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Energy Procedia 78 (2015) 1495 - 1500

6th International Building Physics Conference, IBPC 2015

Heat and moisture transfer properties of mud wall

Application of simultaneous heat and a moisture transfer model for hygroscopic range to high

humidity conditions

Naoya Moriyamaa* Satoru Takadaa

aGraduate School of Engineering, Kobe University Rokkodaicho Nada-ku, Kobe 657-8501, Japan

Abstract

The mud wall is used traditionally for Japanese houses. For effective use, it is necessary to clarify the moisture performance of it quantitatively. Firstly the sorption isotherm and the water vapor permeability of the mud wall were measured. Secondly, the specimen was exposed to the transient absorption and desorption processes including relative humidity of 90 %. The processes were numerically analyzed using hygrothermal model for the hygroscopic range, and the calculated results agreed with the experimental results, which suggests the validity of the measured moisture properties and of the application of the hygroscopic model to the conditions including high humidity.

© 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibilityoftheCENTROCONGRESSI INTERNAZIONALE SRL

Keywords: mud wall; water vapour permeability; equilibrium moisture content; hygroscopic range; simultaneous heat and moisture transfer

Nomenclature

h: Relative humidity [n.d.], Q': Vapor flow [kg/h], A': Water vapor permeability [kg/m/h/(kg/kg')], X: Absolute humidity [kg/kg']

(p: Porosity [m3/m3], S: Moisture permeation area [m2], l: Thickness [m], R': Vapor transfer resistance [m2h (kg/kg')/kg],p: Density [kg/m3]

c: Specific heat [J/kg/K], r: Phase change heat [J/kg], 0: Temperature [°C], t: Time [s], a: Combined heat transfer coefficient [W/m2/K]

k: [kg/m3/(kg/kg')], v: [kg/m3/K], a': Moisture transfer coefficient [kg/m2/s/(kg/kg')], W: mass [kg] A: Heat conductivity [W/m/K]

F: Equilibrium moisture content [m3/m3], x: Axis [m], w: Mass water content [kg/kg]

Suffix

1: high humidity side, 2: low humidity side, s: incubator side, a: cup side, i: incubator, r: incubator side (reverse)

1. Introduction

Mud wall has been shown to be effective for keeping the room temperature constant by its heat capacity [1]. However, the studies on moisture transfer in mud wall and the moisture characteristics of a room with mud wall are insufficient. Therefore it is essential to clarify the moisture properties of mud wall. For the analysis under a humid climate like as Japan, hygrothermal model for high humidity range is important. Several measured values of water vapor permeability and equilibrium moisture content of mud wall [2, 3] have existed. However, the influence of humidity on the moisture properties has not been studied yet. In addition, the adaptability of the moisture transfer model for the

* Corresponding author. Tel.: +81-78-803-6038; fax: +81-78-803-6038. E-mail address: 141t065t@stu.kobe-u.ac.jp

1876-6102 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL doi:10.1016/j.egypro.2015.11.176

hygroscopic range for high humidity should be studied. From this viewpoints, in this study, the equilibrium moisture content and water vapor permeability are measured for different levels of humidity, and a transient moisture content calculated by the simultaneous heat and moisture transfer model for the hygroscopic range is compared with the experimental results of the absorption and desorption experiment including several patterns of step changes in humidity.

2. Samples of mud wall

The mud wall, a Japanese traditional building material, is made from soil, sand, straw, and water. In this study, mud wall made in Komaki-city, Aichi prefecture Japan, by a craftsperson, as a sample for experiments is used (Table. 1). The density of mud wall is measured from the weight and volume of the sample cut to 10 mm cube. The porosity of mud wall is measured by putting the crushed mud wall into a graduated cylinder with distilled water, and by reading the increased amount as the volume of the substance.

3. Measurement of equilibrium moisture content

Equilibrium moisture content of mud wall is measured by desiccator method. The mass of sample (Fig. 1) in the desiccator is measured by electronic balance (A and D, GX400, with an accuracy of 1 mg). Samples finely crushed (10 g) were used for the specimen. These specimens are exposed consecutively to six levels of humidity formed by saturated salt (Table. 2). Temperature is controlled at 23 °C. Absorption process measurement is started with the samples dried under 105 °C for two hours. Desorption process is conducted with the sample placed in a desiccator containing distilled water for 11 days. The results of the measurement (Fig. 2 & Table. 3) show that the moisture content for the desorption process is larger than that for the absorption process especially for high humidity conditions.

