A Study in Solar Housing Technology: The Impact of Trombe Walls in Ladakh

(1)

INOM

EXAMENSARBETE TEKNIK,

GRUNDNIVÅ, 15 HP ,

STOCKHOLM SVERIGE 2020

A Study in Solar Housing

Technology:

The Impact of Trombe Walls in

Ladakh

(2)

Abstract

The aim of this bachelor’s thesis is to examine the effect of installing a Trombe Wall in houses in Ladakh, India, and to evaluate its impacts for energy-saving,

improvement in life quality, and its financial viability. Trombe Walls are a passive solar technology that use a dark wall with a glass covering to slowly heat living spaces by storing solar energy. Passive solar technology involves using the sun’s rays to heat or cool living areas without the aid of mechanical devices. In this thesis, two types of passive solar technologies are studied, Trombe Walls and direct gain technology. Direct gain technology is introduced in order to conduct a comparative study of Trombe Walls. Direct gain technology focuses on maximizing windows area to let in sunlight to warm the room.

This was done through two-pronged approach. In a first quantitative step, data was collected from rooms heated by Trombe Walls and direct gain technology. In each room, data was recorded using temperature, humidity, pressure, and light sensors. This information was then used to analyze the indoor temperature of the rooms and calculate the solar radiation that hit the walls. This showed that Trombe Walls maintain a more stable indoor temperature as compared to direct gain

technology, although often at the expense of the brightness of the room. Furthermore, a numerical model was developed to simulate the indoor temperature of a Trombe Wall.

This quantitative analysis was complemented by a qualitative analysis where inhabitants from two villages in Ladakh were interviewed. All interviewees lived in houses heated by a Trombe Wall. The interviews show that Trombe Walls brings forth a myriad of positive effects, such as increasing indoor air temperature, improving air quality and generally raising the level of wellbeing in a family.

Furthermore, a discussion of the economic feasibility of installing a Trombe Wall follows, to see if it is financially viable for villagers to adopt this technology. The Trombe Wall is analyzed as an investment using economic valuation tools such as the Internal Rate of Return method. Given current fiscal conditions in Ladakh, and that the lifespan of a Trombe Wall is at least 20 years, the Trombe Wall becomes a profitable investment for the individual if their required rate of return is less than 17 %.

Lastly, this thesis concludes with a short discussion of how the quality of the data collected could be improved, as well as suggestions for future improvements to a Trombe Wall. Possible solutions are presented that might help make the Trombe Wall a more appealing heating solution and enable the technology to spread around the world.

(3)

Sammanfattning

Syftet med denna kandidatuppsats är att undersöka effekten av att installera en Trombe-vägg i hus i Ladakh, Indien och därigenom utvärdera dess bidrag till värmebesparing, förbättring av livskvaliteten och andra minskade kostnader.

Trombeväggar använder en mörk vägg med en glasbeläggning för att långsamt värma upp hus genom att lagra solenergi. Trombe-väggar är en typ av passiv solteknik, en kategori som innefattar ett flertal olika teknologier som alla använder solens strålar för att värma eller kyla områden utan mekanisk hjälp. I denna uppsats studeras två typer av passiv solteknologi: Trombe-väggar och maximering av ljusinsläpp (Direct Gain Technology). Maximering av ljusinsläpp fokuserar på att tillföra så mycket solstrålning som möjligt in till rummet, och dessa studeras för att möjligöra en jämförande studie av Tromebväggens effekt.

Studien utfördes i två steg. I ett första kvantitativt steg samlades data in från rum uppvärmda av Trombeväggar och maximering av ljusinsläpp. I varje rum registrerades data med hjälp av temperatur-, fuktighets-, tryck- och ljussensorer. Denna information användes sedan för att registrera rumstemperaturen inomhus och beräkna den mängd solstrålningen som träffade väggarna. Följande analys visade sedan att Trombe-väggar håller en mer stabil inomhustemperatur jämfört med

maximering av ljusinsläpp, även om det ofta är på bekostnad av ljusstyrka. Dessutom gjordes ett försök att simulera inomhustemperaturen i ett Trombeväggs-rum med hjälp av en numerisk modell.

Den kvantitativa analysen kompletterades i ett andra steg med en kvalitativ analys där invånare från två byar i Ladakh intervjuades. Alla intervjuade bodde i hus uppvärmda av Trombeväggar och hade begränsad tillgång till elektricitet. Intervjuerna visar att Trombe Walls ger upphov till en flertal positiva effekter, från att öka

inomhuslufttemperaturen och förbättra luftkvaliteten till att höja välbefinnandet hos en familj.

Därefter följer en ekonomisk analys av att installera en Trombevägg för att se om det är ekonomiskt lönsamt för bybor. Trombeväggar analyseras som en

investering med hjälp av ekonomiska värderingsverktyg som IRR-metoden, Internal Return of Rate. Under antagandet att en Trombväggs livslängd är minst 20, är det en lönsam investering givet att en avkastningskravet på kapital är lägre än 17 %.

Slutligen avslutas denna kandidatexamen med en kort diskussion om hur kvaliteten på de insamlade uppgifterna kan förbättras, samt förslag till framtida förbättringar av Trombeväggar. Möjliga lösningar presenteras som kan hjälpa till att göra Trombeväggar till en mer tilltalande värmelösning, och göra det möjligt för

(4)

1. Introduction

1.1 Background

Ladakh, a region nestled in the foothills of the Himalayas in the northern-most part of India, presents an interesting case for the adoption of passive solar technology. Ladakh is characterized by a harsh desert climate. Winters are severely cold and large amounts of energy are needed to survive. Additionally, Ladakh is situated at a very high altitude, with villages located at 3500m to 4500m above sea level, which makes it difficult for them to receive basic commodities such as food and electronics from other parts of the country. During the winter months, the only two roads leading to Ladakh are closed due to heavy snowfall, leaving air transport as the only way to access the region (1).

With winter temperatures that plummet to -40 degrees centigrade (2), and roughly 320 sunny days a year, Ladakh presents an ideal environment for harnessing solar energy (3). Furthermore, Ladakh is not connected to the national power grid, and depends on a large hydropower station to power its capital city, Leh and nearby villages (4). Villages in more desolate parts of the region receive no access to central electricity, and often rely on stand-alone diesel generators or heating stoves as their energy source. Traditionally, the people of Ladakh have relied on a mixture of fuelwood, kerosene, cow dung and Liquefied Petroleum Gas (LPG) to heat their homes. However, each of these sources of fuel has their own drawbacks. They are expensive and some cause poor indoor air quality. With these disadvantages in mind, passive solar technology could prove to be a potential solution for people in Ladakh. There are advantages with passive solar technology. Previous research suggests that it has low variable costs, it is renewable and environmentally friendly (5).

However, the main drawbacks of solar technology are its unreliability, high initial cost and the costs of storing solar energy (6). Furthermore, critics say that often solar technology has not developed enough to act as an independent heating source, and is therefore dependent on additional heating solutions to provide enough warmth throughout the year (7).

Solar thermal technology is categorized into either active, or passive solar technology. Active solar energy technology creates energy by converting the sun’s rays into usable energy, often with the help of solar panels or other mechanical devices. In contrast to this, Passive solar technology uses the sun’s energy to heat or cool living spaces directly, without the aid of mechanical devices (8). This thesis focusses on a type of Passive Solar Technology, Trombe Walls. Their potential advantages and disadvantages will be explored through quantitative, as well as socio-economic, approaches.

(7)

1.2 The Energy Situation in Ladakh

The energy situation in Ladakh has improved significantly in recent times. Thirty years ago, there was very little access to electricity, and the few people that had access relied on small, stand-alone diesel generators (9).

