CAUDAL DIFERENCIAL CEGA
5. Zonas húmedas
5.1 Identificación y Modelo Conceptual
Parallel-plate heat and mass exchangers are the most common stationary enthalpy exchangers to recover both sensible heat and moisture. This is due to their simple structure and large packing densities. The analyzed heat and mass exchanger is schematically shown in Figure 5. The membrane surfaces are positioned parallel to each other. An air stream is blown across each surface of the membrane. The difference in
partial pressure of water vapor across the membrane is the driving force for the water transport mechanism.
Figure 5. ERV system cross-flow flat-plate heat exchanger
The main assumptions for the model development are: 1. The height of feed and sweep channels are identical.
2. Heat and mass transfer is steady state, steady flow, and is assumed to be in one direction perpendicular to the surface of the membrane.
3. The velocity, temperature, and concentration profiles are assumed to be fully developed.
4. Both airflows are assumed to be unmixed.
5. Thermal and concentration profiles are a function of the velocity profile and do not affect each other.
6. The fouling factor is neglected since an air filter is assumed to remove any materials that would foul the system.
7. Heat transfer between the heat exchanger and surroundings is zero.
Exhaust fan
Exhaust air
Return Air
Exhaust side filter
Outdoor air
Intake side filter Supply fan
Supply air
ERV core
8. Kinetic and potential energy changes in the air streams are zero. 9. Friction factor is estimated by the Zigrang equation.
10. All heat transfer and thermodynamic properties are estimated at an average airflow temperature.
11. Water vapor diffusion in air is considered to be equal to the diffusion in pure nitrogen at the same conditions.
According to the Effectiveness-NTU method, the maximum possible heat transfer rate, through a counterflow heat exchanger with infinite length, will occur when one of the fluids experiences a maximum temperature difference [69]:
𝑞𝑚𝑎𝑥,𝑇 = min(Ch; Cc) ∙ (𝑇ℎ,𝑖− 𝑇𝑐,𝑖), [𝑘𝑊]; (37) where: Ch; Cc – heat capacity rate of each flow (mass flow times specific heat); 𝑇ℎ,𝑖; 𝑇𝑐,𝑖 – inlet temperature of each airflow.
The corresponding governing equation for the maximum possible mass transfer rate through the counterflow heat exchanger is:
𝑞𝑚𝑎𝑥,𝑚 = min (ṁc∙𝜔𝑐,𝑖 𝑐𝑐,𝑖 ; ṁh∙𝜔ℎ,𝑖 𝑐ℎ,𝑖 ) ∙ (𝑐ℎ,𝑖 − 𝑐𝑐,𝑖), [ 𝑘𝑔 𝑠 ]; (38)
where: 𝑐ℎ,𝑖; 𝑐𝑐,𝑖 – molar concentration of water at the flow inlet, [𝑘𝑚𝑜𝑙𝑚3 ]; ṁh; ṁc – mass flow rate of humid air in each stream, [𝑘𝑔
𝑠 ]; 𝜔𝑐,𝑖; 𝜔ℎ,𝑖 – humidity ratio at the flow inlet.
Based on the maximum possible heat transfer rate, the thermal effectiveness can be defined as the ratio of the actual heat transfer for the heat exchanger to the maximum possible heat transfer rate:
εT ≡𝑞qT 𝑚𝑎𝑥,𝑇 =
Ch∙(𝑇ℎ,𝑖−𝑇𝑐,𝑖)
min(Ch;Cc)∙(𝑇ℎ,𝑖−𝑇𝑐,𝑖). (39)
An equivalent equation for the mass transfer effectiveness can be defined in a similar way: εm≡ 𝑞qm 𝑚𝑎𝑥,𝑚 = ṁh∙𝜔ℎ,𝑖 𝑐ℎ,𝑖 ∙(𝑐ℎ,𝑖−𝑐ℎ,𝑜) min(ṁc∙𝜔𝑐,𝑖 𝑐𝑐,𝑖 ; ṁh∙𝜔ℎ,𝑖 𝑐ℎ,𝑖 )∙(𝑐ℎ,𝑖−𝑐𝑐,𝑖) . (40)
To estimate heat transfer, an additional parameter can be defined as the number of heat transfer units (NTUT):
NTUT ≡ min(CUT∙A
h;Cc); (41)
where: A – membrane area [m2];
UT –total thermal conductivity (including convection and conduction coefficients) [mkW2∙K].
Number of mass transfer units:
NTUm ≡ Um∙A min(ṁc∙𝜔𝑐,𝑖
𝑐𝑐,𝑖 ;ṁh∙𝜔ℎ,𝑖𝑐ℎ,𝑖 )
; (42)
where: Um – total mass transfer conductivity (including convection mass
transfer coefficients and permeation coefficient through the membrane as given by Equation (21) [𝑚/𝑠].
For a counter-flow heat exchanger, the relation between thermal effectiveness and NTUT can be expressed by the following equation [69, 70, 77]:
εT = 1−exp(−NTU∙(1−Cr,T))
1−Cr,T∙exp(−NTU∙(1−Cr,T)) ; (43)
where: Cr,T– heat capacity ratio.