Table. 3 Equation approximated to equilibrium moisture content curve of mud wall for absorption process

h<0.5900

[kg/kg] -3.63 X 10-3/(h+0.33)+1.11 X 10-2

h = 0.5900

-7.01 X 10-4/(h-0.99)+5.39 X 10-3

Table. 1 about sample of mud wall

composition Soil, Sand, Straw, Water

density 1720 [kg/m3]

porosity 0.415 [m3/m3]

thickness 10 [mm]

Table. 2 Humidity in desiccator containing saturated salt

11% 33 % 58 % 75 % 85 % 94 %

LiCl MgCl2 NaBr NaCl KCl KNO3

Fig. 1 Schematics of measurement of equilibrium moisture content (The top hook is snagged to electric balance.)

-0.02 -■

£0.01 -■

Absorption 1st time . -B-Absorption 2nd time ■ ^Desorption 1st time -©-Desorption 2nd time . —Approximate curve

■ —■ ■ ■ ■ i

Humidity [%]

Fig. 2 Equilibrium moisture content of mud wall and its approximate curve for absorption process

4. Measurement of water vapor permeability

Water vapor permeability is measured by the wet cup method based on equations (1) and (2), forming a steady vapor flow. Two specimens are cut (cuboid, 30 mm x 40 mm) from one block of mud wall (called sample A and sample B in Fig. 6). The edge of the sample are sealed by epoxy resin adhesive, and covered by aluminum tape (Fig. 3). The cup is placed on the electronic balance (A and D, GX400, with an accuracy of 1 mg) in an incubator kept at constant temperature and humidity. A wind protection is placed around the cup. The specimens are exposed to a constant temperature and humidity condition formed in the incubator. Measurement interval is 1 minute. When mass change converges to ±5 % of moving average for 5 hours, it is regarded as reaching the steady state.

Fig. 3 Schematics of experimental setup for wet cup method

Q-= Ux -x ),

R'=R' + l +R'

(1, 2)

S R 1 2 s x a

The moisture transfer resistances R's (top surface) and R'a (bottom surface) at both surface of the specimen are determined independently, given as 0.0286, 0.1965 [m2h(kg/kg')/kg], respectively. For the top surface, based on air velocity measurement, the convective heat transfer coefficient determined from the empirical equation [5] is converted to moisture resistance using Lewis relationship (with Lewis number of 1). For the bottom surface, water vapor permeability of static air, 0.0916 [kg/m/h/(kg/kg')] and the thickness of air layer (18 mm) give the value (Fig. 4, 5). The vapor flow is assumed to be one dimensional. As shown in Fig. 6, the water vapor permeability is almost constant for humidity lower than 65 %, while for higher humidity it is significantly higher. Although the equation (1) is based on water vapor transfer, the liquid water movement might account for the increase in high humidity conditions.

0.700 -,

0.600 -

0.500 -

£ 0.400 -

* £" 0.300 -

3"E 0.200 -

o IE 0.100 -

0.000 -

: Upside of mud walls

l / X :

Internal of mud walls

R': Total moisture transfer resistance

: Static air in the cup

Fig. 5 Moisture resistance around the specimen Table. 4 Conditions for measurement of water vapour permeability (23°C)

Air above specimen (% rh) 50 70 90 30 50 80

Specimen (% rh) 30 40 50 65 75 90

Air below specimen (in the cup) (% rh) 11 11 11 100 100 100

Content of the cup Saturated salt (LiCl) Water

Direction of vapor flow down down down up up up

Table. 5 Approximate function of water vapor permeability

[kg/m/h/(kg/kg')]

0.30ShS0.65

0.0233

0.65ShS0.90

2.97 X 10'1 X (h-0.65)2+2.33 X 10-2

5. Possibility of applying a hygroscopic model for high humidity conditions

Here the experiments in which the mud wall specimen is exposed to the absorption and desorption processes given by several patterns of the step change in humidity are conducted, and the numerical analysis based on simultaneous heat and moisture transfer equation for hygroscopic range is performed for the conditions of the experiment.

