Due to space requirements, I'm going to start a new section dedicated specifically to the internal heat Exchange methods and how to design and calculate capacity.
I'm going to start out with a tried and true method of heating water and explain how we can determine our capacity from that information. The basis of most all water heating calculations is boiler horsepower. More specifically the amount of energy a boiler can convert into steam. We are only heating water not making steam. Hopefully... For everybody's sake.... I will not get into all the technical details at this very moment, but the heat transfer rate measured in btu is the same regardless of heating water or making steam.
1 boiler horsepower =33,475 btu per hour
We can use the specific heat capacity of steel, most grades of carbon steel are very very close in value, to determine the transfer rate of heat through the material. This rate is rather constant. Velocity doesn't have a very large effect, but turbulence does. Also, due to something called laminar air flow, the temperature of the flue gas does not have as large of an influence as one would think. The delta T between two different heat carrying materials usually determines the rate of heat transfer. This is very true for water. But when hot air flows through a tube or pipe, there is a thin layer of molecules that sticks to the surface and does not flow with the rest. This layer has an insulating effect, as the heat from the moving air mass must transfer its heat to these molecules, then to the steel surface. Most gasses have a very poor heat transfer rate, air especially. Which is why it is the best insulation and what holds heat in our home. More on that later.....
So, after my long winded explanation, we come to our next bit of information.
It takes 5 square feet of horizontal traveling surface area, or 10 square feet of vertical traveling surface area, to conduct one boiler horsepower worth of heat from flue gas to water.
There are many things we can do to increase this efficiency, I will discuss that momentarily, Just the basics for now.
First we will look at horizontal traveling flue gas. The reason that horizontal flue passages conduct heat better is because of the natural buoyancy of hot gasses. First think of the hot flue gas flowing through in a very smooth and steady stream. This is not reality, but paints a nice mental picture. Picture each hot gas molecule following one another in a single file line, in perfect rows, much like a marching battalion. If this where to happen, the molecules on the outer edges would cool as they travel down the side of the pipe until they reach the same temperature as the pipe. But the ones in the middle would still be hot because they haven't touched the cooler pipe yet to give up their heat. We would waste massive amounts of heat. This is where physics come into play. The molecules on the outer edges cool and figuratively fall to the bottom of the pipe as they are cooler and more dense than the hot center molecules. Now that the cool molecules are moving out of the way, the hotter center ones rise to the top of the pipe where they give up their heat upon contact, and the process repeats itself about a million times over. The word is turbulence. Our best friend in this circumstance. When flue gasses travel horizontally they have convection currents that cause turbulence and allow more heat carrying molecules to get stired around and make contact with the tube or pipe surface. Hence the greater heat conducting. Vertical flue passages don't get to experience this phenomenon naturally as the hot gasses rise right up and out and the cooler parts almost cling to the surface and insulate it rather than transfer heat. To counter act this the use of turbulators can cause the needed turbulence to help promote efficiency. They can be spiral shaped, flat waves, I have even seen chains used. The turbulators are inserted in the tube or pipe that the flue gas travels in to help stir things up a bit. They can be used in both horizontal and vertical flue passages, but have a greater effect on vertical.
Now I'm going to show a few examples and some simple math to investigate some different scenarios and boiler tube designs based on our above home heating example.
Horizontal 5 square feet =720 square inches
Vertical 10 square feet = 1440 square inches
Both are capable of creating 33,475 btu/hr
I am going to use the horizontal method for our example. Simply double the area requirement for vertical, unless using turbulators as the efficiency will be near that of horizontal and those figures can be used. I am also going to round numbers to the next higher inch or foot. As once again more is better.
We are going to take our above calculated heat capacity of 919,440 btu and say we want to create that in a period of 6 hours, half our needed storage time.
So first we must divide 919,440 by 6 hours to determine our required btu/hr output.
919,440/6=153,240
Now divide that by 33,475 to determine boiler horsepower
153,240/33,475=4.57boiler horsepower. We will round it to 5 boiler HP.
Multiply by 5 to calculate required surface area in square feet.
5*5=25 square feet
But before we can play with different combinations of tube or pipe diameter and amounts of tubes we have one more very important calculation to make.
Now that we have determined our burn rate of approximately 153,000 btu/hr we need to make some airflow calculations to determine our minimum flue size, which will determine a number of other factors when it comes to the fire tubes in our boiler. Once we determine our minimum flue size we will calculate the surface area, and the sum of the surface area of our boiler tubes must be equal or greater than the sum of the flue area to prevent major air restrictions and quite possibly a very pressurized fire box that could turn explosive. Although this is generally only possible when a fire has been idle and smoldering for hours and the fire box is full of flammable wood gas.
To calculate our flue size we need to first determine airflow needed to feed the fire to make our required heat of 153,240 btu in one hour. We will use 20% MC wood again as this is well seasoned and best to use.