In 2003, the government of India built a 45 megawatt (MW) hydro power plant, and expanded the local power grid, electrifying the capital city, Leh, and neighboring villages (10). This created enough electricity to power Leh through most of the day, although on most days, there are power outages for one or two hours during the early afternoon. However, this might change with the Indian government’s new project to connect the Himalayas to the national grid (11). Having allegedly pledged 11 000 crore rupees, (15.1 billion SEK), the government plans to connect the state of Ladakh, and the neighboring state Jammu and Kashmir, to the national power grid (12).

(8)

However, not everyone in Ladakh is happy with the government’s plan to connect Ladakh to the power gird. Many people fear that big companies will invade Ladakh and drain the state of natural resources, polluting the land for the local inhabitants and destroying the fragile local eco-system, already endangered by commercial interests (16).

Furthermore, most of the power generated is meant to be transported to the rest of India, providing further disincentives for local Ladakhis to support the new power grid plan. Although the new plan promises to improve access to electricity in Ladakh, many people are skeptical about the overall impact for Ladakh (17).

Ultimately, the future of Ladakh is uncertain, and dependent on how well politicians can contain large companies from exploiting Ladakh’s natural resources.

1.3 Problem Discussion

Traditionally, many households in Leh have heated their homes using a mixture of wood, kerosene, LPG, diesel generators and cow dung. This has stemmed from the poor energy situation in Ladakh, forcing inhabitants to resort to fuel options that cause negative externalities.

Firstly, fuel is expensive and causes a significant economic burden for many villagers in Ladakh. Many villagers work as day laborers during the summer months, but struggle to find work during the cold winter months. Many people living in villages earn around 120 000 rupees per year (16 000 SEK) (9). According to local sources in the region, it is common to spend around 10 000-20 000 rupees per year on fuel, (1300-2600 SEK), which is a noticeable part of an inhabitant’s annual salary (9). Additionally, fuelwood in Ladakh is expensive, with vegetation being scant in the desert climate. Kerosene, LPG and diesel all have to be imported from outside Leh, and during the winter months when fuel is needed the most, only shipment by air is possible, which provides a significant additional cost for fuel sources. (18)

Secondly, burning fuel indoors gives rise to dangerous particles in the air, which can cause several respiratory diseases. This is also a gendered question, since women are disproportionately affected by this problem, as they are most often responsible for the cooking and heating at home. (19) Therefore, finding a clean, reliable source of fuel becomes an important social issue, as well as a heating issue.

Thirdly, heating solutions that involve burning fuel provide an unstable indoor climate. According to local villagers, when burning fuelwood, the stove needs to be stoked with wood every 15 or 20 minutes, forcing inhabitants to continuously fuel the fire or risk the temperature dropping dramatically.(9) This becomes impossible at night, which means that during most nights, temperatures can drop to zero degrees centigrade, or even freezing.(20) Hence, to improve the living conditions of the Ladakhi people, both in terms of indoor climate as well as socially, there is clearly a need for a new clean and sustainable heating technology. These negative heating factors, in combination with a local climate that is well adapted to embrace solar technology, make Ladakh a fruitful region to conduct this study in.

This study focusses on one type of solar technology, passive solar technology. There are several types of passive solar technologies, and this thesis compares

Trombe Walls to the direct gain approach. Trombe Walls are walls that trap solar energy using energy dense material and air pockets, and then slowly release the stored solar energy into the room during the day.(21) In comparison, the direct gain

approach maximizes window area to let as much sunlight into the room as possible to heat and light up the room. (22) Another type of solar technology, active solar

(9)

solar technology, and hence a less feasible option given limited fiscal resources of many Ladakhi citizens.

1.4 Purpose of Study

The purpose of this thesis is to investigate the effectiveness of installing Trombe Walls in Ladakh. This will be investigated through a comparative study with direct gain technology, from the perspectives of their relative effectiveness in heating, social appreciation and financial viability. Hence, the aim is to draw well-rounded

conclusions about Trombe Walls and how they can be used as heating sources. Hopefully, this thesis will serve as an guideline on Trombe Walls for prospective investors or house owners, in order to see if it is worth installing a Trombe Wall.

1.5 Research Questions

RQ 1. What is the effectiveness of a Trombe Wall as a heating solution in Ladakh? RQ 2. What is the social appreciation of installed Trombe Walls among users? RQ 3. What is the financial viability of Trombe Walls as a heating solution for the inhabitants of Ladakh?

1.6 Design of Project

This project was conducted with the help of two colleagues, Leo Björkman and Rita Nordström. Together, we collected data for both the quantitative and qualitative parts of the study. However, this thesis is written solely by undersigned, and hence the text will vary from using the personal pronoun “I” when I want to voice my own opinion, to “we”, when I am describing a part of the project that we conducted together. Furthermore, all graphs were created using the same data set, and hence they might also appear in their report, titled A Study on the Effectiveness of Passive Solar

Housing in Ladakh.

1.7 Possible Contributions

With our data collection and subsequent analysis, this thesis provide an insight into how effective Trombe Walls are as a heating solution for the inhabitants of Ladakh. Hopefully, this can be used in future decision-making when choosing what heating solution to implement. Furthermore, I show that there are sustainable ways to heat a home using solar energy, which may prove important in future housing projects that wish to reduce their environmental impact. We also build a simple model of the

(10)

EEB, Energy Efficient Buildings, Attached Greenhouse Techniques or Advanced Window Control Systems. (23) Additionally, the regional area in which the Trombe Walls will be discussed is limited to Ladakh, India. Passive solar technology naturally varies in effectiveness depending on the local climactic conditions around the world, but that will not be taken into consideration in this thesis.

1.9 Partner Organization, LEDeG

Ladakh Ecological Development Group is an environmental NGO in Leh, Ladakh. LEDeG works towards promoting “ecological and sustainable development which harmonizes with and builds on traditional culture”. (24) All the quantitative data was collected from rooms in LEDeG’s hostel, and the interviews were organized with the help of LEDeG staff. With over twenty years of knowledge and work with sustainable development and energy questions in Ladakh, LEDeG was an invaluable partner organization for this project.

(11)

2. Literature Review

This section gives a brief overview of the existing research on passive solar technology. First, sources of information used in the thesis are discussed. This is followed by a brief introduction to different types of passive solar technologies, and an in-depth review of Indirect Passive solar technology and Direct Passive solar technology. Lastly, this section focusses on Trombe Walls and how they function.

2.1 Sources of Information

In order to better under how Trombe Walls and passive solar technology work, we have considered earlier research on the topic. Much of our information stems from the article, Trombe Wall vs. Direct gain: A Comparative Analysis of Solar Heating

Systems, written by Wray and Balcomb.(25) This article describes the fundamentals

of both different solar technologies, and goes on to compare them in a further analysis. For more specific knowledge regarding Ladakh, we consulted a manual developed by several Ladakhi NGOs on low energy consumption design- written by Franck Clottes called L.E.C Integration Design Manual gives an in-depth account of building energy efficient houses in the state of Jammu & Kashmir and Ladakh.(26) The manual focuses specifically on Trombe Walls and other solar technologies that reduce energy demand. The book is set in the region of Ladakh and provides an excellent source of information for this study. This source, with general information about Ladakh, was complemented by key interviews. These three main sources served as the bulk of the literature but were complemented by additional sources such as articles on solar irradiance in Ladakh.

2.2 Overview of Passive Solar Technologies

There are two main types of Passive Solar Technologies prevalent in Ladakh, direct gain technology and Trombe Walls. Direct gain involves south-facing windowpanes that can admit as much sunlight as possible to heat a room (27). In comparison, Trombe Walls are designed so that solar radiation heats pockets of air located

between an inner and outer wall. This energy is then slowly transferred into the room, either by convective currents through openings in the wall or by conduction through the wall.