5.1. Method of absorption and desorption experiment

Before starting the experiment, the specimen is exposed to the thermal environment of the laboratory (17-23°C, 30-40 %rh c.a.) .The specimen is exposed to the air in the incubator for 9 hours at a humidity and then the humidity is suddenly changed, and the exposure continues for 12 hours. The combinations of the humidity are shown in Table. 6. The specimen is 30 mm in width, 40 mm in depth, 10 mm in thickness, and the side surfaces are sealed like as the specimen for the water vapor permeability measurement by the cup method (Fig. 8). The specimen is hung to the electronic balance (Vibra, HTR220, accuracy 0.1 mg) in the incubator with a protection against wind (Fig. 7). The mass is measured with the interval of 5 minutes.

■S 0.050

s 0.045

1 0.035

1 0.025

A Mud wall sample A □ Mud wall sample B X Mean value —Approximate curve

/ ' □

Lj-a--:

0 20 40 60 80 100

Humidity [%]

Fig. 6 Measured water vapor permeability of mud wall and its approximate curve

Fig. 7 Schematics of set up of transient experiment

5.2. Method of analysis

The object of the analysis is 2nd step of humidity (12 hours, 2nd condition in Table 6). Thus, the initial condition is the last condition of the 1st condition. The one-dimensional simultaneous heat and moisture transfer equations for hygroscopic range for the mud wall are shown as equations (3)

to (11). Basically, the dependencies of water vapor permeability and equilibrium moisture content on relative humidity are taken into account based on our measured results as shown in Fig. 2 and 6. Equilibrium moisture content approximate curve for the absorption process shown in Fig. 2 is used. In addition, two

cases of calculations are performed: One is a case with a constant water vapor permeability at 50 % of relative humidity (к* and walues depending on humidity), and the other is a case with a constant к* and walues at 65 % of relative humidity (water vapor permeability depending on humidity) (Table. 8). The measured values of the temperature and humidity of the air around the specimen are inputted to the calculation program. These equations are solved by finite difference method (Fig. 8), time forward scheme with the time interval of 0.01 second.

5.3. Results and discussions

The total mass of the specimen is converted to average moisture content based on a measured mass at 50 % of relative humidity and the equilibrium moisture content curve. Hereafter, the average moisture content based on measured mass and the calculated moisture content averaged for whole the specimen volume are compared.

For the relative humidity combination of 30 and 50 % (patterns A and B), the calculated results agree well with the experimental results. The change of moisture content is slower in patter A. This is because the step change of the humidity in the incubator was accidentally slower than scheduled.

For the relative humidity change from 90 to 50 % (pattern C), the calculated results respond faster than the experimental results and the terminal moisture content is lower. Although the dependency of water vapor permeability on humidity slightly influences, the dependency of the moisture capacity (к* and v) has larger effects. For the relative humidity change from 50 to 90 % (pattern D), the calculated results for the case of considering moisture properties dependence on humidity show good agreement with the experimental results. As a whole, the influence of humidity-dependency of water vapor permeability on the change in moisture content is slight, and that of к*and v is larger.

Next, another approximation of the equilibrium moisture content is tried (Fig. 10), and calculations based on it are performed for patterns C and D (Fig. 11). Using the modified equilibrium moisture content curve, the calculated results of patters C shows better agreement with the experimental results and that of pattern D does not show significant change. The change in equilibrium moisture content between 60 to 90 % rh might account for this.

The calculations using hygroscopic model reproduce the moisture absorption and desorption process including high humidity (90 %) show with a good precision.

dX , дв д2в — гк_+ (cp + rv)_= Д_

dt dt dx2

(Фр +*) =

a dt dt dx2

к=р,\

(dFЛ fdF^ F F( x) (5, 6, 7)

■i\-d-\ ,v=-p11 ш I , = в, '

К X )в У Jx

дв dX

-Я- I ,= a(ûl-ûI),-Я' — \ =0/(xt -x, ) (8, 9)

& 1 & ls v ' s '

, =а{в-в), -Я' =d(X - (¥o, 11)

дв, I )

I r r i

ОХ о r ri

Mud wall Desorption

Absorption

Table. 6 Step humidity change patterns

1st condition (9 h) 2nd condition (12 h)

