Low Swirl Intensity Research Articles

Influence of swirl intensity on combustion dynamics and emissions in an ammonia-enriched methane/air combustor

Ammonia (NH3) has been widely considered as a promising carbon-free energy and hydrogen carrier for various applications. The large-scale direct utilization of NH3 as fuel in gas turbine engines is currently attracting significant interest, with strong focuses on improving the efficiency and stability of the system and reducing the emissions of pollutants. The present study experimentally examined the impacts of swirl intensity on combustion stability and emissions in an NH3-enriched premixed swirl-stabilized CH4/air combustor under a wide range of equivalence ratios. Simultaneous high-speed OH* chemiluminescence and particle image velocimetry measurements suggested that increasing swirl intensity resulted in more compact flame shapes and expanded the recirculation zone, which promoted flame stability at higher NH3 ratios. However, under specified conditions, enhancing swirl intensity could increase the instability frequency and amplitude of pressure oscillations. The flame dynamics exhibited different behaviors depending on the swirl intensity. At high swirl intensity, the flames underwent high-frequency, small-amplitude periodic motion. At low swirl intensity, the flames oscillated axially with large amplitude and low frequency. For flow dynamics, the stability of the vortex at high swirl intensity contrasted with the periodic vortex shedding at low swirl intensity. Furthermore, the two-dimensional Rayleigh index indicated that the dominant positive thermoacoustic coupling regions were located near the flame shear layers and flame tail at low and high swirl intensities, respectively. Finally, the experimental results showed that swirl intensity affected pollutant emissions by influencing the temperature of combustion chamber and gas mixing efficiency. The pathway of fuel-type NOx was found to be dominant in the NOx emission of the NH3/CH4/air flames.

Experimental characteristics of adding biogas to premixed self-excited oscillating methane swirling flames

This work is the first to examine the influence of renewable energy biogas addition on the characteristics of methane self-excited thermoacoustic oscillation and pollutant NOx emission. Meantime, the swirl intensity and methane enrichment degree that affect the biogas combustion are also explored. Results indicate that the methane premixed self-excited oscillation swirling flames are effectively suppressed during the biogas addition and present two dynamic combustion states: high-frequency self-excited oscillation and swirl stable combustion. Furthermore, the overall flame temperature and NOx emissions have been reduced, which reveals that the introduction of biogas has effectively restrained thermoacoustic oscillation and limited NOx emissions. Notably, the combustion and emission characteristics of methane/biogas co-firing under low swirl intensity are superior to those under high swirl intensity. However, enriching biogas with more methane results in better flame dynamics of biogas/methane but comes with the cost of higher NOx generation. Regarding the flame and schlieren morphology, with the increase of biogas content in the fuel, the flame shape gradually transforms from the compact and robust M-typed flame to the loose and trumpet V-typed steady flame. The flame schlieren's visualization characterizes the flow field and vortex structures' stretching and deformation in methane-air premixed flame with biogas addition. The distribution appearance of the flame flow field and vortex under lean combustion are more complex and diverse than those under rich combustion. The study's conclusions may contribute to optimizing and improving the combustion and emission performance of premixed combustors primarily based on fossil fuel methane.

Interaction of fuel spray and air swirl on the combustion of residue oils

Effervescent atomization technology was applied in Waste Lubricant Oils (WLO) combustion. The tests were conducted in a 150 kW prototype boiler with a horizontally oriented cylindrical shape combustion chamber in which the combustion process was studied in terms of the interaction between a swirling air flow and fuel spray pattern. The combustion performance was assessed by continuously monitoring gaseous emissions, particularly carbon monoxide (CO) emission. Two different air feeding strategies were tested, varying in swirl number and six different configurations of the injection nozzle orifice. Three nozzles had a single orifice varying in diameter and discharge end geometry, and the others had three divergent orifice arrangement varying in cone angle and diameter. At the same time, the gas-to-liquid ratio (GLR) of the effervescent atomizer was also investigated, allowing to draw important illations about its influence on the combustion efficiency. The results show that the use of effervescent atomizers allows to burn of WLO, with CO emissions as low as 15 ppm at 8% of oxygen (O2) when using a three orifice of 1 mm with 15° of cone angle nozzle. This result was achieved by applying high-intensity combustion air flow swirl. However, the one orifice nozzles with penetrant spray pattern combined with low swirl intensity air flow also produced satisfactory results. With CO emissions of 27 ppm at 8% of O2 with a 1.2 mm single orifice nozzle. Furthermore, it was also demonstrated that the increment of the GLR in a range between 0.25 and 0.35 can be responsible for the reduction of 40 to 50% of the CO emissions when burning WLO.

