The impact of rotational speed and water volume on textile translational motion in a front-loading washer

Abstract

Textile motion in a front-loading washer has been characterized via video capturing, and a processing system developed based on image geometric moment. Textile motion significantly contributes to the mass transfer of the wash solution in porous materials, particularly in the radial direction (perpendicular to the rotational axis of the inner drum). In this paper, the velocity profiles and residence time distributions of tracer textiles have been investigated to characterize the textile dynamics in a front-loading washer. The results show that the textile motion varies significantly with the water volume and rotational speed, and that the motion path follows certain patterns. Two regions are observed in the velocity plots: a passive region where the textile moves up with low velocity and an active region where the textile falls down with relatively high speed. A stagnant area in the residence time profile is observed. This corresponds to the passive region in the velocity profile. The stagnant area affects the mechanical action, thus influencing washing efficiency and textile performance. The findings on textile dynamics will help in the development of better front-loading washers.

Keywords

mass transfer textile motion velocity profiles washing machine

In a drum washer, the cleaning process is a soil transfer process, involving significant deformation of clothes and three-dimensional motion of both the cloth and fluid. However, the modern drum washer is typically seen as a ‘black box’; the design and optimization of the washer is usually through full-scale trials rather than a theoretical understanding of the textile and fluid dynamics. The optimization is often less than ideal, leading to washer designs that cause resource waste and environment pollution.¹ Inadequate understanding of the process can lead to soil deposition and textile deformation.^2–4 The rotation of the inner drum during washing is to enhance the mass transfer within the textiles.⁵ The inner drum rotation can be alternated between clockwise and anti-clockwise directions to increase the interaction of the fluids and textiles, resulting in soil loosening from the textiles. Therefore, it is important to study the mechanics of textile rotation with the inner drum.

A great number of recent studies have focused on factors affecting mass transfer in porous soft materials. Common factors include agitator speed, cloth/liquor ratio, hydrodynamic flow, textile porosity, temperature, stroke angle, initial placement and the concentration of detergent.^6–13 Several mathematical models of the washing process have been developed for both top- and front-loading washers.^14–16 However, accurate information about soft porous material properties (porosity, stiffness, etc.), the dynamic viscosity of the mixture and textile/liquid flow patterns is required for modeling. These parameters cannot be seen as constants due to the dynamic nature of the washing process.¹⁷ Therefore, many of these models were established based on oversimplified assumptions,^18,19 due to a lack of information about the interaction of the fluid and fabrics, and the properties of wet textiles. Textile dynamics in a front-loading washer are not only influenced by the wash load, but also the rotational speed and water volume. Hence, to develop an optimized washer, it is necessary to study the effect of rotational speed and water volume on the textile dynamics, including the textile velocities and residence time distribution.^17,20,21

Many researchers have focused on factors that influence the textile flow pattern and wash performance, such as washing efficiency, wrinkling and shrinkage.^22–29 For example, a high-speed camera was used to record the fabric movement and the outlines of the textiles’ motion were recorded for data analysis.^30–32 Textile motion was classified into four patterns: sliding, falling, rotating and centrifugal. Complex motion patterns including sliding, falling and rotating led to greater washing efficiency and more severe abrasion of the textiles. However, it is not clear how the textile motion was tracked. Mac Namara^11,17 used the technique of positron emission particle tracking to investigate the textile dynamics in a front-loading washer for different washing load sizes, but the experiments had to be performed in a special environment due to radioactivity.

In this study, we developed a new and more practical method to record textile motion based on image geometric moments. We investigated the effects of washing rotational speed and water volume on the velocity distribution and residence time of textiles. The information obtained deepens our understanding of the mechanism of textile motion and provides guidance for the optimization of washing parameters for front-loading washers.

Experimental methods and materials

Recording fabric movement

In order to analyze fabric movement, a video capturing and processing system was developed. This system consists of three parts: the video capturing rig, the image processing system, and the input and output system. The video capturing rig used a high-speed GoProHERO 5 camera at a speed of 120 frames per second.

