Wang Rz_rser_2008_a Review of the Mathematical Models for Predicting Rotary Desiccant Wheel

• Periodical List
• Elsevier Public Health Emergency Collection
• PMC7125891

Energy Build. 2012 Jul; l: 251–258.

An assay of the rut and mass transfer roles in air dehumidification by solid desiccants

C.E.L. Nóbrega

^aDepartamento de Engenharia Mecânica, Centro Federal de Educação Tecnológica – CEFET-Rio – Av. Maracanã, 229, Bloco East, 20271-110 Rio de Janeiro, Brazil

N.C.L. Brum

^bDepartamento de Engenharia Mecânica, Universidade Federal do Rio de Janeiro – P.O.6853, Rio de Janeiro, Brazil

Received 2011 Aug 7; Revised 2012 Mar x; Accepted 2012 Mar 25.

Highlights

► Sensitivity assay of enthalpy recovery wheels to atmospheric weather. ► Sensitivity assay of active desiccant wheels to regeneration temperature. ► Thorough assay of the transport phenomena in solid desiccant air drying.

Keywords: Desiccant, Dehumidification, Enthalpy recovery

Abstruse

Although Passive and active solid desiccant dehumidification have been increasingly investigated and practical in modern air-conditioning design, some discrepancies regarding the effectiveness and the psychrometric representation of the two processes tin exist found in the literature. Passive desiccant wheels are commonly practical every bit an free energy saving technique for vapor-compression cooling systems, unburdening the cooling gyre from treatment the humidity of outside ventilation air stream. In dissimilarity, agile desiccant wheels are designed to promote a thorough dehumidification of outside ventilation air, many times assuasive for the apply of an evaporative cooler and achieving an observable cooling effect, using simply water equally the refrigerant. The present piece of work is comprised of a comparative study of the roles played by heat and mass transfer in passive and active adsorptive air dehumidification. The adequate definition of effectiveness for desiccant wheels is as well discussed.

Nomenclature

a

constant

c

abiding

C _wr

wall specific heat (kJ/kg K)

d

constant

f

desiccant mass fraction

F _i

feature potential

h

convective rut transfer coefficient (kW/chiliad²)

h _y

convective mass transfer coefficient (kg/thou² s)

h _v

heat of vaporization (kJ/kg)

H

enthalpy of air (kJ/kg)

Fifty

length of the cycle (1000)

m ˙

air mass menstruation rate (kg/s)

m _west

mass of the wall (kg)

P _atm

atmospheric force per unit area (Pa)

P _ws

saturation pressure (Pa)

P _wt

wetted perimeter of flow channel (g)

Q

heat of adsorption (kJ/kg)

t

fourth dimension (s)

T

temperature (°C)

u

air flow velocity (m/due south)

Y

air accented humidity (kg H_iiO/kg air)

Y _L

adsorbed air layer absolute humidity (kg/kg air)

W

desiccant humidity (kg of moisture/kg of desiccant)

x

coordinate (chiliad)

Greek letters

λ ₁

auxiliary parameter

λ ₂

auxiliary parameter

H

desiccant wheel feature potential effectiveness

ϕ _w

relative humidity of air layer

ɛ

effectiveness

Subscripts

1

air

ci

cold inlet

co

cold outlet

dw

desiccant cycle

EA

Inbound Apparatus (fan-coil)

er

enthalpy recovery

EXH

exhaust stream

hi

hot inlet

ho

hot outlet

IA

Insufflated Air

in

inlet

LA

leaving apparatus (fan-roll)

OA

exterior air stream

out

outlet

RA

room air

sabbatum

saturation

w

wall

Superscript

*

not-dimensional

1. Introduction

The conscientious control of ambient air moisture content is of concern in many industrial processes, with various applications such every bit in metallurgic or pharmaceutical production. In the ac field, the increasingly concern with sick building syndrome has brought the humidity control into a new perspective. Underestimated ventilation rates commonly result in poor indoor air quality, with a high concentration of volatile organic compounds, smoke, leaner and other contaminants [1]. Epidemiological studies indicate a direct connection between inadequate levels of moisture and the incidence of allergies, in addition to infectious respiratory diseases. Events such as the outbreak of Legionella in 1976 and the more recent SARS (severe acute respiratory syndrome) shed a new light over indoor air quality control and regulations [two].

The standard procedure for reducing the concentration of contaminants is to increase the menses of fresh air, known as ventilation rate. In fact, the required fresh air book per occupant/hour imposed by indoor air-quality standards has typically doubled over the last three decades [three], [four]. However, since the outside fresh air has to be brought to the thermal condolement status, increased ventilation rates likewise imply increased thermal loads, which in turn will demand air chillers with increased cooling capacity. Accordingly, there is a trade-off between indoor air quality and energy consumption, which is as well of main business concern of individual and public sectors.

