A Method to Design and Optimize Axial Flow Cyclones for Gas–Liquid Separation

Axial flow cyclones act as a gas–liquid separation device and have a wide range of applications in industry such as oil and gas purification [1,2], power generation [3], and wastewater treatment [4]. Compared with other popular liquid separation devices such as reverse flow cyclones, wire mesh demisters, and vane type demisters, axial flow cyclones have a high liquid separation efficiency due to the large centrifugal forces induced by small tube diameters [5]. In addition, the inline construction and relatively small size of axial flow cyclones allow them to be added in parallel into existing piping structures while requiring minimal effort to maintain the desired operation [6–9]. Furthermore, axial flow cyclones require a short residence time to achieve separation, thus minimizing heat losses from the cyclone in high temperature applications [10].

Despite the wide range of benefits and applications of axial flow cyclones, there are several design parameters and performance indicators important to wastewater treatment applications that have not been studied in great detail. Furthermore, most of the literature that does exist has been focused strictly on the water collection efficiency $(ηwater collection)$ and pressure drop across the separator [11–14]. The water collection efficiency is defined as the amount of water successfully captured in the desired water collection chamber over the water supplied to the system. The pressure drop is defined by the change in pressure from the inlet to the outlet of the separation device. This experimental study adds to the existing literature by quantifying the effect of design parameters on both the water collection efficiency and the air bypass efficiency $(ηair bypass)$ defined as the ratio of the air mass flowrate exiting through the desired air exit, over the inlet air mass flowrate. It also adds relative humidity data to the air bypass exit to quantify the water vapor losses from the system.

Reverse flow cyclones can be used to separate gas–liquid mixtures; however, these separators present some drawbacks. At high flow rates, liquid droplets can be separated effectively to the outside of the device due to large tangential velocities present in the swirling flow pattern. The pressure at the cyclone core drops in high flow rate applications, causing gas to remain trapped within the separator as opposed to being rejected to the ambient as intended. Conversely, at low flow rates, the pressure at the cyclone core increases allowing for effective gas separation, but lower tangential velocities fail to properly centrifuge smaller the liquid droplets to the enclosure walls, thus making liquid separation ineffective [15].

Wire mesh demisters operate via impingement of liquid droplets on a mesh of small-diameter strands followed by coalescence of droplets until gravity can act to pull them away from the surface on which they concentrated. The difficulty with this style of gas–liquid separation device is that the wire mesh must be sized to collect the desired amount of liquid while not causing flooding of the water collection exit. Smaller wire diameters can trap smaller droplets which increase in the water collection efficiency, however, flooding followed by re-entrainment of the liquid back into the gaseous stream negates this effect in many cases. If larger wires are used, they will only collect larger droplets thus reducing the pooling issue but as a consequence will result in a lower water collection efficiency [16].

Similar to wire mesh demisters, vane type demisters operate on the principles of impingement and coalescence on a surface. The surface in a vane-type demister is a sheet of material or vane, that is curved in such a way to allow gas to flow through while forcing liquid droplets to come in contact with the walls of the curves. Once the force of gravity on the droplet overcomes its drag force on the surface, the droplet falls downward to the water collection chamber below. Vane-type demisters often have a re-entrainment issue when the gas velocity is high. An additional drawback to this design is that complex vane geometries cause higher pressure drops due to an increase in turbulence in the two-phase flow [17].

Rotating phase separators have similar advantages to axial flow cyclones when compared to other separation technologies. The difference is that this type of separator uses an electrically driven rotor to create a centrifugal force that acts on liquid droplets, forcing them to coalesce around the perimeter of the device [18]. This type of separator has been shown to successfully separate droplets with diameters as small as 1 μm at flow rates of ten times what is possible using a reverse flow cyclone [19]. Drawbacks of this kind of separator include the additional electrical energy input and the increased complexity of the moving rotor when compared to standard, axial flow cyclones.

In most power generation systems that utilize steam as the working fluid, the separation of liquid droplets from the feed stream is critical to preventing damage to the turbine. Specifically, in geothermal power generation plants, liquid droplets can contain corrosive chemicals that can cause cracking and fouling of turbines and other downstream devices [20]. In many geothermal and nuclear power plants, several of the aforementioned separators are used in tandem to achieve water separation efficiencies in the range of 99.5% to 99.8%. An axial flow cyclone is generally used as the first component in the separation line due to its minimal pressure drop. If high liquid loads are present, several axial flow cyclones may be installed in parallel. Directly before the turbine, a combination of the wire mesh and vane-type demisters may be used to “polish” the steam to the desired level of dryness. With most of the moisture and contaminates removed by the axial flow cyclones, and a lower operating pressure due to the decrease in the moisture content of the stream, many of the drawbacks to the impingement-based separators are mitigated [4]. Without the use of axial flow cyclones, however, the fouling of the mesh pads would prove too costly to be an effective solution on its own.

