NRC wave pump tests for numerical model development

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NRC wave pump tests for numerical model development

Boileau, Renee; Raman-Nair, Wayne

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OCRE-TR-2013-030

NATIONAL RESEARCH COUNCIL CANADA OCEAN, COASTAL AND RIVER ENGINEERING

NRC wave pump tests for numerical model

development

Technical Report

Renee Boileau and Wayne Raman-Nair May 17, 2013

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DATE May 17, 2013

REPORT NUMBER PROJECT NUMBER SECURITY CLASSIFICATION DISTRIBUTION

OCRE-TR-2013-030 A1-001189 Unclassified Unlimited

TITLE

NRC wave pump tests for numerical model development

AUTHOR(S)

Renee Boileau and Wayne Raman-Nair

CORPORATE AUTHOR(S)/PERFORMING AGENCY(S) PUBLICATION(Journal or Conference name)

- n/a

SPONSORING AGENCY(S)

College of the North Atlantic

RAW DATA STORAGE LOCATION(S) MODEL# PROP#

\\nrcsjsfs1\Testdata\Test_A1001189\OEB n/a n/a

PROJECT(NPArC) PEER REVIEWED EMBARGO PERIOD GROUP(NPARC)

CNA Wave Pump Development - Exper-imental Validation of Pump Numerical Code - CRA Addendum #2

No 0 months Research

PROGRAM(NPArC) FACILITY(NPArC)

Marine Energy St.John’s: P.O. Box 12093, Arctic Ave, St. John’s, NL A1B 3T5

KEYWORDS PAGES TABLES FIGS.

wave pump, numerical model, validation, positive displacement pump, recipro-cating pump, College of the North Atlantic, CNA

vii, 37, App A-D 6 26

SUMMARY

The National Research Council Canada (NRC) has developed a numerical model of a double-acting reciprocating pump to support the design of a wave pump for the College of the North Atlantic. A validated model could reduce design cost by reducing the number of physical models and tests. A series of validation tests with a prototype wave pump were conducted at the NRC Ocean Engineering Basin. The numerical model predicts piston motion and applied force on the piston rod; however, it does not predict cylinder pressures. Further development is needed to adapt the model for unsteady flow.

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National Research Council Canada Ocean, Coastal and River Engineering Conseil national de recherches Canada Génie océanique, côtier et fluvial UNCLASSIFIED

NRC wave pump tests for numerical model development

OCRE-TR-2013-030

Renee Boileau and Wayne Raman-Nair

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OCRE-TR-2013-030 Contents

List of Figures

1 NRC wave pump prototype . . . 1

2 Kinematics comparison . . . 8

3 Flow rate comparison . . . 8

4 Orifice flow coefficient time series . . . 9

5 Velocity dependence of orifice flow coefficient . . . 10

6 Pressure comparison . . . 10

7 Force comparison . . . 12

8 Force-driven motion comparison . . . 12

9 Force-driven flow rate comparison . . . 13

10 Kinematic error . . . 14

11 Pressure drop across cylinder outlet valves . . . 14

12 Components of model applied force . . . 16

13 Force vs flow rate . . . 17

14 Force vs pressures . . . 17

15 Numerical model of a double-acting reciprocating pump . . . 22

16 NRC wave pump prototype . . . 25

17 Linear actuator motor and screw mounted on test frame . . . 26

18 Outlet head . . . 27

19 Test set-up . . . 28

20 Viscous damping force results for dry friction runs (Cv = 1600) . . . 31

21 Viscous damping force results for wet friction runs (Cv = 1600) . . . 32

22 Applied force results for flow runs (H1, T=3-8 s) . . . 33

26 Applied force results for flow run (H3, T=5 s) . . . 36

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OCRE-TR-2013-030 List of Tables

List of Tables

1 Wave pump dimensions . . . 3

2 Sensor ranges and resolutions . . . 4

3 Completed test matrix . . . 6

4 Linear actuator force limit . . . 26

5 Turbulent transition flow rate . . . 27

6 Channel calibration list . . . 29

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OCRE-TR-2013-030 Symbols

Glossary

hose barb short push-fitting pipe section for connecting flexible tubing injected calibration data channel calibration in which a series of known

volt-ages from the manufacturer’s sensor data sheet is applied as an input in place of the sensor and the output data (post-conditioning, multiplexing and digitization) becomes a digital representation of the input signal

stroke length of peak-to-trough cyclic motion (double amplitude)

Acronyms

CFD computational fluid dynamics CNA College of the North Atlantic ID inner diameter

NPT National Pipe Thread (pipe sizing standard) NRC National Research Council Canada

OEB Ocean Engineering Basin

Symbols

As sliding surface area

Corif ice orifice flow coefficient

cp piston clearance

Cv viscous flow coefficient

µ dynamic viscosity

|v| absolute velocity (speed)

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1 Introduction

The College of the North Atlantic (CNA) engaged the NRC in the design of a wave pump to supply water to an onshore aquaculture centre at Lord’s Cove. The pump must supply a minimum continuous flow requirement based on typical sea state conditions.∗

To aid in pump sizing, the NRC has developed a numerical model of a double-acting positive displacement pump. A validated model could reduce design cost by reducing the number of physical models and physical tests to converge on an optimal design.

