Formulas for Solar Hot Water Systems
09 Apr 08 | Solar Hot WaterSomething that I get asked quite often is “How do you know this will make enough hot water?” That is a very good question and there are several rules of thumb regarding the size of Solar Domestic Hot Water (SDHW) systems. A properly sized SDHW system will provide between 70-80% of the annual hot water. While it would be nice to provide 100 percent, this is not a realistic goal in the Northeast because of the limited daylight hours during December and January.
General rules of thumb are:
- Allow 20 gallons per day of use for the first two people
- Allow 15 gallons per day of use for each additional person
So the basic house with four people would need 70 gallons of hot water per day. The closest conventional water heater sized to that use is 80 gallons, therefore an 80 gallon SDHW system would be appropriate for that household.
Solar Collector surface area is based on the size of the solar storage tank. Again, these are rules of thumb that have been tried and tested since the 1970’s for SDHW systems:
- Northern New England: 1Ft2/0.75 gallons
- Northeast, New England, Mid Atlantic and Northwest: 1ft2/1.0 gallons
- Midwest and Mountain States: 1Ft2/1.25 to 1.5 gallons
- Southeast, Sunbelt and Hawaii: 1Ft2/1.5 to 2 gallons
- Sunbelt desert areas: 1Ft2/1.75 to 2.25 gallons
Calculating Energy to heat water
If you are not interested in rules of thumb, here is how to calculate the actual energy required for any SDHW system. First, use the Hot Water Formulas and Calculations to determine how much hot water will be used. That use needs to be converted to a unit of energy. In the US, we use BTU, while the rest of the world uses Joule as a measurement of energy.
The basic formula is:
Energy (BTU)= Vgal x 8.345 x (Texpected - Tin) x eff
Where:
Vgal is the volume of water in gallons
Texpected is the expected hot water temperature
Tin is the temperature of the cold water supply
Eff is the system losses
The temperature for both the cold water supply and the expected hot water need to be know to calculate (Texpected - Tin). This is called the Δ T (delta T), or change in temperature. For example, the incoming water supply from a well is 45 degrees F. The expected hot water temperature is 125 degrees, this leads to a Δ T of 125 degrees - 45 degrees = 80 degrees.
From the above rules of thumb, or the Hot Water Formulas and Calculations, the example household is using 70 gallons of hot water per day.
A gallon of water weighs 8.345 pounds. It takes 1 BTU to warm 1 pound of water 1 degree Fahrenheit.
Therefore, 70 gallons of water x 8.345 pounds is 584.15 pounds of water. To 584.15 pounds x 80 degrees F = 46,732 BTU, plus efficiency losses and system losses. Efficiency losses in a SDHW system are in the solar collector glazing transmissivity, heat exchangers, pumps, etc. Generally they run around 10 to 15 percent. System losses are stand by tank loss, piping loss, etc. Generally they run about 10 percent.
Therefore, the entire solar collector array will need to collect 125 percent of the required BTUs noted above, or 46,732 BTU x 1.25 = 58,415 BTU per day.
Below are comparisons of how much conventional fuel would be used to heat the water in the example household:
- Electricity has 3,413 BTU per kWh. Electric hot water systems are 100 percent efficient, but have standby losses. Therefore (46,732 BTU x 1.10)/3,413 = 15 kWh per day. At $0.175 per kWh utility company rates, that equals $2.625 per day
- Propane has 91,600 BTU per gallon. Propane hot water systems are about 65 percent efficient and have stand by losses. Therefore (46,732 BTU x 1.55)/91,600 = 0.80 gallons of propane per day. At $3.05 per gallon, that equals $2.41 per day
- Natural gas has 100,000 BTU per Therm (Therm is 1 CCF or 100 cubic feet). Natural gas hot water systems are about 65 percent efficient and have stand by losses. Therefore (46,732 BTU x 1.55)/ 100,000 = 0.73 CCF per day. At 1.60 per Therm, that is $1.15 per day
- Heating oil (#2 distillate) has 140,000 BTU per gallon. Oil fired hot water systems are generally 80 to 85 percent efficient and may or may not have standby losses. Therefore (46,732 BTU x 1.2)/ 140,000 = 0.40 gallons per day. At $3.97 per gallon, that is $1.59 per day.
