Development of new and validation of existing convection correlations for rooms with displacement ventilation systems

Transcription

1 Energy and Buildings 38 (2006) Development of new and validation of existing convection correlations for rooms wit displacement ventilation systems Atila Novoselac *, Brendon J. Burley, Jelena Srebric Department of Arcitectural Engineering, Pennsylvania State University, University Park, PA, USA Received 17 February 2005; received in revised form 18 April 2005; accepted 30 April 2005 Abstract Building airflow, termal, and contaminant simulation programs need accurate models for te surface convective boundary conditions. Tis is, especially, te case for displacement ventilation (DV) systems, were convective buoyancy forces at room surfaces significantly affect te airflow pattern and temperature and contaminant distributions. Neverteless, for DV, as a relatively new ventilation system, te convective correlations are adopted from more traditional mixing ventilation correlations, or non-existent. In tis study, te existing recommended correlations are validated in a full-scale experimental facility representing an office space. In addition, new correlations are developed for floor surfaces because te current literature does not provide necessary correlations, even toug, te floor surface is responsible for >50% of te total convective eat transfer at te envelope. Te convective correlations are typically functions of a surfaceair temperature difference, airflow parameters, and caracteristic room dimensions. Validation results sow tat te floor convection correlations expressed as a function of volume flow rate are muc stronger tan te correlations expressed as a function of a temperature difference between te surface and local air. Consequently, te new convection correlation for floor surfaces is a function of te number of ourly room air canges (ACH). Tis correlation also takes into account buoyant effects from local floor eat patces. Experimental data sow tat te existing correlation can be successfullyappliedtoverticalandceilingsurfacesinspaceswitdvdiffuser(s).overall,te new and te existing convection correlations are tabulated for use in building simulation programs, suc as annual energy analyses or computational fluid dynamics. # 2005 Elsevier B.V. All rigts reserved. Keywords: Convection correlation; Displacement ventilation; Commercial buildings; Laboratory experiment 1. Introduction One of te most important factors in designing mecanical systems for buildings is defining accurate termal boundary conditions. Convection at te internal room surfaces as a large impact on te total eat transfer and varies based on te ventilation system being used. Wit ventilation systems tat utilize displacement diffusers, te temperature field is vertically stratified and te low-momentum supply jet is attaced to te floor as sown in Fig. 1. Tis specific airflow pattern and temperature distribution as several potential advantages related to air quality wen compared to distributions in traditional mixing ventilation systems [1]. Te popularization of displacement ventilation (DV) systems * Corresponding autor. creates an incentive to validate existing convection correlations or develop new correlations specifically for tese systems. In te past decade, several simplified models were developed for te temperature stratification calculations in rooms wit DV [2,3]. Furtermore, Cen et al. [1] developed design guidelines for calculation of te temperature difference between te occupants ead and ankles. Te design guidelines also give an equation for calculating ventilation effectiveness at te breating level. Even toug, temperature stratification and ventilation effectiveness models are very sensitive to wall convection coefficients, tey do not include correlations for teir calculations. Cen et al. [1] used average convection coefficients, suc as 4 W/ (m 2 K) for floor surfaces. Oter researcers recommend similar average values or use of convection correlations developed for room surfaces wit all natural convection in /$ see front matter # 2005 Elsevier B.V. All rigts reserved. doi: /j.enbuild

2 164 A. Novoselac et al. / Energy and Buildings 38 (2006) ACH air canges per our [ 1 ] c coefficient for determining forced convective eat transfer coefficient c L coefficient for determining convective eat transfer coefficient under laminar flow C L coefficient for determining Nusselt number under a laminar flow c T coefficient for determining convective eat transfer coefficient under turbulent flow C T coefficient for determining Nusselt number under a turbulent flow D ydraulic diameter [m] convective eat transfer coefficient [W/ (m 2 K)] k conductivity of te air [W/(m K)] m exponent coefficient for forced convection n exponent coefficient in Curcill and Usagi equation Nu Nusselt number Pr Prandtl number q eat flux [W/m 2 ] Re Reynolds number T temperature [8C] DT caracteristic temperature difference [8C] v air viscosity of te air [m 2 /s] V room volume of te room [m 3 ] V supply supply flow rate from te diffuser [m 3 /s] te room [4], isolated surfaces and free edge eated plates [5], or room surfaces wit well mixed air and eated room surfaces [6]. Currently, tese correlations ave not been experimentally validated for use in rooms wit displacement ventilation systems, rater tey are recommended based on te surface flow similarities to te flow condition in te original experiments. Te use of constant convective coefficients creates inaccuracies, especially for floor surfaces were a major part of te convective eat flow at te room envelope occurs (>50%). Te existing correlations for natural convection do not take into account effects from te DV diffuser jet. On te oter and, existing forced convection correlations are not suitable because tey are developed for a standard ceiling diffuser [7], or for diffusers were te jet discarge velocity as a large impact on convection at te floor [8], wic is not te case wit DV diffusers. Accordingly, te first objective of te present study is to develop a new convection correlation for te floor surface in rooms wit te sidepositioned DV diffuser. Te second objective is to validate te existing wall surface correlations for application wit te DV system. To accomplis tese two objectives, full-scale experiments were conducted in test cambers wit displacement ventilation. Fig. 1. A caracteristic airflow pattern and temperature stratification in a room wit displacement ventilation. 2. Metodology for deriving convection correlations Te experiments in te full-scale environmental camber followed a metodology based on te conservation of energy at room surfaces. Tis metodology is similar to te metodology used by Kalifa and Marsall [9], Spitler et al. [10], and Awbi and Hatton [4]. All of tese studies developed convection correlations for application wit different eating and cooling systems tat create relatively uniform room temperature distribution. Fig. 2 presents te conservation of energy at internal room surfaces, under steady-state eat flow, for determining te convective eat fluxes. Te conservation of energy results in te convective eat flux (q convective ) as a function of te radiative (q radiation ) and conductive fluxes (q conduction ): q convective ¼ q radiation q conduction (1) Te conductive eat flux q conduction is calculated based on te termal resistance of te wall and te temperature difference between te internal wall surface and te outdoor air. For Fig. 2. Te energy balance at an internal wall surface used to develop convection correlations.

