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Accepted Manuscript Title: A Theoretical Model to Predict Frosting Limits in Cross-Flow Air-to-Air Flat Plate Heat/Energy Exchangers Author: Peng Liu Mohammad Rafati Nasr Gaoming Ge Maria Justo Alonso Hans Martin Mathisen Farhad Fathieh Carey Simonson PII: DOI: Reference:
S0378-7788(15)30372-8 http://dx.doi.org/doi:10.1016/j.enbuild.2015.11.007 ENB 6252
To appear in:
ENB
Received date: Revised date: Accepted date:
22-6-2015 30-9-2015 3-11-2015
Please cite this article as: P. Liu, M.R. Nasr, G. Ge, M.J. Alonso, H.M. Mathisen, F. Fathieh, C. Simonson, A Theoretical Model to Predict Frosting Limits in Cross-Flow Air-to-Air Flat Plate Heat/Energy Exchangers, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.11.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Theoretical Model to Predict Frosting Limits in Cross-Flow Air-to-Air Flat Plate Heat/Energy Exchangers
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Peng Liu1, Mohammad Rafati Nasr2, Gaoming Ge2, Maria Justo Alonso3, Hans Martin Mathisen1, Farhad Fathieh2, Carey Simonson2
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Corresponding author: Peng Liu Tel: +47 735 92 744 Fax: +47 735 93 580 [email protected] Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway 1
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Department of Energy and Process Engineering, NTNU, Trondheim, Norway. Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada. 3 SINTEF Building and Infrastructure, Trondheim, Norway. 2
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Abstract
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In cold climates, the water vapor in the warm and moist exhaust air may condense and form frost
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on the heat/energy exchangers’ plate. In this study, a simplified theoretical model to predict the
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inlet conditions under which frost will form in the flat plate heat/energy exchangers is developed.
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The model uses the exchanger design parameters and operating conditions to determine the
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frosting limit. Experimental tests are conducted to validate the frosting limits model. The results
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show that the predicted frosting limits have consistent agreements with experiments, and energy
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exchangers have a lower risk of frosting than the heat exchangers. Furthermore, a parametric
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analysis using the theoretical model is performed to estimate the impacts of number of heat and
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moisture transfer units (
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membrane permeability on frosting limits of heat/energy exchangers. It is found that air flow
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rate has significant impacts on frosting limits. The combinations of sensible and latent
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and
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effectiveness ensuring no frost inside energy exchanger are studied theoretically. The model can
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be applied to improve the design of exchangers to reduce or avoid frosting for cold climates. The
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frosting limits of cross-flow membrane energy exchanger can also be regarded as criteria to
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conduct selection and feasibility analysis of energy exchanger and compare with counter-flow
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exchanger as a reference in future study.
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Keywords
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Frosting limit; heat exchanger; membrane energy exchanger; cross-flow
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Introduction
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Air-to-air heat/energy recovery ventilators (HRVs/ERVs) have been widely used in heating,
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ventilation and air-conditioning (HVAC) systems to reduce energy consumption for ventilation
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and the green-house air emission, especially in hot and humid climates or cold climates. In these
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systems the outdoor fresh air and the indoor stale air enter the exchangers by separated sides.
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Sensible heat, latent heat, or both are transferred from one air stream to another, depending on
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the temperature and moisture gradients. When warm and moist exhaust air passes over the cold
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plate surface of an exchanger, water vapor condenses and frost forms on the surface if the plate
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temperature is lower than both the air dew point and water freezing point. In cold climates
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defined by international climatic zones with thermal criteria [1] such as Canada and northern
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Europe, frost often forms inside the HRVs/ERVs and would negatively impact the performance
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of the exchangers in winter[2]. This frosting issue is more critical when the outdoor temperature
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is extremely low.
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Defrosting or protecting heat/energy exchangers from frosting has remained as an important
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topic for decades. A recent numerical simulation for a residential house under Canadian winter
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condition by [3] showed that the yearly demand of defrosting cycle for a heat exchanger is 3.5
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times higher than an ERV. The reason is that ERVs transfer both heat and moisture
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simultaneously between supply and exhaust air streams, which encounter frosting at a lower
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temperature compared to HRVs in cold climates. [4] and [5] indicated that the frost occurred
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approximately 5 to 10
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study by Rafati [6] indicated that the ERV is more efficient than the HRV under frosting
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conditions. It also concluded that preheating the supply air to prevent frosting is more efficient
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than bypassing the supply air method to defrost the exchangers, and the prediction of the frosting
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limits is critical for the exchangers in practical applications. The recent literature reviews on the
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use of heat/energy exchangers in cold climates, frost and frosting control strategies for air-to-air
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exchangers found that the flat plat (membrane) energy exchanger has promising potentials in
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reducing or avoiding the frost instead of conventional heat exchanger. [2][7].
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The research work in frosting of flat plate heat/energy exchangers can be divided in two
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categories. The first type is dealing with predicting the properties of a frost layer such as density,
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heat conductivity and surface roughness as a function of time and temperature. Most of these
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models are correlations or combination of theoretical and experimental results on frost
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properties. Detailed reviews in frost properties and models were published [8]–[10]. However,
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most of these models are limited to some specific geometries and a range of temperature of the
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cold surface. Therefore, it is not easy to apply those results to other air-to-air exchangers with
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different exchanger configurations and operating conditions. In addition, there is a lack of
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lower in a desiccant wheel (ERV) than conventional HRVs. Another
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quantitative dependency analysis of the frost-air interface temperature which plays a very
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important role in heat transfer analysis.
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In the second category, effect of frosting in the performance of the heat or energy exchangers
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was described. Bantle [11] used an empirical heat transfer coefficient for a frosted surfaces to
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predict the performance of a counter-flow exchanger. Philips et al. [12] applied a numerical
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method to determine changes in effectiveness in a counter-flow exchanger under frosting
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condition. He calculated the frost thickness and evaluated its effect on the effectiveness. In other
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works [13], [14], Phillips assumed the frosting limit as a known parameter and based on that he
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theoretically calculated the energy impact of different defrosting strategies for a counter-flow
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exchanger using weather data.
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The frosting limit in this study refers to the specific combinations of supply (outdoor) air
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temperature and exhaust (indoor) air relative humidity which initiate frosting in the flat plate
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heat/energy exchangers. There are only few works which investigated the effects of operating
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conditions on frosting limits. Ruth [5] conducted tests on an aluminum heat-wheel and found that
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occurrence of frosting was greatly dependent on the exhaust air humidity. Frosting was observed
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at outdoor temperature ranged from -26
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between 25% and 30%. Fisk [4] compared frosting limits for different cross-flow exchangers
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experimentally. He used an analytical model to predict the frosting limit for a counter-flow
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exchanger as a reference in the work. In his model, the influence of the heat released from
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condensation on temperature of the plat was considered. He further investigated the indoor and
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outdoor environmental conditions that initiated freezing with experiments for cross- and counter-
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to -16
when the relative humidity of exhaust air was
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flow flat plate heat exchangers and a cross-flow energy exchanger. The frosting limits of the
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exchangers were plotted in the research [15]. However, the theoretical frosting limit model was
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not given in the research. Tests were conducted to determine the frosting limits for a pure-
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counter-flow heat exchanger [16]. The frosting limits ranged linearly from -23
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outdoor air temperature with exhaust air RH from 58% to 32% when the exhaust air temperature
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was 24°C. The criterion of determining the limits was not either presented. Holmberg[17] used
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CFD method to solve coupled heat and mass transfer equations in a two dimensional space to
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predict temperature distribution in a single and double pass cross-flow heat exchanger under
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steady state conditions. In another work, Holmberg [18] theoretically calculated the frosting
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limits for energy wheels. In his model two types of wheels with constant effectiveness for fixed
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inlet conditions were presented. Through a field test for a house in Ontario (Canada), Zhang [3]
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found energy exchanger performance was not deteriorated until supply air temperature reached
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. In recent years, Liu et al. [19], [20] developed a one-dimensional theoretical model to
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determine frosting limits for counter flow heat and energy exchangers. Liu applied this model
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with weather data of Norway to predict frosting operation conditions throughout the daily coldest
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outdoor temperature of a year for a counter-flow energy exchanger in Oslo. In the model, two
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conditions to cause frosting formation are subzero surface temperature and condensation over the
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surface. The counter-flow heat/energy exchangers are widely used since the counter-flow
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arrangement usually provides higher effectiveness compared to other arrangements [21].
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However, the high effectiveness nature of counter-flow may lead to a higher frosting risk due to
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the colder exhaust air being created. The frost tends to occur at higher outdoor air temperature or
of
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to -9
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lower indoor relative humidity. Frosting up inside the exchangers could conversely reduce the
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initially-designed high effectiveness.
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In general, following shortcomings are noticed in the literature:
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• Previous researches were mainly based on experiments that were limited to specific
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design or operating conditions.
• The proposed models were limited to counter-flow heat/energy exchangers.
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• Most of theoretical works were validated with experiments only for a specific design or
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operating condition.
• The main type of energy transfer was sensible heat. Very few studies have considered
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latent heat in the form of mass transfer.
• The authors did not find the specific theoretical model in the literature which predicted
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the theoretical frosting limit for cross-flow air-to-air flat plate heat/energy exchangers.
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In this study, a theoretical model to predict the critical operating conditions for frosting in
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cross-flow heat/energy exchangers is developed. The frosting limits of heat/energy
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exchangers for a residential use are theoretically and experimentally studied. The effects of
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design parameters are evaluated which may guide the frost-free air-to-air cross-flow flat plate
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heat/energy exchangers design. The cross-flow frosting limits model can be the reference to
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further compare cross-flow and counter-flow with respect of frosting limits in future
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research.
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Mathematical model
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The main goal of this study is to develop a theoretical model to predict the critical operating
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conditions in which the onset of frosting occurs in cross-flow exchangers. It is important to
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include the exchanger physical and design parameters (such as air channels spacing, heat
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conductivity and water vapor diffusivity of the plates) and operating conditions (such as air-flow
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rate, temperature and relative humidity). Due to two-dimensional nature of heat and mass
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transfer in cross-flow flat plat exchangers, modeling is more complex than the counter-flow
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arrangement.
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Two necessary conditions to trigger frosting are subzero temperature of the plate surface and
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condensation formation at the most likely frosting positions. These two conditions are used to
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derive frosting limits for different exchangers in this study. If the exchanger configuration and
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air flow rate are given then supply air (outdoor) temperature and exhaust inlet (indoor) relative
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humidity play more important roles in the frosting limit [22].