To validate the numerical model, a series of tests has been conducted with a pro-totype wave pump (Figure 1) at NRC (St. John’s). In these tests the pump was driven sinusoidally by a linear actuator. The test data is compared with the predictions of the numerical model for motion, flow rate, net force applied to the piston rod and cylinder pressures. The results show that further model development is needed.

(a) prototype F(t) outlet pout inlet pin x(t) p1 p2 q q closed closed (upstroke) (b) numerical model

Figure 1: NRC wave pump prototype

This report describes the validation tests and compares their results to numerical predictions. The numerical model is described in Section 2. (The equations are de-rived in Appendix A.) The physical pump and other test apparatus are described in Section 3, followed by the test program in Section 4, including assumptions made. The results from the tests are compared in Section 5 and discussed in Section 6.

Sec-∗

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OCRE-TR-2013-030 3 Test apparatus

tion 7 provides conclusions, followed by lessons learned in Section 8; future work for the numerical model and its validation is recommended in Section 9. Photos of the test apparatus are shown in Appendix B sensor calibrations are reported in Appendix C and a summary of test results are in Appendix D.

2 Numerical model theory

A generic wave pump has been modelled numerically to find piston motion, upper and lower cylinder pressures and flow rate, given the applied force acting on the piston rod and a set of parameters (pump dimensions, fluid characteristics, test conditions) as inputs. This numerical model relies on an assumption of steady flow for relating flow rate and pressure drop across an orifice; it estimates cylinder pressures based on static inlet and outlet head pressures. (See Appendix A for a derivation of the equations.)

For the validation experiments, the pump piston is driven using position control; applied force, input and output pressures and flow rates are measured. For this case, the equation of motion is solved for applied force as a function of piston position (§ A.1). To validate the numerical model, the dimensions of a wave pump prototype and a set of test conditions are provided to the model and the results are compared to the test data from the physical pump.

3 Test apparatus

The test apparatus used to validate the numerical model includes the NRC prototype wave pump assembly, sensors and a data acquisition system. The wave pump is mounted on a steel frame and driven by a linear actuator. The pumped fluid (fresh water) is transferred through flexible tubing from the supply tank to a catch basin. The inlet head is controlled strictly by the height of the water in the supply tank; outlet head is controlled by raising and lowering the outlet hose.

3.1 Wave pump

The NRC wave pump is a double-acting reciprocating pump constructed from an acrylic cylinder with aluminium rod, piston and end plates and rubber piston rings. Table 1 lists critical dimensions∗ used in the numerical model. (The pump is shown disassembled and as an assembly in Appendix B.)

∗

all units SI unless otherwise noted

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OCRE-TR-2013-030 3 Test apparatus

Table 1: Wave pump dimensions

dimension units piston mass 1.8303 kg piston diameter 6.35 cm rod diameter 3.00 cm cylinder length 43.0 cm orifice diameter (1/2” NPT) 1.58 cm lower valve height* 0.680 m upper valve height* 1.166 m

*centreline from floor

3.2 Hoses and check valves

The pump takes in fresh water from the Ocean Engineering Basin (OEB) northwest corner tank and discharges it in to an acrylic catch basin through flexible 5/8-inch ID plastic tubing. One-way check valves control the direction of flow through each of the four pump ports (2 inlet, 2 outlet). The catch basin is drained manually through a tap back into the supply tank between runs.

A rope-and-pulley apparatus is used to raise the outlet hose and vary outlet head. (See Figure 18 in Appendix B). A one-way valve is plumbed into the outlet hose at the highest (lifting) point to prevent syphoning after the pump stops.

3.3 Linear actuator

An Aerotech R _{model BM1400-UF linear actuator is attached to the test frame and the} piston rod. The position of the actuator is controlled through ascii files, which specify either position or velocity (in this test program, position). (See Figure 17 in Appendix B).

3.4 Sensors

Piston motion and the resulting loads are measured using nine sensors. Force applied to the piston rod is measured by a load cell; a combination transducer measures pis-ton position and velocity. Source tank and catch basin levels are measured with two capacitive wave probes. A Hall-effect paddle wheel flow meter measures flow rate.

Four diaphragm-type pressure sensors measure pressures in the inlet and outlet hoses: one sensor is in the common inlet hose before the inlet check valves; the other three are installed before each outlet check valve and in the common outlet hose after the valves.

The sensor models used for this test program and their ranges are listed in Table 2.

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OCRE-TR-2013-030 4 Test program

Table 2: Sensor ranges and resolutions

data channel sensor model range resolution

force Sensotec 417A 77-01-01 0–1000 lb* unspec.

pressure Dylix R _GXR3-PPX14 _{-14.7–50 psi**} _{0.6 psi (0.1%FSO}‡₎

flow rate Digiflow R _F3.00.H.01 _{2.8-150 L/s} _{0.15 L/s (0.1%FSO)} (with TEA007ES 3/4 in ID tee)

tank level Akamina R _{AWP-24 Wave Height Gauge}

· supply (relative to wire length) 0–0.6 m _{±3 µm} · output " " " 0–0.9 m _{±4.5 µm}

CelescoTM DV301-0050 position and velocity transducer

position _{· potentiometer} 0–50 in† _{±0.05 in (0.1%FSO)}

velocity _{· tachometer} not stated _{±3 %}

*pound **pound per square inch †_inch ‡_{full scale output}

3.5 Data acquisition and pre-processing

Each sensor is excited by an external voltage with a multi-channel Transducer Excita-tion Unit (NRC# TEU–16), then amplified and filtered by an NEFF Instruments signal conditioner and finally sampled and digitized by a DAQBoard 2000 data acquisition board.