3 A. Novoselac et al. / Energy and Buildings 38 (2006) surfaces wit small termal resistances, te conductive eat flux was directly measured using a system of eat flux meters. Furtermore, te radiative eat flux q radiation is calculated based on te surrounding wall surface temperatures and view factors using a computer program for building energy and airflow (BEAF) simulations [11]. For tis calculation, all of te enclosure surfaces need te long-wave emissivity (e) and temperatures (T) as input data. To precisely calculate radiative eat fluxes, te enclosure was divided into a large number of smaller sub-surfaces were te temperature of eac sub-surface was precisely measured. Knowing te convective eat flux (Eq. (1)), surface (T surface ), and air (T air ) temperatures, te convection coefficient () is calculated as: ¼ q convective T surface T : (2) air Based on Eq. (2), calculations of need measured temperatures and eat flux data. Tis way calculated convection coefficient often combines bot natural and forced convection effects. For example, te jet velocity at te floor surface is very low, but it still produces effects of forced convection on a large portion of te floor surface, wic is combined wit natural convection effects created by surface-air temperature difference. In our study, te correlation for floor surfaces is developed as a function of supply volume airflow rate, normalized by room volume. Spitler et al. [12] provided justification for tis approac. Teir study as sown tat te eat transfer coefficient is relatively insensitive to supply jet velocity and supply jet momentum. Furtermore, Fiser and Pedersen [7] suggested tat convection correlations require a pysical understanding in terms of te room control volume, rater tan in terms of te surface boundary layer. Terefore, for te floor surface, is given as a function of te room number of air canges per our (ACH). A simplified relation between and ACH can be obtained by considering general relationsips between Nusselt (Nu), Prandtl (Pr), and Reynolds numbers (Re). Tese relations define forced convection along a plate [13]: for laminar flow : Nu ¼ C L Re 1=2 Pr 1=3 ; (3) for turbulent flow : Nu C T Re 4=5 Pr 0:43 ; (4) Nusselt and Reynolds numbers can be expressed as functions of room volume (V room ) and supply volume airflow rate (V supply ): Nu ¼ V1=3 room (5) k air Re ¼ V supply (6) v air Vroom 1=3 Substituting Eqs. (5) and (6) into expressions (3) and (4) and substituting values for constant Prandtl number (Pr), air conductivity (k air ), and dynamic viscosity (v air ), te following expressions are obtained for laminar and turbulent flows: forced laminar ¼ c L ACH 1=2 (7) forced turbulent ¼ c T Vroom 1=5 ACH4=5 (8) Te room volume term (Vroom) 1=5 in Eq. (8) is usually neglected, so te forced convection at a flat room surface is a function of volume flow rate [7]: forced ¼ c ACH m (9) Tere are a large number of previously developed convection correlations for natural convection in a room. Terefore, te intention of tis study is to identify an appropriate existing correlation for wall surfaces in a room wit displacement ventilation. Alamdari and Hammond [5], Awbi and Hatton [4], and Min et al. [6] developed natural convection correlations typically used in building design and researc practice. All tese correlations express natural convection as a function of temperature difference between te wall surface and air (DT = T surface T air ). In addition, some correlations use a caracteristic lengt scale, suc as eigt of te vertical surfaces or ydraulic diameter for orizontal surfaces. In tis study, te local air temperature (T air_local ) is used. It is defined as te average temperature of te air layer close to te surface. Karman s correlation for te ratio between boundary layer tickness and caracteristic lengt [14] sows tat for typical room dimensions and temperature differences (DT) boundary layer tickness is almost always <0.1 m. Even wit a very small temperature difference, suc as DT = 0.3 8C, and a large caracteristic lengt, 5 m, te tickness is <0.1 m. Terefore te distance of 0.1 m ensures tat local air is defined as air tat is close to te surface but outside of te boundary layer. To combine te effects of natural and forced convection at floor surfaces in te room wit displacement ventilation, te present study used te Curcill and Usagi [15] metod originally proposed for interpolation between limiting solutions of two independent variables. Wit tis metod, te convective coefficient combines forced ( forced ) and natural ( natural ) convection in te following way: combined ¼ð n natural þ n forced Þ1=n : (10) Eq. (10) enables te larger term to take over te final value of combined and in tis way to represent te dominant convection penomenon. Te coefficient n is an arbitrary constant tat defines te degree at wic te final value of combined reflects te dominant term. For example, Fig. 3 sows ow natural and forced convection can be combined for n =2,3, and 6. Te appropriate value of n varies based on te penomena tat are combined and can be obtained from experimental results.