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In cold regions condensation and frosting is potential to take place in the exhaust side in
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HRVs/ERVs [2]. The temperature and humidity distributions across a cross-flow exchanger are
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not uniform (Zhang, 2008), therefore the possibility of frosting at some locations is higher than
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other parts. According to experiments [24] and numerical model (Holmberg, 1989; Zhang,
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2008), frost more likely first appears at the exhaust air outlet closest to the supply air inlet for the
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cross-flow exchangers which is known as “cold corner” (the navy blue triangle) as shown in
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Figure 1(b). In this study, the outlets of first exhaust channels at the corner are regarded as the
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most likely frosting positions. A detailed view of the most likely frosting spots and the research
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domain channels for this paper is presented in Figure 1(c). The frosting limits can be obtained by
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determining the critical frosting conditions at these positions. Developing the frosting limits
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subsequently becomes to express the temperature and moisture at these positions with inlet
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operating and design parameters. The following part deals with determination of the temperature
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and the moisture at the “cold corner”.
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Figure 1 (a) Qualitative membrane temperature distribution, (b) The schematic view of cross-
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flow exchanger structure with corrugated aluminum spacer and channels with highest risk of
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frosting, (c) A detailed view of most likely frosting spot and the research domain for developing
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frosting limits model
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Assumptions
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The following assumptions are used in this research:
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1. Frosting initially forms in the outlets of exhaust air channels that are closest to the supply inlet in both heat and energy exchangers (the navy blue triangles in Figure 1(b) and (c));
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2. Air flows through all channels are homogeneous and incompressible;
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3. The air mass flow rate in each channel of supply and exhaust air is identical;
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168 169 170
4. The convection heat and mass transfer coefficients are constant throughout the exchanger; 5. The specific heat capacity of both air streams are equal and constant throughout the air channels of exchangers;
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6. No air leakage occurs from/to the exchangers or between two air streams;
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7. The thermal resistance of the exchanger plates is negligible due to the thin thickness;
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8. Condensation occurs only on the exhaust side;
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9. Condensation heat has a negligible impact on frosting in energy exchanger. The effect on
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plate heat exchangers can also be omitted when the indoor air relative humidity is below
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30% [25];
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10. The thermal properties of both fluids and exchanger walls do not vary with temperature;
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11. The velocity, temperature, and humidity distributions of the fluids are uniform at the
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inlets of the exchanger;
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12. There is no heat sources and heat sinks in the air stream;
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13. The exchangers are well insulated and no heat is transferred between the exchanger and
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surrounding.
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Frosting limits
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The frosting limits of membrane energy exchanger combine the critical outdoor temperature and
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the condensation limit which are corresponding to the two necessary frost forming conditions.
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Frosting starts occurring when the operating conditions meet the two necessary frosting 10
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conditions. In other words, the outdoor temperature is lower than the critical outdoor air
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temperature and the indoor RH simultaneously exceeds the condensation limits. The definitions
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and derivations of critical outdoor air temperature and condensation limit are addressed in the
191
follow sections.
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Critical supply (outdoor) air temperature
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A critical outdoor air temperature is defined as the lowest outdoor air temperature to maintain the
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membrane temperate over the freezing point at the most likely frosting positions. The critical
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outdoor air temperature corresponds to the aforementioned first necessary frost forming
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condition which is the sub-zero temperature of the membrane/film. The heat transfer through the
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first exhaust channels to supply air side is calculated by equation (1).
(1)
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is the log mean temperature differences which is defined in equation (2) for cross-flow
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exchanger. Heat gain by exhaust air from inlet to outlet in the first exhaust channel is given by
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equation (3).
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(2)
(3)
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The energy changes through the supply air channels within research domain as shown in Figure
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1 (c) is 11
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(4)
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Based on energy conservation, we have
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(5)
The mass flow rates in supply and exhaust air sides in the research domain have the following
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relationship,
can be derived from equations (3) to (6),
The
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(6)
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(7)
In general, when the channel number n is more than 30, the right term in equation (7) can be
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omitted based on author’s calculation. The supply air temperature changes is negligible
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compared to the maximum temperature changes in the exchanger. As a result, the correction
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factor
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by replacing
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is 1 as
is nearly equal to
with
[26]. The error of the log mean temperature difference
is under 6%. The channel number in this study is 31.
combining equations (1) to (5) and
can be expressed as a function of ,
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(8)
To meet frosting condition, the plate temperature
should be equal to or lower than freezing
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point. When the thermal resistance of plate is negligible due to the thin thickness, the
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temperature drop across the plate is omitted[27]. The plate temperature can be computed from
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equation (9).
(9)
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According to assumption 6, the convective heat transfer coefficient on the supply and exhaust air
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sides are equal. Thereafter, the plate temperature at exhaust outlets for the first channels can be
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expressed equation (10).
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Where the number of heat transfer unit for the first exhaust air channel
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equation (11).
(10)
is defined by
(11)
is expressed in equation (12) when
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The critical supply air temperature
. This
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temperature shows the outdoor air temperature value at which the plate temperature reaches
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freezing point at the most likely position of frosting. 13
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(12)
Condensation limit
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The condensation limit is the combination of indoor relative humidity and outdoor air
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temperature resulting in the exhaust air starting to condensate at most likely frosting positions.
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The condensation limits correspond to the second necessary frost forming condition namely the
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exhaust air adjacent to the membrane at the exhaust air outlet reaching saturation.
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Using mass conservation, the moisture content of the exhaust outlet air close to most likely
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frosting position can be expressed as equation (13) based on the derivation of equation (8). The
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moisture content of exhaust inlet (indoor) air is presented with equation (14) through rearranging
234
equation (13). Number of moisture transfer unit
is given in equation (15).
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(13) (14) (15)
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is the moisture content of supply (outdoor) air and regarded as known values which are
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usually very low for cold climates. The relationship between moisture content and relative
237
humidity is described using Clapeyron equation to represent the saturation vapor pressure as
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shown in equation (16)[23]. 14
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(16)
The water vapor starts to condense when the exhaust air close to the surface reaches saturation
240
namely relative humidity of exhaust air at outlet being 100%. The condensation limits can be
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described through equations (13) to (16). The limits can be expressed as a function of the inlet
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temperature and moisture parameters.
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The
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calculated and validated in this study. The frosting limits of sensible-only heat exchanger can be
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obtained with this model by substituting
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exhaust and supply air sides.
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Experimental Validation
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Test facility
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A test facility was built up to test full size cross-flow air-to-air exchangers. This facility enables
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researchers to test different exchangers under non-frosting and frosting conditions. The layout of
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the test facility is shown in Figure 2. The test rig consists of two environmental chambers, four
252
fans, a test section, and connecting pipes.
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used in the critical outdoor air temperature and condensation limits are
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since there is no moisture transfer between
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and
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Figure 2. Schematic of the experimental setup for air-to-air cross-flow exchangers
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This test setup is designed as an open loop with two fans in each air stream. Air is drawn from
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each chamber in a separate air stream using two fans; one before and one after the test section, in
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each air stream. Flow rates are adjusted by voltage regulator connected to each fan. Presence of
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two fans at each air stream allows to control the pressure at the exchanger to minimize the air
259
leakage to or from the ambient, and to produce balanced flow rate. The exchanger can be tested
260
at any temperature between -30°C to 30°C, while relative humidity can be 10% to 90% for the
261
flow rate equal to
262
(Figure 2). Pipes are connected to the exchanger with inlet expansion and outlet contraction
263
diffusers. These headers are designed to produce uniform flow fields at the exchanger inlet face.
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Velocity measurement at the face of the exchanger confirmed uniform profile for the inlet air.
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Moreover, heat loss in the headers is negligible.
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Different parameters such as temperature, relative humidity, flow rate and pressure drop are
267
measured or calculated in experiments. Temperature of air is measured using T-type
268
thermocouples (cupper-nickel). Vaisala humidity and temperature sensors are used to measure
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. In the test section the exchanger is located in an insulated test box
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both relative humidity and temperature. Air flow rate is measured by employing an orifice plate
270
with the standard[28]. Pressure drop is measured by two types of pressure transducers. Pressure
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drops across the orifice plates (for flow rate measurement) are gained by general purpose
272
diaphragm pressure transducers, while low pressure transducers are used to capture changes in
273
pressure drop across the exchanger. Performance of the exchanger is evaluated by effectiveness
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which is the ratio of the actual energy transfer over the maximum possible energy transfer [29].
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Uncertainty of sensors are determined according to ASME PTC 19.1 [30]. Each sensor is
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calibrated with a calibrator where its signals are recorded by a data acquisition (DAQ). Once the
277
data are collected, precision and bias are calculated for the sensor. Then calibration curves are
278
developed where they are applied to raw data from experiments.
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Frosting detection methods
280
During the design of the test facility, possible methods of frost detection were reviewed [2]. The
281
visual technique and pressure drop method are used in this study, since they are more accurate in
282
detecting the frosting limit. In the visual technique, two endoscope cameras are used to view the
283
exchanger during the experiments. These endoscopes are installed just after the outlet face, one
284
in the exhaust side and one in the supply side. The endoscopes are 9 mm in diameter which is
285
larger than the channel spacing, therefore, it is not possible to insert the endoscope inside the
286
channels. Static pressure drop across the exchanger is also monitored during the entire
287
experiment. An increase in pressure drop across the exchanger is a sign of frosting due to partial
288
blockage of the channels by frost. More details for these methods were presented in [22].
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In all experiments, the pressure drop across the exchanger and the pictures are analyzed to detect
290
frosting. It takes approximately 3 hours for each experimental test. Figure 3(a) shows a
291
comparison of the pressure drop in two experiments for heat and energy exchangers. It is clear
292
that pressure drop in the exhaust side where the risk of frosting is higher, increased, while no
293
change in the supply side was captured. This means there is no frost in the supply side and that
294
was in agreement with visual method. Figure 3(b) shows partial frost formation at the exhaust
295
outlet of the energy exchanger by visual method in the energy exchanger experiment. It can be
296
seen that the channels at the exhaust outlet are covered with frost. Such situation was observed
297
for heat exchanger under the similar working conditions. Thus, in this example the working
298
conditions were considered in the frosting zone.
299 300
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Figure 3. Frosting detection method when:
.
(a) Pressure drop method, (b) View of the energy exchanger at the end of experiment.
302
To find the frosting limit experimentally, each exchanger is tested at different
303
the rest of operating conditions are fixed. The lowest
at each
and
while
or in another word, the
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304
highest
305
method defines the experimental frosting limit. To check the repeatability and accuracy of the
306
results, exchangers are tested twice at some of the frosting limit points.
307
Results and Discussion
308
Model validation:
309
The numbers of heat and moisture transfer units are indispensable to compute the frosting limits
310
using the developed model in this study. This section will illustrate the method to calculate the
311
number of heat and moisture transfer units and model the performance of the exchangers with
312
aluminum cross-corrugated spacers. Two geometrically identical exchangers are tested in the
313
study. The energy exchanger is made with polymer membranes to separate the supply and
314
exhaust air streams, which are permeable to water vapor, while the heat exchanger is made with
315
impermeable polymer films with the same thickness (Figure 4). The corrugated aluminum
316
spacers are placed inside the supply and exhaust air channels to support the elastic and flexible
317
membrane/film and enhance the convective heat transfer.
and
of heat/energy exchanger
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with frosting that is captured with either by pressure drop or visual
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at each
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Figure 4. Tested exchangers and their geometrical parameters
320
The conjugate heat and moisture transfer and NTU calculation for air-to-air cross-flow
321
exchangers using design and physical properties of the exchanger are available in detail in [23].
