Week 3 - Pitot tube
Aim:
- To understand how Pitot-Static Tube works.
- Simulate the case on Ansys Fluent and match the velocity.
Take Away:
By the end of the article one would be able to,
- Know the physics behinde the pitot-static tube.
- Simulate, plot the resultsand contours and draw some conclusion.
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History:
- A pitot tube (pitot probe) measures fluid flow velocity.
- It was invented by a French engineer, Henri Pitot, in the early 18th century, and was modified to its modern form in the mid-19th century by a French scientist, Henry Darcy.
- It is widely used to determine the airspeed of aircraft; the water speed of boats; and the flow velocity of liquids, air, and gases in industry.
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Operation:
- The basic pitot tube consists of a tube pointing directly into the fluid flow.
- As this tube contains fluid, a pressure can be measured; the moving fluid is brought to rest (stagnates) as there is no outlet to allow flow to continue.
- This pressure is the stagnation pressure of the fluid, also known as the total pressure or (particularly in aviation) the pitot pressure.
- There are different designs of Pitot Tube. They are shown below:
- Bernoulli's Equation States thats,
Stagnation Pressure = Static Pressure + Dynamic Pressure
Which can be written as,
`p_t = p_s + ((rhou^2)/2)`
Rearranging the terms, velocity can be expressed as,
`u=sqrt((2(p_t-p_s))/(rho))`
u = velocity of the fluid
`p_t` = Stagnation Pressure or Total Pressure
`p_s` = Static Pressure
`rho` = Density of the fluid
- The above equation is applicable to incompressible flows
- Liquids are considered to be incompressible and gases under certain conditions.
- Dynamic Pressure is the difference between the Stagnation Pressure and Static Pressure.
Reference: Link
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Working of Pitot-Static Tube:
- Pitot-Static tubes, which are also called Prandtl tubes, are used on aircraft as speedometers.
- The actual tube on the aircraft is around 10 inches (25 centimeters) long with a 1/2 inch (1 centimeter) diameter.
- Several small holes are drilled around the outside of the tube and a center hole is drilled down the axis of the tube.
- The outside holes are connected to one side of a device called a pressure transducer.
- The center hole in the tube is kept separate from the outside holes and is connected to the other side of the transducer. The transducer measures the difference in pressure in the two groups of tubes by measuring the strain in a thin element using an electronic strain gauge.
- The pitot-static tube is mounted on the aircraft, or in a wind tunnel , so that the center tube is always pointed in the direction of the flow and the outside holes are perpendicular to the center tube.
- On some airplanes the pitot-static tube is put on a longer boom sticking out of the nose of the plane or the wing.
Limitations:
- If the velocity is low, the difference in pressures is very small and hard to accurately measure with the transducer. Errors in the instrument could be greater than the measurement! So pitot-static tubes don’t work very well for very low velocities.
- If the velocity is very high (supersonic), we’ve violated the assumptions of Bernoulli’s equation and the measurement is wrong again. At the front of the tube, a shock wave appears that will change the total pressure. There are corrections for the shock wave that can be applied to allow us to use pitot-static tubes for high speed aircraft.
- If the tubes become clogged or pinched, the resulting pressures at the transducer are not the total and static pressures of the external flow. The transducer output is then used to calculate a velocity that is not the actual velocity of the flow. Several years ago, there were reports of icing problems occurring on airliner pitot-static probes. Output from the probes was used as part of the auto-pilot and flight control system. The solution to the icing problem was to install heaters on the probes to insure that the probe was not clogged by ice build-up.
Reference: Link
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Cases Discussed:
|
Velocity(m/s) |
Gauge Pressure (Pa) |
|
240 |
-2817 |
|
100 |
33287 |
|
62 |
65780 |
Simulation Procedure:
Directly import the file provided.
- Blue and red represent the inlet and outlet respectively.
- The L shaped pipe is the Pitot-Static tube.
- And the plane in grey is the XY-Cut Plane for better contour visualization.
- Select Laminar flow under Viscous tab.
- Choose fluid as air and must have following property:
- Up until this point everything is same for all the cases.
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Boundary Condition:
- Velocity Inlet:
- Pressure outlet:
- Run the solution for 1000 iterations.
- For all the other cases the vlaue of velocity and pressure is changing and rest is same.
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Results:
Case 1:
Velocity = 240 m/s and Outlet Pressure = -2817 Pa
- Residual:
- Static Pressure Contour:
- Total Pressure Contour:
- Static Pressure Plot:
- Total Pressure Plot:
- Validating the Velocity:
`u= sqrt((2(p_t-p_s))/(rho))`
Substituting the values,
`u=sqrt((2(33446.176-(-2403.2217)))/(1.225))`
`u` = 241.9289 m/s
Given velocity = 240 m/s
Error % = 0.8307 %
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Case 2:
Velocity = 100 m/s and Outlet Pressure = 33287 Pa
- Residual:
- Static Pressure Contour:
- Total Pressure Contour:
- Static Pressure Plot:
- Total Pressure Plot:
- Validating the Velocity:
`u= sqrt((2(p_t-p_s))/(rho))`
Substituting the values,
`u=sqrt((2(39575.438-33393.578))/(1.225))`
`u` = 100.4630 m/s
Given velocity = 100 m/s
Error % = 0.4630 %
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Case 3:
Velocity = 62 m/s and Outlet Pressure = 65780 Pa
- Residual:
- Static Pressure Plot:
- Total Pressure Plot:
- Validating the Velocity:
`u= sqrt((2(p_t-p_s))/(rho))`
Substituting the values,
`u=sqrt((2(68193.297-65844.828))/(1.225))`
`u` = 61.9212 m/s
Given velocity = 62 m/s
Error % = 0.1270 %
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Conclusion:
| CASES |
TOTAL PRESSURE (Pa) (CFD) |
STATIC PRESSURE (Pa) (CFD) | CALCULATED VELOCITY (m/s) | GIVEN VELOCITY (m/s) | PERCENTAGE ERROR (%) |
| CASE 1 | 33446.176 | -2403.2217 | 241.9289 | 240 | 0.8307 |
| CASE 2 | 39575.438 | 33393.578 | 100.4630 | 100 | 0.4630 |
| CASE 3 | 68193.297 | 65844.828 | 61.9212 | 62 | 0.1270 |