Pressure Testing

Basic Principles

Pressure testing generally relies on one simple value, the pressure coefficient. The pressure coefficient is a ratio of the pressure measurements taken along the test article to the freestream dynamic pressure. For low speed, non-compressible flows, the pressure coefficient cannot physically exceed 1, however depending on the accuracy of the experimental setup, small variances may be observed. The reason for this is that the stagnation point measured at the test article can only be as high as that measured by the pitot tube, as tunnel speed and static pressure are the same (provided the pitot is not placed in the boundary layer of the tunnel or in disturbed flow). There are three pieces of equipment which are required for pressure testing.

  1. A pitot-static tube

  2. A pressure tapped test article

  3. A multitube manometer or digital pressure scanner

Pitot-Static Tube

The diagram to the left shows a cross-sectional view along the centreline of a pitot-static tube. A pitot-static tube is able to measure the total (or stagnation) pressure as well as the static pressure. The orifice shown in blue measures the pressure as the fluid is brought to rest, while a series of ports around downstream of the tip are connected to the red chamber, which measures the static pressure. The tip of the pitot tube should be oriented such that the tip is perfectly co-linear with the flow and the static ports around the pitot are perpendicular to the freestream. Two pressure lines come from the static and total ports as indicated in the diagram, which are connected to a multitube manometer or a digital pressure scanner. Note that the pitot-static tube does not directly measure the dynamic pressure or the wind tunnel velocity!

Pressure Tapped Test Article

Deciding on the pressure tap layout of a test article is critical and is driven by multiple factors. Some considerations include:

  1. Model scale

    • The model scale will determine how many taps can physically fit inside the model. Remember, all taps and tubing need to be contained within the model to avoid flow interference.

    • Care needs to be taken when using CAD software to analyse space requirements as it often appears as if there is more space than in a real world environment.

    • Assuming a setup where all taps fit, do not forget to check how the taps and tubing will be installed. If the taps are placed in the middle of a closed piece, how will you access them? Is there a risk of tubes becoming squashed?

  2. Equipment

    • The upper limit of taps is not only determined by the available space in the model, but also by the equipment taking the pressure measurements. If the manometer/pressure scanner has 64 ports, the number of taps should not exceed this. Also, do not forget the two taps for the pitot-static pressures in this calculation!

    • If, for example, the model has 128 taps, it is theoretically possible to run the experiment in two runs (first half and second half of taps), but the risk is that the data is not consistent. For example, small errors in the AoA controller may result in run 1 for top surface taps at 5.1 degrees AoA and the second run for bottom taps at 4.9 degrees AoA.

    • Depending on the tapping method (using brass tube, flexible tube, or both), your tap diameter will be determined by standard sizes. In addition, the interface of the pressure measurement device will determine if you need adapters. For example, if you have tube lines with 0.8mm internal diameter and your pressure scanner has nipples of 0.8mm, then no adapters are necessary. If the tubing is 0.5mm diameter, some conversion pieces are required. Note that conversion pieces may cause problems with leaks or degraded response times.

  3. Sufficient coverage

    • The main goal is generally to place taps in locations where the entire pressure distribution can be accurately represented. It is key that the taps are placed in higher concentrations at regions of interest or large pressure gradients.

    • Ideally the number of taps should be minimised, while capturing the entire pressure field.

    • Some tricks can be applied, for example if you know your aerofoil shape you can use something like x-foil or cfd for predictions of pressure distributions​. Do not forget to compromise between all AoAs!

Measurement Equipment

Deciding on what measurement equipment to use for the experiment is also an important step. AMME has access to both multitube manometers and Scanivalve miniature pressure scanners. Static data can easily be taken using a multitube manometer, while dynamic or unsteady data is best recorded using the Scanivalve. This is because measurements using a manometer are taken visually, with no easy way to document the data fluctuations. The Scanivalves, used in conjunction with the Matlab software, are able to write time history datafiles at frequencies up to 800Hz and for a user defined sample time. Where available, the Scanivalve is the preferred device for experiments for ease of use compared to manual data input from the manometers.

Running Tests and Processing Data

The testing technique is the same as other tests described on this website. The test article is subjected to the conditions of interest, i.e. various AoA, and data is recorded.

Data generally takes the form of a table, with numbers assigned to each pressure tap, their x/y/z co-ordinates and with a corresponding pressure value. An example of results for the first 20 taps from a 2D aerofoil test are presented below.

