Today s menu. Last lecture. Measurement of volume flow rate. Measurement of volume flow rate (cont d...) Differential pressure flow meters
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1 Last lecture Analog-to-digital conversion (Ch. 1.1). Introduction to flow measurement systems (Ch. 12.1). Today s menu Measurement of volume flow rate Differential pressure flowmeters Mechanical flowmeters Vortex flowmeters Measurement of mass flow Measurement of tricky flows" Ultrasonic measurement systems. 1 2 Measurement of volume flow rate Differential pressure flow meters These are the most common industrial flowmeters for clean liquids and gases. ½ 1 P 1 Pressure sensors P 2 z 1 z 2 Differential pressure flow meters (cont d...) Cross section average velocity v 1 v 2 m/s Pressure P 1 P 2 N/m 2 Fluid cross section area A 1 A 2 m 2 Fluid density ρ 1 ρ 2 kg/m 3 Total energy/mass E 1 E 2 J/kg Elevation above datum z 1 z 2 m A 1 v 1 v 2 A 2 E 2 ½ 2 E 1 Venturi tube 3 4
2 Differential pressure flow meters (cont d...) Assumptions when deriving the equations: Frictionless flow No heat losses Conservation of energy (pressure + kinetic + potential), i.e. Differential pressure flow meters (cont d...) Horizontal pipe, i.e. z 1 = z 2. This means that the equation simplifies to P 1 ρ v2 1 = P 2 ρ v2 2 E 1 = P 1 ρ v2 1 + gz 1 = E 2 = P 2 ρ v2 2 + gz 2 Incompressible fluid, i.e. ρ 1 = ρ 2 = ρ. Conservation of volume flow rate, i.e. Q 1 = A 1 v 1 = Q 2 = A 2 v 2. v 2 2 v = P 1 P 2 ρ 5 6 Differential pressure flow meters (cont d...) We now have all the equations we need to solve for the theoretical volume flow rate, Q, i.e. Q = A 1 v 1 A 1 v 1 = A 2 v 2 v 2 2 v which gives (after some calculations...) Q = A 2 1 ( A2 A 1 ) 2 = P 1 P 2, ρ 2(P 1 P 2 ) ρ Differential pressure flow meters (cont d...) Some assumptions are not fulfilled in practice: Frictionless flow is not obeyed, but for well-established turbulent flow (Re > 1 4 ) the losses are small. The cross section area of the flow is not the same as the cross section area of the pipe. This depends on the velocity and the pipe diameter ratio. For gases, the fluid is compressible. To account for this, correction factors are introduced. This is then determined in calibration experiments. See the book for the details on how the equation is simplified. 7 8
3 Differential pressure flow meters (cont d...) General characteristics of D/P flowmeters: No moving parts; robust, easy to maintain; widely established and accepted. Permanent pressure loss due to frictional effects. This could mean a significant cost in increased pumping energy. Non-linear devices; The useful range is limited to between 25% and 1 % of maximum flow. Can only be used for clean fluids. Limited accuracy ( 1.5 %). Mechanical flowmeters A mechanical machine is placed in the flow, which moves with a cycle f proportional to the flow rate, i.e. f = KQ. Mechanical flowmeters measure the volume V that has been delivered per time period T, i.e. by counting the number of cycles over the time T. T T N = fdt= K Qdt= KV. 9 1 Mechanical flowmeters (cont d...) Mechanical flowmeters (cont d...) Turbine flowmeters t Turbine flowmeters The blades of the turbine are usually made of a ferromagnetic material. The rotation can be picked up by an electromagnetic sensing element, which output voltage will be a sinusoidal with a frequency proportional to the volume flow rate
4 Mechanical flowmeters (cont d...) Properties of turbine flowmeters Moving mechanical parts; ageing and wear of bearings leading to high maintenance costs. Poor reliability. Flow rate found by calibration. Vortex flow meters General principle Based on a natural phenomenon called vortex shedding. When a fluid flows over a body, vortices will form in the flow due to boundary conditions. The vortex frequency is proportional to the flow rate, as f = S v d, where d is the diameter of the bluff body and S is the Strouhal number (constant for a wide range of flow). The vortices give rise to local changes in pressure and velocity, which enables counting" or detection of the vortices Vortex flow meters (cont d...) Vortex flow meters (cont d...) flow bluff body Detection of vortices: Piezoelectric Flexible diaphragms (membranes) in the bluff body react to the local variations in pressure. Thermal For small flows (see Ch and 14.3 for details). Ultrasonic The ultrasound signal is modulated in both amplitude and frequency because of local variations in pressure and velocity. vortex shedding 15 16