Calculating size of solar array based on energy needed
Here is where things get a bit complex. Every location has a different amount of Insolation which is the amount of solar radiation received on a given surface. The NREL (National Renewable Energy Lab) has a program called PVWATTS which can give very specific data on a month by month basis. This is important for sizing of solar thermal space heating systems. Usually this data is given in units of kWh/Meter2 per day. That is acceptable because that can be converted to BTU/Ft2 per day by multiplying kWh/M2 by 317. Each kWh equals 3,413 BTU, A M2 equals 10.76391 Ft2. Therefore 3,413 BTU/10.76391 = 317.
I like to pick a moderate month, such as April or September, and size the SDHW system to meet 100 percent of the load in that month. I often find that this is the best compromise for the New York region as it will give more hot water than needed during the summer months, and less during the winter.
The example household requires 58,415 BTU per day from the solar system. According to the PVWATTS program, a solar collector tilted at latitude for the month of April will receive 4.63 kWh/M2 per day. Convert to BTU per Ft2, 4.63 kWh/M2 x 317 = 1,579 BTU/Ft2, therefore 58,415 BTU/1,579 BTU/Ft2= 37 Ft2.
That would be a perfect world theoretical solar collector and it is a good median figure. Like many things, there are other considerations:
- The efficiency of the collector absorber plate coating
- The efficiency of the Heat Transfer Fluid (HTF)
- The incident angle of the sun on the surface of the collector in both the horizontal and vertical axis
- The ambient temperature of the collector
- The internal temperature of the collector and the HTF
At this point, the equation becomes a calculus problem and a somewhat complex one at that. The general idea is to increase size to overcome the collector losses. Field work indicates that in the Northeast, doubling the theoretical size works well. This equates to about a 50% loss over the theoretical model noted above. This is how the above noted rules of thumb on collector size vs. storage tank size are formed.
1. Absorber plate coating also called “Black Chrome.” Solar selective coating has come a long way since the 1970’s. Basically, it is a type of paint that accepts and converts more energy, in the form of visible, infrared and UV light, from the sun and converts it to heat without radiating it back into the atmosphere. These are highly specialized products and are not normally available to the general public.
2. Heat Transfer Fluid or HTF. HTF removes the heat from the absorber plate and transfers it to a heat storage tank. It can be water, antifreeze, oil, etc. Water is the best HTF as far as efficiency is concerned, but can present freezing problems.
3. Sun incident angles on the collector surfaces. A solar collector is at it’s optimum when the sun is 90 degrees from the surface. The further away the sun is from perpendicular, the less dense the energy is that is striking the surface.
4. The solar collectors have operating categories based on the ambient temperature (Ta) that the collector is in vs the water temperature within the collector (Ti). This is known as the Ti-Ta. In the summer time when the Ti-Ta is 36 or less degrees Fahrenheit, the collector is operating as a Category C unit. In the winter time when the Ti-Ta can be 90, 100 degrees or even greater, the collector is operating as a Category D unit.
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Tags: SDHW, Solar Hot Water
Solar Thermal Systems
21 Feb 08 | GeneralWhen you say solar, most people assume that you are talking about photovoltaics. Solar thermal systems have been around for longer than photovoltaics and have a proven track record of working well and paying back there costs many times over.
I install both types, and lately I have been receiving quit a few calls regarding solar thermal (i.e. solar hot water, or radiant floor heating) systems. I think this will continue as the price of energy goes up.
A solar thermal system move fluid through solar collectors, which collect heat. The fluid is then stored or used in the building. In reality, a solar thermal system is about plumbing. A Solar Domestic Hot Water (SDHW) system has three unique parts that other hot water systems or heating systems don’t have. The first is the solar collectors, the second is some type of heat exchanger and the third is some type of controller. As regarding the solar collectors, I believe that SDHW systems work best with flat plate collectors.
The flat plat collector design has been around for many years. Newer solar selective coatings have been created that increase the system efficiency. In addition to that, better insulation and better high transmisity glass have all improved on the flat plate collector design. Evacuated tubes run at higher temperatures and have problems with the seals between the glass tube and the copper pipe on the inputs and outputs of each tube.
The next unique thing in a solar system is the heat exchanger. The heat exchanger takes the hot fluid from the solar collector and cools it with the fluid from the solar hot water tank. This can be implemented in a number of ways. Some heat exchangers are part of the solar storage tank, some are a part of a drainback tank, and some are external. All heat exchangers are made of metal (stainless steel or copper) and use counter-flow properties to move the heat from one fluid reservoir to another.
