Propulsão e Impulso
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概述
Source: Alexander S Rattner; Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA
Aircraft, rockets, and ships produce propulsion by accelerating surrounding fluid or high temperature combustion products to high velocity. Because of the principle of conservation of momentum, the increased fluid velocity results in an effective thrust force on the vehicle. The thrust capabilities of propulsion systems are often measured with static thrust tests. In these tests, propulsion systems are mounted and operated on fixed, instrumented platforms, and the holding force on the mounts is measured as the thrust
In this experiment, a small-scale static thrust measurement facility will be constructed and modeled. The thrust curves for two model aircraft motors and propeller systems and a computer cooling fan will be measured. Thrust efficiencies will also be evaluated (thrust force / electrical power input). Measured thrust values will be compared with theoretical predictions based on measured air velocities.
Principles
Open-operation fluid propulsion mechanisms, such as boat props, airplane propellers, or fanjet aircraft engines produce thrust by accelerating ambient fluid to a high velocity. During operation, such devices draw in intake fluid from a large upstream area, and exhaust it downstream as a narrow high velocity jet (Fig. 1). The exhaust area is approximately equal to the propeller face air. Mass and momentum flow rate balances over the control volume including the upstream intake and exhaust jet yield the following results:
(1)
(2)
Here, 
is the mass flow rate, ρ is the fluid density, A is the flow area, U is the fluid velocity, and T is the resulting thrust force. As shown in Fig. 1, the intake area is much greater that the exhaust jet area and the inlet and outlet densities are approximately equal. As such, the exhaust velocity must be much greater than the inlet velocity (
, and the inlet momentum flow rate is negligible (
). The theoretical resulting thrust is:
(3)
The thrust from model aircraft propulsion systems is relatively small, less than 0.1 N in many cases. To enable measurement of these forces, a lever-arm based test stand will be constructed here (Fig. 2a). The test stand structure pivots on a low-friction bearing such that the torque from the propeller at the end of one arm (length Lprop from bearing axis to center of motor) balances the torque from a digital scale depressed by a shorter moment arm (Lscale). This configuration amplifies the thrust force on the scale to yield more accurate readings. If the scale is tared (zeroed) when the propeller is turned off, than the measured thrust during propeller operation can be determined with Eqn. 4. Here, m is the mass reading on the scale.
(4)
The electrical power supplied to the propeller or fan can be determined as 
, where I is the current (in amps) and V is the voltage. A thrust efficiency can be defined as 
(in Newtons per Watt).
Figure 1: Control volume for flow through a fluid propulsion device
Figure 2: a. Schematic of static thrust test facility. b. Detail view of pivot assembly. c. Photograph of experimental facility.
Procedure
1. Fabrication of static thrust test system (see schematics and photograph, Fig. 2)
- Form two cylindrical bushings on a lathe with outer diameter 42.16 mm, length ~10 mm, and bore through the center axis of 9.50 mm.
- Press one flanged ball bearing into the bore on each bushing. Insert the bushings flush into the two parallel ports of the 4-way tee fitting, with the bearings on the outside. The bushings should fit snugly in the tee fitting. (See the pivot assembly schematic in Fig. 2b.
- Cut two 100 mm long lengths of the aluminum right-angle extrusion. Drill a 3.2 mm hole in the middle of the longer side of the extrusions, ~45 mm up from the base. Drill two mounting holes near the ends of the shorter sides of the extrusion.
- Insert the shaft through the two bearings in the 4-way tee fitting. Even lengths should be exposed on each end. Slide the right-angle extrusions onto the exposed shaft ends. Screw the right angle extrusion to the work surface through the mounting holes. Install the shaft collars on the exposed ends of the shaft to keep the assembly centered between the right-angle brackets.
- Cut short (~18 mm) and long (~36 cm) lengths of 42.16 mm outer diameter PVC pipes. Insert the short length into the horizontal port on the 4-way tee fitting, and the long length into the vertical port. Insert a pipe cap on the end of the horizontal length.
- Position a precision digital scale (±0.1 or ±0.01 g recommended) under the horizontal pipe arm cap.
- Mount the propeller motors and fan on pipe caps. The propellers should be offset so that the caps do not block the airflow. It is recommended that the propeller motors are glued to the heads of thin screws installed on pipe caps (Fig. 2c).
2. Performing experiments
- Mount the smallest propeller and motor pipe cap onto the vertical pipe arm.
