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#  Improvement in sealing effectiveness of air curtains using positive
buoyancy

Tanmay Agrawal, Narsing K. Jha and Vamsi K. Chalamalla

Department of Applied Mechanics, IIT Delhi, Hauz Khas, 110016, India

ABSTRACT
Air curtains are commonly employed in building applications to facilitate
aerodynamic sealing against the exchange flow that occurs through an open
doorway due to the density differences owing to buoyancy. Such situations
often prevail due to temperature gradients across a doorway of an air-
conditioned building, e.g., during the summer season in an Indian
subcontinental situation. In the present study, we numerically investigate the
performance of ‘positively buoyant’ air curtains. In such installations, the
density of the jet fluid is larger than the density of the fluid contained
within the building space. Using the two-dimensional Reynolds-averaged Navier-
Stokes (2D RANS) formulation, we compute the temperature distribution in the
flow domain and estimate the associated sealing effectiveness for various
values of positive jet buoyancy and operating velocities of the air curtain.
These estimates of sealing effectiveness are compared with that of a neutrally
buoyant air curtain to assess the influence of positive buoyancy. We report an
increase in sealing effectiveness of up to 10%, whereas its peak value
improves by about 5%.

Keywords: Building flows, stratified flow, air curtains, positively buoyant
jets.

##  1 INTRODUCTION

The prevalence of buoyancy-induced density gradients is quite common in
building flow applications, e.g., consider a doorway across which the fluids
are maintained at different temperature levels. As a result, a driving force
is manifested, which leads to bulk fluid transport across the door. To counter
such exchange flows, air curtains (AC) are generally installed in the vicinity
of a doorway to facilitate aerodynamic sealing. In addition to this
inhibition, they also allow free passage for the building occupants without
imposing a physical obstruction, thereby making them usable in a multitude of
situations. Their other common applications include shopping complexes, food
plazas, refrigerated cabinets, medical facilities, restriction of smoke in
tunnel fires, etc. A typical AC installation utilizes a planar (rectangular)
nozzle in which the air supply is sent by a blower after necessary flow
conditioning. The supplied fluid can be taken either from within the
room/building under consideration or from its ambient. Most usually, these
installations are downward blowing, and in such cases, the air curtain
impinges vertically on the floor. In other installations, the AC jet could be
upward or sideways blowing with some angular tilt from the doorway. A brief
comparison of various such arrangements was explored numerically by Gonçalves
et al. [1] around a decade ago.

While the initial patent for the air curtain technology dates back to the
early 20${}^{\text{th}}$ century, it was only in the late 1960s that the
performance of AC was first quantified systematically by Hayes and Stoecker
[2]. They measured velocity and temperature profiles along the air curtain
axis in a full-scale experimental setup. Based on these measurements, they
defined a dimensionless parameter, referred to as the deflection modulus,
$D_{m}$, representing the ratio of the initial momentum flux contained within
the AC jet and the ‘stack-effect’ induced transverse force as a result of
buoyancy difference. Mathematically, $D_{m}$ is written as

$D_{m}=\frac{\rho_{0}b_{0}{u_{0}}^{2}}{gH^{2}(\rho_{d}-\rho_{l})}=\frac{b_{0}{u_{0}}^{2}}{gH^{2}(\frac{T_{0}}{T_{d}}-\frac{T_{0}}{T_{l}})}$
(1)

where the subscripts $0$, $l$, and $d$ are associated with the curtain, light,
and dense fluids, respectively. $T$ denotes the fluid temperature, and its
density, $\rho$, has been obtained using the ideal gas law. The rectangular
nozzle has a width, $b_{0}$, and the mean exit velocity is represented as
$u_{0}$, assuming a top-hat distribution. Lastly, $H$ denotes the doorway
height, and $g$ refers to the gravitational acceleration. Hayes and Stoecker
demonstrated that the stability of an AC installation could be assessed based
on the ‘reach’ of the planar jet, which can be characterized through $D_{m}$.
If the jet fluid impinges on the other side of the doorway, i.e., the floor of
the room when the AC is downwards blowing, it is said to be stable and is
deemed unstable (or breakthrough) otherwise. This transition from an unstable
installation to a stable AC occurs at a minimum deflection modulus,
$D_{m,min}$, the value of which is affected by the geometrical aspects
($b_{0}$, $H$) as well as the operating conditions ($\rho_{0}$, $\rho_{c}$,
$\rho_{d}$). Other pathways of fluid leakage, e.g., windows for natural
ventilation, etc., can also affect this critical value of $D_{m}$.