Finally, the system controller, which measures the temperature of the collector outputs and the solar storage tank. If there is enough energy in the collectors to transfer to the storage tank, the controller turns the system on, which begins collecting energy.
Beyond that, a solar system is copper piping, valves, drains, hot water tanks, pumps, and other miscellaneous hardware which is all available at the local plumbing supply house.
Solar thermal systems that are designed for space heating are very similar to SDHW, only they are usually quit a bit larger with more storage.
In most cases, all solar thermal systems should have some way of operating in backup mode in case there is a long period of inclement weather. These back up systems entail some type of conventional heating system installed in parallel with the solar system. For example a SDHW system may have an electric tank or electric element in the solar tank designed to turn on if the water temperature gets too cool. A radiant floor heating system may have a small oil or gas fired backup furnace in standby duty.
A well designed solar system should be designed to produce about 80 to 85 percent of the energy needs. More than that and the system design will be too large, causing it to over produce and over heat under normal operating conditions. Less than that and you are leaving a good deal of money on the table, to be taken by the gas/oil companies.
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Tags: radiant floor heat, SDHW, Solar Hot Water, solar thermal
Does solar hot water work in cold climates?
03 Jan 08 | Solar Hot WaterI was at a lecture this past September when the speaker stated “Solar thermal just doesn’t work in this climate (the Northeast), it is not a consideration…” I wanted to stand up, raise my hand and say “Um, excuse me, but you are wrong.” There is a persistent misconception that solar thermal only works in temperate climates. The truth is that is works in cold climates as well. As evidence I submit the following:
It is January, the temperature outside is 17 degrees (that was the high temperature of the day) with a foot of snow on the ground.
The water temperature coming back from the solar collectors on my roof is 150 degrees.
Furthermore, last night it was 0 degrees and I suffered no freeze damage to the collectors or piping, even though I use distilled water as my heat transfer fluid.
This is no accident, of course. A properly designed and installed solar hot water (solar thermal) system can work in almost any climate. The snow surrounding the collector reflects sunlight unto the collector itself, making it more efficient. I have a drain back system, so when the sun goes down and the temperature drops, all the water drains out of the collectors into a reservoir inside the house. The collectors and piping all are sloped so that the water drains out properly thus providing excellent freeze protection without the use of expensive anti freeze.
Naturally, I didn’t say anything to the photovoltaic guy who made the above statement. After all, we are playing on the same team.
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Tags: SDHW, Solar Hot Water, solar thermal
Gravity Film Heat Exchangers or GFX
29 Dec 07 | Conservation, Environment, Solar Hot WaterUpdate: Sun Volt Solar is now an authorized dealer of ECO-GFX gravity film heat exhangers! For more information, check out our GFX web page.
I am always looking for ways to improve efficiency, especially in energy use. I came across something called a Gravity Film Heat Exchanger or GFX system. These units recover heat from waste water and return it to the hot water tank. Since 80-90 percent of household hot water heat goes down the drain, literally, what a great way to recover some of that energy and reuse it.
Here is how they work: Hot water from a shower or sink runs down the drain and out into the sewer. If there is a vertical run of pipe, the water, because of adhesion, runs down the wall of the pipe (and not the center). If the pipe is metal, heat is transfered from the water to the metal pipe wall until the pipe is the same temperature as the water. All of this happens in any sewer line. If the vertical section of pipe has a heat exchanger attached to the outside of it, the heat from the metal pipe is conducted away to be reused. Most often cold water feed into the hot water tank is run through the heat exchanger. The system efficiency depends on the difference in temperature between the waste water and the incoming cold water. The greater the difference, the higher the efficiency.
This system only works where there is simultaneous hot water use and immediate drainage, say a show or sink. Something like a bath or laundry would not work well because the hot water is drawn off, used, then drained away.
It appears that the system is around 45-50 percent efficient. Therefore, if you use 70 percent of your hot water in showers or sink use, you would recover 30-35 percent of your total hot water energy. Not too bad.
These systems would work very well with solar hot water systems. I am contemplating installing one at my house to see if they work as advertised. The only requirement is that they be installed vertically. In fact, in order to work properly, great care should be taken to make sure the unit is perfectly vertical. For more information, see the NREL website on waste water heat recovery or this .pdf file called Heat Recovery from waste water using Gravity Film Heat Exchangers.
