The Equations!
Pressure Drop
Professional engineers and HVAC designers calculate the pressure drop (head loss) for a given duct system. You can use similar equations for earth tube design. If the pressure losses in the system exceed the pressure driving the flow (passive or active), the flow will stop and the duct will become useless. When air flows through a duct, there is pressure drop due to friction losses as well as dynamic losses which are caused by change in direction or velocity (usually at the fittings). For a commercial HVAC duct system, 1 Pa/m loss is typical.
Pressure drop can kill a passive system or require an active system to use a lot more electricity (and make more noise) than would other wise be necessary.
Frictional Pressure Losses
I will move the actual calculation to this page (link coming).
However, even without entering numbers, the equations tell most of what you need to know about the relationship between the parameters. Understanding these relationships leads to design insight.
- The DArcy equation predicts the frictional pressure losses in ducted air systems like Earth Tubes
The friction losses are due to viscous interactions between the air and the pipe walls and can be expressed with the D’Arcy-Weisbach Equation. In this equation;
–∆Pf = frictional pressure drop
–λf = friction factor (based on material, Re and Dm)
–L = length of duct
–v = mean duct velocity
–g = gravitational constant
–Dm = hydraulic mean diameter (cross sectional area / perimeter)
Some things are immediately apparent from the equation; for instance, the pressure drop is proportional to the friction factor. In other words, the rougher the pipe wall, the higher the frictional pressure loss (which seems pretty obvious). This should affect your material choice; PVC is 200 times smoother than concrete, HDPE is even smoother. Increased length is also a factor; while we want length to provide more contact for heat exchange, too much and the flow could stop. Velocity is very important because this is squared. In other words, if you double the velocity, the pressure drop is affected by a power of 4. If we reduce our velocity from 700 to 175 ft/min, we reduce the velocity by a factor of 4, and our pressure losses by a factor of 16. Passive systems tend to move the air relatively slowly, but adding a fan to increase the velocity may actually be counter productive (choose a fan with high pressure rather than high velocity ratings).
On the bottom of the expression, we see the hydraulic diameter (proportional to pipe radius), which means increasing the pipe radius reduces the frictional pressure drop.
Dynamic Pressure Losses
The dynamic pressure losses can usually be found in tables. For instance, for a given velocity, the pressure drop around a 90 degree mitered turn may be 50%. The same flow around a smooth bend may only lose 15%. The problem is that most of the tables are for higher velocities used in home or industrial HVAC systems. However, looking at these charts, you quickly get the idea that fewer fittings is a good idea. You can also see that lower velocities have lower losses for a given fitting.
Gentle curves are much better than tight turns. A gentle turn has a radius at least 6 times the pipe diameter. However, even gentle curves or serpentine layouts cause the flow to change direction and, therefore, induce dynamic losses that will reduce your flow rate or increase your energy costs.
The charts also show that diverging or converging sections should be as gradual as possible. Most HVAC texts suggest that divergence should not exceed 12° and convergence should not exceed 30°.
Reynolds Number and Turbulence
A second equation, important for understanding earth tubes, is “Reynolds number”. When scientists were studying flow, they knew that it was sometimes laminar and then as the velocity would increase, it would transition to turbulent. They could graph it but it took until 1883 before Osborn Reynolds showed that the change depended on ρVd/μ, which was named “Reynolds Number” in his honor (and usually shown as “Re”).
This is important because the turbulence of the flow affects both the pressure drop and heat transfer rate of the system. By calculating the Reynolds number for a given design, you can predict if the flow will be turbulent or laminar. In a viscous flow, friction is able to stop the air molecules adjacent to the wall. If the flow is laminar, layers form with each layer away from the wall moving a little faster than the layer below it. This forms a “boundary layer profile”. The flow is called “laminar” because these layers are stable. Streamlines stay nice and straight and never cross. While the flow at the walls is stopped, the majority of the flow moves easily and smoothly thru the duct/pipe. The problem is that heat transfer between the walls and the majority of the flow is greatly reduced. In turbulent flow, the fluid is always mixing and the system is better able to transfer heat from the walls to the majority of the flow or vice versa.
Many Earth tube designers incorrectly assume that their flow will be laminar. They tell you that you need to “add turbulence” to increase heat transfer by choosing tubes with rough or corrugated surfaces, laying the tubes in serpentine patterns, etc. These “enhancements” increase pressure drop dramatically. A few quick Re calculations show that they are not necessary for most earth tubes.