4 166 A. Novoselac et al. / Energy and Buildings 38 (2006) Fig. 3. Grapical interpretations for combined effects of forced and natural convection. 3. Experimental facility used for convection correlation development Te experiments were conducted at te building environmental simulation and testing facility at Te Pennsylvania State University. Tis facility is a state-ofte-art installation for researc related to energy, airflow, termal comfort, and air quality in buildings. Fig. 4 represents tis facility wit two adjacent cambers. Eac of te cambers as an individual eating, ventilating, and airconditioning (HVAC) system for air andling, and te environmental camber also as a ydronic surface cooling system. To insulate te facility from external termal influences, te camber walls are built from insulating material tat provides a conduction resistance of R = 5.3 (m 2 K)/W. An important part of tis facility is te sopisticated data acquisition system used for measurements of energy and airflow parameters, suc as surface eat fluxes, surface and air temperatures, and air velocities in different parts of te facility. Bot te environmental and climate camber ad displacement ventilation diffusers (Fig. 4). Te climate camber tests provided data for te convection correlation development at floor surfaces, wile te experiments in te environmental camber enabled te validation of existing correlations for natural convection wit and witout DV diffusers. Te size of te climate camber is 2.5 m 3.9 m 2.7 m. In tis camber, te eat sources were low temperature eating panels positioned at te floor, and te DV system provided cooling as sown in Fig. 4(a). Te dimensions of te environmental camber are 6.0 m 3.9 m 2.4 m. Te eat sources were also low temperature eating panels positioned at te floor and wall surfaces (Fig. 4(b)). In tis camber, cooling was delivered by DVor by cooling panels positioned at te ceiling. To accurately calculate te radiative eat fluxes at different surfaces using conservation of energy, te envelope of te climate camber was divided into 21 sub-surfaces. Eac surface ad attaced termistor sensors, wic measure surface temperature wit an accuracy of 0.1 8C. Te number of sensors positioned on a surface depended on te importance of te surface for te overall eat flow in te camber. To account for te uneven floor surface temperature, te floor in te climate camber ad 8 sub-surfaces wit 10 attaced termistors. An additional eigt termistors were propped 0.1 m above te floor surface sensors to measure local air temperatures. Aluminum tin foil sielded te termistors from radiative eat excange. Supply and exaust air temperature measurements also used termistors. A system of flow stations measured te supply volume airflow rate wit an accuracy of 5%. Electric eating panels, regulated by a transformer, covered te floor of te climate camber. Te overall accuracy of te total eat flux measurements at te electric panels was 2.5%. Te environmental camber ad 38 caracteristic subsurfaces wit te total of 48 surface termistor sensors (accuracy of 0.1 8C). An additional 38 termistors obtained air temperatures 0.1 m from all of tese surfaces. Furter away from te surfaces, 28 air temperature sensors, 24 RTD and 4 termistor sensors wit accuracies of 0.2 Fig. 4. Scematics of building environmental simulation and testing facility cambers: (a) climate camber and (b) environmental camber.