In addition, the flowmeter channel is run through an NRC-built RPM Prescaler and RPM-to-Analog box to convert the flowmeter counts to an (unsaturated) voltage pro-portional to the flow rate. The flowmeter channel is then processed through the TEU with the other channels.

4 Test program

Pump tests are performed in a small tank in the corner of the NRC OEB, including dry∗ and wet†_{friction tests and flow tests with variations in period, stroke and output head.}

4.1 Calibrations

Each channel in the data acquisition system is calibrated prior to the tests using in-jected calibrations. Manufacturers’ calibrations are used for interpreting sensor output voltages.

∗_{dry test: pump drained}

†

wet test: pump filled but no head (empty hoses)

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4.2 Test protocol

The supply tank level is measured relative to the reference (concrete floor) before each set of tests. The maximum outlet head for each test condition is measured using a tape measure (±1 cm) when the outlet hose height is changed.

Each test is a sinusoidal series of at least 5 piston strokes based on position control. Prior to each test, the piston is sent to the “home” (centred) position, the catch basin is drained into the supply tank and tank levels (wave probes) are zeroed.

4.3 Completed tests

All data channels were calibrated prior to testing. (See calibration report in Appendix C.) Pressure sensor channels were calibrated during testing when the sensors were re-placed. The output tank level was re-zeroed before each test.

Friction tests were completed in August, 2012. Pressure sensor failures deferred the flow tests to December, 2012. Flow tests were completed with the minimum outlet head at varied periods with maximum stroke and with varied strokes at a single period above the observed cavitation limit. Tests with varying periods at maximum stroke were also completed with the outlet hose raised halfway to the ceiling of the OEB. A single test was made with outlet hose raised to the ceiling.

The completed test matrix is given in Table 3. In total, 67 tests (including repeats) were completed for 33 conditions:

◦ friction tests varying stroke and period (4 “dry”, 5 “wet”)

◦ flow tests at lowest output head varying period (12) and stroke (4) ◦ flow tests at intermediate output head varying period (8)

◦ flow test at highest output head (1) Most tests were repeated.

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Table 3: Completed test matrix

period (s) 3 5 7

25 dry/wet

100 dry/wet

240 dry/wet wet dry/wet

period (s) 3 4 5 6 7 8 9 10 12 14 16 20 25 1x 50 3x 150 1x 240 3x 3x 3x 3x 3x 3x 1x 1x 1x 3x 1x 1x period (s) 4 5 6 7 8 9 12 14 stroke (mm) 240 4x 4x 4x 1x 1x 4x 1x 7x period (s) 5 stroke (mm) 240 1x stroke (mm) stroke (mm)

mean output head = 0.64 m

mean output head = 4.04 m friction tests

mean output head = 9.13 m

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OCRE-TR-2013-030 5 Comparison of model results to test data

5 Comparison of model results to test data

The numerical model (laboratory test version) predicts upper and lower cylinder pres-sures, flow rate and and applied force based on piston motion. The model is run using MatlabTM scripts to extract the test conditions from data for each physical test; results for the numerical model are compared to experiment data with some assumptions.

5.1 Assumptions

The comparisons between numerical and physical model data are based on the follow-ing assumptions:

◦ incompressible flow

◦ negligible force to pump or compress air (friction runs and cavitation bubbles) ◦ negligible effects due to local transient pressure changes (cavitation)

◦ negligible exit flow drop

◦ negligible Coulomb (dry) friction∗

◦ negligible force to open and close check valves

5.2 Kinematics

Each test specifies stroke and period, from which a sinusoidal drive signal is calculated at discrete time steps to control the actuator. The drive signal–position and velocity transducer data correlation is lowest near the home position and near zero velocity. Given the average measured stroke and period as test condition inputs, the model simulates the expected motion with machine accuracy. The model and sensor data agree well, as shown in the example for two periods extracted from a typical test in Figure 2.

∗_{The entire cylinder is filled with fluid, so the piston ring is continuously lubricated; although the rod}

seal/bearing is not immersed, the rod is wetted on every stroke (except friction tests).

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OCRE-TR-2013-030 5 Comparison of model results to test data 0 2 4 6 8 10 −200 −100 0 100 200 time (s) piston displacement (mm) 0 2 4 6 8 10 −200 −100 0 100 200 piston velocity (mm/s) drive signal x test x model v test v model

Figure 2: Sample model position and velocity compared to drive signal and test data

5.3 Flow rate

The numerical model calculates volumetric flow rate from the (ideal) piston motion. The model results are compared to flowmeter data. Flowmeter data lags the predicted results and consistently exceeds predictions by about 10%. (Flow rate is also estimated from output tank level data, but with greater lag and much lower real time accuracy.) The comparison for a sample run is shown in Figure 3.

0 2 4 6 8 10 0 200 400 600 time (s) flow rate (mL/s) q flowmeter q wave probe q model

Figure 3: Sample model flow rate compared to test data

5.4 Cylinder pressures

Cylinder pressures are modelled on Bernoulli’s orifice flow equation for steady incom-pressible flow. The model requires a constant (speed-independent) coefficient to relate pressure drop and flow rate.

