## Abstract

Vortex amplifiers (VA) use fluidic phenomena to modify flow through a containment breach, when used to protect glove box workers from exposure to the contents. The influence of control port geometry on swirl, operating characteristics, global flow, and momentum characteristics is studied experimentally. Shape and size of the control flow channels and the pressure applied at the tangential ports are critical in determining the trajectory of the jet issuing from the tangential ports and deflection of radial flow and vortex strength. Dominance of control-to-exit area ratio is confirmed. A clear improvement in performance is noted for a practical geometry derived from shaped passages of the device. Flow and momentum characteristics provide additional design data. The relationship of swirl number to output flow is demonstrated. Global flow and momentum characteristics provide insight into design and operation that is useful when avoiding back diffusion.

## Introduction

### VA Operation.

A VA is an in-line flow device. It can be connected in series between a glove box space and extract plenum by affixing it to the inside of the glove box wall surrounding the extract. In this arrangement, the VA is used to control the rate at which the glove box atmosphere is drawn from the glove box.

A VA consists of a thin cylindrical chamber into which radial flow is introduced at the curved periphery, via ports and channels cut radially into the casing. Flow travels through the radial port into the chamber, before turning 90 deg to leave the chamber axially via an outlet stub protruding through a hole in the flat casing side-wall and glove box wall. Modulation is achieved by flow through the control inlet nozzle, fixed at a tangent as shown in Fig. 1 (based on sketches in Refs. [1] and [2]). Fluid from this nozzle deflects flow entering at the radial inlet and mixes with it, creating swirl in the chamber.

Fig. 1
Fig. 1
Close modal

Together, the two fluid streams spiral towards the outlet. The response of the output flow to increasing control port pressure generally takes the form of a negative gain characteristic (see, for example, in Fig. 1). If control pressure is raised sufficiently, then a “cut-off” point is reached where radial flow is prevented from entering the chamber by the expanding tangential jet.

Figure 2 shows the effect of control pressure on flow through a typical VA used to protect workers on glove boxes containing alpha-emitting radiological substances. The solid plot lines show how the device can be operated over a wide range of radial “supply” pressures. Reduction in output for increasing control pressure is much steeper than was shown in Fig. 1. Introduction of control flow initially has negligible effect on the output, but once sufficient tangential flow is introduced a vortex is established and output falls dramatically. This characteristic enables speedy switching from the foot of the low pressure curve to a substantially greater output flow, in the event of a sudden increase in supply pressure.

Fig. 2
Fig. 2
Close modal

When used on UK nuclear plant, it is usual for the operating characteristics to be presented in a modified form, but the switching nature is still evident. First, it is control port flow (rather than control port pressure) that is presented on the abscissa and second, output flow measurements are normalized by the maximum generated at the selected glove box depression (i.e., with nil control flow).

### Service on Nuclear Glove Boxes.

In the USA, balancing valves or “donkin” valves are typically used to protect glove box workers from airborne contaminants [4], although in recent years VAs have also been introduced [5]. In the UK, it is commonplace for a VA to be used in preference to a valve, since it has no moving parts to compromise reliability [6]. The device is affixed to the glove box wall and the glove box atmosphere is slowly drawn into the VA through four radial ports and then diverted by tangential flow to establish a vortex in the chamber, and the device normally exists at the lower end of the operating characteristic (as seen in Fig. 2).

In normal operation, flow through the system is restricted by the tight glove box fitting and carefully controlled purge flow into the glove box. The glove box depression only returns to near-atmospheric if the containment is breached, when that increase in pressure drives flow through the radial supplies with increased momentum, to overcome and destroy the vortex and thereby reduce overall restriction to flow and promote inward flow through the breach, reducing risk of exposure to airborne radionuclides.

Use of VAs on nuclear glove box service is well documented (e.g., Refs. [7] and [8], etc.). Design guidance is available (e.g., Refs. [2] and [9], etc.). The influence of various geometrical parameters on the operating characteristics of VAs is well established (e.g., Refs. [10] and [11], etc.). Sources of periodic structures and instability have also been considered (e.g., Refs. [12] and [13], etc.). Various geometries have been used for site-based VAs (e.g., Refs. [14] and [15], etc.) and working derivatives have been patented (e.g., Refs. [16] and [17], etc.).

Early in this century a new design of VA became commonplace at the Sellafield site. The “mini-VA” (as it is known at the Sellafield site) was produced by geometrically scaling down a previous VA model and altering some of the assembly connected to the exit port. This was done for ergonomic reasons. Performance of the mini-VA has been disappointing. High levels of oxygen were recorded inside glove boxes purged with inert gas and served by the mini-VA. As the result of back diffusion of control air from the units into the glove boxes, this problem was significant as inert gas purging rates had to be increased to compensate.

Early site experience of the mini-VA stimulated research looking at new problems associated with this old technology. Reports of recent computational fluid dynamics (CFD) studies [18,19] and prototype testing [6] to overcome the back diffusion problem have already been published, but the experimental laboratory work supporting that development process has until now only been reported in theses.

This paper reports previously unpublished theoretical and experimental work on a restricted range of geometries aimed at mitigating the back diffusion problem.

## Experimental Apparatus

### Test Geometry.

Two sets of experiments are reported in this study, whereby the influence of control port design was investigated. In the first, 28 tests were conducted in the laboratory to study the influence of different geometric parameters on VA performance. The size and shape of various flow passages were systematically altered from a “standard” geometry. Thus, control port size was confirmed as a major variable. The four tests involving changes to the control port were labeled 3.9, 3.10, 3.11, and 3.12, with the “standard” geometry named 3.1 [7]. To achieve this, modeling clay of different widths was inserted into the control port passage along the promontory wall, to produce successively four narrower but straight control port passages of oblong cross section.