Cr,T=maxmin((CCh;Cc)
h;Cc) . (44)
The analogous equations for mass transfer are:
εm=
1−exp(−NTU∙(1−Cr,m)) 1−Cr,m∙exp(−NTU∙(1−Cr,m)) ;
(45) where: Cr,m– mass capacity ratio.
Cr,m= min(ṁc∙𝜔𝑐,𝑖 𝑐𝑐,𝑖 ; ṁh∙𝜔ℎ,𝑖 𝑐ℎ,𝑖 ) max(ṁc∙𝜔𝑐,𝑖 𝑐𝑐,𝑖 ; ṁh∙𝜔ℎ,𝑖 𝑐ℎ,𝑖 ) (46)
The relation for a single-pass, cross-flow heat exchanger thermal effectiveness with both fluids unmixed can be expressed by the following equation [69, 70]:
εT = 1 − exp[NTUT0.22
Cr,T ∙[exp(−Cr,T∙(NTUT)
0.78)− 1]] (47)
The mass transfer effectiveness for a single-pass, cross-flow heat exchanger with both fluids unmixed has the same format with thermal coefficients replaced by mass coefficients.
To verify the calculation results, the overall thermal and mass balance can be used for each fluid. Heat transfer from one fluid to another can be described using the logarithmic mean temperature difference as the driving force:
qT = UT∙ A ∙ΔTlm ; (48)
ΔTlm = ln ΔT(ΔT2−ΔT1
2/ΔT1) . (49)
Mass transfer from one fluid to another can be described by the logarithmic mean concentration difference as the driving force:
qm = Um∙ A ∙Δclm ∙ M,[
𝑘𝑔
𝑚3] (50)
where: M – molecular weight of water.
Δclm = Δc2− Δc1 ln(ΔcΔc2
1)
,[𝑘𝑚𝑜𝑙
𝑚3 ] (51)
For the counter-flow exchanger, the endpoint temperature difference is defined as:
{ΔT1 ≡ Th,i− Tc,o
ΔT2 ≡ Th,o− Tc,i (52)
In this equation indices ℎ and c describe hot and cold airflow, while 𝑖 and 𝑜 indicates the inlet and outlet condition. Rewriting the above equations for concentration:
{Δc1 ≡ ch,i− cc,o
For the cross-flow heat exchanger, a correction factor needs to be applied to the counter-flow configuration:
ΔTlm = F ∙ln ΔT(ΔT2−ΔT1
2/ΔT1) . (54)
The value of the correction factor can be found in Incropera and DeWitt [69]. The total effectiveness of a single pass heat exchanger is equal to the actual total energy transfer divided by the product of the minimum energy capacity rate and the enthalpy difference: εΣ= m ̇ h∙(ℎℎ,𝑖−ℎℎ,𝑜) min(m ̇ h;m ̇ c)∙(ℎℎ,𝑖−ℎ𝑐,𝑖) ; (55)
where: ℎℎ,𝑖; ℎℎ,𝑜 - enthalpy values of inlet and outlet hot air streams.
Another parameter used to estimate performance of the ERV is the Recovery
Efficiency Ratio (RER). It is a ratio of energy recovered divided by energy expended in
the energy recovery process, according to the ANSI/ASHRAE Standard 84-2008 [78].
RER= m ̇ h∙ (ℎℎ,𝑖− ℎℎ,𝑜) (∆𝑃ℎ∙𝜂𝑄ℎ 𝑓ℎ+ ∆𝑃𝑐∙ 𝑄𝑐 𝜂𝑓𝑐 + 𝑞𝑎𝑢𝑥) ; (56)
where: ∆𝑃ℎ; ∆𝑃𝑐 – the pressure drop across the hot and cold sides of the exchanger respectively;
𝑄ℎ; 𝑄𝑐 – the hot and cold side volume flow rates;
𝜂𝑓ℎ; 𝜂𝑓𝑐 – the hot and cold side air fan and drive total effectiveness; 𝑞𝑎𝑢𝑥 – the auxiliary total power input to the exchanger (e.g. control
The pressure drop across the ERV system can be found [22]: ∆𝑃=(𝑓𝑖 𝐿 𝑑𝑒 + 𝜉) ∙ V 2 2ρa (57)
where fi – Darcy friction factor of flow channels;
ξ – local friction coefficient that reflects the entrance and exit losses; V – mass flux of air, [mkg2∙s];
L – length of flow channels, [𝑚];
de – effective diameter of the rectangular channel, [𝑚].
For fully developed laminar flow in parallel plate channels with infinite width the friction factor can be defined by the formula:
𝑓𝑖=96Re (58)
The ERV system simulation models were programmed in Engineering Equation Solver (EES) V9.195 based on the relations described above [79]. The program was verified with the methodology described in the dissertation of Kistler [80]. A distinctive characteristic of the EES software is the availability in the program of physical properties for solids, liquids and gases. Model input parameters include the inlet airflow velocity, temperature, and relative humidity for each air stream, as well as the membrane size, heat and mass transfer properties.