# Modeling the effect of HVAC operation on transport of gaseous species to indoor surfaces.

INTRODUCTIONHumans spend approximately 90% of their lives in indoor environments and for this reason, a large portion of a person's exposure to hazardous pollutants occurs indoors. Many researchers have studied indoor pollutants and created methods for modeling and controlling the movement and presence of pollutants in indoor environments. The motivation for the current study issues from two distinct areas of study related to the indoor environment. The first is accurate modeling of indoor environments. Many models exist which account for the various means by which indoor pollutant concentrations are altered in indoor environments, such as deposition, reaction, generation, etc. To the authors' knowledge, however, none of these models include the effect of HVAC operation. When reactive surfaces exist near diffusers, as is the case with some ceiling tiles near commonly used ceiling diffusers, the effect of HVAC operation may be significant. Secondly, a few researchers are beginning to investigate ways in which indoor pollutant concentrations may be controlled without the use of any additional energy. These strategies include taking advantage of boundary layer transport in diffuser supply jets to bring pollutants to reactive materials (Passive Removal Materials or PRM's) nearby where they are decomposed or deposited. Design of this type of strategy and quantification of its effects requires intimate knowledge of boundary layer transport near diffusers.

PREVIOUS RESEARCH

Transport of species to indoor surfaces is usually given in the form of a space-averaged deposition velocity (Nazaroff et al. 1993). This model is usually used with a single value of deposition velocity for a single space, which implies either a static value or an appropriate time-averaging, and an insensitivity to various parameters such as type and operation of HVAC system, type of surfaces in the space, space temperatures, etc. Shortcomings of this model include its lack of a clear reference concentration and inability to account for different airflow patterns within a space. Improvements to the model have been proposed by Cano-Ruiz et al. (1993) who among other improvements, suggested decoupling various components of transport by use of a more complex model. One potential challenge with the use of this convention is the identification of a proper driving force for transport between the air adjacent to the surface in question and the air in the bulk space. The classic model for flux across a film (Bird et al. 2007) can be employed if the driving force across the film is known. However, in modeling of real spaces, this driving force is rarely known, and the overall transport is often a function of fluid mechanics which are much more complex than a simple boundary layer.

Several groups have sought to refine the models of mass transfer to indoor surface through various means. Sparks et al. (1996) attempted to give an idea of the magnitude of this influence through use of moth cakes (nearly pure paradichlorobenzene) in a small chamber or a test house and varying flow conditions in the space. The group of Morrison and colleagues has provided methods for determination of more refined models of transport of indoor pollutants. These include gravimetric methods (Morrison et al. 2003), which will be employed in the current study. In 2006, the group of Morrison et al. used the method they had previously validated to quantify the effect of the temporal averaging of deposition velocities over long time periods during which central HVAC systems were cycling on and off and other perturbations in flow fields such as ceiling fans were running.

Many of the challenges present in indoor-surface mass transfer modeling have also been dealt with by researchers modeling heat transfer at indoor surfaces. Spitler et al. (1991) developed convection correlations for situations in which large ventilation rates (>15 Air Changes per Hour (ACH)) were employed. The results of their investigation suggested that at ventilation rates greater than 15ACH, jet momentum and inlet velocity become relatively unimportant compared to ventilation rate. Additional investigations by Fisher and Pederson (1997) and Goldstein and Novoselac (2010) and Clark and Novoselac (2012) confirmed that this was the case for a variety of lower ventilation rates and geometries, including all flow rates used in the current investigation. These three papers also concluded that the inlet temperature was the best reference temperature for their correlations. Lastly, they all three found that correlations of the form h=C*V0.8 work in a variety of situations in which forced convection is present.

OBJECTIVES AND HYPOTHESES

This work aims to accomplish the following objectives:

1. Demonstrate that the naphthalene sublimation technique (Mendes 1991) is capable of quantifying mass transfer to indoor surfaces by comparison of experiments with natural convection theory

2. Use the validated technique to quantify forced convection mass transfer for two diffuser layouts.

We expect the forced convection correlations to conform to a model of the form k=C*V0.8, as was previously found in similar heat transfer experiments. We also expect supply concentration and volumetric supply flow rate to be suitable variables for correlation of the results.