Together with smoke visualization tests [18], results of set 1 led to proposals for improved geometry. These are the subject of the second set of tests reported here, which in turn, led to the development of prototypes and subsequent field trials on site [6]. The second set of tests involved geometrical change to the control port aimed at reducing back diffusion of control port air into the glove box. The relevant tests were labeled 7.0, 7.1, 7.2, 7.3, and 7.4 [8]. The midplane geometry of test 3.1 is identical to that of test 7.0. See Appendix A for a description of the standard test geometry and how it was created in the test rig. See Appendix B for further construction details of inserts for all ten tests.

Figure 3 shows an example 2D sketch of the fluid flow path. All devices tested had four radial supply and four tangential control ports. All five main tests reported here from each set had the same supply port sizes. Note that the fluid enters along the 65 mm wide supply paths that are 68 mm long (radially along the center line) and through the 19 mm wide tangential control passages (supplied from 20 mm diameter holes), with a promontory separating these two fluid streams.

Fig. 3
Fig. 3
Close modal

All tests were conducted on a VA with a swirl chamber of nominal diameter of 140 mm. In the example 2D sketch of the fluid flow path geometry in Fig. 3, the pitch circle diameter (PCD) to the right angle at the corner of the radial and tangential port supply slots is 140 mm. Flow toward the center through the 65 mm wide radial slots is deflected by flow issuing from the 19 mm wide tangential slots (fed by 20 mm diameter holes in the end plate) to generate the swirl (anticlockwise in the figure). The exit port is not shown.

Table 1 gives details of the key geometric parameters tested in set 1 and Table 2 gives details for set 2. Tests 3.9–3.12 introduced modeling clay to reduce port width in the device manufactured to test geometry 3.1. However, tests 7.0–7.4 involved engineering manufacture of parts for each test individually. Geometry 3.1 is identical to geometry 7.0, except that the control port inserts were measured at 9.58 mm thick in series 3 (set 1) and 10.0 mm thick in series 7 (set 2). Thus, the supply port area rose from 2491 mm2 in set 1 to 2600 mm2 in set 2. This is considered negligible since a separate systematic study of supply port width using modeling clay to reduce the passage width showed that this had almost no influence on VA performance (not reported here). In common with set 1, the tests for geometries 7.0, 7.1, and 7.4 have straight (tangential) control port inflows of constant section, but 7.2 and 7.3 have shaped approach flow paths (see Appendices).

Table 1

Geometry of the five early control port tests (series 3)

Test 3.9Test 3.10Test 3.11Test 3.12Test 3.1
Acmm248824014673728
As/Ae3.803.803.803.803.80
Ac/Ae0.740.370.220.111.11
PsePa110110110110110
Test 3.9Test 3.10Test 3.11Test 3.12Test 3.1
Acmm248824014673728
As/Ae3.803.803.803.803.80
Ac/Ae0.740.370.220.111.11
PsePa110110110110110
Table 2

Geometry of the five later control port tests (series 7)

Test 7.1Test 7.2aTest 7.3aTest 7.4Test 7.0
Acmm2760488456760760
As/Ae3.943.943.943.943.94
Ac/Ae1.150.740.691.151.15
PsePa150150150150150
Test 7.1Test 7.2aTest 7.3aTest 7.4Test 7.0
Acmm2760488456760760
As/Ae3.943.943.943.943.94
Ac/Ae1.150.740.691.151.15
PsePa150150150150150
a

Tests 7.2 and 7.3 were with shaped control port channels reminiscent of site devices.

In Tables 1 and 2, the areas quoted are the cross-sectional areas (i.e., flat planar areas of the minimum section) of the control, supply, and exit ports. For test/geometry of 7.0, it can be seen in the drawings in Appendix A that the curved chamber wall between the radial and tangential port is located at the end of a thin promontory. The tangential jet, if extending far enough across the face of the radial channel, will impact on the opposing corner of the curved chamber wall and radial channel. Test/geometry 7.1 has part of the promontory cut-away so as to allow the jet to pass the radial supply channel before impact. Test/geometry 7.4 has the promontory shaped so as to divert impacting flow back toward the chamber. Test 7.1 led to further developments incorporated in one of the eventual solutions to the back diffusion problem, tested as a prototype on site [6].

Test/geometry 7.2 is almost identical to the mini-VA geometry now used on site in combination with cowl [6]. Its nozzle is slightly larger than the site device. The profiling of geometry 7.2 control flow channels enables 20% of the chamber wall to remain curved, which is thought to augment the development of swirl. The nozzle is not exactly tangential. In short, the channel is profiled to encourage control flow to enter the swirl chamber. Test/geometry 7.3 is a slightly modified version of 7.2, with reduced control port area and hence, 22% of the chamber wall is formed by the curved surface. The tangential control flow is, therefore, aligned slightly more upstream in relation to the radial channel.

### Test Rig.

Figure 4 shows a schematic layout of the test rig (not to scale).

Fig. 4
Fig. 4
Close modal

The supply valve can be used to increase or decrease purge flow rates into the glove box (and into the radial supply ports of the VA). The exit pipe is a straight pipe (i.e., without a tapered diverging section or radial diffuser), not to be confused with the short stub pipe and “control” valve that appears in the foreground immediately in front of the exit pipe in Fig. 4, which is used as the intake for the tangential ports. “Pse” is the differential pressure between the glove box and exit pipe and “Pce” is the differential between the control pressure entering the tangential nozzles and the exit pipe pressure. Control ports on the VA were open to atmosphere via an annular chamber, short stubby pipe, and control valve restriction; unlike the operational units on site, no in-line filters were fitted so the valves were used to simulate the additional restriction due to filters.

