1. Introduction
Precise measurement technology is the foundation of energy management. Energy metering is centered around flow meters. The following types of flow meters are commonly used in industry today:
○ Differential pressure flow meters: standard orifice plate, standard nozzle, venturi tube, averaging pitot tube, bend tube and other flow meters.
○ Impeller flow meter: turbine flow meter, impeller water meter.
○ Vortex flow meter
Electromagnetic flowmeter
○ Ultrasonic flow meter
The five types of flow meters mentioned above are widely used in industry, especially differential pressure flow meters, which are indispensable in high-temperature and high-pressure applications such as power plants, chemical plants, and steel mills. This article mainly discusses standard orifice plates and standard nozzles in differential pressure flow meters, as their data is comprehensive and can be analyzed and discussed quantitatively. Other types of flow meters are only compared with differential pressure flow meters to facilitate selection.
The so-called quantitative analysis and discussion means: installing a flow meter, how much flow rate passes through, how much resistance loss occurs, how much energy is lost, and by converting this to how many kilowatt-hours of electricity, multiplying by the electricity price, we can determine how much money a flow meter costs per year. Through economic accounting, we can re-examine the practical application of flow meters in industry.
2. Flowmeter energy consumption calculation
If a differential pressure flow meter, such as a standard orifice plate or nozzle, is installed on a pipeline, there will inevitably be a pressure loss, which is:
Where ξ is the drag coefficient
ρ is the fluid density in kg/ m³
u is the average velocity in the pipe (m/s)
δp represents the pressure loss in Pa;
Make some transformations to formula (1):
In the formula, D is the inner diameter of the pipe (mm).
qv represents the volumetric flow rate in m³ /h.
Substituting formula (2) into formula (1) yields:
Where ξ is for standard orifice plates and standard nozzles:
The derivation is omitted.
d is the orifice diameter of the orifice plate or nozzle (in mm).
D is the inner diameter of the pipe (mm).
C is the outflow coefficient.
This allows us to calculate the resistance coefficients of the orifice plate and nozzle.
The energy loss formula is:
Where δp is the pressure loss in Pa.
qv represents the volumetric flow rate in m³ /h.
△wh represents the energy loss per hour (kJ/h).
Substituting formula (3) into formula (5) and converting it to kWh, 1 kWh = 3600 kJ, we get:
△wh" represents the energy loss per hour (kWh/h).
If the flow meter operates for 7500 hours per year, then
△wy represents the annual energy loss in kWh/y.
If we take into account the efficiency of the motor and water pump
Given that the motor η <sub>electric</sub> = 0.90 and the water pump η <sub>pump</sub> = 0.70, the actual annual energy loss is:
If the electricity price is X yuan per kWh, then the total annual loss "cost" is:
As can be seen from the above formula (8), energy loss is directly proportional to the cube of the volumetric flow rate qv and inversely proportional to the fourth power of the pipe diameter D. Generally speaking, the volumetric flow rates of gases and steam are very large, while the volumetric flow rates of liquids (water) are very small. Therefore, the energy loss of gases and steam is much greater than that of liquids (water).
3. Calculation of the resistance coefficient ξ for standard orifice plate and standard nozzle.
Standard orifice plate: Reynolds number Re = 7 × 10⁴ . As shown in Table 1, when designing orifice plates, the β value should be as large as possible, preferably greater than 0.60.
Standard nozzle: Reynolds number Re = 7 × 10⁴ . As shown in Table 2, when designing the nozzle, the β value should be as large as possible, preferably greater than 0.50.
Thus, the drag coefficient is less than 10.
For other Re values, C and ξ differ very little.
4. Calculation of resistance coefficient for other flow meters
1) Turbine flow meter:
Table 3 is derived from calculations based on the manufacturer's data.
2) Vortex flow meter:
When d/D = 0.281, the drag coefficient ξ = 2.4
3) Bend pipe flow meter
As D increases, the drag coefficient ξ ranges from 1.5 to 0.5.
5. Example of energy consumption calculation
Ten examples of energy consumption calculations are listed in Table 4; the specific calculations are omitted.
Table 4 Compilation:
1) Groups 1, 2, and 10 are used as a single unit. The medium is water. Under the same parameters, pipe diameter, and flow rate, the energy consumption of orifice plate, nozzle, and turbine is compared. Nozzle is better than orifice plate, and turbine is better than nozzle.
2) Groups 3 and 4 are used together. The medium is air. Under the same parameters, pipe diameter, and flow rate, the energy consumption of the nozzle is compared between the orifice plate and the nozzle. The nozzle is superior to the orifice plate.
3) Groups 5, 6, and 7 are used as a medium, which is superheated steam. Under the same parameters, pipe diameter, and flow rate, the energy consumption of nozzles, orifice plates, and venturi nozzles is compared. Nozzles are better than orifice plates, and venturi nozzles are better than spray nozzles.
4) Groups 8 and 9 are used together. The medium is saturated steam. Under the same parameters, pipe diameter, and flow rate, the energy consumption of the bend pipe and the vortex street is compared. The bend pipe is better than the vortex street.
6. Discussion
1) As shown in Table 4, the energy consumption calculation table for flow meters reveals that different flow meters have different energy consumption for different media, with gas and steam consuming significantly more energy than liquids (water). Particular attention should be paid to the measurement of steam flow. For example, numbers 5, 6, and 7 in Table 4 represent typical examples of measuring high-temperature, high-pressure superheated steam using nozzles, orifice plates, and Venturi nozzles, respectively. The resistance coefficients of the orifice plate, nozzle, and Venturi nozzle are 4.72, 1.34, and 0.1747, respectively, with energy consumptions of 441× 10⁴ , 125.2× 10⁴ , and 16.3× 10⁴ kWh/y. For current 300MW and 600MW large-scale generator units, calculations show that if a nozzle is used as the measuring device, the annual energy consumption is 250× 10⁴ to 450× 10⁴ kWh. If a Venturi nozzle is used, the annual energy consumption is 32× 10⁴ to 54× 10⁴ kWh. The difference between the two is very obvious.
2) From a design perspective, when orifice plates or nozzles are required, nozzles are preferable, with the β value as large as possible and the differential pressure ΔP as small as possible. In cases where orifice plates or nozzles are optional, other flow meters can be used. Flow meters with no or low pressure loss can be selected, such as electromagnetic flow meters, ultrasonic flow meters, vortex flow meters, turbine flow meters, and elbow flow meters.
3) When selecting a flow meter, an additional evaluation metric should be added, namely its own energy consumption, so that users can compare their one-time investment with their daily consumption and determine a more reasonable application plan.
4) For instrument manufacturers, it is necessary to provide users with resistance coefficient tables or energy consumption indicators so that users can make selections.
7. Conclusion
The above calculations and analyses demonstrate that the energy consumption of flow meters is considerable. Economic development places higher demands on energy conservation, making the improvement and selection of flow meters a crucial consideration. For users, the daily energy consumption and initial investment of flow meters need to be analyzed and weighed. For manufacturers, determining which flow meters best meet user requirements requires careful consideration. This is also an important issue facing instrument research institutions.
