missile systems that operate solid rocket motors in the upper atmosphere and beyond. As missions increasingly demand precise thermal margins rather than conservative overdesign, knowing that the submicron-to-micron transition in alumina particle size is the critical regime, and that aluminum loading drives heating upward, allows engineers to target both their propellant specifications and their thermal protection layouts more intelligently. The study also highlights the growing power of multiscale simulation, in which molecular-level gas kinetics, particle mechanics, and radiative transfer are stitched together to illuminate phenomena that neither wind tunnels nor flight tests can easily isolate. As validation matures, frameworks of this kind could become standard instruments for predicting the invisible thermal weather that surrounds every rocket climbing toward orbit.

Subject of Research: Radiative base heating from alumina particles in high-altitude solid rocket motor exhaust plumes

Article Title: Effect of Particle Size and Propellant Composition on Base Heating in High-Altitude SRM Plumes

Article References: Joo, H. C., Kim, J. S., & Kim, M. Y. (2026). Effect of Particle Size and Propellant Composition on Base Heating in High-Altitude SRM Plumes. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01252-1

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01252-1

Keywords: solid rocket motor, exhaust plume, base heating, alumina particles, particle size, propellant composition, direct simulation Monte Carlo, rarefied flow, radiative heat transfer, discrete ordinates method, Lagrangian particle tracking, high altitude