The glove box was fabricated from 25 mm thick Monolux board, with external dimensions of 1500 mm long × 600 mm wide × 1000 mm high, giving a nominal volume of 0.758 m3, comparable to that of a small glove box used at Sellafield: internal volume of 0.813 m3. Openings were formed in the walls of the glove box to accommodate the supply ductwork, the VA assembly, and various pressure and temperature transducers. A large opening was also made in the front of the glove box unit. The latter opening was covered by a 5 mm clear sheet of Perspex. Gasket material was used to maintain a good seal around the Perspex cover. Penetrations through the walls of the glove box by services and fixings were sealed with a silicon-based fire sealant. The sealant, once cured, formed a flexible impermeable seal preventing passage of air or smoke.

### Instrumentation.

Being a three-terminal device and Kirchoffian in nature, only four independent variables are needed to measure VA performance (i.e., two flow variables and two pressure variables). The instrumentation monitored VA supply flow ($Qs$), VA exit flow ($Qe$), and the two aforementioned pressure differentials ($Pse$ and $Pce$), plus control-to-supply differential pressure ($Pcs$) and glove box depression below atmosphere ($Pg$) and various fluid temperatures. The flows reported here are practically isothermal.

Volumetric flow rates were monitored using two in-line gas flow transmitters. One was sized for 50 mm nominal bore ductwork and the other for 25 mm nominal bore ductwork. They were located in a straight length (between fittings) of approximately 3250 mm, at 1385 mm from the upstream fitting, reducing additional measurement uncertainty from velocity profiles to negligible proportions. Both transmitters were subject to a 10-point calibration prior to installation in the test rig. Accuracy following calibration was quoted as being $±2%$.

Static pressure readings from the glove box and VA were measured using CMR Controls Ltd. calibrated low air pressure “p-sensors” and inclined fluid-filled manometers. Hypodermic tubing was used to create pressure tapings at the outlet and control port plenum; a third pressure tapping was formed at the rear of the glove box. Calibration checks were carried out before each test session but recalibration was never required.

The data logger was a Squirrel SQ1000 with eight event/digital channels: four “K-Type” thermocouple inputs and four voltage/current inputs. Manufacturer's data for the unit suggest an uncertainty for voltage measurement of ±0.1% of a reading and ±0.1% over the range; for current measurement, this increases to ±0.2% of the reading and ±0.1% over the range.

### Test Procedure for Operating Characteristics.

At the start of each geometric investigation, the control port valves were closed and the supply/exit pressure differential $(Pse)$ was set to 70, 110, or 150 Pa using the throttling and manual pressure relief valves. Gauge and differential pressure measurements were recorded using the fixed manometers and p-sensors; the manometers also being used to check the accuracy of the p-sensors. A further check of instrument accuracy was made by summing the differential pressure readings across all three LCD p-sensors; the Kirchoffian nature of the VA requiring that the sum of the differential pressures equal zero (i.e., $Pce=Pse+Pcs$). Glove box depression (Pg) was recorded throughout the tests. Volumetric flow rates were recorded using the gas transmitters. Where possible, initial checks were made to ensure that, when operated with pure supply flow (i.e., Qc = 0), readings from both transmitters were identical. Mass flow rates were calculated using air temperature measurements recorded at the ductwork supply inlet, control port supply inlet, and inside the glove box.

Once initial calibration checks were made, the control port valves were gradually opened until the differential pressure across the mock VA unit ($Pse$) increased by 40 Pa. The throttling valve was then adjusted until the differential pressure across the mock VA unit returned to 150 Pa; once the unit had stabilized records of all instrumentation readings were made. This process was repeated and continued until both control valves were fully open (but $Qs≠0)$. At this point, the supply valve was used to gradually reduce airflow into the glove box, eventually imposing pure control flow conditions $(Qs=0)$ on the VA. Differential pressure across the VA unit was adjusted in increments of 40 Pa for every variation in geometry. The same test procedure was adopted for every variation in geometry. For some geometric extremes, the tests were repeated to ensure reliability of the results.

## Performance and Operating Characteristics

### Performance Measures.

In addition to the shape of operating characteristics, VA performance is typically assessed using flow and pressure ratios. “Turn down ratio” ($T$) relates exit flow at the maximum flow condition (i.e., at Qc = 0) to the exit flow at the minimum flow condition (i.e., at “cut-off,” Qs = 0). “Critical pressure ratio” ($G*$) relates the control-to-exit pressure differential (Pce) to the supply-to-exit pressure differential (Pse) under minimum flow conditions. This can be combined with turn down ratio to produce the “Performance Index.” An ideal VA will have a high turn down ratio and performance index and a low critical pressure ratio and in this way maximum control can be achieved with minimal input.
$T=Qe(Qc=0)/Qe(Qs=0)$
(1)
$G*=Pce(Qs=0)/Pse(Qs=0)$
(2)
$PI=T/G*$
(3)
Another measure of VA behavior is the swirl number (S). Assuming perfect (no loss) mixing of the tangential and radial flow streams and that angular momentum is conserved across the chamber, the swirl number of a VA can be defined as follows:
$S=Wc·Vc·ro/Wo·Vz·re$
(4)
$S=[QcQc+Qs]2.rore.AeAc$
(5)

Equation (5) can be derived from Eq. (4) where a flat velocity profile is assumed across the control and exit ports. Thus, the swirl number given by Eq. (5) will be less than that given by Eq. (4), because the exit velocity outside of the vortex core occupies only a portion of the exit and so, due to continuity, must have a greater local velocity than the mean value inherent in Eq. (5).

In Eqs. (4) and (5), “re” and “ro” are radii of the exit port and swirl chamber, respectively. “Qc” and “Qs” are aggregate volumetric flow rates through the control port(s) and radial supply port(s), respectively. “Wc” and “Wo” are mass flow rates in the control and exit ports (respectively). “Vc” and “Vz” are mean normal velocities crossing the narrowest part of the control inlet and leaving axially through the plane of the exit port (respectively). “Ac” is the cross-sectional area of the narrowest part of the control inlet and “Ae” the planar area of the axial exit port.

