DEVELOPMENT OF MEASUREMENT STANDARD FOR DYNAMIC PRESSURE AT MIKES Sari Saxholm, Antti Lakka, Martti Heinonen, Kari Riski MIKES, Centre for Metrology and Accreditation Tekniikantie 1, Espoo Finland telephone: +358-29-5054456, e-mail: antti.lakka@mikes.fi
Table of contents 1. Introduction 2. Measurement standard as a target 3. Starting point 4. Current status Pressure calculations Measurements Flow simulations 5. Next steps 6. Summary 2
1. Introduction EMRP-project IND09 Dynamic - Traceable dynamic measurement of mechanical quantities started one year ago MIKES is focusing on WP2 Dynamic pressure One of the aims of WP2 is to develop facilities providing primary dynamic pressure standards, which can be used to calibrate reference pressure transducers MIKES is developing a primary dynamic pressure standard based on the drop weight principle for the measuring range 100 MPa to 500 MPa with the targeted relative measurement uncertainty in the order of 1 % New primary dynamic pressure standard will provide traceability to the measurements in the different areas, e.g. hydraulic systems, engine, ammunition and firearms industries 3
2. Measurement standard as a target The main objective is to upgrade an existing dynamic pressure calibrator of AVL from a secondary level to primary measurement standard Drop weight method is used The measurement standard generates a pressure transient The maximum pressure of the transient can be calculated Traceability is based on knowledge of parameters (values, uncertainty) affecting on the pressure peak Four dynamic pressure transducers can be calibrated simultaneously 4
2. Measurement standard as a target The device is controlled and data is gathered with a host PC and a Labview program Transducers being calibrated produce a charge, which is converted to a voltage with a charge amplifier Analog voltage is converted to digital with a DAQ device 5
2. Measurement standard as a target 6
Structure An existing dynamic pressure calibrator is used as a starting point Main parts are a measuring head, an impact mass, guidance rods, a carrying arm with an electromagnet and a foundation mass Measuring head contains a cylindrical pressure chamber filled with glycerol, a piston capable of moving in the cylinder and attachments for four dynamic pressure transducers 7
Working principle An impact mass is released by an electromagnet and falls along guidance rods At the end of the fall the impact mass collides with a piston, much smaller than the mass of the impact mass The bodies experience an inelastic collision and they continue moving downwards with the same speed The distance traveled together is relatively small (ca 0,4 mm with 100 MPa nominal pressure) 8
Working principle The piston compresses glycerol causing pressure rise Eventually the piston-impact mass assembly is stopped Nearly all the potential energy of the impact mass has been converted to compression energy of glycerol Glycerol inside the chamber starts expanding as glycerol starts giving energy back to the assembly The piston and the falling mass are forced to move upwards 9
Working principle The piston and the impact mass move upwards with the same speed until the initial volume inside the chamber is reached The piston stops while the impact mass still moves upwards Finally the impact mass is catched by the electromagnet of the carrying arm and is lifted back to its initial position Duration of a produced pressure peak is ca. 3 ms 10
Uncertainty factors 11
4. Current status Data acquisition hardware is integrated into the dynamic pressure calibrator setup Mathematical modelling of impact is underway to achieve pressure calculation techiques Test measurements have been made to provide information about the device, glycerol and the piston motion Numerical simulations are underway to support mathematical modelling 12
Pressure calculations Pressure inside the chamber could be, in theory, calculated by using the Navier-Stokes equations of fluid flow and solving for pressure In practice, finding an exact solution for the differential equations is very difficult An easier way is to find an equation of state for glycerol and then evaluate fluid flow effects Pressure inside the chamber can also be estimated with keeping in mind a few fundamental laws of physics 13
Approximate equations Approximate values can be obtained considering Newton s second law and solving for pressure Also, the law of conservation of energy canbeusedas a starting point Energy conservation equation assumes that all the potential energy is converted to compression energy and pressure is constant F E pot p p Ma p A Mgh p max ghm Ax max max Ax M a max p max = maximum pressure M = the mass of the object a max = maximum acceleration of the object A = the area of the piston g = gravitational constant h = falling height of the object x = max piston displacement A 14