In the presence of a stack effect where $\rho_{l}\neq\rho_{d}$, the
performance of an air curtain is measured by estimating the sealing
effectiveness, $E$. Physically, $E$ represents the exchange flow suppression
obtained after employing an air curtain in comparison to that of an open door
scenario, i.e.,

$E=1-\frac{q}{q_{OD}}$ (2)

Here, $q$ is the volumetric exchange flow rate through the door with the air
curtain installed, whereas $q_{OD}$ denotes the open-door-based exchange flow
rate. Thus, the effectiveness of unity corresponds to a perfectly sealed
doorway where the infiltration of the ambient fluid has been completely
brought down. On the other hand, a value of zero suggests an absence of an air
curtain, i.e., an open door situation. The existing literature suggests that
AC can inhibit up to approximately 80% of the total buoyancy-driven exchange
flow across a doorway [1, 3, 4, 5, 6, 7, 8] based on eq. 2.

In a typical installation, the air curtain feeds on the fluid in its vicinity,
i.e., the blower sucks in the indoor fluid when the AC is installed inside the
building space and vice versa. Most usually, this supply fluid does not
undergo any thermal treatment before being sent to the nozzle exit and is thus
neutrally buoyant for the surrounding fluid. In the present study, we
numerically investigate the relevance of positive buoyancy in the context of
air curtain flows, i.e., the density of the air curtain fluid is larger than
that of the surrounding fluid. From a thermodynamic perspective, we consider
the case when the supply fluid is cooled before blowing vertically downwards
through the AC nozzle. This situation was first studied experimentally by
Howell and Shibata [9], who also observed a minimum deflection modulus below
which the air curtain was not effective towards aerodynamic sealing. The
dynamical aspects of a ‘negatively’ buoyant air curtain were recently pursued
by Frank and Linden [10] where the air curtain was lighter than the ambient
fluids. To the best of the authors’ knowledge, there hasn’t been any study
investigating the performance of positively buoyant AC using numerical
methods. Therefore, this work primarily focuses on estimating the sealing
effectiveness of such air curtain installations using two-dimensional (2D)
Reynolds-averaged Navier-Stokes (RANS) simulations. We seek to understand the
influence of operating conditions (through varying $D_{m}$) on the
effectiveness of these positively buoyant AC.

The computational setup and methodology are discussed briefly in section 2.
The results obtained from the present simulations are presented in section 3.
We first present the temperature distribution in the computational domain for
different operating conditions, followed by the estimates of sealing
effectiveness. Lastly, we present estimates of jet spillage in the building
space in the presence of a transverse buoyancy. Further considerations of
fluid mixing and flow structures are a work in progress and are not included
in the current paper.

##  2 METHODOLOGY

Figure 1: Schematic of the simulated domain and the corresponding boundary
conditions (not per scale).

Reynolds-averaged Navier-Stokes (RANS) formulation has been adopted to
numerically simulate the positively buoyant air curtains. Herein, any
instantaneous quantity is decomposed in its mean value and a fluctuating part.
In all the simulations reported, water is chosen as the working fluid to
facilitate a direct comparison with the experimental data (described later)
obtained for the neutrally buoyant AC. In practical situations, different
densities required in the flow can be achieved using dissolved salts (ocean),
thermal gradients (atmosphere), suspended particles, etc. For the present
simulations, we employ temperature inhomogeneities to create the required
density difference, and the corresponding temperature levels are chosen to
reflect the thermal comfort requirement in the Indian subcontinental
situation. The fluid is assumed to be incompressible, and the density
differences are small such that the Boussinesq approximation can be adopted.
The following equations are numerically solved to simulate positively buoyant
AC:

$\frac{\partial{\overline{u_{i}}}}{\partial{x_{i}}}=0,$ (3)
$\rho\frac{\partial{\overline{u_{i}}}}{\partial{t}}+\rho\overline{u_{k}}\frac{\partial{\overline{u_{i}}}}{\partial{x_{k}}}=-\frac{\partial{\overline{p}}}{\partial{x_{i}}}+\frac{\partial}{\partial{x}_{k}}\left[\mu\frac{\partial{\overline{u_{i}}}}{\partial{x}_{k}}-\overline{\rho{u_{i}^{\prime}}{u_{k}^{\prime}}}\right],$
(4)
$\frac{\partial{\overline{T}}}{\partial{t}}+\overline{u_{k}}\frac{\partial{\overline{T}}}{\partial{x_{k}}}=\frac{\partial}{\partial{x}_{k}}\left[\kappa\frac{\partial{\overline{T}}}{\partial{x}_{k}}-\overline{{u_{i}^{\prime}}{T^{\prime}}}\right],$
(5)

These are mathematical representations of the conservation of mass, momentum,
and energy, respectively. Here, $u_{i}$, $p$ and $T$ represent the $i^{th}$
velocity component ($i$ = 1, 2), pressure and the temperature respectively.
The symbols $x_{i}$ and $t$ denote the $i^{th}$ spatial coordinate and time.
$\mu$ represents the dynamic viscosity of the fluid, $\rho$, its density, and
$\kappa$ denotes the thermal diffusivity. In these equations, an overbar
represents an averaged (or mean) quantity, while a super-scripted ′ represents
the corresponding fluctuating quantity. The unclosed terms in these equations
e.g. $-\overline{\rho{u_{i}^{\prime}}{u_{k}^{\prime}}}$,
$\overline{{u_{i}^{\prime}}{T^{\prime}}}$, are modelled using the
renormalization group (RNG) k$-\epsilon$ turbulence model [11]. We use the RNG
k$-\epsilon$ model over other turbulence closure models based on its
superiority to simulate plane turbulent jets as was suggested by the extensive
RANS simulations conducted by Khayrullina et al. [12].

###  2.1 Computational setup and boundary conditions

As described in the preceding section, we study the positively buoyant AC
using RANS-based two-dimensional numerical simulations. Towards this, the
computational box employed in this study, the size of which is $L=$ 2.1 m,
$H=$ 0.35 m, along with the corresponding boundary conditions, is shown in
Fig. 1. For the present simulations, the space under consideration (indoor)
that requires sealing spans from the left wall ($x$ = 0) to the domain center
($x$ = 1.05 m), and is initially filled with a cold fluid ($T$ = 25∘C). An air
curtain is provided at the top, just inside the building space, that blows air
at a temperature lesser or equal to that of the indoor fluid. In this work, we
report simulations with the jet temperatures ranging between 15∘C and 25∘C.
Outside the doorway, a warm fluid ($T$ = 45 ∘C) fills in the rest of the
computational domain thus resulting in a reduced gravity,
$g^{\prime}=g\frac{\Delta\rho}{\rho_{av}}\approx$6.7 cm/s2. Here, $\rho_{av}$
is taken as the average density of the indoor and outdoor fluid densities.
This setup replicates the temperature levels prevalent in the Indian
subcontinent in summer situations and thus seeks optimization of the thermal
comfort of building occupants using air curtains. We use ten grid points
across the nozzle width at the AC exit based on the recommendation of [13] and
a grid independence study (not shown) where the jet statistics were evaluated
and compared with the data available in the literature. In order to resolve
the spatial instabilities in the air curtain jet and the sharp density
gradient at the doorway location, the central region of the domain is locally
refined symmetrically (refer to the hatched region in Fig. 1). This local
refinement allows accurate estimation of the volumetric exchange that
primarily initiates at the center of the domain as a result of initial
horizontal stratification. At the jet exit, which has a nozzle width of
$b_{0}=$ 5 mm, a top-hat velocity profile is supplied, and the supply
temperature is systematically varied to study its effect on the temperature
distribution in the indoor space and the corresponding sealing effectiveness.
The resulting doorway height to nozzle-width ratio, $\frac{H}{b}$, is fixed at
84 in our simulations which is similar to that of real-scale air curtain
installations [3]. The side walls of the computational domain are assigned as
outflows to simulate a large ambient situation. We also conducted some
simulations using a ‘pressure-outlet’ boundary condition, and no significant
differences were observed in bulk flow estimates. All the other walls of the
computational domain are treated as insulated with no slip and no fluid
penetration across them.

