비디오: Nozzle Analysis: Mach Number and Converging-diverging Nozzle

Nozzle Analysis: Variations in Mach Number and Pressure Along a Converging and a Converging-diverging Nozzle

Overview

Source: Shreyas Narsipur, Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC

A nozzle is a device that is commonly used to accelerate or decelerate flow by virtue of its varying cross-section. Nozzles are widely used in aerospace propulsion systems. In rockets, propellant that is ejected from the chamber is accelerated through a nozzle to create a reaction force that propels the system. In jet engines, a nozzle is used to transform energy from a high-pressure source into kinetic energy of the exhaust to produce thrust. The isentropic model along the nozzle is sufficient for a first-order analysis as the flow in a nozzle is very rapid (and thus adiabatic to a first approximation) with very little frictional loses (because the flow is nearly one-dimensional with a favorable pressure gradient, except if shock waves form and nozzles are relatively short).

In this experiment, two types of nozzles are mounted on a nozzle test rig, and a pressure flow is created using a compressed air source. The nozzles are run for different back-pressure settings to analyze the internal flow in the nozzles under varying flow conditions, identify the various flow regimes, and compare the data to theoretical predictions.

Procedure

In this demonstration, a nozzle test rig was used, which consisted of a compressed air source that channels high-pressure air through the nozzles being tested, as shown in Figure 5. The flow pressure ranges from 0 - 120 psi and is controlled using a mechanical valve. While the pressures are measured using an external sensor, the mass flow rates in the nozzle are measured by a pair of rotameters placed right before the exhaust of the nozzle test rig.

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Results

The following constants were used in the analysis: specific heat of dry air, γ: 1.4; reference nozzle area, A_i = 0.0491 in², and standard atmospheric pressure, P_atm = 14.1 psi. Figures 8 and 9 show the variation in pressure ratio and Mach number across the length of the nozzle (normalized based on total nozzle length) for various back-pressure settings for the converging and converging-diverging nozzles, respectively. The mass

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Application and Summary

Nozzles are commonly used in aircraft and rocket propulsion systems as they offer a simple and effective method to accelerate flow in restricted distances. In order to design nozzles to suit a given application, an understanding of the flow behavior and factors that affect said behavior for a range of flow conditions is essential for designing efficient propulsion systems. In this demonstration, the converging and converging-diverging nozzles - two of the most common nozzle types used in aerospace applications - were tes

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Tags

Nozzle Analysis Variations Mach Number Pressure Converging Nozzle Converging diverging Nozzle Flow Velocity Throat Choked Flow Subsonic Regime Back pressure Stagnation Pressure Back pressure Ratio

In this demonstration, a nozzle test rig was used, which consisted of a compressed air source that channels high-pressure air through the nozzles being tested, as shown in Figure 5. The flow pressure ranges from 0 - 120 psi and is controlled using a mechanical valve. While the pressures are measured using an external sensor, the mass flow rates in the nozzle are measured by a pair of rotameters placed right before the exhaust of the nozzle test rig.

Figure 5. Nozzle test rig. Please click here to view a larger version of this figure.

1. Measuring Axial Pressure in Converging and Converging-diverging Nozzles

Mount the converging nozzle in the center of the nozzle test rig, as shown in Figure 5. The 2-D section for the converging nozzle with labels for the pressure taps are shown in Figure 6.

Figure 6. Geometry of converging nozzle. Please click here to view a larger version of this figure.

Connect the 10 static pressure ports and the stagnation pressure port to the pressure measurement system using flexible, high-pressure PVC tubes.
Connect the pressure measurement system to the graphical software interface for real-time pressure data reading.
Take the zero/no-flow condition reading.
Open the mechanical flow control valve to start the airflow.
Rotate the valve to adjust the flow rate to obtain a back-pressure ratio (p_B/p_O) of 0.9. Note that the back-pressure for both the converging and converging-diverging nozzles correspond to the pressure data read-out from port 10.
Record the data corresponding to Table 1.
Decrease the back-pressure ratio in steps of 0.1 until p_B/p_O = 0.1 repeating step 7 for each setting. Additionally, repeat step 7 for a p_B/p_O = 0.5283 to capture flow data at the theoretical choked flow condition.
Replace the converging nozzle with the converging-diverging nozzle and repeat steps 1.2 - 1.8. The 2-D section for the converging nozzle with labels for the pressure taps are shown in Figure 7.
On completion of the tests, disconnect all systems and dismantle the nozzle test-rig.

Figure 7. Geometry of converging-diverging nozzle. Please click here to view a larger version of this figure.

Table 1. Data collected for the nozzle experiment.

Tap number	Axial Position of Tap (in)	Nozzle Area Ratio (A/A_i)	P_static (psi)	P_o (psi)	Mass Flow Rate (slugs/s)	P_atm (psi)	T_o (°F)
Figure 6/7	Table 2	Table 2	Gauge pressure	Gauge pressure	Rotameter	Gauge pressure	Temperature sensor

Table 2. Nozzle geometry data.

Tap number	Converging Nozzle		Converging-Diverging Nozzle
Tap number	Axial Position of Tap (in)	Nozzle Area Ratio (A/A_i)	Axial Position of Tap (in)	Nozzle Area Ratio (A/A_i)
1	0	60.14	0	60.14
2	1	51.379	4.5	6.093
3	2	35.914	6.5	1
4	3	23.218	6.9075	1.053
5	4	13.275	7.3795	1.222
6	5	6.094	7.8515	1.403
7	5.5	3.54	8.3235	1.595
8	6	1.672	8.7955	1.802
9	6.5	1	9.2675	2.02
10	7	60.041	9.5	60.041

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Concepts

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Measuring Axial Pressure in Converging and Converging-Diverging Nozzles

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Results

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