Pressure calculations using bulk modulus To obtain more accurate values, an equation of state for glycerol should be formulated An equation including the glycerol bulk modulus K can be used K is dependent on pressure and temperature The equation can be derived from the definition of the bulk modulus dp dv K V dp K dv V x Adx p K( p, T ) 0 V0 Ax p = pressure K = the bulk modulus T = temperature V = volume V 0 = initial volume A = the area of the piston x = piston displacement 15
Pressure calculations using the bulk modulus Currently an approximation including the constant bulk modulus is underway No temperature effects have been considered so far Initial volume can be measured by calculating the mass of glycerol in the chamber Piston area can be calculated if the radius of the piston is known Piston displacement can be measured with a laser interferometer p p x K V 0 0 K Adx Ax ln(1 Ax ) V K = the bulk modulus A = the area of the piston x = max piston displacement V 0 = initial volume 0 16
The bulk modulus According to the Newton- Laplace equation the bulk modulus depends on speed of sound and density in the media c c 2 2 K K 4 3 G If the flow is compressible, shear modulus G must be included in the equation c = speed of sound = density K = the bulk modulus G = the shear modulus 17
The bulk modulus Glycerol works like a spring Motion can be modeled by using a damped harmonic oscillator equation of motion Certain parameters can be calculated, e.g. spring constant, damping parameter and the amplitude of the motion These parameters have a close relationship with material related parameters, e.g. the bulk modulus F ma m d 2 dt x 2 kx C m = the mass of the piston and the impact mass a = acceleration x = piston displacement k = spring constant C = damping parameter dx dt 18
Compressible flow Pressure calculated using an equation of state is thermodynamical pressure (that is, pressure dependent on volume and temperature), i.e. compressible flow and shear strain are not considered In the Navier-Stokes equations for a Newtonian fluid shear strain is included in the stress tensor Dv Dt g τij p nabla operator D material derivative Dt density v = velocity p = pressure g = gravitational constant ij = stress tensor 19
Measurements Test impacts have been made during development process of the device Piezoelectric transducers have been used to measure pressure peaks Acceleration of the piston has been measured with accelometer The shape of the pressure peak can be used to evaluate successfulness of pressurization of the pressure chamber 20
Pressure and acceleration curves 1400 800 Pressure (bar) 1200 1000 800 600 400 200 700 600 500 400 300 200 100 Acceleration (m/s^2) 0 0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035 Time (s) 0 Pressure Acceleration 21
Acceleration, velocity and displacement of the piston 0,8 0,0006 0,6 0,0005 v (m/s) a (km/s^2) 0,4 0,2 0,0-0,2-0,4 0,0004 0,0003 0,0002 0,0001 0,0000 x (m) -0,6-0,0001-0,8-0,0002 0,0000 0,0005 0,0010 0,0015 0,0020 0,0025 0,0030 time (s) v (t0=1,44 ms) integr a_filtered x (t0= 1,44ms) 22
Measurements The motion of the foundation mass during an impact has been measured with an accelometer Amplitude of the motion is a few per cents of the amplitude of the piston The foundation mass and the measuring head escape from the piston 23
Flow simulations Glycerol flow simulations with Comsol Multiphysics software are in early development phase The main objective is to reveal the nature of pressure waves inside the chamber Other major topic is to evaluate the main uncertainty factors 24
5. Next steps Laser interferometer will be assembled and even more accurate measurements involving piston travel will be excecuted Comsol simulations will be continued and simulation models will be improved An in-depth study concerning the bulk modulus of glycerol will be executed Temperature effects will be included in pressure calculations Compressibility of glycerol flow will be studied 25
6. Summary MIKES is developing a primary dynamic pressure standard based on the drop weight principle Pressure peak produced by the device can be calculated when the parameters are known In the pressure peak calculations, following parameters have key roles: piston area and displacement, initial volume and the bulk modulus Work continues with deeper studies for key parameters, simulations and temperature effects Next deadlines: Data sets from the drop weight device available in August 2013 Report of comparison between different primary dynamic pressure standard systems in June 2014 26
The end. Thank You for Your attention The research within the project has received funding from the European Union on the basis of Decision No 912/2009/EC. It is carried out in the European Research Programme (EMRP) project IND09 Traceable dynamic measurement of mechanical quantities. antti.lakka@mikes.fi 27