PERFORMANCE OF NEEDLE VALVES

Transcription

1 Br. J. Anaesth. (1986), 58, PERFORMANCE OF NEEDLE VALVES P. HUTTON AND R. W. BOADEN The use of needle valves to control theflowof gas in anaesthetic breathing systems is almost universal. We became interested in their detailed performance when assessing the suitability of various types offlowregulator for incorporation to a digital valve which was to be used to control the flow of anaesthetic gases. This is described in detail elsewhere (Boaden and Hutton, 1986). An extensive search of the literature and enquiries at several government laboratories produced no publication describing the behaviour of needle valves. In practice, their design appears to be largely empirical and devoid of any theoretical basis. Consequently, it was decided to investigate their properties and see whether, over a clinical range of flows, they behaved as simple flow resistances or whether they possessed nonlinearities and discontinuities in their performance curves which depended upon the upstream or downstream pressures. MATERIALS AND METHODS The basic apparatus required to investigate the effects of changes in upstream and downstream pressures on a needle valve is shown diagrammatically in figure 1. In the experiments described the high pressure gas supply was from Size J oxygen, medical gas cylinders fitted with an adjustable two-stage regulator. The upstream and downstream pipeline pressures were measured by Bourdon gauges which had themselves been calibrated against a Budenberg deadweight pressure gauge tester (Type 240). The downstream or "back" pressure on the needle valve under test could be increased by adjusting a variable resistance placed before theflowmeter (fig. 1). All P. HUTTON, B.SC., PH.D., M.B. CH.B., F.F-A.R.CS., Sir Humphry Davy Department of Anaesthesia, University of Bristol, Bristol Royal Infirmary, Bristol. R. W. BOADEN, B.SC., M.B., BJ., F.F.A.R.C.S., Bristol Royal Infirmary, Bristol. SUMMARY The pressure-flow characteristics of needle valves used on anaesthetic equipment were investigated. It was found that, under normal conditions of use, the valves behaved in a manner similar to convergent nozzles with sonic velocity at the throat. This means that, once the valve has been set, the mass flow rate of gas is effectively independent of the downstream changes in resistance and compliance encountered in normal anaesthetic practice. The error in a preset flow induced by the permissible variations in the upstream pipeline pressure was measured. the flows were measured on a, Platon Gapmeter Lab Kit. This is a set of metering tubes and floats which can be selected in combination to produce the optimum working range. Specially commissioned calibration charts for oxygen and nitrous oxide were supplied on request by the manufacturers. The accuracy quoted by the manufacturers was ± 1.25 % of full scale deflection. The anaesthetic needle valve, when mounted in its usual place below the rotameter block, cannot have its characteristics tested realistically because increases in downstream pressure cause the seals around the rotameters to leak and the glass to crack. Therefore, a standard, new BOC valve was fitted into a gas-tight brass block for our purposes (fig. 2). The outlet pressure of all pressure regulators depends upon cylinder pressure and flow (Hill, 1980). Consequently, when each set of readings was taken, the downstream variable resistance and the cylinder pressure regulator had to be adjusted together to achieve the required upstream and downstream pressures on the calibrated Bourdon gauges. Two sets of investigations were carried out.