In the experiments, a tracer textile with a specific color (yellow) was used. The images of the textile captured by the high-speed camera were RGB color images. The RGB image depends on the reflected light, which is affected by the lightness.^33,34 This image is not appropriate for further processing. The HSV (hue saturation value) color space describes perceptual color relationships more accurately than the RGB color space, and it is computationally simple. The HSV color space enables the identification of specific colors more easily by hue. Thus, we convert the captured RGB image into the HSV space. The HSV image is then converted into a binary image by segmentation with a threshold. As the tracer textile is yellow, the corresponding threshold range in hue is between 30–50. Finally, the mass centroid of the connected region of the tracked textile is calculated based on geometric moments using equations (1) and (2)³⁵:

m_{ij} = \sum_{x, y} (I (x, y) \cdot x^{i} \cdot y^{j})

(1)

u_{ij} = \sum_{x, y} (I (x, y) \cdot (x - \bar{x})^{j} \cdot (y - \bar{y})^{j})

(2)

Where

m_{ij}

is the raw moment of a raster image,

I (x, y)

is the pixel intensity of the image,

u_{ij}

is the central moment of the image, and

\bar{x}

and

\bar{y}

are the center of gravity of the binary image.

Using binary images, the gray value function $I (x, y)$ becomes:

\begin{matrix} I (x, y) = {\begin{matrix} 1 & Object \\ 0 & Background \end{matrix} \end{matrix}

(3)

The coordinates $\bar{x}$ and $\bar{y}$ of the center of gravity of the binary image are simply calculated by the raw moments of first order $m_{10}$ and $m_{01}$ divided by the zero order moment $m_{00}$ , using expression:

\bar{x} = \frac{m_{10}}{m_{00}}

(4)

\bar{y} = \frac{m_{01}}{m_{00}}

(5)

The centroid of the tracer textile was calculated and the motion of the centroid was considered as the motion of the textile. No detergent was added during textile motion observation in order to reduce the impact of bubbles.

Experimental details

Washer

Experiments were carried out in a Haier WH7560P2 modified according to ISO (International Organization for Standardization) 7330:2012 with a capacity of 7 kg. The diameter of the inner drum is 490 mm and the depth is 275 mm. The drum rotational speed was set according to the adjustable range of the washing machine. The water volume was set based on the water level seen in the inner drum. The lowest water volume was set at 6 L when there was no free water in the inner drum; the highest water volume was set at 12 L when the textiles were just completely immersed in water.

Specimens

Cotton pillowcases were placed inside the machine to achieve a 1 kg wash load, the detailed specifications of the pillowcases are show in Table 1. Detailed information regarding the experiments is shown in Table 2 and Table 3.

Table 1.

Specifications of the textile samples

Fiber content	Weave type	Size (cm × cm)	Weight (g/piece)
100% cotton	Plain	50 × 80 (±5)	240 ± 5

Table 2.

Washing parameters with controlled drum speed

Temperature (℃)	Drum speed (rpm)	Water volume (L)	Washing time (min)	Rinsing runs	Rinsing Time (min)
30 ± 2	30/40/50/60	8	30	2	3

Table 3.

Washing parameters with controlled water volume

Temperature (℃)	Drum speed (rpm)	Water volume (L)	Washing time (min)	Rinsing runs	Rinsing Time (min)
30 ± 2	40	6/9/12	30	2	3

EMPA 106 soiled with carbon black and mineral oil was utilized to evaluate washing performance. A total of 10 EMPA 106 samples were included in each experiment. Two of the pillowcases were attached with five EMPA samples each. The IEC (International Electrochemical Commission) 60456 Reference Base Detergent Type A* (no phosphate) was used.

Data analysis

During each rotation period, the inner drum rotation can be alternated between clockwise and anti-clockwise directions, lasting 25 seconds at a controlled rotational speed. Thus, from each experiment, two data subsets were obtained: clockwise and anticlockwise tracer textile locations. The plots obtained from the anti-clockwise and clockwise directions are almost symmetrical. In order to present all data obtained from one experiment, the clockwise data subset was horizontally flipped relative to the axis of rotation of the drum. Thus, the plots present anti-clockwise data and ‘flipped’ clockwise data.

Lagrangian velocities were calculated according to Mac Namara et al.¹⁷and Bakalis et al.³⁶ A polynomial line was generated for a number of successive points as a function of time and the slop of the line at the midpoint of these data was taken as the Lagrangian velocity, u_i, as shown in Figure 1. The number of points ‘n’ used to polynomial was determined by minimizing the least squares error. For example, if there was a sudden direction change in the trajectory (Figure 1), fewer points would be more accurate. The detailed information for and illustration of the velocity calculation can be found in the paper cited above.

Figure 1.

Trajectory of tracer textiles and calculation of Lagrangian velocity.

