Objectives	Theoretical Background	Apparatus
Experimental Procedure	Report Specifications	Experiment 7 Data Sheet

Objectives

The objectives of this experiment are to :

1. Establish a calibration curve for the relation between the voltage output of a hot-wire/film anemometer bridge circuit and the velocity of a jet.
2. Measure the jet centerline velocity as well as the jet velocity profile at various downstream distances from the nozzle. These measurements will illustrate the physical nature of the jet.

Theoretical Background

Hot-Wire/Film Anemometer

        Hot-Wire/film anemometers are commonly operated in two basic modes, the constant current mode and the constant temperature mode. Both modes employ the same physical principle of forced convection heat transfer. In the constant current mode, a nearly fixed electric current is flowing through a small diameter film that is exposed to the flow velocity. The film attains an equilibrium temperature resulting from the balance between the internal heat generation due to electrical resistance and the convective heat loss from the fluid velocity. The film temperature must adjust itself to changes in the convective losses until a new equlibrium temperature is obtained. Since the convection coefficient is a function of the flow velocity, the equilibrium film temperature is a measure of the velocity. The film temperature can be measured in terms of its electrical resistance. In the constant-temperature mode (as will be used in this experiment), the current through the film is adjusted to maintain a constant film tmeperature. The current required to compensate the convective heat loss can then be used to measure the flow velocity.

        For equilibrium, the energy balance equation of a hot-wire/film is

where I is the current, R_f is the film resistance, T_f is the film temperature, Ta is the surrounding fluid (in this case, air) temperature, h is the convection coefficient and A is the surface heat transfer area. For a wide range of velocities, the convection heat transfer coefficient, h, can be related to the instantaneous convection velocity V. Based on the empirical evidence, the King's law has been shown to be valid for a thin film operated in constant temperature mode. King's law states

where A₀ and A₁ are considered to be constants under fixed operating conditions. For a properly designed system, the supplied current can be directly related to the anemometer output, E, that is,

where C₀ and C₁ are constants that are to be determined, and E₀ is the voltage measured at zero jet velocity.

Jet Flow Measurement

        A jet is formed by flow issuing from a nozzle into ambient fluid which can be at rest (a free jet) or moving (a coflowing jet). A jet is one of the basic flow configurations which has many practical applications such as jet engines combustion, chemical lasers, ink-jet printer heads, etc. The velocity at the exit of the nozzle of a typical laboratory jet has a smooth profile and a low turbulence level, about 0.1% - 0.5% of the mean velocity. Due to the velocity difference between the jet and the ambient fluid, a thin shear layer is created. This shear layer is highly unstable and is subjected to flow instabilities that eventually lead to the formation of large scale vortical structures. The interaction of these structures produces strong flow fluctuations, entrains ambient fluid into the jet flow and enhances the mixing. The shear layer and consequently, the jet spreads along the streamwise direction. In the central portion of the jet, a region with almost uniform mean velocity is called the potential core. Because of the spreading of the shear layer, the potential core eventually disappears at about four to six diameters distance downstream from the nozzle. The entrainment process continues further beyond the end of the potential core region such that the velocity distribution of the jet eventually relaxes to an asymptotic bell-shaped velocity profile as illustrated in Figure 1. In Figure 1, the half-width of the jet, y_1/2, is defined as the distance between the axis and the location where the local velocity equals half of the maximum centerline velocity, U₀. The downstream increase of the jets half-width can be considered as a result of the spreading of the jet. Due to the spreading, the jet centerline velocity, Vc, decreases downstream beyond the potential core region.

Figure 1. Schematics of a free jet flow and its downstream development

IMPORTANT NOTICE: THE HOT-WIRE/FILM PROBE IS EXTREMELY FRAGILE. IT CAN BE BROKEN BY SIMPLY TOUCHING THE TIP OF THE PROBE. THEREFORE, IT MUST BE HANDLED VERY CAREFULLY. DO NOT REMOVE THE PROBE BY YOURSELF. CONTACT THE LAB INSTRUCTOR FOR ASSISTANCE.