2 920 BRITISH JOURNAL OF ANAESTHESIA Adjustable two-stage pressure regulator Upstream calibrated pressure gauge Downstream calibrated pressure gauge High accuracy (lowmeter 1 Needle valve under test Variable resistance FIG. 1. Diagrammatic representation of test apparatus. The effect of changes in downstream pressure on the flow through the needle valve over a range of clinical flow rates The needle valve (fig. 2) was fitted into the apparatus (fig. 1) and, with the valve discharging directly to atmosphere via the flow meter at the required nominal flow rate (zero value of variable resistance (fig. 1)), the upstream pressure was adjusted to 414 kpa gauge. The flow rate was then recorded accurately and measurements made of the discharging gas temperature and the atmospheric pressure. The variable resistance was then adjusted so that the back pressure on the needle valve increased and the differential pressure drivingflow through it decreased. If there was any change in the upstream pressure, this was readjusted to 414 kpa gauge. The flow was then allowed to stabilize and the upstream and downstream pressures, the discharging flow rate and the discharging gas temperature were recorded. The value of the variable resistance was then increased incrementally until the back pressure approached the driving pressure, at which point the flow was, by definition, zero. At each incremental step the upstream pressure was re-set to 414 kfa and the measurements described above recorded. Readings were taken with six different initial flow rates spanning the range 1-9 litre min" 1. The effect of changes in upstream pressure on the flow through the needle valve over a range of clinical settings With the needle valve in its test block (fig. 2) fitted into the apparatus (fig. 1) it was adjusted, with an upstream pressure of 414 kpa, to discharge directly to atmosphere via the flow meter at a nominal flow rate of 1 litre min" 1 (zero value of variable resistance (fig. 1)). The upstream pressure was then varied over the range kpa gauge and the resulting flow rates were measured. This was repeated for nominal initial flow rates of 3, 5 and 7 litre min" 1. RESULTS The results of these two experiments with the volume flow rates corrected to ATP (20 C, FIG. 2. Needle valve in brass block.

3 PERFORMANCE OF NEEDLE VALVES 921 g Q 0. -= 4 e o g o Upstream pressure (kpa gauge) Downstream pressure (kpa gauge) 400 FIG. 3. The effect of changes in downstream pressure on the flow through the needle valve over a range of clinical settings. Driving pressure = 414 kpa gauge. Atmospheric pressure = kpa kpa) are shown in figures 3 and 4. Correcting all the oxygen flow rates (V) to the same conditions of temperature and pressure implies that all the points plotted will be proportional to the massflowrate (M) of gas. This becomes relevant when the needle valve is compared with a frictionless nozzle. DISCUSSION Figure 3 indicates that, as the downstream pressure was increased from atmospheric, there was initially a plateau phase on the flow-pressure curve before there was any change in the flow through the valve. The extent of the plateau for eachflowis shown approximately by line A (which was drawn in by eye). It can be seen that, at 9 litre min" 1, the downstream pressure had to increase to 80 kpa gauge before flow decreased, and that the plateau increased to considerably more than 1 atm at the four lowest flow rates. The presence of this plateau implies that, under certain conditions, the mass flow of a given gas through a needle valve may be unaltered, despite changes in the pressure drop across it. This contrasts with flow in pipes where, as soon as the pressure gradient changes, the flow (whether laminar or turbulent) follows part passu (although not FIG. 4. The effect of changes in upstream pressure on the flow through the needle valve over a range of clinical settings. The vertical dotted line shows the normal supply pressure of 414 kpa gauge. Atmospheric pressure = 102 kpa. necessarily linearly). To explain this, perhaps unexpected, characteristic of needle valves it is useful to consider the properties of a frictionless convergent nozzle. A convergent nozzle is shown schematically in figure 5A and its behaviour under variations of back pressure is described in many standard textbooks (Shapiro, 1953). In summary, the nozzle (fig. 5A) is considered to be supplied with gas at an absolute static upstream pressure of Pu and the absolute downstream or back pressure on the nozzle Pb is controlled by a valve. The actual absolute pressure at the exit of the nozzle throat ispe. Figures 5B and c show, respectively, the variations in pressure down the nozzle and mass flow through it as Pb is varied. Initially, when Pb = Pu there is no flow (point a) then when Pb is reduced, theflowbegins (point b). With further reductions in Pb this trend is continued until point c is reached. After this, further decreases in Pb to attain points d and e produce no subsequent increase in mass flow through the nozzle. The nozzle in this condition is said to be " choked". In addition, Pe (the true throat pressure) never decreases to less than that at condition c, the further reduction in pressure to Pb occurring after the gas has left the nozzle. The condition of maximum or choked flow occurs when the gas has achieved the local speed of sound (sonic velocity)