322
The physical dimensions of the exchangers and properties of the membranes are presented in
323
Table 1 and Figure 4. A key parameter is the water vapor diffusivity of the membrane which
324
was measured to be
325
Table 1. Physical specification of the heat and energy exchangers tested
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d
according to the method of [31].
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Parameter Number of channels for each flow, n Half duct height, a Half duct width, b Apex angle, Hydrodynamic diameter, Exchanger width , height , depth Membrane thickness, Membrane water vapor diffusivity,
Value
Reference Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement
Thermal conductivity of membrane,
[23]
Thermal conductivity of fin,
[23] [32] [32] [23] [32] Lab measurement
Thermal conductivity of air, Density of air, Water vapor diffusivity in the air, Kinetic viscosity of air, Volumetric air flow rates, 20
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Face velocity, Reynolds Number, Re
Lab measurement Lab measurement
22
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The Reynolds number indicates laminar flow regime inside the air ducts. Using equations in [23]
328
the pressure drop,
329
agreement with the experimental value,
330
[23], heat and mass transfer coefficients (h and
331
to calculate the Nusselt and Sherwood numbers, the total heat and mass transfer coefficients
332
(
333
equations (11), (15) and (17) to (19). The calculated exchanger performance parameters for the
334
design condition are shown in Table 2.
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across the exchanger was calculated as 20.3 Pa. The theoretical
is in
cr
. According to the procedure presented in
us
respectively) and the parameters given in [33]
(17)
te
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an
), NTU, and effectiveness of the cross-flow exchangers are obtained from
Ac ce p
(18)
(19)
335
To verify the
calculated from the theory, both exchangers were tested at AHRI winter test
336
condition [34]. A full uncertainty analysis was conducted to account for propagation uncertainty
337
through the measurements bias and precision error. The results from repeated experiments were
338
within the uncertainty range. Experimental and theoretical results are summarized in Table 3 and
339
shows good agreements. It can be concluded that the theory is reliable in predicting the 21
Page 21 of 45
340
and
341
theoretical model in this study.
342
The
343
energy transfer area and mass flow rate changes at same proportionality for the exhaust air
344
channel shown in Figure 1 (c) in equations (11) and (15).
345
Table 2. Theoretical performance parameters
. A parametric analysis of the frosting limit is conducted using the developed
cr uncertainty
0.04 0.02 0.08 0.09 0.14 0.10 0.14
Ac ce p
347
te
Total Mass Transfer Coefficients Number of Heat Transfer Unit Number of Moisture Transfer Unit 346
since the
Value
d
Nusselt Number Sherwood Number Heat Transfer Coefficients Mass Transfer Coefficients Total Heat Transfer Coefficients
us
Parameter
an
Parameter
and
ip t
for computing domain have same values as
M
and
Table 3. Comparison between the experimental and theoretical effectiveness
Exchanger type
Theoretical Experimental Theoretical Experimental
HRV
ERV
22
Page 22 of 45
Model Validation: Frosting limit
349
To determine the experimental frosting limit, each exchanger is tested under the conditions near
350
the theoretical frosting limit. The theoretical model is used to select the test conditions for the
351
experiments. In the validation experiments, the exhaust inlet temperature and supply inlet
352
relative humidity are approximately constant
353
change between 5% to 50% and -5 to -33 , respectively. Results of these experiments lead to a
354
map for frosting limit, as shown in Figure 5(a) and (b). In this figure only the lowest
and
us
cr
, while
at each
in which frosting captured is presented. In total more than 80 tests were conducted, and each
an
355
ip t
348
was run for 2 to 3 hours.
357
In Table 4 a summary of the uncertainties in measured and calculated parameters are presented.
358
It should be noted that all these values are an approximate, since these may change for each test.
359
Table 4. Uncertainties in measured and calculated values with 95% confidence interval
te
d
M
356
Ac ce p
Parameter Temperature (°C) Relative humidity Vaisala (% RH) Pressure drop (Pa) Mass flow rate (%) Sensible effectiveness (%) Latent effectiveness (%) Humidity ratio (%)
Uncertainty 0.2-0.25 1.5-2 3-7 2 2 2-6 2-6
360
The critical outdoor air temperature and condensation limits are computed from equation (12)
361
and (16) respectively. The overlapping operation conditions in which the critical outdoor air
362
temperature and condensation limits are reached simultaneously consist of the frosting limits. 23
Page 23 of 45
The number of heat and moisture transfer units are calculated from equations (11), (15), (17) and
364
(18) and the required parameters are given in Table 1 and Table 2. The theoretical frosting limits
365
for energy and heat exchanger are respectively plotted in Figure 5(a) and (b).
366
The RH discrepancies between theoretical and experimental frosting limits,
367
Figure 5(a) and (b) as well. The dashed line indicates the critical supply inlet (outdoor) air
368
temperature. The plate temperature at the most likely frosting positions is below the freezing
369
point if the outdoor temperature is lower than the critical temperature (the left area of the dashed
370
line). The experimental and theoretical results have same trends as shown in Figure 5(a) and (b).
371
The lower the supply inlet air temperature is, the less moisture can be carried by the exhaust air
372
without occurring frost in exchangers. The trend is obviously consistent with the engineering
373
experience. Overall, very good agreement between experiments and theoretical predictions are
374
obtained for both heat and energy exchangers. To verify the model at
375
should be less than 10%. These conditions were not obtained in the experiments due to high
376
humidity level in the lab.
ip t
363
°C,
Ac ce p
te
d
M
an
us
cr
, are shown in
24
Page 24 of 45
ip t cr us an M
377
te Ac ce p
379
d
378
25
Page 25 of 45
ip t cr us an
380
Figure 5. Experimental and theoretical frosting limits for the (a) energy exchanger and (b) heat
382
exchanger
383
All the theoretical results slightly over predict the frosting limits compared to the experiments.
384
Theoretical model assumes frost emerging once the frosting conditions are met. However, the
385
amount of the frost is too small to be detected by the pressure or visualization methods when the
386
operating conditions are close to the limits, especially for the low RH of exhaust air (the left
387
points in Figure 5 (a) and (b)). As a result, the theoretical model is more sensitive compared to
388
the experimental tests to detect frosting limits. The researchers or engineers have to be aware of
389
over predicting when they employ the frosting limit model to evaluate or design an exchanger.
390
Comparison between heat exchanger and energy exchanger shows that the energy exchanger has
391
a lower risk of frosting as expected. A bigger gap between heat and energy exchangers frosting
392
limits is observed at a higher
Ac ce p
te
d
M
381
. It results from the significant effect of moisture transfer in 26
Page 26 of 45
energy exchanger on frosting. Therefore, any parameter that affects the moisture transfer such as
394
membrane permeability, membrane thickness, exchanger design and operation conditions, may
395
play an important role in the frosting limit.
396
Considering the results in Figure 5 (a) and (b), these specific exchangers may still have frost
397
problem inside the exhaust channels in the general recommended comfort zone of indoor relative
398
humidity (30%-60%) [32] and at any
399
flow rate. However, it should be noted that in most cold climate regions the actual indoor relative
400
humidity is usually much lower than the recommended level which somehow results in lower
401
risk of frosting in exchangers [7] [35].
402
Parametric analysis
403
A parametric study is conducted to identify important factors for the frosting limit. In this regard,
404
a two-steps process is adopted; the effects of
405
effects of design parameters on
406
presented for the energy exchanger. The analysis for heat exchanger can refer to the parameters
407
only related to heat transfer.
408
Effect of NTU on the frosting limit
409
The effects of
410
shown in Figure 6 and Figure 8. In both figures, the region on the left hand side of critical
411
outdoor temperature (
cr
ip t
393
te
d
M
an
us
when the exchanger is running at nominal air
on the frosting limit, and the
. The results in the parametric analysis are
Ac ce p
and
and
and
on the frosting limit of the cross-flow energy exchanger are
) represents that the plate/membrane surface temperature at the most
27
Page 27 of 45
412
likely frosting position is below freezing point. The condensation occurs in the upper area of the
413
condensation limit (
414
conditions with frosting according to the theoretical model. The lower-right boundary of this
415
overlapping area is then the frosting limit. In Figure 6 and Figure 8, the solid lines represent the
416
base case presented in Table 2. The rest of the lines are developed through changing
417
Figure 6) and
418
In Figure 6 the frosting limit change considerably when
419
rate is not proportional with
420
after the
421
map; however, this measure will in turn reduce the effectiveness (Figure 7) and energy recovery
422
rate in practice. The final counteracted consequence is difficult to estimate only from this
423
research. The design parameters that could affect
424
parametric analysis.
(in
cr
ip t
). Consequently, the upper-left overlapping area shows the operating
can only slightly affect the frosting limit
could narrow-down the frosting region in the
will be investigated in the next part of
Ac ce p
te
d
M
value reaches 3. Decreasing
varies from 1 to 5.The changing
an
. Increasing
us
(in Figure 8).
28
Page 28 of 45
ip t cr us an
425
Figure 6. Effect of
on frosting limit of the energy exchanger. Upper-left area represents the
427
frost zone
428
Figure 8 indicates that if the
429
frosting region will be greatly reduced, especially at higher
430
latent effectiveness could be the reason for the greatly reduced frosting region. Figure 7 which is
431
developed from equation (19) shows that at lower NTU the variation rate of effectiveness is
432
higher. The triangular points in the figure represent the sensible and latent effectiveness of the
433
energy exchanger used in this research.
434
The frost will be completely avoided for typical indoor air moisture levels (
435
the
436
higher latent effectiveness undergo less frost in cold regions. When the indoor moisture
d
M
426
stays constant (1.6), the . The significantly increased
Ac ce p
te
is raised from 0.5 to 3 while
) when
reaches to 3. The results agree with previous findings that the energy exchangers with
29
Page 29 of 45
generation rate is relatively high, the moisture recovery of the energy exchanger may lead to
438
undesired high indoor RH especially for transitional seasons. In cold climates, the effects of
439
membrane energy exchanger with respect to frosting avoidance and low excessive humidity
440
decay need to be further studied. The frosting limits can be employed as criteria to conduct
441
selection and feasibility of membrane energy exchanger in future research.