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5.4.1 Determination of orifice flow coefficient

The orifice flow coefficient is determined experimentally for the fittings between the pressure sensors. The coefficient is calculated from the flow rate and pressure drop across the combined fittings for one run (rearranging A.2):

Corif ice∝

Q √

∆p for constant flow (1)

The orifice is effectively the greatest restriction, in this case, the hose barbs con-necting the elbows and check valve. The pressure drop across these fittings is mea-sured using two pressure sensors mounted on either side. The flow rate is estimated from the velocity data for a single run with minimum outlet head, 3-second period and full stroke (Flow_H1_T3_S10_003).

A plot of the flow coefficient calculated for each data point in Figure 4 shows that it is only constant for part of each stroke. This is consistent across all the runs.

0 5 10 15 20 25 0 2 4 6 time (s)

orifice flow coefficient, C

0 5 10 15 20 25 0 50 100 150 200 speed (mm/s) C flowmeter C_tachometer (q = A.v)

C_model (q = A.v_ideal)

v

abs

Figure 4: Orifice flow coefficient time series for run Flow_H1_T3_S10 (10 cycles) The coefficient is significantly non-linear below a certain speed (_{|v| ≃ 150 mm/s),} as shown in Figure 5, so the coefficient is calculated for each data point above _|v| and averaged. (Since the upper and lower fittings are identically arranged except for relative height and the upper and lower coefficients are similar, their average is used.)

For periods above 8 seconds, there is effectively no data corresponding to the lin-ear range forCorif ice. There is also significant hysteresis in the coefficient. (See

Ap-pendix D for individual test results.)

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OCRE-TR-2013-030 5 Comparison of model results to test data −300 −200 −100 0 100 200 300 0 1 2 3 4 5 6

downstroke piston velocity (mm/s) upstroke

C Flow_H1_T3_S10_003 flowmeter tachometer ideal C_avg = 0.4136

Figure 5: Velocity dependence of orifice flow coefficient (1 run, 10 cycles)

5.4.2 Application of average flow coefficient

The average orifice flow coefficient is applied by the model to predict cylinder pressure for the limited runs when the piston motion is above the significant speed

(|v| > 150 mm/s).

The outlet hose pressure data is compared to model predictions for cylinder pres-sures in Figure 6 for a sample run. The model predicts prespres-sures inside the cylinder while the sensors are in the hoses; further, this is not an accurate prediction because of the assumption of steady flow and constant output pressure, whereas both the pre-and post-valve pressures vary sinusoidally with piston motion.

0 2 4 6 −200 −100 0 100 200 time (s) pressure (kPa) Flow_H1_T3_S10_003 p

out, upper (test)

p_{out, lower}

p

cylinder, upper (model)

p_{cylinder, lower}

Figure 6: Sample model cylinder pressures compared to outlet sensors

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5.5 Applied force

The model predictions for net force applied to the piston rod rely on calculations of the components in the equation of motion (A.1). Piston weight and the net acceleration acting on the piston mass are well-quantified; however, the viscous and pressure terms rely heavily on experimentally-derived coefficients. We have already estimated the orifice flow coefficient for certain piston speeds from pressure and flow measurements in the previous section.

5.5.1 Determination of viscous damping coefficient

The viscous damping coefficient can be calculated if the sliding area As and piston

clearancecp are known:

Cviscous= µAs/cp (2)

whereµ is kinetic viscosity; however measurement of cp is not trivial.

An attempt was made to isolate viscous damping with “friction runs” in which the pump is not pumping fluid. These did not prove sufficiently accurate as model inputs, so the net applied force from one test is used to estimate viscous damping for all runs (on the assumption all other forces are known for that run).

estimates from run Flow_T3_S10_H1_003

Cviscous= 1600 viscous damping coefficient (3)

cp = 5.6 nm piston clearance (4)

5.5.2 Application of viscous damping coefficient

The estimated viscous damping coefficient is applied by the model to predict net ap-plied force on the piston rod for all runs (excluding the run from which the coefficient was estimated). The model results and data for a sample run are compared in Fig-ure 7. (Complete results are shown in Appendix D.) The model predictions agree with experimental data within 30% at lowest output head (much improved with raised hose).

5.6 Force-driven model

Validation tests were not performed with sinusoidal force inputs; however, a comparison of the predicted motion based on a pure cosine force similar in stroke and period to test runs shows, as expected, the displacement will drift with a symmetric applied force due to the constant force of weight (see Figure 8). Piston weight has less effect on the model prediction of piston velocity and so flow rate is reasonably estimated (9% over) given a good estimate of the viscous damping coefficient, as shown in Figure 9.

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OCRE-TR-2013-030 5 Comparison of model results to test data 0 1 2 3 4 5 6 7 8 9 −400 −300 −200 −100 0 100 200 300 400 500 time (s) force (N) Flow_H1_T5_S10_002 load cell model pure cosine

Figure 7: Sample model applied force compared to test data and pure cosine

0 2 4 6 8 10 12 14 −200 −100 0 100 200 position (mm) Flow_H1_T5_S10_002 test data model 0 5 10 15 −200 −100 0 100 200 time (s) velocity (mm/s)

Figure 8: Sample force-input model kinematics compared to potentiometer/tachometer data

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OCRE-TR-2013-030 6 Discussion 0 5 10 15 0 100 200 300 400 500 600 time (s) flow rate (mL/s) Flow_H1_T5_S10_002 flowmeter model

Figure 9: Sample force-input model flow rate compared to flowmeter data

6 Discussion

Results of the comparisons of numerical and physical test data varied in correlation – piston motion, flow rates and applied forces are predicted well, however cylinder pressures are not. Possible sources of error and mitigations strategies are provided here.