All-air systems usually utilize multi-zone air-conditioning equipment, with individual reheat coils. Separate single ducts from the air-treatment unit are distributed to each room, which is individually controlled. When the room air humidity exceeds a limit value, the humidistat takes command of the cooling curl, calling for additional cooling and so as to dehumidify the air to the desired level. At this signal, the air is excessively cold to exist supplied to the room, which causes the thermostat to set off the reheat coil, with the objective of bringing the air temperature back to the condolement condition, equally depicted in Fig. 1 . The steepness of the room sensible heating ratio, represented by the dashed line, prevents the fan-curlicue procedure (curve EA–LA) to intersect it, which can simply be achieved past the reheat process. Although it provides a satisfactory individual control of each zone, this constitutes a very energy wasteful blueprint, since the air is continuously cooled and reheated. Moreover, information technology requires both temperature and humidity sensors and controls, which might correspond a meaning increment to the full cost of the system.

Psychrometric representation of standard air-conditioning system.

In addition, the different kinematics of heat and mass transfer makes it very difficult for the humidistat to respond as fast as the thermostat, many times resulting in an ineffective command. The strategy of bringing the air temperature value forth and back is an evidence of the cooling coil disability to simultaneously handle the sensible and the latent components of the thermal load [v].

The previous reasoning expresses a favorable scenario for the application of air dryers, particularly solid sorbent dryers. Adsorption is primarily used for component separation from a gaseous mixture, and is widely employed in the chemical industry. The main advantage is that the fabric pore size can be designed for selective adsorption of a given component, allowing even trace amounts to be removed. In air-conditioning systems, silica-gel has been used to remove the air humidity to an acceptable level, unburdening the cooling whorl from the dehumidification task. Silica-gel is a form of silicon dioxide derived from sodium silicate and sulfuric acid, which has proficient affinity to water vapor and an adsorbing chapters of as much as 40% of its own weight. It can be manufactured every bit a substrate, and practical as a coating to a cylindrical drum, fitted with a micro-channel mesh. This equipment is often referred to as a desiccant wheel. The air dehumidification can be passive or thermally activated, equally explained in the next section.

Although the modeling of desiccant wheels has been addressed by many publications [half dozen], [7], [8], [nine], [10], [eleven], [12], [thirteen], [14], [15], [16], [17], [18], the discussion about the definition of efficiency for desiccant wheels is yet to exist settled [19]. The mathematical modeling used to simulate the dynamic beliefs of the desiccant wheel [16], [17], [18] is briefly described in the next section.

2. The mathematical modeling of air drying by solid desiccants

The modeling of the desiccant cycle is described by the following system of fractional differential equations. The first and second equations account for mass balances within the period channel and the desiccant layer, respectively. Similarly, the third and fourth equations represent energy balances within the menstruum channel and the desiccant layer, respectively.

∂ Y ∂ ten * = Y Fifty − Y ∂ W ∂ t * = λ 2 ( Y − Y Fifty ) ∂ T 1 ∂ x * = T w − T ane ∂ T w ∂ t * = ( T 1 − T w ) + λ 1 ( Y − Y 50 )

(1)

The independent variables are the not-dimensional position

and the not-dimensional time

with the auxiliary parameters given past

λ 1 = ( ( ∂ H 1 / ∂ w ) − ( 1 / f ) ∂ H west / ∂ W ) ( ∂ H ane / ∂ T 1 ) = Q ( ∂ H ane / ∂ T 1 )

(5)

Q is the heat of adsorption, given past [20],

Q = h v ( 1.0 + 0.284 e − 10.28 W )

(6)

and the enthalpy of the air H_one tin can exist written as [21]

where

a = ane.00 kJ / kg ° C d = 2501 kJ / kg c = 1.86 kJ / kg ° C

In that location are 4 equations to be solved [one], and five unknowns, T ₁, T _w, West, Y and Y _L. The equation that relates the absolute humidity of the air in equilibrium Y _L (or its relative humidity) to the moisture content and the temperature of the solid is the adsorption isotherm, and for silica gel RD is given past [22]

ϕ w = 0.0078 − 0.0579 W + 24.16554 W 2 − 124.78 W 3 + 204.2264 W 4

(8)

the pressure level of saturated water vapor given by

P ws = exp 23.196 − 3816.44 T westward − 46.13

(9)

and the accented humidity at the adsorbed layer given by

Y L = 0.62188 p w p atm − p w = 0.62188 ϕ w ( p atm / p ws ) − ϕ westward

(ten)