EXPERIMENTAL AND ANALYTICAL METHODS

All data is analyzed by assuming transport from the naphthalene samples to the bulk space according to the model:

N=kA([C.sub.surface]-[C.sub.ref])

where N is the total rate of mass transfer of naphthalene [g/s, lb/s],

[C.sub.surface] is the air concentration just above the surface [g/[m.sup.3], lb/[ft.sup.3]],

[C.sub.ref] is the air concentration responsible for mass transfer across the boundary layer [g/[m.sup.3], lb/[ft.sup.3]],

A is the area of the sample in contact with the air [[m.sup.2], [ft.sup.2]], and

k is the mass transfer coefficient [m/s, ft/s].

Each term in this equation presented unique challenges. The first term, N, was quantified using gravimetric methods. Naphthalene is used as the species of interest in these experiments, owing to its high volatility, and inexpensiveness. Naphthalene plates (9cm x 9cm, 3.5in x 3.5in) are constructed by melting commonly available moth balls (99.9% naphthalene) onto aluminum sheets as shown in in Figure 1. These sheets are weighed, and then affixed to the surface of interest with a Velcro-type adhesive in a controlled environmental chamber. Once a certain amount of time has elapsed (usually 1-3 days), the sample is removed, and weighed again. The difference in mass between the two measurements is the amount of naphthalene that was volatilized during the experiment. This quantity divided by the time elapsed and then by the area of the sample is the mass flux. Samples are left in the chamber under a certain set of circumstances for a minimum of a day each to minimize time-dependent effects and ensure a greater degree of precision. With this convention and the precision of the balance (electric balance with a precision of 0.1g, 2.2e-4lb) the quantity N had an uncertainty of roughly 1%.

[FIGURE 1 OMITTED]

The driving concentration difference also needed to be quantified precisely. Conservative calculations confirmed that the bulk concentration in the room, even under conditions of high mass transfer rates and large amounts of naphthalene present, never reached beyond 1% of the equilibrium concentrations. The supply air was filtered through an activated carbon filter and also had a naphthalene concentration of virtually zero. Therefore, it was assumed that the reference concentration was zero in the space for all situations analyzed. The surface concentration was assumed to be the concentration in equilibrium with the vapor pressure of the solid at the temperature of the solid.

The last challenge was in separating the two terms k and A once the other terms were known. On solidification, the naphthalene samples were observed to form a fuzzy surface (see Figure 1), which meant the surface area available for sublimation was not simply the 2-dimensional, or projected, surface area. To quantify the actual available area, three samples were analyzed with a non-contact profilometer (details of the profilometer can be found in Yao et al. (2008)) The ratio of the actual surface area to the two-dimensional surface area of each of the three samples was averaged and this ratio was assumed to be the ratio for all samples tested. The standard deviation for the three ratios was less than 6% of the average value, suggesting a fairly consistent surface for various samples.

[FIGURE 2 OMITTED]

Three sets of experiments were conducted: natural convection experiments, radial square ceiling diffuser experiments and high-sidewall diffuser experiments. Natural convection experiments were conducted in a well-insulated 4.5m x 5.5m x 2.4 m (14.8ft x 18ftx 7.9ft)environmental chamber with a dedicated complete HVAC system. The back wall of the chamber contains a hydronic heating/cooling system which can create a hot/cold surface on the interior of the chamber. The chamber's HVAC system maintained a set point temperature in the space of 23[degrees]C (73[degrees]F). Natural convection results are presented in terms of a wall-room temperature difference. The wall temperature was taken as an average of 8 randomly distributed thermistors (accurate to 0.1[degrees]C, 0.2[degrees]F) on the heated wall. Room temperature was taken as the average of four thermistors spaced equally in the interior of the space and was very close ([+ or -]0.4[degrees]C, 0.7[degrees]F) to the set point temperature for all experiments. Temperatures of the naphthalene samples were measured with a calibrated infrared thermometer with a precision of 0.1[degrees]C (0.2[degrees]F) so as to not disturb the samples.