The first step in post-processing the results is to determine the values of pressure coefficient. As has been already mentioned, the pressure coefficient is simply a ratio of dynamic pressures from the test article and the freestream. Pressure coefficients are used to allow meaningful comparison between tests of different scales and flow conditions. Note that this is said with caution as ideally any comparisons in the low speed regime will be for tests conducted at identical Reynolds and Mach numbers. However, with the assumption of incompressibility below Mach 0.3, freestream speed can be somewhat neglected if both tests are conducted below this condition as Reynolds number is dominant.

Dynamic Pressure, Velocity and Pressure Coefficient Calculations

Dynamic pressure calculations can easily be completed using the pressure data from the Scanivalve.

Dynamic Pressure =Total Pressure - Static Pressure

Using manometer heights, an extra step is required converting the dynamic pressure as a column height to a value in Pascals.

Dynamic Height = Height (Total) - Height (Static)

Dynamic Pressure = Dynamic Height x Gravitational Acceleration x Density (Manometer Fluid) x sin(Manometer Inclination Angle)

If using dynamic pressure for velocity calculations, the following relationship can be used.

Dynamic Pressure = 0.5 x Air Density x Velocity^2

Where dynamic pressure is known and air density is calculated based on atmospheric temperature and pressure (note SI units, where R = 287.05 Kg.K).

Air Density = Air Pressure/(287.05 x Temperature)

Pressure coefficients for each tap can be calculated using the following relationships.

Pressure Coefficient = Dynamic Pressure (Tap)/Dynamic Pressure (Freestream) = Dynamic Height (Tap)/Dynamic Height (Freestream)

Pressure Coefficient and Distributions

Sample pressure coefficient data from a 2D NACA0012 aerofoil is presented below. 2D pressure distribution data is typically presented for a non-dimensional chord length (x/c), where x is the fraction the chord length, c. The y-axis is also flipped to correlate the pressure on the top and bottom surfaces easily.

From the plots, some easy observations can be made.

  1. As angle of attack increases, the magnitude of the low pressure on the top surface increases rapidly.

  2. The highest suction pressure is always within the first quarter of the wing, as this is the region of highest local flow acceleration.

  3. The stagnation point, where the pressure coefficient is equal to one, shifts rearwards with angle of attack.

  4. The wing is completely stalled at 20 degrees AoA.

Pressure data is typically used to understand and identify important flow characteristics such as separated regions, vortices or areas of local accelerations.

Calculations for Lift, Drag and Pitching Moment

Given that we have the entire pressure distribution around the aerofoil, it is quite simple to calculate the lift, drag and pitching moment coefficients. Each tap represents a panel of a certain length, s, with some inclination angle based on the tap location and geometry of the aerofoil. The pressure is assumed to act normal to the panel, so the X and Y components of pressure can be found easily using trigonometry.

Pressure (Y Component) = Pressure (Wall Normal) x cos(Panel Inclination Angle)

Pressure (X Component) = Pressure (Wall Normal) x sin(Panel Inclination Angle)

From basic mechanics, we know that:

Force = Pressure x Area

Therefore the X and Y forces acting on a panel are the respective pressure components multiplied by the panel area. The total X and Y forces are calculated by summing each individual panel force.

The pitching moment is then found by picking a reference point (typically the quarter chord) and considering the distance between each tap and the reference point to observe the following relationship:

Moment = Y Force x Distance (along X-axis) + X Force x Distance (along Y-axis)

A single tap example is shown below.

It is important to note that these forces are calculated in the body axis, i.e. a coordinate system which remains locked to the aerofoil. Lift and drag however, are perpendicular and parallel to the airstream, meaning that the X and Y forces are only equal to lift and drag when the aerofoil is at 0 degrees AoA. To correct this, the lift and drag can then be found using:

Lift Force = Normal Force x cos(AoA) - Axial Force x sin(AoA)

Drag Force = Normal Force x sin(AoA) + Axial Force x cos(AoA)

This process is best done with spreadsheets or code using a program such as Matlab. This is because for configurations with a large amount of taps becomes time consuming and prone to calculation errors.

An alternative to calculating individual panel forces is using a numerical integration of the pressure distribution to provide an estimate. For normal forces, the pressure distribution is plotted perpendicular to the chord, with the result of the integration showing the normal force. Note that this assumes that the pressure acts perpendicular to the chord line and that at small AoA the normal force is approximately equal to lift. This process can also be done for estimating the force along the chordline. Numerical integrations can be easily done using the trapezoidal rule (or some equivalent). Matlab has an inbuilt function "trapz" which performs this without any need to write your own functions.