442
Ac ce p
te
d
M
an
us
cr
ip t
437
443
Figure 7. Effectiveness VS NTU for both sensible and latent heat
444
One of the manners to raise
445
resistance of the membrane. The membrane moisture diffusion and convection resistance will be
446
discussed in the following analysis.
without changing
is to reduce the moisture transfer
30
Page 30 of 45
ip t cr us an M
447
Figure 8. Effect of
449
the frosting zone
450
The developed frosting limit model can also be used to guide the design of heat/energy
451
exchangers to avoid frosting. In the model, the specific combinations of sensible and latent NTU
452
can be applied to predict if the exchanger is under frosting condition or not when the operating
453
condition is known. The process of computing the combinations is similar to determine frosting
454
limits by changing variables and knowns. The sensible and latent effectiveness is only the
455
function of
456
plat heat/energy exchangers. The minimum
457 458
on frosting limit of the energy exchanger. Upper-left area represents
Ac ce p
te
d
448
and
and
respectively as shown in Figure 7 for mass balanced air-to-air flat required to prevent frosting at different values of
are shown in Figure 9 when the indoor RH is a constant (30%). The more wildly used
and straightforward combinations of sensible and latent effectiveness which can theoretically 31
Page 31 of 45
ensure frost free design are given in Figure 9. It can be seen that an exchanger with a higher
460
sensible effectiveness requires a higher latent effectiveness to prevent frosting. The required
461
lowest latent effectiveness is slightly lower than sensible effectiveness to completely prevent
462
frosting under the designated operating conditions.
463
Ac ce p
te
d
M
an
us
cr
ip t
459
464
Figure 9. Minimum latent effectiveness for frost free energy exchanger VS sensible effectiveness
465
at different
466
Parametric study on NTU
467
After understanding the role of
468
design parameters of exchanger is performed in this section. Among those air channel aspect
and
in frosting limit, a parametric study on the
32
Page 32 of 45
469
ratio, air-flow rate, membrane permeability are selected. Each of these parameters is changed by
470
a factor between 0.25 to 4.00 and the resulting NTU is recorded. Their influence on
ip t
is depicted in Figure 10 and Figure 11 respectively.
471
As it can be seen in Figure 10 and Figure 11, decreasing air-flow rate can significantly increase and
473
which have counteracting impacts on frosting limit indicated in Figure 6 and
cr
472
and
Figure 8. The eventual consequence of changing air-flow rate on frosting limit can be somehow
475
indicated by Figure 9 in respect with different
476
halved in comparison with experiment condition, the
477
respectively which can be found in Figure 10 and Figure 11. The influences of these
. For instance, if the air flow is
and
become 3.3 and 1.0 and
M
an
and
us
474
can then be addressed by using Figure 9. The aspect ratio greatly affects heat transfer
479
while it has negligible influence on moisture transfer. Higher aspect ratio enlarges the frosting
480
area concluded from Figure 8, Figure 10 and Figure 11. Meanwhile the high aspect ratio also
481
increases the pressure drop through the intensive spacer. On the other side, a lower aspect ratio
482
means a wider supporting aluminum spacer at a fixed channel spacing in which case the elastic
483
membrane tends to deform. The deformation probably cause frosting as well which was found
484
with the experiments [36]. An optimal aspect ratio of aluminum spacer air channels can be
485
determined based on these criteria.
486
The
487
has no effects on heat transfer. The influence of membrane permeability on
488
negligible in the tested energy exchanger. The reason is that the diffusion resistance of
489
membrane merely accounts for a small proportion of total moisture transfer resistance and 33
Ac ce p
te
d
478
is independent on membrane permeability, since the membrane moisture permeability can also be
Page 33 of 45
convective resistance dominates in the total moisture transfer resistance. The effective means to
491
improve moisture transfer is to enhance moisture convection in the exchanger.
. The horizontal axis shows the ratio of
d
on
Figure 11. Effects of different design
M
Figure 10. Effects of different design parameters
an
us
cr
ip t
490
te
the values over base value used in this paper
parameters on
. The horizontal axis
shows the ratio of the values over base value
Ac ce p
used in this paper
492
Conclusions
493
A theoretical model is developed to predict frosting limits for cross-flow air-to-air heat /energy
494
exchangers in cold climates. The model involves the exchanger’s design parameters and
495
operating conditions which include air flow rate, supply and exhaust inlet temperature and
496
relative humidity. The frosting limits of these two types of exchangers are plotted in a coordinate
497
with supply (outdoor) air temperature versus exhaust (indoor) air relative humidity using the
498
mathematical model. The theoretical limits are validated with experiments and relatively 34
Page 34 of 45
499
consistent with experimental results. It is found that the energy exchanger is considerably more
500
frost resistant than the heat exchanger. The critical temperature (frosting limit) of the energy
501
exchanger is
502
exhaust air relative humidity
503
The parametric analysis of theoretical frosting limit is conducted for the flat plate (membrane)
504
energy exchanger with respect to
lower than the heat exchanger under the same air flow rate
and
cr
ip t
, which is in consistence with other research.
and
and exchanger design parameters. Changing
us
505
to
merely affect frosting limit in a narrow range while increasing
with fixed
can significantly reduce the frosting zone.
507
The influence of air-flow rate needs to be further investigated due to the counteracting effects on
508
frosting limit. An optimal air channels aspects ratio can be determined in considering the
509
criterion of frosting. The diffusion resistance of this specific membrane accounts for a small part
510
of total moisture transfer resistance in the energy exchanger and has a negligible effect on the
511
frosting.
512
The combinations of sensible and latent effectiveness ensuring no frost are theoretically
513
evaluated for the cross-flow flat plate energy exchanger at different supply (outdoor) air
514
temperatures. The required lowest latent effectiveness is proximately equal to sensible
515
effectiveness when the exhaust air conditions are 21°C and 30% RH.
516
The model is applicable to estimate frosting limits of all flat plate air-to-air heat/energy
517
exchangers as long as the physical properties and performance parameters are available. In a
518
more practical level, this model can be used in programing a HRV/ERV control system to
Ac ce p
te
d
M
an
506
35
Page 35 of 45
activate a frost protection cycle only based on the inlet conditions. However, to get to that level,
520
much more studies and a detailed model validation for different design are recommended.
521
Acknowledgements
522
This research was financially supported by the Research Council of Norway through Norwegian
523
University of Science and Technology, the Research Centre on Zero Emission Buildings (ZEB)
524
and collaboration between University of Saskatchewan and Norwegian University of Science
525
and Technology (NTNU). The authors gratefully acknowledge the support from dPoint
526
Technologies Inc., Smart Net-Zero Energy Building Strategic Research Network (SNEBRN) in
527
Canada, and ASHRAE. The Authors also express their gratitude to Mr. David Kadylak and Mr.
528
Ryan Huizing for their tremendous help in preparing the paper and experimental setup
529
preparation.
Ac ce p
te
d
M
an
us
cr
ip t
519
36
Page 36 of 45
Ac ce p
te
d
M
an
us
cr
ip t
530
37
Page 37 of 45
te
d
M
an
us
cr
ip t
Nomenclature
Ac ce p
531
38
Page 38 of 45
ip t
M
Number of channel Convective heat transfer Volumetric flow rate Axial velocity in an air channel Moisture content Length and height of the exchanger
an
Mass transfer coefficient from the membrane
532
cr
Definition Total heat transfer surface area Hydrodynamic diameter of an air channel Water vapor diffusivity in membrane Water vapor diffusivity in the air Correction factor for cross-flow exchanger Mass flow rate of dry air Convective heat transfer coefficient Air channel length Temperature Total heat/mass transfer coefficient Pressure across the exchanger Half air channel height Half air channel width
us
Parameter
Acronyms
Ac ce p
te
d
Energy Recovery Ventilators Heat Recovery Ventilators Heating Ventilation and Air-Conditioning Number of Transfer Unit Nusselt number Relative humidity Sherwood number Reynolds number in each air channel
Greek letters
Difference ( Log mean for temperature) Heat or mass conductance Apex angle for fin Thickness(membrane, plate, frost) Effectiveness Kinetic viscosity of air Density General variable
Subscripts
39 First channel in exhaust side closest to supply air Exhaust Exhaust Inlet Exhaust Outlet
Page 39 of 45
Ac ce p
te
d
M
an
us
cr
ip t
533
40
Page 40 of 45
533
Reference
535 536
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ip t
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629 630
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cr
ip t
624 625 626
631
us
632 633
an
634 635
M
636 637
640 641 642
d
heat /energy exchangers in cold climates.
te
639
• A theoretical model is developed to predict frosting limits for cross-flow air-to-air
• The theoretical limits are validated with experiments and relatively consistent with
Ac ce p
638
experimental results.
• The parametric analysis of theoretical frosting limit is conducted for the flat plate
643
(membrane) energy exchanger with respect to
644
parameters.
645 646 647 648
and
and exchanger design
• The model is applicable to estimate frosting limits of all flat plate air-to-air heat/energy exchangers as long as the physical properties and performance parameters are available. • The model can be used in programing a HRV/ERV control system to activate a frost protection cycle only based on the inlet conditions. 44
Page 44 of 45
649
Ac ce p
te
d
M
an
us
cr
ip t
650
45
Page 45 of 45
S0378-7788(15)30372-8 http://dx.doi.org/doi:10.1016/j.enbuild.2015.11.007 ENB 6252
To appear in:
ENB
Received date: Revised date: Accepted date:
22-6-2015 30-9-2015 3-11-2015
Please cite this article as: P. Liu, M.R. Nasr, G. Ge, M.J. Alonso, H.M. Mathisen, F. Fathieh, C. Simonson, A Theoretical Model to Predict Frosting Limits in Cross-Flow Air-to-Air Flat Plate Heat/Energy Exchangers, Energy and Buildings (2015), http://dx.doi.org/10.1016/j.enbuild.2015.11.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A Theoretical Model to Predict Frosting Limits in Cross-Flow Air-to-Air Flat Plate Heat/Energy Exchangers
1 2 3
ip t
Peng Liu1, Mohammad Rafati Nasr2, Gaoming Ge2, Maria Justo Alonso3, Hans Martin Mathisen1, Farhad Fathieh2, Carey Simonson2
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Corresponding author: Peng Liu Tel: +47 735 92 744 Fax: +47 735 93 580 [email protected] Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway 1
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Department of Energy and Process Engineering, NTNU, Trondheim, Norway. Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada. 3 SINTEF Building and Infrastructure, Trondheim, Norway. 2
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Abstract
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In cold climates, the water vapor in the warm and moist exhaust air may condense and form frost
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on the heat/energy exchangers’ plate. In this study, a simplified theoretical model to predict the
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inlet conditions under which frost will form in the flat plate heat/energy exchangers is developed.
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The model uses the exchanger design parameters and operating conditions to determine the
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frosting limit. Experimental tests are conducted to validate the frosting limits model. The results
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show that the predicted frosting limits have consistent agreements with experiments, and energy
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exchangers have a lower risk of frosting than the heat exchangers. Furthermore, a parametric
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analysis using the theoretical model is performed to estimate the impacts of number of heat and
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moisture transfer units (
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membrane permeability on frosting limits of heat/energy exchangers. It is found that air flow
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rate has significant impacts on frosting limits. The combinations of sensible and latent
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and
), aspect ratio of aluminium spacer, air flow rate, and
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effectiveness ensuring no frost inside energy exchanger are studied theoretically. The model can
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be applied to improve the design of exchangers to reduce or avoid frosting for cold climates. The
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frosting limits of cross-flow membrane energy exchanger can also be regarded as criteria to
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conduct selection and feasibility analysis of energy exchanger and compare with counter-flow
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exchanger as a reference in future study.