A 50% 30%

B 30% 50%

C 90% 50%

D 50% 90%

Table. 7 Analysis conditions

Heat conductivity [W/m/K] 0.233[3]

Wind velocity in incubator [m/s] 1.3

Convective heat transfer coefficient [W/(m2 • K)] 9.72

Radiant heat transfer coefficient [W/(m2 • K)] 4.65

Moisture transfer coefficient [kg/m2/s/(kg/kg')] 0.0097

Table. 8 Analysis cases

K, V Water vapor permeability Л '

Casel: basic Depending on RH Depending on RH

Case2: Л' constant Depending on RH Constant at RH (50%)

Case3: к, v constant Constant at RH (65%) Depending on RH

3 0.007 g 0.0065 0.006 0.0055 0.005

-•-Experiment -Analysis(case1: basic ) —Analysis(case3: K, v constant) -♦-Absolute humidity (incubator)

»0.012

8 0.01

S 0.008

0.022 »

0.007 £

0.006 ! £

0.005 I c

0.004 «•

Pattern A (humidity 50% to 30%)

a 0.0065 S

f 0.006 | 0.0055

g 0.005

11 13 15 17 19 21 Time [h]

Pattern C (humidity 90% to 50%)

Experiment —Analysis(case1: basic) —Analysis(case3: k, v constant) Absolute humidity (incubator)

15 17 |Time [h]|

0.009^

0.008 ^

0.007 ^ £

0.006J

0.005«;

Pattern B (humidity 30% to 50%)

Fig. 9 Moisture content of whole specimen

— - 0.018 ^ «

■ Experiment —-Analysis(case1: basic) ■ ■ Analysis(case2: X' constant) — Analysis(case3: k, v constant) Absolute humidity (incubator)

0.004 ■

0.014 ~

0.01 | 0.006

11 13 15 17 19 21 Time [h]

Pattern D (humidity 50% to 90%) (Comparison between results of experiment and analysis)

0.016 ■

»0.014 ■

i Experiment

■ Modified analysis (equilibrium moisture content)

- Not modified analysis

S 0.012

Humidity [%]

Fig. 10 Modification of approximate curve of the equilibrium moisture content

6. Conclusion

For mud wall, one of the Japanese traditional building materials, the sorption isotherm and the water vapor permeability were measured with consideration of dependency on humidity. As the results, for both properties, strong dependency on humidity was found especially for humidity ranges from 65 to 90 % of relative humidity. In addition, the moisture content change in the transient absorption and desorption processes including relative humidity of 90 % were measured. The processes were numerically analyzed using hygrothermal model for the hygroscopic range, and the calculated results agreed with the experimental results, which suggests the validity of the measured moisture properties and of the application of the hygroscopic model to the conditions including high humidity up to 90% of relative humidity.

13 15 17 Time [h]

Pattern C (humidity 50% to 90%)

Experiment

—Modified analysis (equilibrium moisture content) •Not modified analysis

15 17 19 21 Time [h]

Pattern D (humidity 90% to 50%) Fig. 11 Influence of modification in approximate curve of the equilibrium moisture content on moisture content of whole specimen (Comparison between results of experiment and analysis)

References

[1] Yokobayashi, S. Sato, M. A numerical analysis of the hygrothermal environment in renovated house that is constructed of Nakanurituchi and an examination into the educational system on succession of traditional skill. Architectural Institute of Japan. Summaries of Technical Papers of Annual Meeting, pp. 207-208, 2010.

[2] Takada, S. Uno, Y. Ota, M. Study on Hygrothermal Behavior of Mud Wall, Measurement of Sorption Isotherm and Analysis on Indoor Temperature and Humidity. Architectural Institute of Japan. 2014. pp. 177-180

[3] Yokobayashi, S. Sato, M. A study on Heat and Moisture Properties of "Tsuchikabe" that is a specialty of Hyogo prefecture. Architectural Institute of Japan. Meeting for Technical Papers in Kinki. pp. 121-124, 2007.

[4] Miyano, N. Kamiya, K. Mizutani, A. Miyano, A. On The Moisture Adsorption and Desorption of Earth Walls and kind of Earth Product as "Humidity Conditioning Materials". Architectural Institute of Japan. pp. 521-524, 2001.

[5] ASHRAE Handbook - Fundamentals (SI) 9.8, 2009.