4 922 BRITISH JOURNAL OF ANAESTHESIA Maximum e d c Mass flow rate of gas Distance down nozzle Pb/Pu FIG. 5. Schematic diagram of nozzle characteristics. in the narrowest part of the nozzle. This is often termed the "critical flow condition". The minimum pressure drop across the nozzle necessary to produce chokedflowoccurs at a given Pb: Pu ratio (in absolute pressures) which depends on the gas in use. It is denned (Shapiro, 1953) as jtor choking I_Y+ 1 ' where y = the ratio of the specific heats for the gas in question. Critical flow devices have been used previously in the Pneumotron ventilator (Mushin et al., 1980), in gas analysers (Hill, 1980), in scavenging systems (Vaughan et al., 1977) and to meter accurately the flow of natural gas and the output from compressors (Ower and Pankhurst, 1966). We do not, however, know of any previous publications which have identified needle valves as possessing these properties. Comparing figure 3 withfigure 5c, the similarity in performance between a needle valve and a convergent nozzle is obvious. The critical pressure ratio for oxygen (y = 1.4) calculated from equation (1) is 0.53 and is shown plotted as line B on figure 3. Above 2.5 litre min" 1 the plateau region of the valve characteristic decreases gradually from 171 kpa gauge (where Pb/Pu = 0.53) to approximately 80 kpa gauge at 9 litre min" 1 (where Pb/Pu = 0.35). This decrease in the value of Pb/Pu from the ideal of 0.53 is almost certainly the result of the increased frictional losses in the input and output sections of the needle valve. These increase dramatically with increases in gas velocity. When the pressure decrease caused by these becomes of the same order of magnitude as the nozzle loss, then the actual input pressure to the nozzle is not Pu, but Pu minus the frictional loss of pressure head up to the entrance of the nozzle. Consequently, the downstream pressure for choking flow based on Pb/Pu = 0.53 is reduced. Despite these frictional losses, even at the high flow rates, the nozzle flow is invariant with increases of downstream pressure up to 80 kpa gauge. Since the least compliant lungs one would ever ventilate in practice would almost never need an inflation pressure greater than 10 kpa gauge, any anaesthetic ventilating system fed by a needle valve from normal pipe line or cylinder pressures effectively becomes a constant flow generator. In addition, if the pressure in the patient breathing system or ventilator supply line increases, any change in the rotameter readings does not imply a change in the massflowrate of gas through the needle valves. The increase in downstream pressure does of course reduce the volume flow rate. In addition, the rotameters (which are very sensitive to downstream pressure) are calibrated at a specific downstream gas pressure of one standard atmosphere. When the downstream pressure increases, they are effectively being forced onto a different calibration curve. The effect of changes in upstream pressure on the mass flow rate of gas through the nozzle when the downstream pressure is constant at atmospheric are shown in figure 4. It can be seen that, for any given nominal setting, increasing the upstream