### Results and Operating Characteristics.

Results of the earlier test series are plotted in Fig. 5(a) as operating characteristics, where $Wo*$ is dimensionless total flow and $Wc*$ is dimensionless control flow

Fig. 5
Fig. 5
Close modal
$Wo*=Qeimax{Qei} (i=1,2,3,…,N)$
(6)
$Wc*=Qcimax{Qei} (i=1,2,3,…,N)$
(7)

The maximum flow to leave the VA occurs when the control port flow is artificially shut off. The minimum occurs when the tangential control flow is sufficient to achieve “cut-off” and stop radial flow entering the chamber.

Figure 5(a) exhibits four operating regimes. All curves start at the point (0,1) because the valves isolating the feed to the control ports are closed at the commencement of the test, so all exit flow comes from the radial supply port. When control flow is initiated, it has little influence on discharge from the eye until substantial control flow is established. At values of $Wo*$ in the region of 0.95, the characteristic turns to generate a roughly linear portion of negative gain. Then, at values of $Wo*$ in the region of 0.6, it enters a discontinuity, except for the example of the largest control port whose characteristic begins to turn back toward the origin (hysteresis). The last regime is at the foot of the discontinuity where arguably, the curve begins once again to display a short area of negative gain before reaching the cut-off line.

The smallest control port area is obviously the best. It requires less control flow to modulate the device and gives a repeatable switching characteristic, with minimum flow through the device at the foot of the curve (i.e., normal operating conditions). Thus, the turn down ratio is high with a low critical pressure ratio.

The curves in Fig. 5(a) can be compared with an inviscid analysis [10] which shows that in the absence of friction, the peak control flow should occur at $Wo*$= 0.707. In Fig. 5(a), the peaks seem to be approached at around $Wo*$= 0.6. This is where the discontinuity (or sudden drop) is initiated. Further analysis of Fig. 5(a) reveals that the value of control flow at this peak exhibits a linear relationship with the control-to-exit port area. Turn down ratio for each device is given in Table 3. Results shown for the repeated tests are average values.

Table 3

Control port shaping performance figures (series 3)

GeometryAc/AeTG*PI
3.11.114.251.403.04
3.90.745.271.393.79
3.100.376.981.365.12
3.110.227.981.266.33
3.120.119.741.208.12
GeometryAc/AeTG*PI
3.11.114.251.403.04
3.90.745.271.393.79
3.100.376.981.365.12
3.110.227.981.266.33
3.120.119.741.208.12
Wormley and Richardson [20] showed how variation in control flow rates for different size control ports can be scaled using a simple square law relationship.
$Wc/Ac/Ae$
(8)

By application of this concept to Fig. 5(a), the operating characteristics can be made more general, as shown in Fig. 5(b). Here, the four regimes are superimposed. Recalling that the characteristics all start from the coordinate (0,1), the first regime ceases as the characteristic turns to form an almost linear negative gain and that ceases where a sudden drop (or discontinuity) is experienced, before recovery of a negative gain.

With the exception of the smallest control port, the results have collapsed to a single (if rather broad) curve in Fig. 5(b). Results from the smallest area are brought closer to the others and especially in regimes I and II. These results span an order of magnitude in area ratio.

Operating characteristics for the second set of tests (series 7) are shown in Fig. 6. Unlike series 3, the geometries in series 7 do not all use the same straight flow path to the control port. In Fig. 6, between $Wo*$ = 1.0 and 0.7 (regimes I and II) and also between $Wo*$ = 0.2 and 0.4 (regime IV), geometries 7.0, 7.1, and 7.4 all have a characteristic that bears a resemblance to that of test 3.1 (i.e., the earlier test with similar port sizes and ratios). This is to be expected. A practical device used for glove box protection would be expected to operate in the latter regime and then switch to one of the former when a breach occurs. Of these three tests, geometry 7.4 fares best by achieving modulation with least control flow. It has a shaped chamber wall opposite the tangential opening intended to divert any impacting jet back toward the chamber.

Fig. 6
Fig. 6
Close modal

For geometry 7.2, the value of Wc* required to operate the VA through its full characteristic is less than for 7.0, 7.1, and 7.4 (taking reduced area ratio into account). Moreover, the characteristic appears less hysteretic and generally more conducive to switching. Comparison with test 3.9 for a similar control-to-exit area ratio on a simple VA shows that geometry 7.2 performs much better than 3.9. It needs far less control flow to achieve modulation. It also has a better turn down ratio. Turn down ratio for each device is given in Table 4.

Table 4

Control port shaping performance figures (series 7)

GeometryAc/AeTG*PI
7.01.154.2461.0534.032
7.11.154.0991.0473.916
7.20.745.9791.0735.571
7.30.695.3531.0734.988
7.41.154.5501.0534.320
GeometryAc/AeTG*PI
7.01.154.2461.0534.032
7.11.154.0991.0473.916
7.20.745.9791.0735.571
7.30.695.3531.0734.988
7.41.154.5501.0534.320

When undertaking the second set of tests an unexpected instability was noted close to the peak control flow. Sudden changes were noted from ostensibly steady conditions and/or, major changes were observed in control port flow for very minor valve shifts. Control of the VA remained difficult over the midoperating range of the characteristic (i.e., around $Wo*$ = 0.5 to 0.6), with easy control only being re-established at $Wo*$ = 0.4.

It is difficult to account for the instability near the peak control flow but fortunately, it occurs only at entry to regime III, which is of less importance than other regimes in regard to the VA purpose and performance. A system and VA interaction are suspected. The change of fan and use of longer but straight ducts between the VA and flow meter for series 7 may be to blame. This would influence two known sources of noise in the exit piping: (i) vortex precession and (ii) a detached vortex core moving up and down the pipe at certain swirl values. However, transport delay has also been associated with system interaction (usually upstream of the device). Surge is less likely, since test series 3 did not suffer this phenomenon.