Effects of swirl intensity on flame stability and NO emission in swirl-stabilized ammonia/methane combustion

Ammonia is an attractive clean fuel for its potential to reduce CO2 emission and fossil fuel consumption. However, ammonia combustion has been mainly discouraged by the low flammability and the high fuel NOx emissions. This study numerically investigates the effects of swirl intensity on combustion characteristics in swirl-stabilized ammonia/methane combustion. Large eddy simulation was performed by using OpenFOAM, and the accuracy of numerical results was validated by the experiment. The results show that swirl intensity will significantly affects the flow field and flame structure, and flame stability decreases with the swirl number increasing. The high swirl intensity leads to extinguishing at the flame root, while the low swirl intensity cannot generate the central recirculation zone to stabilize the flame. Selective non-catalytic reduction of NO (SNCR) is the key to controlling NO emission, the decrease of temperature will promote the reduction of NO, while the decrease of residence time will inhibit the reduction of NO. Meanwhile, SNCR will weaken the correlation between NO and OH in ammonia/methane combustion. NO emission will decrease with the swirl intensity increasing. In a word, medium swirl number (S ≈ 0.76) is proper to control NO emission and ensure flame stability.

Numerical Study on Flame Stabilization and NO x Formation in a Novel Burner System for Sulfur Combustion.

Numerical simulations have been conducted for a novel double-concentric swirl burner, which is specifically designed for combustion of sulfur with a high power density. The burner serves as a major component of an enclosed conversion cycle, which uses elemental sulfur as a carbon-free chemical energy carrier for storing solar energy. The focus of the work is to assess operability of the burner and NO x formation at fuel-lean conditions with an equivalence ratio of ϕ = 0.5, which is crucial regarding flame stabilization and evaporation. To quantitatively evaluate the NO x formation, a new reaction mechanism for sulfur combustion along with S/N/O and NO x reactions has been developed and used for the simulation. In comparison to our previous simulations using a higher ϕ, the flame is lifted slightly and the overall flame temperature is lowered in the current case, leading to a weakened evaporation performance. Accordingly, an increased share of sulfur droplets hitting the chamber wall and escaping the domain has been confirmed. The local NO x share has been shown to increase strongly with the flame temperature from a threshold value of approximately 1600 K. In addition, the NO x formation from the burner setup with a high swirl intensity (HSI) has been shown to be 2 times higher than that with a low swirl intensity (LSI). This is attributed to a higher flame temperature and longer residence time caused by a strong inner recirculation flow. However, the HSI setup yields a better evaporation performance and a reinforced flame stabilization. The results reveal a trade-off for operating the sulfur burner with different burner designs and equivalence ratios.

Numerical evaluation of a novel double-concentric swirl burner for sulfur combustion

A burner system for the efficient and clean combustion of sulfur is introduced, which serves as a key component in a novel solar power cycle using sulfur as chemical storage medium of solar energy. In order to validate the proposed design concept, highly-resolved numerical simulations have been performed. The current setup is operated with a thermal load of 20 kW or power density of 5 MW/m3. Two nozzle configurations with different swirl intensities (SI) of the airflow are studied. A large inner recirculation zone is observed for the nozzle with a high SI (HSI), which leads to a strong radial dispersion of the sulfur spray and a broad, short flame in the combustion chamber; although this HSI design is beneficial from the viewpoint of flame stabilization, it causes a large number of sulfur droplets hitting the chamber wall. In contrast, the nozzle design with a low SI (LSI) yields a narrow spray and a long jet flame, with much less droplets hitting the wall. The HSI nozzle shows an overall higher flame temperature compared with the LSI nozzle, which is confirmed to be caused by burning at a higher local fuel equivalence ratio. This is attributed to the strong inner recirculation flow generated by the high swirl intensity, which results in an enhanced evaporation and mixing of sulfur droplets with air. In terms of operability and NOx emission, the LSI burner is preferred due to less sulfur droplets hitting the chamber wall and the lower flame temperature.