5 Vortex flow meters (cont d...) Ultrasonic imaging of vortices Vortex flow meters (cont d...) Ultrasonic imaging of vortices flow cylindrical obstacle x y transducer arrays digitizing electronics longitudinal distance (mm) transversal distance (mm) 17 J. Carlson, R.-K. Ing, J. Bércoff, and M. Tanter, Ultrasonic vortex imaging using two-dimensional speckle correlation", IEEE Int. Ultrason. Symp Measurement of mass flow rate Inferential methods Here, the mass flow is computed from volume flow and density, i.e. Ṁ = ρq and M = ρv. Examples of ultrasonic mass flow metering will be given next lecture. Measurement of mass flow rate (cont d...) Direct methods - the coriolis effect This means measuring the mass flow directly. The most common direct mass flow meter in use today is the coriolis meter. flow F driving oscillation flow F 19 2
6 Measurement of mass flow rate (cont d...) Direct methods - the coriolis effect (cont d...) General principle: The flow of a certain mass passes through a U-shaped tube section that rotates with a certain angular frequency. The mass experiences a force proportional to the flow velocity, the mass, and the rotation frequency. The force variations can be measured using for example strain gauges. Read the details on your own. Measurement of tricky flows" Examples The flow is slow (laminar) or transitional Re < 1 4. Differential pressure meters work poorly. The fluids are highly corrosive or toxic. Mechanical meters like turbine meters can not be used. Multiphase flows. The flow contains liquids, solids and gases. Physical modeling leading to the equations become extremely difficult. No obstruction can be tolerated. For example, measuring blood flow, or in situations where no pressure drops can be tolerated. Read the remaining sections as an overview Ultrasonic measurement systems What is ultrasound? Acoustics may be defined as the generation, transportation, and reception of energy in the form of vibrational waves. What is Ultrasound (cont d...)? Compression waves: Particle displacement and wave propagation in same direction. The sound propagation arises from internal elastic forces between atoms or molecules, when they are displaced from their equilibrium. Ultrasound is defined as sound of frequencies above the audible range, that is above 2 khz. particle motion wave propagation 23 24
7 What is Ultrasound (cont d...)? Transversal waves: Particle displacement normal to wave propagation. What is Ultrasound (cont d...)? We differ between pulsed sound particle motion wave propagation time What is Ultrasound (cont d...)?...and continuous-wave ultrasound Reflection and Transmission When a sound wave encounters a boundary between two different materials, part is reflected and part is transmitted. The reflection coefficient (number between and 1) is defined as R 12 = z 2 z 1 z 1 + z 2, where z 1 and z 2 are the acoustic impedances of medium 1 and 2, respectively. time This means that the amplitude of the reflected wave is A R 12, where A is the amplitude of the incident wave