5 and 0.1 8C, respectively, collected te room air temperatures. Similar to te climate camber measurements, te number of sensors positioned in te vicinity of te surfaces depended on te importance of te surface for te overall eat flow in te camber. Besides, surface and air temperature measurements in te environmental camber, 24 air velocities in te vicinity of te surfaces were also measured. Tese velocities revealed weter te convective regime at a certain surface was predominantly forced or buoyant. Similar to measurements in te climate camber, supply and exaust temperatures, volume flow rate, and total eat flux at te eating and cooling panels were monitored. A. Novoselac et al. / Energy and Buildings 38 (2006) Experimental procedure for convection correlation development Te climate and environmental cambers provided data for two main tasks: development of convection correlation for floor surfaces in te climate camber; validation of existing convection correlations in te environmental camber. Te climate camber was used for te correlation development because its smaller size enabled precise measurement of eat fluxes along te entire floor surface. Te experiments in te environmental camber enabled evaluation of natural convection correlations by way of te installed ydronic cooling panel system. Table 1 presents te total number of conducted experiments and additional specifications for te two experiment types based on te purpose of te collected data. In te climate camber experiments, te convective eat fluxes at te floor were measured at different supply volume airflow rates. Te variation of volume flow rate was in te range of ACH in te room. In addition, te experiments used tree different power adjustments for eating panels at te floor surfaces, wic provided an approximate floor convective eat flux of 7, 15, and 40 W/ m 2. Te floor eating panels were regulated to provide bot, uniform total eat flux on te wole floor, and non-uniform total eat flux by using only te eating panels in te central part of te floor (see Fig. 4(a)). For te environmental camber experiments, validation of existing natural convection correlations was conducted Fig. 5. An example of temperature recording for determination of steadystate conditions in te environmental camber for natural convection validation. wit te DV system eiter on or off. Heating panels created appropriate temperature differences and convective eat flu-xes at te wall surfaces. In te experimental cases, wen te DV system was on, tis system removed te eat gains. In te cases wen te DV system was off, tere was no supply air and te ceiling cooling panels worked as eat sinks (Fig. 4(b)). In experiments related to te validation of existing natural convection correlations at floor surfaces, te ventilation system was off. In tis case, te ceiling cooling panels extracted te entire cooling load. Power variation of te floor eating panels created different temperature gradients at te floor surface for different experiments. For all of te experiments conducted in te environmental camber, local velocities were measured to calculate Gr/Re 2 ratio. Tis ratio determined te surfaces wit dominant forced convection, were Gr/Re 2 < 1, or buoyant convection, were Gr/Re 2 > 1 [16]. To ensure te accuracy of te measured parameters for te calculation of convective eat fluxes, measurements were conducted for steady-state airflow and conductive eat flow in different elements of te camber s structure. For eac experiment: controlled parameters, suc as te air supply temperature and volume flow rate and/or water flow and temperature for radiant panels were adjusted to a set point; surface and air temperatures for 32 reference points were recorded every 50 s (as sown in Fig. 5) until a steadystate temperature distribution was attained; Table 1 Types, number, and specification of experiments used in data analysis Type of experiments Experiment specifications Total number Camber Area of eat source Heat sink(s) Development of convection correlation for floor surfaces Validation of existing convection correlations Forced convection correlation development 10 Climate Entire floor DV system New correlation testing for floor eat patces 3 Climate Local floor DV system Measurements of convection at walls 3 Environmental Wall DV system Measurements of natural convection at walls 5 Environmental Wall Cooling panels Measurements of natural convection at floor 7 Environmental Local floor Cooling panels

6 168 A. Novoselac et al. / Energy and Buildings 38 (2006) values for steady-state temperature and velocity at all installed sensors were recorded for 2 min and ten averaged. To test te validity of measurements, an energy balance ceck was conducted for eac experiment by comparing te eat gains wit te energy extracted by te DV ventilation system or ceiling cooling panels. Te energy balance sowed tat in all of te experiments, te difference between te eat gain and extraction was <6%. Tis small difference proves tat steady-state was reaced and tat te experiments were conducted under well controlled conditions. 5. Results and discussions Te experimental part of tis study took place over a course of several monts. Te total number of conducted experiments is 28, as presented in Table 1. Te experimental results are te base for te development of new floor convection correlations and validation of te existing correlations for natural convection at te vertical and floor surfaces Convection correlation development for floor surfaces Table 2 Variation of local values for Gr, Re, and Nu numbers wit floor position and airflow Volume flow rate 3.4 ACH 6.1 ACH 1.4 m a 3.2 m a 1.4 m a 3.2 m a Gr Re Nu a Distance from diffuser. Experiments wit displacement ventilation sow tat te major convective eat transfer occurs at te floor surfaces. In tose experiments, te measured convective eat flux at te floor surface was from 51 to 82% of te total convective surface eat flux. Te smaller percentage values are for experimental cases were te eating panels were at wall surfaces, wile te larger values are for cases were te eating panels were at te floor surface (Table 1). Tis large portion of convective eat transfer at te floor suggests tat te cool air supplied at te floor level by DV diffusers significantly cools down te floor surface, wic represents a radiative sink for te oter room surfaces. Considering tis penomenon, special attention is dedicated to te development of accurate convection correlations for te floor surface wit DV. Vertical temperature stratification is a well-known penomenon wit DV. However, in addition to tis stratification, tere is also a non-uniform orizontal air temperature distribution in te vicinity of te floor. In our climate camber experiments, tis orizontal stratification created a considerable floor surface temperature variation. Fig. 6 sows te influence of a non-uniform vertical temperature distribution on local convection coefficients for one test set-up. Fig. 6(a) sows tat te surface temperature in te vicinity of te diffuser was lower tan te temperature furter away. On te oter and, te variation of temperature difference between te surface and local air is relatively small (Fig. 6(b)). However, non-uniform surface temperatures created non-uniform convective eat fluxes due to nonuniform radiative eat excange wit oter surfaces. As a result, te variation of local convection coefficients was considerably large (Fig. 6(c)). Oter test cases provided similar results. Because of te non-uniform floor surface temperature and non-uniform temperature distribution of te air layer above te floor, te convection correlations were developed for average surface and average local air temperatures. Tese averaged temperatures enable practical use of te newly developed correlation. Variation of te local values for temperature difference, velocity, and convection coefficients resulted in te variation of local values for Gr, Re, and Nu numbers. Table 2 presents te impact of local flow by presenting te variation of tese Fig. 6. Variation of temperatures and local convection coefficients wit orizontal distance from te DV diffuser. Te measurements were at te diffuser centerline and 0.1 m above te floor. Te supply temperature was C and volume airflow rate provided 4.6 ACH in te climate camber: (a) surface temperature distribution; (b) local temperature differences; (c) local convection coefficients.