11/17/11
Ok so apparently I have misplaced my notes on thermal expansion calculations and thermal dynamics. So I will edit this info in later on when I come across it.
For now we can use some figures based on commercial built gasifier boilers.
6" flue= 140,000 btu/ hr max
8"=205,000
10"=275,000
As soon as I find the info ill put it up, and also show how a draft inducer can actually move more air through the same size pipe with negative pressure. But for now, and most builds actually, the above sizes will be reasonably close.
Slightly larger diameter piping is ok when using a fan to meter air flow conditions through a fire. Technically, there is no reason to worry about a draft so one could go as large as economically possible. But it is important to never undersize and choke a fire or wood gas could back up and the results could potentially become catastrophic when fresh oxygen is being forced in.
So using the above numbers and calculations we see that we must use at least an 8" diameter flue pipe for our heat requirements. It is the surface area of this flue diameter that'll help us determine our heat exchanger tubes. We must never have a total combined cross sectional surface area smaller than the flue.
11/26/11
Now that we have our flue diameter we can calculate our cross sectional surface area required and then we will start running numbers on different pipe diameter to determine a good combination of size and quantity that will make 25 square feet and provide us with our heating needs.
Some basic geometry will give us the area of the flue:
Surface area of a circle
(pi)r^2
(3.14)4^2=50.24
Now if we where using a very high efficiency exchanger consisting of hundreds of very small diameter tubes the .24 inches would be significant, but most of us will use something larger and more easily available so we will round to 50 square inches for our value. Having the flue slightly larger than the exchanger is always better any way.
Now there is one little rule if circles that's very handy and can make this a very simple matter.
If you have a circle that is half the diameter of another, its area is 1/4 that of the larger.
So for an 8" flue, we would need four 4" tubes to retain the same surface area and for the internal pressure to remain constant.
Every time you cut the size in half, multiply the quantity by 4
For a 8" flue:
4@4"
16@2"
And so on...
If you want to use 1.5" pipe you need to calculate the area of 1.5" pipe (1.76) and divide 50.24" by that for the number of tubes needed.
50.24/1.76=28.54
28 tubes would suffice, as we are going to be operating at the lower end of the 8" flue capacity. I would make it 29 if it where at The upper end.
I'm going to use 16 2" inside diameter tubes for our example of how to calculate the minimum length needed for the surface area of our heat exchanger tubes.
So we know we need 25 square feet.144 square inches in a square foot tells us we need 3600 square inches of surface area minimum. If the design of your boiler allows more length always use it. More surface area is better than less or the minimum.
To determine the surface area of a tube we must calculate the circumference first, then multiply by the length. If you where to cut a slit down one side of a tube and un roll it you would have a rectangle, where area is length times width.
It is best to use th inside diameter measurement of the tube for surface area as this is the actual contact area. The actually measurements of our tube when ordering will be 2.25"x.125" wall thickness to give us 2" I.D.
Formula for circumference is Pi*diameter or PiD
3.14*2=6.28
Now we can combine all of our tubes as though they where one large flat sheet:
6.28*16=100.48"
That gives us the length if one side of our rectangle. Now using the formula for surface area:
L*W=A
We can work backwards with some simple math rules:
5 boiler horsepower equals 25 square feet or 3600 square inches.
100.48*W=3600
Or...
3600/100.48=35.82 inches long
Seems pretty short, but technically it will suffice. Of course if you make them longer, say the length of your boiler, you will ensure the efficiency if heat transfer. When designing your boiler, gasifier or burner, play with different sizes and combinations to see what works best with the materials you have at hand. Keep in mind that this example is based on mathematically calculated value, real world results always differ. So keep in mind that one thing they don't teach in engineering school,
just because it works on paper doesnt always mean its true.
There are also a number of other factors to include. thermal expansion, gas temperatures, Charles laws of thermodynamics. But I will touch upon these more in the gasifier section. As a multiple pass boiler would become too easily plugged by the creosote of a naturally burning wood burner.
***I just realized I made a few errors in my math, I will correct them next time I work on this. The surface area for the tubes calculated to 5 square feet and I should have calculated for 25 square feet. If you wish to calculate your own in the mean time don't forget this important multiplication as I have currently in the above example.****
7/13/12- corrected calculations for tube length.
I want to point out that round shapes are better in boiler design. They may net fewer inches of surface area, but are stronger. There is much physical moment within the metal as it heats and cools. Expansion and contraction. A Sharp corner or weld joint creates a stress riser, a point where stresses concentrate and cause physical material failure. A round tube is like an endless line, the stress is always perfectly and evenly distributed around the circumference. All metal fails eventually. It's called fatigue, if ee can minimize these dresses we can prolong the lifespan of our creation.