Reynolds number is proportional to the density, velocity and diameter and inversely proportional to the dynamic viscosity. The density and viscosity are properties of the fluid (such as air) and are both inversely proportional to the temperature. Thicker fluids (like syrup) have higher viscosity and tend to form laminar flows (Low Re), air is not very “viscous” and goes turbulent easily. The velocity and diameter are aspects of the duct design, increasing either parameter will increase your Reynolds number and turbulence.
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- The Reynolds Number can be used to predict transition to turbulent flow (Re > 2300 for round ducts)
ρ = fluid density
- V = mean flow velocity
- d = hydrolic diameter (inside tube diameter) (keep in mind that this may be different from the “nominal diameter”)
- μ = dynamic viscosity of the fluid
Lower Reynolds number flows are laminar. Higher Reynolds number flows are turbulent. For a round duct/pipe, this transition happens around Re~2300. We can easily calculate a table of Reynolds numbers for various nominal duct sizes (actual diameters would vary based on duct material). In this chart (above), I have colored Reynolds numbers >2300 red. These are turbulent flows.
Using the velocity and the nominal diameters (again, the actual internal diameters would vary based on duct material), we would get this table showing cubic feet per minute. Again, the “turbulent” flows are colored red. If you can stay below these flow rates, you may have laminar flow (flow could still be made turbulent by seams/joints, dirt, upstream turbulence from the fan, etc.) which would flow with less resistance, but much less heat transfer (much less slope for pressure drop over velocity).
- Flow rate in cubic feet per minute was calculated in this table, and colored red to indicate turbulence based on the previous table. It shows that for any significant flow rate, you should expect turbulent flow, even in a straight smooth air duct.
A related question is how quickly the turbulence will form. Assuming the flow enters the duct as laminar flow (unlikely), how far will it go before it becomes fully turbulent?
- A flow profile will form within a short distance of the inlet, and in almost all Earth Tubes, this flow will be turbulent.
Friction between the flow and the walls (friction exists even in a relatively smooth pipe) will bring the molecules immediately adjacent to the wall to a stop. This slows the flow next to it, and the flow next to that, etc. The result is a growing boundary layer profile that shows the gradient between the stopped flow at the wall and the free stream velocity. This boundary layer grows as the flow moves down the pipe until it meets in the middle and a stable flow profile develops. If the viscosity is high enough that the Re<2300, the flow can remain laminar. However, if the flow is not viscous enough, the friction at the wall can actually cause some flow reversal (wall roughness can cause this to happen even sooner). This flow reversal starts transition to a fully turbulent flow. A boundary profile can still develop in a turbulent flow, but it is really the “mean” turbulent velocity profile; the average of many small fluctuations in velocity and direction. Since this average is relatively constant, the resulting wall shear is constant and the pressure drop becomes linear with X.
- The distance to a stable flow profile is between 18 and 20 times the diameter up to Re = 10000
The distance before this stable profile develops is a function of the Reynolds number and Diameter and can also be calculated. Often this distance is expressed over the diameter. For all the Reynolds numbers on the above chart, this works out to between 18 and 20 times the diameter, which for these pipes is between 6 and 20 ft. Any ridges, fans, screens or other upstream obstacles will only cause this to happen sooner.
Just in-case my point got lost in the engineer speak… here it is plainly. Turbulence is good for heat conduction, but trying to intentionally induce additional turbulence is unnecessary and bad for pressure loss. In designing your system, you can assume the flow in your earth tubes will be turbulent no matter how smooth the walls are. There is no need to add features to increase turbulence, they will only increase your back pressure and reduce your flow.
Progress Update
Well, according to our Gantt chart (schedule), my wife started getting permits last week… Except we are not actually there yet. Instead we will be filing banking paperwork on Monday. I don’t want to bother with the permits until the loan is approved. And we were waiting on a tax return and an extra paycheck to beef up our funds before we applied for this year. So, its a good thing I padded the schedule a bit so this delay shouldn’t affect the date we hoped to break ground. I am still nervous about dealing with the mortgage company though.
Virtual Build
Things have been a bit busy at work and I am working on a paper for my “adult onset MBA”, so progress on the virtual build has been slow the past few weeks.
I did manage to get the Skylight curbs on. They look like industrial chimneys now, but they will be mostly covered in earth and that should soften them up. I may need to adjust their elevations a little. Originally, I had them over the showers. I installed skylights above the showers in my current home and I really enjoy showering in the sunlight. Of course, it would be a lot easier for someone to just walk up and look in the skylights of an earth sheltered home, so I will need to use frosted glass. The architect moved them to the middle of each room (for symmetry). But the virtual build revealed that I would need to cut central steel arches, so I moved them back.