7 A. Novoselac et al. / Energy and Buildings 38 (2006) Fig. 7. Measured convection coefficients () for te floor wit displacement ventilation as a function of a local temperature difference (DT) and te supply flow rate (ACH): (a) as a function of DT and (b) as a function of ACH. numbers wit floor position for two different volume flow rates. Variation of te local distribution of te Gr number wit distance from te diffuser was not large, since te distribution of local temperature difference was relatively uniform (refer to Fig. 6(b)). On te oter side, local distribution of local velocities resulted in considerable variation of locally defined Re numbers. Te cange of tese locally defined Re numbers wit supply volume flow rate was even larger. Te cange of te flow rate from 3.4 to 6.1 ACH doubled te values for local velocities and corresponding Re numbers (Table 2). Te local distribution of resulted in a large variation of locally defined Nu numbers wit orizontal distances from DV. Also, te cange of ACH affects te Nu number since velocity (Re number) increases and affect convective eat transfer. Local air temperatures measured 0.1 m above te floor (T local_air ) and te supply air temperature (T supply ) were te two reference temperatures used for te experimental data analysis. Wen te reference temperature is te supply air temperature, te convective eat flux is calculated as q surface = supply [T surface T supply ] and te convection coefficient ( supply ) is a function of te supply volume airflow rate expressed in ACH. Fig. 7 presents te measurement results as a function of a local temperature difference (DT = jt surface T air j) and ACH. Tese results indicate tat te convection correlation expressed as a function of volume flow rate is stronger tan te correlation given as a function of a temperature difference of te local air and floor surface. Terefore, te forced convection correlation at a floor surface wit te displacement ventilation system as te form of Eq. (9). For measured velocities in te vicinity of te floor ( m/s) and a room floor ydraulic diameter of D =3m, te local Re number for flow near to te floor surface was in te range of 10 4 to Tis range of local Re numbers indicates a laminar flow regime [13]. Terefore, te exponent m, in general, Eq. (9) sould be 0.5 as indicated in Eq. (8). However, experimental results and function fitting of general Eq. (9) sow tat te exponent m in Eq. (9) as a value close to 0.8 (Fig. 8). Tis value for coefficient m corresponds to te exponent coefficient for turbulent flow (Eq. (8)). Te exponent value of m = 0.8 was also obtained in researc studies conducted by Fiser [17], and Fiser and Pedersen [7]. Tey conducted experiments wit ceiling diffusers and found tat m = 0.8 fits te best for forced convection at all surfaces (ceiling, walls, and floor), even toug, te Reynolds number at floor surfaces was rater small (< ). A possible reason for tis turbulent flow beavior for Re numbers < is tat te properties of room airflow are different from te flows on free surfaces due to te space confinement. Using function-fitting and te experimental results presented in Fig. 8, te coefficient c for te forced convection correlation is m = 0.8, so Eq. (9) becomes: force ¼ 0:48 ACH 0:8 : (11) Fig. 8. Experimental data wit uncertainties compared to te new equation for te convection correlation for floor surfaces wit DV diffuser (exponent, m = 0.8).