High sidewall diffuser experiments were conducted in the same environmental chamber as the natural convection experiments, in order to simulate a geometry in which they would be used. A 0.5m x 4cm (20in x 1.6in) high sidewall diffuser was installed with its horizontal centerline 3 cm (1.2in) below the ceiling, centered on one of the short walls. Fourteen samples were distributed throughout the chamber in a random pattern on each surface: Four were placed on the ceiling; three on the wall housing the diffuser and the one being hit directly by it, two on the floor and two on the other walls. Isothermal conditions were maintained in the chamber at all times and the samples were assumed to be at the temperature of the average of four sensors distributed throughout the chamber.

Radial ceiling diffuser experiments were conducted in a 2.4m (7.9ft) cubic chamber with insulated and sealed walls, but no dedicated temperature control system. Four samples were distributed randomly on the ceiling, two on each of the walls and two on the floor. A 2ft x 2ft (0.6m x 0.6m) 4-way square cone diffuser was installed in a drop ceiling, centered on the ceiling. Isothermal conditions were again maintained and the samples were assumed to be at the temperature of the supply, which was virtually equal to both the room temperature and the temperature of the surroundings.

RESULTS

Results are first presented for the natural convection experiments conducted to validate the naphthalene sublimation technique for application in modeling mass transfer to indoor surfaces. Results are shown in Figure 3 below. Experimental results are shown as a solid black range and theoretical correlations, based on analogy with heat transfer (Bird), are shown as dashed lines. Theoretical and experimental Sherwood numbers are calculated with the range of diffusion coefficients which have been published for naphthalene (Keumnam et al.1992), which results in a range of Sherwood numbers for each temperature difference, both in the theoretical prediction (which is a weak function of diffusion coefficient) and in the experimental data. Since theoretical correlations are given in dimensionless form, the diffusion coefficient enters directly into the calculation of the Sherwood number for experimental data in order to compare. In reality, simply the mass transfer coefficient was calculated and the experimental uncertainty is much less. Nonetheless, Figure 3 shows that the results of the natural convection experiments were well within an order of magnitude of the theoretical correlations, and showed very good agreement at lower temperature differences.

[FIGURE 3 OMITTED]

Next, results are presented for the high-sidewall diffuser in Figure 4. Also shown in Figure 4 are equally spaced lines depicting correlations of the form k=C*V0.8. A few observations can be made when looking at Figure 4. First, data for the ceiling and the wall opposite the diffuser appear to follow a trend which has an exponential dependence on flow rate of greater than 0.8. Exponential dependences of convective transport on characteristic velocity greater than 0.8 arise in impinging jet situations, which is present to some degree on these surfaces. The effect of spatial averaging likely played a role in the deviation from the expected dependence as well. One should also note that mass transfer at the wall opposite the diffuser appears to be greater than on the ceiling, despite the diffuser being located on the ceiling send a jet along the ceiling surface. This is almost certainly due to the averaging process, which averaged samples which weren't in the diffuser jet with ones which were. This convention is adopted to simplify the modeling process.

[FIGURE 4 OMITTED]

Lastly, in Figure 5, the results of the forced convection experiments employing a radial square ceiling cone diffuser are displayed. A few more observations can be made from Figure 5. First, the correlations for the ceiling are roughly a factor of four less than those for the high-sidewall diffuser. This is due to the nature of the different jets issuing from the two diffusers. While the high-sidewall diffuser issues a high-velocity jet which ensures air distribution by entraining a great deal of room air from below, the radial ceiling diffuser has a much lesser face velocity and distributes air by spreading across the ceiling and then falling into the room. Figure 5 is shown, as was Figure 4, with lines depicting an exponential dependence of 0.8. It is clear that no strong statements can be made about the exponential dependence of mass transfer in this situation. Furthermore, one notices to the left side of the figure and in the Floor data that a lower bound may be present around 0.05cm/s (0.002ft/s). This may be thought of as a good assumption for the boundary layer component of mass transfer in room in which the HVAC system is either not in operation or has a negligible effect on the surface of interest.