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Keywords
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Frosting limit; heat exchanger; membrane energy exchanger; cross-flow
33
Introduction
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Air-to-air heat/energy recovery ventilators (HRVs/ERVs) have been widely used in heating,
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ventilation and air-conditioning (HVAC) systems to reduce energy consumption for ventilation
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and the green-house air emission, especially in hot and humid climates or cold climates. In these
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systems the outdoor fresh air and the indoor stale air enter the exchangers by separated sides.
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Sensible heat, latent heat, or both are transferred from one air stream to another, depending on
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the temperature and moisture gradients. When warm and moist exhaust air passes over the cold
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plate surface of an exchanger, water vapor condenses and frost forms on the surface if the plate
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temperature is lower than both the air dew point and water freezing point. In cold climates
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defined by international climatic zones with thermal criteria [1] such as Canada and northern
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Europe, frost often forms inside the HRVs/ERVs and would negatively impact the performance
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of the exchangers in winter[2]. This frosting issue is more critical when the outdoor temperature
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is extremely low.
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Defrosting or protecting heat/energy exchangers from frosting has remained as an important
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topic for decades. A recent numerical simulation for a residential house under Canadian winter
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condition by [3] showed that the yearly demand of defrosting cycle for a heat exchanger is 3.5
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times higher than an ERV. The reason is that ERVs transfer both heat and moisture
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simultaneously between supply and exhaust air streams, which encounter frosting at a lower
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temperature compared to HRVs in cold climates. [4] and [5] indicated that the frost occurred
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approximately 5 to 10
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study by Rafati [6] indicated that the ERV is more efficient than the HRV under frosting
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conditions. It also concluded that preheating the supply air to prevent frosting is more efficient
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than bypassing the supply air method to defrost the exchangers, and the prediction of the frosting
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limits is critical for the exchangers in practical applications. The recent literature reviews on the
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use of heat/energy exchangers in cold climates, frost and frosting control strategies for air-to-air
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exchangers found that the flat plat (membrane) energy exchanger has promising potentials in
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reducing or avoiding the frost instead of conventional heat exchanger. [2][7].
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The research work in frosting of flat plate heat/energy exchangers can be divided in two
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categories. The first type is dealing with predicting the properties of a frost layer such as density,
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heat conductivity and surface roughness as a function of time and temperature. Most of these
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models are correlations or combination of theoretical and experimental results on frost
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properties. Detailed reviews in frost properties and models were published [8]–[10]. However,
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most of these models are limited to some specific geometries and a range of temperature of the
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cold surface. Therefore, it is not easy to apply those results to other air-to-air exchangers with
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different exchanger configurations and operating conditions. In addition, there is a lack of
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lower in a desiccant wheel (ERV) than conventional HRVs. Another
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quantitative dependency analysis of the frost-air interface temperature which plays a very
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important role in heat transfer analysis.
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In the second category, effect of frosting in the performance of the heat or energy exchangers
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was described. Bantle [11] used an empirical heat transfer coefficient for a frosted surfaces to
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predict the performance of a counter-flow exchanger. Philips et al. [12] applied a numerical
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method to determine changes in effectiveness in a counter-flow exchanger under frosting
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condition. He calculated the frost thickness and evaluated its effect on the effectiveness. In other
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works [13], [14], Phillips assumed the frosting limit as a known parameter and based on that he
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theoretically calculated the energy impact of different defrosting strategies for a counter-flow
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exchanger using weather data.
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The frosting limit in this study refers to the specific combinations of supply (outdoor) air
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temperature and exhaust (indoor) air relative humidity which initiate frosting in the flat plate
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heat/energy exchangers. There are only few works which investigated the effects of operating
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conditions on frosting limits. Ruth [5] conducted tests on an aluminum heat-wheel and found that
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occurrence of frosting was greatly dependent on the exhaust air humidity. Frosting was observed
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at outdoor temperature ranged from -26
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between 25% and 30%. Fisk [4] compared frosting limits for different cross-flow exchangers
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experimentally. He used an analytical model to predict the frosting limit for a counter-flow
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exchanger as a reference in the work. In his model, the influence of the heat released from
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condensation on temperature of the plat was considered. He further investigated the indoor and
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outdoor environmental conditions that initiated freezing with experiments for cross- and counter-
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to -16
when the relative humidity of exhaust air was
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flow flat plate heat exchangers and a cross-flow energy exchanger. The frosting limits of the
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exchangers were plotted in the research [15]. However, the theoretical frosting limit model was
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not given in the research. Tests were conducted to determine the frosting limits for a pure-
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counter-flow heat exchanger [16]. The frosting limits ranged linearly from -23
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outdoor air temperature with exhaust air RH from 58% to 32% when the exhaust air temperature
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was 24°C. The criterion of determining the limits was not either presented. Holmberg[17] used
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CFD method to solve coupled heat and mass transfer equations in a two dimensional space to
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predict temperature distribution in a single and double pass cross-flow heat exchanger under
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steady state conditions. In another work, Holmberg [18] theoretically calculated the frosting
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limits for energy wheels. In his model two types of wheels with constant effectiveness for fixed
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inlet conditions were presented. Through a field test for a house in Ontario (Canada), Zhang [3]
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found energy exchanger performance was not deteriorated until supply air temperature reached
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. In recent years, Liu et al. [19], [20] developed a one-dimensional theoretical model to
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determine frosting limits for counter flow heat and energy exchangers. Liu applied this model
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with weather data of Norway to predict frosting operation conditions throughout the daily coldest
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outdoor temperature of a year for a counter-flow energy exchanger in Oslo. In the model, two
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conditions to cause frosting formation are subzero surface temperature and condensation over the
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surface. The counter-flow heat/energy exchangers are widely used since the counter-flow
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arrangement usually provides higher effectiveness compared to other arrangements [21].
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However, the high effectiveness nature of counter-flow may lead to a higher frosting risk due to
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the colder exhaust air being created. The frost tends to occur at higher outdoor air temperature or
of
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to -9
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lower indoor relative humidity. Frosting up inside the exchangers could conversely reduce the
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initially-designed high effectiveness.
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In general, following shortcomings are noticed in the literature:
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• Previous researches were mainly based on experiments that were limited to specific
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design or operating conditions.
• The proposed models were limited to counter-flow heat/energy exchangers.
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• Most of theoretical works were validated with experiments only for a specific design or
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operating condition.
• The main type of energy transfer was sensible heat. Very few studies have considered
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latent heat in the form of mass transfer.
• The authors did not find the specific theoretical model in the literature which predicted
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the theoretical frosting limit for cross-flow air-to-air flat plate heat/energy exchangers.
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In this study, a theoretical model to predict the critical operating conditions for frosting in
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cross-flow heat/energy exchangers is developed. The frosting limits of heat/energy
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exchangers for a residential use are theoretically and experimentally studied. The effects of
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design parameters are evaluated which may guide the frost-free air-to-air cross-flow flat plate
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heat/energy exchangers design. The cross-flow frosting limits model can be the reference to
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further compare cross-flow and counter-flow with respect of frosting limits in future
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research.
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Mathematical model
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The main goal of this study is to develop a theoretical model to predict the critical operating
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conditions in which the onset of frosting occurs in cross-flow exchangers. It is important to
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include the exchanger physical and design parameters (such as air channels spacing, heat
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conductivity and water vapor diffusivity of the plates) and operating conditions (such as air-flow
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rate, temperature and relative humidity). Due to two-dimensional nature of heat and mass
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transfer in cross-flow flat plat exchangers, modeling is more complex than the counter-flow
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arrangement.
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Two necessary conditions to trigger frosting are subzero temperature of the plate surface and
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condensation formation at the most likely frosting positions. These two conditions are used to
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derive frosting limits for different exchangers in this study. If the exchanger configuration and
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air flow rate are given then supply air (outdoor) temperature and exhaust inlet (indoor) relative
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humidity play more important roles in the frosting limit [22].
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In cold regions condensation and frosting is potential to take place in the exhaust side in
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HRVs/ERVs [2]. The temperature and humidity distributions across a cross-flow exchanger are
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not uniform (Zhang, 2008), therefore the possibility of frosting at some locations is higher than
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other parts. According to experiments [24] and numerical model (Holmberg, 1989; Zhang,
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2008), frost more likely first appears at the exhaust air outlet closest to the supply air inlet for the
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cross-flow exchangers which is known as “cold corner” (the navy blue triangle) as shown in
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Figure 1(b). In this study, the outlets of first exhaust channels at the corner are regarded as the
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most likely frosting positions. A detailed view of the most likely frosting spots and the research
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domain channels for this paper is presented in Figure 1(c). The frosting limits can be obtained by
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determining the critical frosting conditions at these positions. Developing the frosting limits
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subsequently becomes to express the temperature and moisture at these positions with inlet
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operating and design parameters. The following part deals with determination of the temperature
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and the moisture at the “cold corner”.
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Figure 1 (a) Qualitative membrane temperature distribution, (b) The schematic view of cross-
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flow exchanger structure with corrugated aluminum spacer and channels with highest risk of
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frosting, (c) A detailed view of most likely frosting spot and the research domain for developing
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frosting limits model
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Assumptions
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The following assumptions are used in this research:
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1. Frosting initially forms in the outlets of exhaust air channels that are closest to the supply inlet in both heat and energy exchangers (the navy blue triangles in Figure 1(b) and (c));
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2. Air flows through all channels are homogeneous and incompressible;
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3. The air mass flow rate in each channel of supply and exhaust air is identical;
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168 169 170
4. The convection heat and mass transfer coefficients are constant throughout the exchanger; 5. The specific heat capacity of both air streams are equal and constant throughout the air channels of exchangers;
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6. No air leakage occurs from/to the exchangers or between two air streams;
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7. The thermal resistance of the exchanger plates is negligible due to the thin thickness;
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8. Condensation occurs only on the exhaust side;
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9. Condensation heat has a negligible impact on frosting in energy exchanger. The effect on
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plate heat exchangers can also be omitted when the indoor air relative humidity is below
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30% [25];
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10. The thermal properties of both fluids and exchanger walls do not vary with temperature;
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11. The velocity, temperature, and humidity distributions of the fluids are uniform at the
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inlets of the exchanger;
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12. There is no heat sources and heat sinks in the air stream;
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13. The exchangers are well insulated and no heat is transferred between the exchanger and
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surrounding.
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Frosting limits
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The frosting limits of membrane energy exchanger combine the critical outdoor temperature and
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the condensation limit which are corresponding to the two necessary frost forming conditions.
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Frosting starts occurring when the operating conditions meet the two necessary frosting 10
Page 10 of 45
conditions. In other words, the outdoor temperature is lower than the critical outdoor air
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temperature and the indoor RH simultaneously exceeds the condensation limits. The definitions
190
and derivations of critical outdoor air temperature and condensation limit are addressed in the
191
follow sections.
