A diffuser with an angle of 4 degrees and 10 degrees with gas inlet will be used in this experiment. The diffusers will have the same geometry as the diffusers mentioned in Chapter 3.5, with the exception of several adjustments:
Figure 3.28: Cross-sectional view of the 10 degree diffuser with closed gas inlet.
Figure 3.29: Cross-sectional view of the 10 degree diffuser with open gas inlet.
• A gas inlet with a hole diameter of 7.5 mm will be placed 10 mm before the
diffuser entry. A pin can be placed inside this hole to block the gas inlet and test the diffuser without a gas inlet (Figure 3.28 and 3.29). This provides the possibility to compare the results with the results obtained from Experiment D.
• A 1 mm hole is drilled through the diffuser wall at each pressure tap location.
A 3 mm chamber is drilled on top of the 1 mm holes in which the pressure taps are mounted (Figure 3.30). The holes on the inside of the diffusers are cleared of any burrs. This ensures that the holes on the inside of the diffuser are as smooth as possible.
• Holes that are drilled on the oblique side of the diffuser are drilled perpendicu-
lar to the oblique side (Figure 3.31).
The mass flow at the gas inlet is created by the difference between the static pressure before the diffuser entry and the ambient pressure. The flow rate in the gas inlet can be determined based on this pressure difference. The size of the gas inlet
Figure 3.30: Cross-section of a pressure tap on the 10 degree dif- fuser.
Figure 3.31: Pressure tap holes drilled on the oblique side of the 10 degree diffuser.
is chosen based on the gas to air ratio used in appliances. The mass stoichiometric ratio is the ratio of oxidizer to fuel where all the fuel and oxidizer are used [19]. It is defined as: s= YO YF st , with Yk = mk mtotal (3.6)
WhereY0 and YF are the mass fractions of oxidizer and fuel, respectively. The
choice of gas and oxidizer (in this case air) will define the stoichiometric ratio. The equivalence ratio can then be defined as:
φ =sYF YO
(3.7) Appliances operate at an equivalence ratio lower than one. This implies that more air than needed for stoichiometric combustion is present in the air-gas mix- ture. This is done for safety reasons, since an equivalence ratio ofs >1will result in
incomplete combustion and thus the formation of carbon monoxide. An equivalence ratio which is too low is also unwanted, since it will result in acoustic instability of the burner flame (instable flame). At a certain value ofφ the flamability limit is reached.
3.6. EXPERIMENTE: DIFFUSER WITH GAS INLET 31
appliances is typically around 0.8. The combination of the equivalence ratio, appli- ance output power and type of gas result in values for the mass flow of the gas and air. Choosing an output power of 30kW (which is typical for a regular household), G20 gas and atmospheric operating conditions results in the following mass flow rates of unburnt gas and air:
˙
mgas = 6.0403·10−4 kg/s mair˙ = 1.2990·10−2 kg/s (3.8)
The mass flow of air is generated by the fan and can be monitored with the orifice flow meter. The mass flow of gas is generated by the underpressure which is present before the diffuser entry. A hole is drilled at the location at which the gas is to be injected, on which a tube is mounted. This tube will ensure a better developed entry flow. The inlet length of the tube is chosen to be 10 pipe diameters. No extra flow meter is used to measure the mass flow rate of the gas or the total mass flow rate. Instead, the mass flow is estimated based on the amount of underpressure at the gas inlet location, the hole diameter and the amount of resistance the tube for the gas inlet will generate. Also, the G20 gas is replaced by air for practical reasons. This will result in different behavior of the flow inside the diffuser due to the difference in density, viscosity and amount of mass flow. The goal of the measurements is to validate simulations, which will also be performed with air as a replacement for gas.
Figure 3.32: Schematic of the diffuser set-up with gas inlet.
The hole diameter needed to achieve a mass flow of 6.0403·10−4 kg/s of air at
the inlet can be estimated by analysing the static pressure at the gas inlet location from previous experiments at a flow rate of 1.2990·10−2 kg/s. The location of the
gas inlet is chosen to be 1 cm upstream of the diffuser entry. In experiment D, at
ReD = 40280 the mass flow rate was1.117·10−2 kg/s for the 4 degree diffuser. The
-438 Pa compared to the ambient pressure. The hole diameter can be determined by applying Bernoulli’s equation:
p1 + 0.5ρv12 =p2+ 0.5ρv22 (3.9)
Where0.5ρv2 is the dynamic pressure. Figure 3.32 shows that the dynamic pres-
sure at location 1 is zero, since the velocity in the y-direction is zero. At location 2, the static pressure is assumed to be ambient. This results in:
p1 =pambient+ 0.5ρv22 (3.10)
p1−pambient = 0.5·1.2∗v22 =−438 (3.11)
The negative pressure indicates thev2 operates in negative y-direction.
v2 =
r
438
0.6 ≈27m/s (3.12)
The gas inlet diameterDg follows from the known mass flow rate:
˙ m= 0.25πd 2v ρ (3.13) Dg = r ˙ mρ 0.25πv ≈5.84mm (3.14)
Since this calculated diameter does not include the pressure loss that occurs in the pipe, this diameter will have to be larger in reality. An estimation of the pressure loss can be made by assuming a pipe with a diameter of 5.8 mm and length of 58 mm (10 pipe diameters). Applying the Darcy-Weisbach equation gives the amount of pressure loss:
∆P =f L
Dg ρv2avg
2 ≈136.09Pa (3.15)
This value can be added to the static pressure used in Equation 3.11 to correct for the pressure loss due to skin friction. Equation 3.12 to 3.14 can be re-evaluated to obtain a new value for the diameter: Dg = 6.5mm.
Detailed drawings of the set-up with both diffusers and the exact location of each static pressure tap can be found in Appendix A and B, respectively. Measurements will be performed at approximately the same Reynolds numbers as in Experiment D.
3.7. EXPERIMENTF: DIFFUSER WITHOUT GAS INLET,EXTRA PRESSURE TAPS 33