- Record the distances (moment arms) from the pivot axis to the propeller motor axis (Lprop) and from the pivot axis to the contact point of the horizontal arm on the scale.
- Connect the propeller motor to a variable voltage DC power supply (turned off).
- Turn on the scale, and tare (zero) the reading.
- Turn on the power supply and vary the voltage in ~0.4 V increments up to 3.8 V. For each case, record the voltage, supplied current, scale reading (in grams), and scale range during steady operation (typically oscillates by ~0.3 – 5.0 g). It may be necessary to tap the propeller blade to start it spinning. Ensure that the airflow is in the right direction (flowing toward the rear of the motor). If not, reverse the positive and negative leads on the power supply.
- If available, use a thermal anemometer to measure the air velocity just behind (downstream) the propeller at a few conditions. The velocity varies over the propeller face area, so this is only an order-of-magnitude measurement.
- Repeat Steps 2.1 – 2.6 for the other motor and propeller and the PC cooling fan. The fan can operate up to 12 V.
3. Analysis
- Using Eqn. 4, calculate the propeller and fan thrusts (T) for each measured case. The major source of uncertainty is the variation/oscillation in the scale reading during operation. Substitute this range (Step 2.5) for m in Eqn. 4 to determine the thrust uncertainty.
- For each case, compute the input power . The uncertainty can be estimated as
, where ΔI and ΔV are the current and voltage measurement uncertainties (0.005 A and 0.005 V here). - For each case compute the thrust efficiency
. The uncertainty for thrust efficiency would be 
. - Compare the measured thrusts with estimated theoretical values using the anemometer velocities (Eqn. 3). Here the outlet area can be estimated as the propeller/fan face area, less the hub or motor area:
. How do these compare with measured values?
Fluid propulsion systems are ubiquitous in mechanical design and are utilized anytime a relative force needs to be applied between a mechanical system and a fluid. All air and water craft employ fluid propulsion systems to provide propulsion forces or thrusts needed for acceleration and steering through the surrounding fluid. Their use is not limited to vehicles though. Stationary systems such as HVAC equipment also use propulsion systems. But in these cases they drive circulation of the fluid itself. This video will illustrate how thrust is produced by open operation fluid propulsion systems, a category that includes propellers and fans. And demonstrate how thrust and thrust efficiency can be estimated and measured in the laboratory.
The thrust from open operation fluid propulsion systems, such as airplane propellers or boat props, is produced by accelerating ambient fluid to a high velocity. These systems draw in fluid from a large upstream area and exhaust it downstream in a narrow jet. With an out flow area approximately the same as the area of the propeller face. Let’s see how thrust is generated by taking a control volume approach. Begin by constructing a control volume along the stream lines around the propeller, extending from the intake area to the out flow area. The mass flow rate into the control volume at the intake is the product of the upstream fluid density, the intake area, and the upstream fluid velocity. Similarly, the mass flow rate out of the control volume at the exhaust is the product of the downstream fluid density, the outflow area, and the downstream fluid velocity. No mass flow will occur across the streamline boundary by definition. During steady operation the mass inside the control volume must remain constant. Then, by conservation of mass, the rate of mass exiting through the outflow area must equal the rate of mass entering through the intake area. Now because the intake and outflow densities are approximately equal, the outflow velocity will be equal to the intake velocity scaled by the ratio of intake to outflow area. Since the intake area is much larger than the outflow area, the outflow velocity will be much higher than the intake velocity. In a similar fashion, conservation of momentum requires that any difference in the momentum flow rates out of and into the control volume manifests as a force on the propeller, the thrust. Since the mass flow rates in and out are balanced and the outflow velocity is much higher than the intake velocity, the contribution from the intake velocity term is negligible. Expanding the mass flow rate term in this result shows that the thrust is well approximated by the outflow area and velocity. In any propulsion system power is supplied by an external source to generate the thrust. The thrust efficiency of the system, denoted here by the Greek letter eta, is defined as the ratio of the thrust generated to the input power. For example, model aircraft propellers and PC fans are driven by an electric motor. If the thrust is known, dividing it by the electrical input power will yield the thrust efficiency. In the following sections we will measure the thrust and thrust efficiency of some small propulsion systems using a static test stand. And then compare the measured thrust to an estimate based on the outflow velocity.