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Apparatus

The following apparatus will be used for this experiment:

        1. A rectangular jet, with a nozzle of dimensions 6 cm ´ 1 cm.
        2. An air pump to force air stream through the jet nozzle.
        3. A hot-wire/film anemometer, and its associated digital circuitry.
        4. A pitot-static tube and a digital manometer.
        5. A Pentium-based PC with LabVIEW software and an associated ADC card.
        6. An oscilloscope.

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Experimental Procedure

Calibration of the hot film.

1. Turn on the air pump to establish the jet flow. Estimate the jet exit velocity by measuring the stagnation pressure inside the reservoir chamber. The difference between the stagnation pressure and the total free stream pressure is a good approximation of the dynamic pressure of the exit stream.
2. Carefully move the hot-wire/film probe into the potential core region of the jet where the velocity is supposed to be uniform and fluctuation free. Confirm this by monitoring the output signal from the hot-wire/film on the oscilloscope.
3. Connect the anemometer output to the analog-to-digital converter (ADC) and the oscilloscope. Determine the time-averaged anemometer voltage output using the ADC and the LabVIEW software.
4. Record the ADC output.
5. Repeat the calibration procedure for the velocity range from 0 (the lowest velocity available to the maximum velocity.
6. Record 10 data points.

1. Set the dynamic pressure of the jet exit velocity at the maximum stable setting (usually 0.06 - 0.07 psi). Note: The digital pressure gage has an upper limit of 0.1 psi. Do not overload the unit!
2. Beginning at a position approximately at the jet nozzle, move the pitot-static probe along the center axis of the jet. Measure the jet centerline velocity at 1cm intervals for 31 data points.
3. Move the probe to another downstream location at x/D = 4. (The height D of the jet nozzle is 1cm) Measure the cross stream velocity profile by using the computer-controlled traverse and the computer, by obtaining the ADC output.
4. Record the ADC output for the location.
5. A total of 8 points with a 1 mm increment should be measured.
6. Move the prove to another downstream location at x/D = 10 and measure the velocity profile.
7. Record the ADC output for this location also
8. Use 8 points and a 3 mm increment.
9. Measure the profile at x/D = 20 and 30 and record the ADC output. Use a 5mm increment.

Report Specifications

1. Use the data collected in part A, verify the Kings Law. Plot (E-E₀)² vs.and determine the constants C₀ and C₁. Discuss the types of errors present in the experiment.
2. Plot the variation of the jet velocity along the center axis, that is, V_c/V_exit vs. x/D. Discuss your results.
3. Can you identify the end of the potential core based upon your time-averaged velocity data?
4. Plot the time averaged mean velocity profiles at x/D=4, 10, 20, and 30, that is V(y)/Vc vs y/D. Plot the variation of the half jet width, y _1/2 vs x/D. Discuss the results of both plots.

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Note: Please note the units of the quantities which are being measured, when recording data. For example, when measuring voltage, if the voltmeter reads 16 mV, then write down 16 mV instead of just 16.

1. Nozzle dimensions: 10 cm X 1 cm
2. Equation 3: 

 I Hot Film Probe Calibration
 

 II: Jet Centerline Velocity:

1. Set dynamic pressure of jet at highest value (~0.07psi).
2. Use the pitot tube to take the pressure measurements.
3. Record the data in the following table

III. Velocity profile measurements:

1. Set dynamic pressure of jet at highest value (~0.07psi).
2. Use the pitot tube to take the pressure measurements.
3. Take the measurements for x/D=4, 10, 20 and 30, where x = distance from nozzle exit (cm) and D = height of nozzle = 1 cm

YOU NEED TO GET THE LAB INSTRUCTOR'S SIGNATURE BEFORE LEAVING.

The student has performed the experiment satisfactorily and has cleaned the work area.

__________________________ _______________

(Lab assistant's signature)                           Date

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