distilled water and perfluorodecalin (F2 Chemicals Ltd,. United Kingdom), a PFC ... (Flowmaster 2DPIV, LaVision, Germany; Nd:YAG laser). Liquids were seeded ...
A Flowmeter for Unsteady Liquid Flow Measurements in Total Liquid Ventilation 2
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A. Beaulieu1, E. Foucault , P. Braud , P. Micheau , P. Szeger , R. Robert , H. Walti
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de génie mécanique – Université de Sherbrooke, Sherbrooke (Québec), J1K 2R1, Canada Pprime CNRS - Université de Poitiers - ENSMA Département Fluides, Thermique, Combustion – SP2MI Boulevard Marie et Pierre Curie, BP 30179, F86962 Futuroscope Chasseneuil Cedex, France 3 Pediatric Department – Université de Sherbrooke, Sherbrooke (Québec), J1K 2R1, Canada 2 Institut
Abstract— A promising alternative to the use of conventional mechanical ventilators to treat pulmonary syndromes such as acute respiratory distress and meconium aspiration consists of employing total liquid ventilators, an experimental device which uses an oxygenated perfluorochemical liquid instead of a gas mixture of air and oxygen. Liquid ventilator development is an active field of research, as most components cannot be directly imported from gas ventilators and must be completely redesigned. The addressed problem is to provide a reliable measurement of the liquid flow in and out of the lungs considering that it must take into account unsteady effects to produce accurate measurements. An unsteady flowmeter was developed for implementation in the Inolivent-4, our total liquid ventilator prototype developed at Université de Sherbrooke. It consists of a symmetrical venturi tube comprising three pressure sensors and in which flow measurement is obtained by numerically solving a slightly modified version of the unsteady Bernoulli equation. A prototype was validated in-vitro by applying zero-mean sinusoidal flows. Low-frequency characterization determined the venturi discharge coefficient as a function of the Reynolds number, and higher-frequency measurements determined the applicable bandwidth of the device. The velocity profiles were measured in the venturi by particle image velocimetry (PIV), and the device was calibrated by comparison with an ultrasonic flowmeter and measurements from a piston pump. Results showed that quasi-steady flows could be accurately measured in the 5 ml/s - 60 ml/s range, while low-amplitude (≤10 ml/s) oscillatory flows were well measured for frequencies below 3 Hz. Finally, PIV experiments showed that the flat velocity profile assumption required for a simple solution of the flowmeter equation was valid within the operating range.
I. INTRODUCTION
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N the last decade, experimental studies have shown both the efficacy of total liquid ventilation (TLV) in pediatric animal models [1]. Total liquid ventilation is a respiratory support that utilizes a perfluorochemical liquid (PFC) to completely fill the lungs and ventilate with a tidal volume of PFC using a dedicated liquid ventilator. Dedicated liquid ventilators development is an active field of research, as most components cannot be directly imported from gas ventilators and must therefore be completely redesigned. Following a round table discussion between most active teams in TLV [2], which included a list of all principal functions that liquid ventilators must possess, a consensus was reached in that they must provide a reliable
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measurement of the liquid flow in and out of the lungs. During a typical TLV respiratory cycle, both the inspiratory and the expiratory flows exhibit acceleration and deceleration phases, hence the flowmeter must take into account these unsteady effects to produce accurate measurements. Moreover, concomitant works involving measurement of the respiratory system mechanical impedance using sinusoidal flow oscillations of frequencies up to 2 Hz and 7.5 ml/s amplitude [3] are currently ongoing, thus requiring a reliable measurement of the associated lowamplitude pulsating flows. In addition to an adequate frequency response and the ability to measure laminar and turbulent bidirectional flows, the application context also poses a number of design constraints such as being sterilizable or disposable, low cost, exhibit a fail-safe operation or redundancy as well as small physical dimensions. Flow measurement by means of a venturi is well known and has the potential to comply with the above criteria. An unsteady flowmeter was developed for implementation in the Inolivent-4, our total liquid ventilator prototype developed at Université de Sherbrooke (fig. 1). The venturi principle first needed be adapted to unsteady flow conditions. Thus a new flowmeter equation developed using the methodology proposed in [4] had to be slightly modified because of the present use of three pressure sensors. Furthermore, there is no theoretical evidence that the hypotheses required for the development of the equations hold for all flow conditions encountered by the prototype, and therefore must be validated experimentally, and correctly compensated to account for dissipative effects.
Fig. 1. Prototype of liquid ventilator Inolivent-4.
Fig. 2. Scaled drawing of the unsteady venturi flowmeter. Gray arrow indicates positive velocity direction [11]. Major diameter is 5.5 mm, diameter ratio is 0.73, and overall length is 60 mm.