Flow field instability and downstream system interaction are unlikely to remain when the VA is fitted with a radial diffuser immediately downstream of its outlet. Development of radial diffusers for ergonomic reasons had the added benefit of greatly shortening the length of exit pipe in which the vortex core can protrude from the chamber [21] and recirculating regions that may travel up and down the exit pipe (to and from the chamber) are similarly prevented.

### Further Analysis.

In his review of the work carried out by Syred [22] and Savino and Keshock [23], King [9,11] explained how in VA's with very small $Ac/Ae$ ratios, the centrifugal forces generated by the augmented tangential velocities lead to a reversal of radial flow along the center line of the vortex chamber. The loss of angular momentum created by the reversed radial flow weakens the vortex, reducing the radial pressure gradient across the chamber. It is this effect, together with the viscous losses through the tangential inlets which result in an optimum figure of 0.33 for $Ac/Ae$, based upon the value of $PI$. However, from Table 2, it can be seen that postscale-down to the mini-VA, a practical device (7.2 and 7.3) has much greater control-to-exit area ratios than the optimum of established wisdom. Moreover, a mildly hysteretic characteristic is predicted by accepted design charts [10].

Figure 7 shows how the reduced control port areas of geometries 7.2 and 7.3 generate greater angular momentum at lower values of Wc (compared with geometries 7.0, 7.1, and 7.4). Figure 8 shows the relationship between the normalized exit port flow and the device swirl number for the same characteristic investigations. Swirl number (Eq. (5)) remains very low until cut-off is approached, but grows monotonically as total flow reduces.

Fig. 7
Fig. 7
Close modal
Fig. 8
Fig. 8
Close modal

This result agrees with the graph of optimum design geometry (King [9,11]). Comparing the $Ac/Ae$ and ro/re ratios for the five geometries against the graph of optimum design, it can be seen that $Ac/Ae$ and ro/re ratios for geometry 7.3 line up with the curve of optimum performance, whilst the geometric ratios of geometry 7.2 are also very close.

## Flow and Momentum Characteristics

### Form of Characteristics.

Discharge coefficients are used to classify valves and other in-line flow devices [24]. A VA has the valve function: but the VA uses a control jet rather than a disk lift position to control flow rate. Characteristics can be plotted showing variation of a dimensionless flow or discharge coefficient against a measure of control. The form of coefficient used here (Cd) is the fraction of ideal incompressible volumetric flow through the exit port, as shown in Eq. (9) (and is taken also to be the discharge coefficient, hence Cd). The control measure is the steady flow ratio Qc/Qe
$Cd=Qsπ·re22Pseρ$
(9)

In Eq. (9), an ideal flow (Cd = 1) would see the total flow through the radial supply ports (Qs) equal the theoretical inviscid flow through an orifice of equal size to the exit port, given the pressure difference across that orifice equal to the radial supply: exit differential.

Furthermore, a momentum characteristic can be derived in which angle Φ is plotted against $Qc/Qe$. Here, Φ is the notional angle between the resultant WsVs + WcVc and pure control momentum WcVc plotted on an Argand diagram and flow in the radial and tangential ports is considered to be one-dimensional and radial/tangential, respectively. Velocities and mass flow rates are taken as an average across the four radial “supply” and four tangential “control” ports (nominally through their cross sections).

It is possible to show that
$tan(Φ)=Qs2AcQc2As$
(10)

As $Ac/Ae$ increases, then with a fixed value of $As$, from Eq. (10), $tan(Φ)$ would also increase. Ф is a simple parameter based on one-dimensional flow assumed to enter the swirl chamber radially and tangentially. In three dimensions, the supply and control flow mix in the outer radii of the swirl chamber on its midplane, whilst a greater proportion of the radial flow in the chamber is along the side-walls [18]. Nevertheless, the momentum angle Ф is an indicator of the likelihood of cut-off being achieved and should be an indicator of vortex strength. Equation (10) implies that swirl number is closely related to the area ratio Ac/As and the pressures at the control and radial supply port generating flow through those ports. So long as the exit is large enough, changes in exit area should have no effect on the swirl number, and it is well known that changes in supply port area have little effect when As/Ae > 3 [25].

### Results.

Figures 9 and 10 show how the control to exit port ratio affects the characteristics. The test for $Ac/Ae$ equal to 0.11 was repeated twice (to generate results (1), (2), and (3)) and 0.22 repeated once.

Fig. 9
Fig. 9
Close modal
Fig. 10
Fig. 10
Close modal

In Fig. 9, all curves start close to one point (0,0.85), and end at one point (1,0). Except for these two extremes, the curves are different. As $Ac/Ae$ increases, the curves become more linear in appearance and provide more flow. The highest curve on the graph was produced for a control to exit port ratio of 1.11 (i.e., geometry 3.1). This is expected. The larger control port generates reduced velocity and hence reduced momentum for a set control flow, thereby having less chance of achieving cut-off and leaving a greater opportunity for flow to enter the swirl chamber from the radial ports. Figure 10 again shows the impact of applying Eq. (8) to the x-axis. Although (like Fig. 9) the curves in Fig. 10 all approach end coordinates (0,90) and (1,0), for the majority of angles they collapse together.

Figure 10 is an example of a momentum characteristic. For a control-to-exit area ratio of 1.11, an equal balance of control and supply mass flow rate leads to an angle of about 15 deg only. This result is due to the high velocity of the flow issuing from the control port (its area being significantly smaller than the radial supply port area). Obviously, the effect is even more pronounced as the control port area is further reduced. A piecewise approximation lends itself to prediction using Fig. 10.

