As part of the the open source Earthbag Village (Pod 1), we will be building and are open source project-launch blueprinting a water-saving and heat-recycling communal shower design. These multi-shower structures will recycle the shower water heat for pre-heating incoming water and heating the Tropical Atrium, demonstrate environmental and design elements for increasing comfort and reducing water use, and function as testing space for comparing and identifying the most user-friendly and effective water-saving shower head designs.

**PAGE UNDER CONSTRUCTION**

This page discusses the communal eco-shower designs with the following sections:

- What is a Communal Eco-shower
- Why Open Source an Eco-shower
- Ways to contribute
- Consultants
- Communal Eco-shower Details
- Shower Heat Exchanger(Counterflow)
- Heat Exchanger Piping – Length Calculation Report
- Sustainable Power
- Sustainable Water Heating
- Water Heat Cycling
- Water Saving Methods
- Grey Water and Heat Use in the Tropical Atrium
- Resources
- Summary
- FAQ

*NOTE: THIS PAGE IS NOT CONSIDERED BY US TO BE A COMPLETE AND USABLE TUTORIAL **UNTIL WE’VE BUILT IT, TESTED IT, AND ADDED ALL THE NOTES AND MODIFICATIONS FROM THAT EXPERIENCE TO THIS PAGE*

CLICK HERE FOR THE LOW-FLOW SHOWER HEAD RESEARCH PAGE

The communal eco-shower design will be built four times as part of the Earthbag Village (Pod 1). They will all be adjacent to the Tropical Atrium, with two built in the South and one each on the East and West side. Having four of these structures will provide enough showers to meet the needs of the complete Earthbag Village (Pod 1).

Communal Eco-showers for the Earthbag Village by One Community – Created by Gilberto Martini de Oliveira

The eco-elements incorporated into the shower designs include:

- Power provided 100% by renewable energy
- Water heating provided renewably and with maximum efficiency
- Water Heat Recycling
- Water Saving Methods
- Shower Heads
- Environmental comfort controls
- Thermostatic Mixing Valves

- Greywater and heat use in the Tropical Atrium

The images below show the locations of these showers:

The communal eco-shower designs will provide a replicable option for sustainable showers in eco-communities, campgrounds, or other group settings. They will demonstrate two ways to recycle the heat from shower water, multiple ways to improve the shower environment so people naturally take shorter showers and use less water, and they will function as a testing space for gathering data and user feedback on water-saving shower heads.

SUGGESTIONS ● CONSULTING ● MEMBERSHIP ● OTHER OPTIONS

Adolpho Maia: Mechanical Engineering Student

Amauri Tavares: Bachelors of Science and Technology and Aerospace Engineering Student

Diogo Rozada: Civil Engineering Student

Douglas Simms Stenhouse: Architect and Water Color Artist

Fernando Bitencourt: Civil Engineering/Construction Engineering Management Student

Gilberto Martini de Oliveira: 3D Animation Designer

Jorge Antonio Ricardo: Mechanical Engineering Student

Matheus Manfredini (Civil Engineering Student specializing in Urban Design)

Sayonara Batista de Oliveira: Architecture and Urban Planning Student

The communal eco-shower designs are purposed to demonstrate innovative approaches to saving water and energy through sustainable construction and design. This includes construction with earthbags as part of the complete Earthbag Village (Pod 1) and integration of the following open source components:

- Power provided 100% by renewable energy
- Water heating provided renewably and with maximum efficiency
- Water Heat Recycling
- Water Saving Methods
- Shower Heads
- Environmental comfort controls
- Thermostatic Mixing Valves

- Greywater and heat use in the Tropical Atrium

A heat exchanger is a semi-closed thermodynamic system that transfers energy in the form of heat from a hot gas or liquid to a cold gas or liquid. To maximize efficiency, the two fluids flow in opposite directions (counter flow).