There are several advantages of passive solar technologies according to established research. In their paper, Wray and Balcomb describe how passive solar technology is an affordable way to provide heating (25). They discuss how passive solar energy is environmentally friendly, causing no pollution or environmental degradation. Furthermore, passive solar technology does not require connectivity to a

(12)

2.2.1 Direct gain Technology

Direct gain technology involves constructing rooms so that they absorb as much sunlight as needed. To successfully implement the direct gain technique, one must adhere to four important factors according to the LEC integration manual. (26)

Firstly, the windows must be oriented towards the south, with a maximum deviation of ±20° from south. Depending on if the room is used mainly during the night, it is preferable to orient the windows 20° southwest from south, in order to maximize solar absorption during the afternoon. Conversely, if the building is mainly used during the day, the windows may be oriented 20° southeast from south, to maximize solar absorption during the morning.

Secondly, it is important to avoid any obstructions that might prevent the incidence of sunlight. Near obstructions, such as buildings or trees, might be possible to move in order to construct direct gain housing. However, one must also be aware of distant obstructions, such as mountains or hills. These obstructions are impossible to move, and therefore require forethought and careful planning when constructing the house.

Thirdly, the size of the direct gain windows must be optimized in order to ensure that the maximum amount of sunlight can be collected. One must strike a balance between allowing the maximum amount of sunlight to enter the room, whilst also minimizing heat loss through the windows during nighttime when temperatures cool outside. To gain a rough estimate of the optimal size of direct gain windows, an equation has been developed by local NGO’s in Ladakh.

𝑅 '𝑔𝑙 𝑓𝑙+ = 𝑔𝑙𝑎𝑧𝑖𝑛𝑔 𝑎𝑟𝑒𝑎 𝑓𝑙𝑜𝑜𝑟 𝑎𝑟𝑒𝑎 = 𝑔𝑙 𝑓𝑙 (2.1) Where

• 𝑓𝑙 is the floor area

• 𝑔𝑙 is the net area of windows which sunlight can enter through, usually defined as the area of glazed glass of a window.

A rough estimate of 𝑔𝑙 shows that it should be approximately 60 % of the total area of the window. Depending on where in Ladakh the house is being built, there is an optimal R-factor range, which depends on several factors such as the sun’s path and the average temperature.

Lastly, the level of thermal mass in the room must be optimized for what time during the day the room is used. Thermal mass is the ability of material to absorb and store energy. (28) If a room has a high thermal mass, this will increase the capability of the room to store energy, but also increase the time it takes for the room to heat up. Thus, if the room is mainly used during the night, more thermal mass should be added in order to ensure that the room is warm during the night. On the other hand, if the room is mainly used during the day, less thermal mass should be added so that the room will quickly heat up during the first hours of the room’s occupation.

Overall, direct gain technology is simple to implement and is relatively

inexpensive. This makes direct gain technology accessible to a wide variety of people. However, the efficiency of direct gain greatly decreases during cloudy days.

Furthermore, ensuring that a direct gain room has enough thermal mass can be expensive due to material costs. If the room does not have enough thermal mass, the indoor temperature may fluctuate greatly, causing temperatures to become too hot during the day and very cold at night.

(13)

2.2.2 Trombe Walls and Indirect gain Technology

Indirect gain technology aims to store solar energy and slowly heat up a room through the redirection of energy. The most prominent example of indirect gain technology is the Trombe Wall. Trombe Walls are outer walls made by a dark, energy dense

material, covered by a glazing that works much like greenhouse glass. As sunlight hits the Trombe wall, it heats up the dark, energy dense material and thus indirectly the air between the glazing. The air naturally rises as it becomes warmer and is then funneled back into the house through the use of an airshaft, heating the interior of the house and creating a flow of air through different rooms. The Trombe wall also transfers heat through the inner wall of the house, providing additional warmth. (29)

To construct a house with a Trombe Wall, one still needs to consider most of the key factors of direct gain technology. Buildings need to be facing south, with a deviation up to ±20°, whilst additionally avoiding any obstructions that can impair the path of sunlight. However, the methods differ when it comes to thermal mass and the size of windows.

When building a Trombe Wall, the layers of glazing presents an optimization problem. Additional layers provide better insulation, however at a greater cost with diminishing returns. Furthermore, the dark wall needs to be made of a material with very high specific heat capacity to store as much heat as possible. Additionally, the wall needs to be of a certain thickness, as it determines how fast energy may pass into the inside room. When the sun shines, we can imagine an energy wave that hits the outer side of the Trombe Wall. This energy wave will slowly pass through the outer wall to the inner wall to heat up the inside of the room. It is important to construct the

(14)

where, • 𝑥 = 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑤𝑎𝑙𝑙 [𝑚] • 𝜆 = 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 [_&∗(% ] • 𝜌 = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑎𝑙𝑙 [_&)*_!] • 𝐶_$= 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 [_()*∗(]+ ] • 𝑇 = 𝑇𝑖𝑚𝑒 [ℎ𝑜𝑢𝑟𝑠]

Usually, for walls made of mud or cement, the acceptable thickness of the wall is around 20 to 30 centimeters.

Furthermore, apart from the time it takes for the heat wave to travel through the wall, the amplitude of the heat wave will also be reduced as it travels through the wall. This will reduce the amount of energy available in the room, and depends on the thickness and materials of the wall. The damping phenomenon is given by the

following relationship. 𝐷𝑎𝑚𝑝𝑒𝑛𝑖𝑛𝑔 = 𝐸𝑥𝑝 ⎝ ⎜ ⎛ −𝑥 ∗ > 𝜋 24 ∗ 3600 ∗_{𝜌 ∗ 𝐶}𝜆 $ ⎠ ⎟ ⎞ = 𝐴. 𝐴_/ (2.3) where, • 𝑥 = 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑤𝑎𝑙𝑙 [𝑚] • 𝜆 = 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 [ % &∗(] • 𝜌 = 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑎𝑙𝑙 [_&)*_!] • 𝐶$= 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 [_()*∗(]+ ] • 𝐴_. 𝑎𝑛𝑑 𝐴_/ = 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 ℎ𝑒𝑎𝑡 𝑤𝑎𝑣𝑒𝑠 [%]

Most of the Trombe Walls in Ladakh are built with a double-glazed window in the middle. This is to let sunlight into the room to illuminate the living space. However, as with most parameters in a Trombe Wall, one must find the optimal size of the window, balancing enough luminance with heat loss at night. This glazing area referred to here is of the window in the middle of the Trombe Wall that lets in light, and is not to be confused with the glazing area that covers the rest of the Trombe Wall. The equation for window size in Trombe Walls is given by the same relationship as for the window size in direct gain walls.

𝑅 '𝑔𝑙 𝑓𝑙+ = 𝑔𝑙𝑎𝑧𝑖𝑛𝑔 𝑎𝑟𝑒𝑎 𝑓𝑙𝑜𝑜𝑟 𝑎𝑟𝑒𝑎 = 𝑔𝑙 𝑓𝑙 = 10 𝑡𝑜 12 % (2.4) • 𝑓𝑙 is the floor area

• 𝑔𝑙 is the net area of windows which sunlight can enter through, usually defined as the area of glazed glass of a window

The optimal value is within 10-12 % for the Ladakhi region, according to L.E.C

Integration Design Manual.