###  2.2 Solver settings

The ANSYS FLUENT package is used to solve the governing equations of fluid
flow and heat transfer. We employ a second-order upwind scheme to approximate
the spatial derivatives present in the advective and viscous terms of the
governing equations and that associated with the turbulence model. To
discretize the temporal field, a first-order implicit method is used, and the
time step requirement is constrained by the CFL number of 0.8. The coupled
algorithm is used to link the pressure and velocity fields in these
incompressible simulations. Three different jet temperatures are simulated in
the present work: 15∘C, 20∘C and 25∘C that results in the reduced gravity
between the indoor and curtain fluid,
$g^{\prime}=g\frac{\Delta\rho_{IC}}{\rho_{0}}$ of approx. 2 cm/s2, 1 cm/s2 and
0. For each of these cases, eight simulations are conducted at various values
of $D_{m}$ ranging between 0.05 and 1.5. An additional simulation is also
conducted without an air curtain installed, i.e., $D_{m}$ = 0. This scenario
is formally known as a lock-exchange flow (LEF) [14] and has been used as a
base case for comparison with the air curtain cases. The exchange flow
associated with the LEF case is mathematically evaluated as $q_{OD}$, whereas
that with the AC installations is estimated as $q$ (refer eq. 2). Thus, a
total of 25 distinct simulations are reported in this paper.

##  3 RESULTS AND DISCUSSION

The results from the present simulations are now discussed. The adopted
simulation methodology based on the 2D RANS simulation and the RNG
k-$\epsilon$ turbulence model was first validated against the analytical
solution and data available in the literature. The validation was performed
for the cases of a pure jet (equivalent to an air curtain under isothermal
conditions) and that of a neutrally buoyant air curtain where the buoyancy
difference between the air curtain and indoor fluid is zero. These validation
metrics are discussed in detail in Agrawal et al. [8] and are not presented
here. Overall, a good agreement is observed using the adopted computational
methodology.

###  3.1 Effect of deflection modulus

First, we present the temperature distribution in the computational domain for
different values of deflection modulus to illustrate the effect of jet
‘strength’ on the aerodynamic sealing in a qualitative way. Figure 2 shows the
temperature contours for the cases of $D_{m}$ of 0, 0.1, 0.4 and 1.5 when the
jet inlet temperature is 15∘C. The corresponding no AC case, i.e., the LEF
scenario, as illustrated in the top panel, allows a free exchange of the two
fluids across the doorway. This results in a gradual increment in the room
temperature following convection-driven bulk transport, mixing, and thermal
diffusion, which is highly undesirable from a thermal comfort perspective. In
comparison, when an air curtain is installed, this exchange is significantly
suppressed, as shown in the other panels.

When the jet is relatively weaker ($D_{m}\leq$ 0.1), it deflects towards the
dense fluid owing to buoyancy and pressure forces and also allows some
buoyancy-driven exfiltration (see the blue patch beyond $x>$ 1.6 $m$ in the
second panel). Such AC installations are usually termed unstable or
breakthrough as they do not impose a complete sealing across the height of the
doorway. Irrespective of the magnitude of positive buoyancy imposed at the jet
exit, we observe similar behavior of positively buoyant AC at small values of
$D_{m}$, which is consistent with their neutrally buoyant counterpart. In the
present study, we increase the initial jet momentum flux to increase $D_{m}$
and observe that the jet impinges almost vertically on the floor at higher
values of $D_{m}$ (see the third and fourth panels). This ensures proper
sealing across the doorway, and the air curtain installation is deemed stable.
No exfiltration is observed at these values of deflection modulus, and the
primary source of bulk fluid transport appears to stem from the fluid
entrainment and turbulent mixing along the edges of the jet and near the
impingement region. When the deflection modulus increases further, it can be
observed that the fluid is very well mixed as compared to the other cases. The
quantitative implications of the deflection modulus on sealing effectiveness
are discussed in the next section.

Figure 2: Temperature distribution (∘C) in the domain for different values of
$D_{m}$ at $t^{*}=t\sqrt{\frac{g^{\prime}}{H}}=$ 7 and with $T_{0}=$ 15∘C.