Swirl intensity as a control mechanism for methane purification in supersonic gas separators

Supersonic gas separator is proposed for methane purification. One-dimensional analysis is performed to examine the design aspects associated with the converging-diverging nozzle and the liquid separation chamber. The results indicate that at low swirl intensities, the separation chamber length is about 100 times of the nozzle throat. Increasing the swirl intensity would lower this length sharply and it will be less than 10 for swirl intensity of unity which is equivalent to a swirl angle of 45°. In addition, a sensitivity analysis of the separator performance to the inlet conditions like the temperature, pressure, and composition of the mixture is carried out. It is observed that increasing the inlet temperature will reduce the condensation rate and separation performance, while an increase in the inlet pressure and methane mole fraction will boost the flow condensation rate. Further, changes in the inlet condition will affect the critical droplets diameter and required separation length. In this regard, the separation length will increase with decreasing inlet temperature and increasing inlet pressure and methane mole fraction. The results reveal that the operation envelope of the supersonic separator is more sensitive to the variations in the inlet flow temperature where high swirl intensity is required at low inlet temperature in order to maintain the separation chamber length. Finally, the results support that, for a fixed geometry of the supersonic gas separator, in order to maintain the performance, single or combined variations in the inlet conditions can be compensated by changing the swirl intensity within a reasonable envelope.

Stability and structure of inverse swirl diffusion flames with weak to strong swirl

Flame stabilization in many practical devices is achieved primarily through swirl; however, the application of swirl to an inverse diffusion flame and its effect on both flame stability and structure have not yet been reported. Therefore in this work, flame stability and structure of inverse diffusion swirling flames are investigated. The most stable flame is achievable at a critical swirl intensity, Scr. Lifted swirl jet-like flames at swirl intensity <Scr, and compact flames at swirl intensity >Scr are observed. Simultaneous PIV/OH-PLIF measurements are conducted to investigate the flame-flow interaction for three flames. The flame at Scr is stabilized due to the mutual dependence of two flame zones, the conical flame, and the flame root. The conical flame zone is located along with the inner shear layer (ISL) between the internal recirculation zone and the jet flow, while the flame root is positioned close to the burner nozzle. The ISL is favorable for flame stabilization due to the enhancement of the mixing of burned gas and fresh-fuel/air associated with the frequently-formed vortices. The flame root is stabilized due to the instantaneous opposed flow between the hot burned gas and the fresh reactants. The flame root essentially requires the upstream flow of hot exhaust gases associated with the IRZ. It is inherently unstable at high swirl intensities due to the high strain rate coupled with the strong IRZ. At low swirl intensities, the flame root is extinguished by the high momentum of the central jet, and a lifted flame is anchored in low-velocity regions of the jet, with the flame adjusting axially and radially to meet this criterion. These results emphasize the crucial role of the flame root in stabilizing the flame and suggest that well-aimed modifications of the flow field to further enhance mixing in this region may increase the stability of lifted jet-like swirling flames.

Experimental and Numerical Study of Swirling Flows and Flame Dynamics

Abstract The effect of swirling air on the flow dynamics was investigated for the cold non-reacting flows and the flame arising at thermo-chemical conversion of biomass pellets downstream of a cylindrical channel. Under experimental and numerical investigation was the swirling flow dynamics with the primary axial air supply below a biomass layer and swirling air supply above it. The results indicate that for cold flows the swirling air jet outflow from tangential nozzles leads to the formation of a complex flow dynamics which is influenced both by upstream and downstream air swirl propagation near the channel walls, with correlating swirl-enhanced formation of the upstream and downstream axial flows close to the flow centreline depending on the swirling air supply rate. These axial flows can be completely balanced at their stagnation within the axial recirculation zone. It is shown that at equal boundary conditions for the swirling flame and the cold flows the swirling flow dynamics is influenced by the upstream air swirl-enhanced mixing of the reactants below the air swirl nozzles. This determines the formation of a downstream reaction zone with correlating development of the flow velocity, temperature and composition profiles in the downstream flame regions with improved combustion stability. The low swirl intensity in these regions prevents the formation of a recirculation zone

