Transcript Lecture04 - Lcgui.net

Measurements in Fluid Mechanics
058:180:001 (ME:5180:0001)
Time & Location: 2:30P - 3:20P MWF 218 MLH
Office Hours: 4:00P – 5:00P MWF 223B-5 HL
Instructor: Lichuan Gui
[email protected]
http://lcgui.net
Lecture 4. Measurement systems and static response
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Measuring systems and their components
Essential systems in fluid mechanics experiment
1. Physical system: flowing fluids, flow-producing apparatus, test models etc.
2. Measuring system: sensors, electric and electronic circuits, data acquisition and
processing devices, and software
3. Experimenter(s): person(s) who plans, executes, and interprets the measurements
Response of measuring system - relationship between values of an input and an output
Inputs of measuring system
1. Desired inputs
2. Undesirable inputs
a. interfering inputs
- add noise to desired inputs
b. modifying inputs
- change response to desired inputs
Example: hot-wire anemometer used to measure air jet flow from a nozzle to lab room
- The draft of air produced by ventilation system in lab acts as interfering inputs.
- The room temperature change acts as modifying inputs.
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Filtering, compensation, and output correction
Filters - used to reduce or eliminate undesirable input effects
Filters classified according to frequency range:
- no-pass filters remove all fluctuations, permitting only a steady component
- low-pass filters remove fluctuations with frequencies above a cut-off value
- high-pass filters remove fluctuations with frequencies below a cut-off value
- band-pass filters remove all fluctuations except those with frequencies within a certain band
- band-reject filters remove all fluctuations with frequencies within a certain band
Filters classified in terms of physical operation
- electrical-electronic filters, applied to electric signals;
- mechanical filters, designed to filter motion or force fluctuations,
e.g. shock absorbers used to reduce vibration of an apparatus;
- thermal filters, designed to remove temperature fluctuations, e.g. thermal insulation
- electromagnetic filters, designed to remove the interfering effects of electric and magnetic fields
- digital filters, applied to recorded signals
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Filtering, compensation, and output correction
Compensation - introduce additional interfering or modifying inputs to partly or
entirely cancel the original undesirable effects.
Example: Bonded strain gauge - sensitive to ambient-temperature fluctuations
𝑉=
V0
𝑅3
𝑅1 +𝑅3
𝑅𝑠1
2 +𝑅𝑠1
+𝑅
∙ 𝑉0
𝑅𝑠1 = 𝛼 ∆𝑇 𝑅𝑠 + ∆𝑅
Rs1
Measuring gauge
𝑉=
𝑅3
𝑅1 +𝑅3
=
𝑅3
𝑅1 +𝑅3
=
𝑅3
𝑅1 +𝑅3
𝑅𝑠1
𝑠2 +𝑅𝑠1
+𝑅
𝑅𝑠2 = 𝛼 ∆𝑇 𝑅𝑠
∙ 𝑉0
+
𝛼∙ 𝑅𝑠 +∆𝑅
𝛼∙ 𝑅𝑠 +∆𝑅 +𝛼∙𝑅𝑠
+
𝑅𝑠 +∆𝑅
2𝑅𝑠 +∆𝑅
∙ 𝑉0
Rs2
∙ 𝑉0
Reference gauge
V0
𝑅𝑠1 = 𝛼 ∆𝑇 𝑅𝑠 + ∆𝑅
Rs1
Measuring gauge
Analytical correction
- remove undesirable effects & errors from output
according to knowledge of undesirable inputs & system responses
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Modes and functions of measuring system components
Operation modes:
- analogue, discrete (digital, binary, etc.), or hybrid
Response modes:
1. Passive – output energy supplied by input
2. Active – output energy supplied by external
excitation source
Functions of measuring system components:
1. Sensing
used to produce output
2. Convection and conditioning
used to transform output to a form,
amplitude, or both more suitable for
observation or further processing
3. Transmission
used to transfer signals or other information
from one component to another
4. Processing and storage
used display or store output
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Static response and static calibration
Static system
- constant or slowly varying input and output
Static response
1. Theoretically determined by physical law
e.g. liquid manometer for gas pressure
difference measurement, Fig. (a)
Hydrostatic law:
2. More commonly determined by static calibration, e.g. variable-reluctance pressure transducer, Fig. (b)
calibrated with liquid manometer:
Static calibration:
- performed separated for each desired input
- determine input-output relationship (calibration curve) with standard system
- accuracy depends on that of instruments used as standard
Effects of undesirable inputs:
1. Zero drift – parallel shift of primary calibration curve
2. Sensitivity drift – a change in the slope of the primary calibration curve
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Static response and static calibration
Static performance characteristics:
non-linear
• Static sensitivity - slope of input-output relationship
- constant in linear system
- local sensitivity varies over input range in non-linear system
linear
• Scale readability
Input
- minimum change in output can be observed
• Span (input full-scale)
- range of input to be measured with acceptable accuracy
span
• Full-scale output - range of output values measured from minimum to maximum input values
• Dynamic range - ratio of largest to smallest values of input
• Non-linearity - maximum deviation of actual response from
straight line determined by least-square fit of
calibration measurements
• Threshold - smallest input level for detectable output
• Resolution - smallest input change for detectable output change
• Hysteresis - difference between the output value corresponding
to an input value reached from below and the output
value corresponding to the same input value
reached from above.
Elastic hysteresis of an band
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Normality test and removal of outliers
Normality test
- Used to assess randomness of repeat measurement values
• Rearrange a number of repeat values xi, i=1,2,,N , so that xi  xi+1
• Compute percentage of repeat values that are not more than xi , i.e. 𝑦𝑖 = 100
• Compute mean value and variance as
1
𝜇𝑥 =
𝑁
𝜎𝑥 2
𝑖−1
%
𝑁
𝑁
𝑥𝑖
𝑖=1
1
=
𝑁−1
𝑁
𝑥𝑖 − 𝜇𝑥
2
𝑖=1
• Normalize the repeat values as
𝑥𝑖 ∗ =
𝑥𝑖 − 𝜇𝑥
𝜎𝑥
• Plot yi vs. xi* on probability
graph paper as right
• Assess deviation of plotted
points from the Gaussian line
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Normality tests and removal of outliers
Outliers
• Spurious values due to
(1) human error, e.g. misreading of an instrument’s output
(2) Temporary or intermittent undesirable input
• Identified by application of Chauvenet’s criterion
Value xi is a outlier if
𝜏 ∙ 𝜎𝑥 ≤ 𝑥𝑖 − 𝜇𝑥
Linear least-square fit (LLSF)
A set of calibration measurements:
LLSF line equation:
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Homework
- Read textbook 2.1-2.2 on page 19-31
- Questions and Problems: 1, 4 on page 41
- Due on 08/31
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