###  3.2 Sealing effectiveness

Based on eq. 2, the performance of an air curtain is obtained using the
fraction of exchange flow that it suppresses as compared to the case of a
doorway with no air curtain installed. In the absence of an AC, the volumetric
exchange can be theoretically estimated using the orifice equation as:

$q_{OD}=\frac{1}{3}C_{d}A\sqrt{g^{\prime}H}$ (6)

Here, $C_{d}$ represents the coefficient of discharge, and $A$ is the cross-
sectional area available at the exchange site and is taken as the doorway
height for the present 2D computations. The exchange flow, $q_{OD}$, obtained
from our simulations for the case of $Q=$ 0, results in a $C_{d}$ of 0.56,
which agrees very well with the empirical estimate of 0.6 for a rectangular
orifice. To estimate the exchange flow in the presence of an air curtain, we
use the mass conservation in the indoor space [6]:

$q=\frac{V_{0}}{t}\left(\frac{\rho_{d}-\overline{\rho}}{\rho_{d}-\rho_{l}}\right)+{\beta
Q}\left(\frac{\rho_{0}-\overline{\rho}}{\rho_{d}-\rho_{l}}\right)$ (7)

Here, $V_{0}$ is the constant volume of the indoor space, and $Q$ denotes the
volumetric flow rate (in m2/s) supplied by the AC per unit width. $\beta$
represents the spillage fraction of the AC jet fluid inside the room after
impingement on the floor. We take $\beta$ as 0.5 following the discussion in
[6]. Lastly, $\overline{\rho}$ is the mean fluid density inside the room at
any time instant $t$.

(a) Effectiveness as a function of deflection modulus for all the present
simulations.

(b) Percentage increase in effectiveness as compared to the neutrally buoyant
AC.

Figure 3: Sealing effectiveness of the positively buoyant air curtains.

The sealing effectiveness estimates for all the simulations reported in the
present study are shown in figure 3(a) and also compared with the experimental
estimates of Jha et al. [6] who measured the effectiveness of neutrally
buoyant AC using bulk density measurement techniques. First, it can be seen
that a good agreement exists between the present neutrally buoyant AC and
those of Jha et al.. While the RANS simulations over predict the quantitative
values by a certain amount, especially at higher deflection modulus, the
overall behavior with varying $D_{m}$ is captured well. At low values of
deflection modulus, owing to jet deflection, the effectiveness is rather small
for the breakthrough case. Once the $D_{m}$ increases, the sealing becomes
more prominent. We obtain the peak effectiveness in the range of
$D_{m}\approx$ 0.2 - 0.4, which is similar to that of experimental results.
Upon increasing the deflection modulus further, there is a gradual decrease in
$E$, which is usually attributed to more mixing in the computational domain
due to turbulence. In comparison to the neutrally buoyant AC, upon supplying
the air curtain fluid with positive buoyancy, we observe an increase in
sealing effectiveness. This is because the additional buoyancy in the AC jet
assists in maintaining the indoor fluid density (temperature), and as a
result, the corresponding density difference, $\rho_{d}-\overline{\rho}$,
decreases, resulting in larger effectiveness. In extreme cases, it is also
possible that the added buoyancy in the air curtain can nullify the effects of
fluid transport from the outdoor space. However, that possibility was not
explored in the present study and could be considered in future studies.

As illustrated in figure 3(b), the percentage increase in the sealing
effectiveness, as compared to its neutrally buoyant counterpart, is a weak
function of $D_{m}$ when the air curtain is stable ($D_{m}>$ 0.1). For smaller
values of $D_{m}$, the relatively higher $\Delta E$ is due to the deflection
of positively buoyant air curtain inside the room, which increases the mean
indoor fluid density. For the cases of $T_{0}$ being 15∘C and 20∘C, we
calculate the maximum relative increment in the effectiveness of stable AC to
be of the order of approx 10%. Whereas the maximum sealing effectiveness is
found to be 5% larger than its corresponding value for a neutrally buoyant air
curtain. This maximum is achieved at the deflection modulus of approximately
0.4.