Assemble the test stand as described in the text, and set it up on the work bench. The stand has a rigid “L” section supported by a pivot at the joint. Position the precision scale under the end of the short horizontal arm. Torque from the digital scale on the short arm will balance any torque generated by thrust on the long arm. And the difference in lengths amplifies the force measured by the scale to yield more accurate readings. With the test stand assembled, mount the smallest propeller on to the long vertical arm and align the propeller axis so that it is parallel with the short arm. Measure and record the prop diameter and the hub diameter. Now measure and record the lengths of both moment arms. The long arm should be measured from the pivot axis to the propeller axis. And the short arm should be measured from the pivot axis to the contact point on the scale. Connect the motor to a variable DC power supply and turn it on to check the direction of airflow, which should be directed so that there is a downward force on the scale. Turn off the supply, and if necessary correct the airflow direction by reversing the electrical connection. When the motor is completely still tare the scale. Turn on the supply and increase the voltage from zero volts, in point four volts increments, up to but not exceeding the motors maximum supply voltage. For each step in voltage wait for the motor to stabilize and then record the voltage, current, average scale reading, and the scale range. If a thermal anemometer is available, measure the outflow air velocity for a low input voltage and high input voltage. Note that the outflow velocity will vary with position, so this is only an order of magnitude measurement. Repeat this process for the larger motor and the PC fan. Once the measurements are complete you are ready to analyze the data.
Look at the data collected for the small propeller. For each supply voltage there is also a supply current and the scale readings. You should also have a few measurements of the outflow air velocity. Perform the following calculations for every value of supply voltage. Calculate the thrust from the scale reading. The force on the scale is the reading times the acceleration due to gravity. And the thrust is this force magnified by the ratio of the moment arms measured earlier. Now compute the input power to the motor, which is simply the product of the voltage and current. Next compute the thrust efficiency by taking the ratio of the thrust and the input power. If the outflow velocity was measured you can use it to predict the thrust. First calculate the approximate outflow area by taking the difference between the prop and hub areas. Then combine this result with the measured velocity to estimate the thrust using the thrust equation from before. Propagate your measurement uncertainties as shown in the text to determine the uncertainty in your final results. Repeat these calculations for the large propeller and fan.
Begin by plotting the thrust as a function of input power for all three devices. The PC fan produces the highest thrust of the three, and has a much higher maximum input power. The small propeller produces slightly more thrust than the large one at any given input power, but the large fan is capable at operating at higher powers. Now compare the thrust efficiency as a function of the input power. The thrust efficiency of the large propeller remains fairly constant, but the efficiency drops with increasing power for the other two devices. If you took any measurements of the outflow air velocity compare the estimated range of thrusts based on these to the thrust measured from the test stand. You should find good agreement between the prediction and measurement. But due to the approximate measurement of outflow velocity, this analysis should only be interpreted as qualitative.
Fluid propulsion systems are ubiquitous in a variety of mechanical and naturally occurring systems. Mobility is critical to many underwater creatures for survival, and a large variety of natural propulsion systems have evolved as a result. Jet propulsion from cephalopods, fins on fish, and flagella on amoeba are just a few examples. Learning how these systems work is important for understanding how these animals live and interact with their environment. Windmills and turbines work on the same principles covered in this video, but applied in reverse. Instead of using stored power to generate thrust, these systems extract momentum and energy from the air. The rotating shaft of the windmill can drive a mechanical process or else be connected to a generator to produce electricity.
You’ve just watched Jove’s introduction to propulsion and thrust. You should now understand the basic principles of generating thrust with an open operation fluid propulsion system. You have also learned how to perform small scale static thrust tests and determine the thrust efficiency. Thanks for watching.
Results
In Fig. 3a, the thrust vs. power curves are presented for the three propulsion devices evaluated in this experiment. The fan achieves the highest thrust, reaching 0.68 ± 0.02 N at 11.83 ± 0.08 W input power. The smaller propeller produces slightly more thrust per input power than the larger propeller, but reaches its maximum operating voltage at 2.66 ± 0.04 W. Fig. 3b presents the thrust efficiency for the three devices. For the small propeller and fan, the efficiency generally decreases with increasing power input. The efficiency of the larger propeller is relatively constant at η ~ 0.03 N W-1.
Theoretical thrust values based on measured outlet velocities are compared with directly measured thrust values in Table 1. For these cases, the measured velocities vary over the propeller/fan face areas, so velocity and predicted thrust ranges are reported, rather than single values. In general, reasonable agreement is found between predicted and measured values, which provides confirmation for the theory outlined in the Principles section. However, measured velocity ranges were quite wide in some cases, so this analysis should be is only qualitative.