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Critical supply (outdoor) air temperature
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A critical outdoor air temperature is defined as the lowest outdoor air temperature to maintain the
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membrane temperate over the freezing point at the most likely frosting positions. The critical
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outdoor air temperature corresponds to the aforementioned first necessary frost forming
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condition which is the sub-zero temperature of the membrane/film. The heat transfer through the
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first exhaust channels to supply air side is calculated by equation (1).
(1)
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is the log mean temperature differences which is defined in equation (2) for cross-flow
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exchanger. Heat gain by exhaust air from inlet to outlet in the first exhaust channel is given by
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equation (3).
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(2)
(3)
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The energy changes through the supply air channels within research domain as shown in Figure
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1 (c) is 11
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(4)
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Based on energy conservation, we have
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(5)
The mass flow rates in supply and exhaust air sides in the research domain have the following
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relationship,
can be derived from equations (3) to (6),
The
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(6)
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(7)
In general, when the channel number n is more than 30, the right term in equation (7) can be
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omitted based on author’s calculation. The supply air temperature changes is negligible
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compared to the maximum temperature changes in the exchanger. As a result, the correction
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factor
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by replacing
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is 1 as
is nearly equal to
with
[26]. The error of the log mean temperature difference
is under 6%. The channel number in this study is 31.
combining equations (1) to (5) and
can be expressed as a function of ,
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(8)
To meet frosting condition, the plate temperature
should be equal to or lower than freezing
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point. When the thermal resistance of plate is negligible due to the thin thickness, the
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temperature drop across the plate is omitted[27]. The plate temperature can be computed from
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equation (9).
(9)
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According to assumption 6, the convective heat transfer coefficient on the supply and exhaust air
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sides are equal. Thereafter, the plate temperature at exhaust outlets for the first channels can be
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expressed equation (10).
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Where the number of heat transfer unit for the first exhaust air channel
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equation (11).
(10)
is defined by
(11)
is expressed in equation (12) when
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The critical supply air temperature
. This
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temperature shows the outdoor air temperature value at which the plate temperature reaches
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freezing point at the most likely position of frosting. 13
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(12)
Condensation limit
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The condensation limit is the combination of indoor relative humidity and outdoor air
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temperature resulting in the exhaust air starting to condensate at most likely frosting positions.
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The condensation limits correspond to the second necessary frost forming condition namely the
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exhaust air adjacent to the membrane at the exhaust air outlet reaching saturation.
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Using mass conservation, the moisture content of the exhaust outlet air close to most likely
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frosting position can be expressed as equation (13) based on the derivation of equation (8). The
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moisture content of exhaust inlet (indoor) air is presented with equation (14) through rearranging
234
equation (13). Number of moisture transfer unit
is given in equation (15).
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(13) (14) (15)
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is the moisture content of supply (outdoor) air and regarded as known values which are
236
usually very low for cold climates. The relationship between moisture content and relative
237
humidity is described using Clapeyron equation to represent the saturation vapor pressure as
238
shown in equation (16)[23]. 14
Page 14 of 45
(16)
The water vapor starts to condense when the exhaust air close to the surface reaches saturation
240
namely relative humidity of exhaust air at outlet being 100%. The condensation limits can be
241
described through equations (13) to (16). The limits can be expressed as a function of the inlet
242
temperature and moisture parameters.
243
The
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calculated and validated in this study. The frosting limits of sensible-only heat exchanger can be
245
obtained with this model by substituting
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exhaust and supply air sides.
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Experimental Validation
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Test facility
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A test facility was built up to test full size cross-flow air-to-air exchangers. This facility enables
250
researchers to test different exchangers under non-frosting and frosting conditions. The layout of
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the test facility is shown in Figure 2. The test rig consists of two environmental chambers, four
252
fans, a test section, and connecting pipes.
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used in the critical outdoor air temperature and condensation limits are
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since there is no moisture transfer between
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and
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Figure 2. Schematic of the experimental setup for air-to-air cross-flow exchangers
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This test setup is designed as an open loop with two fans in each air stream. Air is drawn from
256
each chamber in a separate air stream using two fans; one before and one after the test section, in
257
each air stream. Flow rates are adjusted by voltage regulator connected to each fan. Presence of
258
two fans at each air stream allows to control the pressure at the exchanger to minimize the air
259
leakage to or from the ambient, and to produce balanced flow rate. The exchanger can be tested
260
at any temperature between -30°C to 30°C, while relative humidity can be 10% to 90% for the
261
flow rate equal to
262
(Figure 2). Pipes are connected to the exchanger with inlet expansion and outlet contraction
263
diffusers. These headers are designed to produce uniform flow fields at the exchanger inlet face.
264
Velocity measurement at the face of the exchanger confirmed uniform profile for the inlet air.
265
Moreover, heat loss in the headers is negligible.
266
Different parameters such as temperature, relative humidity, flow rate and pressure drop are
267
measured or calculated in experiments. Temperature of air is measured using T-type
268
thermocouples (cupper-nickel). Vaisala humidity and temperature sensors are used to measure
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Ac ce p
. In the test section the exchanger is located in an insulated test box
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Page 16 of 45
both relative humidity and temperature. Air flow rate is measured by employing an orifice plate
270
with the standard[28]. Pressure drop is measured by two types of pressure transducers. Pressure
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drops across the orifice plates (for flow rate measurement) are gained by general purpose
272
diaphragm pressure transducers, while low pressure transducers are used to capture changes in
273
pressure drop across the exchanger. Performance of the exchanger is evaluated by effectiveness
274
which is the ratio of the actual energy transfer over the maximum possible energy transfer [29].
275
Uncertainty of sensors are determined according to ASME PTC 19.1 [30]. Each sensor is
276
calibrated with a calibrator where its signals are recorded by a data acquisition (DAQ). Once the
277
data are collected, precision and bias are calculated for the sensor. Then calibration curves are
278
developed where they are applied to raw data from experiments.
279
Frosting detection methods
280
During the design of the test facility, possible methods of frost detection were reviewed [2]. The
281
visual technique and pressure drop method are used in this study, since they are more accurate in
282
detecting the frosting limit. In the visual technique, two endoscope cameras are used to view the
283
exchanger during the experiments. These endoscopes are installed just after the outlet face, one
284
in the exhaust side and one in the supply side. The endoscopes are 9 mm in diameter which is
285
larger than the channel spacing, therefore, it is not possible to insert the endoscope inside the
286
channels. Static pressure drop across the exchanger is also monitored during the entire
287
experiment. An increase in pressure drop across the exchanger is a sign of frosting due to partial
288
blockage of the channels by frost. More details for these methods were presented in [22].
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In all experiments, the pressure drop across the exchanger and the pictures are analyzed to detect
290
frosting. It takes approximately 3 hours for each experimental test. Figure 3(a) shows a
291
comparison of the pressure drop in two experiments for heat and energy exchangers. It is clear
292
that pressure drop in the exhaust side where the risk of frosting is higher, increased, while no
293
change in the supply side was captured. This means there is no frost in the supply side and that
294
was in agreement with visual method. Figure 3(b) shows partial frost formation at the exhaust
295
outlet of the energy exchanger by visual method in the energy exchanger experiment. It can be
296
seen that the channels at the exhaust outlet are covered with frost. Such situation was observed
297
for heat exchanger under the similar working conditions. Thus, in this example the working
298
conditions were considered in the frosting zone.
299 300
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Figure 3. Frosting detection method when:
.
(a) Pressure drop method, (b) View of the energy exchanger at the end of experiment.
302
To find the frosting limit experimentally, each exchanger is tested at different
303
the rest of operating conditions are fixed. The lowest
at each
and
while
or in another word, the
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304
highest
305
method defines the experimental frosting limit. To check the repeatability and accuracy of the
306
results, exchangers are tested twice at some of the frosting limit points.
307
Results and Discussion
308
Model validation:
309
The numbers of heat and moisture transfer units are indispensable to compute the frosting limits
310
using the developed model in this study. This section will illustrate the method to calculate the
311
number of heat and moisture transfer units and model the performance of the exchangers with
312
aluminum cross-corrugated spacers. Two geometrically identical exchangers are tested in the
313
study. The energy exchanger is made with polymer membranes to separate the supply and
314
exhaust air streams, which are permeable to water vapor, while the heat exchanger is made with
315
impermeable polymer films with the same thickness (Figure 4). The corrugated aluminum
316
spacers are placed inside the supply and exhaust air channels to support the elastic and flexible
317
membrane/film and enhance the convective heat transfer.
and
of heat/energy exchanger
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with frosting that is captured with either by pressure drop or visual
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at each
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318
Figure 4. Tested exchangers and their geometrical parameters
320
The conjugate heat and moisture transfer and NTU calculation for air-to-air cross-flow
321
exchangers using design and physical properties of the exchanger are available in detail in [23].
322
The physical dimensions of the exchangers and properties of the membranes are presented in
323
Table 1 and Figure 4. A key parameter is the water vapor diffusivity of the membrane which
324
was measured to be
325
Table 1. Physical specification of the heat and energy exchangers tested
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d
according to the method of [31].
Ac ce p
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Parameter Number of channels for each flow, n Half duct height, a Half duct width, b Apex angle, Hydrodynamic diameter, Exchanger width , height , depth Membrane thickness, Membrane water vapor diffusivity,
Value
Reference Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement Lab measurement
Thermal conductivity of membrane,
[23]
Thermal conductivity of fin,
[23] [32] [32] [23] [32] Lab measurement
Thermal conductivity of air, Density of air, Water vapor diffusivity in the air, Kinetic viscosity of air, Volumetric air flow rates, 20
Page 20 of 45
Face velocity, Reynolds Number, Re
Lab measurement Lab measurement
22
326
The Reynolds number indicates laminar flow regime inside the air ducts. Using equations in [23]
328
the pressure drop,
329
agreement with the experimental value,
330
[23], heat and mass transfer coefficients (h and
331
to calculate the Nusselt and Sherwood numbers, the total heat and mass transfer coefficients
332
(
333
equations (11), (15) and (17) to (19). The calculated exchanger performance parameters for the
334
design condition are shown in Table 2.
ip t
327
across the exchanger was calculated as 20.3 Pa. The theoretical
is in
cr
. According to the procedure presented in
us
respectively) and the parameters given in [33]
(17)
te
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an
), NTU, and effectiveness of the cross-flow exchangers are obtained from
Ac ce p
(18)
(19)
335
To verify the
calculated from the theory, both exchangers were tested at AHRI winter test
336
condition [34]. A full uncertainty analysis was conducted to account for propagation uncertainty
337
through the measurements bias and precision error. The results from repeated experiments were
338
within the uncertainty range. Experimental and theoretical results are summarized in Table 3 and
339
shows good agreements. It can be concluded that the theory is reliable in predicting the 21
Page 21 of 45
340
and
341
theoretical model in this study.
342
The
343
energy transfer area and mass flow rate changes at same proportionality for the exhaust air
344
channel shown in Figure 1 (c) in equations (11) and (15).