5 PERFORMANCE OF NEEDLE VALVES 923 pressure increases the flow of gas through the needle valve and decreasing it does the reverse. This is in agreement with the theory of critical flow devices (see Appendix) which predicts that, under given initial conditions, the mass flow rate of gas per unit cross sectional area of nozzle is proportional to the absolute upstream pressure (Shapiro, 1953). For there to be perfect agreement with the theory, all the lines on figure 4 should, when extrapolated backwards, intersect the abscissa at an absolute upstream pressure of zero and they do not do so. This discrepancy is the result of pressure losses in the piping between the pressure gauges and needle valve (fig. 1), viscosity effects in real fluids which are omitted from the theoretical solution, and the changes in the geometry of the orifice of the needle valve as it is adjusted to give the initial set flow. The data of figure 4 can be replotted with the gradient dp^/dpu against flow (P^) to produce an empirical expression to predict the deviation of any given initial flow with variations in upstream pressure. Using a least squares best fit, this results (for our experimental model and needle valve) in the equation: Change in flow = change in pressure (kpa) (litre min- 1 ) x ( (initial flow rate (litre min- 1 )) lo" 3 (2) Statistical analysis shows that r = and the 95% confidence limits for the coefficients are ((1.8±0.9) x 10" 3 litre min- 1 kpa" 1 ) and ((2.2±0.2)xl0" 3 kpa- 1. The variations in gas flow rate as a result of permitted variations in gas supply pressure (393-^434 kpa gauge) (D.H.S.S., 1977) can be calculated easily. For example, a flow rate of 7 litre min" 1 (ATP) set at a pipeline pressure of 414 kpa gauge would increase to 7.34 litre min" 1 at a pipeline pressure of 434 kpa gauge and decrease to 6.64 litre min" 1 at a pipeline pressure of 393 kpa gauge. Several different types of needle valve were subjected to the type of bench testing described above. They did not all approximate to a perfect nozzle to the same degree. A general conclusion was that the physically bigger the valve, the more closely it conformed to theory at higherflow rates. This was thought to be mainly a result of the reduction in frictional losses in the entrance piping of the larger valves. The whole series of tests was repeated with nitrous oxide (y = 1.3) and the results were essentially the same as those described above for oxygen. They are not shown since they would merely repeat the data in figures 3 and 4. APPENDIX The theory of critical flow devices (Shapiro, 1953) predicts that, under conditions of choking flow, the mass flow rate per unit area of nozzle (M) is given as: where Pu = absolute upstream pressure of static gas, y = ratio of specific heats, R = universal gas constant and T = absolute temperature of upstream gas. For a given gas with a given T, the quantity under the square root sign is constant (k). Therefore: M ^M and, since M is proportional to V (see Results above), Pu~ dpu (3) Using the data of figure 4, the absolute upstream pressure at the initial flow rate is = 516 kpa. Re-arranging equation (3) results in: change in flow _ change in pressure (kpa) (litre min" 1 ) 516 kpa x initial flow rate (litre min" 1 ) = change in pressure (kpa) x initial flow rate (litre min" 1 ) x 1.94 x 10"* Comparing this expression with our empirical results (see above, equation (2)) the experimental coefficient of (1.8 x 10"') litre min" 1 kpa" 1 differs significantly from zero at the P < 0.05 level, but there is no significant difference between the experimental coefficient of (2.2 x 10"*) kpa" 1 and the theoretical value of (1.94 x 10"') kpa" 1. It can be seen (equation (2)) that the major deviation from theoretical behaviour occurs at low flow rates where the error in the predicted change in flow approaches 50%. To achieve a low flow through the needle valve requires the needle to be advanced a relatively long distance into its sleeve. This simultaneously reduces the cross sectional area available to the flow and increases the length of the throat section. Both these factors increase viscous losses and encourage deviation from theoretical predictions based on a perfect gas. ACKNOWLEDGEMENTS The authors acknowledge the loan of a Platon Gapmeter Lab Kit from Mr A. Burleton and a Budenberg deadweight pressure gauge tester from the Department of Aeronautical Engineering, University of Bristol. REFERENCES Boaden, R. W., and Hutton, P. (1986). The digital control of anaesthetic gas flow. Anaesthesia, 41, 413. Department of Health and Social Security (1977). Piped medical gases, medical compressed air and medical vacuum installations: and supplement. Permit to work lystem. Hospital Technical Memorandum No. 22.

6 924 BRITISH JOURNAL OF ANAESTHESIA Hill.D. W. (1980). Physics Applied to Anaesthesia, 4thEdn, pp. Shapiro, A. H. (1953). The Dynamics and Thermodynamics of 71, 189. London: Butterworths. Compressible Fluid Flow, Vol. 1, pp. 91, 84, 85. New York: Mushin, W. W., Rendell-Baker, L., Thompson, P. W., and The Ronald Press Co. Mapleson, W. W. (1980) Automatic Ventilation of the Lungs, Vaughan, R. S., Willis, B. A., Mapleson, W. W., and Vickers, 3rd Edn, p Oxford: Blackwell Scientific Publications. M. D. (1977). The Cardiff Aldavac anaesthetic scavenging Ower, E., and Pankhurst, R. C. (1966). The Measurement of system. Anaesthesia, 32, 339. Airflow, pp. 196, 250. New York: Pergamon Press.