Confirmation that supply port area changes are not significant at control flow rates where switching can occur was provided when supply port area was reduced using modeling clay to produce area ratios below the limiting condition quoted in literature and yet for substantial control flow, the supply-to-exit port area had almost no influence on the flow characteristic.

### Analysis.

$Qe=Qs+Qc$
(11)

Consider the results at $Qc/Qe=0.4$, from Eq. (11), $Qs=1.5Qc$. Now, for a given pressure differential $ΔPce$ and exit port, if one increases $Ac/Ae$ then $Qc$ will increase too, as there is less restriction to the flow of control air and $Qs$ also increases at any set ratio of $Qc/Qe$ as the momentum of the control jet is reduced and there is more potential for radial supply to enter the chamber. Thus, from Fig. 9, where $Ae$, $ΔPse$, and ρ are all keep the same value, $Cd$ will increase when $Ac$ increases.

Figures 9 and 10 can be used to assess the influence of changes to design geometry on total flow and swirling flow. From a pragmatic viewpoint, in order to achieve a particular discharge coefficient, a combination of $Ac/Ae$ and $Qc/Qe$ is needed for a unique component design. For example, the mock VA tested could achieve a coefficient of 0.5 not only with $Qc/Qe≈0.14$ and $Ac/Ae≈0.11$ but also with $Qc/Qe≈0.32$ and $Ac/Ae≈1.11$ and with other combinations too. At these two extremes, the angle Ф is about 55 deg in both cases. By a similar process, to achieve a coefficient of 0.2, similar combinations can be obtained, but all lead to Ф = 9 deg. Existing design guidance [2,9] can be used to determine which combination will produce the best operation and performance. Figures 9 and 10 imply the vortex strength to be expected.

There is a relationship between momentum angle (Ф) and coefficient of discharge ($Cd$) for all values of $Ac/Ae$ as shown in Fig. 11. The following may be derived:

Fig. 11
Fig. 11
Close modal
$Φ=arctan(AcAe2As.2PseρQc2.Cd2)$
(12)
$S=Qc4Qe2Qs2.rore.AsAeAc2.tan(φ)$
(13)

Thus, swirl number can be estimated from the momentum characteristic.

In the preceding work, the ratio $Ac/Ae$ was altered by changing Ac. In this latter part of the paper, $Ac/Ae$ is altered by changing $Ae$ and hence, the ratio $As/Ae$ is altered simultaneously (i.e., tests 4.1, 4.2, 4.3, and 4.4 from the 28 tests in set 1). By changing exit port area, its effect on the VA can be derived. Figure 12(a) shows the effect on the discharge coefficient. In Fig. 12(b), repeated test results are lumped together. As exit area is changed, the ratio As/Ae varies with Ac/Ae.

Fig. 12
Fig. 12
Close modal

Compare Fig. 12(a) with Fig. 8

• In Fig. 8,As/Ae = 3.8 throughout. At $Qc/Qe=0.4$ and $Ac/Ae=0.37$ in Fig. 8, it can be seen that $Cd=0.22$; trebling $Ac/Ae$ to give $Ac/Ae=1.11$ gives $Cd=0.38$.

• Now in Fig. 12(a), at Qc/Qe = 0.4 and $Ac/Ae=0.35$, As/Ae is only 1.21, but the value for $Cd$ is again 0.22; trebling $Ac/Ae$ to 1.11 gives $Cd$ of 0.38 again, despite the value of As/Ae also trebling to 3.8. This is not unexpected, so long as the exit port is not choked.

Figure 13 shows the influence of $As/Ae$ on the momentum parameter Ф, or rather, its lack of influence when the exit area is changed. In Fig. 9, the significant effect of changing the area ratio $Ac/Ae$ on the momentum angle was clearly shown. However, in Fig. 13, all plot points collapse to one curve. In Fig. 9, $Ac/Ae$ was varied with $As/Ae$ fixed. In Fig. 13, ratios $Ac/Ae$ and $As/Ae$ are varied together, such that $Ac/As$ remains roughly constant. Again, this is expected. The angle Ф is based on a one-dimensional assumption of radial and tangential momentum, so the control-to-supply area ratio determines the angle at any control flow rate (see Eq. (10)). So, as the control pressure is increased, control flow increases and supply flow reduces according to the ratio $Ac/As$ (see Eq. (12)). Therefore, for a set supply to exit pressure differential, there should be a unique variation of Ф with the proportion of total flow entering by the control ports.

Fig. 13
Fig. 13
Close modal

## Conclusions

Influence of control port geometry and size on operating flow and momentum characteristics of a mini-VA has been investigated. It is obvious that shaping of the control port channels has had a beneficial influence on modulation of the mini-VA. Shaping of the impacting surface for a tangential jet also had a beneficial influence, but is not necessary when the channels are shaped and angled so as to promote flow into the vortex chamber. Indeed, the curved surface of the chamber wall is thought to promote swirl.

So long as the exit port is not the minimum restriction to flow, its influence on the flow rates and internal momentum exchange is minor. So long as the supply port area exceeds the exit port by a factor of 3, it too has little effect, since the controlling influence is the momentum of the jet issuing from the control port. The radial and especially the tangential control port areas are instrumental in controlling discharge and operation of the mini-VA. The resultant angle of ostensibly radial and tangential jet momentum is essentially unique for a value of Ac/As.

The following conclusions are derived:

1. (1)

The control port geometries 7.2 and 7.3 are both close to the actual design of a practical device and close to the design optimum for VA performance, based upon the criteria T, G*, and PI. However, the control port to outlet area ratio is substantially higher than the published optimum. Nevertheless, control flow needed to modulate geometry 7.2 is substantially less than that needed to modulate a simple mini-VA.

2. (2)

Geometries 7.0, 7.3, and 7.4 require significantly more control flow than 7.1 or 7.2 to maintain swirl and also, produced lower peak swirl numbers in the tests reported here, but the shaped promontory of geometry 7.4 assisted in producing better performance than 7.0 or 7.1.