8 170 A. Novoselac et al. / Energy and Buildings 38 (2006) Tis correlation is based on te supply air temperature and needs to be modified for use wit te local air temperature (or te room average temperature): c local ¼ jt surface T supply j 0:48 ACH 0:8 (12) DT Eq. (12) sould be used carefully because at some surfaces te local air and surface temperature difference DT is very small and close to zero. In tese cases, c_local takes unrealistic values. Tis is, especially, te case, wen tis equation is used wit automatic iterations, suc as in energy simulation or computational fluid dynamics (CFD) programs [11,18]. To avoid tis division problem resulting in unrealistically ig c_local, te simulation programs sould include restrictions for te denominator DT. Wen DT < e, te term jt surface T supply j/e sould substitute for te term jt surface T supply j/dt, were e is any temperature difference at wic te convective eat flux is small Convection correlation for floor surfaces wit eat patces Te floor convection correlation, given by Eq. (11), is based on measurements, were te entire floor area as a uniform eat flux. In reality, some parts of te floor may ave larger temperatures and convective eat fluxes tan te rest of te floor. For example, surfaces eated by direct solar radiation (sun patces) or surfaces eated by local ligting system ave a considerably iger temperature tan te surfaces in te vicinity of te displacement diffuser. To test te new floor convection correlations, additional experiments wit eat patces were conducted. In tese experiments, a part of te floor was releasing a relatively larger eat flux (convection portion 38 W/m 2 ), wile te eat flux at oter parts of floor was negligible. Fig. 9 presents te experimental results for floors wit eat patces. Based on Fig. 9, te new correlation for forced convection (Eq. (11)) cannot predict convective eat transfer for local eat patces, were buoyant airflow is predominant. Te measurements sow tat Eq. (11) under-predicts te convective eat flux at eat patces from 30 to 50%. To account for te buoyant convective effect of local eat patces, Eq. (12) is combined wit natural convection correlations using te Curcill and Usagi [15] metod (Eq. (10)). To find te appropriate natural convection correlations for floors wit eat patces, existing convection correlations were tested. Several measurements of convection coefficients were conducted at floor surfaces in te environmental camber wit no air supply and T floor > T air. Fig. 10 sows te comparison of tese measured convection coefficients wit previously developed convection correlations [4 6]. Te comparison results are for a caracteristic lengt of 2.6 m, wic is te ydraulic diameter of te eating panels at te floor (see Fig. 4(b)). As Fig. 10 sows, te correlation developed by Awbi and Hatton agrees well wit te new experimental results. Consequently, tis correlation is selected for te floor area wit eat patces, were te natural convection is te dominant penomenon. Eq. (10), wit te exponent coefficient n = 6, combines effects of forced and natural convection. Neiswanger et al. [19] establised tat for Rayleig numbers (Ra) >10 11, te ideal value of n is 3.2. However, in present experiments wit displacement ventilation, Ra was below tis tresold. Te value of n = 6 was cosen based on good agreement wit experimental data. Te general form of te convection correlations for floor surfaces wit T floor > T air in rooms wit DV diffusers is: 2:175 DT 0:308 combined ¼ þ D 0:076 6 DT 0:48 ACH0:8 jt s T supply j 6 1=6 (13) Fig. 9. Forced convection correlations for te floor wit a DV diffuser including te convection coefficients measured at te eat patc floor area. Fig. 10. Performance of te existing natural convection correlations and measured data for floor surfaces, were T floor > T air.

9 A. Novoselac et al. / Energy and Buildings 38 (2006) Analysis of te overall results sows tat te largest difference between measured and predicted eat flux (by Eq. (13)) is <19%, including eat patces. Terefore, Eq. (13) is appropriate for te estimate of te convective eat transfer from warm floor surface (T floor > T air ) Validation of existing natural convection correlations To account for te convective eat transfer at te oter room surfaces besides te floor, existing convection correlations may be appropriate if a rigorous validation process justify teir use. Due to te low air velocities in rooms wit DV, te assumption is tat te airflow at room surfaces is driven by te temperature difference between te local air and surface. To confirm tis assumption, DV was on and off in tests conducted in environmental camber. In bot types of test, te Grasof (Gr) and Reynolds (Re) numbers were calculated in te vicinity of te surfaces to obtain te ratio Gr/Re 2. In all experiments, wit and witout DV, te ratio Gr/Re 2 for vertical surfaces was considerably above 1. Tis ratio indicated tat natural convection is te dominant eat transfer penomenon at vertical wall surfaces in rooms wit a DV diffuser. Terefore, additional test measurements were conducted to determine wic of te tree previously developed natural convection correlations: (1) Alamdari and Hammond [5], (2) Awbi and Hatton [4], or(3) Min et al. [6], was te most appropriate for application at vertical surfaces in rooms wit DV. Fig. 10 sows te result of tese tests. In all of te correlation equations, te eigt of te camber walls (2.35 m) was te caracteristic lengt. Fig. 11 sow tat correlations developed by Awbi and Hatton [4] ave better agreement wit