Experimental Comparison of Three Floating Wind Turbine Concepts

Beyond many of Earth's coasts exists a vast deepwater wind resource that can be tapped to provide substantial amounts of clean, renewable energy. However, much of this resource resides in waters deeper than 60 m where current fixed bottom wind turbine technology is no longer economically viable. As a result, many are looking to floating wind turbines as a means of harnessing this deepwater offshore wind resource. The preferred floating platform technology for this application, however, is currently up for debate. To begin the process of assessing the unique behavior of various platform concepts for floating wind turbines, 1/50th scale model tests in a wind/wave basin were performed at the Maritime Research Institute Netherlands (MARIN) of three floating wind turbine concepts. The Froude scaled tests simulated the response of the 126 m rotor diameter National Renewable Energy Lab (NREL) 5 MW, horizontal axis Reference Wind Turbine attached via a flexible tower in turn to three distinct platforms, these being a tension leg-platform, a spar-buoy, and a semisubmersible. A large number of tests were performed ranging from simple free-decay tests to complex operating conditions with irregular sea states and dynamic winds. The high-quality wind environments, unique to these tests, were realized in the offshore basin via a novel wind machine, which exhibited low swirl and turbulence intensity in the flow field. Recorded data from the floating wind turbine models include rotor torque and position, tower top and base forces and moments, mooring line tensions, six-axis platform motions, and accelerations at key locations on the nacelle, tower, and platform. A comprehensive overview of the test program, including basic system identification results, is covered in previously published works. In this paper, the results of a comprehensive data analysis are presented, which illuminate the unique coupled system behavior of the three floating wind turbines subjected to combined wind and wave environments. The relative performance of each of the three systems is discussed with an emphasis placed on global motions, flexible tower dynamics, and mooring system response. The results demonstrate the unique advantages and disadvantages of each floating wind turbine platform.

Utilizing preferential vaporization to enhance the stability of spray combustion for high water content fuels

In a previous study on the stability of spray combustion for mixtures of alcohols (ethanol or 1-propanol) and water, the feasibility of burning fuels heavily diluted with water was demonstrated. In that study it was found that the preferential vaporization of alcohols in water can significantly enhance flame stability. Due to their high volatility and high activity coefficient in aqueous solution, the alcohols quickly evaporate from the droplets and generate a concentrated fuel vapor at the base of the jet. Therefore, a flame can be ignited and stabilize even though the water content of the fuel is quite high (up to 90wt%) (Yi and Axelbaum, 2013). In this study, we develop a procedure for selecting chemical fuels showing strong preferential vaporization in water. t-Butanol was identified as an excellent candidate based on its physical and chemical properties, including activity coefficient, vapor pressure, heat of vaporization and heat of combustion. Flame stability was evaluated for aqueous solutions of both ethanol and t-butanol using a spray burner where the extent of swirl was adjustable. Under both high and low swirl intensity, the flame stability of t-butanol aqueous solutions was better than that of ethanol. The characteristic time for fuel release from a droplet was modeled for both ethanol and t-butanol. The time to release 99% of the fuel from the droplet for t-butanol is over 70% shorter compared to that for ethanol, which supports the improved flame stability observed for t-butanol in the experiments.

On the effect of the nozzle design on the performances of gas–liquid cylindrical cyclone separators

This paper constitutes an experimental study of the separation performances of a gas–liquid cylindrical cyclone (GLCC) separator that interests the oil industry. The global hydrodynamics behavior in the GLCC is characterized by flow visualization under various inflow operating conditions. The effect of the inlet nozzle design on the performances of the separator is studied by using three different nozzles, and it proves to be a key parameter. With an insufficient nozzle restriction, low swirl intensity is imparted to the flow. Due to inadequate centrifugal effects, liquid is prematurely carried over by the gas as flooding occurs in the separator upper part. High amounts of gas are also carried under by the liquid stream. On the other hand, with a too severe nozzle convergence, the important drag applied by the gas leads to liquid “short circuiting” the cyclone toward the gas outlet. In addition to the nozzle design, the separator performances are influenced by phenomena such as liquid bridging or the occurrence of the slug flow regime at the cyclone inlet. This paper leads to a better understanding of the links between the hydrodynamics in the GLCC and its operational limits, which is necessary to enable reliable scaling up tools.

Numerical investigations on swirl intensity decay rate for turbulent swirling flow in a fixed pipe

Due to the importance of predicting the SIDR 1 1 Swirl Intensity Decay Rate. associated with engineering problems such as combustion chambers, draft tube of the Francis and Kaplan turbines, heat exchanger tubes, separators and so forth, in this research the trend of SIDR and its affecting factors, through a turbulent swirl decay pipe flow have been investigated. The swirling flow is created by means of a rotating honeycomb which produces solid body rotation at the inlet of a fixed pipe. First of all, turbulent swirling decay flow has been numerically surveyed using different flow conditions at the pipe inlet. The numerical results have been validated and compared with the existing experimental data and mathematical relations, showing satisfactory coincide. The obtained results show that, the SIDR depends mainly on the Reynolds number of the passing flow. On this basis, correlations have been proposed in order to improve the predictions of swirl intensity decay rate at upstream regions as well as those with high swirl intensity. In addition, conducted analyses demonstrates (analyses have been made to demonstrate) that the previous developed correlations for predicting swirl intensity decay rate, agree with those provided in this study only for regions far enough from downstream having the low swirl intensity. This implies that the swirl intensity decay rate should be a function of the type of swirl generator at the pipe inlet.