As many conveniently located oil and gas reserves dry up or become inactive, large numbers of new operations are moving toward drilling in remote and isolated areas. Since space and weight are some of the most pressing constraints in these operations, there is a substantial need to confine many of the secondary purification and wastewater management operations to the extraction site [2]. One essential component that can be used to separate impurities from valuable substances is an axial flow cyclone [1]. As mentioned above, these gas–liquid separation devices operate on relatively simple mechanical concepts and have a small footprint compared to many alternatives. They have also been shown to maintain high separation efficiencies in high velocity and high-pressure applications, critical to wet gas flows often found in oil and gas extraction operations [21–23]. In addition, the tube-shaped geometry of axial flow cyclones allows them to be placed parallel with one another allowing near 100% separation of the liquid and gas phases [24]. Furthermore, the high centrifugal forces present in axial flow cyclones allow for small droplets to be separated (> 1 μm). The ability to separate small droplets under high flow rate conditions is critical in the natural gas industry as there are huge volumes of gas to be treated by relatively small equipment [25]. Together, these traits make axial flow cyclones an ideal candidate for the gas–liquid separation component vital to many oil and gas extraction operations. The natural gas industry is already familiar with inline separation technology as supersonic nozzles are often used to remove liquid water from a gas stream [26].

Some oil and gas extraction techniques involve blasting a highly pressurized water–sand–chemical mixture into existing wells with the goal of releasing oil from solid bedrock formations located far below the surface [27]. This process produces large amounts of highly contaminated wastewater that must be stored in injection wells, reused in other extraction operations, or reintroduced to the local environment after extensive treatment [27,28]. Storage of produced wastewater in injection wells can cause earthquakes and groundwater contamination if the wells burst, creating dangerous living conditions for communities surrounding drilling locations [27]. Furthermore, wastewater can only be reused a finite number of times in an extraction operation due to increases in large particulates that can plug wells [28]. This leaves treatment of produced wastewater as the only viable long-term solution to the environmental and human health-related problems caused by this oil production byproduct.

Traditional water treatment methods currently available for use in oil and gas extraction operations have several major downsides including high energy inputs, large capital investment, and fouling [29–32]. These shortcomings have led to roughly 90% of produced water from oil and gas operations to be discarded into injection wells, where it poses a greater risk of harming nearby communities and the environment in which they reside [33]. As an alternative to traditional wastewater treatment strategies, Oregon State University's (OSU) Water and Energy Technology (WET) Lab is developing an efficient, modular, and scalable wastewater treatment device [34]. This technology utilizes an axial flow cyclone to separate the contaminates from the purified water. In this application, both the water yield and gas–liquid contact postseparation are critical design criteria. The former is important for the economic viability of the technology and the latter can cause recontamination and must be avoided.

This work aims to experimentally quantify the water collection and air bypass efficiencies of an axial flow cyclone based on new operational and geometrical parameters. The experimental data are used to create a design guide for axial flow cyclones in wastewater treatment applications based on a correlation predicting the flow pattern of the two-phase mixture.

The following Materials and Methods section outlines the critical components of the experimental setup, as well as the methodology behind the chosen design parameters and their ranges.

Using information gleaned from several preliminary experiments and a comprehensive literature review, an axial flow cyclone test model was fabricated. A single demister was used to collect the water because most of the liquid collection occurs at the first demister location if multiple demisters are used [35]. The experimental setup was sized based on observations made during the preliminary cyclone experiments. Rough air and water flow rate ranges were determined using SolidWorks CFD analysis of mixing fluids within the tube. A clear acrylic pipe was used as the cyclone body due to its large and easy to observe size, as well as the quality of its material. A schematic and physical layout of the experimental setup including all fluid inlets, outlets, and measurement device locations is provided in Figs. 1(a) and 1(b). The make, model, and calibrated ranges for all measurement equipment are provided in Table 1.

