© EDP Sciences, 2018

1 Introduction

The dilemma of ventilation thermal and humidity comfort presents a serious optimization problem for energy efficiency engineers [1–6]. Users choosing the eco-renovation solutions innovative and some energy supply strategies promote low pollution. However, in several situations, as floor cooling, a stagnant area induces a non-mixing area which could not fit with some indoor air quality (IAQ) requirements. Some ventilation strategies could improve the indoor air quality but must be a compromise with the energy consumption increase.

The reduction of energy consumption, as well as the control of energies, constitutes one of the major issues of our society. The main sources of current energy are fossil (oil and coal for example) with a stock more and more limited therefore more and more expensive. Our energy consumption is such that the induced pollution is high [7], including a large amount of greenhouse gases released into the atmosphere. It is, therefore, necessary to control energy consumption and develop other sources of energy, especially so-called renewable energies which, in recent years, have developed considerably (at least in rich countries). However, today, the power provided by such sources is far too low to ensure sufficient energy consumption. For example, it is still very expensive to ensure the energy autonomy of a building with solar panels. It is therefore mandatory today to control our energy consumption in order to preserve our natural resources and reduce the emission of greenhouse gases. Residential houses or dwellings are about half of our energy consumption. Energy consumption characteristics of the residential sector are complex and the main use of energy concerns comfort, mainly heating in winter and air conditioning in summer. Impacts on heating and cooling cause very large natural and mixed convection flows in the living room.

Thus, in order to optimize these systems, consideration is given to the natural and combined forced convection flows induced by heating or air conditioner.

The use of natural ventilation by large openings, to keep the premises of acceptable thermal well-being conditions, is a concept perfectly integrated into the traditional architecture of countries located in the Mediterranean region or in tropical climate. In a temperate climate where the architecture is generally not designed to respond to warm climatic conditions, the use of natural ventilation is seasonal and is done at the initiative of the occupants acting on the opening. The interest in Europe for natural ventilation, as passive building cooling technology, is growing and has been the subject of a research program commissioned by the European Community (PASCOOL program for PASsive COOLing) Research has focused on studying the balance between energy expenditure and user comfort [8,9]. To achieve this balance, studies have been carried out to understand the mechanism of air infiltration in buildings, aiming at controlling and sometimes reducing occasional ventilation with a view to saving energy. Ventilation can be fundamentally defined as the result of air infiltration to building rooms. Its purpose is to provide a supply of fresh air to confined spaces and dilute the concentrations of different indoor pollutants. Therefore, knowledge of the dynamic, thermal and mass fields is essential for a better design of the ventilation systems. In the context of numerical simulations, buildings are often modeled as closed or unclosed cavities where fluid movement can be induced by both temperature and contaminant concentration gradients. When the movement is induced by the joint action of thermal and mass gradients, there is coexistence of so-called buoyant forces acting in parallel. In buildings, beings are the most important source of indoor carbon dioxide (CO₂) production. As a result, air- CO₂ mixtures are important ingredients when implementing predictions of heat transfer and air quality problems [9]. On the other hand, as the flows inside are often turbulent, it is important to proceed to a statistical treatment based on models of turbulence type k-e or large scales (LES). For real ventilation [10], the pressure field is a very important parameter: in similar situations, the position where the inlet conditions are imposed and the nature of the inlet conditions completely changes the simulated flow in the room.