A heat exchanger can help to save energy that would otherwise be lost. Energy can’t be created or destroyed, energy can only be transformed from one form to another. Based on thermodynamics’ laws it is possible to understand that every time that we use an available form of energy to realize any work desired, some percentage of this energy is lost as heat, vibration, or other form of mechanical energy. A heat exchanger can reutilize this residual energy.

The amount of energy required to heat water for taking a shower is almost completely lost because the water reaches the drain with almost the whole amount of energy used to heat it. This water is typically at a relatively high temperature (≈35˚C / ≈98˚F).

It is possible to reuse this energy in the form of heat to pre-heat any desired fluid. This reduces the money that you would spend on energy and also helps to reduce the environmental impact caused by the mass “production” of energy and its side effects.

Show Heat Exchanger Details

For our calculations, we used an average shower temperature of 40.5˚ C / 102˚ F and a minimum temperature of 12.78˚ C / 55˚ F for the incoming water. For any amount we pre-heat the water before it reaches the shower there will be a reduction in the amount of energy that the shower demands to heat the water to the desired temperature. The amount of energy required to heat the water can be calculated using the following equation.

Running this equation in a software called MATLAB® produces the following plots showing the relation between the temperature of the pre-heated water and the energy spent by the shower.

As shown above, if you can pre-heat the water to the desired temperature the shower would not need to use energy at all.

The project below was designed to be made with regular objects that can be found in your average hardware store.

The project consists of a tubular heat exchanger. This exchanger is made of copper tube (transporting warm water from the shower drain) inside a PVC tube (transporting cold water to the shower). Copper is recommended for the warm shower-drain water because it conducts heat very well. PVC is recommended for the cold water traveling to the shower head because it can isolate the heat well enough.

Heat exchange occurs between the hot water (after the shower) and cold water (which comes from the reservoir). The water from the reservoir is pre-heated and then passes through the electrical heater in the shower. For this exchanger to be sufficiently efficient to justify its use, we need at least two degrees Celsius increase in the temperature of the water from the reservoir traveling to the shower head.

Key design factors to be considered were:

- The necessary pipe diameters for sufficient grey water flow
- The necessary pipe diameters for sufficient shower water flow
- Average temperature of the in-flow water ready to be used
- Desired average temperature of the water for use during a shower
- Standard pipe sizes available in most hardware stores

Duplicable hand calculations are shown below for various lengths of the heat exchanger. Software calculations (also shown below) were used to simulate the more complex temperature, pressure and heat transfer rates and behaviors.

For every calculation and simulation presented in this report we considered that the walls in the heat exchange system are adiabatic, which means the system will not lose heat to the environment. While this is in actuality not true, it simplifies the calculations to match known heat transfer’s rules and equations without compromising the accuracy of these equations for evaluating the design itself.

For the theoretical calculation of the heat exchanger, we had to consider some extreme conditions to ensure that the system achieves the desired results. Below we display all the equations that we used to determine the piping length needed according to how much we wanted to increase the water temperature entering the shower.

The water properties specified above were calculated for the mean temperature in each condition of the water. For example, the first condition, hot water going from 35º C to 33º C. So the mean temperature in this case is (35+33)/2 which results in 34º C. With this value we can then reference water property tables to provide the data points needed for the necessary calculations:

For the internal and external fluids, we considered the following conditions:

- Fluid temperature entering (from the drain) – Th,i (Temperature
*Hot*In): 35º C = 308.15 K = 95º F; - Fluid temperature coming out (grey water) – Th,o (Temperature
*Hot*Out): 33º C = 306.15 K = 91.4º F; - Mean temperature: 34ºC (93.2ºF);
- Water mass flow: 227.4 kg/h = 0.06316667 Kg/s = 1 GPM;
- Specific Heat (constant pressure – Cp): 4.1796 KJ/Kg.K;
- Thermal conductivity (K): 621.716 mW/m.K;
- Viscosity (µ): 734.92 µPa.s;
- Density (ρ): 994.314 Kg/m³.