The demister portion of the device was drawn up in SolidWorks and three-dimensional printed on a MakerBot Replicator +. This demister was designed to fit snuggly in the clear cyclone body and is shown in Figs. 2(a) and 2(b).

In order to collect the volume of water required for running all experimental trials, a large enough sealed container had to be obtained. The required volume for the collected water was calculated by multiplying the flow rate of water (4 kg/h) by the duration of water collection (1 h).

To cover this volume of water (4 kg or ∼1 gal) and still have enough space to insert the inlet-water line and the air bypass exit line above the pool of collected water, a sealed 2-gal bucket was selected. The screw on the lid of the selected bucket ensured that outside air did not interfere with measurements of the bypass air flow rate.

In order to generate mist flows from a solely water feed stream, a full cone nozzle was selected. This nozzle was chosen based on the type of spray pattern it produced from a low flow rate such as the roughly 1 gph flow rate to be used in this experiment. A spray cone angle of 80 deg was chosen in a full cone pattern to provide a fine and evenly distributed mist generation method. The chosen nozzle had standard eighth-inch male NPT threads to easily attach it to the lab water hose fittings. Schematics of the selected nozzles and its specification can be found in Fig. 3.

The clear cyclone body was cut to a length that provided adequate space for the swirling flow pattern observed in past experiments to form after the mixing of the mist and air flows. The hole for the air inlet was drilled into the tube starting with the smallest drill bit (1/16 in.) and then increased incrementally to a 1/4 in. so the acrylic pipe would not crack. The hole was drilled tangential to the circumference of the tube to induce a rotational flow pattern and was altered in such a way to allow the angle of the air injection nozzle to be adjusted.

All flow stream measurement equipment was sized and calibrated using previously established flow rates and operating conditions determined from preliminary experiments. All measurement equipment was ordered from Omega Engineering. Each unit that was ordered included a 0–5 VDC (volts direct current) output that could be connected to National Instruments (NI) equipment to record flow rates and fluid properties in real time.

To connect the three volumetric flow meters and the pressure transducer to LabVIEW, the NI-9205 control module was used as it had four input channels and a sample rate that was compatible with the measurement devices used. Temperature data were collected using the NI-9213 control module which included several specific features for reading thermocouple signals. In order to power the control modules and all the measurement equipment, a Mean Well DR-120-24 power supply was used. This power supply could generate a maximum of 120 W at 24 VDC and 5 A which far exceeded the power requirements of all the devices that were connected to it. The LabVIEW block diagram interface was used to write a code that could covert the voltage signals from each measurement device to meaningful physical values that could be recorded by a computer. All data were recorded in Excel spreadsheets for easy organization of experimental results.

Many influential and inter-related parameters affect the separation performance of an axial flow cyclone. These include, but are not limited to, the air flow rate, water flow rate, angular velocity, cyclone diameter, air exit diameter, water exit diameter, thickness of the demister gap, and length of the tube [5]. In order to determine the most influential parameters on the separation performance, several dimensionless groups of variables were formed using the Buckingham Pi Theorem. These dimensionless groups allowed for a large range of conditions to be tested without the need for running an enormous number of trials. These normalized parameters were also used to generalize the results of this work so they could more easily be applied to further research in this field.

The dimensionless quantities that were created to test the effects on the previously defined efficiencies were the cyclone length times the demister gap thickness over the cyclone inner diameter times the air exit inner diameter (⁠$Ltube · tgap/dtube · dexit,a$⁠) the angle of the air injection nozzle in degrees (⁠$θinlet,a$⁠) and the inlet air mass flow rate over the inlet water mass flow rate (⁠$M˙inlet,a/M˙inlet,w$⁠). All of these dimensionless quantities were tested at a range from high and low values determined by observations of the device in operation. Temperature and pressure conditions of the inlet air stream varied between 19 °C and 21 °C and 100–200 kPa, respectively. Data were collected using a NI Data Acquisition system (DAQ) and recorded using the LabVIEW software.

In order to test all parameters over the desired ranges, four different tube geometries were constructed to test the following: air to water ratio, air injection angle, tube length, and demister gap thickness. Tube geometries 1 and 3 had the same tube length of 370 mm but a different demister gap thickness. Similarly, tube geometries 2 and 4 had the same tube length of 300 mm but different demister thicknesses. A table of the different design parameters and their ranges can be found in Table 2.