8 Reflection and Transmission (cont d...) The acoustic impedance of a material is given by: z = ρ c, where ρ is the density and c is the speed of sound. The acoustic impedance is measured in Pa s/m. Attenuation When a sound wave propagates through a medium, its is also attenuated with distance, often modeled as: A 1 = A e αx, where x is the propagation distance, α is the attenuation coefficient, and A is the amplitude of the transmitted wave What can we measure? We can directly measure speed of sound and attenuation. From attenuation and speed of sound we can calculate various properties, such as: Reflection and transmission coefficients Fluid density Elastic properties (viscosity, Young s modulus, Bulk modulus, etc.) Since sound propagation is a particle motion, we can also use sound velocity measurements to estimate volume flow rate. Acoustic Properties of Materials Speed of sound in different media: Gases: 25 4 m/s. Water: m/s. Plastics: Very different, but typically in the range 25-3 m/s (for PMMA). Steel: 58 m/s. Aluminium: 642 m/s. All depend on temperature, sound frequency, and pressure
9 Acoustic Properties of Materials Speed of sound in Biological tissue (at 37 C): Blood: 156 m/s. Bone: m/s (trabecular and cortical bone). Fat: 145 m/s. Liver: 156 m/s. Acoustic Properties of Materials (cont d...) Frequencies for different applications: Ultrasound in gases, typically below 1 MHz. Ultrasound in liquids, 5 khz 3 MHz, but often 3-1 MHz. Medical ultrasound, 3-1 MHz, in the most common systems. All depend on temperature, sound frequency, and pressure Application examples Doppler flowmeter. Cross-correlation flowmeter. Transit-time flowmeter. Velocity profile measurements in multiphase flows (speckle-correlation). Application examples (cont d...) Doppler flowmeter flow containing scatterers transmitter receiver The frequency of the received signal will shift depending on the flow velocity, i.e. a Doppler effect. See the text book for details
10 Application examples (cont d...) Cross-correlation flowmeter flow containing scatterers (a) transducer transmitted pulse received backscatter signal (b) Application examples (cont d...) Cross-correlation flowmeter (cont d...) flow containing scatterers receiving transducers The signal received at one time instant is cross-correlated with a signal received a short time later. The shift of the signal in time depends on the flow velocity. transmitting transducers Application examples (cont d...) Application examples (cont d...) Transit-time flowmeter Velocity profile measurements transducer 1 flow x transducer 2 39 Going into more advanced instrumentation, it is possible to use the backscattered signals as a fingerprint" (speckle pattern) of the entire flow profile. Cross-correlating two consecutive pattern, we can create a velocity profile of particles in the flow. axial distance, y (mm) (a) 5 1 particle velocity (cm/s) axial distance, y (mm) transversal distance, x (mm) transversal distance, x (mm) (b) particle velocity (cm/s) 4
11 Application examples (cont d...) References Velocity profile measurements (cont d...) Looking at the velocity profile at the center of the pipe, we obtain the following: particle velocity,v(cm/s) axial distance, y (mm) 41 J. Carlson and R. K. Ing, Ultrasonic Speckle Correlation Imaging of 2D Particle Velocity Profiles in Multiphase Flows", Flow Measurement and Instrumentation, vol. 14, no. 4 5, pp , 23. J. Carlson and P.-E. Martinsson, A Simple Scattering Model For Measuring Particle Mass Fractions In Multiphase Flows," Ultrasonics, vol. 39, no. 8, pp , June 22. J. E. Carlson, J. van Deventer, and M. Micella, Accurate Temperature Estimation in Ultrasonic Pulse-Echo Systems", in Proc. of World Congress on Ultrasonics, (Paris, France), pp , September 7 1, 23. J. E. Carlson, J. van Deventer, A. Scolan, and C. Carlander, Frequency and Temperature Dependence of Acoustic Properties of Polymers Used in Pulse-Echo Systems", in Proc. of IEEE Int. Ultrasonics Symposium, (Honolulu, Hawaii, USA), pp , October 5 8, Summary Measurement of volume flow rate Differential pressure flowmeters Mechanical flowmeters Vortex flowmeters Measurement of mass flow Measurement of tricky flows" Ultrasonic measurement systems. Recommended exercises
12 Questions? 45
Today s menu. Last lecture. Ultrasonic measurement systems. What is Ultrasound (cont d...)? What is ultrasound?
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