I also worked a bit on the front of the house. I got the steel structure up in the front wall and added the concrete sun shade to the front of the house. It still has a long way to go. For instance, I need to put the steel structure to support the concrete shade, add a bunch of roof structures and the front door is still missing.
One thing to note is the way the foundation dips on the right hand side… This is the cost of having a basement that comes closer to that corner.
Sourcing
As we get closer to the build, I have been getting updated prices on things like the steel arches. The price has actually come down some what. Also, since I get charged “by the bend”, regardless of how long the bend is, I have adjusted the order so that pieces of the same radius can be bent as one long piece and then be cut to length. That will save me some money.
I did find that the 5/8th inch thick steel support plates that the engineer specified in many locations are somewhat difficult to find. All the steel suppliers I called said they would need to order that specially for me. I had only needed a few square feet, and special ordering has some minimum area requirements which will raise the cost for me significantly… Not sure what to do about that yet.
Do-it-yourself Electrical?
The biggest change to my sourcing plan was due to a conversation I had with an electrician two weeks ago. He is out of the business now, but still licensed in my state. He looked at my pictures and said he could understand why the bids were so high. Electricians don’t want to figure out how to do my unusual house when they can just get regular jobs. The FUD (fear, uncertainty and doubt) translate into a high bid. But there were also real reasons why it would cost more. They would need to use more conduit, need to more carefully secure the boxes, etc.
He suggested that I should just do it myself. I told him that I was already planning on taking on too much of this build myself. I have wired a few outlets and lights, but never something as serious as an electrical panel or a large as a whole home (or even a whole room)… He said he thought I was smart enough to take care of it and I could save 3/4 of the bid price. Anyway, I am seriously thinking about it and got several books on wiring and the electrical building code this week. I do know some home builders who did their own electrical. Perhaps, I will do most of it and hire someone to come out and give it a once over…? At the very least, I can handle my own “finish” electrical.
We also attended a local building show this week. It cost us $10 at the door, plus we bought some of those roasted nuts for $6 more… Those shows are never really worth going to, are they? We talked to a few people, but nothing really changed.
Website
Well, I am up to about 2700 visits a month (over 5000 page views), which isn’t bad even if half of those are robots or mistakes. This past month I had a couple interesting encounters on the web.
Comment on other sites?
First, someone on the the Malcolm Wells Yahoo group posted a link about Earth Tubes. I jumped on it right away and found it was my page on Earth Tubes, but on another site. It was the sort of site that has a number of revenue generating adds and the writing at the top of the page said “Written by David”. They had done a full copy and paste, so the images were actually still on my site, but hyper-linked into place. The site had no contact information anywhere on it, but using some Google search, I found a video related to the site. Scrolling down in the YouTube chat, I found where “David” had a conversation with someone and ended up giving his email address. From that I was able to find his google+ page and his LinkedIn page. Eventually, I even found his mailing address (in the USA). I emailed “David” and asked them to give credit where it is due.
While waiting for a reply, I looked around the site and found that pretty much everything was just copied from other sites, but all claiming to be written by David. About 2 hours later, he wrote me back to say he was sorry and had added a line at the top with my name and a link to my website… Oh well.
I saw another website (in Czechoslovakia) had also linked to my site and described it as a “very long, but detailed, overview of Earth tube design”. I guess I need to work on being more concise ;^)
Comment on my site?
Of course, the opposite also happens. I had referred to Larry Larson on my page about Earth Tube design. However, while I gave him a “nod of the hat” as an expert in the field (literally since he professionally installs earth-tubes out in the “field”), I disagreed with his opinion that the tubes need to be corrugated and laid in a serpentine path to generate heat exchanging turbulence. I also made some generally disparaging remarks about the use of corrugated HDPE pipe ;^).
Larry contacted me.
Actually, nothing too dramatic. He just wanted to discuss my concerns. He writes even longer emails than I do, but we had a number of back and forth email exchanges. It may not be quite over yet, but I am still pretty certain that his serpentine layout is detrimental to performance. However, I have softened on my critique of the corrugated pipes in general. He argues that they win in terms of “bang for buck”, and perform well if installed well. When I have the time, I will go back and adjust my text a little.
One good thing that came out of our exchange is that Larry is going to post some earth tube performance data on his site. The data (which I am privileged to have already seen) shows the inlet and outlet temps and humidity of the earth tubes in his own home (in Iowa) over a 10 year time frame. He showed me some graphs and they were pretty interesting, but the samples were taken by hand. He said that my soil temperature experiment inspired him to get some small data loggers from Thermoworks and install them in his home and in some of the other homes that he installed earth tubes for. Including one that has better performance than his own home. He plans to publish the graphs of the inlet and outlet temps for each home every 3 months or so.