345
Table 2. Theoretical performance parameters
. A parametric analysis of the frosting limit is conducted using the developed
cr uncertainty
0.04 0.02 0.08 0.09 0.14 0.10 0.14
Ac ce p
347
te
Total Mass Transfer Coefficients Number of Heat Transfer Unit Number of Moisture Transfer Unit 346
since the
Value
d
Nusselt Number Sherwood Number Heat Transfer Coefficients Mass Transfer Coefficients Total Heat Transfer Coefficients
us
Parameter
an
Parameter
and
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for computing domain have same values as
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and
Table 3. Comparison between the experimental and theoretical effectiveness
Exchanger type
Theoretical Experimental Theoretical Experimental
HRV
ERV
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Model Validation: Frosting limit
349
To determine the experimental frosting limit, each exchanger is tested under the conditions near
350
the theoretical frosting limit. The theoretical model is used to select the test conditions for the
351
experiments. In the validation experiments, the exhaust inlet temperature and supply inlet
352
relative humidity are approximately constant
353
change between 5% to 50% and -5 to -33 , respectively. Results of these experiments lead to a
354
map for frosting limit, as shown in Figure 5(a) and (b). In this figure only the lowest
and
us
cr
, while
at each
in which frosting captured is presented. In total more than 80 tests were conducted, and each
an
355
ip t
348
was run for 2 to 3 hours.
357
In Table 4 a summary of the uncertainties in measured and calculated parameters are presented.
358
It should be noted that all these values are an approximate, since these may change for each test.
359
Table 4. Uncertainties in measured and calculated values with 95% confidence interval
te
d
M
356
Ac ce p
Parameter Temperature (°C) Relative humidity Vaisala (% RH) Pressure drop (Pa) Mass flow rate (%) Sensible effectiveness (%) Latent effectiveness (%) Humidity ratio (%)
Uncertainty 0.2-0.25 1.5-2 3-7 2 2 2-6 2-6
360
The critical outdoor air temperature and condensation limits are computed from equation (12)
361
and (16) respectively. The overlapping operation conditions in which the critical outdoor air
362
temperature and condensation limits are reached simultaneously consist of the frosting limits. 23
Page 23 of 45
The number of heat and moisture transfer units are calculated from equations (11), (15), (17) and
364
(18) and the required parameters are given in Table 1 and Table 2. The theoretical frosting limits
365
for energy and heat exchanger are respectively plotted in Figure 5(a) and (b).
366
The RH discrepancies between theoretical and experimental frosting limits,
367
Figure 5(a) and (b) as well. The dashed line indicates the critical supply inlet (outdoor) air
368
temperature. The plate temperature at the most likely frosting positions is below the freezing
369
point if the outdoor temperature is lower than the critical temperature (the left area of the dashed
370
line). The experimental and theoretical results have same trends as shown in Figure 5(a) and (b).
371
The lower the supply inlet air temperature is, the less moisture can be carried by the exhaust air
372
without occurring frost in exchangers. The trend is obviously consistent with the engineering
373
experience. Overall, very good agreement between experiments and theoretical predictions are
374
obtained for both heat and energy exchangers. To verify the model at
375
should be less than 10%. These conditions were not obtained in the experiments due to high
376
humidity level in the lab.
ip t
363
°C,
Ac ce p
te
d
M
an
us
cr
, are shown in
24
Page 24 of 45
ip t cr us an M
377
te Ac ce p
379
d
378
25
Page 25 of 45
ip t cr us an
380
Figure 5. Experimental and theoretical frosting limits for the (a) energy exchanger and (b) heat
382
exchanger
383
All the theoretical results slightly over predict the frosting limits compared to the experiments.
384
Theoretical model assumes frost emerging once the frosting conditions are met. However, the
385
amount of the frost is too small to be detected by the pressure or visualization methods when the
386
operating conditions are close to the limits, especially for the low RH of exhaust air (the left
387
points in Figure 5 (a) and (b)). As a result, the theoretical model is more sensitive compared to
388
the experimental tests to detect frosting limits. The researchers or engineers have to be aware of
389
over predicting when they employ the frosting limit model to evaluate or design an exchanger.
390
Comparison between heat exchanger and energy exchanger shows that the energy exchanger has
391
a lower risk of frosting as expected. A bigger gap between heat and energy exchangers frosting
392
limits is observed at a higher
Ac ce p
te
d
M
381
. It results from the significant effect of moisture transfer in 26
Page 26 of 45
energy exchanger on frosting. Therefore, any parameter that affects the moisture transfer such as
394
membrane permeability, membrane thickness, exchanger design and operation conditions, may
395
play an important role in the frosting limit.
396
Considering the results in Figure 5 (a) and (b), these specific exchangers may still have frost
397
problem inside the exhaust channels in the general recommended comfort zone of indoor relative
398
humidity (30%-60%) [32] and at any
399
flow rate. However, it should be noted that in most cold climate regions the actual indoor relative
400
humidity is usually much lower than the recommended level which somehow results in lower
401
risk of frosting in exchangers [7] [35].
402
Parametric analysis
403
A parametric study is conducted to identify important factors for the frosting limit. In this regard,
404
a two-steps process is adopted; the effects of
405
effects of design parameters on
406
presented for the energy exchanger. The analysis for heat exchanger can refer to the parameters
407
only related to heat transfer.
408
Effect of NTU on the frosting limit
409
The effects of
410
shown in Figure 6 and Figure 8. In both figures, the region on the left hand side of critical
411
outdoor temperature (
cr
ip t
393
te
d
M
an
us
when the exchanger is running at nominal air
on the frosting limit, and the
. The results in the parametric analysis are
Ac ce p
and
and
and
on the frosting limit of the cross-flow energy exchanger are
) represents that the plate/membrane surface temperature at the most
27
Page 27 of 45
412
likely frosting position is below freezing point. The condensation occurs in the upper area of the
413
condensation limit (
414
conditions with frosting according to the theoretical model. The lower-right boundary of this
415
overlapping area is then the frosting limit. In Figure 6 and Figure 8, the solid lines represent the
416
base case presented in Table 2. The rest of the lines are developed through changing
417
Figure 6) and
418
In Figure 6 the frosting limit change considerably when
419
rate is not proportional with
420
after the
421
map; however, this measure will in turn reduce the effectiveness (Figure 7) and energy recovery
422
rate in practice. The final counteracted consequence is difficult to estimate only from this
423
research. The design parameters that could affect
424
parametric analysis.
(in
cr
ip t
). Consequently, the upper-left overlapping area shows the operating
can only slightly affect the frosting limit
could narrow-down the frosting region in the
will be investigated in the next part of
Ac ce p
te
d
M
value reaches 3. Decreasing
varies from 1 to 5.The changing
an
. Increasing
us
(in Figure 8).
28
Page 28 of 45
ip t cr us an
425
Figure 6. Effect of
on frosting limit of the energy exchanger. Upper-left area represents the
427
frost zone
428
Figure 8 indicates that if the
429
frosting region will be greatly reduced, especially at higher
430
latent effectiveness could be the reason for the greatly reduced frosting region. Figure 7 which is
431
developed from equation (19) shows that at lower NTU the variation rate of effectiveness is
432
higher. The triangular points in the figure represent the sensible and latent effectiveness of the
433
energy exchanger used in this research.
434
The frost will be completely avoided for typical indoor air moisture levels (
435
the
436
higher latent effectiveness undergo less frost in cold regions. When the indoor moisture
d
M
426
stays constant (1.6), the . The significantly increased
Ac ce p
te
is raised from 0.5 to 3 while
) when
reaches to 3. The results agree with previous findings that the energy exchangers with
29
Page 29 of 45
generation rate is relatively high, the moisture recovery of the energy exchanger may lead to
438
undesired high indoor RH especially for transitional seasons. In cold climates, the effects of
439
membrane energy exchanger with respect to frosting avoidance and low excessive humidity
440
decay need to be further studied. The frosting limits can be employed as criteria to conduct
441
selection and feasibility of membrane energy exchanger in future research.
442
Ac ce p
te
d
M
an
us
cr
ip t
437
443
Figure 7. Effectiveness VS NTU for both sensible and latent heat
444
One of the manners to raise
445
resistance of the membrane. The membrane moisture diffusion and convection resistance will be
446
discussed in the following analysis.
without changing
is to reduce the moisture transfer
30
Page 30 of 45
ip t cr us an M
447
Figure 8. Effect of
449
the frosting zone
450
The developed frosting limit model can also be used to guide the design of heat/energy
451
exchangers to avoid frosting. In the model, the specific combinations of sensible and latent NTU
452
can be applied to predict if the exchanger is under frosting condition or not when the operating
453
condition is known. The process of computing the combinations is similar to determine frosting
454
limits by changing variables and knowns. The sensible and latent effectiveness is only the
455
function of
456
plat heat/energy exchangers. The minimum
457 458
on frosting limit of the energy exchanger. Upper-left area represents
Ac ce p
te
d
448
and
and
respectively as shown in Figure 7 for mass balanced air-to-air flat required to prevent frosting at different values of
are shown in Figure 9 when the indoor RH is a constant (30%). The more wildly used
and straightforward combinations of sensible and latent effectiveness which can theoretically 31
Page 31 of 45
ensure frost free design are given in Figure 9. It can be seen that an exchanger with a higher
460
sensible effectiveness requires a higher latent effectiveness to prevent frosting. The required
461
lowest latent effectiveness is slightly lower than sensible effectiveness to completely prevent
462
frosting under the designated operating conditions.
463
Ac ce p
te
d
M
an
us
cr
ip t
459
464
Figure 9. Minimum latent effectiveness for frost free energy exchanger VS sensible effectiveness
465
at different
466
Parametric study on NTU
467
After understanding the role of
468
design parameters of exchanger is performed in this section. Among those air channel aspect
and
in frosting limit, a parametric study on the
32
Page 32 of 45
469
ratio, air-flow rate, membrane permeability are selected. Each of these parameters is changed by
470
a factor between 0.25 to 4.00 and the resulting NTU is recorded. Their influence on
ip t
is depicted in Figure 10 and Figure 11 respectively.
471
As it can be seen in Figure 10 and Figure 11, decreasing air-flow rate can significantly increase and
473
which have counteracting impacts on frosting limit indicated in Figure 6 and
cr
472
and
Figure 8. The eventual consequence of changing air-flow rate on frosting limit can be somehow
475
indicated by Figure 9 in respect with different
476
halved in comparison with experiment condition, the
477
respectively which can be found in Figure 10 and Figure 11. The influences of these
. For instance, if the air flow is
and
become 3.3 and 1.0 and
M
an
and
us
474
can then be addressed by using Figure 9. The aspect ratio greatly affects heat transfer
479
while it has negligible influence on moisture transfer. Higher aspect ratio enlarges the frosting
480
area concluded from Figure 8, Figure 10 and Figure 11. Meanwhile the high aspect ratio also
481
increases the pressure drop through the intensive spacer. On the other side, a lower aspect ratio
482
means a wider supporting aluminum spacer at a fixed channel spacing in which case the elastic
483
membrane tends to deform. The deformation probably cause frosting as well which was found
484
with the experiments [36]. An optimal aspect ratio of aluminum spacer air channels can be
485
determined based on these criteria.