The periodic nature of the problem implies an iterative procedure. Both initial distributions of temperature and humidity within the solid are guessed, and Eq. [one], presume the form of tridiagonal matrices, as a outcome of the discretization using the finite-volume technique [23], with a fully implicit scheme to represent the transient terms and an upwind conception for the convective terms. By the end of the cycle, both calculated temperature and moisture fields are compared to the initially guessed. If at that place is a difference in any nodal point bigger than the convergence criteria established for temperature and moisture content,

Crit . Conv. temp = T due west ( x , 0 ) − T w ( guess ) ( x , 0 ) T w ( x , 0 )

(xi)

Crit . Conv . mass = W ( x , 0 ) − W ( guess ) ( x , 0 ) W ( 10 , 0 )

(12)

the procedure is repeated, using the calculated fields every bit new guesses for the initial distributions. The average "hot outlet" enthalpy during a bicycle is defined as

Since the bicycle is to store neither free energy nor mass subsequently a complete cycle,

or else

m ˙ h H h i + g ˙ c H c i = m ˙ h 1 p h ∫ 0 p h H h o d t * + m ˙ c 1 p c ∫ 0 p c H c o d t *

(fifteen)

the normalized difference between the two sides of equation [15] is defined as the Heat Balance Error (HBE):

HBE = m ˙ h H h i + chiliad ˙ c H c i − ( yard ˙ h ( 1 / p h ) ∫ 0 p h H h o d t * + thousand ˙ c ( 1 / p c ) ∫ 0 p c H c o d t * ) one thousand ˙ h H h i + m ˙ c H c i

(16)

All cases exhibited extremely low values of HBE (less than 0.01%) at moderate values of grid size and temperature and mass convergence criteria. The results were obtained for a grid of 91 points with a time interval δt of ten⁻³, with a HBE of 0.0022% afterward 173 iterations.

Although the mathematical model previously described is suitable for both passive and active dehumidification, the result of the simulation and the roles played by heat and mass transfers are substantially distinct in each instance.

Consider Fig. two(a), which shows a scheme of a passive desiccant cycle in an ac organization. It operates swinging between the outside air and the frazzle room streams. The exterior air stream is forced through the wheel, flowing through the micro-channels as it exchanges oestrus and mass with the desiccant coated walls. Since the objective is to recover enthalpy, the outside air stream is expected to simultaneously transfer heat and mass to the desiccant material. On the other side, when the room exhaust stream is forced through the bicycle, information technology cools and dries the desiccant coated walls, dumping the oestrus and mass dorsum to the atmosphere. Equally enthalpy is to exist recovered, is expected some enthalpy storage within the desiccant fabric during the adsorptive period, which should exactly friction match the enthalpy deficit during the desorptive period, in steady country functioning. Accordingly, the outside air stream is non expected to undergo an isenthalpic procedure when submitted to passive desiccant dehumidification. In fact, it is expected that the outside air stream will experience an enthalpy decrease between the bike inlet and outlet, every bit depicted by the dashed line in Fig. three .

Schematic representation of active and passive dehumidification.

Psychrometric clarification of active and passive dehumidification.

Moreover, information technology should exist observed that passive desiccant wheels exhibit a limited dehumidification chapters. This can be explained by observing that desorption, which is an endothermic process, is promoted past the low temperature room frazzle stream. In a similar way, at the opposite process, the outside air stream cooling occurs simultaneously to the adsorption. Accordingly, the cooling process is rather ineffective, since adsorption is an exothermic process. It can be concluded that the estrus and the mass transfers play off-setting roles from the enthalpy recovery viewpoint. Heat and mass are expected to have the same management of migration, from the air to the desiccant felt during adsorption, with this direction being reversed during desorption. The enthalpy recovery effectiveness tin can be defined as [xvi]

ε er = H OAin − H OAout H OAin − H EXHin

(17)

If lower levels of absolute humidity are to be achieved, the dehumidification has to be thermally activated, as depicted in Fig. 2(b). When compared to passive wheels, active desiccant wheels incorporate a greater weight of silica-gel, or even uses a different desiccant material, with stronger affinity to water vapor. A high temperature regeneration stream provides the sensible energy required to purge the humidity from the solid, assuasive for a thorough dehumidification. During desorption, heat is transferred from and mass is transferred to the air stream, whereas during adsorption these directions are reversed. As a result, an isenthalpic process is expected when air is submitted to active desiccant dehumidification, such every bit depicted past the continuous line in Fig. 3. Since the efficiency as described by Eq. [17] would be null, Eq. [18] has been proposed [14], [xv] to represent the desiccant wheel efficiency. Notwithstanding, since it does not carry any enthalpy terms, it can only stand for a dehumidification effectiveness,

(18)

The ideal outside air humidity at the wheel outlet would be nil. The deviation of the isenthalpic behavior was suggested as a measure of inefficiency [24], as calculated by Eq. [3]. The adequacy of this definition volition exist addressed at the side by side section.