- Fluid temperature entering (from the reservoir) – Tc,i (Temperature
*Cold*In)::12.78 ºC = 285.93 K = 55 ºF; - Fluid temperature coming out (entering on the shower) – Tc,o (Temperature
*Cold*In):: 14.77 ºC = 287.92 K = 58.58 ºF; - Mean temperature: 13.775 ºC (56.79ºF)
- Water mass flow: 227.4 kg/h = 0.06316667 Kg/s = 1 GPM;
- Specific Heat (Cp): 4.1911 KJ/Kg.K;
- Thermal Conductivity (K): 586.1205 mW/m.K;
- Viscosity (µ): 1195.529 µPa.s;
- Density (ρ): 999.2629 Kg/m³.

The grey water needs at least a 2” pipe to drain efficiently.

- Internal copper pipe diameter: 52.5 mm
- External copper pipe diameter: 60.33 mm

The section area between the two pipes (3”-2”) should be 1” to maintain pressure and flow rate:

- Internal PVC pipe diameter: 77.93 mm
- External PVC pipe diameter: 88.90 mm

The first thing to calculate is the heat flow (Q) that the internal fluid (hot water) is capable of transferring within the system, considering that this water will lose 2 ºC (from 35º C to 33º C). The equation to calculate this is:

We’ll call this Equation 1 (EQ1): Q = m x Cp x ∆t

Where,

- Q = Heat flow [J/s];
- m = Mass flow [Kg/s];
- Cp = Specific Heat at constant pressure [J/Kg.K];
- ∆t = Temperature variation [ºC] or [K].

So,

- Q = 0.06316667 [Kg/s] x 4179.6 [J/Kg.K] x (35 – 33) [K] = 528 [J/s]

Now we can use the same equation (EQ1) while assuming the heat going from the hot water is going exclusively to the cold water, because the hot water is traveling exclusively inside the cold water for the heat exchange. Equalizing these equations it’s possible to find out the final temperature of the pre-heated water (which is the exchange of heat from the hot water with the heat received by the cold) as the external fluid temperature entering in the shower:

- Qh = mh x Cph x ∆th = mc x Cpc x ∆tc

Where ‘h’ means all the data for the hot water (inside the internal tube) and ‘c’ means all the data for the cold water.

So,

- 528.02 [J/s] = 0.06316667 [Kg/s] x 4191.1 [J/Kg.K] x (T2 – 12.78) [K]

After this, we will calculate the ∆t1 and ∆t2, which are used to calculate the Logarithmic mean temperature difference (LMDT), which will be used in another equation by the end of this project:

Equation 2 (EQ2): ∆t1 = Th,i – Tc,o

Equation 3 (EQ3): ∆t2 = Th,o – Tc,i

Equation 4 (EQ4): LMTD = (∆t2 – ∆t1) ÷ [ln (∆t2 ÷ ∆t1)]

So,

- ∆t1 = 35 ºC – 14.77 ºC = 20.23 ºC
- ∆t2 = 33 ºC -12.78 = 20.22 ºC
- LMDT = (20.22 – 20.23) ÷ [ln (20.22 / 23.23]

Next we need to calculate the internal heat transfer coefficient (hi), which means how much heat the inner flow (water inside the copper tube) is able to transfer to the system. For this, we need to calculate some dimensionless parameters, like Reynolds number inside the copper tube and Nusselt number inside the copper tube:

First, for Reynolds number we will use the following equation:

Equation 5 (EQ5): Re,i = (4 x mi) ÷ π x Di x µ

Where,

- Re,i = Reynolds number inside the internal tube
- mi = Water flow inside the internal tube [Kg/s]
- Di = Copper tube internal diameter [m]
- µ = Viscosity [Pa.s]
- π = 3.1416