A study [11,12] has been carried out on mixed convection heat transfer in laminar flow in a ventilated cavity, under a constant heat flux imposed on the wall. The analysis parameters concern a Rayleigh number of 10³ < Ra_T < 10⁶ and a Reynolds number 5 < Re < 5.10³. Two configurations were considered: in the first configuration, an air inlet located on the lower side of the wall left vertical and the air outlet is located on the upper side of the right vertical wall, and in the second configuration, both, entry and exit are located on the lower side of the vertical walls. The authors showed that configuration one was not suitable for heat removing. Moreover, they showed the increase in the average temperature of the cavity inducing very high values compared to the second configuration. A numerical study was performed [13] in a differentially heated rectangular cavity for a double diffusive convection for the cooling of the indoor environment. The goal is to identify the best configuration for the air inlets and outlets and to improve the position and efficiency of the cooling. The study was undertaken for a Reynolds ranging from 5.10¹ to 5.10³ and a Richardson number respectively as 0, 0.1, 1 and 10. The authors concluded that the cavity should be fed with fresh air from the lower side and having an outlet placed on the upper side of the hot wall with a high temperature. Simulations on cavities representing dwelling units have been performed by pioneers [14–17] in computational fluid dynamic methods (CFD). These research works were focused on: (1) the characterization of the flow field in the cavities, (2) the influence of the geometry parameters related to the locations of the air inlets and outlets, (3) the influence of the efficiency of ventilation in mixed convection. To highlight the parameters characterizing indoor air quality and to ensure a good numerical prediction in ventilated cavities, it is recommended [18] the use of turbulence models in boundary conditions to take into account the recirculation zones developed in input and output. In addition, studies using CFD, based, full-scale and small scale focused on natural ventilation through windows with diverse factors such as their type, aperture angles, dimensions, holes configuration, orientations and construction, air velocities and temperatures [19–30].

A numerical study [31] has been carried out on the analysis of heat and mass transfers in four different configurations whose air inlet and outlet are placed differently. These configurations are broken down in laminar flow. The fluid considered is an air- CO₂ mixture. The aim is both to highlight the location of the air outlets; to study the behavior of the flow and the quality of air inside the cavities by considering three different values of the contaminant of CO₂ (1, 2 and 3 × 10³ PPM). The air inlet is located on the lower side of the hot vertical wall of the cavity. The air velocity considered is a function of the Reynolds number (10 < Re < 500). The output has been placed in three different positions. The authors concluded that when the air inlet and outlet are placed on the same side of the heat source and the contaminant give better thermal comfort and air quality conditions for Reynolds values ranging from 50 to 100.

We consider a part of a housing compound a refreshing floor. This floor is maintained at a constant cold temperature and the one vertical wall of the room is maintained at a hot temperature and the rest of the walls are adiabatic, the air outlet is located at the top of the right vertical wall, while the inlet is placed according to the configuration studied. Indeed, different configurations were analyzed with different locations of the air intake grille (Fig. 1). The air enters the cavity at a temperature T_H. In order to study the influence of the parameters characterizing the flow on the quality of the air and the thermal comfort, we fixed the Reynolds number Re equal to 100. It should be noted that it was chosen a fixed Rayleigh number Ra = 10⁶. This work is the continuity of the work done by Morsli et al. [32], so some details will not be explicated and the readers can find more technical informations in the previous work.

Fig. 1 Configuration, boundary conditions (a) and ventilation strategies and positions (b).

2 Computational model

It has been chosen to solve the present-coupled problem by using numerical simulation allowing large explorating possibilities and access to field details. Problem definition and governing equations, mathematical formulation, numerical tools and finally simulation results such approach is submitted to verification and grid validation.

The studied configuration is a classical room shape of L_x, L_y and L_z size filled with air P_r = 0.71 (Fig. 1). The floor temperature is maintained at lower temperature T_C and the left vertical wall temperature is heated at T_H. Other bonding walls are assumed to be adiabatic. Air is injected at the corresponding external hot temperature from a small window and extracts the same amount of air from a similar window on the opposite side. Different scenariis are undertaken for different ventilation strategies. The used fluid is supposed to be Newtonian and incompressible and satisfies Boussinesq's hypothesis.

Using the following dimensionless variables:

, where v is the fluid kinematical viscosity and is the velocity vector.

The steady state equations governing the conservation of mass, momentum and energy in non-dimensional form can be written as, (1) (2) (3) where  is the unit vector in Z direction, Ra = gβ_TΔTL_z³/(να) is the thermal Rayleigh number and Pr = ν/α is the Prandtl number.

