HotWire Anemometry Cảm biến dây nhiệt

HotWire Anemometry Cảm biến dây nhiệt Chapter 10: HotWire Anemometry Fundamentals Thermal anemometry is a method for measuring fluid velocities by sensing the changes in heat transfer from a small, electrically heated sensor exposed to the fluid motion. The most common thermal anemometer is the hotwire anemometer. The hotwire sensor is a very fine (and easily broken) cylindrical wire. A typical hotwire diameter is about 4μm Use hotwire anemometry to investigate the characteristics of a turbulent air jet, by measuring The radial velocity profile of a round air jet at various axial locations, The mass flux as a function of increasing distance from the jet exit, and hence the entrainment of fluid into the jet The momentum flux at various axial locations The angle associated with the spread of the jet

Chapter 10:

Hot-Wire Anemometry

Hot Wire Sensors & Anemometry Experiment

Hot-Wire Calibration Air Jet Properties

• Thermal anemometry is a method for measuring fluid velocities by sensing the changes in heat transfer from a small, electrically heated sensor exposed to the fluid motion.

• The most common thermal anemometer is the hot-wire anemometer.

• The hot-wire sensor is a very fine (and easily broken) cylindrical wire A typical hot-wire diameter is about 4μm.

Chapter 10:

Hot-Wire Anemometry

Part 1: Hot-Wire Sensor

Sketch of Hot Wire Sensor

1.0 mm

Sensing Length

Gold plated stainless

steel supports

How a Hot wire Sensor Works

Current flow through wire

The current i flowing through the wire generates heat (i2Rw)

In equilibrium, this must be balanced by heat lost (primarily convective) to the surroundings Flow Field

How a Hot wire Sensor Works (cont’d)

Flow Field

Current flow through wire

The rate of which heat is removed from the sensor is directly related to the

velocity of the fluid flowing over the sensor

The hot wire is electrically heated

If velocity changes, convective heat transfer changes, wire temperature will change and eventually reach a new equilibrium.

Principles of Operation

• In a constant temperature hot-wire, a feedback control acts to vary the current flowing through the wire so that its temperature remains constant.

• The fluid velocity can be determined from the measurement of the amount of current (or voltage) required to maintain the sensor at constant temperature

Hot Wire Response

Non-linear response of hot wire sensor

n

BV A

Chapter 10:

Hot-Wire Anemometry

Part 2: Anemometry Experiment

• Understand the principle of operations of a hot-wire sensor

• Use hot-wire anemometry to investigate the characteristics of a turbulent air jet, by measuring

– The radial velocity profile of a round air jet at various axial locations,

– The mass flux as a function of increasing distance from the jet exit, and hence the entrainment of fluid into the jet

– The momentum flux at various axial locations

– The angle associated with the spread of the jet

Electronics Module

Chapter 10:

Hot-Wire Anemometry

Part 3: Hot-Wire Calibration

Hot-Wire Sensor Calibration

• The measurement of the fluid velocity from the hot-wire response:

requires knowing the calibration constants A, B and n.

• The purpose of the calibration process is to empirically determinate A, B and n

• This requires measuring the fluid velocity, V, using a standard (other sensor than the hot-wire) and the

corresponding output hot-wire voltage, E, under the same flow conditions for a certain number of data points (at the very least 2).

n

V B A

• Set a flow condition (one fluid velocity at some location)

• Measure flow velocity at that location with a standard (for instance, a Pitot tube) → Vi

• Expose hot-wire anemometer to same flow and measure voltage → Ei

• Repeat the measurement for different flow conditions → N data points (Vi, Ei)

• Generate non-linear calibration based on theory → determine A, B and n in E 2 = A + B V n from the N data points (Vi, Ei).

Manipulating Response Equation

n

BV A

B ( ln )

E E

(

0 2

Noting properties of the ln function…

) V ln(

n )

B ln(

) E

E

0 2

Determining the calibration constants…

) V ( ln n )

B ( ln )

E E

(

0 2

Given that you have measurements of E vs V and that you

know the value of E0 from your no flow reading, simply define:

) V ( ln

The plot of Y vs X then has a slope of n

and an intercept of ln (B) !

) E E

( ln

Y = 2 − 0 2 and

Chapter 10:

Hot-Wire Anemometry

Part 4: Air Jet Properties

Air Jet Properties

• As an air jet issues out of a tailpipe a shear layer develops

• The jet entrains ambient air due to this shear and the diameter of the jet increases with axial distance

• Hence, the mass flow rate increases with axial distance

• No energy is added to the flow, so momentum flux should remain constant with increasing axial distance.

Calculating Mass Flux

r ( V

m

0

2 π ρ



r R

Two Methods for Mass Flux

• V(r) = A + Br + Cr2 +

• V(r) = A + B exp(Cr)…

• Be sure you have good fit (very high R2)

• Be sure that there are no substantial deviations or

oddities in the profile (particularly at large r)

• Substitute into mass flux equation and integrate