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 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;

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.

• 

  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).

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?

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 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.

Basement under the home in the Earth?

Most earth sheltered homes do not have a basement…  This is mostly due to concerns about natural lighting, depth to the water table, etc.   Structurally speaking, two buried floors would experience a lot more lateral forces from the earth.  If you don’t want to rely on a sump pump, you also need to dig deeper drains, etc.

However, in my case, with a nice big hill of sandy loam soil that would have relatively low lateral forces and great drainage.  I also liked the idea of using QuadDeck ICF (Concrete) flooring that would act like a “shear floor” against lateral loading.  After not having the benefits of a basement in my current home, adding one seemed like a good idea to me.  I just had to work out the egress exit/natural lighting and figure out where to give up space for the stairs and I was ready to go.

For the stairs, I tried a number of locations before I figured that out.  I explained that process in a post a while back.

For the basement egress, since the basement was only on the North side, I had to put a window well on the north side.  That was the side I originally planned to bury, but since I had such nice views there, I had already relaxed on that and put in a few windows.  Now I would need to put the basement egress directly under one of those windows.  Rather than a small “vertical shaft” window well, I thought it may be more interesting to put in a larger conversation pit.  I could use the pit to get closer to the side of the hill and perhaps actually end up with an egress with a view, as well as a cool sheltered place to hang out.

Count the cost

While it is true that a basement is a relatively inexpensive way to gain square footage, mostly because it doesn’t need an additional roof, it does still need its own walls and floor and electrical and plumbing and that all adds up.   also, the suspended floor over the basement costs considerably more than the slab on grade floor that would be needed without the basement.

Eliminating the basement would also simplify the construction process starting with a much simpler excavation,  shallow drainage pipes, etc.

My specific design only called for a partial basement.  I hoped to limit the complexity, but because I have a sandy site, the engineer specified a slope of 1/2.  Meaning that my 10 ft deep basement will affect the construction for 20 ft around.  The design with the basement required more expensive step footings, taller stem walls, two levels of french drains, etc.

On the north side, the egress window was a challenge for earth sheltering the house because I needed to be a lot more careful about retaining the earth around it.   The plan looked good in 2D, but my 3D model revealed some concerns about the scale and cost of the retaining walls  that will be required to keep earth from spilling into the basement.

In my original gantt chart (building schedule), I planed to spend 1/5th of my costs and a month of my schedule on the basement…  Knowing that I wouldn’t have the option to come back and decide to add a basement later, and generally adding space to an earth shelteted home is difficult and because it would make a lot of my passive HVAC stuff work better, I decided to go for it.   

Reality update

The basement is in now and I can say that the costs were well estimated.  Shotcrete went considerably over estimates, but I saved money in other areas and ended up with a fairly affordable basement in the thirty-something-dollars per square ft range for a rough basement.  If I decide to plaster the walls or finish the floor, that will raise costs, but I don’t need to spend that money until I need the space.  At that point, it will seem like a bargain compared to adding space from scratch.

However, I didn’t factor in what a disruption it would be on the building site, and therefore to the building schedule.  The excavators and footings contractors didn’t like the step footings.  I checked with the building inspector and he didn’t like them either.  This meant that I was not able to do the footings all at once.  Keep in mind that the basement is only under a portion of the house.  I would need to backfill the basement before I could do the footings for anything else.  Before I could backfill, I needed the basement shotcrete, waterproofing, plumbing, septic field (and the trench to get there), etc.  Each of these things had delays, especially the septic field which slowed us down by a month due to a gravel shortage and trouble getting the septic tanks ordered.  By the time we got the footings in for the rest of the house, it was pretty much the end of the summer construction season.

The silver lining is that the basement was a bit of a trial run.  We got to see shotcrete applied in a less critical area of the home.  The resulting mess has lead to some adjustments in the plan for the main level.  If we had started with the main level, where the walls are higher and the shotcrete also needs to be applied overhead, it could have been much worse.

Structural considerations

With lateral loading on either side of a shear wall or shear floor, the connection across that support dramatically effects the deflection in the walls.    It is important that the basement wall acts like a single element from footing to the roof.  If there is a joint between the basement floor and the main floor, the shear floor between them will not be nearly as effective.

(I will come back another time with some illustrations)