Boundary conditions for the velocities are no slip condition (U = V = W = 0) on all solid boundaries;

except on the ventilating windows (X = 0, 1, for opening ΔY = 0.44 and ΔZ = 0.15 centered on different position, i.e. see Tab. 1) where constant velocity is applied (4)

The thermal boundary conditions are θ = 1 on the heated left side wall (X = 0) and θ = 0 on the cooled bottom surface (Z = 0), all other walls are adiabatic, i.e. ∂θ/∂ n = 0_.

3 Numerical tools

Fluent industrial software [33] based on a finite-volume method was used as a CFD approach, let's start by defining what is the “computational fluid dynamics” (CFD) approach: in a flow, the parameters related to the fluid are governed by partial differential equations, the CFD then defines the numerical method resolution of these equations. The CFD approach, strongly related to the power of computers, is therefore increasingly used for the prediction of mass and heat transfers in buildings, both in the case of a ventilated room [34–38] than for much larger structures (for example an airport terminal [39]).

This approach is used to produce numerical solution of the Navier–Stokes set of fluid flow in primitive variables (P, V, T). The industrial software provides also solutions for transport by solving partial differential equations describing elementary phenomena as convection, diffusion, and reaction for each constituent. The computational solutions have been performed on a 3D dimensional configuration. The mesh has been refined close to the walls (presence of boundary layers with strong gradients). The Finite Volumes method consists in discretizing the computational domain in sub-domains or control volumes whose faces follow the lines of coordinates. Fluent allows choosing the discretization schemes for different operators. A “segregated” solver that calculates each equation separately is chosen. The pressure equation is discretized by the standard scheme. The interpolation is done by using the coefficients of the equation of momentum. This procedure works well for small variations in pressure between the centers of the cells. Strong pressure gradients between the cells generate inaccuracy on estimating the velocity on the faces. This is the case of a swirling flow at high speed generally the pressure is unknown and there is no obvious equation for its determination.

On the obtained results, the problem was solved numerically by considering different grid ranges. The tests were carried out for meshes ranging from 150 × 150 to 250 × 250 for Rayleigh number equal to 10⁶. All these meshes were refined near the walls in order to captivate the stiff solution gradient neighboring the walls. Finally, the study led us to mesh 200 × 200 for the rest of this study.

4 Results and discussion

Since the interest is on the thermal comfort of using floor cooling. The temperature and the velocity contours in the enclosure are presented and discussed for different ventilating position (see Fig. 1b). The results presented concern simple room geometry.

Figure 2 shows temperature and flow structure for non-ventilated and ventilated (P12) case. This analyzed case named P12 corresponds to row named 1 and column named 2 in Table 1 where the centered windows position is indicated (in bold for this case) and ventilated window size of Y = 0.44 and ΔZ = 0.15 Y–Z.

In ventilated situation (Fig. 2a) the flow is induced by the thermal buoyancy forces in the direct vicinity of the vertical surface and is in competition with the stabilizing applied floor cooling. The flow is mainly 2D structure if excluding the effect of lateral surfaces. Such induced clock-wise thermal cell exhibits a thermally stratified area in the core of the enclosure because of the downward flow on the opposing vertical surface. The results show sharp temperature gradient near the floor and gradually the temperature increases toward the ceiling. In lower part, temperature is almost uniform in planes parallel to the floor, except near the connection between the heated and cooled wall. The singularity contact between the hot and cold surface will induces high heat transfer on such contact line and could be avoided by classical existing technological realization (not included in the present study).

The presented ventilated case (Fig. 2b) has an injection on the hot surface and extraction on the opposing surface so the forced flow is cooperating with the thermal induced convective cell. The injected flow goes toward the ceiling by the Coanda effect and get out of the domain directly after flowing in horizontal way. Such added new airflow is with practically non-efficient mixing with the main convective cell. We observe, in such cooperating effect, an enhancement of the convective thermal cell intensity with stronger temperature stratification. We mention also the less 2D flow because of the flow injection on only part of the wall. Lateral flow interacting with the recirculating flow above injection domain is illustrated.