I also plan to adjust my plans a little and have a corrugated earth tube come into my new home “for experimental purposes”. If it causes any problems, I will just block it off. The delta cost will be small since I plan to use my drain tile for the job.
A wide variety of fans are available on the market. The main two categories are axial and centrifugal. You can also get various configurations such as with the motor in the duct or outside the duct. Fans can be direct drive or belt driven. They can have a single speed or variable speed. Fixed pitch or adjustable, or even “variable pitch in flight”… You can Google to get lots of general info on fans, or even more specifically for residential HVAC, so we won’t get into all of that. Here we specifically interested in driving an Earth Air Heat Exchanger (Earth tube) system, so we are expecting lower speed flows where back pressure is the primary concern.
This is roughly what you would expect from a backward facing centrifugal fan curve chart. Note the power peaks at about 80% of max flow and the max fan pressure is still good in this range. A forward facing fan curve chart would have a positive power slope all the way to 100% and the pressure curve would fall off much more quickly.
Fans are often rated on pressure and flow rate. These parameters are not independent because the flow rate is dependent on the system pressure (the pressure the fan must overcome to move the air). This system pressure is the sum of all the pressure losses including dynamic and friction losses as discussed on the Earth Tube Design page, plus losses due to air filters, coils (heating or cooling), dampers, grills, etc. 1 Pa/m is a typical loss in a straight section of duct. An air filter could add 25 to 50 Pa of loss.
The energy required to run fans is a significant portion of the cost of running an HVAC system. Careful selection of the fans to size them correctly to the flow requirements and back pressure of the system is important if you want your home to be as economical and as green as possible. If you look at a fan curve (pressure, flow rate, power and efficiency chart that should be provided by the manufacturer), you will find that they are only efficient within a very small range. Since you are probably on a budget, you may not have much control over the speed or power. However, if you have a good estimate the total system pressure (plus some safety factor) and your required volume flow rate, you can buy the fan designed for that combination. If you get an overly oversized fan, even at a great price, your efficiency will be much lower and you will pay more over the long run. And of course, if your fan is undersized…
It is also important to note that pressure drop is proportional to the square of the velocity of the flow in the system. Earth tube systems can be more efficient if the airflow is slower. Since they are typically needed only for ventilation, they can be run at a small fraction of the speed needed by typical HVAC systems. One way to reduce the speed is to increase the area of the pipe. If you do so, make sure to transition gradually. If you are using any coils (heat transfer) in your flow, keep in mind that constrictions in the flow increase both speed and dynamic losses. Look for “low face velocity” coils for reduced losses. These cost more upfront (paying for the advanced design), but have lower lifetime operating costs.
I am really only including this section to tell you why you should not use Axial fans ;^)
Axial fans are the “propeller” type fans that push the air along their axis of rotation. Of course, human beings are very creative, so there are a number of different types of axial fans, you can google for more information. The little fan that cools your computer is an axial fan, and so is the propeller on the front of a WWII bomber. The designs can be improved in many ways, such as by reducing the tip gap (if it is ducted) to increase the pressure (increasing precision increases cost) or by adding vanes to straighten out the flow and increase efficiency. In general, axial fans are more efficient than centrifugal fans for their design range because they don’t have dynamic losses associated with changing flow direction and they are often directly connected to their motors, avoiding transfer losses. However, their design range is low pressure flows. You can also pick up a basic axial fan for much less money than a centrifugal fan.
This link to the Lowes home hardware site shows a six inch booster fan for only $26.77. The fans are “inline” which makes installation easy and compact. They are sold as booster fans for furnace systems and proudly state 250CFM on the box… That is 250 cubic feet per minute for less than $30!!! But a closer inspection of the literature will explain that this is the maximum they will “allow”… These “booster” fans are meant to be used in a furnace system with a centrifugal fan as the primary blower, at this maximum flow (generated by the main blower), the booster fan actually starts inhibiting the flow. These axial fans can help increase flow thru parts of the system that had low CFM, but really can’t be used to drive the system. In this case, the fan labeled “250 CFM” could actually move “free air” at 160 CFM with no duct resistance. Any resistance at all would quickly reduce its ability to move air. These are quite unsuitable for Earth Tube systems.
An axial fan (in this case without vanes) can move the air efficiently when there is low back pressure, but high back pressure causes the majority of the flow to circulate near the blades.