###  3.3 Fractional spillage of the AC jet

In this section, we present estimates of $\beta$ for the case of positively
buoyant AC for varying deflection modulus. To compute this, we introduce a
passive scalar in the air curtain jet and compute the mean spatial
concentration of this scalar in the computational domain. In isothermal case,
i,e. $\rho_{l}=\rho_{d}=\rho_{0}$, the jet divides itself symmetrically across
the doorway i.e. $\beta=$ 0.5, if the outlets are symmetrical. However, it is
known that the transverse buoyancy affects the longitudinal path traveled by
jet, especially at lower values of $D_{m}$ (see the second panel in figure 2).
Therefore, the fractional spillage, $\beta$, might differ from the isothermal
value of 0.5 if the effect of transverse buoyancy is substantial. The
estimates of $\beta$ are inherently difficult to obtain through experiments
due to the number of species involved in such measurements. Generally, either
salt or heat is used to create density differences required for the initial
horizontal stratification. If detailed quantitative information is sought,
then other scalars, for example, a fluorescent dye to measure the scalar
field, are also used. However, direct measurements of a passive scalar to
compute $\beta$ have not been reported to the best of our knowledge.

Figure 4: Spillage fraction, $\beta$, for different values of $D_{m}$ with
$T_{0}=$ 15∘C.

Figure 4 shows the variation of the spillage fraction, $\beta$, for various
deflection modulus for the case of $T_{0}=$ 15∘C. The unusually high value of
$\beta$ at low $D_{m}$ of 0.1 is due to the jet deflection (refer to the
figure 2). However, once the air curtain is stable, the nominally assumed
value of $\beta=$ 0.5 appears to be a reasonable estimate. In the range of
deflection modulus between 0.4 and 1.5, this does not introduce an error of
more than 5% in the estimates of sealing effectiveness. An interesting
observation from figure 4 is that $\beta$ reduces slightly with an increase in
$D_{m}$. This might be attributed to the different density fluids in the
computational domain in which the air curtain jet penetrates. Consider the
indoor space, for example, where the effective density difference for the
incoming jet $\rho_{0}-\rho_{d}$, is smaller than its ambient counterpart,
$\rho_{0}-\rho_{l}$. This results in a larger penetrating force in the outside
space and, thus, a smaller $\beta$.

##  4 CONCLUSIONS

This paper reported 2D simulations of positively buoyant air curtain flows
using the Reynolds-averaged Navier-Stokes (RANS) methodology. The computations
employed the RNG k-$\epsilon$ model for turbulence closure and were performed
in ANSYS FLUENT. The sealing effectiveness of air curtains was estimated using
these simulations for a range of deflection modulus between 0.05 and 1.5 and
for three different jet temperature levels. It was shown that the sealing
effectiveness increased as the extent of positive buoyancy increased. In
comparison to the neutrally buoyant case, the peak effectiveness of the
positively buoyant AC was found to be 5% larger, whereas the maximum increment
was computed to be approximately 10%. The jet spillage fraction was also
estimated by introducing a passive scalar in the air curtain jet. It was
observed that the isothermal value of 0.5 does not introduce errors of more
than 5% in the computation of sealing effectiveness when the deflection
modulus is larger than approximately 0.4.

NOMENCLATURE

$Re$ | Reynolds number | –
---|---|---
$\beta$ | Spillage fraction | —
$t^{*}$ | Dimensionless time | –
$D_{m}$ | Deflection modulus | –
$E$ | Sealing effectiveness | –
$C_{d}$ | Coefficient of discharge | –
$t$ | Time | [s]
$A$ | Cross-sectional area | [m2]
$b_{0}$ | Nozzle width at exit | [m]
$T_{0}$ | Exit jet temperature | [K]
$H$ | Doorway height | [m]
$u_{0}$ | Nozzle velocity at exit | [m/s]
$u_{i}$ |  $i^{th}$ velocity component | [m/s]
$g^{\prime}$ | Reduced gravity | [m/s2]
$q$ | Exchange flow rate | [m3/s]
$q_{OD}$ | Exchange flow without air curtain | [m3/s]
$p$ | Pressure | [Pa]
$T$ | Temperature | [K]
$\rho$ | Density | [kg/$m^{3}$]
$\mu$ | Dynamic viscosity | [Pa$\cdot$s]

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