6.1 Kinematics

Predicting the piston motion is trivial for the model, however the position and velocity data exhibited hysteresis. The uncertainties in position and velocity are largest near the home position and at low speed, respectively, as shown in Figure 10. Assuming the sensor is meeting its stated 1% accuracy, the remainder may be due to (unspecified) inaccuracy in the actuator motor itself.

6.2 Flow rate

At all measurable flow rates (see Table 5), this system is operating in the turbulent flow regime. The model predictions are reasonable, given that the flowmeter was operating below it’s manufacturer’s calibration range and is better suited to constant flow, due to apparent time for the impeller and/or the data acquisition system to react to a change in velocity. For a positive displacement pump, calculations based on piston motion may be more useful than flowmeter measurements.

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OCRE-TR-2013-030 6 Discussion 0 1 2 3 4 5 6 7 8 9 10 −150 −100 −50 0 50 100 150 time (s) position (mm) 0 1 2 3 4 5 6 7 8 9 10−150 −100 −50 0 50 100 150 error (%)

(a) position error

0 1 2 3 4 5 6 7 8 9 10 −200 0 200 time (s) speed (mm/s) 0 1 2 3 4 5 6 7 8 9 10−150 −100 −50 0 50 100 150 error (%) (b) velocity error

Figure 10: Relative uncertainty in position and velocity

6.3 Cylinder pressures

Here the model diverges because the orifice flow equation (A.2) assumes steady flow and constant output pressure. The orifice flow coefficient appears constant over some range of speeds; arguably, the region of interest is the highest speeds, at which the highest forces are developed; however, the model is based on measurements of two time-varying pressures, making it ineffective for predicting cylinder pressures. A differ-ent method for relating cylinder pressure to flow rate is needed.

Elimination of other potential sources of error:

◦ backflow: The pressure drop across the fittings is apparently negative (ie back-ward flow) for a portion of each cycle as shown in Figure 11. (The negative pressure drop is within the resolvable sensor range (>4 kPa).) Possible reasons: hysteresis in the diaphragm sensor or a transient effect as a valve closes.

0 5 10 15 −25 −15 −5 5 15 25 time (s) o u tl et p re ss u re d ro p (k P a ) Flow_H1_T5_S10_001 0 5 10 15 0 100 200 piston speed (mm/s) upper lower

Figure 11: Pressure drop across cylinder outlet valves

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OCRE-TR-2013-030 6 Discussion

◦ cavitation: Build-up of air in the cylinder over several tests may affect flow rate, since air is compressible. However, the pump was purged whenever noticeable air bubbles remained after a test.

◦ exit pressure drop: The assumption that outlet hose pressure is equivalent to cylinder pressure is based on the assumption that exit pressure drop is an order of magnitude lower than drop across valve and fittings, based on a sample com-putational fluid dynamics (CFD) run at 800 mL/s. This may not be valid at other speeds.

◦ sensor location: The outlet pressure sensors are at different heights. The sen-sors were tared at atmospheric pressure, so there is a constant offset between each pair, ultimately affecting the calculation of orifice flow coefficient.

6.4 Applied force

The applied force is replicated in the flow runs using an empirically-derived viscous damping coefficient for one flow run; accuracy of force predictions is much improved with higher output hose height. Other factors may be affecting the results, however.

accelerated flow The acceleration of the fluid is not considered in the equation of motion. The missing term should be in phase with piston acceleration.

viscous damping Force to overcome viscous damping is significant in this pump, as evidenced in the dry and wet friction tests, in which the load cell registered 10% of the maximum load in the equivalent flow test.

Calculation of the viscous damping coefficient relies on an accurate estimate of piston clearance; the empirically-estimated coefficient implies an extremely small clear-ance, which is impractical to measure. This is further complicated by a second lubri-cated sliding region: the piston rod (through a bearing and seal) with water on one side only (whereas the cylinder with water on both sides).

While a value of 1600 aligns the model results with the flow data, the model does not predict the force in the friction tests well. The viscous damping term in the equation of motionc ˙x is valid only for thick films – perhaps too little water remains to maintain a complete film, and the coefficient becomes a function of velocity also [2]. An assay into tribology is beyond the scope of this work, other than to note that thin film lubrication is non-linear, with higher friction during acceleration due to changing film thickness and it exhibits hysteresis [3].

binding On high speed runs (T <= 5s), chattering (jerky motion) is observed (see load cell data in Figure 7), which indicates that the pump is binding. This is reflected in the load cell data, especially on the upstroke. It was determined after testing that the pump was overconstrained: the bottom pivot point had extra bolts preventing self-alignment and the upper rod connection is also tightly constrained.

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OCRE-TR-2013-030 7 Conclusions

The relative sensitivity of model to orifice flow and viscous damping coefficients is demonstrated in the magnitude of the related forces for a sample run in Figure 12, which shows the net applied force broken into its components.