3. (3)

When treated as a valve, the VA flow and momentum characteristics demonstrate the importance of control port to supply port area ratio and, within the range considered here, the relative unimportance of the exit port area. These characteristics assist in understanding of the VA operation and hence, will be useful in design.

4. (4)

Combinations of control to total flow ratio and control to exit port area ratio can be used to derive specified flow rates under normal operation for set pressure differentials across the device. It appears that in the absence of the exit being the minimum restriction, control to supply area ratios determine a unique momentum parameter for a device.

Although a niche use of almost vintage technology that started in the USA and UK, VA design for protection of radiological glove boxes is spreading to other countries as they develop their civil nuclear power capability (e.g., Ref. [26]). The results of this study, together with the visualization studies, prototype testing and CFD studies forming part of the same project series has led to VA geometry adjustments for use in the latest plant currently being designed to render nuclear materials chemically inert at the Sellafield site [27].

## Acknowledgment

The authors gratefully acknowledge the financial and in-kind support of Sellafield Limited (formerly British Nuclear Group and BNFL Engineering Limited when part of British Nuclear Fuels PLC) and in particular the generous assistance of Dr. Raymond Doig. The authors also acknowledge in-kind support from Telereal Trillium.

### Appendix A: Test Geometry 7.0

Figure 14 shows the fluid regions of test geometry 7.0 in set 2. The central chamber is thin and cylindrical, based on a pitch circle diameter of 140 mm, with four 65 mm wide passages leading radially to the chamber from the extremities of the device. Four narrower passages lead tangentially to the chamber, arranged so as to promote axisymmetric flow around the chamber, leading to an exit port (not shown).

Fig. 14
Fig. 14
Close modal

Supply areas were calculated using 4-off 65 mm wide slots of 10 mm height to give 2600 mm2.

Imagine a large square metal plate laid flat on top of the flow passages shown in Fig. 14 and extending beyond the device. The (open) ends of the radial “supply” ports lead from the glove box atmosphere, entering on the underside of the imaginary plate. The tangential “control” ports are fed from an annular chamber mounted on the other (upper) side of the plate, via 20 mm diameter holes in the plate. The axial outlet also protrudes through the plate.

In fact, the plate is real, but not shown in Fig. 14. Figure 15 shows the assembly of the annular chamber, stub pipes, mounting plate (first flat casing side-wall), port inserts (forming the chamber), and the backing plate (or the second flat casing side-wall).

Fig. 15
Fig. 15
Close modal
Fig. 16
Fig. 16
Close modal
Fig. 17
Fig. 17
Close modal
Fig. 18
Fig. 18
Close modal
Fig. 19
Fig. 19
Close modal
Fig. 20
Fig. 20
Close modal
Fig. 21
Fig. 21
Close modal

Air flows through two copper stub pipes into the annular chamber that protrudes through the glove box wall from the square mounting plate. The plate is fixed to the inner surface of the glove box wall by four holes in the outer corners. From the annular chamber, air flows through four holes drilled in the mounting plate coincident with the axes of the 20 mm diameter holes at the head of each tangential channel. In normal operation, this air deflects the radial supply entering between the four inserts, mounting plate and solid backing plate. Exit pipes of various sizes (not shown) can be fitted to the large central exit hole in the mounting plate, surrounded by the annular chamber.

### Appendix B: Laboratory VA Assembly

This Appendix shows the engineering drawing and schematics used during manufacture of the inserts that are used to change control port geometry in tests 7.0–7.4. The geometry created by addition of modeling clay to reduce the control port width is also shown for tests 3.9–3.12.

All components were manufactured to a general tolerance of ± 0.25 mm. The five sets of supply/control port inserts were manufactured from 10 mm thick clear Perspex, Figs. 16–20 show engineering drawings of the supply/control port inserts. The gaps between them formed four radial supply inlets which when fixed between the VA front and rear wall, each had a free inlet area of 650.0 mm2. Total supply port area for each set of inserts was thus 2600.0 mm2. The axisymmetric arrangement of the inserts was such that a notional $ø$140.0 mm × 10.0 mm vortex chamber was formed at the center of the insert arrangement. The back of each “tangential” control slot terminated in a $ø$20.0 mm opening, which aligned with holes in the chamber/rear wall sections and the outlets from the control port plenum.

Note that the walls of the control port slot extend right up to the 140 mm diameter swirl chamber (as do both walls of each supply port). This means that directly opposite each control port lies a curved swirl chamber surface and part of the opening of the next control port and any jet leaving the control port and not being turned into the chamber will, upon expanding, impact slightly on the radial port wall forming the corner with the swirl chamber.

Test 3.1 was conducted with an insert geometrically identical to that of Test 7.0, except that it was made of Perspex measured at 9.58 mm thickness. Figures 21 shows how this insert was amended using modeling clay to reduce the 19 mm wide control port channel to 12.5 mm, 6 mm, 4 mm, and 2 mm (nominally 67%, 33%, 20%, and 10% of original width).