The influence of fuel-air swirl intensity on flame structures of syngas swirl-stabilized diffusion flame

Flame structures of a syngas swirl-stabilized diffusion flame in a model combustor were measured using the OH-PLIF method under different fuel and air swirl intensity. The flame operated under atmospheric pressure with air and a typical low heating-value syngas with a composition of 28.5% CO, 22.5% H2 and 49% N2 at a thermal power of 34 kW. Results indicate that increasing the air swirl intensity with the same fuel, swirl intensity flame structures showed little difference except a small reduction of flame length; but also, with the same air swirl intensity, fuel swirl intensity showed great influence on flame shape, length and reaction zone distribution. Therefore, compared with air swirl intensity, fuel swirl intensity appeared a key effect on the flame structure for the model combustor. Instantaneous OH-PLIF images showed that three distinct typical structures with an obvious difference of reaction zone distribution were found at low swirl intensity, while a much compacter flame structure with a single, stable and uniform reaction zone distribution was found at large fuel-air swirl intensity. It means that larger swirl intensity leads to efficient, stable combustion of the syngas diffusion flame.

Control of flames by tangential jet actuators in oxy-fuel burners

The active control of oxy -fuel flames from burners with separated jets is investigated. The control system consists of four small jet actuators, placed tangential to the exit of the main jets to generate a swirling flow. These actuators are able to modify the flow structure and to act on mixing between the reactants and consequently on the flame behavior. The burner (25 kW) is composed of separated jets, one jet of natural gas and one or two jets of pure oxygen. Experiments are conducted with three burner configurations, according to the number of jets, the jet exit velocities, and the separation distance between the jets. OH chemiluminescence measurements, particle image velocimetry, and measurements of NO x emissions are used to characterize the flow and the flame structure. Results show that the small jet actuators have a significant influence on the behavior of jets and the flame characteristics, particularly in the stabilization zone. It is shown that the control leads to a decrease in lift-off heights and to better stability of the flame. The use of jet actuators induces high jet spreading and an increase in turbulence intensity, which improves the mixing between the reactants and the surrounding fluid. Pollutant measurements show important results in terms of NO x reductions (up to 60%), in particular for low swirl intensity. The burner parameters, such as the number of jets and the spacing between the jets, also impact the flame behavior and NO x formation.

Modeling and Simulation of Effects of Turbulence on Vaporization, Mixing and Combustion of Liquid-Fuel Sprays

The objective of this work is twofold. Firstly, the effects of turbulence intensity variations on the turbulent droplet dispersion, vaporization and mixing for non-reacting sprays (with and without swirl) are pointed out. Secondly, the effects of the coupling of the turbulence modulation with external parameters, such as swirl intensity, on turbulent spray combustion are analyzed in configurations of engineering importance. This is achieved by using advanced models for turbulence, evaporation and turbulence modulation implemented into FASTEST-LAG3D-codes: (1) To highlight the influence of turbulence modulation on some spray properties, a thermodynamically consistent modulation model has been considered besides the standard assumption and the well known Crowe's model. For turbulent droplet dispersion, we rely on the Markov-sequence formulation. (2) In order to characterize phase transition processes ongoing on droplets surfaces, a non-equilibrium evaporation model shows better agreement with experiments in comparison with the quasi-equilibrium-based evaporation models often used. (3) The results of turbulence intensity variations reveal the existence of a limited range out of which the increase or decrease of the turbulence intensity affects no more the efficiency of the heat and mass transfer. A derived characteristic number, a vaporization Damkholer number, possesses a critical value which separates two different behavior regimes with respect to the turbulence/droplet vaporization interactions. (4) Under reacting conditions, it is shown how the evaporation characteristics, mixing rate and combustion process are strongly influenced by swirl intensity and turbulence modulation. In particular, the turbulence modulation modifies the evaporation rate, which in turn influences the mixing and the species concentration distribution. In the case under investigation, it is demonstrated that this effect cannot be neglected for low swirl intensities (Sw.Nu. ≤ 1) in the region far from the nozzle, and close to the nozzle for high swirl number intensities. In providing these particular characteristics, a reliable control of the mixing of gaseous fuel and air in evaporating and reacting sprays, and a possible optimization of the mixing process can tentatively be achieved.