Eulerian velocities were represented graphically in a user-defined two-dimensional cell grid and the loading area was divided into cells of equal size. The Eulerian data was the time-weighted average throughout each respective cell, as shown in Figure 2.³⁷ Lagrangian and Eulerian velocities depicted in this study are all non-dimensional ratios with reference to the maximum velocity that was observed in the experiments.

Figure 2.

Two-dimensional cell grid and calculation of Eulerian velocity.

Residence time plots represent the average time that the tracer textiles stay in every cell, as defined in the Eulerian velocity calculation.³⁷ These values were calculated as the cumulative residence time divided by the number of passes.

Results and discussion

Effect of rotational speed and water volume on textile speed distribution

Speed distributions for different rotational speeds and water volumes

Figures 3 and 4 present textile speed maps from the front of the washing machine for each experimental condition. The velocity of textile was calculated by combining the velocities in the x and y directions, as in equation (6),

U_{total} = \sqrt{U_{x}^{2} + U_{y}^{2}}

(6)

Where U_x and U_y are the centroid speeds in the x and y directions, respectively.

Figure 3.

Eulerian velocity distribution of textiles with different washing rotational speeds. (a)–(d) Velocity distribution in the x direction and (e)–(h) velocity distribution in the y direction. (i)–(l) Velocity distribution.

Figure 4.

Eulerian velocity distribution of textiles with different water volumes. (a)–(c) Velocity distribution in the x direction and (d)–(f) velocity distribution in the y direction. (g)–(i) Velocity distribution.

The estimated Eulerian velocities are all non-dimensional with reference to the maximum observed velocity, as shown in Figure 3 and Figure 4. The results show that the speed distribution greatly depends on the drum rotational speed and water volume. It is clear that U_x relies on the tangential velocity of the inner drum. For all rotational speeds and water volumes, the highest U_x appears near the top and bottom of the drum, where the tangential velocity of the drum in the x direction is also the greatest, as described in Mac Namara et al.¹⁷ However, due to the falling motion of textiles, U_y is at a maximum at the right-side drum wall, where U_y is greater than the velocity of the inner drum.

The velocity couture plots of textile motion can be divided into two regions: a ‘passive’ region where textiles are lifted up by the drum wall and baffles, and an ‘active’ region where textiles fall freely under gravity. This has also been observed in canned product processes.³⁸ The passive region is situated in the area close to the left-side drum wall, where textiles follow the drum wall’s rotation with a relatively slow speed as the drive force is mainly derived from the rotating drum. When the textiles are lifted to the top of the drum to achieve the dynamic repose angle (the slope at which the textiles will stabilize and come to rest when the inner drum is rotating at a slow speed^5,39,40), the dominant drag force changes from centrifugal force to gravity. The active region is formed when the textiles start falling under gravity and move faster than the rotating drum. Both the rotational speed and water volume have a significant impact on textile speed in the active region. The variation of textile speed in the active region may contribute to the agitation of the textile and water solution at the bottom of the drum, namely, the impact region, thus enhancing the convective mass transfer in textiles.⁵ Overall, the high velocity impact of textiles at the bottom of a front-load washer is likely to result in higher overall flow rates through the textile pores.¹¹

From Figure 3, it could be seen that textile motion took an inverse ‘D’ shape during washing and that the size of the inverse ‘D’ shape increased with the rotational speed, until an ‘O’ shape was formed at 60 rpm. The increased centrifugal force makes the textiles rotate with the inner drum, preventing them from free-falling. However, when the rotational speed increased to 60 rpm, the tangential velocity of the drum is about 1.76 m/s, which is almost equal to the critical centrifuging speed (at the top of the inner drum, centrifugal force is equal to gravity), resulting in the textiles rotating with the drum instead of falling under gravity. The estimated number of turnovers per minute (number of turnovers by the lifter⁴¹ per minute) is shown in Figure 5. It is clear that the estimated turnovers increase with the rotating speed from 30–50 rpm, but decrease at 60 rpm. The washing efficiency of carbon black-stained strips follows the same trends. The carbon black soil is sensitive to rubbing action, while hydrodynamic flow and flexing actions have no significant effect on the removal of carbon black soil.²² As discussed above, textiles rotated with the drum when the rotational speed increased to 60 rpm, resulting in less relative motion between textiles and decreasing rubbing action on carbon black soil.

Figure 5.

Washing efficiency and the estimated number of turnovers with different rotating speeds.