An analogous venturi approach had already been developed [4]. Other authors developed a similar momentum balance technique based on pressure gradient measurement in a high-pressure hydraulic pipeline application, where compressibility effects and wave travel speeds had to be taken into account [5]. On the other hand, for laminar and incompressible unsteady flows, some authors used an analytical flow model to enhance flow measurements obtained from pressure gradient [6] or centerline velocity [7,8,9]. These latter centerline velocity methods use laser Doppler velocimetry which implies high setup costs, while other velocimetry methods such as hot wire [10] can be difficult in the presence of mucus or other impurity deposits. Consequently, the design of the model herein focused on a pressure measurement-based approach. This document consists of a condensed version of an already published article [11]. II. MATERIAL AND METHOD The concept of a symmetrical unsteady venturi flowmeter, with three pressure sensors, was considered for this application. A schematic drawing of the prototype is shown in figure 2. The prototype was constructed of clear polycarbonate, and vapor polished to enhance its optical properties for particle image velocimetry (PIV) measurements. The endotracheal tube is attached to the right of the device by means of a standard Cobb fitting, and the left side fitting is to be bonded to the liquid ventilator’s wyepiece, as indicated in figure 3 (see [12] for a description of the ventilator’s main components). The device comprises three medical grade pressure sensors (Model 1620, Measurement Specialties Inc., USA), allowing to measure the pressure difference between the entrance and the throat, regardless of flow direction, while simultaneously measuring gauge pressure near the upper airways for ventilator control purposes.
Fig 3. Implementation of the flowmeter in the liquid circuit.
The device uses a slightly modified version of the unsteady Bernoulli equation to determine flow based on differential pressure. Previous simulations showed that, with the given geometry of the device, accounting for unsteadiness in the hereafter proposed manner is mandatory in order to obtain a valid measurement of the low-amplitude (5-10 ml/s) flow components above 0.1 Hz, and is therefore necessary in the application context [11]. If a uniform (or flat) 1D velocity profile is assumed, the unsteady Bernoulli relation can be expressed in terms of flowrate and differential pressure [13]. Since this relation is used for term has measuring bidirectional oscillating flows, the | to be direction-sensitive, and is replaced by | as proposed in [4] and [5]. This yields the compact differential relation (7), of which the solution gives the instantaneous flowrate. |
|
P
0
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where , B= and ∆ is the pressure difference between the throat and the entrance (or between the other entrance and the throat depending on the direction of the flow). When unsteady effects are negligible, this difference has to be positive for forward flows (as defined in figure 2) and negative for reverse flows. Due to experimental constraints – mainly minimizing PFC usage – the flow is driven by a piston pump (Model SPS 3891, ViVitro Systems, Canada) as shown in figure 4. The three pressure signals from the venturi were independently conditioned (9300 Series, Sensorex, France) and calibrated (Druck DPI 610, GE Sensing, USA). All signals were digitized to 24 bits at 1 kHz (PCI-4472, National Instruments, USA). Tests were conducted with two fluids: distilled water and perfluorodecalin (F2 Chemicals Ltd, United Kingdom), a PFC having ρ=1917 kg/m3 and μ=5.33mPa⋅s at 25°C. An ultrasonic flowmeter (T110R, Transonic Systems Inc., USA) was used to measure instantaneous flow near the proposed venturi meter. Its relative accuracy was ± 4 % after on-site calibration, and the measurement bandwidth was 100 Hz. The flowmeter was calibrated by comparing its quasi stationary flow response with the piston pump volume output. However, because of the high PFC density, this flowmeter cannot be used with this liquid without hardware modification.
Fig. 4. Scheme of the experimental setup. [11]
The piston pump controller outputs the piston position measured by a linear variable displacement transducer (LVDT), measuring the pump volume with a maximal error of 0.64 ml. This value is used to obtain a measurement of the flow at the pump for subsequent ultrasonic flowmeter calibrations, and for low-frequency tests with PFC, when the ultrasonic flowmeter is unusable. Herein, the flow rate was estimated by harmonic analysis: the Fourier coefficients of the volume signals were calculated from spectral density function estimates and then multiplied by j2πf. PIV measurements provided velocity field in the venturi (Flowmaster 2DPIV, LaVision, Germany; Nd:YAG laser). Liquids were seeded with 0.5 g/l of 10 μm silver-coated hollow glass spheres (S-HGS-10, Dantec Dynamics A/S, Denmark). The main difficulty was to precisely position the laser sheet in the meridional plane of the 4 mm diameter venturi throat. The velocity fields were computed using multipass cross-correlations with 50% overlap for an interrogation window of 1616 pixels, providing a spatial resolution of approximately 0.16×0.16 mm (i.e. 0.04 mm per pixel). The maximal particle displacement was approximately 4 pixels with a sub-pixel error of ±0.1 pixel. The timeperiodic flow signals allowed phase averaging of the velocity fields: each period was divided into 20 frames, and 100 records were acquired for each frame. This process removed the majority of measurement noise. The PIV-measured flow was calculated by integration of the velocity profiles at the throat, and the scale corrected as with the ultrasonic flowmeter. In addition, the experimental PIV velocity profiles were compared with the theoretical profiles given by (8) to determine the applicability of using this model to enhance frequency response in the context of our studies. The venturi flowmeter performance was first assessed in quasi steady flows to