So,

- Re,i = (4 x 0.06316667[kg/s]) ÷ (3.1416 x 0.0525[m] x 0.00073492[Pa.s])

Now, the Nusselt number inside the tube using the following equation:

Equation 6 (EQ6): Nu,i = 0.023 x Re,i ^ (0.8) x Pr ^ (0.4)

Where,

- Nu,i = Nusselt number inside the internal tube (copper)
- Pr = Prdtl number for the mean temperature (Pr = 4.994)
- Re,i = Reynolds number inside the internal tube

So,

- Nu,i = 0.023 x 2084.48 ^ (0.8) x 4.994 ^ (0.4)

With these numbers we are able to calculate the internal heat transfer coefficient (hi) by the equation:

Equation 7 (EQ7): hi = (Nu,i x K) ÷ Di

Where,

- hi = Internal heat transfer coefficient [W/m².K]
- Nu,i = Nusselt number inside the internal tube (copper)
- K = Thermal conductivity for the mean temperature [W/m.K]
- Di = Copper tube internal diameter [m]

So,

- hi = (19.78 x 0.621716[W/m.K]) ÷ (0.0525 [m])

After calculating the internal heat transfer coefficient we have to calculate the external heat transfer coefficient (he). For that we need to recalculate the dimensionless numbers (Reynolds number and Nusselt number) again, but now for the external water (between the PVC pipe and the copper tube).

First we calculate the external Reynolds’ number:

Equation 8 (EQ8): Re,e = (4 x mo) ÷ [π x (De + Di) x µ]

Where,

- Re,e = Reynolds number inside the external pipe (between PVC and copper)
- mo = External water mass flow (between PVC and copper) [Kg/s]
- π = 3.1416
- De = PVC pipe internal diameter [m]
- Di = Copper tube internal diameter [m]
- µ = Viscosity [Pa.s]

So,

- Re,e=(4×0.06316667[Kg/s])÷[πx(0.07793+0.0525)[m]x1195.529×10^-6[Pa.s]]

Now, to calculate the external Nusselt number we have to use the table 8.2 from the textbook Fundamentals of Heat and Mass Transfer: 6th Edition. :

Our Di/De is given by (52.5/77.93) which is equal to 0.6736.

As we do not have this specific value in the table, we have to make an interpolation by the following way:

Now it is possible to calculate the external heat transfer coefficient (he) using the parameters that we calculated:

- he = (K x Nu,e) ÷ (De – Di)

Where,

- he = External heat transfer coefficient [W/m²K];
- K = Thermal conductivity for the mean temperature [W/m.K];
- Nu,e = External Nusselt number between PVC and copper;
- De = PVC pipe internal diameter [m];
- Di = Copper tube internal diameter [m].

So,

- he = (586.1205 x 10^-3[W/m.K] x 4.575) ÷ (0.07793 – 0;0525)

After that we are able to discover the global heat transfer coefficient (U) that considers both he and hi in your calculation:

U = 1 ÷ ([1/he] + [1/hi])

Where,

- U = Global heat transfer coefficient [W/m².K];
- he = External heat transfer coefficient [W/m².K];
- hi = Internal heat transfer coefficient [W/m².K].

So,

- U = 1 ÷ ([1/105.44] + [234.23])

Finally, with all these results, we can include the linear length needed to heat the cold water from 12.78ºC (55ºF) to 14.77ºC (58.58ºF) by the following equation:

- L = Q ÷ (U x π x Di x LMTD)

Where,

- L = Linear length needed;
- Q = Heat flow [J/s];
- U = Global heat transfer coefficient [W/m².K];
- π= 3.1416;
- Di = Copper tube internal diameter [m];
- LMTD = Logarithmic mean temperature difference [K] or [ºC].

