MEASUREMENTS IN FLUID MECHANICS

LABORATORY SESSION Nr.9.:

Measuring the characteristics of the diffuser

Location of measurement: Department of Fluid Mechanics, Laboratory

1. The aim of measurement:

The efficiencies () of diffusers with circular cross section are to be defined. The efficiency has to be measured and illustrated as a function of the angle of the diffuser () and the flow rate (qv). Three different angles (6°, 15°, 30°) and a Borda-Carnot element can be built into the measuring device. The flow rate of the diffuser is adjustable.

2. Description of the measuring device

The sketch of the measuring device can be seen in Figure 1. We calibrate the inletorifice plate (5) by the help of a built in standardized orifice plate (6) by the use of the upper, so-called calibration line (7). After the calibration of the inlet orifice plate (5) it has to be built in the lower measurement section and the actual measuring can begin.

Figure 1. Calibration Device

Figure 2. Measuring device to determine efficiency

INLET ORIFICE PLATE CALIBRATION

The air is delivered into the device via a radial ventilator built into the table (1) which is connected to the calibration tube(7). By the use of the calibration line (6), we can determine the flow number of the inlet orifice plate, by measuring the pressure difference on the standard built-in orifice plate and the inlet orifice plate simultaneously. Volume flow rate can be calculated based on the standard orifice plate, then it can be substituted into the equation describing the inlet orifice plate, where the only unknown variable will be the flow number. A calibration diagram can be constructed if the corresponding pressure differences are recorded and displayed in a diagram.

DIFFUSER EFFICIENCY MEASUREMENT

The suction tube of the ventilator and the inlet orifice plate has to be connected to the measurement section (3). We attach the diffusers to be measured (4) between the measurement section and the inlet orifice plate. The flow rate can be calculated based on the pressure differences, with the help of the calibration diagram recorded previously.

The efficiency of the diffuser can be calculated from the increase of pressure measured on the pressure taps before and after the diffuser with an inclined micromanometer. There are more pressure taps on the measurement section after the diffuser to evade pressure measurement in the separated flow.

3. The theory of the measuring

The variables in the next theoretical definitions are always average variables applied to pressures and velocities in whole cross sections. Cross section ‘1’ is the diffuser entry cross section while cross section ‘2’ is the diffuser exit cross section (the cross section to the measurement section).

What does it mean, and how do we define that a diffuser is good?

We use a diffuser if we want to establish a cross section expansion between two sections with two different cross sections, that is an A1/A2 cross-section expansion. The expansion should be established with the lowest possible loss of total pressure. The diameter expansion could be achieved with sudden increase in diameter (a Borda-Carnot element) with greater separation loss, or the other extreme, a high wall friction, infinite, expanding tube. With regard to the given flow, the best possible solution seems between the two, a diffuser with the lowest loss (an optimal opening angle, best efficiency) see table 1 below.

DIAMTER EXPANSION SOLUTION / Diffuser opening angle / REASON FOR PRESSURE LOSS IN THE SYSTEM / RATE OF EFFICIENCY
separation / Wall friction
Borda–Carnot component
(sudden increase in diameter) / 180 / BIG / - / BAD
Diffuser /  / LITTLE / LITTLE / MAXIMUM
Infinite expanding tube section / ~ 0 / - / BIG / BAD

Table 1.

For the characteristics of a diffuser in numbers, we define the rate of efficiency of a diffuser:

,

that relates the actual increase in pressure to the ideal increase in pressure , where there is no loss and which can be calculated with a simple Bernoulli equation:

,

The diffuser efficiency grade is the ratio of the actual (measured) and the ideal pressure increase.

The other characteristic, which is used to characterize components (valves, angles, etc) is the loss factor, which can be determined in case of a diffuser with following quotation:

.

The pressure loss in the diffuser is by the entrance dynamic pressure. Of course, between the efficiency and the loss factor is a close relationship, which is following: (on the right side of the equation using the continuity.)

4. The process of measuring

Calibration of the inlet orifice plate

The equation of the flow rate to the inlet orifice plate is following:

where

flow number

dbinner diameter of inlet orifice plate

1density of air

pbpressure drop measured on the inlet orifice plate

The flow number of the inlet orifice plate can be determined with a calibration tube (figure 1). The calibration tube contains a standardizedorifice plate, on which we can measure the flow rate with the standard method. During calibration we have to measure the pressure drop of the standard orifice plate and the inlet orifice plate at different flow rates. The flow rate can be deduced from the pressure drop of the standard orifice plate, which compared to the pressure drop of the inlet orifice plate determines the flow rate in the equation. (In lack of time flow factor of the inlet orifice plate can be changed to 1, so the pressure drop on the component will be nearly identical with the local dynamic pressure.)

The formula to calculate the flow rate of the standard orifice plate:

where

CFlow component

Measure brim relation to diameter (here =0,6587)

Compressibility factor (=1, since change in the pressure of the medium is low)

dHole diameter of measure brim (here d=38.8mm)

pPressure drop on measure brim

Formula to calculate flow component C:

where

ReDthe Reynolds number calculated with the diameter before the measure brim (here D=58,9mm)

Since the Reynolds number is dependent of the velocity, and velocity is dependent of the flow component, which is again dependent of the Reynolds number, it is advisable to use iteration to do the task. The flow number in the first iteration cycle shall be C=0,6. We shall determine flow rate at the given flow number, the velocity before the standard orifice plate, the Reynolds number, and finally we shall determine the flow number. From here the cycle starts all over again, we calculate flow rate with the new flow number, the velocity, etc. The results converge swiftly and after 2 or 3 iteration cycles we get the actual results (we can consider the solution final, if the relative difference of substituted C and the calculated C value is below 5%).

Pressure drop and velocity
andvelocities can be calculated with the volumetric air flow measured with the help of the inlet orifice plate:

,

We have to measure the pressure drops between the pressure tap before the diffusor (p1) and the pressure taps of the so called measuring section (p2). From the pressure drop and the velocity we can calculate the efficiency ().

5. Checking and comparing the results with data from the literature:

The geometrical data of the diffusers have to be recorded during the measurement. The measured velocities and pressure values have to be shown in diagrams. After the measurements the efficiency () has to be determined.

You can find the requirements of the report at the homepage of the Department of Fluid Mechanics.

Keep in mind while measuring

  • While evaluation we have to determine measuring mistakes resulting from imprecise measurement. These affect the results.
  • Before turning on the measuring device and while operating it, we must make sure that all conditions of safe operation are fulfilled. Nearby colleagues should be warned before turning on the device or if there are modifications in function.
  • The temperature and atmospheric pressure needs to be recorded in every case.
  • Recording the figures and units on the measuring devices as well as factors that affect them.
  • Record the type and the serial number of measuring devices, and the density of fluid used in them.
  • Compare the units of the measured data and the data used in calculations.
  • U-tube manometers can only be used if they are leveled properly.
  • When connecting the manometer, we must be precautious with selecting the measurement limits and the + and – ends of the terminals. We must be careful with all manometers – especially with the inclined manometer, to attach the rubber tube extremely carefully to the manometer, constantly checking the measurement fluid for changes or unusual activity. If the level of measurement fluid approaches the maximum deflection before the tubes are secured, the measurement limit has to be reset. If this does not help either, another device has to be used that is suitable for measurements with higher pressure. If we ignore the problem, fluid might flow into the connecting tube adulterating the results or making the entire measuring impossible.
  • The pressure transmitting rubber or silicone tubes have to be checked before and while working with them, because if these tubes should rip, all results will be lost. Checking can be made by surveying or pressure testing. Critical points are the places where the tubes are connected to the instruments.