486
The
487
has no effects on heat transfer. The influence of membrane permeability on
488
negligible in the tested energy exchanger. The reason is that the diffusion resistance of
489
membrane merely accounts for a small proportion of total moisture transfer resistance and 33
Ac ce p
te
d
478
is independent on membrane permeability, since the membrane moisture permeability can also be
Page 33 of 45
convective resistance dominates in the total moisture transfer resistance. The effective means to
491
improve moisture transfer is to enhance moisture convection in the exchanger.
. The horizontal axis shows the ratio of
d
on
Figure 11. Effects of different design
M
Figure 10. Effects of different design parameters
an
us
cr
ip t
490
te
the values over base value used in this paper
parameters on
. The horizontal axis
shows the ratio of the values over base value
Ac ce p
used in this paper
492
Conclusions
493
A theoretical model is developed to predict frosting limits for cross-flow air-to-air heat /energy
494
exchangers in cold climates. The model involves the exchanger’s design parameters and
495
operating conditions which include air flow rate, supply and exhaust inlet temperature and
496
relative humidity. The frosting limits of these two types of exchangers are plotted in a coordinate
497
with supply (outdoor) air temperature versus exhaust (indoor) air relative humidity using the
498
mathematical model. The theoretical limits are validated with experiments and relatively 34
Page 34 of 45
499
consistent with experimental results. It is found that the energy exchanger is considerably more
500
frost resistant than the heat exchanger. The critical temperature (frosting limit) of the energy
501
exchanger is
502
exhaust air relative humidity
503
The parametric analysis of theoretical frosting limit is conducted for the flat plate (membrane)
504
energy exchanger with respect to
lower than the heat exchanger under the same air flow rate
and
cr
ip t
, which is in consistence with other research.
and
and exchanger design parameters. Changing
us
505
to
merely affect frosting limit in a narrow range while increasing
with fixed
can significantly reduce the frosting zone.
507
The influence of air-flow rate needs to be further investigated due to the counteracting effects on
508
frosting limit. An optimal air channels aspects ratio can be determined in considering the
509
criterion of frosting. The diffusion resistance of this specific membrane accounts for a small part
510
of total moisture transfer resistance in the energy exchanger and has a negligible effect on the
511
frosting.
512
The combinations of sensible and latent effectiveness ensuring no frost are theoretically
513
evaluated for the cross-flow flat plate energy exchanger at different supply (outdoor) air
514
temperatures. The required lowest latent effectiveness is proximately equal to sensible
515
effectiveness when the exhaust air conditions are 21°C and 30% RH.
516
The model is applicable to estimate frosting limits of all flat plate air-to-air heat/energy
517
exchangers as long as the physical properties and performance parameters are available. In a
518
more practical level, this model can be used in programing a HRV/ERV control system to
Ac ce p
te
d
M
an
506
35
Page 35 of 45
activate a frost protection cycle only based on the inlet conditions. However, to get to that level,
520
much more studies and a detailed model validation for different design are recommended.
521
Acknowledgements
522
This research was financially supported by the Research Council of Norway through Norwegian
523
University of Science and Technology, the Research Centre on Zero Emission Buildings (ZEB)
524
and collaboration between University of Saskatchewan and Norwegian University of Science
525
and Technology (NTNU). The authors gratefully acknowledge the support from dPoint
526
Technologies Inc., Smart Net-Zero Energy Building Strategic Research Network (SNEBRN) in
527
Canada, and ASHRAE. The Authors also express their gratitude to Mr. David Kadylak and Mr.
528
Ryan Huizing for their tremendous help in preparing the paper and experimental setup
529
preparation.
Ac ce p
te
d
M
an
us
cr
ip t
519
36
Page 36 of 45
Ac ce p
te
d
M
an
us
cr
ip t
530
37
Page 37 of 45
te
d
M
an
us
cr
ip t
Nomenclature
Ac ce p
531
38
Page 38 of 45
ip t
M
Number of channel Convective heat transfer Volumetric flow rate Axial velocity in an air channel Moisture content Length and height of the exchanger
an
Mass transfer coefficient from the membrane
532
cr
Definition Total heat transfer surface area Hydrodynamic diameter of an air channel Water vapor diffusivity in membrane Water vapor diffusivity in the air Correction factor for cross-flow exchanger Mass flow rate of dry air Convective heat transfer coefficient Air channel length Temperature Total heat/mass transfer coefficient Pressure across the exchanger Half air channel height Half air channel width
us
Parameter
Acronyms
Ac ce p
te
d
Energy Recovery Ventilators Heat Recovery Ventilators Heating Ventilation and Air-Conditioning Number of Transfer Unit Nusselt number Relative humidity Sherwood number Reynolds number in each air channel
Greek letters
Difference ( Log mean for temperature) Heat or mass conductance Apex angle for fin Thickness(membrane, plate, frost) Effectiveness Kinetic viscosity of air Density General variable
Subscripts
39 First channel in exhaust side closest to supply air Exhaust Exhaust Inlet Exhaust Outlet
Page 39 of 45
Ac ce p
te
d
M
an
us
cr
ip t
533
40
Page 40 of 45
533
Reference
535 536
[1]
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537 538 539
[2]
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540 541 542
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[10] J. Iragorry, Y.-X. Tao, and S. Jia, “Review Article: A Critical Review of Properties and Models for Frost Formation Analysis,” HVAC&R Res., vol. 10, no. 4, pp. 393–420, Oct. 2004.
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[12] E. G. Phillips, R. E. Chant, B. C. Bradley, and D. R. Fisher, “A model to compare freezing control strategies for residential air-to-air Heat Recovery Ventilators,” ASHRAE Trans., vol. 95, pp. 475–483, 1989.
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[13] E. G. Phillips, D. R. Fisher, and R. E. Chant, “Freeze-control strategy and air-to-air energy recovery performance,” ASHRAE J., pp. 44–49, 1992.
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[14] E. G. Phillips, L. C. Bradley, R. E. Chant, and D. R. Fisher, “Comparison of freezing control strategies for residential air-to-air heat recovery ventilators,” ASHRAE Trans., pp. 484–490, 1989.
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[15] W. J. Fisk, R. E. Chant, K. M. Archer, D. Hekmat, F. J. Offermann, and B. S. Pedersen, “PERFORMANCE OF RESIDENTIAL AIR-TO-AIR HEAT EXCHANGERS DURING OPERATION WITH FREEZING AND PERIODIC DEFROSTS.,” in ASHRAE Transactions, 1985, vol. 91, no. pt 1B, pp. 159–172.
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[16] H. J. Sauer, R. H. Howell, and J. R. Wray, “Frosting and leakage testing of air to air energy recovery systems,” ASHRAE Trans., vol. 87, pp. 211–234, 1981.
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[17] R. B. Holmberg, “Sensible and latent heat transfer in cross-counterflow gas-to-gas heat exchangers,” J. Heat Transfer, vol. 111, no. February, pp. 173–177, 1989.
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[18] R. B. Holmberg, “Prediction of condensation and frosting limits in rotary wheels for heat recovery in buildings,” ASHRAE Trans., vol. 95, no. 32, pp. 64–69, 1989.
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[19] P. Liu, H. M. Mathisen, and M. J. Alonso, “Critical Sensible and Latent Effectiveness for Membrane Type Energy Recovery Ventilator ( ERV ) in Cold Climates,” in IAQ 2013 Environmental Health in Low Energy Buildings Conference, 2013, vol. 2500, no. Lstiburek 2002.
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[20] P. Liu, M. J. Alonso, M. Rafati Nasr, H. M. Mathisen, and C. J. Simonson, “Frosting Limits for Counter-flow Membrane Energy Exchanger (MEE) in Cold Climates,” in 13th International Conference on Indoor Air Quality and Climate,Hong Kong, 2014.
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[23] L. Zhang, Total heat recovery: heat and moisture recovery from ventilation air. New York, NY, USA: Nova Science Publishers, Inc., 2008.
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[25] W. J. Fisk, R. E. Chant, K. M. Archer, D. Hekmat, F. J. Offermann, and B. S. Pedersen, “Onset of freezing in residential air-to-air heat exchangers.,” in ASHRAE Transactions, 1985, vol. 91, no. pt 1B, pp. 145–158.
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[26] J. Holman, Heat Transfer. McGraw-Hill Education, 2009.
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[27] J. L. Niu and L. Z. Zhang, “Membrane-based Enthalpy Exchanger : material considerations and clarification of moisture resistance,” vol. 189, pp. 179–191, 2001.
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[28] ISO 5167-1, “Measurement of fluid flow by means of pressure differential devices - Part 1: Orifice plates, nozzles and Venturi tubes inserted in circular cross-section conduits running full,” International Standards Organization, Geneva, Switzerland., 2003.
611 612 613
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614 615
[30] ASME, “ASME PTC 19.1 test uncertainty,” THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS, New York., 2005.
616 617 618
[31] G. Ge, G. I. Mahmood, D. G. Moghaddam, C. J. Simonson, R. W. Besant, S. Hanson, B. Erb, and P. W. Gibson, “Material properties and measurements for semi-permeable membranes used in energy exchangers,” J. Memb. Sci., vol. 453, pp. 328–336, 2014.
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621 622 623
[33] L.-Z. Zhang, “Heat and mass transfer in plate-fin sinusoidal passages with vaporpermeable wall materials,” Int. J. Heat Mass Transf., vol. 51, no. 3–4, pp. 618–629, Feb. 2008.
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ip t
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[34] AHRI Standard1061, Performance Rating of Air-to-Air Heat Exchangers for Energy Recovery Ventilation Equipment. Arlington, USA: Air-Conditioning & Refrigeration Institute, 2011.
627 628
[35] K. Kumaran and C. Sanders, Annex 41 MOST-ENG Subtask 3: Boundary Conditions and Whole Building HAM Analysis, 1st ed. International Energy Agency (Exco ECBCS), 2008.
629 630
[36] S. M. Aarnes, “Membrane Based Heat Exchanger,” Master's thesis. Norwegian University of Science and Technology, Trondheim, Norway. June, 2012.
cr
ip t
624 625 626
631
us
632 633
an
634 635
M
636 637
640 641 642
d
heat /energy exchangers in cold climates.
te
639
• A theoretical model is developed to predict frosting limits for cross-flow air-to-air
• The theoretical limits are validated with experiments and relatively consistent with
Ac ce p
638
experimental results.
• The parametric analysis of theoretical frosting limit is conducted for the flat plate
643
(membrane) energy exchanger with respect to
644
parameters.
645 646 647 648
and
and exchanger design
• The model is applicable to estimate frosting limits of all flat plate air-to-air heat/energy exchangers as long as the physical properties and performance parameters are available. • The model can be used in programing a HRV/ERV control system to activate a frost protection cycle only based on the inlet conditions. 44
Page 44 of 45
649
Ac ce p
te
d
M
an
us
cr
ip t
650
45
Page 45 of 45