Ultimately, the building of a successful Trombe Wall involves several different factors. One must carefully adhere to orientation, avoid obstructions, thoughtfully

(15)

choose materials and make sure that the wall is of optimal thickness. If successful, the Trombe Wall reaps several advantages. Due to its storage of solar energy, a Trombe Wall can provide heat day and night, providing a stable temperature throughout the day, unlike direct gain technology. Additionally, it can also be effective during one or two cloudy days due to its ability to store thermal energy. However, Trombe Walls are more complicated and expensive to build compared to direct gain windows. Furthermore, the room may become too dark and people may not like the distinct aesthetic of the Trombe Wall.

2.3 Comparison of Direct gain and Trombe Walls

Existing research on the subject suggests that Trombe Walls are usually better at sustaining a stable indoor temperature. This is due, in part, to the extra thermal mass, as well as the possibility to determine the thickness of the Trombe Wall, which enables control of when the energy wave hits the indoor room. Hence, Trombe Walls can sustain a stable temperature that direct gain technology usually cannot. However, Trombe Walls rooms are slow to heat up, unlike direct gain room that can reach much higher temperatures during the day and are significantly brighter. Trombe Wall rooms are dark unless a window is added. Trombe Wall are much more expensive than direct gain technology and are difficult to build. What is best for the citizens of Ladakh was not clear, and hence the need for further exploration was needed.

(16)

3 Method

3.1 Research Design

When planning this study, the aim was to investigate how Trombe Walls compared to direct gain technology in terms of efficiency, social appreciation and financial

viability. Thus, a mixed methods approach was adopted – with a quantitative and qualitative study. In the quantitative study we built and installed sensors in rooms heated by Trombe Walls, and then used the data we collected to study room

temperature och brightness. In the qualitative study we asked villagers in Ladakh how Trombe Walls impacted them, in terms of indoor climate and fiscal savings, as well as if it contributed to saved time. To do this, we visited two villages in Ladakh, Palam village and Khardung village, where a LEDeG project had built Trombe Wall houses after a flash flood in 2010 and interviewed people living in houses heated by Trombe Walls. Together these two approaches combine to give a better understanding of Trombe Walls, in terms of how much energy is saved, as well as how it affects peoples’ lives. Mr. Chemet Rigzin was also interviewed, in order to gain a deeper understanding of the socio-technical landscape of Ladakh. Mr. Rigzin is the lead engineer at LEDeG, an established inventor who has worked in Ladakh for over fifteen years and has extensive knowledge within the field of solar technology, as well about the region of Ladakh.

3.2 Quantitative Method

In the quantitative study, we compared the way Trombe Wall and direct gain technologies influenced indoor climate. The standard way of doing this is to collect data that gives an indication of how comfortable a room is for the individual. (30) We therefore measured temperature, pressure, humidity and luminance in rooms with DG or TW technologies over a period of time. We recorded the data using nine sensor kits that we constructed with a microcomputer unit, Arduino Nano, that were connected to compatible sensors. The sensor kits where then placed in nine different rooms in LEDeG’s hostel, and data was collected.

3.2.1 Designing and Building Measuring Equipment

We decided to build our own sensor kits due to budgetary restraints. This had both advantages and disadvantages. By assembling the sensors ourselves, we were able to afford nine sensor kits, which otherwise would have been too expensive for this project. Additionally, we could design our sensor kits to the exact specifications of each room.

However, there were also several drawbacks in constructing our own sensor kits. They broke easily. This led to a reduced amount of collected data since we had to spend several days fixing sensor kits or waiting for products to arrive so we could fix our sensors. All this required a lot of work and took a long time. We spent a lot of time soldering, connecting wires and writing code for our sensor kits to work. Additionally, the electronics purchased were not of the highest quality, which led to sensors suddenly breaking without an apparent reason.

(17)

Building the sensor kits started by choosing a microcontroller. A

microcontroller is a programmable computer chip that can control other sensors or electronic equipment (31). The Arduino nano was chosen, which is a small

microcontroller with an ATmega328P processor, because of its low energy consumption and ability to handle 3.3 volts logic and 5 volts logic. The ability to support both 3.3, and 5 volts logic means that the Arduino can function with sensors that run on both 3.3 volts and 5 volts. Additionally, low energy consumption is important because the sensor kits were powered by 2200 mAh LiPo batteries and needed to run as long as possible.

We used the following sensors described in table 1.

Table 1: Sensors

Name Measurements Accuracy Sensors used per

kit DHT22 (32) Temperature and Humidity 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦 ± 5% 𝑇𝑒𝑚𝑝 ± 0.5 ℃ 5 TSL2561 (33) Luminous Intensity 0.01 𝐿𝑢𝑥 1 BMP280 (34) Pressure, Humidity, Altitude, Temperature 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 ± 1 ℎ𝑃𝑎 𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦 ± 1 % 𝐴𝑙𝑡𝑖𝑡𝑢𝑑𝑒 ± 1𝑚 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 ± 2

Using a circuit board, we soldered together the Arduino with the sensors. We also used an SD card reader and an electronic clock module to save our data and record the time of each measurement.

(18)

The wiring diagrams in figure 3 depicts how to connect all the sensors and modules to the Arduino.

Figure 4: Wiring diagram

1. DHT 22 (Temperature and Humidity sensor)

2. BMP 280 (Temperature, Humidity, Altitude and Pressure sensor) 3. TSL 2561 (Lux sensor)2

4. DS3231 (clock module) 5. Micro SD Card reader 6. Arduino Nano

7. Pull-up resistors

3.2.2 The Hostel

(19)

LEDeG hostel was built approximately ten years ago as a way for travelers to visit Leh whilst minimizing their carbon footprint. The hostel aims to have as low environmental impact as possible and relies on solar energy for indoor heating and warm water. The toilets are water free, eco-friendly compost pits and the food is vegetarian and locally sourced. The hostel is situated on a small hill, with Trombe Walls on the southern side to absorb as much sunlight as possible (seen in the picture). The hostel has six rooms on each floor, with three rooms in each wing. The two rooms at the end of each wing on the bottom floor has half Trombe Walls, and the two rooms above those have only glass windows, with no Trombe Walls. The last eight rooms are identical rooms with full Trombe Walls. There is no other source of heat than solar energy, and a 1.2 kW SPV plant nearby powers all electrical sockets. (35)

The following image is a floor plan of LEDeG’s hostel, room 1 being Direct gain or half Trombe Wall rooms, 2 being storage rooms, 3 being Trombe Wall rooms, 4 being the common area and room 5 the entrance.

From the outside, a Trombe Wall looks like this. Here we can see the dark wall behind the window glass, except for in the center of the wall, where a window was built to let in more light into the room.

(20)

From the inside, the Trombe Wall rooms in LEDeG’s hostel looks like this.

The Direct gain rooms are designed in the following way, slightly larger than the Trombe Wall rooms and filled with windows.

Figure 8: A Trombe Wall from the inside

(21)

Lastly, the half-Trombe Wall rooms are a mix of the Trombe Wall technology and Direct gain technology.

3.2.3 Installing the sensors in the Hostel

We installed our sensors in LEDeG’s hostel, where we had access to eight rooms of which four had Trombe walls, two had half Trombe Wall and two were Direct gain rooms. In each Trombe Wall room, we placed five temperature sensors, two air pressure sensors and one light sensor. We wanted to collect enough data to get a sense of how the Trombe Wall functions, and therefore we placed the five temperature sensors in the Trombe Wall and the room. The two pressure sensors were placed in the air hole in the Trombe Wall in order to see if the heating and circulation of air caused a perceptible pressure difference. Lastly, the light sensor was placed on a small table near the center of the room to see how bright the room was. The red dots in the figure represent temperature sensors, whilst the blue dot symbolize pressure sensors.