0 1 2 3 4 5 6 7 8 9 10 −600 −400 −200 0 200 400 600 run Flow_H3_T5_S10_001 c visc = 1600 time (s) force(N)

applied (load cell) applied (model) weight viscous bernoulli m · a

Figure 12: Components of model applied force

7 Conclusions

The ultimate goal of the numerical model is to predict flow rate and cylinder pressures for a given input force, to aid in choosing a wave pump design. The current numerical model can be used to predict flow rate if we know the force applied to the piston, subject to a good estimate of the viscous damping coefficient; however, it does not predict dynamic pressure.

From physical tests, the relationship between force and flow rate appears linear, as shown in Figure 13, which the model predicts well (10% over), but the numerical model relies on an empirical viscous damping coefficient, which is not predicted yet. Likewise, the relationship between force and pressure is also close to linear, as shown in Figure 14, but the cylinder pressures are not predicted by this model since it relies on a steady flow relation.

Improvements to the numerical model are needed to successfully predict cylinder pressures and the viscous damping coefficient without building each version of the pump.

In addition, pump design should ensure large enough clearances for improved ro-bustness while sacrificing some efficiency, which in turn will be make the design pre-dictable using thick film viscous damping theory.

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OCRE-TR-2013-030 7 Conclusions −1000 −8000 −600 −400 −200 0 200 400 600 800 1000 100 200 300 400 500 600 700 800 900 flow rate (mm/s) force (N) T = 3 s T = 4 s T = 5 s T = 6 s T = 7 s T = 8 s T = 9 s T = 10 s T = 14 s T = 16 s T = 20 s

Figure 13: Force vs flow rate for all runs at minimum height, 10-inch stroke

−1000 −800 −600 −400 −200 0 200 400 600 800 1000 −100 −50 0 50 100 150 200 250 300 force (N) pressure (kPa) T = 3 s T = 4 s T = 5 s T = 6 s T = 7 s T = 8 s T = 9 s T = 10 s T = 14 s T = 16 s T = 20 s

Figure 14: Force vs combined pressures for all runs at minimum height, 10-inch stroke

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OCRE-TR-2013-030 8 Lessons learned

8 Lessons learned

Poor pressure sensor selection resulted in repeated failures, delays and changes to the test program. Cavitation was also noticed, which could affect future testing and certainly affects the design life of a wave pump.

8.1 Pressure sensor failures

In a reciprocating pump, pressure sensors must be rated for dynamic loads, including vacuum (suction).

The initial selection of pressure sensors only considered estimated peak pres-sure. The replacement sensor did not consider cyclic loads. Dylix provided a sample vacuum-rated sensor for fatigue-testing before replacement.

sensor test dates note

Omegadyne R _PX209-200GI _{August 28–30, 2012} _{failed - not vacuum-rated} Omegadyne R _{PX209-30V135GI} _{Sept. 14–21, 2012} _{failed - not rated for}

dy-namic (cyclic) loads Dylix R _{GXR3-PPV14.7V-PP500} _{Oct. 11–Dec. 18 2012} _{vacuum-rated, pre-tested}

8.2 Cavitation

Test programs and final pump design should avoid cavitation to prevent pump damage and unexpected effects.

When the pressure cycles below the fluid vapour pressure∗_{, entrained gases are}

released in bubbles (flashing) and are reabsorbed as the bubbles collapse (cavitation). These implosions cause severe pressure spikes that pit and damage pump internal parts and cause vibrations.

Video of the pump cylinder was recorded for most of the tests. Bubbles are ob-served in the pump cylinder in tests with a period less than 4 seconds. Cavitation is not modelled in the numerical model. While this may not affect overall cylinder pressures, it is possible to fracture a fluid cylinder and/or piping and damage the pump drive end internals with high pressure surges that occur when fluid is cavitating. [4]

∗

1.9 kPa at 17◦C_{supply tank water temperature}

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OCRE-TR-2013-030 References

9 Future work

The following work is required to develop the numerical model so it can predict a power transfer function for the Lord’s Cove wave resource:

1. Find an alternative method for predicting viscous damping and/or cylinder clear-ances.

2. Modify the model to determine pressures based on unsteady flow. 3. Include acceleration of the fluid in the model.

4. Validate the model in a series of sea states (force-input tests).

5. Conduct further CFD runs at different speeds to confirm exit pressure drop can be neglected.

6. Create model inputs for typical Lord’s Cove sea states.

Modifications are also needed to the test apparatus to ensure binding and other effects do not affect results:

7. Remove extra constraints (lower bolts). 8. Allow lateral self-alignment in crosshead.

9. Re-orient outlet pressure sensors horizontally (if required).

References

[1] R. Boileau, “Wave resource assessment for Lord’s Cove, Newfoundland – 2012 sur-vey,” Technical Report OCRE-TR-2013-008, National Research Council Canada, January 2013.

[2] R. Overney, “Introduction to tribology – friction.” course website, undated. UWash. ChemE554.

[3] F. Al-Bender, “Fundamentals of friction modeling,” in ASPE Spring Topical Meeting on Control of Precision Systems, pp. 117–122, MIT, April 2010.

[4] P. J. Singh and N. K. Madavan, “Complete analysis and simulation of reciprocating pumps including system piping,” in 4th International Pump Symposium, pp. 55–73, 1987.