Figure 3: (a) Thrust and (b) thrust efficiency curves for the three studied propulsion devices.
| Propulsion device (Aout) | Power Input (W) | Outlet Velocity Range (m s-1) | Predicted Thrust Range (N) | Measured Thrust (N) |
| Small Propeller (0.0016 m2) |
0.49 ± 0.02 | 3.0 – 5.0 | 0.017 – 0.048 | 0.034 ± 0.005 |
| 1.56 ± 0.03 | 4.0 – 6.2 | 0.030 – 0.073 | 0.068 ± 0.005 | |
| Large Propeller (0.0042 m2) |
0.73 ± 0.03 | 2.0 – 3.0 | 0.020 – 0.045 | 0.020 ± 0.004 |
| 2.39 ± 0.05 | 4.0 – 5.0 | 0.080 – 0.125 | 0.066 ± 0.004 | |
| PC Cooling Fan (0.0077 m2) |
2.16 ± 0.03 | 4.0 – 5.5 | 0.145 – 0.275 | 0.180 ± 0.007 |
| 9.98 ± 0.07 | 8.0 – 8.4 | 0.581 – 0.641 | 0.593 ± 0.014 |
Table 1 – Comparison of predicted thrusts based on measured outlet velocity ranges with directly measured thrusts.
Applications and Summary
This experiment introduced the basic operating principles of fluid propulsion devices found in aircraft and watercraft. A static thrust test platform was constructed to measure the propulsion capability of model aircraft propellers and a pc cooling fan. The resulting thrusts and propulsion efficiencies (thrust per input power) were measured and compared. Theoretical thrust values were also estimated based on downstream jet velocities. Measurement and rating of propulsion system performance, as demonstrated here at small scales, is a key stage in fluid propulsion system development, and is critical to ensuring engines deliver required thrust levels.
Fluid propulsion systems are employed in nearly all aircraft and watercraft. In the configuration considered here, upstream ambient fluid is accelerated to a high velocity downstream jet, also at ambient pressure. In devices such as HVAC air handlers, air compressors, or steam power plant liquid pumps, a significant portion of input work is supplied to pressurize fluid rather than just to increase flow velocity. However, the same general principles of analysis can be applied, based on control volume mass and momentum flow balances. Devices such as wind turbines and steam turbines also operate on similar principles, but extract momentum and energy from fluid flow to produce mechanical and electrical power.
成績單
Fluid propulsion systems are ubiquitous in mechanical design and are utilized anytime a relative force needs to be applied between a mechanical system and a fluid. All air and water craft employ fluid propulsion systems to provide propulsion forces or thrusts needed for acceleration and steering through the surrounding fluid. Their use is not limited to vehicles though. Stationary systems such as HVAC equipment also use propulsion systems. But in these cases they drive circulation of the fluid itself. This video will illustrate how thrust is produced by open operation fluid propulsion systems, a category that includes propellers and fans. And demonstrate how thrust and thrust efficiency can be estimated and measured in the laboratory.
The thrust from open operation fluid propulsion systems, such as airplane propellers or boat props, is produced by accelerating ambient fluid to a high velocity. These systems draw in fluid from a large upstream area and exhaust it downstream in a narrow jet. With an out flow area approximately the same as the area of the propeller face. Let’s see how thrust is generated by taking a control volume approach. Begin by constructing a control volume along the stream lines around the propeller, extending from the intake area to the out flow area. The mass flow rate into the control volume at the intake is the product of the upstream fluid density, the intake area, and the upstream fluid velocity. Similarly, the mass flow rate out of the control volume at the exhaust is the product of the downstream fluid density, the outflow area, and the downstream fluid velocity. No mass flow will occur across the streamline boundary by definition. During steady operation the mass inside the control volume must remain constant. Then, by conservation of mass, the rate of mass exiting through the outflow area must equal the rate of mass entering through the intake area. Now because the intake and outflow densities are approximately equal, the outflow velocity will be equal to the intake velocity scaled by the ratio of intake to outflow area. Since the intake area is much larger than the outflow area, the outflow velocity will be much higher than the intake velocity. In a similar fashion, conservation of momentum requires that any difference in the momentum flow rates out of and into the control volume manifests as a force on the propeller, the thrust. Since the mass flow rates in and out are balanced and the outflow velocity is much higher than the intake velocity, the contribution from the intake velocity term is negligible. Expanding the mass flow rate term in this result shows that the thrust is well approximated by the outflow area and velocity. In any propulsion system power is supplied by an external source to generate the thrust. The thrust efficiency of the system, denoted here by the Greek letter eta, is defined as the ratio of the thrust generated to the input power. For example, model aircraft propellers and PC fans are driven by an electric motor. If the thrust is known, dividing it by the electrical input power will yield the thrust efficiency. In the following sections we will measure the thrust and thrust efficiency of some small propulsion systems using a static test stand. And then compare the measured thrust to an estimate based on the outflow velocity.