When the water volume increases, the total motion region decreases because textile–fluid interaction forces such as the viscous drag force increase, thus limiting the motion of textiles. It seems that water volume had a greater effect on U_y than on U_x (see Figure 4(a)–(c)), particularly in the active region. This is because U_x is dependent on the tangential velocity of drum, while U_y relies on the free-fall motion of the textiles. Too much water could restrict the lifting action of the lifter on textiles due to the increase of buoyant force, thus affecting the height that the textiles could reach during rotation within the inner drum. The estimated turnovers per minute declined with increasing water volume. However, the washing efficiency is lowest at 6 L, with the value of 40% (47% for 9 L and 44% for 12 L). The soil removal is typically a synergistic effect between chemical and mechanical action.⁴² Surfactants can change the surface energy of water and soil, facilitating the penetration of water between textiles and adhered soil.^43–45 The rinsing of stains is governed by water flow and mechanical action such as rubbing.⁶ Water mainly exists at the bottom of the inner drum. A smaller water volume shortens the reaction time between soil and detergent, resulting in insufficient wetting and emulsification. This weakens the effects of water flow and mechanical action, and thus leads to poorer performance.

Discussions

Force analyses of textiles were carried out to qualitatively explain the difference in textile motions for different rotational speeds and water volumes. In the drum system, the textile motion can be determined by equation (7) at the bottom of the drum and equation (8) at the top of the drum, based on Newton’s second law.^38,46

m_{i} \frac{d V_{i}}{{dt}_{i}} = m_{i} \vec{g} + F_{f} + F_{s} + \sum F_{I}

(7)

m_{i} \frac{d V_{i}}{{dt}_{i}} = m_{i} \vec{g} + F_{s} + F_{c} + \sum F_{I}

(8)

Where

V_{i}

denotes the speed of textile centroid, m_i denotes the wet textile mass,

F_{f}

denotes the textile–fluid interaction force, which includes buoyancy and viscous drag,

F_{s}

denotes the normal force from the inner drum and lifter,

F_{c}

denotes the centrifugal force provided by the rotational drum, and

F_{I}

is the textile–textile interaction force including friction, compression and shear forces.

The movement of textiles is the result of the combined actions of all of the forces involved. When textiles are out of water, there is no textile–liquid interaction. Textile rotation is maintained by centrifugal and friction forces.²¹ The centrifugal force increases with rotational speed, leading to greater height of the textiles. In addition, as U_x depends on the tangential velocity of the drum, it increases with drum speed. These are the reasons why the area of textile motion gets larger with increasing rotational speed. However, when the linear velocity of the drum approaches or exceeds the critical centrifugal velocity, it is possible for the textiles to rotate with the inner drum instead of free-falling.

At the bottom of the drum, textile motion is controlled by gravity, textile–fluid interaction force, and forces arising from interactions and collisions between solids (i.e. the textiles and drum wall). The flow of the textile–liquid mixture is complex due to textile–fluid coupling and interactions between the textiles. The textile–fluid interaction force changes with water volume. In order to explain how water volume influences the textile motion, fabrics are simplified as the fabric plug with radius r, as shown in Figure 6. As textiles move, liquid surrounding the textiles is moved by the textiles. The quantity of liquid that moves with the textile can be referred to as added mass.^47,48 The added mass can be calculated as equation (9). The water in the washing machine is limited, and the water displaced by the textiles is influenced by the water and textile volumes. The added mass increases with water volume before the textiles totally immerse in water. This is due to the increase of displaced water by textiles. The added mass can be calculated as equations (9) and (10). The motion of the fluid results in a lower speed of the textiles and the kinetic energy of the textiles is dissipated into the surrounding fluid. The magnitude of the kinetic energy of a fluid depends on added mass and can be calculated as equation (11).¹⁶ The increase of added mass increases the dissipated kinetic energy. In addition, the buoyance force also increases with water depth as the water displaced by the textiles increases. This decreases the contact between the textile and the lifter, weakening the lifting action of the lifter and lowering the maximum height that the textiles can reach. This might cause more sliding movement instead of free-falling or tumbling.

m_{added} = α \times ρ_{f} V_{f}

(9)

Where, m_t is the mass of the fabric plug,

m_{added}

is the added mass, α is the added mass coefficient,

ρ_{f}

is the water density and V_f is the displaced water volume, which could be calculated by equation (11).¹⁶ Once textiles are completely immersed in water, the V_f equals

(\frac{2}{3}) π r^{3}

.⁴⁹

V_{f} = π h^{2} (\frac{r - h}{3})

(10)

K_{fluid} = \frac{1}{2} (\frac{m_{fabric}}{\frac{m_{fabric}}{m_{added}} + 1}) \times u_{1}^{2}

(11)

Where,

m_{fabric}

is the mass of the textile plug and u₁ is the velocity of the textiles impinging in the water surface.