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OCRE-TR-2013-030

Appendices

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OCRE-TR-2013-030 A Mathematical model

A

Mathematical model

A piston of mass mp moves in a vertical cylinder under the action of an applied force

F (t) where t is time. The cylinder has inlet and outlet valves as shown in Figure 15. The pressures in the cylinder chambers above and below the piston arep1, p2

respec-tively and the corresponding piston cross-sectional areas are A1, A2. The ambient

pressure at valve inlets is denoted bypin and the required outlet pressure is denoted

by pout. The viscous damping coefficient is denoted by cvisc and we assume that the

Coulomb frictional resistance is negligible. The displacement of the piston from its lowest position isx (t), positive upwards, where t is time. The equation of motion is

F (t) + p2A2− p1A1− cvisc˙x − mpg = mp ··

x (A.1)

whereg is the acceleration due to gravity.

one-way valve F(t) outlet ambient outlet pressure, pout inlet ambient inlet pressure, pin x(t) datum p1 p2 A1 A2 piston area

Figure 15: Numerical model of a double-acting reciprocating pump

The pressures p1 and p2 are related to the piston velocity ˙x as follows. The flow

rates through the inlet valves are denoted by qin,k and through the outlet valve by

qout,k (k = 1, 2) . We assume that the flow rate q through a valve is related to the

pres-sure drop∆p across the valve by the equation q = (CA)_valver 2

ρ(∆p) 1

2 (A.2)

where(CA)_valve is the product of a valve orifice coefficient Corifice and a valve orifice

areaAorifice . If the piston cross-sectional area isA then q = A ˙x and we rewrite (A.2)

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OCRE-TR-2013-030 A Mathematical model as (∆p)12 = αA ˙x (A.3) where α =r ρ 2 1

(CA)_valve (A.4)

Consider the following cases: Case (1) ˙x ≥ 0

For cylinder chamber1, qin,1 = 0 , p1 > p_outand for chamber2, q_out,2 = 0, p_in > p2.

Using equation (A.3) we write

(p1− pout) 1 2 = αA₁˙x (pin− p2) 1 2 = αA2˙x (A.5) from which we have

p2A2− p1A1= (p_inA2− p_outA1) − (α ˙x) 2

A31+ A 3

2 sign ( ˙x) (A.6)

where sign( ˙x) is defined as

sign( ˙x) =    1 ( ˙x > 0) 0 ( ˙x = 0) −1 ( ˙x < 0) (A.7) Case (2) ˙x < 0

For cylinder chamber1, qout,1 = 0 , pin > p1and for chamber2, qin,2 = 0, p2 > pout.

Using equation (A.3) we write

(pin− p1) 1 2 = −αA1˙x (p2− pout) 1 2 = −αA2˙x (A.8) from which we have

p2A2− p1A1= (poutA2− pinA1) − (α ˙x) 2

A31+ A 3

2 sign ( ˙x) (A.9)

where we note that sign( ˙x) < 0 for this case. Define the functionβ (t) as

β (t) =

pinA2− poutA1 ( ˙x ≥ 0)

poutA2− pinA1 ( ˙x < 0)

(A.10) Then we can write equations (A.6) and (A.9) in the form

p2A2− p1A1 = β (t) − γ ˙x 2

sign( ˙x) (A.11)

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OCRE-TR-2013-030 A Mathematical model where γ = α2 A3 1+ A 3 2 (A.12) Using (A.11) we re-write the equation of motion (A.1) as

F (t) + β (t) − γ ˙x2sign_{( ˙x) − c}visc˙x − mpg = mpx¨ (A.13)

Equation (A.13) is solved numerically forx and ˙x for different initial conditions. The pressuresp1andp2 are found from (A.5) and (A.8) as

p1 = pout+ (αA1˙x) 2 ( ˙x ≥ 0) pin− (αA1˙x) 2 ( ˙x < 0) (A.14) p2 = pin− (αA2˙x) 2 ( ˙x ≥ 0) pout+ (αA2˙x) 2 ( ˙x < 0) (A.15)

A.1 Laboratory test

For the laboratory test we specify the piston displacement in the form

x (t) = x0+ a0sin (ωt) (A.16)

Substituting into (A.13) gives

F (t) = mp g − ω2a0sin (ωt) + cviscωa0cos (ωt) − β (t) + γω 2 a2 0cos 2 (ωt) sign (cos (ωt)) (A.17) This is compared with the laboratory measurement ofF (t) . The pressures in the pump chambers are found from (A.14) and (A.15).

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OCRE-TR-2013-030 B Test apparatus photos and other information

B

Test apparatus photos and other information

(a) disassembled

(b) assembled

Figure 16: NRC wave pump prototype

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Figure 17: Linear actuator motor and screw mounted on test frame

Table 4: Linear actuator force limit manufacturer’s data for model BM1400-UF

peak torque T 23.6 N

friction constant c 0.2 *

shaft diameter D 19.04 mm

peak screw force F = _cDT 6200 N *assumed steel/zinc-plated threads

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Table 5: Turbulent transition flow rate fresh water density ρ 1000 kg/m3 dynamic viscosity µ 0.001 Pa_·s TygonTM tubing length L 10 m hose size ID 15.9 mm cross-section area _{A = π ∗ ID}2 /4 1.9679 cm2 transition Reynolds number Re = ρvL_µ _{2000 − 4000}

-velocity v = µRe_ρL _{0.1 − 0.2} mm/s transition flow rate q = v/A _{0.02 − 0.04} mL/s

Figure 18: Outlet head

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Figure 19: Test set-up

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OCRE-TR-2013-030 C Calibrations