Since there were two tube lengths, two demister gaps, four air-to-water ratios, and four air inlet angles, a total of 64 trials were conducted in order to test all combinations of the design parameters. The extreme values of all parameters were tested two times in order to check for repeatability. Considering only the extreme levels of each parameter, there were two tube lengths, two demister gaps, two air-to-water ratios, and two air inlet angles, a total of 16 trials were conducted in order to test for repeatability. These repeated data were within 10% of the original measurements.

After completion of the initial 64 trials and the 16 repeatability tests, the data were organized into the test matrix previously mentioned in Table 1. An uncertainty analysis was conducted using the uncertainty propagation tool in Engineering Equation Solver (EES). A table was constructed in EES that included all data that was collected as well as the absolute uncertainties associated with each measurement device. This process calculated the cumulative uncertainty of the final dependent variables based on the accuracy of measurement devices and the relationships between measured quantities. It should be noted that the high uncertainty in the water collection efficiency data resulted from measuring the quantity of water lost from the system with a scale that only reported weight to 0.01 g of precision. The water lost from the system was measured due to the difficulty of accessing the collected water. Since the water that was successfully separated was drained to the sealed water collection bucket, it was not desirable to repeatedly break this seal as that would affect the air bypass measurements. Because the low water collection efficiency data points resulted in large water losses from the system, the low precision of the scale made up a large percentage of the uncertainty associated with these data points. For reference, the highest water collection efficiency points of 100%, had an uncertainty of 0.01%*. The lowest water collection efficiency point of 2.5% had an uncertainty of 6.99%**.

All the data relating to the dependent variables of interest, (⁠$ηair bypass$⁠, $ηWater Collection$⁠, and relative humidity) were plotted against the dimensionless parameters $((Ltube·tgap/dtube·dexit,a),θinlet,a,M˙inlet,a/M˙inlet,w$⁠). Uncertainty minimum, maximum, and average values as a percentage of measured quantities are shown in Table 3. The uncertainty values calculated for each data point are included as error bars in all plots.

The air bypass efficiency, (⁠$M˙exit,a/M˙inlet,a$⁠), water collection efficiency, (⁠$M˙exit,w/M˙inlet,w$⁠), and relative humidity, (⁠$PH20/PH2O sat$⁠), data were plotted in Figs. 4–6 and are discussed in detail in this section. The water collection efficiency provides a comparable standard to measure axial flow cyclones against other gas–liquid separation technologies. The air bypass efficiency and relative humidity measurements give critical insight into whether axial flow cyclones are a suitable candidate for use in wastewater treatment applications. In order to increase readability, results for only one tube geometry per dependent variable were plotted and displayed. All trends show in the plots in this section were followed by the data corresponding to the other tube geometries.

As shown in the plot in Fig. 4, there was a clear trend comparing the air bypass efficiency to the inlet air to water ratio: As the inlet air to water ratio increased from ∼3 to 6, the air bypass efficiency decreased from ∼99% to 92%. The fact that the trend was consistent between all four tube geometries indicated that the geometry of the cyclone had little effect on the air bypass efficiency. These results gave some useful insight into the optimal operating conditions of an axial flow cyclone if air bypass through the water collection chamber is a concern (e.g., air is contaminated and may recontaminate the water). These findings will be discussed further in Sec. 3.5.

A significant finding from the relative humidity data was that even at the maximum recorded value of 87.9% (using Omega HH314A humidity sensor), the total water vapor losses from the system were only 3.24 g or 3.83% of the total water supplied. This implied that the water collection efficiency could be consistently greater than 96%.

In contrast to the plot in Fig. 4, the plot in Fig. 5 had no discernable trend relating the water collection efficiency to the ratio of the flow rates or the air injection angle. The main takeaway from these data as well as observations from the experiment in action was that there was a significant relationship between the swirl pitch, or the distance between streamlines, and the tube geometry. Specifically, if the streamline came in direct contact with the water drain hole located at the bottom of the demister, the water collection efficiency was very high. Alternatively, if the streamline came in contact with the demister at the top or sides of the tube, a disturbance was created causing water droplets to break from the controlled swirling flow pattern and form a pool at the base of the demister. This pool caused the liquid water to re-entrained in the air exiting through the middle of the demister and the water collection efficiency to plummet. A picture of the pooling phenomena (low water collection efficiency) as well as a high water collection efficiency trial are displayed in Figs. 6(a) and 6(b), respectively.