Since the interest is on the thermal comfort of using such floor cooling, the temperature distribution near the active thermal wall is directly related to local Nusselt, i.e. energy demand. The local Nusselt number on the two active thermal wall are represented on (Fig. 3) for the different ventilating opening position (for Ra = 10³, Re = 10²). We compare also the cooperating case and the inverse injection where the ventilation flow is in contrarotative to the main thermal cell.

The local Nusselt map on both surface vertical and horizontal surfaces are presented in vertical way as illustrated in the insert sketch top/right figure. On such chosen observation way, we can find again the previous mentioned singularity on the two surfaces line contact with maximum heat transfer as illustrated by the dark horizontal (red and blue) line. The transfer decreases on both surface function of the distance from the contact line. Such local Nu number tends to relatively constant value on the horizontal direction and confirms the previously weak 3D aspect of the induced flow. The 3D flow and thermal field character is more obvious on the vertical surface (upper square) where the heat transfer became inhomogeneous around the ventilation open rectangular hole. This is because a hot air flow is injected and such flow cover the upper part (see previous discussion on Coanda effect). The induced hot air curtain covers more and more the upper surface with the lower ventilating position, so amplifying zone on which the heat transfer decrease. In contrary, the heat transfer on the lower surface increases because of flow structure modification and the immediate vicinity of the hot injected air with the cooling surface.

The decrease of heat transfer on upper part of the heated surface could be illustrated with heat transfer (averaged on Y) versus the position Z. (5)

The comparison between the different analyzed situation in cooperating case are summarized on Figure 4a. On the same figure, we plot the reference case of purely natural convective situation. It is obvious that the heat transfer is not significantly affected by sliding the ventilation on the top position (P0, P11, P12 and P13). On this Figure 4a, we have as expected a modification on upper part but it has to be analyzed on relative (logarithm drawing scale) to the intense exchange on lower half part. For ventilation localized on the middle or moreover on lower part, it modifies significantly the local heat transfer on below area. It is a direct consequence of the vicinity of hot injected air with the cooling surface. We need to be careful in conclusion because the air is injected at hot temperature and the local heat transfer will be very weak on injection and immediate vicinity part because the injected flow is at same hot surface temperature and advection overcomes the diffusion contribution. We can observe locally some increase of the Z-local heat transfer especially for the two-border situation (injection in contact with roof or ceiling) mainly related to the main cell velocity increase.

The second analyzed configuration reverse injected flow exhibit a more complex 3D flow as illustrated by the local heat transfer on the ceiling (Fig. 3b, d and f). The different hot spot on ceiling are illustrating the secondary flow or local impact jets. The corresponding Nusselt (heat transfer averaged on Y direction) on the vertical surface, Figure 4b, is different from the previous direct injection (Fig. 4a) and confirm the previously underlined complex flow. The heat transfer versus Z compared to reference case without injection could be locally higher when the injected hot fluid reaches such opposing surface to the active injecting opening. When the injection is on lower part the heat transfer is increased locally but decrease on the all other remaining surface. Such decrease is also induced by the decrease on the main cell intensity. This decrease is because of competition between the natural convective cell and the injection flow direction. The corresponding Y-averaged local heat transfer on the ceiling, i.e. horizontal surface is plotted on Figure 5. The heat transfer is enhanced with injection in comparison to the reference naturally ventilated case but remains below the reference for the particularly P11 and P13 cases. (6)

In order to allow global comparison, we use the surface average local Nusselt (Eq. below) at each given injection position. Such average Nu value versus the Y-Z opening ventilation position is plotted on Figure 6. (7)

This confirm that the maximum heat transfer extraction on the bottom horizontal surface (cooling one) correspond to the lower part centered injection (P4). The minimum energy consumption corresponds to upper part injection in both direct and reversed injection flow. We found also interesting situation in cooperating case where the P12 (followed by P22) is also allowing a minimum transfer in both strategies. We observe also that the maximum energy demand is obtained in the opposing (inverted) case.