(22)

In the two Direct gain rooms on the upper floor, sensor placement was similar to that of the Trombe Wall room, the difference being the two sensors placed inside the Trombe Wall. Hence, the direct gain room had three temperature sensors, two pressure sensors and one light sensor were placed. These rooms were used as control rooms as they only had glass windows without any Trombe Walls.

The last two rooms had a half Trombe Wall, half glass wall set-up. We placed out four temperature sensors, two pressure sensors and one light sensor. These rooms were used as an extra source of information, in order to validate the results of the previous rooms.

3.2.4 Advantages and Disadvantages of our Set-up

There were several advantages to our set-up, as well as some weaknesses. One considerable advantage was that all the rooms were located in the same building, which helps us control for some of the main confounding factors when interpreting the results, such as the thickness and material of the walls, the orientation of the building and the way that the local environment shades the building. A factor such as wind would normally be important to consider, but we can assume that on average, the wind will affect the temperature in each room by the same amount. Therefore, when we then compare the differences between the rooms, we assume that the effect of wind can be ignored.

Another positive aspect of our set-up was that we had two or more of each type of room, so we could compare the results of similar rooms. This enabled us to improve the reliability of our measurements. We had four Trombe Wall rooms, and this would in general decrease the standard deviation of our measurements by one half. 1 √𝑛 = 1 √4= 1 2 (3.1)

Lastly, one major advantage with our set-up was that the hostel did not use any other source of heating other than solar energy. This means that we did not have to adjust for any other source of heating, and that we could equate all increase in indoor temperature with solar energy stored by the Trombe Wall.

One disadvantage of our set-up was that the four rooms at the end of each wing, the half Trombe Wall rooms and the direct gain rooms were slightly bigger than the Trombe Wall rooms. This is an important factor to consider because a fixed amount of incident sunlight equates to a certain amount of energy. If this energy is spent heating a larger room, it is natural that this room will become cooler than a smaller room. Therefore, the room size is an important factor we take into consideration whilst performing a comparative analysis of the different types of rooms. The four rooms at the end of each wing had their outer wall in thermal contact with the outdoor temperature, whilst all the Trombe Walls only had Thermal contact with other rooms at each side. This is an additional factor to take into consideration, as it will create further heat loss for the four rooms, which we will have to take into consideration whilst conducting our analysis.

3.3 Qualitative method

We conducted seventeen interviews in two Ladakhi villages, Pallam and Khardung. Pallam is a small village located 10 kilometers from Leh, nestled between a large mountain range and the Indus River. The village was severely affected by the flash floods in 2010, where most houses were washed away or destroyed. (36) As a part of

(23)

the restoration, LEDeG received money to rebuild the village and built solar passive houses, in a project that ran from 2012-2015. (36) In the same project, passive solar houses in Khardung village were also built. Khardung village is located 2 hours from Leh by car, in the Nubra district. This village is at an altitude of 4000m above sea level, and has harsh living conditions, due to the cold temperature as well as the lack of vegetation and trees. Fuelwood needs to be imported from nearby villages, forcing many villagers to resort to burning cow dung to heat their homes.

3.3.2 Structuring the Interviews

When planning our interviews, we adopted the guidelines set out by the book, Den

kvalitativa forskningsintervjun, translated as The qualitative research study. (37) We

adopted a semi-structured interview process, where we encouraged the respondent to share their opinions and thereby gain further insights into how a Trombe Wall can affect people. Two research questions guided the interview process.

1. Does a Trombe Wall affect how people perceive their indoor climate? 2. Does a Trombe Wall affect how people allocate their time?

We then translated the two research questions into twenty-five interview questions, which we then proceeded to ask the interviewees. The full interview schedule with all questions can be found in the appendix. We recorded the interviews, and then

transcribed all recordings.

3.3.3 Reliability and Validity of Results

To gain as reliable results as possible, we asked all the interviewees the same question from our interview sheet. However, since we opted for a semi-structured interview method, we initiated more of a discussion, which caused many people to drift away into their own topics. Hence, all questions were not asked in the same order, nor were they worded in exactly the same way.

We also tried our best to question a varied sample size, both in relation to gender and age. All interviewees lived and worked in small villages in Ladakh consisting of a few hundred people. Out of a total of seventeen respondents, ten were women and seven were men. The average age of all respondents was forty-four years. To maximize variety of age, we grouped people into four categories depending on how old they were and their gender. We defined four categories, young males, young females, all less than thirty years of age, and older males and older females, all above thirty years of age. Looking at our results, we had three young males, one young female, three older males and nine older females. The largest group is clearly older

(24)

3.4 Research bias

The interviews were conducted with the help of an interpreter, and at risk of several potential biases. We tried our best to acknowledge these beforehand to mitigate their impact on the interviews.

Respondent

• Acquiescence bias, also known as yes-saying, is a bias stating that people are more likely to agree or disagree, depending on how the question is

formulated.(38) To minimize the impact of this bias, we made sure to word our interview questions as neutrally as possible. We also carefully went over the interview questions without interpreter beforehand to clarify and avoid any confusion.

• Social desirability bias is a bias stating that respondents would like to answer in a way that will be viewed favorably by others. (39) This bias we saw as a potential threat, since we were strongly associated with LEDeG. LEDeG had built all the Trombe Wall houses years previously, and therefore we suspected that respondents would be hesitant to discuss any negative aspects about their housing, in case it would reflect negatively upon them in the eyes of LEDeG. To avoid this bias as much as possible, we tried to distance ourselves from LEDeG. We also made it clear that we specifically wanted to hear the good things and the bad things about living with Trombe Walls, so that we could get a better picture of how it impacted people.

Researcher

• Confirmation bias, a will to analyze responses in a way to strengthen one’s own beliefs.(40) This was another realistic threat for us, since we employed an interpreter, and she might add her own interpretation of the responses in order to make the answers confirm what we wanted to hear. Furthermore, we also had to take into account that we could probably seek to confirm the answers the interpreter gave us. In order to avoid this, we were careful to strictly tell our interpreter to translate everything the respondent said word by word, without adding anything that can help us understand. This was not immediately adopted by our interpreter but was gradually improved throughout the course of the interviews and is one factor we took into consideration whilst analyzing results. Furthermore, we also employed reflexive practices in order to minimize our own confirmation bias. • Leading questions and wording bias, a bias caused by the wording of the

questions or how the questions are formulated. (41) To avoid this bias, we were carefully thought through how we worded our questions. We also attempted to employ open-ended question that would encourage respondents to speak openly, and shy away from leading questions.

(25)

4 Quantitative Results

In this section, we give an overview of the quantitative results we obtained in our study. We start of by discussing the outdoor climate of Ladakh to gain an

understanding of the heating requirements that are needed. This is contextualized and compared with other countries with the help of Heat Degree Days, an established method of measuring heating need. (42) We then go on to discuss the incident sunlight on the building, and the potential energy that could be harnessed. With the heating requirements and potential energy source identified, we discuss the

temperature graphs of the rooms with Trombe Walls, Direct gain technology and half Trombe Walls.

4.1 Outdoor Climate and Heat Degree Days

To analyze the outdoor climate, we used an established method for gauging heating requirements, Heat Degree Days. HDD shows how many degrees multiplied by the amount of days a building needs to be heated, which gives an insight into how much energy is required to heat houses in similar climates around the world. This approach needed sufficient temperature data. Fortunately for us, LEDeG had set up a weather station on the hostel’s premises, giving us access to data from September of 2019 onwards, with one measurement every hour.

Using this data, we can see that the average temperature near the hostel during February is -4.1 degrees centigrade. During the day, between 08:00 and 18:00, the average temperature is -2.6 degrees, whilst during nighttime, between 18:00 and 08:00; the average temperature falls to -5.6 degrees.