[FIGURE 5 OMITTED]

CONCLUSION AND FUTURE WORK

Through the course of several full-scale experiments, the boundary layer component of mass transfer to indoor surfaces in a few situations was calculated. Natural convection experiments showed that the naphthalene sublimation technique produced results with an acceptable deviation from theory. Forced convection experiments explored mass transfer under flow conditions caused by two different ceiling diffusers. The results of these experiments can be paired with predictions of surface phenomena to more accurately model room air pollutant concentrations and possibly be may be used in design and analysis of passive removal strategies. Forced convection did not conform nicely to an exponential dependence of 0.8 as has been the case in previous work on heat transfer, likely because of the averaging process and the possible presence of impinging jets on some surfaces. Forced convection mass transfer was found to differ by a factor of 4 for the two diffusers analyzed. Lastly, a lower bound of 0.05cm/s (0.002ft/s) was suggested as a result of the forced convection experiments.

Future work will quantify mass transfer under other diffuser layouts and attempt to validate the model put forth herein by pairing boundary layer transport measurements with measurements of reaction probability on ceiling tiles and comparing them with full-scale experiments. Potential issues include the definition of a proper driving force for mass transfer. A comparison of previous heat transfer work for indoor surfaces with this work will be interesting as well, as some information may be gathered on the appropriateness of an analogy, which could be used to model mass transfer in many more situations.

REFERENCES

Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena. New York: John Wiley and Sons, 2007.

Cano-Ruiz, et al. "Removal of reactive gases at indoor surfaces combining mass transport and surface kinetics." Atmospheric Environment, 1993: 2039-2050.

Clark, et al. "Experimental study of convective heat transfer from windows with Venetian blinds" Building and Environment, 59, (2013): 690-700

Colomina, M. et al. "Vapour pressures and enthalpies of sublimation of naphthalene and benzoic acid." The Journal of Chemical Thermodynamics 14, 8, (1982):779-784

Fisher, D.E., and CO. Pederson. "Convective heat transfer in building energy and thermal load calculations." ASHRAE Transactions 103, no. 2 (1997): 137-148.

Goldstein, K. and A. Novoselac. "Convective Heat Transfer in Rooms with Ceiling Slot Diffusers (RP-1416)" HVAC&R Research 16, no. 5 (2010): 629-655

Keumnam, Cho, et al. "Measurement of the diffusion coefficient of naphthalene into air, International Journal of Heat and Mass Transfer, 35, 4, (1992): 957-966

Mendes, P.R. "The naphthalene sublimation technique." Experimental Thermal and Fluid Science, 4, 5, September (1991): 510-523

Morrison, et al. "Rapid measurements of indoor mass transfer coefficients." Atmospheric Environment, 2003: 5611-5619.

Morrison, GC, and DJ Wiseman. "Temporal considerations in the measurements of indoor mass transfer coefficients." Atmospheric Environment, 2006: 3389-3395.

Nazaroff, Gadgil, and Weschler. "Critique of the use of deposition velocity in modeling indoor air quality." In Modeling of indoor air quality and exposure, 81-104. Philadelphia, PA: ASTM, 1993.

Sparks, L. E. "Exposure version 2, a computer model for analyzing the effects of indoor air pollutant sources on individual exposure" EPA-600/8/91/013 (NTIS PB91-201095) (1991)

Spider, J.D., CO. Pederson, and D.E. Fisher. "Interior convective heat transfer in buildings with large ventilative flow rates." AHSRAE Transactions 97, no. 1 (1991): 505-515.

Yao, et al. "Evaluating fabric fuzziness using laser range sensing." Optical Engineering 47,1 (2008)

Jordan D Clark

Student Member ASHRAE

Atila Novoselac, PhD

Member ASHRAE

Jordan Clark is a Ph.D. candidate and Atila Novoselac is an Associate Professor in the University of Texas at Austin, Department of Civil, Architectural and Environmental Engineering, Building Energy and Environment Group in Austin, Texas, USA.

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Author: | Clark, Jordan D.; Novoselac, Atila |
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Publication: | ASHRAE Transactions |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jul 1, 2013 |

Words: | 3029 |

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