ON THE DYNAMICS OF A TWO-PHASE, NONEVAPORATING SWIRLING JET

In this paper, we present direct numerical simulation of a droplet-laden swirling jet, and examine the effects of swirl and two-phase momentum coupling on the jet dynamics and structural characteristics. A time-dependent, multi-dimensional, two-phase algorithm is developed for the simulation. Results for the single-phase swirling jet at a Reynolds number of 800 indicate that the dynamics of large-scale structures are strongly affected by the degree of swirl imparted to the incoming flow. For low and intermediate swirl intensities, the vortex rings roll up closer to the nozzle exit, their frequency increases, and pairing interactions become progressively stronger as the swirl number ( S) is increased. Thus, the addition of swirl to a transitional jet appears to modify its vortex dynamics in a way that enhances the beneficial effects of both swirl and vortex structures on the shear layer growth and entrainment. For a strongly swirling jet, the presence of a central stagnant zone and recirculation bubble causes a dramatic increases in the jet spreading angle, and this has a very dramatic effect on vortex dynamics. Based on a detailed visualization of the dynamic structure, we speculate that vortex structures in turn play an important role in determining the location and size of recirculation bubble. Results for the two-phase swirling jet indicate that for a mass loading ratio of unity, the jet dynamic and time-averaged behavior are strongly affected by both the interphase momentum coupling and swirl intensity. For a nonswirling two-phase jet, the momentum coupling modifies the dynamics of large vortex structures, including their roll-up location and frequency, which leads to enhanced mixing and entrainment of colder fluid into the shear layer. In contrast, for weakly and moderately swirling two-phase jets ( S<0.5), the momentum coupling reduces the shear layer growth, as well as mixing and entrainment rate. As the swirl number is increased, the effect becomes progressively stronger, manifested by the reduced rate of decay of gas velocity and temperature along the jet axis. In addition, the relation between roll-up frequency and swirl is modified in that the frequency increases with S for a single-phase jet, while it becomes independent of S for the corresponding two-phase jet. Consequently, the vortex pairing interactions, which are responsible for enhanced mixing and entrainment for single-phase swirling jets, are suppressed for two-phase jets. For strongly swirling two-phase jets ( S>0.5), the effect of momentum coupling becomes even more dramatic. Results for S=0.75 indicate a drastic reduction in the size of the recirculation bubble for the two-phase jet.

Effects of swirl on the stability of jet diffusion flames

An experimental study was made, using a double-swirl burner, of the stability of swirling-fuel-jet diffusion flames in swirling air streams. The fuels were hydrogen and methane. The primary variables studied were swirl intensities of the fuel jet and the air stream. It was found that the stability of flame depended on the swirl intensity of both the fuel jet and the air stream. The application of swirl to the fuel jet decreased the rim stability of the flame, but increased the blowout stability of the lifted diffusion flame. For low swirl intensity of the air stream, the effect was similar to that of the fuel jet. At higher swirl intensities of the air stream, above a critical value, the flame stability increased noticeably because of the formation of a recirculation zone near the injector exit. Even in strongly swirling air streams, the favorable effect of fuel swirl on stability of the lifted flame was evident, particularly for the methane flame.

An Extension of One-Dimensional Theory to Inviscid Swirling Flow through Choked Nozzles

SummaryA method is presented for determining the swirling compressible flow through a nozzle, given conditions at a reference section. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual for the radial velocity component to be neglected at each section, i e, the usual assumption of one-dimensional compressible flow theory. This method is used to determine choked-flow conditions in the case where there is solid-body rotation at the throat for a range of swirl intensities with the ratio of the specific heats taking various values. Mass-flux coefficients and impulse functions are determined. Sonic surfaces, velocity profiles and other characteristics of interest are also presented. An approximate analysis valid for low swirl intensities is developed and analytical formulae are derived for most quantities of interest. The main conclusion of practical importance is that the introduction of swirl to compressible nozzle flows need not lead to a significant reduction in specific thrust. Further exploration of the possible effects of swirl on noise during the relatively short take-off and landing periods cannot therefore be ruled out on the grounds that swirl would lead to excessive thrust losses.