So,

- L = 528.02[W] ÷ (72.709[W/m².K] x π x 0.0525[m] x 20.22[K])

Therefore, with this example we can see that even with cold water (12.78ºC/55ºF) it is possible to heat the water by two degree Celsius using 2.17 meters of linear piping with the pipes diameters as specified. So, anyone can build a tabulation like that and fit it on their home hydraulic system reducing the energy consumed by the shower or boiler. It is possible that an infinite amount of parameters exist and need to be considered in a heat exchanger design like that, so depending on the diameters, temperatures and mass flow, we can get a lot of different results.

For the calculations, using computer programs, on heat transferred and the necessary tubes length, we are using a Brazilian simple software that is free and can provide all the information that we need. To run the calculations we used the following data and considerations (for winter):

- External copper pipe diameter: 60.33 mm
- Internal copper pipe diameter: 52.50 mm (2”)

- External PVC pipe diameter: 88.90 mm
- Internal PVC pipe diameter: 77.93 mm (3”)

- Hot water temperature entering (going down the drain): 35 ºC (95 ºF)
- Hot water temperature coming out from the system: 33 ºC (91.4 ºF)

- Cold water temperature entering (from the reservoir): 12.78 ºC (55ºF)
- Cold water temperature coming out from the system (entering in the shower): 13.78 ºC (56.8 ºF)

- Shower water flow: 227.4 Kg/h (1 GPM)

- Linear length needed (after calculation): 7.14 m

Below are images from the software and the results generated by it:

With the help of the software, we can see that in order to increase the heat of the cold water by one degree Celsius, we need a 7 meter linear length. This software is much more accurate and takes into consideration many more factors to design. So, basically this software considers more problems that can disrupt the heat exchange which explains why it is necessary to have more length to change just one degree. Another thing to remember is that these calculations are based on using very cold water temperatures coming from the reservoir which occurs in particular places. In a place where the water is warmer less linear length will be needed to build a heat exchanger to transfer the same amount of heat.

After evaluating the calculations handmade and also software calculations based on the software, we used the CAD software Solidworks® to develop a design for the heat exchanger and evaluate it using hydraulics and thermal simulations.

In the first design, we considered a large heat exchange between the reservoir water going to the shower and gray water from the shower. We designed a heat exchanger 300 linear inches long made of PVC pipes with copper pipes inside. The following pictures show the design, the pressure drop inside the system and the amount of heat able to transfer to the water going to the shower:

*Figure **1**: First design.*

*Figure 2: The streamlines generated inside of the heat exchanger system where the colors define the temperature value.*

*Figure 3: Temperature distribution inside the system.*

*Figure 4: Pressure distribution inside the system. *

However, to we had to match all the requirements from the hydraulic team. The grey water coming from the shower drain requires a higher pressure to flow, this way the use of gravity pushing the grey water down helps to eliminate the need to pressurize this water. Our initial solution for solving this problem was to incline the whole system matching the hydraulic system’s slope, however due to the fact that the pipes were parallel to each other we would have both positive and negative gravitational force gradients at work. Therefore the gravity would both help and deter the grey water to flow.

The second idea for a solution for this problem was to incline independently each pipe in this system, however several changes were required such as changing the 180 degrees copper elbow to a 90 degrees copper elbow.

The difference in angle and height made it impossible to connect the pipes in a reliable way. After analyzing and trying several possible solutions the only one that seems viable was to make the design simpler with just one pipe reducing the length to ⅓ of the original.

*Figure 5: The connection problem due to the difference in height and angle in the pipes.*

The second design created can be made using simple hardware found in regular hardware stores such as Home Depot. The items required to build the system are:

- One copper pipe Sch 40 with 2 inches in diameter and 120 inches in length, average price of 43.00 USD for exactly 10 feet.
- One PVC pipe Sch 40 with 3 inches in diameter and 100 inches in length, average price of 245.00 USD for a linear length of 10 feet however since the price for a linear length of 20 feet is still the same I would recommend buying a larger length and cutting it saving the extra pipe for a second design.
- Two PVC reducing tee connections Sch 40 with the diameters of 3x3x1.5 inches, average price of 13.28 USD.
- Two rubber fillings with 3 inches in diameter, average price of 4.44 USD each.