The observed minimum heat transfer does not mean better situation because decrease in energy demand could induce either strong temperature inhomogeneous (stratification) or less mixing in some sub-domain inducing indoor air non-quality.

An example of temperature profile on the vertical mid-line (X = Y = 0.5) is presented on Figure 7. The temperature profile is affected by the injection position and some improvements are seen in case of lower injection nevertheless this situation is the one with maximum heat transfer. So the optimum case must be a compromise between these two different constraints and mainly the mixing ability of the flow. The used vertical line to illustrate the temperature change is not sufficient to get the other part where a 3D flow mixing ability can occur.

As flow structure example, we plot a side view of the domain with cooperating and opposing flow injection (Fig. 8) in case P13. The plotted case is corresponding to the P12 previously presented in Figure 2b. The flow is obvious 3D on both case but more complex in opposing situation (Fig. 8b).

In cooperating case we can see the previously lower convective thermal cell and the ventilation flow travelling directly from the left to right side with weak mixing ability (Fig. 8a). The cooperating thermal cell remains below and induces the classical stratified convective thermal field with side thermal boundary layer. In the situation of opposing flow, a shear stress can occur between the clockwise convective flow and the opposing horizontal injected ventilating flow. The system naturally reduces the shear stress by settling an intermediate recirculating flow. The three domains are represented by the upper part horizontal flow (right to left), the lower clockwise circulating flow with thermal stratification and more over the intermediate around the mid height. The flow exhibits also more complexity because of the injected flow on only part of the wall depth (Y direction). To illustrate the previous discussion competition between the cooperating and the opposing convective cells we represent schematically the flow structures on Figure 9. We can easily understand the weak shear stress on the two sub domain flow in cooperating case (Fig. 9a) and the settle intermediate counterclockwise intermediate cell in order to avoid the strong shear stress between the forced upper part flow and the lower natural convective cell.

Such physical situation and the 3D flow allows more mixing by getting a time resident air particle longer to mix but limited in time in order to avoid dead zone where the fluid is not renewing at all.

Fig. 2 Stream traces and heat field on non-ventilated (a) and ventilated cavity (b).

Fig. 3 Local Nusselt number (NuYZ) on bottom and lateral wall for different ventilating position and cooperating and opposing cases.

Fig. 3 (Continued).

Fig. 4 Average Nusselt function of Z () for the different opening position, in the cooperating (a) and opposing (b) ventilating strategy.

Fig. 5 Average Nusselt function of X () for the different opening position, in the cooperating strategy.

Fig. 6 Average Nusselt function of the ventilation opening center position on the Y-Z plan for cooperating (a) and opposing (b) cases.

Fig. 7 Vertical temperature (thermal comfort) on the mid-line (X = Y = 0.5) for the cooperating case.

Fig. 8 Side view of the domain with cooperating and opposing flow injection (P13 cooperating and opposing equivalent of case on Fig. 2).

Fig. 9 The flow structure in cooperating (a) and (b) opposing cases.

5 Conclusion

Mixed convection in a cubic ventilated cavity was studied numerically in different configurations having air inlet that are placed differently. The stream traces and thermal fields have been studied for a fixed Rayleigh and Reynolds number, 10⁶ and 10², respectively. The relevant parameters cooling power, thermal comfort and indoor air quality (mixing ability and time air resident) where analyzed for different aligned and misaligned ventilation opening. The two strategies of cooperating and opposing cases demonstrated the advantages and disadvantages of the two cases.

The mains conclusions are listed below.

The flow is induced by the thermal buoyancy forces in the direct vicinity of the vertical surface and is in competition with the stabilizing applied floor cooling. The thermal cell exhibits a thermally stratified area in the core of the enclosure. The singularity contact between the hot and cold surface induces high heat transfer on such contact line and must be avoided by classical existing technological realization (not included in the present study).