C

Calibrations

The following table documents the sensor calibrations for this test program. Table 6: Channel calibration list

# channel name sensor serial # calibration date 33* Lower Pressure Out Dylix 121042702 2012-12-04

34 Upper Pressure Out Dylix 121043115 2012-12-05 35 Main Pressure Out Dylix 121043112 2012-12-04 36 Supply Pressure In Dylix 121043113 2012-12-04

38 Flow Rate Dylix 121043113 2012-12-04

41 Supply Tank Level Akamina unspec. 2012-XX-XX

2012-12-18 (recalibration) 42 Output Tank Level Akamina unspec. 2012-XX-XX

2012-12-18 (recalibration) 43 Pump Displacement Celesco BC200591 2012-08-24

44 Stroke Velocity Celesco BC200591 2012-08-24 45 Piston Force Sensotec 507412 2012-08-24

*channel in OEB data acquisition system Data including calibration reports are stored in the following folder:

Testdata(\\nrcsjsfs1):\Test_A1001189\OEB\

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OCRE-TR-2013-030 D Validation test results

D

Validation test results

The following figures present the results of the numerical model force predictions com-pared with pump test data (one run for each set of test conditions).

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OCRE-TR-2013-030 D V alidation test results 0 1 2 3 4 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Dry_T1_S10_001 0 5 10 15 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Dry_T3_S10_001 0 5 10 15 20 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Dry_T5_S10_001 0 10 20 30 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Dry_T7_S10_001 0 10 20 30 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Dry_T7_S1_001 0 10 20 30 −300 −200 −100 0 100 200 300 400 500 force (N) Dry_T7_S4_001

F_appl load cell (Dry_T7_S4_001)

f_visc = F_appl − W + ma

f_visc model c_p = 6E−09 m

Figure 20: Viscous damping force results for dr y fr iction runs (C v = 1600) 31

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OCRE-TR-2013-030 D V alidation test results 0 5 10 15 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Wet_T3_S10_001 0 5 10 15 20 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Wet_T5_S10_001 0 10 20 30 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Wet_T7_S10_001 0 10 20 30 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Wet_T7_S1_001 0 10 20 30 −500 −400 −300 −200 −100 0 100 200 300 400 500 force (N) Wet_T7_S4_001

F_appl load cell (Wet_T7_S4_001)

f_visc = F_appl − W + ma

f_visc model c_p = 6E−09 m

−1 −0.5 0 0.5 1 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Figure 21: Viscous damping force results for w et fr iction runs (C v = 1600) 32

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OCRE-TR-2013-030 D Validation test results 0 1 2 3 4 5 6 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T3_S10_003 load cell model (a) T = 3 s 0 1 2 3 4 5 6 7 8 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T4_S10_002 load cell model (b) T = 4 s 0 1 2 3 4 5 6 7 8 9 10 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T5_S10_002 load cell model (c) T = 5 s 0 2 4 6 8 10 12 14 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T6_S10_001 load cell model (d) T = 6 s 0 2 4 6 8 10 12 14 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T7_S10_002 load cell model (e) T = 7 s 0 2 4 6 8 10 12 14 16 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T8_S10_002 load cell model (f) T = 8 s

Figure 22: Force results for flow runs at minimum height, 3-8 s period, 10 in stroke, Cv = 1600

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OCRE-TR-2013-030 D Validation test results 0 2 4 6 8 10 12 14 16 18 20 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T9_S10_001 load cell model (a) T = 9 s 0 2 4 6 8 10 12 14 16 18 20 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T10_S10_001 load cell model (b) T = 10 s 0 5 10 15 20 25 30 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T14_S10_003 load cell model (c) T = 14 s 0 5 10 15 20 25 30 35 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T16_S10_001 load cell model (d) T = 16 s 0 5 10 15 20 25 30 35 40 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H1_T20_S10_001 load cell model (e) T = 20 s

Figure 23: Force results for flow runs at minimum height, 9-20 s period, 10 in stroke, Cv = 1600

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OCRE-TR-2013-030 D Validation test results 0 1 2 3 4 5 6 7 8 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T4_S10_004 load cell model (a) T = 4 s 0 1 2 3 4 5 6 7 8 9 10 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T5_S10_003 load cell model (b) T = 5 s 0 2 4 6 8 10 12 14 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T6_S10_004 load cell model (c) T = 6 s 0 2 4 6 8 10 12 14 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T7_S10_001 load cell model (d) T = 7 s 0 2 4 6 8 10 12 14 16 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T8_S10_001 load cell model (e) T = 8 s 0 2 4 6 8 10 12 14 16 18 20 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T9_S10_004 load cell model (f) T = 9 s

Figure 24: Force results for flow runs at 5 m output height, 4-9 s period, 10 in stroke, Cv = 1600

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OCRE-TR-2013-030 D Validation test results 0 5 10 15 20 25 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T12_S10_001 load cell model (a) T = 10 s 0 5 10 15 20 25 30 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H2_T14_S10_007 load cell model (b) T = 12 s

Figure 25: Force results for flow runs at 5 m output height, 10-12 s period, 10 in stroke, Cv = 1600 0 1 2 3 4 5 6 7 8 9 10 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 time (s) force (N) Flow_H3_T5_S10_001 load cell model

Figure 26: Force results for flow runs at 10 m output height, 4-9 s period, 10 in stroke, Cv = 1600