determine its discharge coefficient Cv as a function of the throat Reynolds number. Flows ranging from 5 ml/s to 40 ml/s were generated at a 0.1 Hz frequency while a 0.2 Hz signal was used for 60 ml/s experiments. The piston pump was taken as the flow reference because these experiments were conducted with both water and PFC. Experimental data for Cv and Re were obtained by spectral analysis of the pump volume and venturi flow signals, using the standard weighted-overlapped segment averaging (WOSA) procedure (90% overlapped hamming windows, 10 s segments of 10,000 samples each). The measured discharge coefficient Cm,v was calculated as the ratio between the amplitude of the flow measured at the pump qp and the flow estimated by the venturi qv at the excitation frequency. The calculated uncertainty on Cm,v was the sum of the squares of the three main contributors: the prediction errors due to uncertainty on the regression [17], the random errors involved with frequency analysis ([16], Chap11) and the uncertainty due to the sensor themselves [18]. These values were obtained, propagated and combined following the guidelines of ISO’s Guide to the Expression of Uncertainty in Measurement (GUM) [18]. The measurement of unsteady flows was also addressed by applying harmonic flow signals with the piston pump. The experiments were only conducted with water. Two different amplitudes were tested: 5 ml/s and 10 ml/s. Investigated frequencies were 0.1 Hz, and 0.5 Hz to 4 Hz at 0.5 Hz intervals. The recorded data was then processed using the
WOSA frequency analysis procedure to estimate power and cross-power spectral densities (50% overlapped hamming windows, 2 s segments of 2000 samples each). The complex frequency-response function estimate between venturi and ultrasonic flow measurements H( f ) = qv( f )/qus( f ) was used as a mean to assess frequency behavior of the device. Acceptable performance was defined as a modulus of 1.00±0.05 and an angle of 0°±10°. Only spectral data at the excitation frequency where the measured coherence function always respected γ2>0.999 were kept. Validation experiments, with simultaneous PIV measurements, were also conducted with both fluids, at frequencies of 0.1 Hz, 1 Hz, 2 Hz and 4 Hz, at amplitudes of 5 ml/s and 10 ml/s and at 0.2 Hz for the 60 ml/s amplitude. III. RESULTS The venturi discharge coefficient is plotted versus throat Reynolds number in figure 5. The experimental correlation linking the quantities is 1.06
8.2
for Rethr ranging from 740 to 23,000. Since it is expressed in terms of Reynolds number, and determined using two fluids of different mechanical properties, this quasi-steady calibration curve allows the device to be used with all fluids of interest in TLV. The expanded uncertainty on the measured flow ranged from ± 0.6 ml/s to ± 1.4 ml/s for PFC flows from 5 ml/s to 60 ml/s respectively. Figure 6 shows the frequency response between the ultrasonic and venturi flowmeters, both after applying the calibration coefficients previously calculated. The figure shows that, for 10 ml/s, the proposed venturi flowmeter adequately reproduced the measurement obtained with the commercially available ultrasonic meter for frequencies up to 3 Hz. Beyond that limit, the confidence interval of the data laid entirely outside the acceptable magnitude range. For 5 ml/s experiments, all data were within the acceptable values intervals. The 5 ml/s, 0.1 Hz point was removed due to a low γ2 value.
Fig. 5: Venturi discharge coefficient (Cv) versus throat Reynolds number (Rethr) [11]. Error bars indicate random errors obtained from spectral analysis. Dotted lines indicate the 95% nonsimultaneous prediction confidence interval of the regression.
IV. CONCLUSION A venturi flowmeter and a method for retrieving unsteady flowrate from the differential pressure are presented. The device was tested with both water and perfluorodecalin, for quasi-steady and oscillating flows. The venturi discharge coefficient was determined as a function of Reynolds number. Water unsteady characterization presented acceptable dynamic responses for low flows up to 3 Hz, with less than 5% amplitude difference with the reference meter and a 3 Hz was due to the ultrasonic flowmeter or departure of the discharge coefficient from the relation previously determined. For this reason, the authors prefer to remain conservative and limit the specific frequency range to 3 Hz even though previous works [4] have shown good performance at much higher frequencies. Figure 7 shows the flow behavior throughout an oscillation cycle for conditions corresponding to (Rethr= 1150 and Wrthr=0.95). The upper portion of the figure represents the time evolution of the measured velocity profiles compared with values obtained analytically using an unsteady pipe flow model [6,14,15]. The lower portion represents the flow rate evolution for a complete cycle, offering a comparison of all available methods. The profiles were more flat than parabolic, even with that case which should produce a laminar Poiseuille flow according to the developed model. Consequently, the latter cannot be used to enhance the frequency response of our device since it does not yield valid results, even for low Wr. A likely explanation for this phenomenon is that the flow is affected by the section changes between the venturi body and the connecting fluid lines. The resulting profiles are then flattened because the flow is still in the “entrance region” of the venturi body. The existence of an entrance length for oscillating pipe flows have previously been reported [19], with flatter velocity profiles than for fully-developed flows. Nonetheless, this information shows that the flat profile assumption was reasonable in the application context, thus validating the flowmeter equation. This is also demonstrated by the lower portion of the curve, where all measurements agree with each other with good accuracy.
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Fig. 7 - Multi-method measurements at 10 ml/s - 0.1 Hz with PFC (Rethr=1150 and Wrthr=0.95)[11]
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