To quantify the heating need for warming a room to an acceptable indoor temperature in this climate, we use the concept of Heat Degree Days, HDD. HDD uses a set base temperature, in our case 18 degrees Celsius, to see how many degrees, during how many days, a house needs external heating to achieve the base

temperature of 18 degrees. Using hourly temperature measures, we can calculate HDD using the following sum,

𝐻𝐷𝐷 = $(𝑇

_!

− 𝑇

_"

)

#$# "%&

(4.1)

where 𝑇₀ is the base temperature, and 𝑇₁ is the temperature at each hour, and the sum of the difference of the two temperatures is evaluated for all 696 hours of February 2020. Given that we are looking at the month of February, this means that during the month, the total amount of degrees a building needs to be warmed up by is the value

(26)

period. (43) Using data that we received from Sweden’s metrological institute SMHI, we can see that the Stockholm region had a heating requirement of 430 HDD. Kiruna, situated in northernmost Sweden, required 794 degree-days whilst Lund, in southern Sweden, had 363 degree days during February 2020.(44) Hence, we can see that the heating demand for Leh could somewhat be likened to the heating demand of northern Sweden, and is also very similar to that of Alaska. In Alaska, with 677 HDD, the average energy consumption per capita spent heating one’s home for a month is 632 kWh. (45)

4.2 Incident Solar Radiation

Ladakh is renowned for its abundance of sunny days, with an average of 320 sun days per year. (3) This allows for plentiful use of solar energy, which is the hostel’s only source of space heating. Hence, we can assume that the increase in temperature of the rooms is wholly accounted for by solar energy. Therefore, by getting a grasp of the incident solar radiation in Ladakh, we can see how much potential energy there is to harness. According to synenergy.com, the average solar irradiance per day in Leh, Ladakh, for the month is February is 3.77 kWh per square meter of vertical area. (46) Hence, in the month of February, the total solar irradiance would equal 109 kWh per square meter. According to the L.E.C Integration Manual, the average solar irradiance for the month of February is 125 kWh per square meter.(26) Comparing this to the energy consumption of Alaska 632 kWh, we can see that approximately six square meters of windows would be required to cover the monthly energy consumption of an average home in Alaska. This is of course impossible, as we assume a 100 % energy conversion ratio but it still serves as an indication of the possibilities of solar

radiation.

109 kWh or 125 kWh per square meter, per month, is an average value of solar irradiance for the city of Leh. However, we wanted to obtain the amount of solar energy specifically available at the site of the hostel. Due to budgetary restraints, we were unable to purchase a pyranometer, which is used to measure incoming solar irradiance. We opted for a cheaper option and bought a lux sensor.

Lux is a measure of brightness and is defined as the total amount of light that falls on a surface, as perceived by the human eye. (47) Luminous intensity is not a measure of energy and cannot directly be translated into watts. However, after doing some research on the subject, we discovered that there are ways to approximate the solar energy of the sun using Lux values. Based on the experimental research of Peter Michael, he describes in his paper, A Conversion Guide: Solar Irradiance and Lux

Illuminance, a way to convert lux from sunlight to watt. From his research, we

attempted to convert our total lux measurements to watt using the following equation derived by Peter Michael.

𝑊𝑎𝑡𝑡 =

1

119.97 ∗ 𝐿𝑢𝑥 (4.3)

Unfortunately, we were unable to record a full month’s data due to our sensors malfunctioning. However, we saw that on sunny days the lux values seemed to reach approximately the same values, and on cloudy days they were much less. Therefore, we scaled our data by the amount of sunny and cloudy days to receive a total amount of Lux for the month of February.

(27)

In the following graph, our measured Lux values are plotted out against time.

Figure 12: Recorded Lux values

We lack data for the first days of February, the eleventh to the sixteenth and from the nineteenth to the twenty-second. Thus, we have data for nineteen out of twenty-nine days in February. Assuming that the missing days are equal to the average of the observed days, and converting Lux to Watts, we receive 77.3 kWh for the month of February. This is lower than the average value of 109 kWh proposed by synergy.com but serves to give an indication of the amount of solar energy that is available in the region. In India, the cost of purchasing 77.3 kWh of space heating in February of 2020 would be approximately 150 to 200 rupees. (48) This may be an overestimate, as we assume all the sunlight will be used to heat the room. On the other hand, we do not take into the account the addition insulation a Trombe Wall provides, which may balance out this factor However, it does give an indication that one square meter or Trombe Wall may be able to save upwards of 150 rupees per month (20 SEK/month) in heating costs. Given that a Trombe Wall for each room is about 6-7 square meters, this would imply that a whole Trombe Wall could save around 1000 rupees per month (130 SEK/month), and 12 000 rupees per year (1600 SEK/month).

(28)

If we take a closer look at rooms nine, four and three, we see that on average, the temperature seems to oscillate around a mean temperature of 17.4 degrees Celsius. This is slightly colder than the legally acceptable indoor temperature supplied by a third party in Sweden, which is twenty degrees Celsius. (49) With the addition of a small radiator, the average temperature could possibly reach twenty degrees. However, twenty degrees Celsius is the lowest temperature allowed, not the lowest average temperature. Hence, from these graphs it is clear that Trombe Walls contribute to a more comfortable indoor temperature, however, alone they are not enough to heat up a single room to the legal temperature a housing landlord must provide in Sweden.

Comparing the Trombe Wall rooms to the rooms heated by Direct gain

technology, we see that the temperature is much more volatile when a Trombe Wall is not present.

Figure 13: Temperature of Trombe Wall rooms

(29)

In these rooms, the extra windows allow more sunlight to directly pass into the room, heating the room to very high temperatures during the day. However, these windows also allow the warm air to escape during the nights, and the temperatures plunge below ten degrees. This creates a more hostile indoor environment, where the days become too hot and the nights too cold. From these graphs we can distill on of the most important factors of the Trombe Wall, the ability to store and slowly dissipate energy into the room. Both of these rooms have the same amount of window area, and are located very close to each other, implying that on average, they will receive the same amount of incident solar radiation. Additionally, the floor and the inner walls are made of the same material. However, since the Trombe Wall manages to store the heat unlike the Direct gain rooms, a much more comfortable indoor temperature is achieved.

(30)

Comparing these two types of rooms with half Trombe Wall rooms, we see that a half Trombe Wall resembles Direct gain rooms much more than Trombe Wall rooms. Unfortunately, our sensor kits malfunctioned so we were only able to collect data for

parts of the month. Still, we can see that the temperature varies wildly, plunging below ten degrees at night and hitting thirty degrees during some warm days.

Looking at the average temperatures of the three different types of rooms, we see that they differ substantially, with the Trombe Wall being the warmest and the half Trombe Wall the coldest.

Figure 16: Temperature of Half Trombe Wall rooms

(31)

This may be because the Trombe Wall can retain the heat, which brings up the average temperature, unlike in the other rooms, where much heat escapes during the nights. What is most interesting to note is that the Direct gain Room has a higher average temperature than the half Trombe Wall Rooms. This seems counter intuitive, seeing as one would assume the half Trombe Walls would retain more heat than use windows. However, these results must suffer from the fact that we only had partial data from the half Trombe Walls. Therefore, a likely explanation for the Trombe Wall rooms is simply that we did not collect sufficient data, which thus skewed the results. One thing that also needs to be taken into consideration is that the half Trombe Wall rooms and the Direct gain rooms were on the side of each wing. Hence, they had two walls in contact with the cold air outside, whilst the Trombe Wall rooms only had one wall. This would naturally lead to less heat flow out of the room, thus raising the average temperature.