An interesting note was that the pooling problem occurred with both demister gap thicknesses tested, 4.30 and 2.15 mm. The frequency of this pool forming was observed to be less when the larger demister gap thickness was used. As seen in Sec. 3.1, the demister gap thickness did not appear to have a negative impact on the air bypass efficiency. Using this result as a guideline, it is recommended that the demister gap thickness to tube diameter ratio be similar or greater than what was tested in this set of experiments. This ratio was calculated to be 0.085.

In order to maximize the water collection efficiency, an additional set of experiments were conducted to correlate the swirl pitch to the inlet air and water velocities as well as the air injection angle. This experimental correlation is discussed in greater detail in Sec. 3.4.

The above experiments proved that the single most important factor to maximize water collection efficiency is how water streaks interact with the water drainage point. That is, if the water streak impinges directly on the drainage point, water recovery reaches ∼100%. In order to model how the swirl pitch would vary with changing inlet fluid velocities and air injection angle, a series of trials were run using the same experimental setup as shown in Fig. 1. The swirl pitch was recorded while varying the ratio of the axial air-to-water velocities, the air injection angle, and the tube diameter. The air and water velocities were chosen to better capture the dynamics of the swirling flow pattern as opposed to the mass flow rates. The air and water velocities were calculated based on the volumetric flow rates of each fluid and their respective cross-sectional areas in line with the tube. The tube length and ratio of demister gap to tube diameter remained constant for all trials. Values for the tested parameters are shown in the test matrix in Table 4.

The volumetric flow rates for air and water were consistent across all tube geometries, however due to the changing tube areas, the axial air velocity varied considerably in the range of $0.42 m/s≤Vair≤3.38 m/s$⁠. The axial water velocity out of the mist nozzle was relatively consistent but fluctuated between $12.73 m/s≤Vwater≤13.14 m/s$ due to pumping pressure changes in lab water supply line. The large range in the axial air velocities combined with the higher axial water velocities resulted in the relatively small range of axial air-to-water velocity ratios plotted in Figs. 7–9. All air to water velocity ratios tested were a result of using the same air-to-water mass flow ratios used in the air and water separation experiment. The air injection angles were also consistent with those tested in the previous experiment with the exception on the 90 deg angle which was changes to 75 deg to maintain a consistent increment between angles. The combination of the four air to water velocities, four air injection angles, and three tube diameters produced a total of 48 new experimental trials.

In a similar fashion to the air and water separation efficiency experiments, the variables in the swirl pitch experiment were ordered into nondimensional groups using the Buckingham Pi Theorem. The results from this analysis produced Pi groups: $θinlet,a, (Vaxial,a/Vaxial,w)$⁠, and (⁠$Pswirl/Ltube$⁠) where $θinlet,a$ was the injection air angle, $Vaxial,a/Vaxial,w$ was the ratio of air-to-water axial velocity, $dtube/dexit, a$ was the diameter of the tube over the diameter of the air exit, and $Pswirl/Ltube$ was the swirl pitch (dependent variable) over the tube length. A plot showing $Vaxial,a/Vaxial,w$ on the x-axis versus $Pswirl/Ltube$ on the y axis for each air injection angle in all three tube diameters are displayed below in Figs. 7–9.

As seen in the plots above, as the air injection angle decreased, the pitch length increased. This trend was observed in the larger tube diameter to a more extreme extent due to the longer distance the streamline had to travel to complete one pitch in these tubes. It can be seen in Figs. 7–9 that there are two sets of streamlines in the 75 deg trials. In these cases, the two streamlines collapsed into a single streamline by the time it reached the water drainage point (∼300 mm downstream from the air injection port). Each plot includes three repeated trails for every data point. The error bars account for the uncertainty associated with the pitch length measurement.

By calculating the difference between the collected pitch data and the results provided by Eq. (1), summing up the absolute value of these differences, and then minimizing that sum, the coefficients $C1$⁠, $C2$⁠, $C3$⁠, and $C4$ were solved for in a global fit. The same process was repeated for the data sets associated with each tube diameter to produce a unique set of equations for the individual fits. In both the global and individual fits, the predicted values associated with the 75 deg data produced the highest error at around a 30% deviation from the experimental results. The error between the predicted and experimental pitch values for the 30, 45, and 60 deg angles was less than 15% in both the global and individual fits. A plot showing the experimental data versus calculated values from the correlation for the whole dataset can be viewed in Fig. 10.