Assemble the test stand as described in the text, and set it up on the work bench. The stand has a rigid “L” section supported by a pivot at the joint. Position the precision scale under the end of the short horizontal arm. Torque from the digital scale on the short arm will balance any torque generated by thrust on the long arm. And the difference in lengths amplifies the force measured by the scale to yield more accurate readings. With the test stand assembled, mount the smallest propeller on to the long vertical arm and align the propeller axis so that it is parallel with the short arm. Measure and record the prop diameter and the hub diameter. Now measure and record the lengths of both moment arms. The long arm should be measured from the pivot axis to the propeller axis. And the short arm should be measured from the pivot axis to the contact point on the scale. Connect the motor to a variable DC power supply and turn it on to check the direction of airflow, which should be directed so that there is a downward force on the scale. Turn off the supply, and if necessary correct the airflow direction by reversing the electrical connection. When the motor is completely still tare the scale. Turn on the supply and increase the voltage from zero volts, in point four volts increments, up to but not exceeding the motors maximum supply voltage. For each step in voltage wait for the motor to stabilize and then record the voltage, current, average scale reading, and the scale range. If a thermal anemometer is available, measure the outflow air velocity for a low input voltage and high input voltage. Note that the outflow velocity will vary with position, so this is only an order of magnitude measurement. Repeat this process for the larger motor and the PC fan. Once the measurements are complete you are ready to analyze the data.
Look at the data collected for the small propeller. For each supply voltage there is also a supply current and the scale readings. You should also have a few measurements of the outflow air velocity. Perform the following calculations for every value of supply voltage. Calculate the thrust from the scale reading. The force on the scale is the reading times the acceleration due to gravity. And the thrust is this force magnified by the ratio of the moment arms measured earlier. Now compute the input power to the motor, which is simply the product of the voltage and current. Next compute the thrust efficiency by taking the ratio of the thrust and the input power. If the outflow velocity was measured you can use it to predict the thrust. First calculate the approximate outflow area by taking the difference between the prop and hub areas. Then combine this result with the measured velocity to estimate the thrust using the thrust equation from before. Propagate your measurement uncertainties as shown in the text to determine the uncertainty in your final results. Repeat these calculations for the large propeller and fan.
Begin by plotting the thrust as a function of input power for all three devices. The PC fan produces the highest thrust of the three, and has a much higher maximum input power. The small propeller produces slightly more thrust than the large one at any given input power, but the large fan is capable at operating at higher powers. Now compare the thrust efficiency as a function of the input power. The thrust efficiency of the large propeller remains fairly constant, but the efficiency drops with increasing power for the other two devices. If you took any measurements of the outflow air velocity compare the estimated range of thrusts based on these to the thrust measured from the test stand. You should find good agreement between the prediction and measurement. But due to the approximate measurement of outflow velocity, this analysis should only be interpreted as qualitative.
Fluid propulsion systems are ubiquitous in a variety of mechanical and naturally occurring systems. Mobility is critical to many underwater creatures for survival, and a large variety of natural propulsion systems have evolved as a result. Jet propulsion from cephalopods, fins on fish, and flagella on amoeba are just a few examples. Learning how these systems work is important for understanding how these animals live and interact with their environment. Windmills and turbines work on the same principles covered in this video, but applied in reverse. Instead of using stored power to generate thrust, these systems extract momentum and energy from the air. The rotating shaft of the windmill can drive a mechanical process or else be connected to a generator to produce electricity.
You’ve just watched Jove’s introduction to propulsion and thrust. You should now understand the basic principles of generating thrust with an open operation fluid propulsion system. You have also learned how to perform small scale static thrust tests and determine the thrust efficiency. Thanks for watching.