ε dw two = i − H OA out − H OA in H OA in

(19)

3. Results

iii.1. Passive dehumidification

The analysis will exist first carried out for passive desiccant wheels, considering different weather condition for the room exhaust stream, as described past cases (ane)–(3) in Table 1 . Cases (1)–(3) take increasing temperatures and decreasing humidities for the room exhaust stream, in such a way that the enthalpy is kept constant. The outside air stream condition is kept constant in all situations. Referring to Fig. 2(a), cases (1)–(3) in Tabular array 1 correspond to dissimilar room exhaust conditions (EXH_in), whereas land OA_in corresponds to the condition of outside air. The processes undergone past the outside air ventilation stream are shown in Fig. iv . All results show that the outside air stream enthalpy is significantly reduced, equally it would be expected from an enthalpy recovery technique. The deviation from the isenthalpic behavior is indeed a measure of the enthalpy recovery efficiency. Moreover, the enthalpy recovery for cases (1)–(3) is the same, even though they stand for dissimilar bicycle inlet values for the room exhaust stream humidity and temperature. The physical reasoning behind this result is the same offsetting roles played past heat and mass transfers during the enthalpy recovery. The aforementioned behavior is observed, that is, all the cases exhibit the same value for the enthalpy at the outside air stream outlet. In addition, information technology can be inferred by observing (Fig. 4) that the enthalpy recovery capacity is limited. Comparing the outlet states from (1) to (3), information technology is apparent that a greater humidity reduction (i.eastward. latent energy recovery) is associated to a less meaning temperature drop (i.e., sensible energy recovery). Accordingly, the greater is the humidity reduction, the lesser will be the temperature drop of the outside air stream across the desiccant wheel. Moreover, it should exist observed that adsorption is an exothermic procedure, and the released heat hinders the airstream cooling. This event represents an opportunity for combining desiccants with a phase change cloth, which could deed every bit a heat sink which absorbs the released heat of adsorption, allowing for a more significant sensible energy recovery [25], [26]. This ideal procedure would be represented past the dashed line in Fig. 4, leading to state OA_pc.

Table 1

Influence of room condition over the enthalpy recovery.

	T EXHin (°C)	Y EXHin (kg/kg)	H EXHin (kJ/kg)	T OAin (°C)	Y OAin (kg/kg)
Instance ane	22.0	0.0116	51.6	35.0	0.0253
Case 2	25.0	0.0104	51.6	35.0	0.0253
Case iii	29.0	0.0088	51.half-dozen	35.0	0.0253

Influence of room conditions over the enthalpy recovery, conditions of Table 1.

Table ii shows a similar analysis, all the same taking different outside air conditions (in such a way the enthalpy is held constant) and a stock-still condition at inlet for the air exhaust stream, every bit this is the most common situation in air-workout design. The results depicted in Fig. five show that the enthalpy recovery is constant for cases (OA1) to (OA3), which represent adequately singled-out values for outside air temperature and humidity. Appropriately, the enthalpy recovery efficiency, as described by Eq. [1] is oblivious to the exterior air status.

Table 2

Influence of the atmospheric condition over the enthalpy recovery.

	T EXHin (°C)	Y EXHin (kg/kg)	T OAin (°C)	Y OAin (kg/kg)	H OAin (kJ/kg)
Case 1	25.0	0.0099	32.0	0.0212	56.7
Instance 2	25.0	0.0099	35.0	0.0200	56.7
Instance 3	25.0	0.0099	29.0	0.0025	56.seven

Influence of atmospheric conditions over the enthalpy recovery, Table two.

3.2. Active dehumidification

Equally for agile desiccant rotors, Table iii shows iv different conditions for the regeneration air inlet, with the respective outlet conditions shown in Fig. 6 . The exterior air inlet status is kept stock-still for all four cases. It tin be seen that all cases showroom an isenthalpic beliefs (with a minor departure) between inlet and outlet. This result supports the cooperating roles played by heat and mass transfers in active dehumidification. Fig. vii shows that information technology takes a regeneration temperature of 120 °C to produce an appreciable deviation from the isenthalpic process. Information technology is an indication that the maximum moisture removal chapters of the textile has been reached. Fig. six shows that the efficiency, as described by Eq. [three] is of express use, because deviations such equally exhibited by state (1) would yield a value for the efficiency greater than 100%. The nearly isenthalpic behavior for air dehumidification past active desiccant wheels has been previously observed in experimental [27] and numerical investigations [28].