Looking at the average temperature graphs for the three types of rooms, we see that yet again, the Trombe Wall rooms hold a more stable temperature compared to the other two rooms.

(32)

degrees) is 21.64 degrees. Contrasting this to the average temperature difference for the direct gain rooms, we find that it is lower, at 19.00 degrees.

Arguably the most important measurement is the amount of time a Trombe Wall manages to sustain a comfortable indoor temperature. In this case, we define a comfortable indoor temperature as between 15 and 25 degrees. This is low in comparison to other countries around the world, where indoor temperatures seldom drop below 20 degrees, but will suffice in this study. Below follows a graph of the average temperature of the Trombe Walls and direct gain rooms, plotted with the constraints of 15 and 25 degrees.

We can see that the Trombe Wall rooms are mostly between 15 and 25 degrees, whilst the direct gain room varies much more. Computing the percentage of time each room spends in the zone of preferred temperature, we see that the Trombe Wall rooms spend 83.2 % of their time in that temperature range, whilst the direct gain room only spends 22.7 % in the temperature range.

Figure 19: Indoor and outdoor temperature

(33)

This is shown visually by the following graph, where a binary description of whether a room is in the desired temperature range is plotted against time. Note also that no data before the fourth of February was collected, and therefore that section is blank. This clearly shows the most effective aspect of the Trombe Wall, the ability to sustain a comfortable room temperature throughout the day. However, this does come at an extra cost compared to direct gain technology. Furthermore, Trombe Walls by

themselves have a hard time fulfilling inhabitants’ energy needs, as they often need to be complemented by other sources of heating, thereby not reducing equipment costs, only fuel consumption costs.

Overall, we can reinforce the conclusion that with the same amount of incoming solar energy, a Trombe Wall is more effective at distributing energy throughout the day. This means that the average temperature in the room will increase, as well as never dropping or rising to far above the range of comfort.

(34)

5 Model of a Trombe Wall

Based on the qualitative and quantitative results Trombe Walls seem to viable heating solution in Ladakh, but how would a Trombe Wall fare in different climates? This section takes a brief look at this question by analyzing a simple model of a Trombe Wall that we constructed. First the model is discussed, how it has been constructed and the input variables. Then, results from the model are compared with our measured values in an attempt to gauge the accuracy of the simulation. Lastly, the model is rerun with different climactic data in an attempt to see how the Trombe Wall would fare in a different climate.

5.1 The Construction of the Model

We constructed our model with the help of Microsoft Excel, setting up a large system of equations that linked together two input variables, outdoor temperature and solar irradiation, with the output value, indoor temperature of the Trombe Wall room. When constructing this model, it must be noted that we decided to make several simplifications of reality in order to ensure that we could finish the model in time. We studied the temperature of a single room, heated by sunlight passing through a

Trombe Wall. We ignored bordering rooms and treated the Trombe Wall and the room as a closed system. We also adopted the adage, “All models are bad, but some are useful”, and went about constructing the model accordingly.

The model consists of 2 input variables, that produce one output value. In addition, we have also input parameters that can model can be easily adjusted. In total, we have 47 input parameters that can be tweaked, ranging from the dimensions of the room to the material of the walls to the absorptivity of the window. Here is the list of all input parameters.

1. 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑊𝑎𝑙𝑙 (𝑚^2) 2. 𝑇𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝐴𝑟𝑒𝑎 𝑜𝑓 𝐶ℎ𝑎𝑛𝑛𝑒𝑙, (𝑚^2) 3. 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑇𝑟𝑜𝑚𝑏𝑒 𝑤𝑎𝑙𝑙 (𝑚^3) 4. 𝐼𝑛𝑙𝑒𝑡 𝐴𝑟𝑒𝑎, 𝐴𝑖𝑛 (𝑚^2) 5. 𝐿𝑒𝑛𝑔𝑡ℎ (𝑚) 6. 𝑂𝑢𝑡𝑙𝑒𝑡 𝐴𝑟𝑒𝑎, 𝐴𝑜𝑢𝑡 (𝑚^2) 7. 𝑊𝑖𝑑𝑡ℎ (𝑚) 8. 𝐿𝑒𝑛𝑔𝑡ℎ 𝑓𝑟𝑜𝑚 𝑔𝑙𝑎𝑠𝑠 𝑡𝑜 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝑚) 9. 𝐻𝑒𝑖𝑔ℎ𝑡 (𝑚) 10. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑅𝑜𝑜𝑚 (𝑊/ 𝑚 ∗ 𝐾) 11. 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑤𝑎𝑙𝑙 𝑜𝑝𝑝𝑜𝑠𝑖𝑛𝑔 𝑇𝑟𝑜𝑚𝑏𝑒 − 𝑤𝑎𝑙𝑙 (𝑚^2) 12. 𝐺𝑙𝑜𝑏𝑎𝑙 𝐻𝑒𝑎𝑡 𝐿𝑜𝑠𝑠 𝐶𝑜𝑒𝑓𝑖𝑐𝑖𝑒𝑛𝑡 (𝑊/𝑚^2 ∗ 𝐾) 13. 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠𝑖𝑑𝑒 𝑤𝑎𝑙𝑙 (𝑚^2) 14. 𝑊𝑖𝑛𝑑𝑜𝑤 𝐴𝑟𝑒𝑎 (𝑚^2) 15. 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑓𝑙𝑜𝑜𝑟 𝑎𝑛𝑑 𝑟𝑜𝑜𝑓 (𝑚^2) 16. 𝑈 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑊𝑖𝑛𝑑𝑜𝑤 (𝑊/𝑚^2 ∗ 𝐾) 17. 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝐴𝑖𝑟 𝐺𝑎𝑝 (𝑚^3) 18. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝐽/ 𝑘𝑔𝐾) 19. 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝐴𝑖𝑟 (𝑘𝑔/𝑚^3) 20. 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑑𝑥 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝑚) 21. 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐻𝑒𝑎𝑡 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝐴𝑖𝑟 (𝐽/ 𝑘𝑔 ∗ 𝐾) 22. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐷𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝐴𝑖𝑟 (𝑚^2/𝑠) 23. 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝑚) 24. 𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑜𝑓 𝐴𝑖𝑟 (𝑚^2/ 𝑠) 25. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐷𝑖𝑓𝑓𝑢𝑠𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝑚^2/ 𝑠) 26. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝐴𝑖𝑟 (𝐾) 27. 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐻𝑒𝑎𝑡 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝐽/ 𝑘𝑔 ∗ 𝐾) 28. 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑔 (𝑁/𝑘𝑔) 29. 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝑘𝑔/ 𝑚^3) 30. 𝑃𝑟𝑎𝑛𝑡𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑎𝑡 20 𝐷𝑒𝑔𝑟𝑒𝑒𝑠

(35)

31. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝐺𝑙𝑎𝑠𝑠 (𝑊/ 𝑚𝐾) 32. 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐻𝑒𝑎𝑡 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝐺𝑙𝑎𝑠𝑠 (𝐽/𝑘𝑔 ∗ 𝐾) 33. 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑊𝑖𝑛𝑑𝑜𝑤𝑝𝑎𝑛𝑒 (𝑚) 34. 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑔𝑙𝑎𝑠𝑠 (𝑘𝑔/𝑚^3) 35. 𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑊𝑖𝑛𝑑𝑜𝑤 (%) 36. 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑔𝑙𝑎𝑠𝑠 (𝑚) 37. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑊𝑖𝑛𝑑𝑜𝑤 38. (𝑊/𝐾) 39. 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝐺𝑙𝑎𝑠𝑠 (𝑚^3) 40. 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑇𝑟𝑜𝑚𝑏𝑒 𝑊𝑎𝑙𝑙 (𝑊/ 𝐾) 41. 𝐷𝑎𝑚𝑝𝑒𝑛𝑖𝑛𝑔 𝐹𝑎𝑐𝑡𝑜𝑟 42. 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝐸𝑛𝑒𝑟𝑔𝑦 𝑃𝑎𝑠𝑠𝑖𝑛𝑔 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑊𝑎𝑙𝑙 (𝐽) 43. 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑚𝑎𝑠𝑠 (𝑚^3) 44. 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐿𝑜𝑠𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑎𝑡 𝐼𝑛𝑙𝑒𝑡 𝐶1 45. 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐻𝑒𝑎𝑡 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑚𝑢𝑑 𝑤𝑎𝑙𝑙 (𝐽/ (𝑘𝑔 ∗ 𝐾) 46. 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐿𝑜𝑠𝑠 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑎𝑡 𝑂𝑢𝑡𝑙𝑒𝑡 𝐶2 47. 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑚𝑢𝑑 𝑤𝑎𝑙𝑙 𝑘𝑔/𝑚^3 48. 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑓1

Given these input parameters, we can tweak the model, so it fits our needs, changing the size of the room, adjusting the material the room is made of and so forth.