The 3D flow and thermal field character is obvious on the vertical surface in the vicinity of the ventilating opening and near the lateral walls. The inhomogeneity of local heat transfer is amplified by the sliding to bottom the ventilating window. The induced hot air curtain covers more and more the upper surface with the lower ventilating position. In contrary, the heat transfers on the lower surface increases because of flow structure modification and the immediate vicinity of the hot injected air with the cooling surface. The maximum heat transfer extraction on the bottom horizontal surface (cooling one) corresponds to the lower part centered injection (P4). The minimum energy consumption corresponds to upper part injection P12 (followed by P22) in both direct and reversed injection flow.

The observed minimum heat transfer does not mean better situation because decrease in energy demand induces either strong temperature inhomogeneous (stratification) or less mixing in some subdomain inducing indoor air non-quality.

The optimum case must be a compromise between the different constraints: heat transfer, temperature homogeneity and the flow mixing ability.

The flow structures competition between the cooperating and the opposing convective cells was identified and schematically represented. The weak shear stress and the settle intermediate counterclockwise cell between the forced upper part flow and the lower natural convective cell was explained.

The present study amplifies the thermal incomfort but in real case the injected hot air is higher than the heated wall because of insulation and the present study corresponds more to a wall under intense solar radiation to reach equivalent temperature values between the inner surface and injected air temperature.

One of the possible improvements could be the pulsating flow in order to enhance the mixing and avoid the steady state cells and the possible dead zone where pollutant level can increase. It has to be under constraint of users' incomfort air speed variability. The second possible strategy could be the helicoidal air flow which could be obtained by a lateral vertical injection if it can overcome the thermal natural convective cell.

Nomenclature

g: gravitational acceleration [m s⁻²]

L_x: dimension of cavity in x direction [m]

L_y: dimension of cavity in y direction [m]

L_z: dimension of cavity in z direction [m]

T: dimensional temperature [K]

u,v,w: components of dimensionless velocity

x,y,z: dimensionless Cartesian coordinates

Greek symbols

α: thermal diffusivity [m² s¹]

β_T: coefficient of volumetric expansion [K¹]

μ: dynamic viscosity[kg m¹ s]

v: kinematic viscosity [m² s¹]

ρ: mass density kg/m³

θ: dimensionless temperature, (T−T_C)/(T_H−T_C)

Non-dimensional Numbers

A_x: x aspect ratio, L_x/L_z

A_y: y aspect ratio, L_y/L_z

h, d: dimensionless ventilation window

Nu_down: Nu on bottom surface 

Nu_Lat: Nu on lateral walls

Pr: Prandtl number, =ν/α

Ra: Rayleigh number,

Uncited references

[2–5].

Acknowledgement

The authors are grateful to LCOMS & LERMAB Lab, University de Lorraine Metz, France and ‘Tous Chercheurs’ project for providing support on this work.

References

All Tables

All Figures

	Fig. 1 Configuration, boundary conditions (a) and ventilation strategies and positions (b).
In the text

	Fig. 2 Stream traces and heat field on non-ventilated (a) and ventilated cavity (b).
In the text

	Fig. 3 Local Nusselt number (NuYZ) on bottom and lateral wall for different ventilating position and cooperating and opposing cases.
In the text

	Fig. 3 (Continued).
In the text

	Fig. 4 Average Nusselt function of Z () for the different opening position, in the cooperating (a) and opposing (b) ventilating strategy.
In the text

	Fig. 5 Average Nusselt function of X () for the different opening position, in the cooperating strategy.
In the text

	Fig. 6 Average Nusselt function of the ventilation opening center position on the Y-Z plan for cooperating (a) and opposing (b) cases.
In the text

	Fig. 7 Vertical temperature (thermal comfort) on the mid-line (X = Y = 0.5) for the cooperating case.
In the text

	Fig. 8 Side view of the domain with cooperating and opposing flow injection (P13 cooperating and opposing equivalent of case on Fig. 2).
In the text

	Fig. 9 The flow structure in cooperating (a) and (b) opposing cases.
In the text