One reason for the higher error associated with the 75 deg data was that the absolute value of the pitch lengths for this data series was shorter than the pitch lengths associated with other angles, however, the accuracy of the pitch measurements remained the same for all trials. This resulted in the error associated with the 75 deg data making up a greater percentage of the pitch value that was recorded.

Another reason for the poor fit of the 75 deg data was that there were more swirls that formed in the fixed tube length for the larger air injection angle trials. This was accounted for by averaging all the swirl pitches that formed in each trial. As seen in Fig. 11, the pitch lengths for the 75 deg air injection angles were not always consistent as they progressed down the tube. This was likely due to friction between the water streamline and the tube wall, causing a loss of momentum. The inconsistent pitch length affected the average value that was used in the curve fitting data set. Since there were only one-to-two pitch measurements along the 300 mm length of the tube for the other angles, the averaged values followed a more consistent pattern. The algorithm used to calculate the curve fitting coefficients relied on minimizing the cumulative error. This led to better predictions of the pitch lengths associated with the 30, 45, and 60 deg angles, and neglected to account for the inconsistencies in the 75 deg data caused by the larger number of swirls that were averaged. Pictures of the inconsistent pitch lengths during two 75 deg air injection angle trials are displayed in Figs. 11(a) and 11(b).

The axial flow cyclone design process should be broken up into four parts:

1. Identify the minimum air-to-water mass flow ratio that will induce a swirling flow pattern in the desired tube geometry. This will minimize the air bypass through the water collection system if recontamination of the separated water is not desired.

2. Determine the swirl pitch based on the correlation provided in Sec. 3.4 as well as the upstream flow conditions that are used as inputs to this function. The velocity ratios are related to the mass flow rates determined in step 1 through the density of each fluid as well as the cross-sectional area of the swirl tube. If a swirl generator is used, the air injection angle is controlled by the blade angle.

3. Size the tube length between the air injection port (or swirling flow generator) and the demister to be an integer multiple of the swirl pitch length calculated in step 2. This will allow for the water collection efficiency as defined above to exceed 99%. Some iteration may be required.

4. Use a demister gap thickness to cyclone inner diameter ratio of at least 0.085 to reduce the chance of pooling and re-entrainment of liquid droplets in the gas carrier stream as recommended in Sec. 3.3.

This study had two main objectives: First, to quantify the amount of air passing through the water collection chamber, and second to determine a set of design guidelines that can be used to optimize an axial flow cyclone for use in wastewater purification applications It was found that in order to increase the water yield for a given air to water mass flow ratio the system should be designed so the water streamline lands directly in the water collection exit. This can be achieved by following the guidelines in Sec. 3.5.

In order to decrease air bypass through the water collection chamber, the minimum amount of air that will still centrifuge the droplets effectively, should be used. This will also reduce the energy costs of compressed air at higher mass flow rates.

An additional tactic that could be employed to reduce the water pooling issue could be to add a small reservoir in the tube right below the demister section to allow for the water to pool without being re-entrained into the airstream. More water drainage points or a long slit in line with the tube could prevent the water pooling problem from occurring if the streamline is not able to be accurately directed into a single water drainage point. This design would need to be tested to ensure that it would not dramatically affect the air bypass efficiency. In addition, more demisters could be added in series to capture the water that is re-entrained in the airstream after the first demister if the swirling flow pattern could be shown to persist past the first demister.

Although 64 trials were conducted to test the air bypass efficiency, water collection efficiency, and the relative humidity at the system exit, additional trials with a broader range for each of the parameters tested would help expand the design space and elucidate trends that were not discernable in this study.

Future work includes investigating the aforementioned geometry changes in a parametric fashion to give insight into other axial flow cyclone modifications. Also, studying the effects of other combinations of working fluids would add to the applicability of this work by making it more relevant to many industries. Examples could be quantifying the condensation effects of a two-phase air–steam flow on swirl formation or testing the separation efficiency on a broader range of gas–liquid mixtures outside of air and water. Finally, the orientation of an axial flow cyclone should be investigated to determine how gravitational effects would affect the proposed design guidelines. This information would further add to the versatility of these types of separators in commercial applications.

The authors acknowledge the engineering faculty members at OSU Cascades as well as fellow graduate students working in the WET Lab who provided numerous valuable insights into this work.

• United States Department of Energy's Advanced Research Projects Agency—Energy (No. DE-000AR1000; Funder ID: 10.13039/100006133).