## References

1.
Kitsios
,
E. E.
, and
Boucher
,
R. F.
,
1985
, “
Prediction of Transport-Delay Surge in Vortex Amplifier Systems
,”
Int. J. Syst. Sci.
,
16
, pp.
1279
1291
.10.1080/00207728508926751
2.
Belesterling
,
C. A.
,
1971
,
Fluidic Systems Design
, Wiley-Interscience, New York.
3.
Foster
,
K.
, and
Parker
,
G. A.
,
1970
,
Fluidics: Components and Circuits
, Wiley-Interscience, New York.
4.
American Society of Heating, Ventilating and Air-Conditioning Engineers Inc.
, “
Glovebox Ventilation Design
,”
Heating, Ventilating and Air-Conditioning Design Guide for Department of Energy Nuclear Facilities
,
M.
Geshwiler
,
L.
Montgomery
, and
M.
Moran
, eds., ASHRAE, Atlanta, GA.
5.
Crossley
,
M. J.
,
2007
, “
Control of Nuclear Gloveboxes and Enclosures Using the No-Moving-Part Vortex Amplifier (VXA)
,”
Proceedings of Waste Management Conference
,
Tucson, AZ, Feb. 25–Mar. 1
.
6.
Francis
,
J.
,
Zhang
,
G.
, and
Parker
,
D.
,
2012
, “
Case Study: Vortex Amplifier Assemblies for Glovebox Applications Containing Radiological Hazard
,”
Proc. Inst. Mech. Eng. Part E
,
226
(
2
), pp.
157
174
.10.1177/0954408911417513
7.
Zhang
,
G.
,
2005
, “
Performance of Reduced-Scale Vortex Amplifiers Used to Control Glovebox Dust
,” Ph.D. thesis, University of Central Lancashire, Preston, UK.
8.
Parker
,
D.
,
2010
, “
Application of Experimental and Computational Fluid Dynamics Techniques to the Design of Vortex-Amplifiers
,” Ph.D. thesis, University of Central Lancashire, Preston, UK.
9.
King
,
C. F.
,
1979
, “
Some Studies of Vortex Devices - Vortex Amplifier Performance and Behaviour
,” Ph.D. thesis, University College, Cardiff, UK.
10.
Wormley
,
D. N.
, and
Richardson
,
H. H.
,
1967
, “
Experimental Investigation and Design Basis for Vortex Amplifiers Operating in the Incompressible Flow Regime
,” Harry Diamond Laboratories, Technical Report No. HDL Project 31131.
11.
King
,
C. F.
,
1985
, “
Vortex Amplifier Internal Geometry and its Effect on Performance
,”
Int. J. Heat Fluid Flow
,
6
, pp.
160
170
.10.1016/0142-727X(85)90004-9
12.
Tippetts
,
J. R.
,
1981
, “
Static Instability in Vortex Amplifier Circuits
,”
Proceedings of 6th International Fluid Control, Measurement and Visualisation Symposium (FLUCOM 81)
, pp.
293
304
.
13.
Boucher
,
R. F.
, and
Kitsios
,
E. E.
,
1983
, “
Instability in Vortex Amplifier Circuits
,”
Proceedings of ASME Annual Winter Meeting 83
, Boston, MA, Nov. 13–18, Paper No. 83-WA/DSC-12.
14.
Blanchard
,
A.
,
1982
, “
Some Characteristics of Fluidic Vortex Amplifiers in Ventilation Control
,”
Inst. Chem. Eng. Symp. Ser.
76
, pp.
210
219
.
15.
Wormley
,
D. N.
, and
Richardson
,
H. H.
,
1970
, “
A Design Basis for Vortex-Type Fluid Amplifiers Operating in the Incompressible Flow Regime
,”
J. Basic Eng.
,
92
, pp.
369
376
.10.1115/1.3425004
16.
Strong
,
R.
,
Boyle
,
K.
, and
Grant
,
J.
,
1975
, “
Gloveboxes and Similar Containments
,” U.S. Patent No. 3,888,556.
17.
Blanchard
,
A.
,
1983
, “
Fluidic Control Devices
,” U.S. Patent No. 4,422,476.
18.
Parker
,
D.
,
Birch
,
M.
, and
Francis
,
J.
,
2011
, “
Computational Fluid Dynamics Studies of Vortex Amplifer Design for the Nuclear Industry – I. Steady State Conditions
,”
ASME J. Fluids Eng
,
133
(
4
), p.
041103
.10.1115/1.4003775
19.
Francis
,
J.
,
Birch
,
M.
, and
Parker
,
D.
,
2012
, “
Computational Fluid Dynamics Studies of Vortex Amplifer Design for the Nuclear Industry – II. Transient Conditions
,”
ASME J. Fluids Eng.
,
134
(
2
), p.
021103
.10.1115/1.4005950
20.
Wormley
,
D. N.
, and
Richardson
,
H. H.
,
1968
, “
Experimental Study of, and Design Basis for, Vortex Amplifiers Operating In the Incompressible Flow Regime
,” Engineering Projects Laboratory, Massachusetts Institute of Technology, Report No. 70167-1.
21.
Rose
,
A.
,
1995
, “
Vortex Amplifier Design Methods
,” BNFL Project Report, Project No. ET5158/1.
22.
Syred
,
N.
,
1969
, “
An Investigation of High Performance Vortex Valves and Amplifiers
,” Ph.D. thesis, University of Sheffield, Sheffield, UK.
23.
Savino
,
J. H.
, and
Keshock
,
E. G.
,
1965
, “
Experimental Profile of Velocity Components and Radial Pressure Distributions in a Vortex Contained in a Short Cylindrical Chamber
,”
Proceedings of 3rd Fluid Amplification Symposium, Harry Diamond Laboratories
.
24.
Streeter
,
V. L.
, and
Wylie
,
E. B.
,
1981
,
Fluid Mechanics
, 1st SI Metric ed.,
McGraw-Hill Ryerson
,
.
25.
Wormley
,
D. N.
,
1976
, “
A Review of Vortex Diode and Triode Static and Dynamic Design Techniques
,”
Fluid. Q.
,
8
(
1
), pp.
85
112
.
26.
Balakrishnan
,
M. G.
,
Mahule
,
K. N.
, and
Narayan
,
S.
,
1992
, “
Design and Development of a Vortex Amplifier for Pressure Regulation of Glove Boxes
,”
J. Vac. Sci.
Technol., A
,
10
(
6
), pp.
3568
3572
.10.1116/1.577785
27.
Doig
,
R.
,
2013
, personal communication.