Table 3

Influence of the regeneration temperature over the dehumidification effectiveness.

	T exhin (°C)	Y exhin (kg/kg)	T OAin (°C)	Y OAin (kg/kg)
Case 1	50.0	0.0120	35.0	0.0253
Case two	60.0	0.0120	35.0	0.0253
Case 3	lxx.0	0.0120	35.0	0.0253
Case 4	lxxx.0	0.0120	35.0	0.0253
Case 5	120.0	0.0120	35.0	0.0253

Influence of the regeneration temperature over the agile dehumidification, Table 3.

Excessive regeneration temperature in agile dehumidification, case 5, Table 3.

An alternative solution for the procedure undergone by the outside air stream through an agile desiccant wheel tin can be alternatively obtained past transforming the conservation equations into a not-linear arrangement of hyperbolic partial differential equations, which are solved using the moving ridge stupor method [29], [thirty], [31]. The solution leads to Riemann invariants, described past Eqs. (xx) and (21) which are named characteristic potentials F _i . Then, values for the potentials effectiveness of the desiccant wheel are assigned, allowing for the potentials F _one,OAout and F _ii,OAout to exist evaluated using Eqs. (22) and (23). The temperature T _OAout and the humidity Y _OAout are then recovered from the potentials F _1,OAout and F _2,OAout, which form a system of not-linear algebraic equations.

F 1 , i = − 2865 ( T i + 273.fifteen ) ane.49 + 4.344 w i k 0.8624

(20)

F 1 , i = ( T i + 273.xv ) 1.49 6360 − 1.127 due west i k 0.07969

(21)

η F 1 = F 1 , OAout − F 1 , OAin F 1 , EXHin − F 1 , OAin

(22)

η F 2 = F 2 , OAout − F 2 , OAin F 2 , EXHin − F 2 , OAin

(23)

This solution has been applied in several desiccant cycle modeling [31], [32], [33], too as in professional simulation tools [34]. Moreover, it has been compared to experimental results, exhibiting a reasonable understanding [35]. Tabular array four shows the results for the values of η _Fane and η _Ftwo respectively set to 0.05 and 0.95, which correspond to a high performance desiccant bike [31]. Information technology tin can be observed a maximum of deviation of 5% from the isenthalpic behavior, for T _EXHxin = 80 °C.

Table four

Influence of the regeneration temperature, Y _EXHin = 0.014, wave analysis ([1], [24]9).

T EXHin (°C)	T OAin (°C)	Y OAin (kg/kg)	h OAin (kJ/kg)	T OAout (°C)	Y OAout (kg/kg)	h OAout (kJ/kg)
lxx.0	35.0	0.012	67.0	54.8	0.0057	lxx.0
eighty.0	35.0	0.012	67.0	60.2	0.0043	71.seven

A comparison between the dehumidifying capacities of passive and active wheels is provided in Fig. 8 . It tin can exist observed a linear dependence betwixt the inlet and outlet accented humidities. It is besides shown that passive desiccant wheels exhibit a significantly lower dehumidifying capacity than agile wheels, particularly for an increased regeneration temperature.

A comparing of active and passive dehumidifying capacities.

iv. Decision

The present piece of work discusses the definitions for effectiveness of active and passive desiccant wheels, as well as the concrete reasoning underlying the enthalpy recovery and active dehumidification processes. For passive dehumidification, it was ended that estrus and mass transfer have conflicting influences over the enthalpy recovery, making the enthalpy recovery effectiveness oblivious to the atmospheric conditions. Appropriately, an increase in the outside air temperature volition imply in a greater contribution of the sensible free energy to the full enthalpy recovery, at the expense of a lesser contribution of the latent free energy. Conversely, an increase in the exterior air humidity will reverse this scenario, imposing a greater importance of the latent energy contribution. In any case, the enthalpy recovery effectiveness is properly described by Eq. [17].

Equally for the active dehumidification, it was shown that heat and mass transfer have cooperating effects, with the dehumidification capacity increasing with the regeneration temperature, until the maximum dehumidification capacity has been reached. The isenthalpic nature of the process has been confirmed, which prevents a definition of efficiency based on enthalpy, as it occurs for evaporative cooling systems [21]. The results show that silica-gel accomplishes a thorough air dehumidification fifty-fifty for a low reactivation temperature, which allows for the utilise of solar energy or low grade waste product heat to bulldoze the system.

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Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7125891/

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