measured results tan correlations developed by Alamdari and Hammond [5] and Min et al. [6]. Te most likely reasons for tese results are te experimental set-ups used in te previous and current Table 3 Correlations for natural convection developed by Awbi and Hatton [4] Surface and regime Convection correlation Floor wen T s > T air or ceiling wen T s < T air 2.175DT /D 0:076 Ceiling wen T s > T air or floor wen T s < T air 0.704DT /D 0:601 Walls 1.823DT /D 0:121 studies. Awbi and Hatton s natural convection correlations were developed in a similar environmental camber to te one used in te present study, wile te Alamdari and Hammond natural convection correlations were created based on a series of experiments tat were primarily conducted wit isolated surfaces. Te correlations developed by Min et al. were also developed using a full-scale testing room, relatively similar to our environmental camber. Te sligtly better performance of te Awbi and Hatton s correlations tan Min et al. s correlation is probably due to te definition of te air reference temperature. Te Awbi and Hatton s correlations use local air temperature at 0.1 m from te wall surface as te reference temperature, wic is te same reference temperature used in our experiments presented in Fig. 11. On te oter and, Min et al. defined te reference temperature as te temperature in te central part of te room (1.5 m above te floor). Considering te validation results, Awbi and Hatton s correlations are recommended for te calculation of natural convection in rooms wit DV. Table 3 presents Awbi and Hatton s correlations for different surface types and flow regimes. For wall surfaces, te temperature stratification in te air could lead to eat transfer from te lower part of te wall to te air and from te air to te upper part of te wall. Fig. 12 sows te result of experiments wit tis penomenon on te left wall tat represents an internal wall in a room. In situation like tis, use of te equations from Table 3 wit average values for surface and air temperatures (DT) can create a certain error in te convection coefficient () calculation. In te example presented in Fig. 12, te difference between te measured and calculated was >40%. However, total eat flux at surfaces like tis is small (19 W in te presented example) and as small effect on overall energy flow in rooms. It is muc more important tat Fig. 11. Validation of te existing natural convection correlations wit te measured data for vertical wall surfaces in a room wit DV. Fig. 12. Measured temperature and eat fluxes in te experimental facility wit te ot window surface and te internal wall on te opposite side.

10 172 A. Novoselac et al. / Energy and Buildings 38 (2006) te convection correlation predicts precisely te eat flux at surfaces wit large DT, wic create large total eat fluxes. At surfaces wit a large DT eat fluxes ave te same direction in te lower and upper part of te surface and te equation from Table 3 is appropriate. In te experiment presented in Fig. 12, te rigt wall surface represents a ot external window surface. For tis surface, te measured flux is 165 W wile te equation from Table 3 calculates 150 W. For ceiling surfaces, te temperature stratification wit DV often causes iger local air temperatures tan ceiling surface temperatures as sown in Fig. 1. At tese surfaces, te convective eat transfer is similar to te one wit cooled ceiling panels. Terefore, te correlation for cooling ceiling (CC) panels [11] is recommended at tese surfaces wen T s < T air. Te correlation for cooled ceiling as te following form: cooled ceiling ¼ 2:12 DT 0:33 : (14) Wen te ceiling surface as only a sligtly lower temperature tan te local air, Eq. (14) gives similar values as te Awbi and Hatton s correlation for ceilings, were T s < T air. Terefore, for tese surfaces, bot correlations are appropriate. In te case wen T s > T air, suc as surfaces close to lamps or ceiling surfaces in rooms wit large solar eat gains, Table 1 gives te appropriate Awbi and Hatton s correlation Recommended convection correlations for all envelope surfaces in a room wit DV Table 4 summarizes te recommended convection correlations for all different surfaces in a room wit displacement ventilation. Te recommended correlations include newly developed correlations and te correlations developed by Awbi and Hatton [4] and Novoselac [11]. All of tese correlations use te local air temperatures defined as te air temperature in te surface vicinity (0.1 m from te surface). Models developed by Mundt [2], Rees and Haves [3], and boundary condition models used in CFD programs [11,18] can calculate temperature distribution and local air Table 4 Recommended convection correlations for a room wit displacement ventilation Surface Regime Convection correlation Floor T s > T air 2:175DT 0:308 D 0:076 " # 6 1=6 þ jts T 6 supplyj DT 0:48 ACH 0:8 T s < T air 0:704DT 0:133 D 0:601 Ceiling T s > T air 0.704DT /D 0:601 CC panel 2.12DT 0.33 T < T 2.175DT /D 0:076 Walls 1.823DT /D 0:121 " # 6 1=6 þ jts T 6 supplyj DT 0:48 ACH 0:8 temperatures, wic ten can be used for te calculations of. Tese correlations are primarily for use in DV models tat calculate temperature stratification in rooms for termal comfort and air quality evaluations. In addition, models tat present te room air temperature as a single node can also use te developed correlations. For example, te floor convection correlation presented in te form of Eq. (11) is appropriate for energy simulation models or standard design procedures tat are based on te assumption of te uniform air temperature. For tis purpose, Eq. (11) uses supply air temperature as te reference temperature and does not need an air temperature distribution. 