If you look at a fan perfomance curve, you can see that the ability of axial fans to move air efficiently quickly drops off as back pressure increases. If your earth tubes are more than 16 ft long (5 m), (count ever turn as an additional 5 ft) your axial fan won’t be able to overcome the frictional and dynamic losses. This is why they should never used for ducted flow situations. Basically, as the pressure rises, the air will take the path of least resistance, which is usually to flow back up thru the tip gap (between the blade tips and the duct wall). You can increase the speed/power, but you will just end up furiously circulating the air near the fan with very little flow moving thru the duct.
If the back pressure is low, an axial fan will get you more flow per unit of power. But earth tube systems generally have back pressure that reduces axial fan efficiency to near zero, so don’t use these no mater how cheap they look. (See, I am so serious, I put it in a red box this time ;^)
Ducted axial fans are ideal for situations where the duct is very short, such as just passing thru a wall.
Centrigfugal fans produce more pressure for a given air volume, which makes them better suited to longer duct runs. Rather than “screw” their way thru the air, these fans use centrifugal force to throw the air out at a right angle to the intake. Because of their geometry and mode of operation, they require more torque to get started (larger motor), but the higher number of blades can raise their pitch out of our range and they tend to be quieter also.
These fans can be a little more awkward to integrate into the duct system in that they are usually quite a bit larger than the duct. These are the “squirrel cage” blowers that you find in your furnace or auto HVAC. Axial versions are also available, but at double the price and with lower efficiency due to the dynamic losses of straightening the flow again With careful design, you may be able to create a layout that can take advantage of the 90 degree turn thru the cheaper squirrel cage fans.
Centrifugal fans also tend to be quite a bit more expensive; Fantech makes some “inline” centrifugal fans that are easier to add to duct assemblies. A 6 inch fan costs roughly $260, or about 10 times the cost of the axial fan of the same diameter.
You can get backward curved blades (usually airfoil shaped), radial blades or forward curved blades. Each configuration produces a different fan performance curve. The backward curved airfoil shaped fans are the most expensive because they are more difficult to manufacture, but they are also the most efficient. You can also get backward curved fans made of single thickness metal or airfoil shaped plastic that are still very efficient and ideal for higher pressure applications. Radial blades are not at all appropriate for HVAC and forward curved blades are better for high volume at low back pressure.
Backwards curving centrifugal fans are the best choice for earth tube systems, but they also tend to cost the most…
You could leave your earth tube fans running at full blast all the time, or your could build some smarts into the system so they come one only when needed.
Variable speed drive fans cost more, but can save money if you know you don’t plan to run them full speed all the time. This is because they can adjust the fan curve as needed to improve efficiency. For instance, you could set the fan speed to reduce when no one is home. Since the power is proportional to the flow rate cubed, reducing the the flow to 50% with a VSD fan can actually reduce the power required down to 50%^3=12.5% of the maximum power consumption.
Earth sheltered homes have a lot of thermal mass which means that if you want things warm at 6:00 AM, you may need to start quite a while before that. Modern thermostat systems often include technology that learns how long a building takes to heat up or cool down based on variables including outdoor temperature, indoor solar gain, etc. These systems can drive fans to provide ventilating or heated/cooled air in an intelligent way. These systems used to be expensive, but this sort of technology is getting easier and easier to come by.
The 2nd generation of the Nest learning thermostat is available for under $250 and can be installed by the home owner. It includes temperature, humidity motion and light sensors. It doesn’t quite feature Optimal Start-Stop yet, but it is on its way there. Other systems are also on the market.
In addition to the standard temperature sensors included , humidity (20$) and even CO2 sensors (250$) are available. They can be used for monitoring your home or connected to control systems that operate the fans, dehumidifiers, etc. in order to get the most comfort most efficiently. They can also be connected to dampers that would allow you to exhaust stale air based on high CO2 levels or when the weather is pleasant outside, or even shut down the earth tube fans when CO2 levels are low or the intake air is too humid. Sensors could also be used to adjust the ventilation mix between fresh air and return air
Ducted fan efficiency is very much affected by the ductwork up and down stream of the fans. The air near the fan is the most energetic and therefore dynamic losses are greatest. Therefore, if you need to turn the duct or change in cross section area, near the fan is the worst place for those changes (although you could use your centrifugal fan to make the turn). If you must, use turning vanes or keep the slope small (15°). This includes avoiding situations where fans are open to a room, either as an inlet or an outlet. Your fan’s efficiency will be improved if you can put it further along the duct rather than sitting at the opening.
(more to come)