The total price to build one system would be 200.94 USD. However the price can change based on the modifications the user can make in the original design and the suppliers for the parts.

Below is a representation of the design:

*Figure 6: Second design.*

After designing the system, we ran simulations to see where we would have drops in the pressure and how the system would react with the slope required from the hydraulic team.

For this simulation we used the pressure over the hot water coming from the drain as the environmental pressure 101325 Pa and the pressure over the cold water coming from the reservoir as 80 Psi and the temperatures are the same as the calculations already presented.

The results are presented below:

*Figure 7: Pressure value inside of the system.*

*Figure 8: Temperature inside of the system.*

*Figure 9: Flow streamlines simulation inside of the system. *

The third (and final) design created can be made using simple hardware found in regular hardware stores such as Home Depot. The items required to build the system are:

- One copper pipe Sch 40 with 2 inches in diameter and 3.6 feet in length, average price of 43.00 USD for exactly 10 feet.

- One PVC pipe Sch 40 with 3 inches in diameter and 26.48 inches in length, average price of 245.00 USD for a linear length of 10 feet however since the price for a linear length of 20 feet is still the same I would recommend buying a larger length and cutting it saving the extra pipe for a second design.
- Two PVC reducing tee connections Sch 40 with the diameters of 3x3x1.5 inches, average price of 13.28 USD.
- Two rubber fillings with 3 inches in diameter, average price of 4.44 USD each.

The total price to build one system would be 200.94 USD. However, the price can change based on the modifications the user can make in the original design and the suppliers for the parts.

Below are the images of the design and the simulations:

*Figure 10: Final design.*

*Figure 11: Pressure value inside of the system.*

Figure 12: Temperature inside of the system.

*Figure 13: Flow streamlines simulation inside of the system.*

The water coming from the hot water outlet has a temperature equal to 304.27 K or 31.12 ⁰ C (88ºF) and the water coming from the cold water outlet has a temperature equal to 289.7K or 16.55 ⁰ C (61.79ºF). With these results it is possible to reduce the showers power supply by 1.17 Kilowatts knowing that a regular shower has a power supply of 8.5 Kilowatts, the energy reduction would be around 13.76%. The time required for having an economical compensation for the price paid on the heat exchanger depends on the average price for a Kwh in the location that the heat exchanger will be used. Since the average price for a Kwh is normally low takes a little bit of time to receive the economical compensation, however the reduction on environmental impacts is big and also since the showers are not required to be very powerful the use of the heat exchanger allows the purchase of a cheaper shower reducing the costs to build the shower rooms.

Without doubt, the use of this heat exchanger or any device that can be built following the same theory that we used can reduce the amount of energy that is consumed by the shower in a good capacity, reducing the costs to build the shower room. In addition, and more importantly, reducing the demand for electrical energy and therefore reducing the environmental impacts caused by the mass “production” of energy. Heat exchangers have been used in the industry for several years, now it is time to apply the industry’s technology that we normally associate with degrading our environment to help save it. It is time to use energy in a smarter way. Let’s exCHANGE our energy use!

This page discusses One Community’s renewable energy strategy. As we complete the designs, we’ll add here the specifics for how everything integrates with the eco-showers.

This page discusses One Community’s sustainable water heating strategy. As we complete the designs, we’ll add here the specifics for how everything integrates with the eco-showers.

Details and designs coming for heat recycling from shower drains to pre-heat incoming water.

Water saving methods will include:

- Shower Heads
- Environmental comfort controls
- Timers
- Warm and ultra-comfortable shower environments so long and hot showers are less desirable

- Thermostatic Mixing Valves and electric point of use water heaters

Greywater and heat will be recycled into the Tropical Atrium. The Tropical Atrium will also be the initial place for pre-heating water.

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