6. Conclusions Tis paper presented te development of new and validation of existing convection correlations for rooms wit displacement ventilation. Tese correlations were developed and tested using a state-of-te-art experimental facility tat enabled measurements in environments representing rooms in office buildings. Besides te recommended convection correlations presented in Table 4, te measured data and teir analyses also pointed out te importance of convection correlation for floor surfaces. Te major eat transfer from room surfaces to te air appears at te floor surface. Consequently, a precise calculation of convective eat fluxes at te floor is crucial for accurate predictions of energy consumption, air quality, or termal comfort in a room wit displacement ventilation. Te major parameters tat affect eat flux at te floor surface are supply air temperature, volume flow rate, and local air temperature. Generally, te correlation based on normalized volume flow rate (ACH) tat uses supply temperature as a reference temperature is stronger tan te correlation based on a temperature difference between te surface and local air (DT local ). Modeling te forced convection at room surfaces as a function of ACH enables te development of general and practical convection correlations tat are based on parameters readily available in design or simulation procedures. To take into account te buoyant effect of eat patces at te floor, te influence of DT local sould be considered. Te non-uniform orizontal temperature distribution created by displacement ventilation diffusers creates variations in floor surface temperatures. Tis orizontal temperature gradient causes a cange in temperature differences between te local air and floor surfaces, wic results in considerable variation of te local surface convective eat fluxes. Neverteless, tis variable eat flux can be successfully averaged and modeled based on supply air parameters, suc as te air supply temperature and te supply volume flow rate. At te wall and ceiling surfaces, te convective eat flow is primarily driven by natural convection. Te validation experiments of te tree commonly applied convection correlation for natural convection [4 6] sow tat te

11 A. Novoselac et al. / Energy and Buildings 38 (2006) correlations developed by Awbi and Hatton [4] are te most suitable for application in a standard office room wit DV diffusers. Acknowledgement Tis researc was financially supported by te National Science Foundation (NSF Grant No. CTS ). References [1] Q. Cen, L. Glicksman, X. Yuan, S. Hu, Y. Hu, Performance evaluation and development of design guidelines for displacement ventilation, Draft Final Report to ASHRAE TC 5, Room Air Distribution on ASHRAE Researc Project, RP-949, Building Tecnology Program, Department of Arcitecture, Massacusetts Institute of Tecnology, [2] E. Mundt, Te performance of displacement ventilation system, P.D. Tesis, Royal Institute of Tecnology, Sweden, [3] S.J. Rees, P. Haves, A nodal model for displacement ventilation and cilled ceiling systems in office spaces, Proceedings of Building Simulation, 99 1 (1999) [4] H.B. Awbi, A. Hatton, Natural convection from eated room surfaces, Energy and Buildings 30 (1999) [5] F. Alamdari, G.P. Hammond, Improved data correlations for buoyancy-driven convection in rooms, Building Services Engineering Researc and Tecnology 4 (3) (1983) [6] T.C. Min, L.F. Scutrum, G.V. Parmelee, J.D. Vouris, Natural convection and radiation in a panel eated room, Heating Piping and Air Conditioning (HPAC) (May) (1956) [7] D.E. Fiser, C.O. Pedersen, Convective eat transfer in building energy and termal load calculations, ASHRAE Transactions 103 (2) (1997) [8] H.B. Awbi, A. Hatton, Mixed convection from eated room surfaces, Energy and Buildings 32 (2000) [9] A.J.N. Kalifa, R.H. Marsall, Validation of eat transfer coefficients on interior building surfaces using a real-sized indoor test cell, International Journal of Heat and Mass Transfer 33 (10) (1990) [10] J.D. Spitler, C.O. Pedersen, D.E. Fiser, P.F. Menne, J. Cantillo, An experimental facility for investigation of indoor convective eat transfer, ASHRAE Transactions 97 (1) (1991) [11] A. Novoselac, Combined airflow and energy simulation program for building mecanical system design, P.D. Tesis, Te Pennsylvania State University, [12] J.D. Spitler, C.O. Pedersen, D.E. Fiser, Interior convective eat transfer in buildings wit large ventilative flow rates, ASHRAE Transactions (1991) 97 (1) (NY ). [13] A.F. Miles, Heat Transfer, Prentice Hall, NJ, [14] A. Luikov, Heat and Mass Transfer, Mir Publisers, Moscow, [15] S.W. Curcill, R. Usagi, A general expression for te correlation of rates of transfer and oter penomena, AICE Journal 18 (6) (1972) [16] H. Sclicting, Boundary Layer Teory, sixt ed., McGraw-Hill, [17] D.E. Fiser, An experimental investigation of mixed convection eat transfer in a rectangular enclosure, P.D. Tesis, University of Illinois, Urbana, USA, [18] I. Beausoleil-Morrison, Te adaptive coupling of eat and air flow modeling witin dynamic wole-building simulation, P.D. Tesis, University of Stratclyde, Glasgow, UK, [19] L. Neiswager, G.A. Jonson, V.P. Carey, An experimental study of ig Rayleig number mixed convection in a rectangular enclosure wit restricted inlet and outlet openings, Journal of Heat Transfer 109 (1987)