We start our calculations with the incident solar radiation on the windowpane. We assume a transmittivity of 0.9, which we use to calculate the energy in

𝜏 = 0.9 → 𝐸

_"f

= 𝐸

_ghg

𝜏 (5.1)

This solar radiation then proceeds to enter the airgap and heat the Trombe Wall. We assume that all energy hits the outer layer of the wall. This outer layer of the wall is in thermal equilibrium with the air in the airgap, as well as the rest of the wall, acting as a storage of energy. The energy balance between the outer wall and the air is given by a simplification of Fourier’s Law,

𝑄

_ihfj

= 𝑘𝐴(𝑇

_k

− 𝑇

_l"m

) (5.2)

Additionally, we calculated the heat loss through the window based on the temperature of the air gap and the outdoor temperature. This is of course a

simplification, as we first of all assume that all energy is absorbed into the wall, and then the wall heats the air. Additionally, we approximate a double paned window as a single pane by calculating its total U-value. However, these simplifications were deemed necessary to simplify calculations. The heat loss through conduction is modelled by the following equation

(36)

To calculate the heat transfer coefficient, we also needed to Prantl number, the ratio of momentum diffusivity to thermal diffusivity. We looked up the Prantl number for air at 20 degrees given the air pressure of 650 hPa, as measured by our pressure sensors. (50) Using the relation proposed by Churman and Cho, we calculated the heat transfer coefficient for a vertical plane. (51)

ℎ =

ℎ

𝑘

⎝

⎜

⎛

0.825 +

0.387𝑅𝑎

t & #

T1 + U0.492

_{𝑃𝑟 )}

&#$

W

u $

X

.

⎠

⎟

⎞

v

(5.5)

With the heat transfer coefficient, we calculated the total heat loss through the windowpane

𝑄

_ihfw

= ℎ𝐴(𝑇

_k"fjhk

− 𝑇

_hpgq"jr

) (5.6)

Hence, we now achieved energy balance between energy into the Trombe Wall’s air gap and energy out. However, this was achieved with the following simplifications. We assume that no heat is lost to surrounding materials and nor do not take the wind into account

The air in the airgap is warmed as it comes in thermal contact with the outer wall, causing a flow of air. The velocity of air flow is modelled with the help of Ruiz et al.’s equation, derived in A Calculation Model for Trombe Walls and its use as a

Passive Cooling Technique. (52)

𝑣 = ]

2∆𝑃

𝜌(𝐶

_&

a

𝐴

r

𝐴

_"f

b

v

+ 𝑓

𝐻

_{𝑒 + 𝐶}

_v

a

𝐴

r

𝐴

_hpg

b

v

d

& v

(5.7)

The pressure difference can either be calculated from thermal specifications of air and temperature differences or measured. Since we had access to pressure measurements from our sensors, we decided to utilize our data to complement our model.

The total air flow dictated how much air would flow into the room through the holes in the top, and how much air will be sucked in through the bottom hole. At each time step, the air had a certain temperature. Herein hides an important simplification, as we assume that all the air in the airgap is of constant temperature. Physically, this deviates from reality as on one hand we assume that the temperature difference causes the air to rise, and on the other hand we assume constant air temperature in the air hap. However, we assume that the energy from the outer layer of the Trombe Wall heats up the air in the air gap, as well as the air sucked in from the room, to a constant temperature. We calculate a pseudo air velocity, and then use that air flow to

(37)

Energy also passes from the outer layer of the Trombe Wall into the rest of the Trombe Wall and towards the room. The time it takes for the energy to pass through the Trombe Wall is given by the lag time, which is more thoroughly discussed in the literature section.

𝐿𝑎𝑔 𝑡𝑖𝑚𝑒

_klxx

=

1

2 ∗ 𝑥 ∗ g

24 3600 ∗ 𝜋 ∗

_{𝜌 ∗ 𝐶}

𝜆

o

= 𝑇 (5.8)

Additionally, from the perspective of the room, some heat is lost in the process of the energy wave traveling through the wall, and this is modelled by the dampening factor, which has also been touched upon in the literature section.

𝐷𝑎𝑚𝑝𝑒𝑛𝑖𝑛𝑔 = 𝐸𝑥𝑝

⎝

⎜

⎛

−𝑥 ∗

g

𝜋

24 ∗ 3600 ∗

_{𝜌 ∗ 𝐶}

𝜆

o

⎠

⎟

⎞

=

𝐴

&

𝐴

_v

(5.9)

Hence, we now have an inflow of air energy into the room, from both the Trombe Wall and the airflow, which we use to calculate an energy balance in the room. The temperature of the room is calculated by the total energy in the room, divided by the specific heat constants and mass of the air in the room and all the thermal mass.

5.2 Comparing Calculated Results with Measured Results

Based on the results from our model, we obtain the following graph for the indoor temperature of the room, which we plot together with our measured results against the hours of February on the x-axis.

A Study in Solar Housing Technology: The Impact of Trombe Walls in Ladakh

A Study in Solar Housing

Technology:

The Impact of Trombe Walls in

Ladakh

Abstract

Sammanfattning

Table of Contents

1. Introduction

2. Literature Review

3 Method

4 Quantitative Results

𝐻𝐷𝐷 = $(𝑇

− 𝑇

)

(4.1)

𝑊𝑎𝑡𝑡 =

1

119.97

∗ 𝐿𝑢𝑥 (4.3)

5 Model of a Trombe Wall

5.1 The Construction of the Model

𝜏 = 0.9 → 𝐸

= 𝐸

𝜏 (5.1)

𝑄

= 𝑘𝐴(𝑇

− 𝑇

) (5.2)

ℎ =

ℎ

𝑘

⎝

⎜

⎜

⎜

⎜

⎛

0.825 +

0.387𝑅𝑎

T1 + U0.492

𝑃𝑟 )

W

X

.

⎠

⎟

⎟

⎟

⎟

⎞

(5.5)

𝑄

= ℎ𝐴(𝑇

− 𝑇

) (5.6)

𝑣 = ]

2∆𝑃

𝜌(𝐶

a

𝐴

𝐴

b

+ 𝑓

𝐻

𝑒 + 𝐶

a

𝐴

𝐴

b

d

(5.7)

𝐿𝑎𝑔 𝑡𝑖𝑚𝑒

=

1

2

∗ 𝑥 ∗ g

24

3600 ∗ 𝜋 ∗

𝜌 ∗ 𝐶

_{𝑃𝑟 )}

_{𝑒 + 𝐶}

_{𝜌 ∗ 𝐶}

_{𝜌 ∗ 𝐶}