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Tags: Environment, GFX, SDHW, Solar Hot Water
Hot Water Formulas and Calculations
09 Dec 07 | Solar Hot WaterThe general use calculation for hot water heating system design is about 80 gallons of hot water for a family of four. That is a very rough estimate, however, it holds up well in most cases. As far as solar hot water system design, I (and others) recommend installing systems this size on most residential housing units. It is not all that much more expensive than a 60 gallon system, which is the next size down.
Even if less than four people live in that particular house, solar domestic hot water (SDHW) systems have service lives of 25-35 years or more. Chances are good that the property will transfer ownership in that time, possibly to a larger family.
Several years ago, the US Department of energy put a great deal of effort into defining an equation which would more precisely calculate hot water use. Their work is below:
Daily Hot Water Use
Use the following equation to estimate average daily hot water use in gallons per day.
| vol = | ( | -1.78 + 0.9744 x per + 6.3933 x age1 + 10.5178 x age2 + 15.3052 x (age3+age4) -0.1277 x thermostat + 0.1437 x tanksz - 0.1794 x wtmp + 0.5155 x atmp + 10.2191 x athome - (1-dw) x dw_use - (1-cw) x cw_use | ) | x IF(senior_only,0.379,1) x IF(NOT(pay),1.3625,1) |
| variable | units (or equation) | description |
|---|---|---|
| age1 | number of people aged 0-5 yrs | |
| age2 | number of people aged 6-13 yrs | |
| age3 | number of people aged 14-64 yrs | |
| age4 | number of people aged 65- yrs | |
| per | = sum(age1,age2,age3,age4) | total number of people in household |
| tstat | °F | water heater thermostat setpoint |
| tanksz | gals | rated volume of water heater |
| wtmp | °F | inlet water temperature |
| atmp | °F | average annual outdoor air temperature |
| athome | = 1 if TRUE, 0 if FALSE | adult at home during day |
| pay | = 1 if TRUE, 0 if FALSE | residents pay for energy to make hot water |
| senior_only | = 1 if TRUE, 0 if FALSE | only seniors live in household and it is a multifamily residence< |
| dw | = 1 if TRUE, 0 if FALSE | dishwasher present in home |
| cw | = 1 if TRUE, 0 if FALSE | clothes washer present in home |
| dw_use | =0.692^per+1.335^per gal/day | hot water use by household dishwasher |
| cw_use | =1.1688^per+4.7737^per gal/day | hot water use by household clothes washer (if use hot or warm water for clothes washing) |
Daily Water Heater Energy Use
To estimate average daily hot water energy consumption in BTUs per day, use the following equation.
| variable | units (or constants) | description |
|---|---|---|
| vol | gals/day | average daily hot water use. |
| RE | recovery efficiency of water heater | |
| UA | BTU/hr-°F | standy heat loss coefficient of water heater (if not available see section below) |
| Pon | BTU/hr | rated input power of water heater |
| Ttank | °F | tank thermostat set point |
| Tinlet | °F | inlet water temperature |
| Tamb | °F | air temperature around water heater |
| dens | 8.293752 lb/gal | density of water |
| Cp | 1.000743 BTU/lb-°F | specific heat of water |
Annual Water Heater Energy Use
To estimate average annual hot water energy consumption by type of fuel, use the following equations.
| fuel type | equation (with units) | description |
|---|---|---|
| electricity | = 365 * Qin / 3412.76 kWh/yr | annual water heater electricity use |
| natural gas | = 365 * Qin / 100,000 therm/yr | annual water heater natural gas use |
| propane | = 365 * Qin / 91,500 gal/yr | annual water heater propane use |
| fuel oil | = 365 * Qin / 138,690 gal/yr | annual water heater fuel oil use |
| variable | units | description |
Standby Heat Loss Coefficient
To calculate UA, if necessary, use the following equation.
UA has units of BTU/hr-°F. EF, RE and Pon come from water heater product data.
This calculation is based on the DOE Energy Factor test procedure for water heaters.
| variable | units | description |
|---|---|---|
| EF = | Energy Factor | |
| RE = | Recovery Efficiency | |
| Pon = | BTU/hr | rated input power |
| Qout = | 41093.7 BTU/day | Energy content of water drawn from water heater during 24 hour test. |
Source:
1996 Lutz, J. D., Liu, X., McMahon, J. E., Dunham, C., & McGrue, Q. T. “Modeling Residential Hot Water Use Patterns” No. LBL-37805. Lawrence Berkeley National Laboratory. November 1996
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