Figure 6.

Impact of fabric plug.

The textile motion is not only governed by gravity, buoyancy and drag, but also the interaction forces arising from collisions and compressions. These interactions between solids decrease with increasing water volume and vary with the textiles’ location in the drum. The interaction forces and gravity are the dominating forces for the textiles’ motion in the passive region. In this region, textiles pack together and move up at a lower speed. In the active region, there is more space for textiles to cascade down and the interactions between textiles are less significant than in the passive region, resulting in a greater textile speed.

Effect of rotational speed and water volume on residence time

The average time that the tracer textiles stay in a particular region is defined as the textile residence time. This time is a function of the total number of tracer passes in a specific region and also a function of the velocity of the textiles.^17,37 The contribution of the textile motion to convective mass transfer in textiles can be qualitatively indicated by the residence time map. Figures 7 and 8 show contour plots of the residence time for different rotational speeds and water volumes, respectively. Regions with higher residence times are found adjacent to the left-side drum walls. Textiles seem to stay longer at lower heights of the drum. Comparing the residence time plots with the velocity plots, the longest residence time region corresponds to the passive region where the textiles are static or move very slowly. The textiles may slide in this region, leading to lower-impact mechanical action. The magnitude of mechanical action can influence the size of the stagnant inter-fiber regions, where transfer of water/soil only occurs due to molecular diffusion,^5,6 thus affecting the rate of flow thorough the textiles.¹¹ However, water is mainly at the bottom of the drum, thus the slower textile movement in the passive regions might prolong the contact time between stains and detergent, and enhance the interactions between the detergent and soils.

Figure 7.

Residence times of textiles for different rotational speeds. (a) 30 rpm, (b) 40 rpm, (c) 50 rpm and (d) 60 rpm.

Figure 8.

Residence times of textiles for different water volumes. (a) 6 L, (b) 9 L and (c) 12 L.

The residence time for the tracer textiles at the lower left side of the drum decreases as the rotational speed increases, as shown in Figure 7. However, the greater the water volume, the longer the residence time at the lower left side of the drum, as shown in Figure 8. Textile motion is not only governed by gravity, buoyancy and viscous drag forces, but also the interactions between the textiles, and between the textiles and the drum wall. An increase of water volume means a decrease of the textile fraction and an increase in the drag force from water. The greater drag force from the liquid prevents the textiles from moving within the drum, leading to a longer residence time in the passive region.

Conclusions

Textile dynamics in a front-loading washer can be characterized by a video system. The movements of textiles in a front-loading washer are very complex, and significantly depend on the rotational speed and water volume (textiles fraction). Textile motion takes a ‘D’ shape at low or medium rotational speeds, and the size of the ‘D’ shape increases with increasing rotational speed but decreases with increasing water volume. The size of the motion area reflects, to a certain extent, the impact force of the textiles on the liquid and drum during free-fall. Appropriate rotational speeds and water volumes can lead to greater impacts of textiles, forcing the wash solution out of the textiles and resulting in better washing performance due to a higher flow rate through the textiles’ structures.

There are two regions for velocity distribution: a ‘passive’ region where textiles are carried up by the drum wall and lifter, and an ‘active’ region where textiles fall freely. Both the drum rotational speed and water volume significantly influence the configurations of the two regions. The configurations of the two regions are likely to influence soil removal for different stains due to different drag forces in these two regions. It has also been found that the residence time distribution varies significantly with rotational speed and water volume. The longest residence time region matches the passive region in the velocity profiles where textiles seem to be trapped or move at slightly lower speeds, which might decrease the resulting impact action on textiles, resulting in slow flow rates in the textiles. Information gathered during this work is being used to develop a mathematical model that describes the effect of different design parameters on washing efficiency and textile properties after washing, to achieve a better washing process.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Key R&D Program of China (2018YFF0215703), the National Natural Science Foundation of China (71373041 and 61702460), Donghua University (CUSF-DH-D-2017078 & ISN2017-3) and Zhejiang Sci-Tech University (17072067) respectively, the Shanghai Science and Technology Committee (17DZ2202900), Shanghai Summit Discipline in Design (DD18005), and general research projects of Zhejiang Provincial Department of Education (Y201738456).

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