Two days ago, a buddy who designed flue gas pipelines called and asked, "How to calculate the resistance of the expansion joint? I calculate the pressure drop according to the straight pipe section. If the pump is selected small, the test run will trip." Alas, this sounds familiar. Too many people have stumbled in the selection of expansion joints-the system pressure drop is quite accurate, but they have slapped their heads in the expansion joints. Today, let's talk about this matter clearly. After you understand it, you can pat your chest and say that you can count.
First, don't rush to set the formula-what problem does the resistance calculation solve?
I calculate this resistance, what is it for?
To put it bluntly, there are two purposes: first, ensure that the head of the pump or fan is sufficient, so that the system will not be pressurized or the flow rate is insufficient; Second, avoid the pipeline stress exceeding the standard due to excessive local resistance, which will tear the expansion joint.
To put it bluntly, the expansion joint is installed in a pipe, and the fluid passing through it will inevitably cause pressure loss. If this loss is ignored, the chosen pump will either trip like the guy above, or the big horse-pulled cart will waste the electricity bill. Calculate it accurately, and you can match an economical and reliable system.
Second, the physical nature of resistance: the expansion joint is not a straight pipe, and the fluid turns a corner here
What is the structure inside the expansion joint? Take the most commonUniversal corrugated expansion jointFor example, the ripples raise one by one, and when the fluid flows through it, it is like driving a car on a washboard road-every wave peak has to change direction, accelerate, and slow down, and energy is lost in the process. This loss belongs to local resistance, which is completely different from the friction resistance along the pipeline.
If you think about it, a straight pipe of the same caliber and a section of corrugated expansion joint, at the same flow rate, the pressure drop of the latter may be 5 to 10 times that of the former. Why? Because the fluid repeatedly "bends" in the ripples, a large number of vortices are created. This kind of local resistance cannot be applied hard by Darcy's formula, but has to be calculated by a special resistance coefficient method.
Then how to quantify? The empirical formula is as follows: Δ P = ξ · (ρ · v²/2), where ξ is the drag coefficient, ρ is the medium density, and v is the flow rate. The difficulty is all about this.
Third, different types of expansion joints, the resistance difference is greater than you think (metal corrugation vs non-metal vs sleeve)
Different types of expansion joints have very different internal geometries, and the drag coefficients can be different by an order of magnitude.
- Metal corrugated expansion joint(For example, those used in the power station industryHigh temperature axial expansion joint、Large diameter thick wall expansion joint): The ripple bulge is obvious, and the fluid turbulence is violent. The resistance can be two or three times different from the one with a guide tube and the one without one. More on that later.
- Non-metallic expansion joints (fabric fiber expansion joints): The interior is generally a smooth rectangular or circular channel, without obvious corrugated bumps, and the resistance is much less than that of metal corrugated expansion joints. However, it depends on the fabric to bear pressure, and the flow rate cannot be too high, usually controlled within 15m/s.
- Sleeve type pipe expansion joint: The displacement is compensated by the sliding of the inner and outer sleeves, and the inner channel is basically straight through, with the smallest resistance, which can be calculated almost according to the straight pipe section. But seals are prone to wear and tear, which is another matter.
So don't take all models with one formula. You're choosingCompound hinge transverse expansion jointOrCurved tube pressure balance expansion jointWhen the structure is more complicated, the drag coefficient has to be corrected according to the specific wavenumber and waveform.
4. Calculate it hand-in-hand: empirical formula + key parameter values
Okay, straight to the case. Assume a steam pipeline with nominal diameter DN300, design flow rate of 25m/s and medium density of 0.6kg/m³. Select a steam pipeline with guide tubeUniversal corrugated expansion joint, Single Wave.
Check the drag coefficient ξ. According to industry experience, ξ of single-wave metal corrugated expansion joint with guide tube is generally between 0.5 and 1.2. Take 1.0 for conservative points. Without the deflector, ξ can soar above 3.0.
Calculate the pressure head. ρ ·v²/2 =0.6×25²/2=187.5 Pa.
Δ P = ξ ×187.5=1.0×187.5 ≈ 188 Pa. This is just the loss of a single wave. If you choose a multi-wave expansion joint (such asCompound straight pipe bypass pressure balanced expansion joint), also multiply by the wavenumber, but pay attention to the interwave interference, not a simple linear superposition-usually corrected by the square root of the wavenumber.
The contrast system allows pressure drop. If the outlet pressure of the fan is only 500Pa, an expansion joint will dry out 188Pa, plus the loss of the pipe valve, it is definitely not enough. At this time, either change to a low-resistance type with a guide tube, or increase the diameter to reduce the flow rate.
5. Guide tube, flow rate, medium-those "invisible" factors that affect resistance
Just now, we mentioned the guide tube. What is this thing for?Specific Function of Expansion Joint Guide TubeIt is to let the fluid take a relatively straight path inside the corrugation, so as to avoid direct impact on the root of the corrugation to generate large vortex. With it, the drag coefficient can be reduced to one-third or even lower than without it. So don't be reluctant to give up that cost, especially for high-speed airflow pipelines, the guide tube is a power-saving artifact.
Medium viscosity. Gas and water are very different. The gas has low density and low viscosity, and the resistance mainly comes from eddy loss; Liquids such as water or oil have high density and high viscosity. In addition to local resistance, the friction loss of corrugated wall should not be underestimated. When calculating liquid pipeline, it is recommended to refer toMetal hose pressure standardEmpirical data in, or do CFD simulation directly.
In addition, the higher the flow rate, the better. The flow rate doubles and the resistance becomes quadrupled (because v²). Some people choose small diameter expansion joints to save money, but as a result, the pressure drop is too large, and the pump consumes much more energy than the equipment money saved. Tsk, the gain outweighs the loss.
6. Completion of calculation is not equal to completion-common cases of resistance rollover in engineering
Let's tell me a few real rollover scenes.
Case A: The desulfurization flue of a power plant was usedNon-metallic expansion jointIt would have been fine, but the design flow rate was mentioned above 20m/s, and as a result, the fabric layer was torn by the airflow after half a year of operation. Turning back and calculating, the local pressure drop exceeds the standard, resulting in negative pressure fluctuation and fabric fatigue damage. Later replaced with a deflectorMetal rectangular expansion jointJust steady.
Case B: Steam pipeline of a chemical plant, selectedExternal pressure single axial expansion jointThe pressure drop of the deflector is not counted, and as a result, the system safety valve jumps frequently. Finally, it was found that the corrugated root inside the expansion joint accumulated scale, the actual circulation area shrank by 30%, and the resistance tripled. So regular inspections and cleaning are also important.
And guess what? These rollovers all have one thing in common: the expansion joint is regarded as "part of the pipe" in the design stage, and the resistance is not counted separately at all. In fact, the expansion joint is a local resistance member in the pipeline, which must be listed separately in the pipeline hydraulic calculation table.
How is the resistance of the expansion joint calculated?Remember this formula: Δ P = ξ · (ρ V²/2), then honestly check ξ, set the flow rate, and check the system. Don't slap your head, don't be lazy. Understand these steps, and selection is no longer metaphysics.